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Quantum Mechanics

2026-03-28T08:33:09Z

Thakshashila: /* Applications */

= Quantum Mechanics =

'''Quantum Mechanics''' is a fundamental branch of physics that studies matter and energy at the smallest scales, typically atomic and subatomic levels. It departs from classical mechanics by introducing principles such as wave-particle duality, uncertainty, and quantum entanglement, which challenge our classical intuitions about reality.

== History ==
The development of quantum mechanics began in the early 20th century, driven by the need to explain phenomena that classical physics could not, such as blackbody radiation and the photoelectric effect.

* 1900: [[Max Planck]] introduced the concept of energy quanta to solve the blackbody radiation problem.
* 1905: [[Albert Einstein]] explained the photoelectric effect, proposing that light consists of discrete packets of energy called ''photons''.
* 1925–1926: [[Werner Heisenberg]], [[Erwin Schrödinger]], and [[Paul Dirac]] developed the modern mathematical framework of quantum mechanics, including matrix mechanics and wave mechanics.
* 1927: The [[Heisenberg uncertainty principle]] was formulated, stating that certain pairs of physical properties, like position and momentum, cannot be simultaneously known with arbitrary precision.

== Core Principles ==

=== Wave-Particle Duality ===
Quantum entities such as electrons and photons exhibit both wave-like and particle-like properties. This duality is exemplified in the [[double-slit experiment]], where particles create interference patterns characteristic of waves.

=== Superposition ===
Quantum systems can exist in multiple states simultaneously, a phenomenon known as ''superposition''. For example, an electron in an atom can be in a superposition of different energy levels until measured.

=== Entanglement ===
[[Quantum entanglement]] describes a state where particles become correlated in such a way that the state of one particle instantaneously affects the state of another, regardless of distance. Einstein famously referred to it as "spooky action at a distance."

=== Uncertainty Principle ===
Formulated by [[Werner Heisenberg]], this principle limits the precision with which certain pairs of physical properties can be simultaneously known. For instance, the more precisely the position of a particle is known, the less precisely its momentum can be known.

=== Quantum Tunneling ===
Quantum particles can penetrate barriers that would be insurmountable according to classical physics. This effect underpins technologies such as [[tunnel diode]]s and nuclear fusion in stars.

== Mathematical Framework ==
Quantum mechanics is formulated using complex linear algebra and functional analysis. The state of a quantum system is represented by a [[wave function]], usually denoted as ψ (psi), which contains all probabilistic information about the system. Observables, such as energy or momentum, are represented by [[Hermitian operator]]s acting on these wave functions.

The evolution of quantum systems is governed by the [[Schrödinger equation]]:

<math>
i \hbar \frac{\partial}{\partial t} \psi(\mathbf{r}, t) = \hat{H} \psi(\mathbf{r}, t)
</math>

where:
* <math>\hbar</math> is the reduced Planck constant,
* <math>\hat{H}</math> is the Hamiltonian operator representing the total energy of the system.

== Applications ==
Quantum mechanics is foundational to modern technology and scientific research:

* Semiconductors and electronics: Transistors, diodes, and microchips.
* Quantum computing: Exploits superposition and entanglement to perform calculations beyond classical computers.
* Medical imaging: Techniques like [[MRI]] rely on quantum principles.
* Nanotechnology: Manipulation of matter at atomic and molecular scales.
* Quantum cryptography: Provides theoretically unbreakable encryption methods.

== Interpretations ==
Quantum mechanics has multiple interpretations that attempt to explain its counterintuitive phenomena:

* **Copenhagen interpretation:** The wave function represents knowledge of the system; measurement causes collapse.
* **Many-worlds interpretation:** All possible outcomes of a quantum measurement actually occur in branching parallel universes.
* **Pilot-wave theory:** Particles have deterministic trajectories guided by a "pilot wave."

== Challenges and Open Questions ==
Despite its successes, quantum mechanics raises fundamental questions about reality and measurement:

* How to reconcile quantum mechanics with [[general relativity]] into a theory of quantum gravity.
* The measurement problem: why and how a superposition collapses into a definite outcome.
* The role of consciousness, if any, in observation.

== References ==
<references>
* Planck, Max. ''The Theory of Heat Radiation''. 1914.
* Einstein, Albert. ''On a Heuristic Viewpoint Concerning the Production and Transformation of Light''. Annalen der Physik, 1905.
* Heisenberg, Werner. ''Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik''. Zeitschrift für Physik, 1927.
* Dirac, Paul A.M. ''The Principles of Quantum Mechanics''. 1930.
* Nielsen, Michael A.; Chuang, Isaac L. ''Quantum Computation and Quantum Information''. 2010.
</references>

Quantum Mechanics

2026-03-28T08:31:55Z

Thakshashila: Created page with "= Quantum Mechanics = '''Quantum Mechanics''' is a fundamental branch of physics that studies matter and energy at the smallest scales, typically atomic and subatomic levels. It departs from classical mechanics by introducing principles such as wave-particle duality, uncertainty, and quantum entanglement, which challenge our classical intuitions about reality. == History == The development of quantum mechanics began in the early 20th century, driven by the need to expl..."

= Quantum Mechanics =

'''Quantum Mechanics''' is a fundamental branch of physics that studies matter and energy at the smallest scales, typically atomic and subatomic levels. It departs from classical mechanics by introducing principles such as wave-particle duality, uncertainty, and quantum entanglement, which challenge our classical intuitions about reality.

== History ==
The development of quantum mechanics began in the early 20th century, driven by the need to explain phenomena that classical physics could not, such as blackbody radiation and the photoelectric effect.

* 1900: [[Max Planck]] introduced the concept of energy quanta to solve the blackbody radiation problem.
* 1905: [[Albert Einstein]] explained the photoelectric effect, proposing that light consists of discrete packets of energy called ''photons''.
* 1925–1926: [[Werner Heisenberg]], [[Erwin Schrödinger]], and [[Paul Dirac]] developed the modern mathematical framework of quantum mechanics, including matrix mechanics and wave mechanics.
* 1927: The [[Heisenberg uncertainty principle]] was formulated, stating that certain pairs of physical properties, like position and momentum, cannot be simultaneously known with arbitrary precision.

== Core Principles ==

=== Wave-Particle Duality ===
Quantum entities such as electrons and photons exhibit both wave-like and particle-like properties. This duality is exemplified in the [[double-slit experiment]], where particles create interference patterns characteristic of waves.

=== Superposition ===
Quantum systems can exist in multiple states simultaneously, a phenomenon known as ''superposition''. For example, an electron in an atom can be in a superposition of different energy levels until measured.

=== Entanglement ===
[[Quantum entanglement]] describes a state where particles become correlated in such a way that the state of one particle instantaneously affects the state of another, regardless of distance. Einstein famously referred to it as "spooky action at a distance."

=== Uncertainty Principle ===
Formulated by [[Werner Heisenberg]], this principle limits the precision with which certain pairs of physical properties can be simultaneously known. For instance, the more precisely the position of a particle is known, the less precisely its momentum can be known.

=== Quantum Tunneling ===
Quantum particles can penetrate barriers that would be insurmountable according to classical physics. This effect underpins technologies such as [[tunnel diode]]s and nuclear fusion in stars.

== Mathematical Framework ==
Quantum mechanics is formulated using complex linear algebra and functional analysis. The state of a quantum system is represented by a [[wave function]], usually denoted as ψ (psi), which contains all probabilistic information about the system. Observables, such as energy or momentum, are represented by [[Hermitian operator]]s acting on these wave functions.

The evolution of quantum systems is governed by the [[Schrödinger equation]]:

<math>
i \hbar \frac{\partial}{\partial t} \psi(\mathbf{r}, t) = \hat{H} \psi(\mathbf{r}, t)
</math>

where:
* <math>\hbar</math> is the reduced Planck constant,
* <math>\hat{H}</math> is the Hamiltonian operator representing the total energy of the system.

== Applications ==
Quantum mechanics is foundational to modern technology and scientific research:

* **Semiconductors and electronics:** Transistors, diodes, and microchips.
* **Quantum computing:** Exploits superposition and entanglement to perform calculations beyond classical computers.
* **Medical imaging:** Techniques like [[MRI]] rely on quantum principles.
* **Nanotechnology:** Manipulation of matter at atomic and molecular scales.
* **Quantum cryptography:** Provides theoretically unbreakable encryption methods.

== Interpretations ==
Quantum mechanics has multiple interpretations that attempt to explain its counterintuitive phenomena:

* **Copenhagen interpretation:** The wave function represents knowledge of the system; measurement causes collapse.
* **Many-worlds interpretation:** All possible outcomes of a quantum measurement actually occur in branching parallel universes.
* **Pilot-wave theory:** Particles have deterministic trajectories guided by a "pilot wave."

== Challenges and Open Questions ==
Despite its successes, quantum mechanics raises fundamental questions about reality and measurement:

* How to reconcile quantum mechanics with [[general relativity]] into a theory of quantum gravity.
* The measurement problem: why and how a superposition collapses into a definite outcome.
* The role of consciousness, if any, in observation.

== References ==
<references>
* Planck, Max. ''The Theory of Heat Radiation''. 1914.
* Einstein, Albert. ''On a Heuristic Viewpoint Concerning the Production and Transformation of Light''. Annalen der Physik, 1905.
* Heisenberg, Werner. ''Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik''. Zeitschrift für Physik, 1927.
* Dirac, Paul A.M. ''The Principles of Quantum Mechanics''. 1930.
* Nielsen, Michael A.; Chuang, Isaac L. ''Quantum Computation and Quantum Information''. 2010.
</references>

Chemical Thermodynamics

2025-06-12T11:50:21Z

Thakshashila: Created page with "== Chemical Thermodynamics == '''Chemical Thermodynamics''' is the branch of thermodynamics that studies the interrelation of heat and work with chemical reactions or physical changes of state within chemical systems. It provides the framework to predict whether a reaction will occur spontaneously and to what extent it proceeds. === Basic Concepts === Chemical thermodynamics deals with the energy changes and equilibrium conditions in chemical reactions, focusing on va..."

== Chemical Thermodynamics ==

'''Chemical Thermodynamics''' is the branch of thermodynamics that studies the interrelation of heat and work with chemical reactions or physical changes of state within chemical systems. It provides the framework to predict whether a reaction will occur spontaneously and to what extent it proceeds.

=== Basic Concepts ===

Chemical thermodynamics deals with the energy changes and equilibrium conditions in chemical reactions, focusing on variables such as enthalpy, entropy, Gibbs free energy, and equilibrium constants.

Key thermodynamic quantities include:
* Internal Energy (<math>U</math>)
* Enthalpy (<math>H</math>)
* Entropy (<math>S</math>)
* Gibbs Free Energy (<math>G</math>)
* Helmholtz Free Energy (<math>F</math>)

=== Laws of Thermodynamics in Chemistry ===

* '''First Law:''' Conservation of energy in chemical processes. The change in internal energy <math>\Delta U</math> is equal to the heat added to the system plus the work done on the system:

<math>
\Delta U = q + w
</math>

where <math>q</math> is heat and <math>w</math> is work.

* '''Second Law:''' Entropy of an isolated system always increases or remains constant:

<math>
\Delta S_\text{total} \geq 0
</math>

This law defines the direction of spontaneous chemical reactions.

=== Gibbs Free Energy and Reaction Spontaneity ===

The Gibbs free energy change (<math>\Delta G</math>) at constant temperature and pressure determines spontaneity:

<math>
\Delta G = \Delta H - T \Delta S
</math>

where:
* <math>\Delta H</math> = enthalpy change
* <math>T</math> = absolute temperature
* <math>\Delta S</math> = entropy change

A reaction is:
* Spontaneous if <math>\Delta G < 0</math>
* At equilibrium if <math>\Delta G = 0</math>
* Non-spontaneous if <math>\Delta G > 0</math>

=== Equilibrium Constant and Standard Gibbs Energy ===

The relationship between the standard Gibbs free energy change (<math>\Delta G^\circ</math>) and the equilibrium constant (<math>K</math>) is:

<math>
\Delta G^\circ = -RT \ln K
</math>

where <math>R</math> is the gas constant and <math>T</math> is the temperature in Kelvin.

This allows prediction of equilibrium position from thermodynamic data.

=== Applications ===

* Predicting reaction direction and extent
* Calculating equilibrium constants
* Understanding phase changes and solution chemistry
* Designing industrial chemical processes
* Studying biological energetics

=== References ===

* Atkins, P., & de Paula, J. (2010). ''Physical Chemistry''. Oxford University Press.
* Laidler, K. J. (1996). ''Chemical Kinetics''. Harper & Row.

[[Category:Chemistry]]

Entropy

2025-06-12T11:49:49Z

Thakshashila: Created page with "== Entropy == '''Entropy''' (symbol <math>S</math>) is a fundamental thermodynamic property that measures the degree of disorder or randomness in a system. It quantifies the number of microscopic configurations that correspond to a thermodynamic system's macroscopic state. === Definition === Entropy is related to the number of possible microstates (<math>\Omega</math>) by the Boltzmann equation: <math> S = k_B \ln \Omega </math> where: * <math>S</math> = entropy..."

== Entropy ==

'''Entropy''' (symbol <math>S</math>) is a fundamental thermodynamic property that measures the degree of disorder or randomness in a system. It quantifies the number of microscopic configurations that correspond to a thermodynamic system's macroscopic state.

=== Definition ===
Entropy is related to the number of possible microstates (<math>\Omega</math>) by the Boltzmann equation:

<math>
S = k_B \ln \Omega
</math>

where:
* <math>S</math> = entropy
* <math>k_B</math> = Boltzmann constant (<math>1.380649 \times 10^{-23} \, \mathrm{J\,K^{-1}}</math>)
* <math>\Omega</math> = number of accessible microstates of the system

=== Thermodynamic Definition ===
In classical thermodynamics, the change in entropy for a reversible process is defined as:

<math>
dS = \frac{\delta Q_\text{rev}}{T}
</math>

where:
* <math>dS</math> = infinitesimal change in entropy
* <math>\delta Q_\text{rev}</math> = infinitesimal heat absorbed reversibly
* <math>T</math> = absolute temperature

For a finite reversible process between states 1 and 2:

<math>
\Delta S = S_2 - S_1 = \int_{1}^{2} \frac{\delta Q_\text{rev}}{T}
</math>

=== Second Law of Thermodynamics ===
The Second Law states that the total entropy of an isolated system never decreases:

<math>
\Delta S_\text{total} \geq 0
</math>

where equality holds for reversible processes and inequality for irreversible processes.

This law implies that natural processes tend to move towards increased entropy or disorder.

=== Entropy Change in Chemical Reactions ===
The entropy change of a system during a chemical reaction is:

<math>
\Delta S = \sum S_\text{products} - \sum S_\text{reactants}
</math>

This change helps determine the spontaneity of reactions when combined with enthalpy changes in the Gibbs free energy:

<math>
\Delta G = \Delta H - T \Delta S
</math>

=== Statistical Interpretation ===
Entropy can also be viewed as a measure of uncertainty or information content in the system's microscopic state, connecting thermodynamics with information theory.

=== Applications ===
* Predicting spontaneity and direction of chemical reactions
* Explaining phase transitions and mixing phenomena
* Understanding biological processes and energy transfer
* Engineering systems such as engines and refrigerators

=== References ===
* Atkins, P., & de Paula, J. (2010). ''Physical Chemistry''. Oxford University Press.
* Callen, H. B. (1985). ''Thermodynamics and an Introduction to Thermostatistics''. Wiley.

[[Category:Chemistry]]

Phase Equilibrium

2025-06-12T11:49:19Z

Thakshashila: Created page with "== Phase Equilibrium == '''Phase equilibrium''' refers to the condition where multiple phases of a substance coexist in equilibrium without any net change in their amounts over time. It occurs when the chemical potential of each component is the same in all coexisting phases, ensuring no driving force for phase change. === Basics === In a system involving different phases (solid, liquid, gas), phase equilibrium is established when the rates of phase transitions (such a..."

== Phase Equilibrium ==

'''Phase equilibrium''' refers to the condition where multiple phases of a substance coexist in equilibrium without any net change in their amounts over time. It occurs when the chemical potential of each component is the same in all coexisting phases, ensuring no driving force for phase change.

=== Basics ===
In a system involving different phases (solid, liquid, gas), phase equilibrium is established when the rates of phase transitions (such as melting, vaporization, sublimation) between these phases are equal. This results in stable coexistence of phases at certain temperature and pressure conditions.

=== Chemical Potential and Phase Equilibrium ===
The key criterion for phase equilibrium is equality of chemical potentials:

<math>
\mu_i^{(\alpha)} = \mu_i^{(\beta)} = \cdots
</math>

for component <math>i</math> in all phases <math>\alpha, \beta, \ldots</math>.

Here, <math>\mu_i^{(\alpha)}</math> is the chemical potential of component <math>i</math> in phase <math>\alpha</math>.

=== Phase Rule ===
The Gibbs phase rule governs the degrees of freedom (<math>F</math>) in a system at equilibrium:

<math>
F = C - P + 2
</math>

where:
* <math>F</math> = number of degrees of freedom (independent intensive variables, e.g., temperature, pressure)
* <math>C</math> = number of components
* <math>P</math> = number of phases present

This rule helps determine how many variables can be changed without disturbing the equilibrium.

=== Phase Diagrams ===
Phase equilibrium is often represented graphically in phase diagrams showing the stable phases under different conditions of temperature, pressure, or composition.

- For example, the water phase diagram shows regions where ice, liquid water, and steam coexist.
- Lines separating phases are called phase boundaries.
- Points where three phases coexist (e.g., ice, liquid water, and vapor) are called triple points.

=== Clausius-Clapeyron Equation ===
The Clausius-Clapeyron equation describes the relationship between pressure and temperature along a phase boundary, for example between liquid and vapor phases:

<math>
\frac{dP}{dT} = \frac{L}{T \Delta V}
</math>

where:
* <math>L</math> = latent heat of the phase transition
* <math>\Delta V</math> = change in volume during the phase change
* <math>P</math> = pressure
* <math>T</math> = temperature

This equation is fundamental for understanding vapor pressure and boiling point changes with temperature.

=== Applications ===
* Designing distillation and separation processes
* Understanding natural phenomena like frost formation and cloud formation
* Studying materials science and metallurgy
* Predicting behavior of mixtures in chemical engineering

=== References ===
* Smith, J. M., Van Ness, H. C., & Abbott, M. M. (2005). ''Introduction to Chemical Engineering Thermodynamics''. McGraw-Hill.
* Atkins, P., & de Paula, J. (2010). ''Physical Chemistry''. Oxford University Press.

[[Category:Chemistry]]

Thermodynamic Potential

2025-06-12T11:48:33Z

Thakshashila: Created page with "== Thermodynamic Potential == '''Thermodynamic potentials''' are scalar quantities used in thermodynamics to describe the equilibrium and spontaneous behavior of physical systems. They are functions of state variables such as temperature, pressure, volume, and entropy, and provide criteria for spontaneous processes and equilibrium under different constraints. === Overview === Thermodynamic potentials combine the system's internal energy with other thermodynamic paramet..."

== Thermodynamic Potential ==

'''Thermodynamic potentials''' are scalar quantities used in thermodynamics to describe the equilibrium and spontaneous behavior of physical systems. They are functions of state variables such as temperature, pressure, volume, and entropy, and provide criteria for spontaneous processes and equilibrium under different constraints.

=== Overview ===
Thermodynamic potentials combine the system's internal energy with other thermodynamic parameters, allowing us to analyze changes in energy under various conditions such as constant volume, pressure, temperature, or entropy.

The four most common thermodynamic potentials are:
* Internal Energy (<math>U</math>)
* Enthalpy (<math>H</math>)
* Helmholtz Free Energy (<math>F</math> or <math>A</math>)
* Gibbs Free Energy (<math>G</math>)

Each potential is defined to be useful under specific experimental or natural conditions.

=== Definitions ===

* '''Internal Energy (<math>U</math>)''': The total energy contained within the system.

<math>
dU = TdS - PdV
</math>

where:
* <math>T</math> = temperature
* <math>S</math> = entropy
* <math>P</math> = pressure
* <math>V</math> = volume

* '''Enthalpy (<math>H</math>)''': Useful for processes at constant pressure, defined as:

<math>
H = U + PV
</math>

Differential form:

<math>
dH = TdS + VdP
</math>

* '''Helmholtz Free Energy (<math>F</math> or <math>A</math>)''': Useful for processes at constant volume and temperature, defined as:

<math>
F = U - TS
</math>

* '''Gibbs Free Energy (<math>G</math>)''': Useful for processes at constant pressure and temperature, defined as:

<math>
G = H - TS = U + PV - TS
</math>

=== Physical Significance ===
- Thermodynamic potentials help determine the direction of spontaneous processes.
- The potential that decreases at constant constraints (e.g., constant T and P or constant T and V) indicates the tendency toward equilibrium.

For example:
- At constant temperature and volume, the Helmholtz free energy <math>F</math> decreases in spontaneous processes.
- At constant temperature and pressure, the Gibbs free energy <math>G</math> decreases.

=== Relationships Between Potentials ===
Using Legendre transformations, thermodynamic potentials are related as follows:

<math>
H = U + PV
</math>

<math>
F = U - TS
</math>

<math>
G = H - TS = U + PV - TS
</math>

These relations allow switching between natural variables suitable for different experimental conditions.

=== Applications ===
* Predicting spontaneity and equilibrium of chemical reactions
* Designing thermodynamic cycles in engines and refrigerators
* Analyzing phase transitions
* Understanding biochemical processes and energy transfer

=== References ===
* Callen, H. B. (1985). ''Thermodynamics and an Introduction to Thermostatistics''. Wiley.
* Atkins, P., & de Paula, J. (2010). ''Physical Chemistry''. Oxford University Press.

[[Category:Chemistry]]

Gibbs Free Energy

2025-06-12T11:47:35Z

Thakshashila: Created page with "== Gibbs Free Energy == '''Gibbs Free Energy''' (denoted as <math>G</math>) is a thermodynamic potential that measures the maximum reversible work a thermodynamic system can perform at constant temperature and pressure. It is an important concept in chemistry and physics, used to predict the spontaneity of chemical reactions and phase changes. === Definition === Gibbs Free Energy is defined as: <math>G = H - TS</math> where: * <math>G</math> = Gibbs free energy *..."

== Gibbs Free Energy ==

'''Gibbs Free Energy''' (denoted as <math>G</math>) is a thermodynamic potential that measures the maximum reversible work a thermodynamic system can perform at constant temperature and pressure. It is an important concept in chemistry and physics, used to predict the spontaneity of chemical reactions and phase changes.

=== Definition ===
Gibbs Free Energy is defined as:

<math>G = H - TS</math>

where:
* <math>G</math> = Gibbs free energy
* <math>H</math> = enthalpy of the system
* <math>T</math> = absolute temperature (in Kelvin)
* <math>S</math> = entropy of the system

=== Physical Significance ===
* A negative change in Gibbs free energy (<math>\displaystyle \Delta G < 0</math>) indicates a spontaneous process.
* If <math>\displaystyle \Delta G = 0</math>, the system is in equilibrium.
* If <math>\displaystyle \Delta G > 0</math>, the process is non-spontaneous and requires energy input.

=== Relation to Chemical Reactions ===
For a chemical reaction at constant temperature and pressure, the change in Gibbs free energy is given by:

<math>\Delta G = \Delta H - T \Delta S</math>

where <math>\Delta H</math> is the change in enthalpy and <math>\Delta S</math> is the change in entropy during the reaction.

The sign and magnitude of <math>\Delta G</math> determine whether a reaction proceeds spontaneously:

* Exergonic reactions: <math>\Delta G < 0</math>, reaction releases free energy and is spontaneous.
* Endergonic reactions: <math>\Delta G > 0</math>, reaction absorbs free energy and is non-spontaneous.

=== Gibbs Free Energy and Equilibrium Constant ===
The standard Gibbs free energy change (<math>\Delta G^\circ</math>) is related to the equilibrium constant <math>K</math> of a reaction by:

<math>\Delta G^\circ = -RT \ln K</math>

where:
* <math>R</math> is the universal gas constant
* <math>T</math> is the temperature in Kelvin
* <math>K</math> is the equilibrium constant

This relation allows prediction of the position of equilibrium and the spontaneity of the reaction.

=== Applications ===
* Predicting spontaneity of chemical reactions
* Calculating equilibrium constants
* Understanding biological processes such as ATP hydrolysis
* Designing industrial chemical processes

=== References ===
* Atkins, P., & de Paula, J. (2010). ''Physical Chemistry''. Oxford University Press.
* Laidler, K. J. (1996). ''Chemical Kinetics''. Harper & Row.

[[Category:Chemistry]]

Convolutional Neural Network

2025-06-11T11:44:37Z

Thakshashila: Created page with "== Convolutional Neural Networks (CNNs) == A '''Convolutional Neural Network (CNN)''' is a type of deep learning model specially designed for working with '''image data''' 📷. CNNs are widely used in computer vision tasks like image classification, object detection, and face recognition. === 🧠 Why CNNs for Images? === Images are large (millions of pixels), and fully connected neural networks don't scale well with size. CNNs solve this by using convolution operati..."

== Convolutional Neural Networks (CNNs) ==

A '''Convolutional Neural Network (CNN)''' is a type of deep learning model specially designed for working with '''image data''' 📷. CNNs are widely used in computer vision tasks like image classification, object detection, and face recognition.

=== 🧠 Why CNNs for Images? ===

Images are large (millions of pixels), and fully connected neural networks don't scale well with size. CNNs solve this by using convolution operations to detect '''patterns''', '''edges''', and '''shapes''' in a smart and efficient way. 🎯

---

== ⚙️ Key Components of a CNN ==

{| class="wikitable"
! Layer
! Description
! Emoji Hint
|-
| '''Convolutional Layer'''
| Applies filters (kernels) to input image to extract features (edges, textures)
| 🔍🧱
|-
| '''Activation Layer'''
| Applies non-linearity (like ReLU) to activate features
| ⚡🧠
|-
| '''Pooling Layer'''
| Reduces spatial size by keeping the most important info (e.g., max pooling)
| 📉📦
|-
| '''Fully Connected Layer'''
| Final decision-making layer; connects features to output
| 🔗🎯
|-
| '''Softmax Layer'''
| Converts final output to probabilities (for classification)
| 📊✅
|}

---

== 🧮 Convolution Operation ==

The convolution layer slides a small filter (kernel) over the image and performs dot products between the filter and the image pixels.

:<math> y(i,j) = \sum_{m}\sum_{n} x(i+m, j+n) \cdot w(m,n) </math>

Where:
* <math>x</math> = input image
* <math>w</math> = filter
* <math>y</math> = feature map

---

== 🏗️ CNN Architecture Example ==

{| class="wikitable"
! Layer
! Size
! Description
|-
| Input
| 32x32x3
| Color image (RGB)
|-
| Conv Layer
| 28x28x16
| 16 filters, 5x5 kernel
|-
| ReLU
| 28x28x16
| Applies non-linearity
|-
| Max Pooling
| 14x14x16
| 2x2 pooling
|-
| Conv Layer
| 10x10x32
| 32 filters, 5x5 kernel
|-
| ReLU
| 10x10x32
| Activation
|-
| Max Pooling
| 5x5x32
| Reduce again
|-
| Fully Connected
| 1x1x128
| Flatten + dense layer
|-
| Output (Softmax)
| 1x1x10
| For 10-class classification
|}

---

== 📚 Applications of CNNs ==

* 👀 Image classification (e.g., Cats vs Dogs)
* 🧍 Object detection (e.g., YOLO, SSD)
* 🧠 Facial recognition
* 📦 Scene segmentation
* 🩺 Medical imaging (e.g., tumor detection)
* 📄 Optical Character Recognition (OCR)

---

== ⚠️ Advantages of CNNs ==

* Fewer parameters compared to fully connected networks
* Automatically learn features (no manual extraction)
* Translation-invariant — detects the same pattern anywhere in the image

---

== 🔧 Limitations ==

* Require large datasets for training
* Computationally expensive (need GPU for large models)
* Struggles with rotated or distorted objects (unless augmented)

---

== 📝 Summary ==

{| class="wikitable"
! Feature
! CNN Advantage
|-
| Parameter Efficiency
| Shared weights via filters
|-
| Feature Extraction
| Automatic, multi-level (edges → shapes → objects)
|-
| Task Suitability
| Great for images, videos, 2D signals
|-
| Common Use
| Classification, detection, segmentation
|}

---

== 📎 See Also ==

* [[Neural Networks]]
* [[Activation Functions]]
* [[Pooling Layer]]
* [[Convolution Operation]]
* [[Object Detection]]
* [[YOLO]]
* [[ResNet]]

Backpropagation

2025-06-11T11:12:10Z

Thakshashila: Created page with "== Backpropagation == '''Backpropagation''' (short for "backward propagation of errors") is a fundamental algorithm used to train neural networks. It calculates how much each weight in the network contributed to the total error and updates them to reduce this error. === 🧠 Purpose === The main goal of backpropagation is to: * Minimize the '''loss function''' (error) 📉 * Improve model accuracy over time by adjusting weights 🔧 === 🔁 How It Works (Step-by-Ste..."

== Backpropagation ==

'''Backpropagation''' (short for "backward propagation of errors") is a fundamental algorithm used to train neural networks. It calculates how much each weight in the network contributed to the total error and updates them to reduce this error.

=== 🧠 Purpose ===

The main goal of backpropagation is to:
* Minimize the '''loss function''' (error) 📉
* Improve model accuracy over time by adjusting weights 🔧

=== 🔁 How It Works (Step-by-Step) ===

Neural network training has two main steps:

# '''Forward pass''': Inputs go through the network to make a prediction.
# '''Backward pass (Backpropagation)''':
## Calculate the error (loss)
## Compute the gradient (how much each weight affects the loss)
## Update weights using gradient descent

=== 🧮 Mathematical Explanation ===

Let:
* <math>L</math> = Loss function
* <math>y</math> = Actual output
* <math>\hat{y}</math> = Predicted output
* <math>w</math> = Weights
* <math>x</math> = Inputs

Loss:
:<math>L = \frac{1}{2}(y - \hat{y})^2</math>

Gradient of loss w.r.t. weights:
:<math>\frac{\partial L}{\partial w}</math>

The weights are updated as:
:<math>w = w - \eta \cdot \frac{\partial L}{\partial w}</math>

Where:
* <math>\eta</math> = learning rate 🔧

This update rule is applied to each layer using the chain rule from calculus.

=== 📊 Example Workflow ===

Let’s say we have:
* A network with one hidden layer
* Sigmoid activation
* Mean squared error loss

{| class="wikitable"
! Step
! Description
|-
| 1
| Do a forward pass to get predicted output <math>\hat{y}</math>
|-
| 2
| Calculate the error <math>L = (y - \hat{y})^2</math>
|-
| 3
| Compute the derivative of loss with respect to each weight
|-
| 4
| Update weights: <math>w = w - \eta \cdot \frac{\partial L}{\partial w}</math>
|-
| 5
| Repeat this process for many epochs (passes over data)
|}

=== 🔧 Backpropagation Uses ===

* Deep learning (CNNs, RNNs, Transformers)
* Supervised learning tasks (image classification, NLP, etc.)
* Any task where you need to minimize a loss function

=== 💡 Key Concepts ===

* Chain Rule: Used to pass the gradient from the output layer back to the input layer
* Gradient Descent: Optimizer that uses gradients to minimize loss
* Learning Rate: Controls how big the weight updates are

=== 🚫 Challenges ===

* Can suffer from [[Vanishing Gradient Problem]]
* Can also face [[Exploding Gradient Problem]]
* Requires good weight initialization and choice of activation functions

=== 📚 Summary Table ===

{| class="wikitable"
! Concept
! Meaning
|-
| Backpropagation
| Algorithm for updating weights based on error
|-
| Gradient
| Direction and size of weight adjustment
|-
| Chain Rule
| Math rule used to calculate gradients in multi-layer networks
|-
| Loss Function
| Measures how wrong the prediction is
|}

=== 📎 See Also ===

* [[Gradient Descent]]
* [[Loss Function]]
* [[Activation Functions]]
* [[Vanishing Gradient Problem]]
* [[Exploding Gradient Problem]]
* [[Neural Networks]]

Exploding Gradient Problem

2025-06-11T10:09:50Z

Thakshashila: /* 📎 See Also */

== Exploding Gradient Problem ==

The '''Exploding Gradient Problem''' is a common issue in training deep neural networks where the gradients grow too large during backpropagation. This leads to very large weight updates, making the model unstable or completely unusable.

=== 📈 What Are Gradients? ===

Gradients are computed during the backpropagation step of training. They help the model understand how to change its weights to reduce error.

:<math> \text{Gradient} = \frac{\partial \text{Loss}}{\partial \text{Weight}} </math>

If gradients become very large, the weight updates become huge, which can cause the model to diverge (never reach a good solution).

=== ⚠️ When Does It Happen? ===

It usually happens in:
* Very '''deep networks''' with many layers
* '''Recurrent Neural Networks (RNNs)''', especially for long sequences
* When using poor '''weight initialization'''

=== 🧪 Example ===

Let’s assume a layer has a weight matrix and a large gradient. When we compute updates:

:<math> \Delta W = - \eta \cdot \text{Gradient} </math>

If the gradient is large (e.g., 10,000), even a small learning rate <math>\eta</math> leads to massive weight updates.

This can result in:
* Loss becoming NaN (Not a Number) 💥
* Weights exploding to infinity ➡️ ∞
* Model failing to train 😢

=== 🔍 Symptoms of Exploding Gradients ===

* ❌ Loss value jumps or becomes NaN
* 📈 Weights become excessively large
* 🔁 Training fails to converge
* 💥 Network outputs explode to very high values

=== 🔧 Solutions ===

Several techniques are commonly used to fix or prevent this issue:

==== 1. Gradient Clipping ====

Limit (or "clip") the gradients to a maximum value during backpropagation:

:<math> \text{If } \|g\| > \text{threshold, then } g := \frac{\text{threshold}}{\|g\|} \cdot g </math>

This keeps gradients from becoming too large.

==== 2. Better Weight Initialization ====

Use techniques like:
* Xavier initialization for Tanh/Sigmoid
* He initialization for ReLU

These help control the scale of activations and gradients.

==== 3. Use Normalization Layers ====

**Batch Normalization** helps to keep the network outputs within a stable range.

==== 4. Choose Better Activation Functions ====

ReLU and its variants (Leaky ReLU, ELU) tend to work better in deep networks.

=== 📚 Summary Table ===

{| class="wikitable"
! Problem
! Cause
! Effect
! Solution
|-
| Exploding Gradient
| Deep networks, poor initialization
| Huge weight updates, loss divergence
| Gradient clipping, normalization, better activation functions
|}

=== 🧠 Difference from Vanishing Gradient ===

{| class="wikitable"
! Problem
! Gradient Size
! Effect
|-
| Vanishing Gradient
| Near zero
| Training stops (no learning)
|-
| Exploding Gradient
| Extremely large
| Training blows up (unstable learning)
|}

=== 📎 See Also ===
* [[Vanishing gradient problem]]
* [[Backpropagation]]
* [[Gradient Clipping]]
* [[Weight Initialization]]
* [[ReLU]]

Exploding Gradient Problem

2025-06-11T10:09:11Z

Thakshashila: Created page with "== Exploding Gradient Problem == The '''Exploding Gradient Problem''' is a common issue in training deep neural networks where the gradients grow too large during backpropagation. This leads to very large weight updates, making the model unstable or completely unusable. === 📈 What Are Gradients? === Gradients are computed during the backpropagation step of training. They help the model understand how to change its weights to reduce error. :<math> \text{Gradient} =..."

== Exploding Gradient Problem ==

The '''Exploding Gradient Problem''' is a common issue in training deep neural networks where the gradients grow too large during backpropagation. This leads to very large weight updates, making the model unstable or completely unusable.

=== 📈 What Are Gradients? ===

Gradients are computed during the backpropagation step of training. They help the model understand how to change its weights to reduce error.

:<math> \text{Gradient} = \frac{\partial \text{Loss}}{\partial \text{Weight}} </math>

If gradients become very large, the weight updates become huge, which can cause the model to diverge (never reach a good solution).

=== ⚠️ When Does It Happen? ===

It usually happens in:
* Very '''deep networks''' with many layers
* '''Recurrent Neural Networks (RNNs)''', especially for long sequences
* When using poor '''weight initialization'''

=== 🧪 Example ===

Let’s assume a layer has a weight matrix and a large gradient. When we compute updates:

:<math> \Delta W = - \eta \cdot \text{Gradient} </math>

If the gradient is large (e.g., 10,000), even a small learning rate <math>\eta</math> leads to massive weight updates.

This can result in:
* Loss becoming NaN (Not a Number) 💥
* Weights exploding to infinity ➡️ ∞
* Model failing to train 😢

=== 🔍 Symptoms of Exploding Gradients ===

* ❌ Loss value jumps or becomes NaN
* 📈 Weights become excessively large
* 🔁 Training fails to converge
* 💥 Network outputs explode to very high values

=== 🔧 Solutions ===

Several techniques are commonly used to fix or prevent this issue:

==== 1. Gradient Clipping ====

Limit (or "clip") the gradients to a maximum value during backpropagation:

:<math> \text{If } \|g\| > \text{threshold, then } g := \frac{\text{threshold}}{\|g\|} \cdot g </math>

This keeps gradients from becoming too large.

==== 2. Better Weight Initialization ====

Use techniques like:
* Xavier initialization for Tanh/Sigmoid
* He initialization for ReLU

These help control the scale of activations and gradients.

==== 3. Use Normalization Layers ====

**Batch Normalization** helps to keep the network outputs within a stable range.

==== 4. Choose Better Activation Functions ====

ReLU and its variants (Leaky ReLU, ELU) tend to work better in deep networks.

=== 📚 Summary Table ===

{| class="wikitable"
! Problem
! Cause
! Effect
! Solution
|-
| Exploding Gradient
| Deep networks, poor initialization
| Huge weight updates, loss divergence
| Gradient clipping, normalization, better activation functions
|}

=== 🧠 Difference from Vanishing Gradient ===

{| class="wikitable"
! Problem
! Gradient Size
! Effect
|-
| Vanishing Gradient
| Near zero
| Training stops (no learning)
|-
| Exploding Gradient
| Extremely large
| Training blows up (unstable learning)
|}

=== 📎 See Also ===
* [[Vanishing Gradient Problem]]
* [[Backpropagation]]
* [[Gradient Clipping]]
* [[Weight Initialization]]
* [[ReLU]]

Vanishing gradient problem

2025-06-11T10:06:54Z

Thakshashila: Created page with "== Vanishing Gradient Problem == The '''Vanishing Gradient Problem''' is a common issue encountered during the training of deep neural networks. It occurs when the gradients (used to update weights) become extremely small, effectively preventing the network from learning. === 🧠 What is a Gradient? === In neural networks, gradients are values calculated during '''backpropagation'''. They show how much the model's weights should change to reduce the loss (error). The..."

== Vanishing Gradient Problem ==

The '''Vanishing Gradient Problem''' is a common issue encountered during the training of deep neural networks. It occurs when the gradients (used to update weights) become extremely small, effectively preventing the network from learning.

=== 🧠 What is a Gradient? ===

In neural networks, gradients are values calculated during '''backpropagation'''. They show how much the model's weights should change to reduce the loss (error). The gradient is computed using the derivative of the loss with respect to each weight.

:<math> \text{Gradient} = \frac{\partial \text{Loss}}{\partial \text{Weights}} </math>

If this value is small, the model updates the weights slowly. If it is too small (close to zero), learning stops — this is the vanishing gradient problem.

=== ⚠️ When Does It Happen? ===

The problem usually arises in:
* Very deep neural networks with many layers
* Networks that use activation functions like '''Sigmoid''' or '''Tanh''', which squash outputs to small ranges

=== 🧪 Example ===

Let's say we use the Sigmoid function:

:<math> \sigma(x) = \frac{1}{1 + e^{-x}} </math>

Its derivative is:

:<math> \sigma'(x) = \sigma(x)(1 - \sigma(x)) </math>

The maximum derivative value is 0.25. So, if we keep multiplying by small numbers through many layers:

:<math> 0.25 \times 0.25 \times \dots \times 0.25 = \text{Very small number} </math>

This means early layers get almost no signal, and they learn nothing.

=== 🔍 Effects of Vanishing Gradients ===

* 🧠 Early layers learn very slowly or not at all
* 📉 Training becomes inefficient or completely fails
* 🚫 Model accuracy suffers, especially in deep networks

=== 🔧 Solutions ===

Several techniques help reduce or fix the vanishing gradient problem:

==== 1. Use ReLU Activation ====

ReLU (Rectified Linear Unit) avoids squashing outputs too much:

:<math> f(x) = \max(0, x) </math>

This function keeps large gradients alive for positive values.

==== 2. Batch Normalization ====

BatchNorm helps by normalizing inputs at each layer, maintaining healthy gradient flow.

==== 3. Residual Connections (ResNet) ====

ResNet uses skip connections that let gradients bypass some layers, helping the model stay "awake" even in deep networks.

==== 4. Proper Weight Initialization ====

Techniques like Xavier or He initialization reduce the chance of gradients shrinking or exploding.

=== 📚 Summary ===

{| class="wikitable"
! Problem
! Cause
! Result
! Solution
|-
| Vanishing Gradient
| Small derivatives (e.g., from Sigmoid/Tanh)
| Early layers stop learning
| Use ReLU, BatchNorm, ResNet, proper initialization
|}

The vanishing gradient problem was a major obstacle in training deep neural networks. With modern techniques like ResNet and ReLU, it is now more manageable.

=== 📎 See Also ===
* [[Exploding Gradient Problem]]
* [[Backpropagation]]
* [[Activation Functions]]
* [[ReLU]]
* [[ResNet]]

Example of ReLU Activation Function

2025-06-11T09:06:03Z

Thakshashila: Created page with "== ReLU (Rectified Linear Unit) Example == The ReLU function is defined as: :<math>f(x) = \max(0, x)</math> This means: * If ''x'' is '''positive''', it stays the same. * If ''x'' is '''negative''', it becomes ''0''. === Real Number Examples === {| class="wikitable" ! Input (x) ! ReLU Output f(x) |- | -3 | 0 |- | -1 | 0 |- | 0 | 0 |- | 2 | 2 |- | 5 | 5 |} In this table: * Negative numbers become 0 🚫 * Positive numbers pass through ✅ This makes ReLU very fast..."

== ReLU (Rectified Linear Unit) Example ==

The ReLU function is defined as:

:<math>f(x) = \max(0, x)</math>

This means:
* If ''x'' is '''positive''', it stays the same.
* If ''x'' is '''negative''', it becomes ''0''.

=== Real Number Examples ===

{| class="wikitable"
! Input (x)
! ReLU Output f(x)
|-
| -3
| 0
|-
| -1
| 0
|-
| 0
| 0
|-
| 2
| 2
|-
| 5
| 5
|}

In this table:
* Negative numbers become 0 🚫
* Positive numbers pass through ✅

This makes ReLU very fast and useful for deep learning models! 🤖✨

Main Page

2025-06-10T09:45:09Z

Thakshashila:

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Main Page

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Thakshashila:

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= '''<span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">Welcome to Qbase</span>''' =
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</div>

== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">Featured Categories</span> ==
<div style="display: grid; grid-template-columns: repeat(auto-fit, minmax(120px, 1fr)); gap: 15px; margin: 15px 0;">
<div style="background: #007bff; color: white; padding: 15px; border-radius: 10px; text-align: center; font-family: 'Segoe UI', Arial, sans-serif;">
<div style="font-size: 24px; margin-bottom: 5px;">💻</div>
<div style="font-weight: bold;">[[Category:Technology|Technology]]</div>
</div>
<div style="background: #28a745; color: white; padding: 15px; border-radius: 10px; text-align: center; font-family: 'Segoe UI', Arial, sans-serif;">
<div style="font-size: 24px; margin-bottom: 5px;">🔬</div>
<div style="font-weight: bold;">[[Category:Science|Science]]</div>
</div>
<div style="background: #ffc107; color: white; padding: 15px; border-radius: 10px; text-align: center; font-family: 'Segoe UI', Arial, sans-serif;">
<div style="font-size: 24px; margin-bottom: 5px;">💼</div>
<div style="font-weight: bold;">[[Category:Business|Business]]</div>
</div>
<div style="background: #17a2b8; color: white; padding: 15px; border-radius: 10px; text-align: center; font-family: 'Segoe UI', Arial, sans-serif;">
<div style="font-size: 24px; margin-bottom: 5px;">📚</div>
<div style="font-weight: bold;">[[Category:Education|Education]]</div>
</div>
<div style="background: #dc3545; color: white; padding: 15px; border-radius: 10px; text-align: center; font-family: 'Segoe UI', Arial, sans-serif;">
<div style="font-size: 24px; margin-bottom: 5px;">🏥</div>
<div style="font-weight: bold;">[[Category:Health|Health]]</div>
</div>
<div style="background: #6f42c1; color: white; padding: 15px; border-radius: 10px; text-align: center; font-family: 'Segoe UI', Arial, sans-serif;">
<div style="font-size: 24px; margin-bottom: 5px;">🎨</div>
<div style="font-weight: bold;">[[Category:Arts|Arts]]</div>
</div>
</div>

</div>

<div style="flex: 1; min-width: 250px; max-width: 100%;">

<div style="background: #fff3cd; border: 1px solid #ffeaa7; border-radius: 10px; padding: 20px; margin-bottom: 15px;">
== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">Wiki Statistics</span> ==
<div style="text-align: center; font-family: 'Segoe UI', Arial, sans-serif;">
<div style="display: grid; grid-template-columns: repeat(auto-fit, minmax(120px, 1fr)); gap: 15px; margin-top: 15px;">
<div style="background: white; padding: 15px; border-radius: 8px; box-shadow: 0 2px 8px rgba(0,0,0,0.1);">
<div style="font-size: 24px; font-weight: bold; color: #007bff; font-family: 'Segoe UI', Arial, sans-serif;">{{NUMBEROFARTICLES}}</div>
<div style="color: #6c757d; font-size: 14px; font-family: 'Segoe UI', Arial, sans-serif;">Total Articles</div>
</div>
<div style="background: white; padding: 15px; border-radius: 8px; box-shadow: 0 2px 8px rgba(0,0,0,0.1);">
<div style="font-size: 24px; font-weight: bold; color: #28a745; font-family: 'Segoe UI', Arial, sans-serif;">{{NUMBEROFPAGES}}</div>
<div style="color: #6c757d; font-size: 14px; font-family: 'Segoe UI', Arial, sans-serif;">Total Pages</div>
</div>
<div style="background: white; padding: 15px; border-radius: 8px; box-shadow: 0 2px 8px rgba(0,0,0,0.1);">
<div style="font-size: 24px; font-weight: bold; color: #dc3545; font-family: 'Segoe UI', Arial, sans-serif;">{{NUMBEROFEDITS}}</div>
<div style="color: #6c757d; font-size: 14px; font-family: 'Segoe UI', Arial, sans-serif;">Total Edits</div>
</div>
<div style="background: white; padding: 15px; border-radius: 8px; box-shadow: 0 2px 8px rgba(0,0,0,0.1);">
<div style="font-size: 24px; font-weight: bold; color: #ffc107; text-shadow: 1px 1px 2px rgba(0,0,0,0.1); font-family: 'Segoe UI', Arial, sans-serif;">{{NUMBEROFUSERS}}</div>
<div style="color: #6c757d; font-size: 14px; font-family: 'Segoe UI', Arial, sans-serif;">Contributors</div>
</div>
</div>
</div>
</div>

<div style="background: #f1f3f4; border: 1px solid #dadce0; border-radius: 10px; padding: 20px; margin-bottom: 15px;">
== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">Quick Actions</span> ==
<div style="font-family: 'Segoe UI', Arial, sans-serif;">
* [[Special:CreateAccount|Join Our Community]] 🚀
* [[Help:Getting Started|Getting Started Guide]] 📖
* [[Special:Random|Discover Random Article]] 🎲
* [[Special:RecentChanges|Recent Changes]] 📊
* [[Special:Upload|Upload Files]] 📎
</div>
</div>

<div style="background: #e3f2fd; border: 1px solid #bbdefb; border-radius: 10px; padding: 20px;">
== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">Community</span> ==
<div style="color: #1565c0; font-family: 'Segoe UI', Arial, sans-serif;">
Join thousands of contributors who are building the future of knowledge sharing. Every contribution matters, from minor edits to major articles.
</div>
<div style="margin-top: 10px; text-align: center; font-family: 'Segoe UI', Arial, sans-serif;">
[[Special:Community|Community Portal]] | [[Special:Forum|Discussion Forum]]
</div>
</div>

</div>
</div>

== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">Featured Articles</span> ==
<div style="background: white; border: 1px solid #e1e5e9; border-radius: 10px; padding: 20px; margin: 20px 0;">
<div style="display: grid; grid-template-columns: repeat(auto-fit, minmax(280px, 1fr)); gap: 20px;">

<div style="border-left: 4px solid #007bff; padding-left: 15px;">
=== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">[[Introduction to Qbase]]</span> ===
<div style="color: #6c757d; font-size: 14px; margin-bottom: 8px; font-family: 'Segoe UI', Arial, sans-serif;">''Core Documentation''</div>
<div style="font-family: 'Segoe UI', Arial, sans-serif;">Learn the fundamentals of using Qbase effectively, from basic navigation to advanced features.</div>
</div>

<div style="border-left: 4px solid #28a745; padding-left: 15px;">
=== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">[[Best Practices Guide]]</span> ===
<div style="color: #6c757d; font-size: 14px; margin-bottom: 8px; font-family: 'Segoe UI', Arial, sans-serif;">''Guidelines''</div>
<div style="font-family: 'Segoe UI', Arial, sans-serif;">Discover proven strategies for creating high-quality content and maintaining wiki standards.</div>
</div>

<div style="border-left: 4px solid #ffc107; padding-left: 15px;">
=== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">[[Community Guidelines]]</span> ===
<div style="color: #6c757d; font-size: 14px; margin-bottom: 8px; font-family: 'Segoe UI', Arial, sans-serif;">''Policies''</div>
<div style="font-family: 'Segoe UI', Arial, sans-serif;">Understanding our community standards and collaborative principles for a positive environment.</div>
</div>

<div style="border-left: 4px solid #dc3545; padding-left: 15px;">
=== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">[[Technical Resources]]</span> ===
<div style="color: #6c757d; font-size: 14px; margin-bottom: 8px; font-family: 'Segoe UI', Arial, sans-serif;">''Documentation''</div>
<div style="font-family: 'Segoe UI', Arial, sans-serif;">Comprehensive technical documentation for developers and advanced users.</div>
</div>

</div>
</div>

----
<div style="text-align: center; color: #6c757d; font-size: 14px; margin-top: 30px; font-family: 'Segoe UI', Arial, sans-serif;">
<div style="margin-bottom: 10px;">
''Powered by MediaWiki • Built with ❤️ by the Qbase Community''
</div>
[[Special:About|About]] • [[Special:Contact|Contact]] • [[Privacy Policy]] • [[Terms of Service]]
</div>

</div>
__NOTOC__ __NOEDITSECTION__

Main Page

2025-06-10T09:33:01Z

Thakshashila:

{{DISPLAYTITLE:Welcome to Qbase}}
<div style="font-family: 'Segoe UI', Arial, sans-serif;">

<div style="background: linear-gradient(135deg, #667eea 0%, #764ba2 100%); color: white; padding: 30px; border-radius: 15px; margin-bottom: 20px; text-align: center; box-shadow: 0 4px 15px rgba(0,0,0,0.1);">
= '''<span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">Welcome to Qbase</span>''' =
<div style="font-family: 'Segoe UI', Arial, sans-serif; font-size: 18px; margin-top: 15px; opacity: 0.9;">
''Your comprehensive knowledge base and collaborative platform''
</div>
</div>

<div style="display: flex; flex-wrap: wrap; gap: 20px; width: 100%;">
<div style="flex: 2; min-width: 300px; max-width: 100%;"?

<div style="background: #f8f9fa; border: 1px solid #e1e5e9; border-radius: 10px; padding: 25px; margin-bottom: 15px;">
== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">About Qbase</span> ==
<div style="font-family: 'Segoe UI', Arial, sans-serif; color: #495057; line-height: 1.6;">
Qbase is a cutting-edge knowledge management platform designed to foster collaboration, innovation, and information sharing. Our platform serves as a central hub where knowledge meets community, enabling users to create, share, and discover valuable content across diverse domains.

Whether you're a researcher, professional, student, or curious learner, Qbase provides the tools and environment to build comprehensive knowledge repositories that grow with your community's needs.
</div>
</div>

<div style="background: #e8f5e8; border-left: 5px solid #28a745; border-radius: 0 10px 10px 0; padding: 20px; margin-bottom: 15px;">
== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">Our Mission</span> ==
<div style="font-family: 'Segoe UI', Arial, sans-serif; color: #155724; font-weight: 500;">
To democratize knowledge sharing and create accessible, collaborative spaces where information transforms into wisdom, empowering communities to learn, grow, and innovate together.
</div>
</div>

== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">Featured Categories</span> ==
<div style="display: grid; grid-template-columns: repeat(auto-fit, minmax(120px, 1fr)); gap: 15px; margin: 15px 0;">
<div style="background: #007bff; color: white; padding: 15px; border-radius: 10px; text-align: center; font-family: 'Segoe UI', Arial, sans-serif;">
<div style="font-size: 24px; margin-bottom: 5px;">💻</div>
<div style="font-weight: bold;">[[Category:Technology|Technology]]</div>
</div>
<div style="background: #28a745; color: white; padding: 15px; border-radius: 10px; text-align: center; font-family: 'Segoe UI', Arial, sans-serif;">
<div style="font-size: 24px; margin-bottom: 5px;">🔬</div>
<div style="font-weight: bold;">[[Category:Science|Science]]</div>
</div>
<div style="background: #ffc107; color: white; padding: 15px; border-radius: 10px; text-align: center; font-family: 'Segoe UI', Arial, sans-serif;">
<div style="font-size: 24px; margin-bottom: 5px;">💼</div>
<div style="font-weight: bold;">[[Category:Business|Business]]</div>
</div>
<div style="background: #17a2b8; color: white; padding: 15px; border-radius: 10px; text-align: center; font-family: 'Segoe UI', Arial, sans-serif;">
<div style="font-size: 24px; margin-bottom: 5px;">📚</div>
<div style="font-weight: bold;">[[Category:Education|Education]]</div>
</div>
<div style="background: #dc3545; color: white; padding: 15px; border-radius: 10px; text-align: center; font-family: 'Segoe UI', Arial, sans-serif;">
<div style="font-size: 24px; margin-bottom: 5px;">🏥</div>
<div style="font-weight: bold;">[[Category:Health|Health]]</div>
</div>
<div style="background: #6f42c1; color: white; padding: 15px; border-radius: 10px; text-align: center; font-family: 'Segoe UI', Arial, sans-serif;">
<div style="font-size: 24px; margin-bottom: 5px;">🎨</div>
<div style="font-weight: bold;">[[Category:Arts|Arts]]</div>
</div>
</div>

</div>

<div style="flex: 1; min-width: 250px; max-width: 100%;">

<div style="background: #fff3cd; border: 1px solid #ffeaa7; border-radius: 10px; padding: 20px; margin-bottom: 15px;">
== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">Wiki Statistics</span> ==
<div style="text-align: center; font-family: 'Segoe UI', Arial, sans-serif;">
<div style="display: grid; grid-template-columns: repeat(auto-fit, minmax(120px, 1fr)); gap: 15px; margin-top: 15px;">
<div style="background: white; padding: 15px; border-radius: 8px; box-shadow: 0 2px 8px rgba(0,0,0,0.1);">
<div style="font-size: 24px; font-weight: bold; color: #007bff; font-family: 'Segoe UI', Arial, sans-serif;">{{NUMBEROFARTICLES}}</div>
<div style="color: #6c757d; font-size: 14px; font-family: 'Segoe UI', Arial, sans-serif;">Total Articles</div>
</div>
<div style="background: white; padding: 15px; border-radius: 8px; box-shadow: 0 2px 8px rgba(0,0,0,0.1);">
<div style="font-size: 24px; font-weight: bold; color: #28a745; font-family: 'Segoe UI', Arial, sans-serif;">{{NUMBEROFPAGES}}</div>
<div style="color: #6c757d; font-size: 14px; font-family: 'Segoe UI', Arial, sans-serif;">Total Pages</div>
</div>
<div style="background: white; padding: 15px; border-radius: 8px; box-shadow: 0 2px 8px rgba(0,0,0,0.1);">
<div style="font-size: 24px; font-weight: bold; color: #dc3545; font-family: 'Segoe UI', Arial, sans-serif;">{{NUMBEROFEDITS}}</div>
<div style="color: #6c757d; font-size: 14px; font-family: 'Segoe UI', Arial, sans-serif;">Total Edits</div>
</div>
<div style="background: white; padding: 15px; border-radius: 8px; box-shadow: 0 2px 8px rgba(0,0,0,0.1);">
<div style="font-size: 24px; font-weight: bold; color: #ffc107; text-shadow: 1px 1px 2px rgba(0,0,0,0.1); font-family: 'Segoe UI', Arial, sans-serif;">{{NUMBEROFUSERS}}</div>
<div style="color: #6c757d; font-size: 14px; font-family: 'Segoe UI', Arial, sans-serif;">Contributors</div>
</div>
</div>
</div>
</div>

<div style="background: #f1f3f4; border: 1px solid #dadce0; border-radius: 10px; padding: 20px; margin-bottom: 15px;">
== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">Quick Actions</span> ==
<div style="font-family: 'Segoe UI', Arial, sans-serif;">
* [[Special:CreateAccount|Join Our Community]] 🚀
* [[Help:Getting Started|Getting Started Guide]] 📖
* [[Special:Random|Discover Random Article]] 🎲
* [[Special:RecentChanges|Recent Changes]] 📊
* [[Special:Upload|Upload Files]] 📎
</div>
</div>

<div style="background: #e3f2fd; border: 1px solid #bbdefb; border-radius: 10px; padding: 20px;">
== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">Community</span> ==
<div style="color: #1565c0; font-family: 'Segoe UI', Arial, sans-serif;">
Join thousands of contributors who are building the future of knowledge sharing. Every contribution matters, from minor edits to major articles.
</div>
<div style="margin-top: 10px; text-align: center; font-family: 'Segoe UI', Arial, sans-serif;">
[[Special:Community|Community Portal]] | [[Special:Forum|Discussion Forum]]
</div>
</div>

</div>
</div>

== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">Featured Articles</span> ==
<div style="background: white; border: 1px solid #e1e5e9; border-radius: 10px; padding: 20px; margin: 20px 0;">
<div style="display: grid; grid-template-columns: repeat(auto-fit, minmax(280px, 1fr)); gap: 20px;">

<div style="border-left: 4px solid #007bff; padding-left: 15px;">
=== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">[[Introduction to Qbase]]</span> ===
<div style="color: #6c757d; font-size: 14px; margin-bottom: 8px; font-family: 'Segoe UI', Arial, sans-serif;">''Core Documentation''</div>
<div style="font-family: 'Segoe UI', Arial, sans-serif;">Learn the fundamentals of using Qbase effectively, from basic navigation to advanced features.</div>
</div>

<div style="border-left: 4px solid #28a745; padding-left: 15px;">
=== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">[[Best Practices Guide]]</span> ===
<div style="color: #6c757d; font-size: 14px; margin-bottom: 8px; font-family: 'Segoe UI', Arial, sans-serif;">''Guidelines''</div>
<div style="font-family: 'Segoe UI', Arial, sans-serif;">Discover proven strategies for creating high-quality content and maintaining wiki standards.</div>
</div>

<div style="border-left: 4px solid #ffc107; padding-left: 15px;">
=== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">[[Community Guidelines]]</span> ===
<div style="color: #6c757d; font-size: 14px; margin-bottom: 8px; font-family: 'Segoe UI', Arial, sans-serif;">''Policies''</div>
<div style="font-family: 'Segoe UI', Arial, sans-serif;">Understanding our community standards and collaborative principles for a positive environment.</div>
</div>

<div style="border-left: 4px solid #dc3545; padding-left: 15px;">
=== <span style="font-family: 'Segoe UI', Arial, sans-serif; font-weight: bold;">[[Technical Resources]]</span> ===
<div style="color: #6c757d; font-size: 14px; margin-bottom: 8px; font-family: 'Segoe UI', Arial, sans-serif;">''Documentation''</div>
<div style="font-family: 'Segoe UI', Arial, sans-serif;">Comprehensive technical documentation for developers and advanced users.</div>
</div>

</div>
</div>

----
<div style="text-align: center; color: #6c757d; font-size: 14px; margin-top: 30px; font-family: 'Segoe UI', Arial, sans-serif;">
<div style="margin-bottom: 10px;">
''Powered by MediaWiki • Built with ❤️ by the Qbase Community''
</div>
[[Special:About|About]] • [[Special:Contact|Contact]] • [[Privacy Policy]] • [[Terms of Service]]
</div>

</div>
__NOTOC__ __NOEDITSECTION__

Main Page

2025-06-10T09:29:31Z

Thakshashila:

{{DISPLAYTITLE:Welcome to Qbase}}
<div style="background: linear-gradient(135deg, #667eea 0%, #764ba2 100%); color: white; padding: 30px; border-radius: 15px; margin-bottom: 20px; text-align: center; box-shadow: 0 4px 15px rgba(0,0,0,0.1);">
= '''Welcome to Qbase''' =
<div style="font-size: 18px; margin-top: 15px; opacity: 0.9;">
''Your comprehensive knowledge base and collaborative platform''
</div>
</div>

{| style="width: 100%; border-spacing: 10px;"
|-
| style="width: 60%; vertical-align: top;" |

<div style="background: #f8f9fa; border: 1px solid #e1e5e9; border-radius: 10px; padding: 25px; margin-bottom: 15px;">
== About Qbase ==
<div style="color: #495057; line-height: 1.6;">
Qbase is a cutting-edge knowledge management platform designed to foster collaboration, innovation, and information sharing. Our platform serves as a central hub where knowledge meets community, enabling users to create, share, and discover valuable content across diverse domains.

Whether you're a researcher, professional, student, or curious learner, Qbase provides the tools and environment to build comprehensive knowledge repositories that grow with your community's needs.
</div>
</div>

<div style="background: #e8f5e8; border-left: 5px solid #28a745; border-radius: 0 10px 10px 0; padding: 20px; margin-bottom: 15px;">
== Our Mission ==
<div style="color: #155724; font-weight: 500;">
To democratize knowledge sharing and create accessible, collaborative spaces where information transforms into wisdom, empowering communities to learn, grow, and innovate together.
</div>
</div>

== Featured Categories ==
<div style="display: flex; flex-wrap: wrap; gap: 10px; margin: 15px 0;">
{{#widget:CategoryBox|category=Technology|color=#007bff|icon=💻}}
{{#widget:CategoryBox|category=Science|color=#28a745|icon=🔬}}
{{#widget:CategoryBox|category=Business|color=#ffc107|icon=💼}}
{{#widget:CategoryBox|category=Education|color=#17a2b8|icon=📚}}
{{#widget:CategoryBox|category=Health|color=#dc3545|icon=🏥}}
{{#widget:CategoryBox|category=Arts|color=#6f42c1|icon=🎨}}
</div>

| style="width: 40%; vertical-align: top;" |

<div style="background: #fff3cd; border: 1px solid #ffeaa7; border-radius: 10px; padding: 20px; margin-bottom: 15px;">
== Wiki Statistics ==
<div style="text-align: center;">
<div style="display: grid; grid-template-columns: 1fr 1fr; gap: 15px; margin-top: 15px;">
<div style="background: white; padding: 15px; border-radius: 8px; box-shadow: 0 2px 8px rgba(0,0,0,0.1);">
<div style="font-size: 24px; font-weight: bold; color: #007bff;">{{NUMBEROFARTICLES}}</div>
<div style="color: #6c757d; font-size: 14px;">Total Articles</div>
</div>
<div style="background: white; padding: 15px; border-radius: 8px; box-shadow: 0 2px 8px rgba(0,0,0,0.1);">
<div style="font-size: 24px; font-weight: bold; color: #28a745;">{{NUMBEROFPAGES}}</div>
<div style="color: #6c757d; font-size: 14px;">Total Pages</div>
</div>
<div style="background: white; padding: 15px; border-radius: 8px; box-shadow: 0 2px 8px rgba(0,0,0,0.1);">
<div style="font-size: 24px; font-weight: bold; color: #dc3545;">{{NUMBEROFEDITS}}</div>
<div style="color: #6c757d; font-size: 14px;">Total Edits</div>
</div>
<div style="background: white; padding: 15px; border-radius: 8px; box-shadow: 0 2px 8px rgba(0,0,0,0.1);">
<div style="font-size: 24px; font-weight: bold; color: #ffc107; text-shadow: 1px 1px 2px rgba(0,0,0,0.1);">{{NUMBEROFUSERS}}</div>
<div style="color: #6c757d; font-size: 14px;">Contributors</div>
</div>
</div>
</div>
</div>

<div style="background: #f1f3f4; border: 1px solid #dadce0; border-radius: 10px; padding: 20px; margin-bottom: 15px;">
== Quick Actions ==
<div style="display: grid; grid-template-columns: 1fr; gap: 8px;">
* [[Special:CreateAccount|Join Our Community]] 🚀
* [[Help:Getting Started|Getting Started Guide]] 📖
* [[Special:Random|Discover Random Article]] 🎲
* [[Special:RecentChanges|Recent Changes]] 📊
* [[Special:Upload|Upload Files]] 📎
</div>
</div>

<div style="background: #e3f2fd; border: 1px solid #bbdefb; border-radius: 10px; padding: 20px;">
== Community ==
<div style="color: #1565c0;">
Join thousands of contributors who are building the future of knowledge sharing. Every contribution matters, from minor edits to major articles.
</div>
<div style="margin-top: 10px; text-align: center;">
[[Special:Community|Community Portal]] | [[Special:Forum|Discussion Forum]]
</div>
</div>

|}

== Featured Articles ==
<div style="background: white; border: 1px solid #e1e5e9; border-radius: 10px; padding: 20px; margin: 20px 0;">
<div style="display: grid; grid-template-columns: repeat(auto-fit, minmax(300px, 1fr)); gap: 20px;">

<div style="border-left: 4px solid #007bff; padding-left: 15px;">
=== [[Introduction to Qbase]] ===
<div style="color: #6c757d; font-size: 14px; margin-bottom: 8px;">''Core Documentation''</div>
Learn the fundamentals of using Qbase effectively, from basic navigation to advanced features.
</div>

<div style="border-left: 4px solid #28a745; padding-left: 15px;">
=== [[Best Practices Guide]] ===
<div style="color: #6c757d; font-size: 14px; margin-bottom: 8px;">''Guidelines''</div>
Discover proven strategies for creating high-quality content and maintaining wiki standards.
</div>

<div style="border-left: 4px solid #ffc107; padding-left: 15px;">
=== [[Community Guidelines]] ===
<div style="color: #6c757d; font-size: 14px; margin-bottom: 8px;">''Policies''</div>
Understanding our community standards and collaborative principles for a positive environment.
</div>

<div style="border-left: 4px solid #dc3545; padding-left: 15px;">
=== [[Technical Resources]] ===
<div style="color: #6c757d; font-size: 14px; margin-bottom: 8px;">''Documentation''</div>
Comprehensive technical documentation for developers and advanced users.
</div>

</div>
</div>

== Recent Articles ==
<div style="background: #f8f9fa; border-radius: 10px; padding: 20px; margin: 20px 0;">
{{Special:NewPages|limit=8|namespace=0}}
</div>

----
<div style="text-align: center; color: #6c757d; font-size: 14px; margin-top: 30px;">
<div style="margin-bottom: 10px;">
''Powered by MediaWiki • Built with ❤️ by the Qbase Community''
</div>
[[Special:About|About]] • [[Special:Contact|Contact]] • [[Privacy Policy]] • [[Terms of Service]]
</div>

__NOTOC__ __NOEDITSECTION__

Main Page

2025-06-10T09:24:49Z

Thakshashila: /* 📂 Categories */

<div style="border: 1px solid #cccccc; background-color: #f9f9f9; padding: 1em; border-radius: 5px;">

Qbase is created with the sincere goal of promoting '''education''', '''academic exploration''', and '''student-friendly learning'''. Our mission is to make high-quality, accessible knowledge available to everyone — especially learners, educators, and curious minds. Every page is written and curated with clarity, accuracy, and a passion for discovery.

We believe that sharing knowledge is a powerful act for the '''common good'''. If you find this project meaningful, please consider following us and showing your love and support as we grow together in this journey of learning.

</div>

<div style="display: flex; align-items: center; border: 1px solid #ccc; border-radius: 8px; padding: 16px; background-color: #f9f9f9; max-width: 800px; box-shadow: 0 2px 5px rgba(0,0,0,0.1);">

<div style="flex: 0 0 auto; margin-right: 20px;">
[[File:kbaselogo.png|frameless|alt=Logo|style=width: 120px; border-radius: 4px;]]
</div>

<div style="flex: 1;">
<h2 style="margin-top: 0;">Welcome to <i>Qbase</i></h2>
<p>This is the main hub of all knowledge and content on this Qbase. You can browse, search, or explore the categories to find interesting topics.</p>
</div>

</div>

== 🎓 Our Mission ==
<div style="border: 1px solid #ccc; background: #f9f9f9; padding: 1em; border-radius: 5px;">
Qbase is dedicated to supporting <b>education</b> and providing a <b>student-friendly</b> learning space. We create content for the common good and invite you to follow us and share your support as we grow together.
</div>
== 📘 About Qbase ==
This wiki currently contains '''{{NUMBEROFARTICLES}}''' articles and '''{{NUMBEROFEDITS}}''' total edits by '''{{NUMBEROFUSERS}}''' registered users.

== 📂 Categories ==
<div style="display: flex; flex-wrap: wrap; gap: 16px; max-width: 1000px; margin: auto;">

<div style="flex: 1 1 200px; padding: 16px; background: #f9f9f9; border-radius: 8px; text-align: center; border: 1px solid #ddd;">
<div style="font-weight: bold; color: #0078d7;">[[Category:Physics|Physics]]</div>
<div style="font-size: 14px; color: #666; margin-top: 6px;">Topics related to physics and its applications.</div>
</div>

<div style="flex: 1 1 200px; padding: 16px; background: #f9f9f9; border-radius: 8px; text-align: center; border: 1px solid #ddd;">
<div style="font-weight: bold; color: #0078d7;">[[Category:Mathematics|Mathematics]]</div>
<div style="font-size: 14px; color: #666; margin-top: 6px;">Everything about numbers, theorems, and logic.</div>
</div>

<div style="flex: 1 1 200px; padding: 16px; background: #f9f9f9; border-radius: 8px; text-align: center; border: 1px solid #ddd;">
<div style="font-weight: bold; color: #0078d7;">[[Category:History|History]]</div>
<div style="font-size: 14px; color: #666; margin-top: 6px;">Historical events, timelines, and figures.</div>
</div>

</div>

== 🧠 Featured Articles ==
* [[Isaac Newton]]
* [[James Clerk Maxwell]]
* [[Electromagnetic Induction]]
* [[Maxwell's Equations]]

<div style="max-width: 800px; margin: auto; padding: 24px; font-family: 'Segoe UI', Tahoma, sans-serif; background-color: #ffffff; border: 1px solid #e0e0e0; border-radius: 8px;">

<h2 style="margin-top: 0; margin-bottom: 24px; color: #2c3e50; border-bottom: 1px solid #ccc; padding-bottom: 8px;">📊 Statistics</h2>

<div style="display: flex; flex-wrap: wrap; gap: 16px;">

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Total Articles</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFARTICLES}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Total Pages</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFPAGES}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Total Edits</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFEDITS}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Registered Users</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFUSERS}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Active Users</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFACTIVEUSERS}}</div>
</div>

</div>

</div>

== 🛠️ Help & Community ==
* [[Help:Contents|How to edit pages]]
* [[Project:Community Portal|Community Portal]]
* [[Special:RecentChanges|Recent Changes]]
* [[Special:Random|Random Page]]

== 📅 New & Updated Pages ==
See what's new: [[Special:NewPages]] and [[Special:RecentChanges]]

== 🔍 Search Wiki ==
Use the search bar at the top of the page to find specific topics or articles.

<strong>MediaWiki has been installed.</strong>

Consult the [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents User's Guide] for information on using the wiki software.

== Getting started ==
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/postorius/lists/mediawiki-announce.lists.wikimedia.org/ MediaWiki release mailing list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Localisation#Translation_resources Localise MediaWiki for your language]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Combating_spam Learn how to combat spam on your wiki]

Main Page

2025-06-10T09:21:46Z

Thakshashila: /* 📂 Categories */

<div style="border: 1px solid #cccccc; background-color: #f9f9f9; padding: 1em; border-radius: 5px;">

Qbase is created with the sincere goal of promoting '''education''', '''academic exploration''', and '''student-friendly learning'''. Our mission is to make high-quality, accessible knowledge available to everyone — especially learners, educators, and curious minds. Every page is written and curated with clarity, accuracy, and a passion for discovery.

We believe that sharing knowledge is a powerful act for the '''common good'''. If you find this project meaningful, please consider following us and showing your love and support as we grow together in this journey of learning.

</div>

<div style="display: flex; align-items: center; border: 1px solid #ccc; border-radius: 8px; padding: 16px; background-color: #f9f9f9; max-width: 800px; box-shadow: 0 2px 5px rgba(0,0,0,0.1);">

<div style="flex: 0 0 auto; margin-right: 20px;">
[[File:kbaselogo.png|frameless|alt=Logo|style=width: 120px; border-radius: 4px;]]
</div>

<div style="flex: 1;">
<h2 style="margin-top: 0;">Welcome to <i>Qbase</i></h2>
<p>This is the main hub of all knowledge and content on this Qbase. You can browse, search, or explore the categories to find interesting topics.</p>
</div>

</div>

== 🎓 Our Mission ==
<div style="border: 1px solid #ccc; background: #f9f9f9; padding: 1em; border-radius: 5px;">
Qbase is dedicated to supporting <b>education</b> and providing a <b>student-friendly</b> learning space. We create content for the common good and invite you to follow us and share your support as we grow together.
</div>
== 📘 About Qbase ==
This wiki currently contains '''{{NUMBEROFARTICLES}}''' articles and '''{{NUMBEROFEDITS}}''' total edits by '''{{NUMBEROFUSERS}}''' registered users.

== 📂 Categories ==
Browse content by topic:

* [[:Category:Physics|Physics]]
* [[:Category:Mathematics|Mathematics]]
* [[:Category:Chemistry|Chemistry]]
* [[:Category:Biographies|Biographies]]
* [[:Category:Technology|Technology]]

''To view all categories:'' [[:Special:Categories]]

== 🧠 Featured Articles ==
* [[Isaac Newton]]
* [[James Clerk Maxwell]]
* [[Electromagnetic Induction]]
* [[Maxwell's Equations]]

<div style="max-width: 800px; margin: auto; padding: 24px; font-family: 'Segoe UI', Tahoma, sans-serif; background-color: #ffffff; border: 1px solid #e0e0e0; border-radius: 8px;">

<h2 style="margin-top: 0; margin-bottom: 24px; color: #2c3e50; border-bottom: 1px solid #ccc; padding-bottom: 8px;">📊 Statistics</h2>

<div style="display: flex; flex-wrap: wrap; gap: 16px;">

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Total Articles</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFARTICLES}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Total Pages</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFPAGES}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Total Edits</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFEDITS}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Registered Users</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFUSERS}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Active Users</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFACTIVEUSERS}}</div>
</div>

</div>

</div>

== 🛠️ Help & Community ==
* [[Help:Contents|How to edit pages]]
* [[Project:Community Portal|Community Portal]]
* [[Special:RecentChanges|Recent Changes]]
* [[Special:Random|Random Page]]

== 📅 New & Updated Pages ==
See what's new: [[Special:NewPages]] and [[Special:RecentChanges]]

== 🔍 Search Wiki ==
Use the search bar at the top of the page to find specific topics or articles.

<strong>MediaWiki has been installed.</strong>

Consult the [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents User's Guide] for information on using the wiki software.

== Getting started ==
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/postorius/lists/mediawiki-announce.lists.wikimedia.org/ MediaWiki release mailing list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Localisation#Translation_resources Localise MediaWiki for your language]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Combating_spam Learn how to combat spam on your wiki]

Main Page

2025-06-10T09:21:32Z

Thakshashila: /* 📂 Categories */

<div style="border: 1px solid #cccccc; background-color: #f9f9f9; padding: 1em; border-radius: 5px;">

Qbase is created with the sincere goal of promoting '''education''', '''academic exploration''', and '''student-friendly learning'''. Our mission is to make high-quality, accessible knowledge available to everyone — especially learners, educators, and curious minds. Every page is written and curated with clarity, accuracy, and a passion for discovery.

We believe that sharing knowledge is a powerful act for the '''common good'''. If you find this project meaningful, please consider following us and showing your love and support as we grow together in this journey of learning.

</div>

<div style="display: flex; align-items: center; border: 1px solid #ccc; border-radius: 8px; padding: 16px; background-color: #f9f9f9; max-width: 800px; box-shadow: 0 2px 5px rgba(0,0,0,0.1);">

<div style="flex: 0 0 auto; margin-right: 20px;">
[[File:kbaselogo.png|frameless|alt=Logo|style=width: 120px; border-radius: 4px;]]
</div>

<div style="flex: 1;">
<h2 style="margin-top: 0;">Welcome to <i>Qbase</i></h2>
<p>This is the main hub of all knowledge and content on this Qbase. You can browse, search, or explore the categories to find interesting topics.</p>
</div>

</div>

== 🎓 Our Mission ==
<div style="border: 1px solid #ccc; background: #f9f9f9; padding: 1em; border-radius: 5px;">
Qbase is dedicated to supporting <b>education</b> and providing a <b>student-friendly</b> learning space. We create content for the common good and invite you to follow us and share your support as we grow together.
</div>
== 📘 About Qbase ==
This wiki currently contains '''{{NUMBEROFARTICLES}}''' articles and '''{{NUMBEROFEDITS}}''' total edits by '''{{NUMBEROFUSERS}}''' registered users.

== 📂 Categories ==
Browse content by topic:

* [[:Category:Physics|Physics]]
* [[:Category:Mathematics|Mathematics]]
* [[:Category:Chemistry|Chemistry]]
* [[:Category:Biographies|Biographies]]
* [[:Category:Technology|Technology]]

''To view all categories:'' [[:Special:Categories]]

<div style="display: flex; flex-wrap: wrap; gap: 16px; max-width: 1000px; margin: auto;">
<dpl>
namespace=Category
mode=userformat
listseparators=<div style="flex: 1 1 200px; padding: 16px; background: #f9f9f9; border-radius: 8px; text-align: center; border: 1px solid #ddd;">
[[%PAGE%]]<br><span style="font-size: 14px; color: #666;">Description here</span>
</div>
</dpl>
</div>

== 🧠 Featured Articles ==
* [[Isaac Newton]]
* [[James Clerk Maxwell]]
* [[Electromagnetic Induction]]
* [[Maxwell's Equations]]

<div style="max-width: 800px; margin: auto; padding: 24px; font-family: 'Segoe UI', Tahoma, sans-serif; background-color: #ffffff; border: 1px solid #e0e0e0; border-radius: 8px;">

<h2 style="margin-top: 0; margin-bottom: 24px; color: #2c3e50; border-bottom: 1px solid #ccc; padding-bottom: 8px;">📊 Statistics</h2>

<div style="display: flex; flex-wrap: wrap; gap: 16px;">

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Total Articles</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFARTICLES}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Total Pages</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFPAGES}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Total Edits</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFEDITS}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Registered Users</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFUSERS}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Active Users</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFACTIVEUSERS}}</div>
</div>

</div>

</div>

== 🛠️ Help & Community ==
* [[Help:Contents|How to edit pages]]
* [[Project:Community Portal|Community Portal]]
* [[Special:RecentChanges|Recent Changes]]
* [[Special:Random|Random Page]]

== 📅 New & Updated Pages ==
See what's new: [[Special:NewPages]] and [[Special:RecentChanges]]

== 🔍 Search Wiki ==
Use the search bar at the top of the page to find specific topics or articles.

<strong>MediaWiki has been installed.</strong>

Consult the [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents User's Guide] for information on using the wiki software.

== Getting started ==
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/postorius/lists/mediawiki-announce.lists.wikimedia.org/ MediaWiki release mailing list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Localisation#Translation_resources Localise MediaWiki for your language]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Combating_spam Learn how to combat spam on your wiki]

Main Page

2025-06-10T09:18:20Z

Thakshashila: /* 🧠 Featured Articles */

<div style="border: 1px solid #cccccc; background-color: #f9f9f9; padding: 1em; border-radius: 5px;">

Qbase is created with the sincere goal of promoting '''education''', '''academic exploration''', and '''student-friendly learning'''. Our mission is to make high-quality, accessible knowledge available to everyone — especially learners, educators, and curious minds. Every page is written and curated with clarity, accuracy, and a passion for discovery.

We believe that sharing knowledge is a powerful act for the '''common good'''. If you find this project meaningful, please consider following us and showing your love and support as we grow together in this journey of learning.

</div>

<div style="display: flex; align-items: center; border: 1px solid #ccc; border-radius: 8px; padding: 16px; background-color: #f9f9f9; max-width: 800px; box-shadow: 0 2px 5px rgba(0,0,0,0.1);">

<div style="flex: 0 0 auto; margin-right: 20px;">
[[File:kbaselogo.png|frameless|alt=Logo|style=width: 120px; border-radius: 4px;]]
</div>

<div style="flex: 1;">
<h2 style="margin-top: 0;">Welcome to <i>Qbase</i></h2>
<p>This is the main hub of all knowledge and content on this Qbase. You can browse, search, or explore the categories to find interesting topics.</p>
</div>

</div>

== 🎓 Our Mission ==
<div style="border: 1px solid #ccc; background: #f9f9f9; padding: 1em; border-radius: 5px;">
Qbase is dedicated to supporting <b>education</b> and providing a <b>student-friendly</b> learning space. We create content for the common good and invite you to follow us and share your support as we grow together.
</div>
== 📘 About Qbase ==
This wiki currently contains '''{{NUMBEROFARTICLES}}''' articles and '''{{NUMBEROFEDITS}}''' total edits by '''{{NUMBEROFUSERS}}''' registered users.

== 📂 Categories ==
Browse content by topic:

* [[:Category:Physics|Physics]]
* [[:Category:Mathematics|Mathematics]]
* [[:Category:Chemistry|Chemistry]]
* [[:Category:Biographies|Biographies]]
* [[:Category:Technology|Technology]]

''To view all categories:'' [[:Special:Categories]]

== 🧠 Featured Articles ==
* [[Isaac Newton]]
* [[James Clerk Maxwell]]
* [[Electromagnetic Induction]]
* [[Maxwell's Equations]]

<div style="max-width: 800px; margin: auto; padding: 24px; font-family: 'Segoe UI', Tahoma, sans-serif; background-color: #ffffff; border: 1px solid #e0e0e0; border-radius: 8px;">

<h2 style="margin-top: 0; margin-bottom: 24px; color: #2c3e50; border-bottom: 1px solid #ccc; padding-bottom: 8px;">📊 Statistics</h2>

<div style="display: flex; flex-wrap: wrap; gap: 16px;">

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Total Articles</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFARTICLES}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Total Pages</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFPAGES}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Total Edits</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFEDITS}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Registered Users</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFUSERS}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Active Users</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFACTIVEUSERS}}</div>
</div>

</div>

</div>

== 🛠️ Help & Community ==
* [[Help:Contents|How to edit pages]]
* [[Project:Community Portal|Community Portal]]
* [[Special:RecentChanges|Recent Changes]]
* [[Special:Random|Random Page]]

== 📅 New & Updated Pages ==
See what's new: [[Special:NewPages]] and [[Special:RecentChanges]]

== 🔍 Search Wiki ==
Use the search bar at the top of the page to find specific topics or articles.

<strong>MediaWiki has been installed.</strong>

Consult the [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents User's Guide] for information on using the wiki software.

== Getting started ==
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/postorius/lists/mediawiki-announce.lists.wikimedia.org/ MediaWiki release mailing list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Localisation#Translation_resources Localise MediaWiki for your language]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Combating_spam Learn how to combat spam on your wiki]

Main Page

2025-06-10T09:17:22Z

Thakshashila: /* 🧠 Featured Articles */

<div style="border: 1px solid #cccccc; background-color: #f9f9f9; padding: 1em; border-radius: 5px;">

Qbase is created with the sincere goal of promoting '''education''', '''academic exploration''', and '''student-friendly learning'''. Our mission is to make high-quality, accessible knowledge available to everyone — especially learners, educators, and curious minds. Every page is written and curated with clarity, accuracy, and a passion for discovery.

We believe that sharing knowledge is a powerful act for the '''common good'''. If you find this project meaningful, please consider following us and showing your love and support as we grow together in this journey of learning.

</div>

<div style="display: flex; align-items: center; border: 1px solid #ccc; border-radius: 8px; padding: 16px; background-color: #f9f9f9; max-width: 800px; box-shadow: 0 2px 5px rgba(0,0,0,0.1);">

<div style="flex: 0 0 auto; margin-right: 20px;">
[[File:kbaselogo.png|frameless|alt=Logo|style=width: 120px; border-radius: 4px;]]
</div>

<div style="flex: 1;">
<h2 style="margin-top: 0;">Welcome to <i>Qbase</i></h2>
<p>This is the main hub of all knowledge and content on this Qbase. You can browse, search, or explore the categories to find interesting topics.</p>
</div>

</div>

== 🎓 Our Mission ==
<div style="border: 1px solid #ccc; background: #f9f9f9; padding: 1em; border-radius: 5px;">
Qbase is dedicated to supporting <b>education</b> and providing a <b>student-friendly</b> learning space. We create content for the common good and invite you to follow us and share your support as we grow together.
</div>
== 📘 About Qbase ==
This wiki currently contains '''{{NUMBEROFARTICLES}}''' articles and '''{{NUMBEROFEDITS}}''' total edits by '''{{NUMBEROFUSERS}}''' registered users.

== 📂 Categories ==
Browse content by topic:

* [[:Category:Physics|Physics]]
* [[:Category:Mathematics|Mathematics]]
* [[:Category:Chemistry|Chemistry]]
* [[:Category:Biographies|Biographies]]
* [[:Category:Technology|Technology]]

''To view all categories:'' [[:Special:Categories]]

== 🧠 Featured Articles ==
* [[Isaac Newton]]
* [[James Clerk Maxwell]]
* [[Electromagnetic Induction]]
* [[Maxwell's Equations]]

<<div style="max-width: 800px; margin: auto; padding: 24px; font-family: 'Segoe UI', Tahoma, sans-serif; background-color: #ffffff; border: 1px solid #e0e0e0; border-radius: 8px;">

<h2 style="margin-top: 0; margin-bottom: 24px; color: #2c3e50; border-bottom: 1px solid #ccc; padding-bottom: 8px;">📊 Statistics</h2>

<div style="display: flex; flex-wrap: wrap; gap: 16px;">

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Total Articles</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFARTICLES}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Total Pages</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFPAGES}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Total Edits</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFEDITS}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Registered Users</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFUSERS}}</div>
</div>

<div style="flex: 1 1 160px; padding: 16px; background: #f9f9f9; border-radius: 6px; text-align: center;">
<div style="font-weight: 600; color: #555;">Active Users</div>
<div style="font-size: 20px; margin-top: 6px; color: #0078d7;">{{NUMBEROFACTIVEUSERS}}</div>
</div>

</div>

</div>

== 🛠️ Help & Community ==
* [[Help:Contents|How to edit pages]]
* [[Project:Community Portal|Community Portal]]
* [[Special:RecentChanges|Recent Changes]]
* [[Special:Random|Random Page]]

== 📅 New & Updated Pages ==
See what's new: [[Special:NewPages]] and [[Special:RecentChanges]]

== 🔍 Search Wiki ==
Use the search bar at the top of the page to find specific topics or articles.

<strong>MediaWiki has been installed.</strong>

Consult the [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents User's Guide] for information on using the wiki software.

== Getting started ==
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/postorius/lists/mediawiki-announce.lists.wikimedia.org/ MediaWiki release mailing list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Localisation#Translation_resources Localise MediaWiki for your language]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Combating_spam Learn how to combat spam on your wiki]

Main Page

2025-06-10T09:13:42Z

Thakshashila: /* 🗃️ All Pages */

<div style="border: 1px solid #cccccc; background-color: #f9f9f9; padding: 1em; border-radius: 5px;">

Qbase is created with the sincere goal of promoting '''education''', '''academic exploration''', and '''student-friendly learning'''. Our mission is to make high-quality, accessible knowledge available to everyone — especially learners, educators, and curious minds. Every page is written and curated with clarity, accuracy, and a passion for discovery.

We believe that sharing knowledge is a powerful act for the '''common good'''. If you find this project meaningful, please consider following us and showing your love and support as we grow together in this journey of learning.

</div>

<div style="display: flex; align-items: center; border: 1px solid #ccc; border-radius: 8px; padding: 16px; background-color: #f9f9f9; max-width: 800px; box-shadow: 0 2px 5px rgba(0,0,0,0.1);">

<div style="flex: 0 0 auto; margin-right: 20px;">
[[File:kbaselogo.png|frameless|alt=Logo|style=width: 120px; border-radius: 4px;]]
</div>

<div style="flex: 1;">
<h2 style="margin-top: 0;">Welcome to <i>Qbase</i></h2>
<p>This is the main hub of all knowledge and content on this Qbase. You can browse, search, or explore the categories to find interesting topics.</p>
</div>

</div>

== 🎓 Our Mission ==
<div style="border: 1px solid #ccc; background: #f9f9f9; padding: 1em; border-radius: 5px;">
Qbase is dedicated to supporting <b>education</b> and providing a <b>student-friendly</b> learning space. We create content for the common good and invite you to follow us and share your support as we grow together.
</div>
== 📘 About Qbase ==
This wiki currently contains '''{{NUMBEROFARTICLES}}''' articles and '''{{NUMBEROFEDITS}}''' total edits by '''{{NUMBEROFUSERS}}''' registered users.

== 📂 Categories ==
Browse content by topic:

* [[:Category:Physics|Physics]]
* [[:Category:Mathematics|Mathematics]]
* [[:Category:Chemistry|Chemistry]]
* [[:Category:Biographies|Biographies]]
* [[:Category:Technology|Technology]]

''To view all categories:'' [[:Special:Categories]]

== 🧠 Featured Articles ==
* [[Isaac Newton]]
* [[James Clerk Maxwell]]
* [[Electromagnetic Induction]]
* [[Maxwell's Equations]]

<div style="max-width: 800px; margin: auto; padding: 16px; font-family: Arial, sans-serif; background: #fefefe;">

<h2 style="margin-top: 0; margin-bottom: 16px; color: #0078d7; border-bottom: 2px solid #0078d7; padding-bottom: 4px;">📈 Statistics</h2>

<div style="display: flex; flex-wrap: wrap; gap: 16px;">

<div style="flex: 1 1 150px; padding: 16px; border: 1px solid #ccc; border-radius: 8px; background: #ffffff; box-shadow: 0 2px 6px rgba(0,0,0,0.1);">
<strong>Total articles</strong>
<p style="font-size: 18px; margin: 8px 0 0; color: #0078d7;">{{NUMBEROFARTICLES}}</p>
</div>

<div style="flex: 1 1 150px; padding: 16px; border: 1px solid #ccc; border-radius: 8px; background: #ffffff; box-shadow: 0 2px 6px rgba(0,0,0,0.1);">
<strong>Total pages</strong>
<p style="font-size: 18px; margin: 8px 0 0; color: #0078d7;">{{NUMBEROFPAGES}}</p>
</div>

<div style="flex: 1 1 150px; padding: 16px; border: 1px solid #ccc; border-radius: 8px; background: #ffffff; box-shadow: 0 2px 6px rgba(0,0,0,0.1);">
<strong>Total edits</strong>
<p style="font-size: 18px; margin: 8px 0 0; color: #0078d7;">{{NUMBEROFEDITS}}</p>
</div>

<div style="flex: 1 1 150px; padding: 16px; border: 1px solid #ccc; border-radius: 8px; background: #ffffff; box-shadow: 0 2px 6px rgba(0,0,0,0.1);">
<strong>Registered users</strong>
<p style="font-size: 18px; margin: 8px 0 0; color: #0078d7;">{{NUMBEROFUSERS}}</p>
</div>

<div style="flex: 1 1 150px; padding: 16px; border: 1px solid #ccc; border-radius: 8px; background: #ffffff; box-shadow: 0 2px 6px rgba(0,0,0,0.1);">
<strong>Active users</strong>
<p style="font-size: 18px; margin: 8px 0 0; color: #0078d7;">{{NUMBEROFACTIVEUSERS}}</p>
</div>

</div>

</div>

== 🛠️ Help & Community ==
* [[Help:Contents|How to edit pages]]
* [[Project:Community Portal|Community Portal]]
* [[Special:RecentChanges|Recent Changes]]
* [[Special:Random|Random Page]]

== 📅 New & Updated Pages ==
See what's new: [[Special:NewPages]] and [[Special:RecentChanges]]

== 🔍 Search Wiki ==
Use the search bar at the top of the page to find specific topics or articles.

<strong>MediaWiki has been installed.</strong>

Consult the [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents User's Guide] for information on using the wiki software.

== Getting started ==
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/postorius/lists/mediawiki-announce.lists.wikimedia.org/ MediaWiki release mailing list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Localisation#Translation_resources Localise MediaWiki for your language]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Combating_spam Learn how to combat spam on your wiki]

Main Page

2025-06-10T09:05:31Z

Thakshashila: /* 📈 Statistics */

Main Page

2025-06-10T09:04:31Z

Thakshashila: /* Welcome to Qbase */

Main Page

2025-06-10T09:04:07Z

Thakshashila:

Main Page

2025-06-10T09:03:23Z

Thakshashila:

<div style="border: 1px solid #cccccc; background-color: #f9f9f9; padding: 1em; border-radius: 5px;">

Qbase is created with the sincere goal of promoting '''education''', '''academic exploration''', and '''student-friendly learning'''. Our mission is to make high-quality, accessible knowledge available to everyone — especially learners, educators, and curious minds. Every page is written and curated with clarity, accuracy, and a passion for discovery.

We believe that sharing knowledge is a powerful act for the '''common good'''. If you find this project meaningful, please consider following us and showing your love and support as we grow together in this journey of learning.

</div>

<div class="card">
<img src="kbaselogo.png" alt="Logo">
<div class="card-text">
<h2>Welcome to <i>Qbase</i></h2>
<p>This is the main hub of all knowledge and content on this Qbase. You can browse, search, or explore the categories to find interesting topics.</p>
</div>
</div>

<div style="display: flex; align-items: center; border: 1px solid #ccc; border-radius: 8px; padding: 16px; background-color: #f9f9f9; max-width: 800px; box-shadow: 0 2px 5px rgba(0,0,0,0.1);">

<div style="flex: 0 0 auto; margin-right: 20px;">
[[File:kbaselogo.png|frameless|alt=Logo|style=width: 120px; border-radius: 4px;]]
</div>

<div style="flex: 1;">
<h2 style="margin-top: 0;">Welcome to <i>Qbase</i></h2>
<p>This is the main hub of all knowledge and content on this Qbase. You can browse, search, or explore the categories to find interesting topics.</p>
</div>

</div>

<div style="display: flex; align-items: center; border: 1px solid #ccc; border-radius: 8px; padding: 16px; background-color: #f9f9f9; max-width: 800px; box-shadow: 0 2px 5px rgba(0,0,0,0.1);">

<div style="flex: 0 0 auto; margin-right: 20px;">
[[File:kbaselogo.png|frameless|alt=Logo|style=width: 120px; border-radius: 4px;]]
</div>

<div style="flex: 1;">
<h2 style="margin-top: 0;">Welcome to <i>Qbase</i></h2>
<p>This is the main hub of all knowledge and content on this Qbase. You can browse, search, or explore the categories to find interesting topics.</p>
</div>

</div>

= Welcome to ''Qbase'' =
[[File:kbaselogo.png|frameless|alt=Logo|style=float:left; margin-right: 1em; width: 120px]]
This is the main hub of all knowledge and content on this Qbase. You can browse, search, or explore the categories to find interesting topics. modify this to display inside a cardview left side image rightside text
== 🎓 Our Mission ==
<div style="border: 1px solid #ccc; background: #f9f9f9; padding: 1em; border-radius: 5px;">
Qbase is dedicated to supporting <b>education</b> and providing a <b>student-friendly</b> learning space. We create content for the common good and invite you to follow us and share your support as we grow together.
</div>
== 📘 About Qbase ==
This wiki currently contains '''{{NUMBEROFARTICLES}}''' articles and '''{{NUMBEROFEDITS}}''' total edits by '''{{NUMBEROFUSERS}}''' registered users.

== 📂 Categories ==
Browse content by topic:

* [[:Category:Physics|Physics]]
* [[:Category:Mathematics|Mathematics]]
* [[:Category:Chemistry|Chemistry]]
* [[:Category:Biographies|Biographies]]
* [[:Category:Technology|Technology]]

''To view all categories:'' [[:Special:Categories]]

== 🧠 Featured Articles ==
* [[Isaac Newton]]
* [[James Clerk Maxwell]]
* [[Electromagnetic Induction]]
* [[Maxwell's Equations]]

== 🗃️ All Pages ==
You can explore all available pages here: [[Special:AllPages]]

== 📈 Statistics ==
* Total articles: {{NUMBEROFARTICLES}}
* Total pages: {{NUMBEROFPAGES}}
* Total edits: {{NUMBEROFEDITS}}
* Registered users: {{NUMBEROFUSERS}}
* Active users: {{NUMBEROFACTIVEUSERS}}

== 🛠️ Help & Community ==
* [[Help:Contents|How to edit pages]]
* [[Project:Community Portal|Community Portal]]
* [[Special:RecentChanges|Recent Changes]]
* [[Special:Random|Random Page]]

== 📅 New & Updated Pages ==
See what's new: [[Special:NewPages]] and [[Special:RecentChanges]]

== 🔍 Search Wiki ==
Use the search bar at the top of the page to find specific topics or articles.

<strong>MediaWiki has been installed.</strong>

Consult the [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents User's Guide] for information on using the wiki software.

== Getting started ==
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/postorius/lists/mediawiki-announce.lists.wikimedia.org/ MediaWiki release mailing list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Localisation#Translation_resources Localise MediaWiki for your language]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Combating_spam Learn how to combat spam on your wiki]

Main Page

2025-06-10T09:00:51Z

Thakshashila: /* Welcome to Qbase */

<div style="border: 1px solid #cccccc; background-color: #f9f9f9; padding: 1em; border-radius: 5px;">

Qbase is created with the sincere goal of promoting '''education''', '''academic exploration''', and '''student-friendly learning'''. Our mission is to make high-quality, accessible knowledge available to everyone — especially learners, educators, and curious minds. Every page is written and curated with clarity, accuracy, and a passion for discovery.

We believe that sharing knowledge is a powerful act for the '''common good'''. If you find this project meaningful, please consider following us and showing your love and support as we grow together in this journey of learning.

</div>
<style>
.card {
display: flex;
border: 1px solid #ddd;
border-radius: 8px;
padding: 16px;
max-width: 800px;
box-shadow: 0 2px 5px rgba(0,0,0,0.1);
margin: 20px auto;
background-color: #fff;
}

.card img {
width: 120px;
height: auto;
margin-right: 20px;
border-radius: 4px;
}

.card-text {
flex: 1;
display: flex;
flex-direction: column;
justify-content: center;
}
</style>

<div class="card">
<img src="kbaselogo.png" alt="Logo">
<div class="card-text">
<h2>Welcome to <i>Qbase</i></h2>
<p>This is the main hub of all knowledge and content on this Qbase. You can browse, search, or explore the categories to find interesting topics.</p>
</div>
</div>

<div style="display: flex; align-items: center; border: 1px solid #ccc; border-radius: 8px; padding: 16px; background-color: #f9f9f9; max-width: 800px; box-shadow: 0 2px 5px rgba(0,0,0,0.1);">

<div style="flex: 0 0 auto; margin-right: 20px;">
[[File:kbaselogo.png|frameless|alt=Logo|style=width: 120px; border-radius: 4px;]]
</div>

<div style="flex: 1;">
<h2 style="margin-top: 0;">Welcome to <i>Qbase</i></h2>
<p>This is the main hub of all knowledge and content on this Qbase. You can browse, search, or explore the categories to find interesting topics.</p>
</div>

</div>

<div style="display: flex; align-items: center; border: 1px solid #ccc; border-radius: 8px; padding: 16px; background-color: #f9f9f9; max-width: 800px; box-shadow: 0 2px 5px rgba(0,0,0,0.1);">

<div style="flex: 0 0 auto; margin-right: 20px;">
[[File:kbaselogo.png|frameless|alt=Logo|style=width: 120px; border-radius: 4px;]]
</div>

<div style="flex: 1;">
<h2 style="margin-top: 0;">Welcome to <i>Qbase</i></h2>
<p>This is the main hub of all knowledge and content on this Qbase. You can browse, search, or explore the categories to find interesting topics.</p>
</div>

</div>

= Welcome to ''Qbase'' =
[[File:kbaselogo.png|frameless|alt=Logo|style=float:left; margin-right: 1em; width: 120px]]
This is the main hub of all knowledge and content on this Qbase. You can browse, search, or explore the categories to find interesting topics. modify this to display inside a cardview left side image rightside text
== 🎓 Our Mission ==
<div style="border: 1px solid #ccc; background: #f9f9f9; padding: 1em; border-radius: 5px;">
Qbase is dedicated to supporting <b>education</b> and providing a <b>student-friendly</b> learning space. We create content for the common good and invite you to follow us and share your support as we grow together.
</div>
== 📘 About Qbase ==
This wiki currently contains '''{{NUMBEROFARTICLES}}''' articles and '''{{NUMBEROFEDITS}}''' total edits by '''{{NUMBEROFUSERS}}''' registered users.

== 📂 Categories ==
Browse content by topic:

* [[:Category:Physics|Physics]]
* [[:Category:Mathematics|Mathematics]]
* [[:Category:Chemistry|Chemistry]]
* [[:Category:Biographies|Biographies]]
* [[:Category:Technology|Technology]]

''To view all categories:'' [[:Special:Categories]]

== 🧠 Featured Articles ==
* [[Isaac Newton]]
* [[James Clerk Maxwell]]
* [[Electromagnetic Induction]]
* [[Maxwell's Equations]]

== 🗃️ All Pages ==
You can explore all available pages here: [[Special:AllPages]]

== 📈 Statistics ==
* Total articles: {{NUMBEROFARTICLES}}
* Total pages: {{NUMBEROFPAGES}}
* Total edits: {{NUMBEROFEDITS}}
* Registered users: {{NUMBEROFUSERS}}
* Active users: {{NUMBEROFACTIVEUSERS}}

== 🛠️ Help & Community ==
* [[Help:Contents|How to edit pages]]
* [[Project:Community Portal|Community Portal]]
* [[Special:RecentChanges|Recent Changes]]
* [[Special:Random|Random Page]]

== 📅 New & Updated Pages ==
See what's new: [[Special:NewPages]] and [[Special:RecentChanges]]

== 🔍 Search Wiki ==
Use the search bar at the top of the page to find specific topics or articles.

<strong>MediaWiki has been installed.</strong>

Consult the [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents User's Guide] for information on using the wiki software.

== Getting started ==
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/postorius/lists/mediawiki-announce.lists.wikimedia.org/ MediaWiki release mailing list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Localisation#Translation_resources Localise MediaWiki for your language]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Combating_spam Learn how to combat spam on your wiki]

Main Page

2025-06-10T08:59:19Z

Thakshashila: /* 🎓 Our Mission */

<div style="border: 1px solid #cccccc; background-color: #f9f9f9; padding: 1em; border-radius: 5px;">

Qbase is created with the sincere goal of promoting '''education''', '''academic exploration''', and '''student-friendly learning'''. Our mission is to make high-quality, accessible knowledge available to everyone — especially learners, educators, and curious minds. Every page is written and curated with clarity, accuracy, and a passion for discovery.

We believe that sharing knowledge is a powerful act for the '''common good'''. If you find this project meaningful, please consider following us and showing your love and support as we grow together in this journey of learning.

</div>
<style>
.card {
display: flex;
border: 1px solid #ddd;
border-radius: 8px;
padding: 16px;
max-width: 800px;
box-shadow: 0 2px 5px rgba(0,0,0,0.1);
margin: 20px auto;
background-color: #fff;
}

.card img {
width: 120px;
height: auto;
margin-right: 20px;
border-radius: 4px;
}

.card-text {
flex: 1;
display: flex;
flex-direction: column;
justify-content: center;
}
</style>

<div class="card">
<img src="kbaselogo.png" alt="Logo">
<div class="card-text">
<h2>Welcome to <i>Qbase</i></h2>
<p>This is the main hub of all knowledge and content on this Qbase. You can browse, search, or explore the categories to find interesting topics.</p>
</div>
</div>

<div style="display: flex; align-items: center; border: 1px solid #ccc; border-radius: 8px; padding: 16px; background-color: #f9f9f9; max-width: 800px; box-shadow: 0 2px 5px rgba(0,0,0,0.1);">

<div style="flex: 0 0 auto; margin-right: 20px;">
[[File:kbaselogo.png|frameless|alt=Logo|style=width: 120px; border-radius: 4px;]]
</div>

<div style="flex: 1;">
<h2 style="margin-top: 0;">Welcome to <i>Qbase</i></h2>
<p>This is the main hub of all knowledge and content on this Qbase. You can browse, search, or explore the categories to find interesting topics.</p>
</div>

</div>

= Welcome to ''Qbase'' =
[[File:kbaselogo.png|frameless|alt=Logo|style=float:left; margin-right: 1em; width: 120px]]
This is the main hub of all knowledge and content on this Qbase. You can browse, search, or explore the categories to find interesting topics. modify this to display inside a cardview left side image rightside text
== 🎓 Our Mission ==
<div style="border: 1px solid #ccc; background: #f9f9f9; padding: 1em; border-radius: 5px;">
Qbase is dedicated to supporting <b>education</b> and providing a <b>student-friendly</b> learning space. We create content for the common good and invite you to follow us and share your support as we grow together.
</div>
== 📘 About Qbase ==
This wiki currently contains '''{{NUMBEROFARTICLES}}''' articles and '''{{NUMBEROFEDITS}}''' total edits by '''{{NUMBEROFUSERS}}''' registered users.

== 📂 Categories ==
Browse content by topic:

* [[:Category:Physics|Physics]]
* [[:Category:Mathematics|Mathematics]]
* [[:Category:Chemistry|Chemistry]]
* [[:Category:Biographies|Biographies]]
* [[:Category:Technology|Technology]]

''To view all categories:'' [[:Special:Categories]]

== 🧠 Featured Articles ==
* [[Isaac Newton]]
* [[James Clerk Maxwell]]
* [[Electromagnetic Induction]]
* [[Maxwell's Equations]]

== 🗃️ All Pages ==
You can explore all available pages here: [[Special:AllPages]]

== 📈 Statistics ==
* Total articles: {{NUMBEROFARTICLES}}
* Total pages: {{NUMBEROFPAGES}}
* Total edits: {{NUMBEROFEDITS}}
* Registered users: {{NUMBEROFUSERS}}
* Active users: {{NUMBEROFACTIVEUSERS}}

== 🛠️ Help & Community ==
* [[Help:Contents|How to edit pages]]
* [[Project:Community Portal|Community Portal]]
* [[Special:RecentChanges|Recent Changes]]
* [[Special:Random|Random Page]]

== 📅 New & Updated Pages ==
See what's new: [[Special:NewPages]] and [[Special:RecentChanges]]

== 🔍 Search Wiki ==
Use the search bar at the top of the page to find specific topics or articles.

<strong>MediaWiki has been installed.</strong>

Consult the [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents User's Guide] for information on using the wiki software.

== Getting started ==
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/postorius/lists/mediawiki-announce.lists.wikimedia.org/ MediaWiki release mailing list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Localisation#Translation_resources Localise MediaWiki for your language]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Combating_spam Learn how to combat spam on your wiki]

== 📘 About Qbase ==
This wiki currently contains '''{{NUMBEROFARTICLES}}''' articles and '''{{NUMBEROFEDITS}}''' total edits by '''{{NUMBEROFUSERS}}''' registered users.

== 📂 Categories ==
Browse content by topic:

* [[:Category:Physics|Physics]]
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Main Page

2025-06-10T08:57:57Z

Thakshashila: /* Welcome to Qbase */

Accuracy

2025-06-10T06:43:21Z

Thakshashila: /* Limitations of Accuracy */

= Accuracy =

'''Accuracy''' is one of the most commonly used metrics to evaluate the performance of a classification model in machine learning. It tells us the proportion of total predictions that were correct.

== Definition ==

:<math> \text{Accuracy} = \frac{TP + TN}{TP + TN + FP + FN} </math>

Where:
* '''TP''' = True Positives
* '''TN''' = True Negatives
* '''FP''' = False Positives
* '''FN''' = False Negatives

Accuracy answers the question: '''"Out of all predictions made by the model, how many were actually correct?"'''

== Simple Example ==

Let’s say a model is used to detect whether emails are spam. Out of 100 emails:

* 60 are correctly identified as spam (TP)
* 30 are correctly identified as not spam (TN)
* 5 are incorrectly marked as spam (FP)
* 5 are incorrectly marked as not spam (FN)

Then:

:<math> \text{Accuracy} = \frac{60 + 30}{60 + 30 + 5 + 5} = \frac{90}{100} = 90\% </math>

== When is Accuracy Useful? ==

Accuracy is useful when the dataset is **balanced** (i.e., both classes occur in roughly equal numbers).

== Limitations of Accuracy ==

Accuracy can be '''misleading''' in cases of [[Imbalanced Data]].

=== Example: Fraud Detection ===

Imagine 1000 transactions:

* Only 10 are fraudulent.
* A model labels all as “not fraud” and gets 990 correct.

<math> \text{Accuracy} = \frac{990}{1000} = 99\% </math>

Even with 99% accuracy, the model is useless because it failed to detect any fraud.

== Related Metrics ==

* [[Precision]] – Focuses on correct positive predictions
* [[Recall]] – Focuses on correctly identifying actual positives
* [[F1 Score]] – Harmonic mean of Precision and Recall
* [[Confusion Matrix]] – Underlying table for all classification metrics

== Real-World Applications ==

* Image classification (e.g., cat vs dog detection)
* Email spam filters
* Sentiment analysis (positive vs negative review)

== SEO Keywords ==

accuracy in machine learning, classification accuracy, accuracy formula, model evaluation metric, accuracy vs precision, confusion matrix accuracy, balanced data accuracy
[[Category:Artificial Intelligence]]

Accuracy

2025-06-10T06:42:46Z

Thakshashila: /* Limitations of Accuracy */

= Accuracy =

'''Accuracy''' is one of the most commonly used metrics to evaluate the performance of a classification model in machine learning. It tells us the proportion of total predictions that were correct.

== Definition ==

:<math> \text{Accuracy} = \frac{TP + TN}{TP + TN + FP + FN} </math>

Where:
* '''TP''' = True Positives
* '''TN''' = True Negatives
* '''FP''' = False Positives
* '''FN''' = False Negatives

Accuracy answers the question: '''"Out of all predictions made by the model, how many were actually correct?"'''

== Simple Example ==

Let’s say a model is used to detect whether emails are spam. Out of 100 emails:

* 60 are correctly identified as spam (TP)
* 30 are correctly identified as not spam (TN)
* 5 are incorrectly marked as spam (FP)
* 5 are incorrectly marked as not spam (FN)

Then:

:<math> \text{Accuracy} = \frac{60 + 30}{60 + 30 + 5 + 5} = \frac{90}{100} = 90\% </math>

== When is Accuracy Useful? ==

Accuracy is useful when the dataset is **balanced** (i.e., both classes occur in roughly equal numbers).

== Limitations of Accuracy ==

Accuracy can be '''misleading''' in cases of [[Imbalanced data]].

=== Example: Fraud Detection ===

Imagine 1000 transactions:

* Only 10 are fraudulent.
* A model labels all as “not fraud” and gets 990 correct.

<math> \text{Accuracy} = \frac{990}{1000} = 99\% </math>

Even with 99% accuracy, the model is useless because it failed to detect any fraud.

== Related Metrics ==

* [[Precision]] – Focuses on correct positive predictions
* [[Recall]] – Focuses on correctly identifying actual positives
* [[F1 Score]] – Harmonic mean of Precision and Recall
* [[Confusion Matrix]] – Underlying table for all classification metrics

== Real-World Applications ==

* Image classification (e.g., cat vs dog detection)
* Email spam filters
* Sentiment analysis (positive vs negative review)

== SEO Keywords ==

accuracy in machine learning, classification accuracy, accuracy formula, model evaluation metric, accuracy vs precision, confusion matrix accuracy, balanced data accuracy
[[Category:Artificial Intelligence]]

Accuracy

2025-06-10T06:42:06Z

Thakshashila: /* Limitations of Accuracy */

= Accuracy =

'''Accuracy''' is one of the most commonly used metrics to evaluate the performance of a classification model in machine learning. It tells us the proportion of total predictions that were correct.

== Definition ==

:<math> \text{Accuracy} = \frac{TP + TN}{TP + TN + FP + FN} </math>

Where:
* '''TP''' = True Positives
* '''TN''' = True Negatives
* '''FP''' = False Positives
* '''FN''' = False Negatives

Accuracy answers the question: '''"Out of all predictions made by the model, how many were actually correct?"'''

== Simple Example ==

Let’s say a model is used to detect whether emails are spam. Out of 100 emails:

* 60 are correctly identified as spam (TP)
* 30 are correctly identified as not spam (TN)
* 5 are incorrectly marked as spam (FP)
* 5 are incorrectly marked as not spam (FN)

Then:

:<math> \text{Accuracy} = \frac{60 + 30}{60 + 30 + 5 + 5} = \frac{90}{100} = 90\% </math>

== When is Accuracy Useful? ==

Accuracy is useful when the dataset is **balanced** (i.e., both classes occur in roughly equal numbers).

== Limitations of Accuracy ==

Accuracy can be **misleading** in cases of [[imbalanced data]].

=== Example: Fraud Detection ===

Imagine 1000 transactions:

* Only 10 are fraudulent.
* A model labels all as “not fraud” and gets 990 correct.

<math> \text{Accuracy} = \frac{990}{1000} = 99\% </math>

Even with 99% accuracy, the model is useless because it failed to detect any fraud.

== Related Metrics ==

* [[Precision]] – Focuses on correct positive predictions
* [[Recall]] – Focuses on correctly identifying actual positives
* [[F1 Score]] – Harmonic mean of Precision and Recall
* [[Confusion Matrix]] – Underlying table for all classification metrics

== Real-World Applications ==

* Image classification (e.g., cat vs dog detection)
* Email spam filters
* Sentiment analysis (positive vs negative review)

== SEO Keywords ==

accuracy in machine learning, classification accuracy, accuracy formula, model evaluation metric, accuracy vs precision, confusion matrix accuracy, balanced data accuracy
[[Category:Artificial Intelligence]]

Gradient Descent

2025-06-10T06:35:26Z

Thakshashila: Created page with "= Gradient Descent = '''Gradient Descent''' is an optimization algorithm used in machine learning and deep learning to minimize the cost (loss) function by iteratively updating model parameters in the direction of steepest descent, i.e., the negative gradient. == What is Gradient Descent? == Gradient Descent helps find the best-fit parameters (like weights in a neural network or coefficients in regression) that minimize the error between predicted and actual values. I..."

= Gradient Descent =

'''Gradient Descent''' is an optimization algorithm used in machine learning and deep learning to minimize the cost (loss) function by iteratively updating model parameters in the direction of steepest descent, i.e., the negative gradient.

== What is Gradient Descent? ==

Gradient Descent helps find the best-fit parameters (like weights in a neural network or coefficients in regression) that minimize the error between predicted and actual values. It does this by adjusting the parameters gradually to reduce the loss.

== The Basic Formula ==

:<math>
\theta := \theta - \alpha \cdot \frac{\partial J(\theta)}{\partial \theta}
</math>

Where:
* <math>\theta</math> = model parameters (weights)
* <math>\alpha</math> = learning rate (step size)
* <math>J(\theta)</math> = cost/loss function
* <math>\frac{\partial J(\theta)}{\partial \theta}</math> = gradient (slope) of the loss with respect to the parameters

== Types of Gradient Descent ==

=== 1. Batch Gradient Descent ===

* Uses the entire training dataset to compute the gradient.
* Stable but slow on large datasets.

=== 2. Stochastic Gradient Descent (SGD) ===

* Updates weights for each training example.
* Faster but can be noisy and less stable.

=== 3. Mini-Batch Gradient Descent ===

* Uses a subset (mini-batch) of training data to compute each update.
* Combines advantages of both batch and SGD.
* Commonly used in deep learning.

== Learning Rate (α) ==

The learning rate controls how big the step is during each update.
* If <math>\alpha</math> is too small: slow convergence.
* If <math>\alpha</math> is too large: may overshoot or diverge.

== Example ==

Suppose we are minimizing the Mean Squared Error (MSE) in linear regression. Gradient descent updates the weights so that the predicted line fits the data points better over time.

== Visualization ==

Imagine a ball rolling down a curved surface to reach the lowest point (minimum). Gradient descent is the process of rolling the ball by calculating the slope and moving it downhill.

== Applications of Gradient Descent ==

* Training machine learning models (e.g., linear/logistic regression)
* Optimizing deep learning models (e.g., neural networks)
* Used in NLP, computer vision, recommendation systems, etc.

== Related Concepts ==

* [[Learning Rate]]
* [[Loss Function]]
* [[Optimization Algorithms]]
* [[Backpropagation]]
* [[Stochastic Gradient Descent]]
* [[Neural Networks]]

== SEO Keywords ==

gradient descent machine learning, how gradient descent works, types of gradient descent, optimization in ML, stochastic gradient descent, loss minimization, cost function optimization

Normalization (Machine Learning)

2025-06-10T06:34:09Z

Thakshashila: Created page with "= Normalization (Machine Learning) = '''Normalization''' in machine learning is a data preprocessing technique used to scale input features so they fall within a similar range, typically between 0 and 1. This helps improve model performance, especially for algorithms sensitive to the scale of data. == Why Normalize Data? == Some machine learning algorithms (e.g., K-Nearest Neighbors, Gradient Descent-based models, Neural Networks) perform better when input features ar..."

= Normalization (Machine Learning) =

'''Normalization''' in machine learning is a data preprocessing technique used to scale input features so they fall within a similar range, typically between 0 and 1. This helps improve model performance, especially for algorithms sensitive to the scale of data.

== Why Normalize Data? ==

Some machine learning algorithms (e.g., K-Nearest Neighbors, Gradient Descent-based models, Neural Networks) perform better when input features are on a similar scale. Without normalization, features with larger numeric ranges may dominate others, leading to biased results.

== Common Normalization Techniques ==

=== 1. Min-Max Normalization ===

Scales features to a fixed range, usually [0, 1].

:<math>
x' = \frac{x - x_{\text{min}}}{x_{\text{max}} - x_{\text{min}}}
</math>

* Best for bounded data.
* Sensitive to outliers.

=== 2. Z-score Normalization (Standardization) ===

Centers the data around the mean with unit variance.

:<math>
x' = \frac{x - \mu}{\sigma}
</math>

Where:
* <math>\mu</math> = mean of the feature
* <math>\sigma</math> = standard deviation

* Useful for algorithms that assume Gaussian distribution.

=== 3. Max Abs Scaling ===

Scales data by dividing by the maximum absolute value:

:<math>
x' = \frac{x}{|x_{\text{max}}|}
</math>

* Preserves zero entries in sparse data.

=== 4. Robust Scaling ===

Uses median and interquartile range (IQR) to scale:

:<math>
x' = \frac{x - \text{median}}{\text{IQR}}
</math>

* Less sensitive to outliers.

== When to Use Normalization ==

Use normalization when:
* Input features are measured in different units or ranges.
* You use distance-based algorithms (e.g., k-NN, SVM).
* You're training neural networks using gradient descent.

== When Not to Normalize ==

* When using tree-based algorithms like Decision Trees or Random Forests (these are insensitive to feature scale).
* When your features are already on the same scale or naturally bounded.

== Example ==

If feature A ranges from 1 to 1000 and feature B from 0 to 1:
* A normalized model ensures both features contribute equally to model training.
* Without normalization, feature A may dominate due to its larger range.

== Related Pages ==

* [[Feature Scaling]]
* [[Standardization]]
* [[Preprocessing (Machine Learning)]]
* [[K-Nearest Neighbors]]
* [[Gradient Descent]]

== SEO Keywords ==

normalization in machine learning, min max normalization, z score normalization, feature scaling ML, standardization vs normalization, when to normalize data, data preprocessing techniques

Weighted F1

2025-06-10T06:26:19Z

Thakshashila: /* SEO Keywords */

= Weighted F1 Score =

The '''Weighted F1 Score''' is a metric used in multi-class classification to evaluate model performance by computing the F1 Score for each class and taking the average, weighted by the number of true instances for each class (i.e., the class "support").

It is especially useful when working with '''imbalanced datasets''', where some classes are more frequent than others.

== Definition ==

:<math> \text{Weighted F1} = \sum_{i=1}^{C} w_i \cdot F1_i </math>

Where:
* <math> C </math> = Number of classes
* <math> F1_i </math> = F1 Score for class <math> i </math>
* <math> w_i = \frac{\text{Number of true instances in class } i}{\text{Total number of instances}} </math>

== Key Features ==

* Classes with more data have more influence on the final score.
* Helps prevent small classes from skewing the result disproportionately.
* Often the default setting in many ML libraries like Scikit-learn (Python).

== Simple Example ==

Suppose a dataset has three classes with these F1 Scores and supports:

* F1(Class A) = 0.90, Support = 50
* F1(Class B) = 0.70, Support = 30
* F1(Class C) = 0.50, Support = 20

First calculate total support:

<math> \text{Total} = 50 + 30 + 20 = 100 </math>

Now calculate weighted F1:

:<math> \text{Weighted F1} = \frac{50}{100} \cdot 0.90 + \frac{30}{100} \cdot 0.70 + \frac{20}{100} \cdot 0.50 </math>
:<math> = 0.45 + 0.21 + 0.10 = 0.76 </math>

So the Weighted F1 Score is **0.76**, favoring the majority class's performance.

== Weighted vs Macro vs Micro F1 ==

{| class="wikitable"
! Metric
! Weighting
! Best For
|-
| '''Macro F1'''
| Equal weight for all classes
| Equal treatment for each class
|-
| '''Micro F1'''
| Global average over all TP, FP, FN
| Imbalanced data, overall performance
|-
| '''Weighted F1'''
| Weighted by class support
| Imbalanced datasets, with performance emphasis on larger classes
|}

== Use Cases ==

* **Text classification** (e.g., news topics, sentiment analysis)
* **Image classification** where some labels are rare
* **Healthcare diagnosis** with rare but critical outcomes
* **Customer segmentation** with uneven population groups

== Limitations ==

* Might mask poor performance on minority classes if the model performs well on dominant ones.
* If class fairness is a concern, [[Macro F1 Score]] might be more appropriate.

== Related Pages ==

* [[F1 Score]]
* [[Macro F1]]
* [[Micro F1 Score]]
* [[Precision]]
* [[Recall]]
* [[Confusion Matrix]]
* [[Accuracy]]

== SEO Keywords ==

weighted f1 score, f1 score for imbalanced data, machine learning multi-class metrics, class imbalance performance metric, weighted average f1, scikit-learn f1 weighted, macro vs weighted f1
[[Category:Artificial Intelligence]]

Unsupervised Learning

2025-06-10T06:26:08Z

Thakshashila: /* SEO Keywords */

= Unsupervised Learning =

'''Unsupervised Learning''' is a type of machine learning where the model learns patterns and structures from unlabeled data without predefined outputs.

== What is Unsupervised Learning? ==

In unsupervised learning, the input data has no associated labels. The goal is to explore the data’s inherent structure, group similar data points, or reduce the data’s dimensionality.

== Common Types of Unsupervised Learning ==

* '''Clustering:''' Groups similar data points into clusters.
Example: Customer segmentation.
* '''Dimensionality Reduction:''' Reduces the number of variables while preserving important information.
Example: Principal Component Analysis (PCA).
* '''Association Rule Learning:''' Finds interesting relationships or patterns in large datasets.
Example: Market basket analysis.

== How Unsupervised Learning Works ==

1. The model receives unlabeled data.
2. It uses similarity or statistical methods to find patterns.
3. Results may be clusters, components, or association rules depending on the technique.

== Applications of Unsupervised Learning ==

* Market segmentation.
* Anomaly detection.
* Data compression.
* Recommender systems.
* Visualization of complex data.

== Challenges of Unsupervised Learning ==

* No clear measure of accuracy since no labels are available.
* Defining meaningful similarity measures.
* Determining the number of clusters or components.
* Interpreting the discovered patterns.

== Related Pages ==

* [[Clustering]]
* [[Dimensionality Reduction]]
* [[Association Rule Learning]]
* [[K-Means Clustering]]
* [[PCA (Principal Component Analysis)]]
* [[Evaluation Metrics]]

== SEO Keywords ==

unsupervised learning machine learning, what is unsupervised learning, clustering and unsupervised learning, dimensionality reduction, association rules, unsupervised learning examples, machine learning types
[[Category:Artificial Intelligence]]

Underfitting

2025-06-10T06:25:59Z

Thakshashila: /* SEO Keywords */

= Underfitting =

'''Underfitting''' occurs when a machine learning model is too simple to capture the underlying pattern in the data, resulting in poor performance on both training and unseen data.

== What is Underfitting? ==

Underfitting means the model fails to learn enough from the training data. It shows high errors during training and testing because it cannot capture important trends.

== Causes of Underfitting ==

* '''Model Too Simple:''' Using a linear model for data with complex, nonlinear relationships.
* '''Insufficient Features:''' Missing important input variables.
* '''Too Much Regularization:''' Over-penalizing complexity can oversimplify the model.
* '''Not Enough Training:''' Stopping training too early.

== Signs of Underfitting ==

* Low accuracy on both training and validation/test data.
* High bias in the model.

== How to Detect Underfitting ==

* Compare training and validation errors — both will be high.
* Plot learning curves showing poor performance from the start.

== Techniques to Fix Underfitting ==

* '''Increase Model Complexity:''' Use more complex algorithms or add polynomial features.
* '''Add More Features:''' Use relevant input variables.
* '''Reduce Regularization:''' Allow model more flexibility.
* '''Train Longer:''' Give the model more time to learn patterns.
* '''Feature Engineering:''' Create new features that capture important information.

== Example ==

Fitting a straight line to data that follows a curved pattern will result in underfitting because the model is too simple to capture the curve.

== Related Pages ==

* [[Overfitting]]
* [[Bias-Variance Tradeoff]]
* [[Model Selection]]
* [[Regularization]]
* [[Evaluation Metrics]]

== SEO Keywords ==

underfitting in machine learning, underfitting meaning, causes of underfitting, underfitting vs overfitting, fixing underfitting, model complexity, machine learning errors
[[Category:Artificial Intelligence]]

Train-Test Split

2025-06-10T06:25:49Z

Thakshashila: /* SEO Keywords */

= Train-Test Split =

'''Train-Test Split''' is a fundamental technique in machine learning used to evaluate the performance of a model by dividing the dataset into two parts: a training set and a testing set.

== What is Train-Test Split? ==

The dataset is split into:

* '''Training Set:''' Used to train the machine learning model.
* '''Testing Set:''' Used to evaluate how well the trained model performs on unseen data.

This helps measure the model’s ability to generalize beyond the data it was trained on.

== Why is Train-Test Split Important? ==

* Prevents '''overfitting''' by evaluating model on new data.
* Provides an unbiased estimate of model performance.
* Helps tune and compare different models reliably.

== Typical Split Ratios ==

Common split ratios include:

* 70% training / 30% testing
* 80% training / 20% testing
* 75% training / 25% testing

The exact ratio depends on dataset size and problem context.

== How Train-Test Split Works ==

1. Randomly shuffle the dataset to avoid bias.
2. Divide into training and testing subsets based on the chosen ratio.
3. Train the model on the training set.
4. Evaluate the model on the testing set using evaluation metrics like accuracy, precision, recall, etc.

== Example ==

If you have 1000 data samples and choose an 80-20 split:

* Training set size = 800 samples
* Testing set size = 200 samples

The model learns from the 800 samples, then its performance is tested on the 200 unseen samples.

== Limitations ==

* Results can vary based on the random split.
* May not represent all data patterns if dataset is small or imbalanced.
* Does not fully utilize the data for training.

== Related Techniques ==

* [[Cross Validation]] — for more robust evaluation using multiple splits.
* [[Stratified Sampling]] — to maintain class distribution in splits.
* [[Imbalanced Data]] — special care needed in splitting.

== Related Pages ==

* [[Overfitting]]
* [[Underfitting]]
* [[Model Evaluation Metrics]]
* [[Cross Validation]]
* [[Stratified Sampling]]

== SEO Keywords ==

train test split machine learning, train test ratio, splitting dataset for ML, importance of train test split, how to split data in ML, train test split example, model evaluation techniques
[[Category:Artificial Intelligence]]

Threshold Tuning

2025-06-10T06:25:34Z

Thakshashila: /* SEO Keywords */

= Threshold Tuning =

'''Threshold Tuning''' is the process of selecting the best decision threshold in a classification model to optimize performance metrics such as [[Precision]], [[Recall]], [[F1 Score]], or [[Accuracy]]. It is crucial in models that output '''probabilities''' rather than direct class labels.

== Why Threshold Tuning Matters ==

Many classifiers (e.g., Logistic Regression, Neural Networks) output a probability score indicating how likely an instance belongs to the positive class. By default, a threshold of 0.5 is used:

* If probability ≥ 0.5 → classify as positive
* If probability < 0.5 → classify as negative

However, this default might not be optimal, especially in '''imbalanced datasets''' or when different errors have different costs.

== How Threshold Tuning Works ==

1. Vary the decision threshold from 0 to 1.
2. For each threshold, calculate performance metrics (Precision, Recall, F1 Score, etc.).
3. Choose the threshold that best balances metrics according to the problem needs.

== Visual Tools for Threshold Tuning ==

* '''ROC Curve:''' Helps understand trade-offs between True Positive Rate (Recall) and False Positive Rate.
* '''Precision-Recall Curve:''' Useful in imbalanced data for balancing precision and recall.
* '''F1 Score vs Threshold Plot:''' Shows how F1 score changes with thresholds.

== Example ==

In a fraud detection system, a lower threshold (e.g., 0.3) may catch more fraud cases (high recall) but generate more false alarms (low precision). A higher threshold (e.g., 0.7) reduces false alarms but misses fraud cases. Threshold tuning finds the best trade-off.

== Threshold Tuning Techniques ==

* '''Manual Search:''' Try multiple thresholds and pick the best.
* '''Grid Search:''' Automated search over a range of thresholds.
* '''Youden’s J Statistic:''' Maximize (sensitivity + specificity - 1) on the ROC curve.
* '''Cost-based Optimization:''' Incorporate different costs for false positives and false negatives.

== Importance in Real-World Applications ==

* Medical diagnosis where missing a disease (false negative) is costly.
* Spam detection where false positives annoy users.
* Credit risk where false negatives cause financial loss.

== Related Pages ==

* [[ROC Curve]]
* [[Precision-Recall Curve]]
* [[Model Evaluation Metrics]]
* [[Confusion Matrix]]
* [[Overfitting]]
* [[Underfitting]]

== SEO Keywords ==

threshold tuning in machine learning, decision threshold optimization, best classification threshold, tuning classifier threshold, precision recall tradeoff, threshold selection, binary classification threshold
[[Category:Artificial Intelligence]]

Supervised Learning

2025-06-10T06:25:22Z

Thakshashila: /* SEO Keywords */

= Supervised Learning =

'''Supervised Learning''' is a type of machine learning where the model learns to map input data to output labels using a labeled dataset.

== What is Supervised Learning? ==

In supervised learning, each training example includes both the input features and the corresponding correct output (label). The goal is for the model to learn the relationship between inputs and outputs so it can predict the labels for new, unseen data.

== Types of Supervised Learning ==

* '''Classification:''' Predicts a discrete label or category.
Example: Email spam detection (spam or not spam).
* '''Regression:''' Predicts a continuous value.
Example: Predicting house prices based on features like size and location.

== How Supervised Learning Works ==

1. Collect a labeled dataset with input-output pairs.
2. Choose an appropriate model (e.g., decision tree, support vector machine, neural network).
3. Train the model using the training data to minimize prediction errors.
4. Evaluate the model on test data to check its generalization.

== Examples of Supervised Learning Algorithms ==

* Linear Regression
* Logistic Regression
* Decision Trees
* Support Vector Machines (SVM)
* k-Nearest Neighbors (k-NN)
* Neural Networks

== Advantages of Supervised Learning ==

* Provides accurate predictions when sufficient labeled data is available.
* Easier to evaluate model performance with known labels.
* Suitable for a wide range of applications.

== Challenges of Supervised Learning ==

* Requires large labeled datasets, which can be costly to obtain.
* Can overfit if the model is too complex or data is noisy.
* Performance depends heavily on the quality of labels.

== Related Pages ==

* [[Unsupervised Learning]]
* [[Classification]]
* [[Regression]]
* [[Overfitting]]
* [[Underfitting]]
* [[Model Evaluation Metrics]]

== SEO Keywords ==

supervised learning machine learning, what is supervised learning, types of supervised learning, supervised learning examples, classification and regression, supervised vs unsupervised learning, machine learning algorithms
[[Category:Artificial Intelligence]]

Specificity

2025-06-10T06:25:11Z

Thakshashila: /* SEO Keywords */

= Specificity =

'''Specificity''', also known as the '''True Negative Rate (TNR)''', is a performance metric in binary classification tasks. It measures the proportion of actual negative instances that are correctly identified by the model.

== Definition ==

:<math> \text{Specificity} = \frac{TN}{TN + FP} </math>

Where:
* '''TN''' = True Negatives – actual negatives correctly predicted
* '''FP''' = False Positives – actual negatives incorrectly predicted as positives

Specificity answers the question: '''"Out of all real negative cases, how many did the model correctly classify as negative?"'''

== Alternate Names ==
* True Negative Rate (TNR)
* Selectivity

== Simple Example ==

Suppose a test is used to detect a rare disease. Out of 1,000 healthy people:

* 950 are correctly identified as healthy → TN = 950
* 50 are incorrectly diagnosed with the disease → FP = 50

:<math> \text{Specificity} = \frac{950}{950 + 50} = \frac{950}{1000} = 0.95 = 95\% </math>

This means the test correctly identifies 95% of healthy people.

== Importance of Specificity ==

Specificity is vital when false positives can cause unnecessary stress, cost, or risk.

=== Real-World Scenarios ===

* Medical Testing: Avoiding false diagnoses of a disease (e.g., not telling a healthy person they are sick).
* Spam Filters: Ensuring genuine emails are not classified as spam.
* Fraud Detection: Not labeling legitimate transactions as fraudulent.

== Specificity vs Sensitivity ==

These are [[complementary metrics]]:

* '''Sensitivity''' = Ability to detect positives
* '''Specificity''' = Ability to rule out negatives

Together, they form a balanced evaluation of a model, especially in medical or safety-critical applications.

== Combined Evaluation: ROC Curve ==

Receiver Operating Characteristic (ROC) curves plot:

* Sensitivity (True Positive Rate) vs.
* 1 − Specificity (False Positive Rate)

This helps visualize the trade-off between catching positives and avoiding false alarms.

== Related Metrics ==

* [[Sensitivity]] – True positive rate
* [[Precision]] – Positive prediction correctness
* [[Recall]] – Same as Sensitivity
* [[F1 Score]] – Harmonic mean of Precision and Recall
* [[Confusion Matrix]] – Base for all metrics

== SEO Keywords ==

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[[Category:Artificial Intelligence]]

Sensitivity

2025-06-10T06:24:58Z

Thakshashila: /* SEO Keywords */

= Sensitivity =

'''Sensitivity''', also known as '''Recall''' or the '''True Positive Rate (TPR)''', is a performance metric used in classification problems. It measures how well a model can identify actual positive instances.

== Definition ==

:<math> \text{Sensitivity} = \frac{TP}{TP + FN} </math>

Where:
* '''TP''' = True Positives – actual positives correctly predicted
* '''FN''' = False Negatives – actual positives incorrectly predicted as negative

Sensitivity answers the question: '''"Out of all real positive cases, how many did the model correctly identify?"'''

== Alternate Names ==
* Recall
* True Positive Rate (TPR)
* Hit Rate (in signal detection theory)

== Simple Example ==

A disease test is applied to 100 patients who have the disease. The model predicts:

* 90 correctly diagnosed as sick → TP = 90
* 10 wrongly predicted as healthy → FN = 10

:<math> \text{Sensitivity} = \frac{90}{90 + 10} = \frac{90}{100} = 0.9 = 90\% </math>

This means the model successfully detected 90% of the sick patients.

== Importance of Sensitivity ==

Sensitivity is **critical** in applications where missing a positive case can have serious consequences.

=== Real-World Scenarios ===
* Medical diagnosis: Missing a disease can be fatal.
* Security systems: Failing to detect a threat may be dangerous.
* Fraud detection: Missed fraud cases are costly.

== Sensitivity vs Specificity ==

* '''Sensitivity''' measures how well you find actual positives.
* '''Specificity''' measures how well you avoid false alarms (negatives correctly identified).

== Formula for Specificity (for comparison) ==

:<math> \text{Specificity} = \frac{TN}{TN + FP} </math>

Where:
* '''TN''' = True Negatives
* '''FP''' = False Positives

== Related Metrics ==

* [[Recall]] – Sensitivity is another name for Recall
* [[Specificity]] – Measures true negative rate
* [[Precision]] – Measures correctness of positive predictions
* [[F1 Score]] – Balances Sensitivity and Precision
* [[Confusion Matrix]] – Base table for all classification metrics

== SEO Keywords ==

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[[Category:Artificial Intelligence]]

Regularization

2025-06-10T06:24:48Z

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= Regularization =

'''Regularization''' is a technique in machine learning used to prevent '''overfitting''' by adding extra constraints or penalties to a model during training.

== Why Regularization is Important ==

Overfitting happens when a model learns noise and details from the training data, harming its ability to generalize on new data. Regularization discourages overly complex models by penalizing large or unnecessary model parameters.

== Common Types of Regularization ==

=== 1. L1 Regularization (Lasso) ===

* Adds the sum of the absolute values of coefficients as a penalty to the loss function.
* Encourages sparsity, meaning it can reduce some feature weights to zero, effectively performing feature selection.
* Loss function example:
:<math> L = Loss_{original} + \lambda \sum_{i} |w_i| </math>

=== 2. L2 Regularization (Ridge) ===

* Adds the sum of squared coefficients as a penalty.
* Penalizes large weights but does not force them to zero.
* Encourages smaller, more evenly distributed weights.
* Loss function example:
:<math> L = Loss_{original} + \lambda \sum_{i} w_i^2 </math>

=== 3. Elastic Net ===

* Combines L1 and L2 penalties to balance sparsity and weight shrinkage.
* Useful when many correlated features exist.

== How Regularization Works ==

By adding penalty terms, the model’s objective function becomes:

:<math> \text{Objective} = \text{Original Loss} + \lambda \times \text{Penalty} </math>

Where <math> \lambda </math> (lambda) controls the strength of regularization — higher values increase the penalty.

== Benefits of Regularization ==

* Reduces overfitting.
* Improves model generalization on unseen data.
* Can perform feature selection (especially L1).
* Helps in models with many features or noisy data.

== Example ==

In linear regression without regularization, the model might fit the training data perfectly but fail on test data (overfitting). Adding L2 regularization shrinks coefficients, leading to a simpler model that generalizes better.

== Related Pages ==

* [[Overfitting]]
* [[Underfitting]]
* [[Bias-Variance Tradeoff]]
* [[Hyperparameter Tuning]]
* [[Model Evaluation Metrics]]

== SEO Keywords ==

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[[Category:Artificial Intelligence]]

Regression

2025-06-10T06:24:38Z

Thakshashila: /* SEO Keywords */

= Regression =

'''Regression''' is a type of supervised learning used to predict a continuous output variable based on one or more input features.

== What is Regression? ==

In regression tasks, the goal is to model the relationship between input variables (features) and a continuous target variable. The model learns to estimate the output value for new inputs.

== Types of Regression ==

* '''Simple Linear Regression:''' Models the relationship between a single input feature and output as a straight line.
Example: Predicting house price based on size.
* '''Multiple Linear Regression:''' Uses multiple features to predict the output.
* '''Polynomial Regression:''' Models nonlinear relationships by adding polynomial terms.
* '''Other Regression Types:''' Ridge regression, Lasso regression, Logistic regression (for classification), etc.

== How Regression Works ==

The model learns parameters (coefficients) that minimize the difference between predicted and actual values using a loss function, typically Mean Squared Error (MSE):

:<math>
MSE = \frac{1}{n} \sum_{i=1}^n (y_i - \hat{y}_i)^2
</math>

Where:
* <math>y_i</math> = actual output
* <math>\hat{y}_i</math> = predicted output
* <math>n</math> = number of samples

== Applications of Regression ==

* Predicting prices (houses, stocks)
* Estimating temperatures
* Forecasting sales or demand
* Modeling relationships between variables in science and engineering

== Advantages of Regression ==

* Easy to interpret and implement.
* Provides quantitative predictions.
* Useful for understanding relationships between variables.

== Challenges in Regression ==

* Sensitive to outliers.
* Assumes a specific functional form (linear or polynomial).
* Can underfit or overfit if not properly tuned.

== Related Pages ==

* [[Supervised Learning]]
* [[Classification]]
* [[Regularization]]
* [[Overfitting]]
* [[Underfitting]]
* [[Evaluation Metrics]]

== SEO Keywords ==

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[[Category:Artificial Intelligence]]

Recall

2025-06-10T06:24:27Z

Thakshashila: /* SEO Keywords */

= Recall =

'''Recall''' is a metric used in classification to measure how many of the actual positive instances were correctly identified by the model. It is also known as '''sensitivity''' or the '''true positive rate'''.

== Definition ==

:<math> \text{Recall} = \frac{TP}{TP + FN} </math>

Where:
* '''TP''' = True Positives – correctly predicted positive instances
* '''FN''' = False Negatives – actual positives incorrectly predicted as negative

Recall answers the question: '''"Of all actual positive cases, how many did we correctly identify?"'''

== Simple Example ==

A medical test is used to detect cancer. There are 100 people with cancer:

* The test correctly identifies 90 as having cancer (TP = 90)
* It misses 10 people (FN = 10)

:<math> \text{Recall} = \frac{90}{90 + 10} = \frac{90}{100} = 0.9 = 90\% </math>

This means the test correctly detects 90% of cancer cases.

== When to Use Recall ==

Recall is crucial when missing a positive case has serious consequences.

=== Real-World Scenarios ===

* Cancer diagnosis: Missing a sick patient (false negative) is risky.
* Fraud detection: It's better to catch all suspicious activity even if some are false alarms.
* Fire alarms: Better to alert even for minor smoke than miss a real fire.

== High vs Low Recall ==

* '''High Recall''': Most actual positives are identified.
* '''Low Recall''': Many positives are missed (false negatives).

== Related Metrics ==

* [[Precision]]
* [[F1 Score]]
* [[Confusion Matrix]]
* [[Sensitivity]] and [[Specificity]]

== SEO Keywords ==

recall in machine learning, true positive rate, sensitivity, recall formula, classification evaluation, medical test recall, fraud detection model
[[Category:Artificial Intelligence]]

ROC Curve

2025-06-10T06:24:18Z

Thakshashila: /* SEO Keywords */

= ROC Curve =

The '''ROC Curve''' ('''Receiver Operating Characteristic Curve''') is a graphical tool used to evaluate the performance of binary classification models. It plots the '''True Positive Rate (TPR)''' against the '''False Positive Rate (FPR)''' at various threshold settings.

== Purpose ==

The ROC Curve shows the trade-off between sensitivity (recall) and specificity. It helps assess how well a classifier can distinguish between two classes.

== Definitions ==

:<math> \text{True Positive Rate (TPR)} = \frac{TP}{TP + FN} </math>
:<math> \text{False Positive Rate (FPR)} = \frac{FP}{FP + TN} </math>

Where:
* TP = True Positives
* FP = False Positives
* FN = False Negatives
* TN = True Negatives

The ROC curve is generated by plotting TPR vs. FPR for different decision threshold values, typically ranging from 0 to 1.

== How It Works ==

1. A classification model outputs probabilities.
2. These probabilities are converted to class labels using different thresholds.
3. For each threshold, TPR and FPR are computed.
4. Points are plotted to form the ROC curve.

== Ideal ROC Curve ==

* A ''perfect classifier'' reaches the top-left corner (TPR = 1, FPR = 0).
* The ''diagonal line'' (from (0,0) to (1,1)) represents a '''random classifier'''.
* The ''closer the curve is to the top-left'', the better the model.

== Area Under the Curve (AUC) ==

* The ROC AUC score ('''Area Under the Curve''') quantifies overall performance.
:<math> 0 \leq \text{AUC} \leq 1 </math>

* AUC = 1 → Perfect classifier
* AUC = 0.5 → No discriminative power (like random guessing)

== Example Use Case ==

In a medical test to detect cancer:
* A high threshold may miss cancer (low TPR, high specificity).
* A low threshold may raise too many false alarms (high TPR, high FPR).
* The ROC Curve helps decide the optimal threshold balancing both risks.

== ROC vs Precision-Recall Curve ==

{| class="wikitable"
! Curve Type
! Best For
|-
| '''ROC Curve'''
| When classes are balanced or misclassification cost is similar
|-
| '''Precision-Recall Curve'''
| When positive class is rare (imbalanced datasets)
|}

== Limitations ==

* Can be '''overly optimistic''' on highly imbalanced data.
* In such cases, use the [[Precision-Recall Curve]].

== Related Pages ==

* [[Sensitivity]] (TPR)
* [[Specificity]]
* [[F1 Score]]
* [[Confusion Matrix]]
* [[Precision-Recall Curve]]
* [[AUC Score]]
* [[Threshold Tuning]]

== SEO Keywords ==

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[[Category:Artificial Intelligence]]

Precision-Recall Curve

2025-06-10T06:24:07Z

Thakshashila: /* SEO Keywords */

= Precision-Recall Curve =

The '''Precision-Recall Curve''' (PR Curve) is a graphical representation used to evaluate the performance of binary classification models, especially on '''imbalanced datasets''' where the positive class is rare.

It plots '''Precision''' (y-axis) against '''Recall''' (x-axis) for different classification thresholds.

== Why Use Precision-Recall Curve? ==

In many real-world problems like fraud detection, disease diagnosis, or spam filtering, the positive class is much less frequent than the negative class. Traditional metrics like [[ROC Curve]] or [[Accuracy]] can be misleading in such cases.

The Precision-Recall curve focuses on the performance of the positive class, showing how precision and recall change as the classification threshold varies.

== Definitions ==

* '''Precision''' measures the proportion of correctly predicted positive observations to all predicted positives:

:<math> \text{Precision} = \frac{TP}{TP + FP} </math>

* '''Recall''' (Sensitivity) measures the proportion of correctly predicted positive observations to all actual positives:

:<math> \text{Recall} = \frac{TP}{TP + FN} </math>

Where:

* TP = True Positives
* FP = False Positives
* FN = False Negatives

== How to Interpret the Curve ==

- The top-right corner (Precision=1, Recall=1) represents perfect classification.
- A high area under the PR curve indicates both high precision and recall.
- The curve helps to select the best threshold by balancing false positives and false negatives.

== Area Under the Precision-Recall Curve (AUPRC) ==

Similar to ROC AUC, the '''Area Under the Precision-Recall Curve''' (AUPRC) summarizes the model’s ability to balance precision and recall.

* Higher AUPRC means better model performance on the positive class.
* Unlike ROC AUC, AUPRC is more informative with highly skewed data.

== Example ==

Imagine a spam detection system:

- At a low threshold, many emails are classified as spam (high recall) but many legitimate emails are incorrectly flagged (low precision).
- At a high threshold, only very confident spam emails are flagged (high precision) but some spam emails go undetected (low recall).
- The PR curve shows how precision and recall trade off as the threshold changes.

== Precision-Recall Curve vs ROC Curve ==

{| class="wikitable"
! Aspect
! Precision-Recall Curve
! ROC Curve
|-
| Best used when
| Positive class is rare / imbalanced
| Classes are balanced or costs similar
|-
| Focus
| Performance on positive class
| Trade-off between TPR and FPR (sensitivity and specificity)
|-
| Interpretation
| Emphasizes false positives impact on precision
| Emphasizes false positives rate relative to negatives
|}

== Related Pages ==

* [[Precision]]
* [[Recall]]
* [[F1 Score]]
* [[ROC Curve]]
* [[Confusion Matrix]]
* [[Imbalanced Data]]

== SEO Keywords ==

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[[Category:Artificial Intelligence]]

Precision

2025-06-10T06:23:55Z

Thakshashila: /* SEO Keywords */

= Precision =

'''Precision''' is a metric used in classification tasks to measure how many of the predicted positive results are actually correct. It is also known as the '''positive predictive value'''.

== Definition ==

:<math> \text{Precision} = \frac{TP}{TP + FP} </math>

Where:
* '''TP''' = True Positives – correct positive predictions
* '''FP''' = False Positives – incorrect positive predictions

Precision helps to answer the question: '''"Of all the items labeled as positive, how many are truly positive?"'''

== Simple Example ==

Imagine a spam filter that marked 100 emails as spam. Out of these, 80 were actually spam, and 20 were not.

* TP = 80
* FP = 20

Then,

:<math> \text{Precision} = \frac{80}{80 + 20} = \frac{80}{100} = 0.8 = 80\% </math>

This means that 80% of emails flagged as spam were truly spam.

== When to Use Precision ==

Precision is especially important when the cost of false positives is high.

=== Real-World Scenarios ===

* Medical testing: Avoiding telling a healthy person they are sick.
* Email spam detection: Ensuring important emails aren't marked as spam.
* Search engines: Returning highly relevant search results.

== High vs Low Precision ==

* '''High Precision''': Most positive predictions are correct.
* '''Low Precision''': Many false alarms (false positives).

== Related Metrics ==

* [[Recall]]
* [[F1 Score]]
* [[Accuracy]]
* [[Confusion Matrix]]

== SEO Keywords ==

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[[Category:Artificial Intelligence]]

Overfitting

2025-06-10T06:23:44Z

Thakshashila: /* SEO Keywords */

= Overfitting =

'''Overfitting''' is a common problem in machine learning where a model learns the training data too well, including its noise and outliers, resulting in poor performance on new, unseen data.

== What is Overfitting? ==

When a model is overfitted, it captures not only the underlying pattern but also the random fluctuations or noise in the training dataset. This causes the model to perform excellently on training data but badly on test or real-world data.

== Causes of Overfitting ==

* '''Complex Models:''' Models with too many parameters (e.g., very deep neural networks, high-degree polynomials).
* '''Insufficient Training Data:''' Small datasets increase the risk of memorizing noise.
* '''Noisy Data:''' Data with errors or outliers can mislead the model.
* '''Excessive Training:''' Training for too many iterations without regularization.

== Signs of Overfitting ==

* High accuracy on training data but low accuracy on validation/test data.
* Large gap between training and validation errors.

== How to Detect Overfitting ==

Use techniques such as:

* Plot training vs validation accuracy/loss over epochs.
* Use cross-validation to estimate generalization.
* Monitor performance metrics on unseen data.

== Techniques to Prevent Overfitting ==

* '''Simplify the Model:''' Use fewer parameters or simpler algorithms.
* '''Regularization:''' Add penalties for complexity (e.g., L1, L2 regularization).
* '''Early Stopping:''' Stop training when validation performance stops improving.
* '''More Training Data:''' Helps the model learn better general patterns.
* '''Data Augmentation:''' Generate more diverse training data.
* '''Dropout (in neural networks):''' Randomly drop units during training.
* '''Cross-Validation:''' Helps select models that generalize better.

== Example ==

Imagine fitting a polynomial curve to data points:

* A '''degree 2 polynomial''' fits the data with some error but generalizes well.
* A '''degree 10 polynomial''' passes through all points perfectly but oscillates wildly, failing on new data — this is overfitting.

== Related Pages ==

* [[Underfitting]]
* [[Cross Validation]]
* [[Regularization]]
* [[Bias-Variance Tradeoff]]
* [[Evaluation Metrics]]
* [[Model Selection]]

== SEO Keywords ==

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[[Category:Artificial Intelligence]]