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.
Lecture notes on linear neural networks for deep learning optimization and generalization.
Novel power transform unifies various mathematical functions.
Mathematical pipeline identifies structural homology of knotted proteins.
Mathematical analysis shows Delisle-Euler map methods are optimal.
Enhances math problem-solving models with multi-turn preference learning.
The amoebas associated to algebraic varieties are certain concave regions in the Euclidean space whose shape reminds biological amoebas. This term was formally introduced to Mathematics in 1994 by Gelfand, Kapranov and Zelevinski. Some traces of amoebas were appearing from time to time, even before the formal introduct…
Paper examines two methods for FX market volatility modeling.
This paper uses crypto derivatives data to estimate yield curves for cryptocurrencies.
Python tools for 3D shape analysis on Kendall's space.
Mathematical model for focused investing reduces diversification risks.
Recent years have witnessed a trend that advanced mathematical tools, such as algebraic topology, differential geometry, graph theory, and partial differential equations, have been developed for describing biological macromolecules. These tools have considerably strengthened our ability to understand the molecular mech…
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations exist, it is sometimes difficult to gain an overview how differential geometry and…
We introduce the concept of singular values for the Riemann curvature tensor, a central mathematical tool in Einstein's theory of general relativity. We study the properties related to the singular values, and investigate five typical cases to show its relationship to the Ricci scalar and other invariants.
Big data, data science, deep learning, artificial intelligence are the key words of intense hype related with a job market in full evolution, that impose to adapt the contents of our university professional trainings. Which artificial intelligence is mostly concerned by the job offers? Which methodologies and technolog…
A new AI framework reduces costs and improves performance.
The paper examines how macroeconomic control tools lost effectiveness, leading to a 'dark ages' period.
This thesis tackles Optimal Transport on incomparable spaces, proposing new tools and properties.
Quantum GAN improves volatility modeling in finance.
Investigates the effects of nondominated sets of probability measures in robust models of finance.
Mathematical approach assesses human resource competences accurately.
We introduce the historical development and physical idea behind topological Yang-Mills theory and explain how a physical framework describing subatomic physics can be used as a tool to study differential geometry. Further, we emphasize that this phenomenon demonstrates that the interrelation between physics and mathem…
Mathematical framework for field theories on Finsler spacetimes.
BCF models estimate causal effects on multiple outcomes in TIMSS data.
New fast estimation methods stemming from control theory lead to a fresh look at time series, which bears some resemblance to "technical analysis". The results are applied to a typical object of financial engineering, namely the forecast of foreign exchange rates, via a "model-free" setting, i.e., via repeated identifi…
Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus, approximation theory, optimization and linear algebra. This article provides a very…
Develops statistical guarantees for neural networks with regularization.
Turaev transformed knot theory and 3-manifold invariants.
Survey of mathematical foundations for reinforcement learning.
MAD framework learns operators from physics-embedded data efficiently.
A discrete time probabilistic model, for optimal equity allocation and portfolio selection, is formulated so as to apply to (at least) reinsurance. In the context of a company with several portfolios (or subsidiaries), representing both liabilities and assets, it is proved that the model has solutions respecting constr…
We propose a paradigm to deep-learn the ever-expanding databases which have emerged in mathematical physics and particle phenomenology, as diverse as the statistics of string vacua or combinatorial and algebraic geometry. As concrete examples, we establish multi-layer neural networks as both classifiers and predictors …
We study vector fields generating a local flow by automorphisms of a parabolic geometry with higher order fixed points. We develop general tools extending the techniques of [1], [2], and [3]. We apply these tools to almost Grassmannian, almost quaternionic, and contact parabolic geometries, including CR structures, to …
Mathematical conditions and practical computations for adversarial robustness measures are established.
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of the fibre bundle in question] in a more natural way. It starts off with a review o…
We study the problem of estimating a manifold from random samples. In particular, we consider piecewise constant and piecewise linear estimators induced by k-means and k-flats, and analyze their performance. We extend previous results for k-means in two separate directions. First, we provide new results for k-means rec…
Study evaluates different mathematical models for three case studies using statistical fitting.
Survey of weak form's role in equation learning, parameter estimation, and coarse graining.
Geometric techniques reveal new insights into Gromov-Witten invariants.
In this article we present pictorially the foundation of differential geometry which is a crucial tool for multiple areas of physics, notably general and special relativity, but also mechanics, thermodynamics and solving differential equations. As all the concepts are presented as pictures, there are no equations in th…
The study evaluates how prediction helps identify the worst-off in welfare programs.
The restricted Boltzmann machine is a network of stochastic units with undirected interactions between pairs of visible and hidden units. This model was popularized as a building block of deep learning architectures and has continued to play an important role in applied and theoretical machine learning. Restricted Bolt…
Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will focus on their algebraic-geometric aspects, explaining how the representation the…
TIR expands LLM capabilities by enabling problem-solving strategies.
New framework explains deep learning using signal processing techniques.
In this text I present some problems which led to the introduction of special kinds of graphs as tools for studying singular points of algebraic surfaces. I explain how such graphs were first described using words, and how several classification problems made it necessary to draw them, leading to the elaboration of a s…
New transforms improve signal classification and data analysis.
In math.GT/0106017 it was shown that thin position on Heegaard spines can be a useful tool for analyzing the topology of knots in 3-space. The proof there (specifically, of the Goda-Teragaito conjecture) requires masses of technical detail; it is easy to lose track of the underlying ideas. The present paper gives an ov…
We start recalling with critical eyes the mathematical methods used in gauge theory and prove that they are not coherent with continuum mechanics, in particular the analytical mechanics of rigid bodies or hydrodynamics, though using the same group theoretical methods and despite the well known couplings existing betwee…