A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Advanced mathematical relativity course for math and physics students.
We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.
AI aids in mathematics research and problem-solving.
Explains isometric immersions and their applications.
The aim of this paper is to discuss some applications of general topology in computer algorithms including modeling and simulation, and also in computer graphics and image processing. While the progress in these areas heavily depends on advances in computing hardware, the major intellectual achievements are the algorit…
This text arises from teaching advanced undergraduate courses in differential topology for the master curriculum in Mathematics at the University of Pisa. So it is mainly addressed to motivated and collaborative master undergraduate students, having nevertheless a limited mathematical background. Overall this text is a…
These notes have been prepared as reading material for the mini-course given by the author at the "2019 Graduate Summer School" at Park City Mathematics Institute - Institute for Advanced Study. We begin by introducing Higgs bundles and their main properties (Lecture 1), and then we discuss the Hitchin fibration and it…
Mathematical advances needed for Digital Twins, differing from traditional models.
An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.
Improved model predicts wildfire spread on slopes.
This is neither an elementary introduction to singularity theory nor a specialized treatise containing many new theorems. The purpose of this little book is to invite the reader on a mathematical promenade. We pay a visit to Hipparchus, Newton and Gauss, but also to many contemporary mathematicians. We play with a bit …
These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous foundation to modern dynamics, as well as field and gauge theories in physics, engi…
Survey on advanced gauge theory concepts.
Quantum GAN improves volatility modeling in finance.
Researchers study the normalizing constant of a continuous categorical distribution.
Lecture notes on linear neural networks for deep learning optimization and generalization.
Advanced kernels improve Gaussian process accuracy by incorporating domain knowledge.
This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical programming for decision-making under uncertainty, and identifies potential r…
The paper explores Wiener-Granger causality and its computational enhancements.
These lectures were a part of the geometry course held during the Fall 2011 Mathematics Advanced Study Semesters (MASS) Program at Penn State (\url{http://www.math.psu.edu/mass/}). The lectures are meant to be accessible to advanced undergraduate and early graduate students in mathematics. We have placed a great emphas…
Under the assumption of the uniform local Sobolev inequality, it is proved that Riemannian metrics with an absolute Ricci curvature bound and a small Riemannian curvature integral bound can be smoothed to having a sectional curvature bound. This partly extends previous a priori estimates of Ye Li (J. Geom. Anal. 17 (20…
Recently, machine learning (ML) has established itself in various worldwide benchmarking competitions in computational biology, including Critical Assessment of Structure Prediction (CASP) and Drug Design Data Resource (D3R) Grand Challenges. However, the intricate structural complexity and high ML dimensionality of bi…
Deep learning finds mathematical equations from data.
We prove dual attainment for multi-asset financial derivatives pricing.
Mathematical pipeline identifies structural homology of knotted proteins.
Lecture notes on advanced geometry equations and subvarieties.
In this article, we mathematically study several GAN related topics, including Inception score, label smoothing, gradient vanishing and the -log(D(x)) alternative. --- An advanced version is included in arXiv:1703.02000 "Activation Maximization Generative Adversarial Nets". Please refer Section 6 in 1703.02000 for deta…
The goal of this note is to give an introduction to locally conformally symplectic and Kähler geometry. In particular, Sections 1 and 3 aim to provide the reader with enough mathematical background to appreciate this kind of geometry. The reference book for locally conformally Kähler geometry is "Locally conformal Kähl…
Study uses crochet to visualize non-Euclidean geometry.
This paper deals with the explicit design of strategy formulations to make the best strategic choices from a conventional matrix form of representing strategic choices. The explicit strategy formulation is an analytical model which is targeted to provide a mathematical strategy framework to find the best moment for str…
Survey of weak form's role in equation learning, parameter estimation, and coarse graining.
We study the problem of predicting rare critical transition events for a class of slow-fast nonlinear dynamical systems. The state of the system of interest is described by a slow process, whereas a faster process drives its evolution and induces critical transitions. By taking advantage of recent advances in reservoir…
We introduce SIM-CE, an advanced, user-friendly modeling and simulation environment in Simulink for performing multi-scale behavioral analysis of the nervous system of Caenorhabditis elegans (C. elegans). SIM-CE contains an implementation of the mathematical models of C. elegans's neurons and synapses, in Simulink, whi…
Advances in asynchronous optimization methods for machine learning.
Introduces basics of supergeometry for PhD students.
Explains how geometry and statistics intertwine, focusing on information geometry.
Comprehensive review of robust portfolio selection models.
A new mathematical framework simplifies securitization structuring.
Advances in the field of Machine Learning and Deep Neural Networks (DNNs) has enabled rapid development of sophisticated and autonomous systems. However, the inherent complexity to rigorously assure the safe operation of such systems hinders their real-world adoption in safety-critical domains such as aerospace and med…
While it has become common to perform automated translations on natural language, performing translations between different representations of mathematical formulae has thus far not been possible. We implemented the first translator for mathematical formulae based on recursive neural networks. We chose recursive neural…
In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix concentration inequalities, research has advanced to the point where we can conquer many (…
There has been a lot of recent interest in adopting machine learning methods for scientific and engineering applications. This has in large part been inspired by recent successes and advances in the domains of Natural Language Processing (NLP) and Image Classification (IC). However, scientific and engineering problems …
Explains how group representations behave under subgroup restrictions.
New memory effect discovered in gravitational wave behavior.
GeoTop resolves topological ambiguity in diagnostic imaging using geometric-topological analysis.
Site-specific recombination is an enzymatic process where two sites of precise sequence and orientation along a circle come together, are cleaved, and the ends are recombined. Site-specific recombination on a knotted substrate produces another knot or a two-component link depending on the relative orientation of the si…
Simple online monitor detects unsafe LLM outputs.
With the growth of deep learning, how to describe deep neural networks unifiedly is becoming an important issue. We first formalize neural networks mathematically with their directed graph representations, and prove a generation theorem about the induced networks of connected directed acyclic graphs. Then, we set up a …