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.
New method expands seed genes to functionally related clusters.
This study approximates neural network features for modeling relations and attention mechanisms.
The paper develops inequalities for log-concave functions and related surface areas.
New -functions for 3-manifolds connect to Witten invariants and relate to generalized Bernoulli polynomials.
In the paper, the author studies properties of three functions relating to the exponential function and the existence of partitions of unity, including accurate and explicit computation of their derivatives, analyticity, complete monotonicity, logarithmically complete monotonicity, absolute monotonicity, and the like.
As the second part of the sequel, we investigate the variation of rearrangement operators (more precisely, the spectral functions behind) arising in the study of modular geometry on noncommutative (two) tori. We initiate a systematic approach by introducing transformations corresponding to basic operations in calculus,…
Embedding-based methods for knowledge base completion (KBC) learn representations of entities and relations in a vector space, along with the scoring function to estimate the likelihood of relations between entities. The learnable class of scoring functions is designed to be expressive enough to cover a variety of real…
Study optimality conditions for interval-valued optimization problems on Riemannian manifolds.
In this article, we solve the strong openness conjecture on the multiplier ideal sheaves for the plurisubharmonic functions posed by Demailly. We prove two conjectures about the growth of the volumes of the sublevel sets of plurisubharmonic functions related to the complex singularity exponents and quasi-plurisubharmon…
Knowledge graphs are a versatile framework to encode richly structured data relationships, but it can be challenging to combine these graphs with unstructured data. Methods for retrofitting pre-trained entity representations to the structure of a knowledge graph typically assume that entities are embedded in a connecte…
Magnitude of manifolds linked to Riesz energies and beta functions.
For two solutions of the WDVV equations that are related by the inversion symmetry, we show that the associated principal hierarchies of integrable systems are related by a reciprocal transformation, and the tau functions of the hierarchies are related by a Legendre type transformation. We also consider relationships b…
This paper is an exposition of heuristics related to Witten's functional integral, relating it to Vassiliev invariants and to the Kontsevich integrals that can be used to produce Vassiliev invariants of knots and links.In particular, we give a simplified version of the appearance of the Kontsevich integrals in the pert…
This paper was motivated by work of Arnold where he explains how to count "snakes", i.e. Morse functions on the real axis with prescribed behavior at infinity. This leads immediately to a count of excellent Morse functions on the circle, where following Thom's terminology, excellent means that no two critical points li…
Study of Chern-Simons theory and link invariants using gauge fields and skein relations.
We survey results about computational complexity of the word problem in groups, Dehn functions of groups and related problems.
Paper shows equivalence between MM and PH for n-D Morse functions.
Study of a flow related to the Orlicz-Minkowski problem for convex hypersurfaces.
Derives monotonic quantities for -harmonic functions on manifolds.
New insights into X-ray transform on hyperbolic disk, with functional relations and range characterizations.
On simple geodesic disks of constant curvature, we derive new functional relations for the geodesic X-ray transform, involving a certain class of elliptic differential operators whose ellipticity degenerates normally at the boundary. We then use these relations to derive sharp mapping properties for the X-ray transform…
Research extends geodesic length function study to three holed sphere.
NP-PROV separates mean and variance spaces to improve function uncertainty.
We study regularity properties of the dynamic value functions of primal and dual problems of optimal investing for utility functions defined on the whole real line. Relations between decomposition terms of value processes of primal and dual problems and between optimal solutions of basic and conditional utility maximiz…
The study of Morse functions on 3-manifolds and their Reeb graphs.
We briefly review the current situation with various relations between knot/braid polynomials (Chern-Simons correlation functions), ordinary and extended, considered as functions of the representation and of the knot topology. These include linear skein relations, quadratic Plucker relations, as well as "differential" …
We define a Chern-Simons invariant for a certain class of infinite volume hyperbolic 3-manifolds. We then prove an expression relating the Bergman tau function on a cover of the Hurwitz space, to the lifting of the function defined by Zograf on Teichmüller space, and another holomorphic function on the cover of the…
For arbitrary quantizable compact Kaehler manifolds, relations between the geometry given by the coherent states based on the manifold and the algebraic (projective) geometry realised via the coherent state mapping into projective space, are studied. Polar divisors, formulas relating the scalar products of coherent vec…
New lower bounds on the unknotting number of a knot are constructed from the classical knot signature function. These bounds can be twice as strong as previously known signature bounds. They can also be stronger than known bounds arising from Heegaard Floer and Khovanov homology. Results include new bounds on the Gordi…
Tail-GNNs improve protein function prediction using relational reinforcement.
New neural network models for complex functional data analysis.
A mass-type invariant for smooth metric measure spaces and its relation with the fractional Yamabe problem
The abstract conjectures a link between knot homologies and quiver partition functions.
Paper explores connections between loss functions and consistency in binary classification and regression.
Defines a new Upsilon torsion function for knot Floer homology.
We interpret the variational inference of the Stochastic Gradient Descent (SGD) as minimizing a new potential function named the \textit{quasi-potential}. We analytically construct the quasi-potential function in the case when the loss function is convex and admits only one global minimum point. We show in this case th…
The paper defines a new functional and proves related theorems for manifolds with boundary.
Defines concordance of Morse functions on manifolds and presents a condition.
The Witten deformation associated to a Morse function on a closed Riemannian manifold, via Rellich-Kato theorem, relates analytically the spectral package of the Riemannian manifold (eigenvalues and eigenforms) to the Morse complex defined by the pair (Morse function, Riemannian metric) coupled with the "multivariable …
The oriented framed Homfly skein C of the annulus provides the natural parameter space for the Homfly satellite invariants of a knot. It contains a submodule C+ isomorphic to the algebra of the symmetric functions. We collect and expand formulae relating elements expressed in terms of symmetric functions to Turaev's ge…
We show that the algebra of functions on the Grassmann supergroup Gr has a (graded) Hopf algebra structure related to GL.
This article introduces proximal cell complexes in a hyperconnected space. Hyperconnectedness encodes how collections of path-connected sub-complexes in a Alexandroff-Hopf-Whitehead CW space are near to or far from each other. Several main results are given, namely, a hyper-connectedness form of CW (Closure Finite Weak…
We study vector fields of the plane preserving the form of Liouville. We present their local models up to the natural equivalence relation, and describe local bifurcations of low codimension. To achieve that, a classification of univariate functions is given, according to a relation stricter than contact equivalence. W…
This paper deals with some simple results about spherical functions of type , namely new integral formulas, new results about behavior at infinity and some facts about the related functions.
Study of gauge theory blowups and Painlevé VI identity.
Unified cosmological and Einstein polytope theories.
Study connects hyperbolic geometry to membrane shapes.
Scharlemann and Thompson define the width of a 3-manifold M as a notion of complexity based on the topology of M. Their original definition had the property that the adjacency relation on handles gave a linear order on handles, but here we consider a more general definition due to Saito, Scharlemann and Schultens, in w…