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.
Complexity science offers new insights into macroeconomics and finance.
New neural networks model complex phenomena with fewer parameters.
This article demonstrates the possibility of constructing indicators of critical and crisis phenomena in the volatile market of cryptocurrency. For this purpose, the methods of the theory of complex systems such as recurrent analysis of dynamic systems and the calculation of permutation entropy are used. It is shown th…
Paper connects Stokes phenomena to quantum groups and Poisson-Lie groups.
The most commonly encountered types of complex analytic G-structures and Cartan geometries cannot have singularities of complex codimension 2 or more.
TCR simplifies complex models into interpretable causal factors.
New algorithm trains deep neural networks without global optimization.
Classifications of all biharmonic isoparametric hypersurfaces in the unit sphere, and all biharmonic homogeneous real hypersurfaces in the complex or quaternionic projective spaces are shown. Answers in case of bounded geometry to Chen's conjecture or Caddeo, Montaldo and Piu's one on biharmonic maps into a manifold of…
We consider the use of Deep Learning methods for modeling complex phenomena like those occurring in natural physical processes. With the large amount of data gathered on these phenomena the data intensive paradigm could begin to challenge more traditional approaches elaborated over the years in fields like maths or phy…
Use simplified layerwise linear models to understand neural dynamics.
An agent-based computational economical toy model for the emergence of money from the initial barter trading, inspired by Menger's postulate that money can spontaneously emerge in a commodity exchange economy, is extensively studied. The model considered, while manageable, is significantly complex, however. It is alrea…
Study on four-dimensional Dehn twists and Milnor fibrations, revealing new phenomena.
In computer experiments, a mathematical model implemented on a computer is used to represent complex physical phenomena. These models, known as computer simulators, enable experimental study of a virtual representation of the complex phenomena. Simulators can be thought of as complex functions that take many inputs and…
The paper argues against the inefficiency of explaining deep learning phenomena.
In this paper, we consider a concentration of measure problem on Riemannian manifolds with boundary. We study concentration phenomena of non-negative -Lipschitz functions with Dirichlet boundary condition around zero, which is called boundary concentration phenomena. We first examine relation between boundary concen…
We investigate the random dynamics of rational maps on the Riemann sphere and the dynamics of semigroups of rational maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, in most cases, the chaos of the averaged system disappears, due to the cooperation of the generators. We investi…
CantorNet tests geometric and topological complexity in neural networks.
For each nonnegative integer we find an open (4m+9)-dimensional simply-connected manifold admitting complete nonnegatively curved metrics whose souls are non-diffeomorphic, homeomorphic, and have codimension 2. We give a diffeomorphism classification of the pairs (N, soul) when N is a nontrivial complex line bundle ove…
Sharp changes in time series representing market dynamics are studied by means of the self--similar analysis suggested earlier by the authors. These sharp changes are market booms and crashes. Such crises phenomena in markets are analogous to critical phenomena in physics. A simple classification of the market crisis p…
New approach simulates reputation dynamics using information compression.
We survey the Dirichlet problem for the complex Homogeneous Monge-Ampère Equation, both in the case of domains in and the case of compact Kähler manifolds parametrized by a Riemann surface with boundary. We then give a self-contained account of previous work of the authors that connects this with the Hele…
Study on Lane-Emden equation on curved spaces, revealing new existence and non-existence phenomena.
This document contains a description of physics entirely based on a geometric presentation: all of the theory is described giving only a pseudo-riemannian manifold (M, g) of dimension n > 5 for which the g tensor is, in studied domains, almost everywhere of signature (-, -, +, ..., +). No object is added to this space-…
The paper explores higher property T in lattices and its connections to geometric phenomena.
We obtain upper bounds for the first Dirichlet eigenvalue of a tube around a complex submanifold of which depends only on the radius of the tube, the degrees of the polynomials defining and the first eigenvalue of some model centers of the tube. The bounds are sharp on these models. Moreover, when the mo…
In this paper we observe that 2-dimensional 0-surgery occurs in natural processes, such as tornado formation and other phenomena reminiscent of hole drilling. Inspired by such phenomena, we introduce new theoretical concepts which enhance the formal definition of 2-dimensional 0-surgery with the observed dynamics. To d…
We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.
Paper investigates rigidity phenomena for weighted Ricci curvature bounds with Laplacian comparison theorem.
Much recent work has concerned sparse approximations to speed up the Gaussian process regression from the unfavorable O(n3) scaling in computational time to O(nm2). Thus far, work has concentrated on models with one covariance function. However, in many practical situations additive models with multiple covariance func…
Minimal model reveals power laws in financial markets.
Analyzes magnetic Laplacian on hyperbolic surfaces, highlighting key quantum phenomena.
Topological surgery is a mathematical technique used for creating new manifolds out of known ones. We observe that it occurs in natural phenomena where a sphere of dimension 0 or 1 is selected, forces are applied and the manifold in which they occur changes type. For example, 1-dimensional surgery happens during chromo…
Study exotic phenomena in small 4-manifolds using diffeomorphisms.
Analyzes complex structure deformations using cohomology contraction methods.
Predicts language model performance from public models without training.
The paper studies hyperbolic phenomena on closed surfaces using bicorn curves.
Knowing and modelling the migration phenomena and especially the social and economic consequences have a theoretical and practical importance, being related to their consequences for development, economic progress (or as appropriate, regression), environmental influences etc. One of the causes of migration, especially …
Let S be any orientable surface of infinite genus with a finite number of boundary components. In this work we consider the curve complex C(S), the nonseparating curve complex N(S) and the Schmutz graph G(S) of S. When all the topological ends of S carry genus, we show that all elements in the automorphism groups Aut(C…
Few years ago we developed jointly with I.Dynnikov new discretization of complex analysis (DCA) based on the two-dimensional manifolds with colored black/white triangulation. Especially deep results were obtained for the Euclidean plane with equilateral triangle lattice. In the present work we develop a DCA theory for …
Framework augments physical models with deep learning for complex dynamics forecasting.
Method extracts stochastic systems with Lévy noise from data.
Method extracts governing laws from non-Gaussian stochastic systems data.
The paper explains emergent phenomena in deep learning using entropic forces.
The paper studies special Lagrangian submanifolds in complex spaces and derives inequalities and flow methods.
We show that a variety of modern deep learning tasks exhibit a "double-descent" phenomenon where, as we increase model size, performance first gets worse and then gets better. Moreover, we show that double descent occurs not just as a function of model size, but also as a function of the number of training epochs. We u…
Modern ML methods show unexpected behaviors that contradict classical statistics.
Mathematical structures link Gromov-Witten to Donaldson-Thomas invariants.
Many domains of science have developed complex simulations to describe phenomena of interest. While these simulations provide high-fidelity models, they are poorly suited for inference and lead to challenging inverse problems. We review the rapidly developing field of simulation-based inference and identify the forces …