ComputingNotes

ANOVA

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ANOVA is a statistical method used to analyze the differences between groups. There are other different types such as MANOVA and ANCOVA as well. For example, let’s consider a dataset Chickwt in R. If we plot, we can something like below using ggplot(chickwts, aes(x = feed, y = weight)) + geom_boxplot(outlier.shape = NA) + geom_jitter() ... Read More

Multi-Objective Optimization

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Multi-Objective Optimization is an interesting approach where instead of focusing on one objective we simultaneously try to minimize or maximize more than one objective function. The objective functions are conflicting in multi-objective optimization problem because a single solution doesn’t optimize each objective simultaneously. Thus, the solution in multi-objective function is called nondominated or pareto optimal ... Read More

Linear Algebra, Optimization Problem

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Linear algebra is used to solve various optimization problems. Basic concepts in Linear algebra include vectors, vector space, linear transformations, systems of linear equations. While optimization problems can be linear or non linear. Vectors: Reference:C. C. Aggarwal, Linear Algebra and Optimization for Machine Learning: A Textbook. Cham: Springer International Publishing, 2020. doi: 10.1007/978-3-030-40344-7. Y. Geophys, ... Read More

Data Encoding

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Among various types of data encoding, we have angle, phase, dense, basis and amplitude encoding. They can be grouped in two methods based on whether qubit is used or the entangled states are used. In Angle, Phase and Dense encoding, a feature (or two) is encoded on each qubit. Whereas, in the methods like Basis ... Read More

Calculus – Law of Exponential Change: Growth and Decay

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We have differential equation, $\frac{dy}{dt} = ky$ where, $y$ is quantity that increases or decreases at a rate that at any given time $t$ is proportional to the amount present. In order to derive basic equation of growth and decay from differential equation of proportional change, we follow this. Now to derive formal equation for ... Read More

Quantum Fourier Transform

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Fourier Transform – A method of transforming from one basis to another. Pair of bases can be position and momentum or time and frequency. Discrete Fourier Transform – While fourier transform is useful for signal processing applications, for real world application contexts, we usually want to transform a discrete set of data points, not a ... Read More

Multi Agent Reinforcement Learning

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What is an Agent? The three core characteristics of an autonomous system. 1 Autonomous Entity It operates independently as a self-directed entity, without requiring constant human intervention or manual control. 2 Observes Environment It continuously monitors its surroundings, gathering real-time state data and information about the world around it. 3 Chooses How to Act Based ... Read More

Data Structure and Algorithms – Trees

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Data Structures: Tree Basics A tree is a non-linear hierarchical data structure consisting of nodes connected by edges. Hover over nodes to see their terminology. Root Internal Leaf Leaf Leaf Hover over a node to see terminology… N-ary Trees A tree where a node can have at most N children. This example shows a 4-ary ... Read More

Barrage Relay Network – Barrage Relay, Cooperation and BAC

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System Initializing… A B C TDMA Frame 1 A TDMA Frame 2 Barrage Relay How data floods a Barrage Relay Network slot-by-slot TDMA Frame 1 • Slot A The Initial Broadcast The central Source node (black) transmits the first packet. This is visualized as the first expanding blue wave. All nodes that successfully receive this ... Read More

Phase Dithering and Modern Error Correction

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How Networks Survive Chaos Understanding Phase Dithering and Modern Error Correction Transmitter 1 (Static) Transmitter 2 (Dithering) Receiver (Composite Sum) Phase Dithering When multiple antennas transmit the exact same signal simultaneously, there is a risk that the waves will collide out-of-phase and permanently cancel each other out (destructive interference). Phase Dithering is a deliberate, pseudo-random ... Read More
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