Conjecture - PowerPoint PPT Presentation

This content encompasses the introduction and mathematical review covered in CS 345 lecture 1, including topics such as sets, sequences, logarithms, logical equivalences, and proofs. It delves into sets theory, mathematical operations, deductive reasoning, and examples like the conjecture of even nu

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This research explores an additive combinatorics approach to the log-rank conjecture in communication complexity, addressing the maximum total bits sent on worst-case inputs and known bounds. It discusses the Polynomial Freiman-Ruzsa Conjecture and Approximate Duality, highlighting technical contrib

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Delve into the fascinating world of graph colorings, chromatic polynomials, and notable conjectures in discrete geometry. Explore the impact of June Huh in bringing Hodge theory to combinatorics and his proof of various mathematical conjectures. Uncover the significance of the four-color theorem, co

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Explore the realm of constraint satisfaction problems, from Max-Cut to Unique Games, delving into approximation algorithms and NP-hardness. Dive into open questions surrounding the Unique Games Conjecture, the hardness of Max-Cut approximations, and the quest to approximate the Balanced Separator pr

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MathCheck is a project focused on incorporating algorithms from Computer Algebra Systems (CAS) with SAT solvers to enhance problem-solving capabilities in math, such as counterexample construction and bug finding. The goal is to design an easily extensible system with a current focus on graph theory

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Explore the Daubert standard for expert testimony, focusing on the rules of admissibility, qualifications, reliability, and methodology. Learn how judges act as gatekeepers to prevent conjecture and speculation in court. Discover the importance of scientific foundation and peer review in expert opin

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Protocol analysis of non-interactive commitments in classical and quantum settings, including discussions on OWF, NIC, PRS, and quantum communication implications. The results based on the Polynomial Compatibility Conjecture showcase advancements in post-quantum OWF and NIC scenarios.

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Combinatorial Gray codes involve generating combinatorial objects with minimal differences between consecutive objects. The Middle Levels Conjecture focuses on cyclically generating ground set subsets with specific characteristics. This conjecture has led to significant theoretical and experimental

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This work delves into the intricate world of complexity measures for Boolean functions, exploring concepts such as certificate complexity, decision tree depth, sensitivity, block sensitivity, PRAM complexity, and more. It sheds light on the relationships among different complexity measures and provi

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In this research work, the Casas-Alvero conjecture is explored, focusing on polynomials and their derivatives, and the common roots they share. The study delves into the normalization of roots under various transformations, using p-adic methods and Gröbner bases. Noteworthy findings include implica

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Exploring the computational complexity of low-polynomial-time problems, this workshop delves into the Orthogonal Vectors Problem and its conjectures. It introduces concepts like the Sparse OV Problem, first-order graph properties, and model checking in graphs. Discussing the hardness of problems rel

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Linear programming involves maximizing a linear objective function within a set of linear constraints to find the optimal point in a polytope. The simplex algorithm, introduced by Dantzig in 1947, navigates through vertices to reach the optimal solution. Deterministic and randomized pivoting rules,

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Prime numbers, prime counting functions, the prime number theorem, prime k-tuples, admissible k-tuples, and constellations with prime numbers. The concept of admissible prime k-tuples and the conjecture of infinite twin primes are discussed. The numerical evidence supporting the conjecture is highli

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Exploring the famous Goldbach's Conjecture in programming, this content provides a step-by-step approach to implementing a checker for the theorem. From outlining the necessary parts to structuring code and iterating through prime numbers, this guide offers a hands-on perspective on tackling this ma

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This seminar explores unsolved problems in number theory, with a focus on Happy Numbers, UPINT, Birch & Swinnerton-Dyer Conjecture, and more. Students delve into research, presentations, and writing proofs while investigating intriguing mathematical concepts.

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In this study, the authors discuss the computation of B-model Yukawa couplings in heterotic string theory compactified on a Calabi-Yau 3-fold with standard embedding. They explore the classical mirror symmetry, A-model Yukawa coupling conjecture, and non-perturbative corrections via world sheet inst

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Explore the fascinating world of complexity theory and Boolean circuits in this comprehensive guide. Understand concepts like the complexity class BPP, decidable languages, and the P vs. BPP conjecture. Discover how Boolean circuits work and their role in defining functions and computing outputs.

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Explore efficient quantum protocols for XOR functions in communication complexity, including lower bounds and the Log-Rank Conjecture. Learn about computation modes, communication matrices, and connections to Fourier analysis.

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Explore the intriguing Sensitivity Conjecture, its implications, and the relationship between sensitivity, degree, and complexity measures in computer science research. Discover how sensitivity influences communication games, function evaluation, and more.

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Explore cutting-edge research in high-energy physics, focusing on black hole torsion effects, geometrization conjecture, and advanced methods like Ricci flow and entropy formulas. Discover new trends and delve into the intricate relationships between information theory and geometric structures.

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Explore the fascinating world of prime numbers, prime counting functions, and prime k-tuples. Learn about admissible k-tuples, constellations with k primes, and the conjecture on infinite twin primes. Delve into numerical evidence supporting the existence of infinite primes within admissible k-tuple

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Explore the Unique Games Conjecture and implications for optimization problems. Learn about subexponential algorithms, UGC barrier examples, and time vs. approximation trade-offs in solving unique games instances efficiently.

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Explore the concept of Fiat-Shamir and Quantum Forking Conjecture in non-interactive proof systems, sigma protocols, and breaking soundness in a quantum context. Learn about special and strict soundness, zero-knowledge proofs, and the transformation of sigma protocols into non-interactive systems.

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Explore the CAP Theorem, Eric Brewer's Conjecture, and the desirable properties of data systems such as ACID transactions. Learn about the tradeoffs between Consistency, Availability, and Partition Tolerance in distributed environments.

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Explore the intriguing connections between the Cascade Conjecture, Tverberg's Theorem, and the Four-Color Theorem in the realm of combinatorics and topology. Delve into Tverberg's Theorem, colorful Caratheodory, and the Turan ladder, along with other notable problems and conjectures in the field. Wi

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Explore the intriguing concept of Adleman's Theorem in Complexity Theory, which offers insights into the relationship between P, BPP, and PSIZE. Discover how random bits play a crucial role in proving this theorem and its implications for the P versus BPP conjecture.

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Explore the consequences of falsifying the Strong Exponential Time Hypothesis (SETH) and the Orthogonal Vectors Conjecture in the realm of fine-grained complexity theory. Discover the implications for classic complexity theory, multivariate complexity, problem-solving approaches like ?-SAT and Ortho

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Explore the fundamental concepts of geometry such as points, lines, angles, and rays. Understand the process of reasoning in geometry through pattern exploration, conjecture making, and logical verification. Get familiar with important definitions and classifications of angles while learning about c

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