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.
Researchers create integral representations for two-layer ReLU networks with quantitative bounds.
We use Chen's iterated integrals to integrate representations up to homotopy. That is, we construct an A_infty functor from the representations up to homotopy of a Lie algebroid to those of its infinity groupoid. This construction extends the usual integration of representations in Lie theory. We discuss several exampl…
Study constant mean curvature surfaces with integrable boundary conditions.
Researchers prove finiteness of integral representations on specific polytopes.
The method of contact integrable extensions is used to find new zero-curvature representation for Plebañski's second heavenly equation.
Researchers use Mellin-Barnes integrals to study trinomial equations and their braids.
Restricts quantum representations of mapping class groups to integral coefficients.
Generalized Weierstrass representations for generic surfaces conformally immersed into four-dimensional Euclidean and pseudo-Euclidean spaces of different signatures are presented. Integrable deformations of surfaces in these spaces generated by the Davey-Stewartson hierarchy of integrable equations are proposed. Willm…
We develop a class of integrals on a manifold M called exponential iterated integrals, an extension of K. T. Chen's iterated integrals. It is shown that the matrix entries of any upper triangular representation of the fundamental group of M can be expressed via these new integrals. The ring of exponential iterated inte…
The paper analyzes how grid cells perform path integration and learns hexagon grid patterns.
Deforms surface groups to be Zariski dense in SL(n,R)
NKI integrates obfuscated datasets using nonlinear kernels for improved data collaboration.
Closed essential surfaces in a three-manifold can be detected by ideal points of the character variety or by algebraic non-integral representations. We give examples of closed essential surfaces not detected in either of these ways. For ideal points, we use Chesebro's module-theoretic interpretation of Culler-Shalen th…
Unified representation for minimal and constant mean curvature surfaces.
New method improves self-supervised representation learning using probabilistic modeling and Monte Carlo integration.
In this effort, we derive a formula for the integral representation of a shallow neural network with the ReLU activation function. We assume that the outer weighs admit a finite -norm with respect to Lebesgue measure on the sphere. For univariate target functions we further provide a closed-form formula for all po…
Proof shows volumes of certain geometric representations are always integers.
The purpose of this article is to describe all possible beliefs of market participants on objective measures under Markovian environments when a risk-neutral measure is given. To achieve this, we employ the Martin integral representation of Markovian pricing kernels. Then, we offer economic and financial implications o…
We give new explicit formulas for the representations of the mapping class group of a genus one surface with one boundary component which arise from Integral TQFT. Our formulas allow one to compute the h-adic expansion of the TQFT-matrix associated to a mapping class in a straightforward way. Truncating the h-adic expa…
Study forward investment performance in semimartingale markets with stochastic factors.
We extend Lawrence's representations of the braid groups to relative homology modules, and we show that they are free modules over a Laurent polynomials ring. We define homological operators and we show that they actually provide a representation for an integral version for . We suggest an isomorp…
FI-modules were introduced by the first three authors in [CEF] to encode sequences of representations of symmetric groups. Over a field of characteristic 0, finite generation of an FI-module implies representation stability for the corresponding sequence of S_n-representations. In this paper we prove the Noetherian pro…
New parametrizations for minimal timelike surfaces discovered.
Identifies LA-groups via VB-group structure and complementary actions.
Minimalistic model captures head direction system properties.
We combine recent developments on weakly symmetric pseudo--riemannian nilmanifolds with with geometric methods for construction of unitary representations on square integrable Dolbeault cohomology spaces. This runs parallel to construction of discrete series representations on spaces of square integrable harmonic forms…
We construct representations of the braid groups B_n on n strands on free Z[q,q^-1,s,s^-1]-modules W_{n,l} using generic Verma modules for an integral version of quantum sl_2. We prove that the W_{n,2} are isomorphic to the faithful Lawrence Krammer Bigelow representations of B_n after appropriate identification of par…
We study the conditions for a nilpotent Lie group to be foliated into subgroups that have square integrable (relative discrete series) unitary representations, that fit together to form a filtration by normal subgroups. Then we use that filtration to construct a class of "stepwise square integrable" representations on …
Geometrically represents path integral reduction Jacobian for interacting systems.
A representation of generalized Weierstrass formulae for an immersion of generic surfaces into a 4-dimensional complex space in terms of spinors treated as minimal left ideals of Clifford algebras is proposed. The relation between integrable deformations of surfaces via mVN-hierarchy and integrable deformations of spin…
Derives integral representations for a Lévy process and its extremum, hitting time, with fast evaluation.
Geometrically represents the Jacobian for a mechanical system with symmetry.
Extensions of the generalized Weierstrass representation to generic surfaces in 4D Euclidean and pseudo-Euclidean spaces are given. Geometric characteristics of surfaces are calculated. It is shown that integrable deformations of such induced surfaces are generated by the Davey -Stewartson hierarchy. Geometrically thes…
The paper defines and proves the existence of decompositions of integral varifolds.
In this paper we classify Weingarten surfaces integrable in the sense of soliton theory. The criterion is that the associated Gauss equation possesses an sl(2)-valued zero curvature representation with a nonremovable parameter. Under certain restrictions on the jet order, the answer is given by a third order ordinary d…
We find decomposition series of length at most two for modular representations in positive characteristic of mapping class groups of surfaces induced by an integral version of the Witten-Reshetikhin-Turaev SO(3)-TQFT at the p-th root of unity, where p is an odd prime. The dimensions of the irreducible factors are given…
In this paper we provide an integral representation of the fractional Laplace-Beltrami operator for general riemannian manifolds which has several interesting applications. We give two different proofs, in two different scenarios, of essentially the same result. One of them deals with compact manifolds with or without …
Tensor networks improve integration accuracy for high-dimensional problems.
Paper proposes a new FRL algorithm for continuous sensitive attributes using EIPM.
We consider the family of the Bour's minimal surfaces in Euclidean 3-space, and compute their classes, degrees and integral free representations.
The risk minimizing problem in the multidimensional Black-Scholes framework is studied. Specific formulas for the minimal risk function and the cost reduction function for basket derivatives are shown. Explicit integral representations for the risk functi…
Using techniques of integrable systems, we study a Weierstrass representation formula for timelike surfaces with prescribed mean curvature in Minkowski 3-space. It is shown that timelike minimal surfaces are obtained by integrating a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in Minkowski 3-spa…
In the framework of path integral the evolution operator kernel for the Merton-Garman Hamiltonian is constructed. Based on this kernel option formula is obtained, which generalizes the well-known Black-Scholes result. Possible approximation numerical schemes for path integral calculations are proposed.
New LFR algorithm ensures fair predictions with theoretical guarantees.
Method calculates function integrals on complex manifolds.
The paper studies binary icosahedral representations of hyperbolic 3-manifolds.
LORL learns object-centric representations from vision and language.
New integrable systems for marginally trapped surfaces in 4D Lorentz-Minkowski space.