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Uncertainty in Multiclass Classification

Dr. Rishabh Pathak
1. What is Uncertainty in Classification? Uncertainty refers to the model’s confidence or doubt in its predictions. Quantifying uncertainty is important to understand how reliable each prediction is. In multiclass classification , uncertainty estimates provide probabilities over multiple classes, reflecting how sure the model is about each possible class. 2. Methods to Estimate Uncertainty in Multiclass Classification Most multiclass classifiers provide methods such as: predict_proba: Returns a probability distribution across all classes. decision_function: Returns scores or margins for each class (sometimes called raw or uncalibrated confidence scores). The probability distribution from predict_proba captures the uncertainty by assigning a probability to each class. 3. Shape and Interpretation of predict_proba in Multiclass Output shape: (n_samples, n_classes) Each row corresponds to the probabilities of ...
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Oscillatory Motion

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Dr. Rishabh Pathak

Oscillatory motion is a repetitive, back-and-forth movement around a central point or equilibrium position. It is characterized by the periodic variation of a physical quantity, such as displacement, velocity, or acceleration, with respect to time. Here are key points about oscillatory motion:


1.    Characteristics:

o    Periodic Nature: Oscillatory motion repeats itself over regular intervals of time, following a specific pattern or cycle.

o    Equilibrium Position: The central point around which the motion oscillates is known as the equilibrium position, where the object is at rest.

o    Amplitude: The maximum displacement from the equilibrium position is called the amplitude of oscillation.

o    Frequency: The frequency of oscillation refers to the number of cycles completed per unit of time (usually measured in hertz).

o    Period: The period of oscillation is the time taken to complete one full cycle of motion.

2.    Types of Oscillatory Motion:

o    Simple Harmonic Motion (SHM): A special type of oscillatory motion where the restoring force is directly proportional to the displacement from the equilibrium position. Examples include a mass-spring system and a pendulum.

o    Damped Oscillations: Oscillations that decrease in amplitude over time due to damping forces like friction or air resistance.

o    Forced Oscillations: Oscillations that occur when an external periodic force is applied to a system, causing it to oscillate at the frequency of the applied force.

3.    Mathematical Representation:

o    Oscillatory motion can be mathematically described using trigonometric functions such as sine and cosine.

o    The general equation for simple harmonic motion is: x(t) = A×sin(ωt+Ï•), where A is the amplitude, Ï‰ is the angular frequency, t is time, and Ï• is the phase angle.

4.    Applications:

o    Oscillatory motion is prevalent in various natural phenomena and human activities, including:

§  Musical Instruments: Vibrating strings and air columns in musical instruments produce oscillatory motion that generates sound waves.

§  Clocks and Watches: The oscillations of a pendulum or a balance wheel in timekeeping devices regulate the movement of clock hands.

§  Seismic Waves: Earthquakes generate oscillatory motion in the form of seismic waves that propagate through the Earth's crust.

5.    Analysis and Control:

o    Understanding oscillatory motion is essential in fields such as physics, engineering, and biology for analyzing vibrations, designing control systems, and studying wave behavior.

o    Control of oscillatory systems involves adjusting parameters to optimize performance, reduce unwanted vibrations, or enhance stability.

By studying oscillatory motion, researchers and practitioners can gain insights into the behavior of vibrating systems, wave propagation, and dynamic responses in various applications. Analyzing and controlling oscillatory motion is crucial for optimizing performance, enhancing efficiency, and ensuring stability in systems that exhibit repetitive back-and-forth movements.

 

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