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.
Improves Bayesian optimization by focusing on well-behaved structure in objectives.
Starting from the recent classification of quotients of Freund--Rubin backgrounds in string theory of the type AdS_{p+1} x S^q by one-parameter subgroups of isometries, we investigate the physical interpretation of the associated quotients by discrete cyclic subgroups. We establish which quotients have well-behaved cau…
Researchers develop multi-utility representations for incomplete preferences linked to risk measures.
Study of Ricci iterations on Kähler metrics, proving new theorems.
We introduce the notion of an EZ-structure on a group. Delta-hyperbolic groups and CAT(0)-groups have EZ-structures. We show torsion-free groups having an EZ-structure automatically have an action by homeomorphisms on a closed (high-dimensional) ball, which is well-behaved away from a "bad limit set" in the boundary of…
A generalization of expectiles for d-dimensional multivariate distribution functions is introduced. The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by d-dimensional vectors. They are well behaved under common data transformations and the corresponding sample v…
New research shows logistic regression can achieve optimal error rate for agnostic learning of halfspaces.
Study Lie algebras with complex structures, focusing on degenerations and deformations.
Paper proves Whitney stratified spaces can be given a conically smooth structure.
We consider a model for linear transient price impact for multiple assets that takes cross-asset impact into account. Our main goal is to single out properties that need to be imposed on the decay kernel so that the model admits well-behaved optimal trade execution strategies. We first show that the existence of such s…
Study of isometries in spacetimes without observer horizons.
We introduce a novel approach, requiring only mild assumptions, for the characterization of deep neural networks at initialization. Our approach applies both to fully-connected and convolutional networks and easily incorporates batch normalization and skip-connections. Our key insight is to consider the evolution with …
We construct BCOV invariant for Calabi-Yau pairs. The construction covers the classical BCOV invariant and certain equivariant BCOV invariant. The BCOV invariant obtained is expected to be well-behaved under birational equivalence.
A projection maps geodesic currents to Teichmüller space.
In order to look for a well-behaved counterpart to Dolbeault cohomology in D-complex geometry, we study the de Rham cohomology of an almost D-complex manifold and its subgroups made up of the classes admitting invariant, respectively anti-invariant, representatives with respect to the almost D-complex structure, miming…
Causality violations are typically seen as unrealistic and undesirable features of a physical model. The following points out three reasons why causality violations, which Bonnor and Steadman identified even in solutions to the Einstein equation referring to ordinary laboratory situations, are not necessarily undesirab…
Paper shows geometric properties preserved by compactifications in relation to coarse structures and group actions.
Because no closed timelike curve (CTC) on a Lorentzian manifold can be deformed to a point, any such manifold containing a CTC must have a topological feature, to be called a timelike wormhole, that prevents the CTC from being deformed to a point. If all wormholes have horizons, which typically seems to be the case in …
Recent years have seen adversarial losses been applied to many fields. Their applications extend beyond the originally proposed generative modeling to conditional generative and discriminative settings. While prior work has proposed various output activation functions and regularization approaches, some open questions …
The article investigates conditions for isomorphism of singular tangent bundles.
Higher-dimensional spacetimes have well-behaved boundaries.
In a previous paper, we generalized the definition of the framed Kontsevich integral initially presented by Le and Murakami. We also defined an isotopy invariant that is well-behaved under band sum moves. Using this invariant we study the construction of the LMO invariant, the Wheeling Theorem, and th…
Extends Gaussian process regression for non-Gaussian data.
Every oriented 4-manifold admits a folded symplectic structure, which in turn determines a homotopy class of compatible almost complex structures that are discontinuous across the folding hypersurface ("fold") in a controlled fashion. We define folded holomorphic maps, i.e. pseudo-holomorphic maps that are discontinuou…
Let f be an integer greater than one. We study three progressively finer equivalence relations on closed 3-manifolds generated by Dehn surgery with denominator f: weak f-congruence, f-congruence, and strong f-congruence. If f is odd, weak f-congruence preserves the ring structure on cohomology with Z_f-coefficients. We…
We determine loop space decompositions of simply-connected four-manifolds, -connected -dimensional manifolds provided , and connected sums of products of two spheres. These are obtained as special cases of a more general loop space decomposition of certain torsion-free -complexes with wel…
The paper introduces orbifold-like -manifolds with tame properties.
The paper develops glueing theory for topological spaces and applies it to compactifications.
We survey work on the topology of the space AH(M) of all (marked) hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold M with boundary. The interior of AH(M) is quite well-understood, but the topology of the entire space can be quite complicated. However, the topology is well-behaved at many points …
We prove that any regular integral invariant of volume-preserving transformations is equivalent to the helicity. Specifically, given a functional defined on exact divergence-free vector fields of class on a compact 3-manifold that is associated with a well-behaved integral kernel, we prove that $\mat…
Investigates point spectra of vector fields and their properties.
We realise the first and second Grushin distributions as symmetry reductions of the 3-dimensional Heisenberg distribution and 4-dimensional Engel distribution respectively. Similarly, we realise the Martinet distribution as an alternative symmetry reduction of the Engel distribution. These reductions allow us to derive…
I'll describe a general geometric setup allowing for a generalization of Rehren duality to asymptotically anti-de Sitter spacetimes whose classical matter distribution is sufficiently well-behaved as to prevent the occurence of singularities in the sense of null geodesic incompleteness. I'll also comment on the issues …
New 4-manifold invariants from Khovanov-Rozansky link homology.
New kriging method improves mean estimation and uncertainty.
We construct an extension of the Kontsevich integral of knots to knotted trivalent graphs, which commutes with orientation switches, edge deletions, edge unzips, and connected sums. In 1997 Murakami and Ohtsuki [MO] first constructed such an extension, building on Drinfel'd's theory of associators. We construct a step …
We show that the Big Bang singularity of the Friedmann-Lemaitre-Robertson-Walker model does not raise major problems to General Relativity. We prove a theorem showing that the Einstein equation can be written in a non-singular form, which allows the extension of the spacetime before the Big Bang. The physical interpret…
New algorithm optimizes contextual bandits with adaptive exploration.
Two algorithms converge to dictionary learning with geometric rate for non-uniform data.
The Fourier transform of Heegaard Floer d-invariants helps classify 3-manifolds.
Solves parameter non-identifiability in Bayesian LTI system identification.
We study the hypersymplectic geometry of the moduli space of solutions to Hitchin's harmonic map equations on a -bundle. This is the split-signature analogue of Hitchin's Higgs bundle moduli space. Due to the lack of definiteness, this moduli space is globally not well-behaved. However, we are able to construct a sm…
In this work we will focus on the causal character of Carter Spacetime (see B. Carter, Causal structure in space-time, Gen. Rel. Grav. 1 4 337-406, 1971). The importance of this spacetime is the following: for the causally best well behaved spacetimes (the globally hyperbolic ones), there are several characterizations …
New characterization limits sampling with inexact scores.
Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a well-behaved kernel function with smoothness assumptions. We remove the smoothness assumption and generalize the analysis of graph Laplacians to include previously unstudied graphs including kNN graphs. We also introduce a kernel-fr…
Gradient methods work well on overparameterized diagonal linear networks.
The paper introduces new cohomologies and studies harmonic forms on almost complex manifolds.
The manifold hypothesis states that many kinds of high-dimensional data are concentrated near a low-dimensional manifold. If the topology of this data manifold is non-trivial, a continuous encoder network cannot embed it in a one-to-one manner without creating holes of low density in the latent space. This is at odds w…