Notes

Asymptotic Lower Bound – Omega

Data Structure and Algorithm
Resources: What is Asymptotic Lower Bound? In the world of algorithm analysis, Asymptotic Lower Bound, denoted by the Greek letter Omega ($\omega$), is used to describe the “best-case” or the minimum rate of growth for a function as the input size n approaches infinity. Think of it as a guarantee. If an algorithm has a ... Read More

Big Oh Expressions Reference

Data Structure and Algorithm
Big-O Time Complexity O(1) Constant time — stays the same regardless of input size. O(log n) Logarithmic — grows very slowly (e.g., binary search). O((log n)2) Log-squared — slightly faster growth than log n. O(√n) Square root — moderate growth, better than linear. O(n) Linear — grows directly with input size. O(n log n) Efficient ... Read More

2025 ACM A.M. Turing Award Honors Quantum Pioneers

News
2025 ACM A.M. Turing Award Honors Quantum Pioneers Recipients: Charles H. Bennett & Gilles Brassard ACM has named Charles H. Bennett (IBM Research) and Gilles Brassard (Université de Montréal) as the recipients of the 2025 A.M. Turing Award. Often called the “Nobel Prize of Computing,” the award includes a $1 million prize for their foundational ... Read More

Tactical MANETs – Node Mobility, Tx Range, Routing Schemes

Wireless Communication
Tactical MANETs Tactical Mobile Ad-Hoc Networks (MANETs) provide dynamic, infrastructure-less connectivity in environments without traditional networks. Live Simulation: Full Network Packet Routing 1. Node Mobility Tactical devices are constantly moving. Military units travel in swarms or platoons, requiring the network to predict group mobility patterns to maintain stable connections as topology shifts. Simulation: Platoon Movement ... Read More

Quantum Feature Map

Uncategorized
Resources: The Concept: Quantum Feature Maps In classical machine learning, a “kernel trick” is often used to map data into a higher-dimensional space. Quantum computers provide a natural way to do this: Feature Map The process of encoding a classical input vector \( \vec{x} \) into a quantum state \( |\Phi(\vec{x})\rangle \) acts as a ... Read More

Inner or Dot Products – Linear Algebra

Uncategorized
In linear algebra, the dot product (or inner product) is specifically used for vectors. It takes two vectors of the same dimension and results in a single scalar value (a number). 1. Geometric Definition Geometrically, the dot product measures the overlap or projection of one vector onto another. a · b = ||a|| ||b|| cos(θ) ... Read More

Probability – Conditional Probability and Independence

Probability
Resource: What is Conditional Probability? Conditional Probability Conditional probability is the likelihood of an event occurring, given that another event has already happened. It allows us to update our understanding of an outcome based on new information or specific “conditions.” The Formula P(A|B) = P(A ∩ B) P(B) • P(A|B): The probability of event A ... Read More

Probability – Distributions

Probability
Book Probability by Jim Pitman, Page 19 Events and Sets Set Theory & Venn Diagram Gallery Intersection: \(A \cap B\) A B “A AND B” — Elements in both. Union: \(A \cup B\) A B “A OR B” — Elements in either or both. Complement: \(A^c\) A U “NOT A” — Everything outside A. Subset: ... Read More
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