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.
A conjecture about rational curves' formal principle and convergence proved for Goursat type families.
Study shows how to section map between holonomic and formal solutions.
A conjecture of Hirschowitz's predicts that a globally generated vector bundle on a compact complex manifold satisfies the formal principle, i.e., the formal neighborhood of its zero section determines the germ of neighborhoods in the underlying complex manifold of the vector bundle . By applying Cartan's eq…
An optimal control problem associated with the dynamics of the orientation of a bipolar molecule in the plane can be understood by means of tools in differential geometry. For first time in the literature -symplectic formalism is used to provide the optimal control problems associated to some families of partial dif…
The paper extends local h-principles to complex structures on Stein manifolds.
Several large classes of homogeneous spaces are known to be formal---in the sense of Rational Homotopy Theory. However, it seems that far fewer examples of non-formal homogeneous spaces are known. In this article we provide several construction principles and characterisations for non-formal homogeneous spaces, which w…
Study h-principles for non-integrable distributions on manifolds.
New approach to Lagrangian systems using intrinsic geometry.
This article introduces the notion of a loose family of Engel structures and shows that two such families are Engel homotopic if and only if they are formally homotopic. This implies a complete h-principle when some auxiliary data is fixed. As a corollary, we show that Lorentz and orientable Cartan prolongations are cl…
This paper formalizes the h-principle and sphere eversion in differential topology.
Derives time-averaged active inference from control principles.
Principles of financial product synthesis from a few basic financial products constitute an interesting research topic inspired by Islamic finance. We make an effort to answer general questions that should be answered before starting to investigate the main issues concerning this topic with the formalization of financi…
Develops neural networks for learning physics of complex systems by enforcing thermodynamics principles.
Develops thermodynamic formalism for quasimorphisms on negatively curved spaces.
In this paper we study quasi-linear system of partial differential equations which describes the existence of the polynomial in momenta first integral of the integrable geodesic flow on 2-torus. We proved in [3] that this is a semi-Hamiltonian system and we show here that the metric associated with the system is a metr…
A variational principle is proposed for obtaining the Jacobi equations in systems admitting a Lagrangian description. The variational principle gives simultaneously the Lagrange equations of motion and the Jacobi variational equations for the system. The approach can be of help in finding constants of motion in the Jac…
In [CPPP] it was shown that Engel structures satisfy an existence -principle, and the question of whether a full -principle holds was left open. In this note we address the classification problem, up to Engel deformation, of Cartan and Lorentz prolongations. We show that it reduces to their formal data as soon as…
For any Engel 4-fold, we show that the scanning map from the space of Engel knots to the space of formal Engel knots is a weak homotopy equivalence when restricted to the complement of the orbits of the Engel kernel. This is a relative, parametric and close h-principle.
We review some recent results on the theory of Lagrangian systems on Lie algebroids. In particular we consider the symplectic and variational formalism and we study reduction. Finally we also consider optimal control systems on Lie algebroids and we show how to reduce Pontryagin maximum principle.
The study examines Perelman singular manifolds and their properties.
This research formalizes inductive generalization and proposes a new learning paradigm called Inductive Learning.
The workshop focuses on AI principles for structured data.
The fundamental theorem of the theory of optimal control, the Pontryagin maximum principle (PMP), is extended to the setting of almost Lie (AL) algebroids, geometrical objects generalizing Lie algebroids. This formulation of the PMP yields, in particular, a scheme comprising reductions of optimal control problems simil…
The present paper analyses the formal parallelism existing between the laws of thermodynamics and some economic principles. Based on previous works, we shall show how the existence in Economics of principles analogous to those in thermodynamics involves the occurrence of economic events that remind of well-known phenom…
Typical dimensionality reduction methods focus on directly reducing the number of random variables while retaining maximal variations in the data. In this paper, we consider the dimensionality reduction in parameter spaces of binary multivariate distributions. We propose a general Confident-Information-First (CIF) prin…
Unified tensor network formalism for combining neural and symbolic AI.
The h-principle fails for prelegendrians in fat distributions of corank 2.
Information-theoretic bounded rationality describes utility-optimizing decision-makers whose limited information-processing capabilities are formalized by information constraints. One of the consequences of bounded rationality is that resource-limited decision-makers can join together to solve decision-making problems …
During the past few years Boolean matrix factorization (BMF) has become an important direction in data analysis. The minimum description length principle (MDL) was successfully adapted in BMF for the model order selection. Nevertheless, a BMF algorithm performing good results from the standpoint of standard measures in…
Develops Palatini formalism for pseudo-Finsler metrics, recovering classical results.
How can intelligent agents solve a diverse set of tasks in a data-efficient manner? The disentangled representation learning approach posits that such an agent would benefit from separating out (disentangling) the underlying structure of the world into disjoint parts of its representation. However, there is no generall…
Secondary Calculus formalizes PDEs using cohomology, simplifying their study.
Paper improves robustness and sparsity in adversarially trained DNNs.
This paper generalizes wrinkling techniques to Haefliger structures, linking them to foliations.
Typical dimensionality reduction (DR) methods are often data-oriented, focusing on directly reducing the number of random variables (features) while retaining the maximal variations in the high-dimensional data. In unsupervised situations, one of the main limitations of these methods lies in their dependency on the sca…
This paper improves capital efficiency in AMM protocols with leverage.
Classifies convex disks with Legendrian boundary in overtwisted contact 3-manifolds.
Spaces over BO are equivalent to thickened manifolds.
Machine learning (ML) methods have been developing rapidly, but configuring and selecting proper methods to achieve a desired performance is increasingly difficult and tedious. To address this challenge, automated machine learning (AutoML) has emerged, which aims to generate satisfactory ML configurations for given tas…
We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl's law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the D…
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…
Develops a framework for consistent loss functions with variable transformations.
New principle for disentangling latent factors using sparse regularization.
Unified perspective unites Bayesian optimization and active learning for efficient goal-oriented optimization.
S. K. Donaldson asked whether the lower bound of the Calabi functional is achieved by a sequence the normalized Donaldson-Futaki invariants. We answer the question for the Ricci curvature formalism, in place of the scalar curvature. The principle is that the stability indicator is optimized by the multiplier ideal shea…
Fidel-TS creates a new benchmark for time series forecasting models.
The article consists of the Russian and English variants of Ph.D. Thesis in which the answers is given on the following questions: 1. how to construct the spinor formalism for n=6; 2. how to construct the spinor formalism for n=8; 3. how to prolong the Riemannian connection from the tangent bundle into the spinor one w…
Searching normal forms for real analytic submanifolds of C^n involves convergence problems. In 1983, J.K. Moser and S.M. Webster provided examples of real analytic surfaces in C^2 having an isolated hyperbolic (in the sense of E. Bishop) complex tangency, which are formally but not holomorphically normalizable (because…