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Computational Theory and Mathematics

Computational Theory and Mathematics

The mathematical foundations of computing, including algorithms, complexity theory, automata theory, formal languages, cryptography, and the theoretical limits of computation

11 papers in this specialization

Paperzilla Papers in Computational Theory and Mathematics

A Coincidence of Wants Mechanism for Swap Trade Execution in Decentralized Exchanges

This paper presents a mathematically rigorous framework for identifying and completing Coincidence of Wants (CoW) cycles in decentralized exchanges (DEXs) using graph theory and linear algebra. The proposed algorithm aims to detect both complete CoW cycles and generate "bridging orders" to complete partial ones, demonstrating its application on a small real-world Arbitrum swap dataset.

Oct 02, 01:00 PM

Breaking the Sorting Barrier for Directed Single-Source Shortest Paths

This paper introduces a deterministic algorithm for the single-source shortest path (SSSP) problem on directed graphs with non-negative edge weights. The algorithm achieves a time complexity of O(m log^(2/3) n), improving upon Dijkstra's algorithm for sparse graphs. This is the first deterministic algorithm to break the O(m + n log n) time bound in this setting.

2504.17033v2.pdf

Aug 25, 06:15 AM

The Principles of Deep Learning Theory

This book introduces a theoretical framework for understanding deep neural networks, using tools from theoretical physics. It focuses on analyzing preactivation distributions, the Neural Tangent Kernel (NTK), and the flow of information through networks during training. The book delves into the mathematical principles behind deep learning, including Gaussian integrals, perturbation theory, and renormalization group flow.

Aug 23, 04:47 PM

Breaking the Sorting Barrier for Directed Single-Source Shortest Paths

The paper introduces a faster deterministic algorithm for the single-source shortest path (SSSP) problem in directed graphs with non-negative edge weights. Using a recursive partitioning technique, the algorithm achieves a time complexity that outperforms Dijkstra's algorithm on sparse graphs. The algorithm assumes constant in-degrees and out-degrees but proposes a transformation for general graphs.

Aug 11, 06:38 PM

End-to-End Efficient Quantum Thermal and Ground State Preparation Made Simple

This paper introduces new quantum algorithms for thermal and ground state preparation that are simpler and require fewer resources than existing methods, making them suitable for early fault-tolerant quantum computers. The algorithms are theoretically proven to be efficient for several model systems, including single qubit, free fermionic, and commuting local Hamiltonians. Further research is needed to generalize these results to all quantum systems.

Aug 11, 03:50 AM

Scientific Machine Learning Through Physics-Informed Neural Networks: Where we are and What's Next

Physics-Informed Neural Networks (PINNs) offer a novel approach to solving partial differential equations by incorporating physical laws into the learning process. While promising for various applications, including fluid dynamics, optics, and material science, PINNs face challenges related to theoretical understanding, computational cost, and accuracy in complex physical phenomena.

s10915-022-01939-z.pdf

Jul 14, 05:25 PM

DOUBLE PHASE IMPLICIT OBSTACLE PROBLEMS WITH CONVECTION AND MULTIVALUED MIXED BOUNDARY VALUE CONDITIONS

This paper proves the existence and weak compactness of solutions for a double-phase implicit obstacle problem with convection and multivalued mixed boundary conditions. The results are established under general assumptions using fixed-point theory, nonsmooth analysis, and variational methods.

Jul 14, 10:36 AM

A SARS-CoV-2 protein interaction map reveals targets for drug repurposing

This study mapped 332 SARS-CoV-2-human protein interactions, revealing key pathways hijacked by the virus, including translation, vesicle trafficking, and innate immunity. This led to the identification of 69 existing compounds targeting these interactions, with some showing promising antiviral activity in vitro, particularly translation inhibitors and sigma receptor ligands.

s41586-020-2286-9.pdf

Jul 14, 10:36 AM

Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem

The paper describes a new heuristic algorithm for the Traveling Salesman Problem (TSP) with a time complexity of O(n³) that guarantees a solution no worse than 3/2 times the optimal solution when the triangle inequality holds. This represents a 50% improvement over the previous best-known worst-case ratio of 2 for polynomial-time TSP heuristics.

s43069-021-00101-z.pdf

Jul 14, 10:36 AM

Why general artificial intelligence will not be realized

The author argues against the possibility of achieving Artificial General Intelligence (AGI) because computers lack embodiment, lived experience, and the ability to interact with the world like humans. The paper claims that recent advancements in AI, while impressive, are limited to narrow applications (ANI) and do not represent progress towards true general intelligence.

s41599-020-0494-4.pdf

Jul 14, 10:36 AM

GL-LowPopArt: A Nearly Instance-Wise Minimax-Optimal Estimator for Generalized Low-Rank Trace Regression

The paper introduces GL-LowPopArt, a two-stage estimator for generalized low-rank trace regression that achieves near instance-wise optimality. It outperforms existing methods by adapting to instance-specific curvature, and a corresponding minimax lower bound confirms its near-optimality.

2506.03074v1-embedded-msg.pdf

Jul 08, 11:34 AM

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