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.
The paper shows objective derivatives are covariant derivatives on Riemannian metrics.
Optimal transport theory has recently found many applications in machine learning thanks to its capacity for comparing various machine learning objects considered as distributions. The Kantorovitch formulation, leading to the Wasserstein distance, focuses on the features of the elements of the objects but treat them in…
Virtual reality brings non-Euclidean geometry to life.
Mathematical optimization is widely used in various research fields. With a carefully-designed objective function, mathematical optimization can be quite helpful in solving many problems. However, objective functions are usually hand-crafted and designing a good one can be quite challenging. In this paper, we propose a…
Spin networks are at the core of quantum gravity. Our aim is to plug the mathematical community at large into the procedures turn to create a finite quantum theory of general relativity. For this, because of the different cultural backgraund, we would like to change the tack: to relate discrete (combinatorial) objects …
We refurbish our axiomatics of differential geometry introduced in [Mathematics for Applications,, 1 (2012), 171-182]. Then the notion of Euclideaness can naturally be formulated. The principal objective in this paper is to present an adaptation of our theory of differential forms developed in [International Journal of…
The aim of this paper is to obtain on the dual 1-jet space J^{1*}(R;M) the main geometrical objects used in the dual jet geometry of time-dependent Hamiltonians. We talk about distinguished (d-) tensors, time-dependent semisprays, nonlinear connections and their mathematical connections.
A framework evaluates synthetic tabular data quality objectively.
The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The nature of operator manifold provides its elements with both quantum field and geo…
Mathematical advances needed for Digital Twins, differing from traditional models.
Mathematical theory of super fiber bundles and connections developed.
This is an introductory review of topological field theories (TFTs) called AKSZ sigma models. The AKSZ construction is a mathematical formulation for the construction and analyses of a large class of TFTs, inspired by the Batalin-Vilkovisky formalism of gauge theories. We begin by considering a simple two-dimensional t…
We develop the mathematical foundations of the stochastic modified equations (SME) framework for analyzing the dynamics of stochastic gradient algorithms, where the latter is approximated by a class of stochastic differential equations with small noise parameters. We prove that this approximation can be understood math…
In this survey, we discuss several different types of gradient boosting algorithms and illustrate their mathematical frameworks in detail: 1. introduction of gradient boosting leads to 2. objective function optimization, 3. loss function estimations, and 4. model constructions. 5. application of boosting in ranking.
String theory still remains one of the promising candidates for a unification of the theory of gravity and quantum field theory. One of its essential parts is relativistic description of moving multi-dimensional objects called membranes (or p-branes) in a curved spacetime. On the classical field theory level, they are …
Optimizes real estate prices with dynamic strategies.
Neural networks are mathematically represented via quiver representations.
Generative Adversarial Networks (Goodfellow et al., 2014), a major breakthrough in the field of generative modeling, learn a discriminator to estimate some distance between the target and the candidate distributions. This paper examines mathematical issues regarding the way the gradients for the generative model are co…
I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, "Statistical Topology", emerged at the edge of topology and statistical physics of fluctuating non-phantom rope-like objects. This new branch is called…
Importance of theorem dedicated to isomorphisms consist in statement that they allow to identify different mathematical objects which have something common from the point of view of certain model. This paper considers morphisms of \Ts representation of \Hyph algebra and morphisms of \Ts representation of …
This paper is concerned with a recently developed paradigm for population-based optimization, termed particle filter optimization (PFO). This paradigm is attractive in terms of coherence in theory and easiness in mathematical analysis and interpretation. Current PFO algorithms only work for single-objective optimizatio…
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…
Bias and heterogeneity in peer assessment can lead to the issue of unfair scoring in the educational field. To deal with this problem, we propose a reference ranking method for an online peer assessment system using HodgeRank. Such a scheme provides instructors with an objective scoring reference based on mathematics.
This paper argues that the fundamental principle of contemporary financial economics is balanced reciprocity, not the principle of utility maximisation that is important in economics more generally. The argument is developed by analysing the mathematical Fundamental Theory of Asset Pricing with reference to the emergen…
We give a mathematical computation of the number of solutions of Apollonius problem, by use of Lie Sphere Geometry. Unlike in higher dimensions, the number of solutions depends only on the topology of the configuration of the 3 objects. It appears that our classification is non redundant, and far simpler than those obt…
In this paper we construct some natural geometrical objects on the 1-jet space J^1(R,R^3), like a nonlinear connection, a Cartan linear connection (together with its d-torsions and d-curvatures), a jet "electromagnetic" d-field and its geometric "electromagnetic" Yang-Mills energy, starting from a given dynamical syste…
New framework converts multi-objective to single-objective optimisation.
Deep models generate geometric objects with global properties.
Language models help text classification tasks by predicting next words.
We present a new model for prediction markets, in which we use risk measures to model agents and introduce a market maker to describe the trading process. This specific choice on modelling tools brings us mathematical convenience. The analysis shows that the whole market effectively approaches a global objective, despi…
Modeling intraday dispatch for wind-battery assets to meet grid targets.
OGRePy simplifies tensor calculations in general relativity.
New framework trains Schrödinger Bridge models using SDEs for generative tasks.
Lecture notes introduce Abelian differentials and their flat surfaces, focusing on families and Teichmüller dynamics.
Book introduces deep learning methods with math, theory, and applications.
Reconstructs supersymmetry and supergravity in complexified Z/2-graded Algebraic Geometry.
Since Bachelier's thesis in 1900 (laying the foundation of the stochastic process, or Brownian motion, as a model of stock price changes), attempts at understanding the nature of prices and at predicting them have failed. Statistical methods have only found minor regularities/anomalies, and other mathematical and physi…
Unified framework for removing unwanted information from machine learning models.
This article offers an introductory look at Khovanov homology and its historical context.
The paper explores risk-minimization for exponential additive models, providing mathematical expressions and numerical examples.
Optimizes group testing for COVID-19 to reduce test numbers.
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…
Data visualization and interaction with large data sets is known to be essential and critical in many businesses today, and the same applies to research and teaching, in this case, when exploring large and complex mathematical objects. GAP is a computer algebra system for computational discrete algebra with an emphasis…
This paper surveys gradient-based multi-objective deep learning methods.
The central object of synthetic differential geometry is microlinear spaces. In our previous paper [Microlinearity in Frolicher spaces -beyond the regnant philosophy of manifolds-, International Journal of Pure and Applied Mathematics, 60 (2010), 15-24] we have emancipated microlinearity from within well-adapted models…
The Riemannian geometry is one of the main theoretical pieces in Modern Mathematics and Physics. The study of Riemann Geometry in the relevant literature is performed by using a well defined analytical path. Usually it starts from the concept of metric as the primary concept and by using the connections as an intermedi…
The paper synthesizes the mathematics of modeling the future.
OGRe simplifies tensor calculations in general relativity.