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.
Determinants remain constant along specific families of differential operators.
We prove an optimal systolic inequality for CAT(0) metrics on a genus~2 surface. We use a Voronoi cell technique, introduced by C.~Bavard in the hyperbolic context. The equality is saturated by a flat singular metric in the conformal class defined by the smooth completion of the curve y^2=x^5-x. Thus, among all CAT(0) …
SGD without replacement decouples into curvature-following and flatness-regularizing steps.
Study shows how to deform foliated manifolds with flat leaves, leading to geometric characterization.
Ricci curvature was proposed by Ollivier in a general framework of metric measure spaces, and it has been studied extensively in the context of graphs in recent years. In this paper we prove upper bounds for Ollivier's Ricci curvature for bipartite graphs and for the graphs with girth at least 5. We also prove a genera…
The study analyzes implicit biases in neural networks using backward error analysis.
The authors define some secondary characteristic homomorphism for the triple (A,B,\bigtriangledown), in which B\subset A is a pair of regular Lie algebroids over the same foliated manifold and \bigtriangledown:L\rightarrow A is a homomorphism of Lie algebroids (i.e. a flat L-connection in A) where L is an arbitrary (no…
New measure shows various training techniques control model complexity.
The paper studies foliations on smooth projective varieties and their properties.
It is shown that in a tower of coverings the regularized determinant of a generalized Laplacian converges to the -determinant. This shows generic nontriviality of analytic torsion or regularized determinants since the -counterparts are easier to compute. We further have an "Euler product expansion" for regula…
We investigate the Gram determinant of the bilinear form based on curves in a planar surface, with a focus on the disk with two holes. We prove that the determinant based on curves divides the determinant based on curves. Motivated by the work on Gram determinants based on curves in a disk and curves in an an…
Determinant modulo 8 classifies virtual knots based on polynomial coefficients.
Abstract: Determinants and formulas for operators on various spaces.
Paper computes link determinants using Fourier-Hadamard transforms.
Study on Laplacian determinant in isosceles triangles, finding equilateral triangle minimizes determinant.
Study shows exponential growth of Laplacian determinant on random hyperbolic surfaces.
An algorithm determines knot colorability and determinants from petal projections.
Study Gram determinants in knot theory, focusing on a Möbius band determinant.
Identifies images of determinant morphism for specific co-Higgs bundles.
We study the zeta determinant of global boundary problems of APS-type through a general theory for relative spectral invariants. In particular, we compute the zeta determinant for Dirac-Laplacian boundary problems in terms of a scattering Fredholm determinant over the boundary.
Paper introduces VDE, a variance-reduced determinant estimator.
Unified determinants via a single equation.
We give definitions of cohomology determinants for compact, connected, orientable 3-manifolds. We also give formulae relating cohomology determinants before and after gluing a solid torus along a torus boundary component. Cohomology determinants are related to Turaev torsion, though the author hopes that they have othe…
The Gram determinant of type was introduced by Lickorish in his work on invariants of 3 - manifolds. We generalize the theory of the Gram determinant of type by evaluating, in the annulus, a bilinear form of non-intersecting connections in the disc. The main result provides a closed formula for this Gram determ…
We compute the relative zeta-function metric on the determinant line bundle for a family of elliptic boundary value problems of Dirac-type. To do this we prove a general formula relating the zeta-determinant to a Fredholm determinant over the boundary for a class of higher-order elliptic boundary value problems.
The paper connects Chebyshev polynomials and Gram determinants on Möbius bands.
New Gram determinant from Möbius band connects to annulus case.
Study on pseudo-Einstein 3-manifolds, calculating determinant changes under conformal transformations.
Topologies on algebraic and equational theories are used to define germ determined, near-point determined, and point determined rings of smooth functions, without requiring them to be finitely generated. It is proved, that any commutative algebra morphism (without requiring continuity) between near-point determined rin…
Determinants of theta curves and symmetric graphs are studied.
The purpose of this paper is to present the construction of a canonical determinant functional on elliptic pseudodifferential operators associated to the Guillemin-Wodzicki residue trace. The resulting functional is multiplicative, a local invariant, and not defined by a regularization procedure. The residue determinan…
We study the asymptotic behaviour of regularized determinants of certain Laplace type operators with respect to singular deformations of the underlying manifold which are obtained by stretching a tubular neighborhood of an embedded separating hypersurface to a cylinder of infinite length. Using the asymptotic expansion…
Stochastic representation for determinants derived from Brownian loop soups.
Researchers compute zeta-determinants and analytic torsion for metric mapping tori.
Formula found for knot determinant in 3-braid weaving.
We compute the curvature of the determinant line bundle on a family of Dirac operators for a noncommutative two torus. Following Quillen's original construction for Riemann surfaces and using zeta regularized determinant of Laplacians, one can endow the determinant line bundle with a natural Hermitian metric. By using …
We obtain generalizations of some results of Turaev relating leading order terms of the Turaev torsion of closed, oriented, connected 3-manifolds to certain ``determinants'' derived from cohomology operations such as the alternate trilinear form on the first cohomology group given by cup product. These determinants unf…
The volume density of a hyperbolic link is defined as the ratio of hyperbolic volume to crossing number. We study its properties and a closely-related invariant called the determinant density. It is known that the sets of volume densities and determinant densities of links are dense in the interval [0,v_{oct}]. We cons…
We study the geometry and partial differential equations arising from the consideration of Frobenius determinants, also called-group-determinants. This leads us to address some aspects of twistor theory as well as some extensions of Bessel functions.
Paper discusses gluing formula for zeta-determinants with Robin boundary condition.
New proof limits Jones polynomial values for quasi-alternating links.
Algorithms for Gaussian process, marginal likelihood methods or restricted maximum likelihood methods often require derivatives of log determinant terms. These log determinants are usually parametric with variance parameters of the underlying statistical models. This paper demonstrates that, when the underlying matrix …
We construct a determinant of the Laplacian for infinite-area surfaces which are hyperbolic near infinity and without cusps. In the case of a convex co-compact hyperbolic metric, the determinant can be related to the Selberg zeta function and thus shown to be an entire function of order two with zeros at the eigenvalue…
We explain the bundle structures of the {\it Determinant line bundle} and the {\it Quillen determinant line bundle} considered on the connected component of the space of Fredholm operators including the identity operator in an intrinsic way. Then we show that these two are isomorphic and that they are non-trivial line …
Study uniquely determines Riemannian metric derivatives from boundary data.
In \cite{BR1}, \cite{BR2}, a parabolic determinant line bundle on a moduli space of stable parabolic bundles was constructed, along with a Hermitian structure on it. The construction of the Hermitian structure was indirect: The parabolic determinant line bundle was identified with the pullback of the determinant line b…
Traditionally introduced in terms of advanced topological constructions, many link invariants may also be defined in much simpler terms given their values on a few initial links and a recursive formula on a skein triangle. Then the crucial question to ask is how many initial values are necessary to completely determine…
Researchers found counterexamples to a 2-jet determination theorem in higher codimension.