arXiv research

Foundation for robust finance using rough path theory.

CURIE uses cellular automata to detect concept drift in data streams.

In this paper, we study Jacobi operators associated to algebraic curvature maps (tensors) on lightlike submanifolds M. We investigate conditions for an induced Rie- mann curvature tensor to be an algebraic curvature tensor on M. We introduce the notion of lightlike Osserman submanifolds and an example of 2-degenerate O…

Bayes-optimal learning of a neural network with quadratic activations is achieved with GAMP-RIE.

Historically tensor calculus emerged in an attempt to formalize Rie- mann's ideas. We show that tensor calculus can be based also on Lie's idea of a transformation group and this approach leads quite naturally to the concept of deformation of a transformation group and the Kodaira- Spencer map.

Fino and Kath determined all possible holonomy groups of seven-dimensional pseu\-do-Rie\-man\-nian manifolds contained in the exceptional, non-compact, simple Lie group $\mathrm{G}_2^*$ via the corresponding Lie algebras. They are distinguished by the dimension of their maximal semi-simple subrepresentation on the tang…

This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free Probability, with an emphasis on the Marchenko-Pastur equation that provides informatio…

We present new methods to estimate causal effects retrospectively from micro data with the assistance of a machine learning ensemble. This approach overcomes two important limitations in conventional methods like regression modeling or matching: (i) ambiguity about the pertinent retrospective counterfactuals and (ii) p…

Regularization-induced exploration improves contextual bandit performance.

New ladder methods improve numerical accuracy in parallel transport on manifolds.

External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighoring agents. Several critical constellations determine whether this cascade remains finite or reaches the size o…

The asymptotic concentration of the Fr{é}chet mean of IID random variables on a Rieman-nian manifold was established with a central limit theorem by Bhattacharya \& Patrangenaru (BP-CLT) [6]. This asymptotic result shows that the Fr{é}chet mean behaves almost as the usual Euclidean case for sufficiently concentrated di…

Groups with Property (T) have fiber products with Property (T).

We prove recognition theorems for codimension one manifold factors of dimension $n \geq 4$. In particular, we formalize topographical methods and introduce three ribbons properties: the crinkled ribbons property, the twisted crinkled ribbons property, and the fuzzy ribbons property. We show that $X \times \mathbb{R}$ i…

The study shows that several properties are not profinite invariants.

We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note …

The paper explores higher property T in lattices and its connections to geometric phenomena.

Asymptotic property C was introduced by Dranishnikov to study spaces with infinite asymptotic dimension. We show that asymptotic property C is preserved by infinite products. We also show that countable restricted direct products of countable groups with finite asymptotic dimension have asymptotic property C. Then we i…

Groups of importance in group theory have flexible stability properties.

This paper generalizes property (QT) to a broader class of groups.

Proves a vanishing property for symplectic manifold cohomology.

Survey on foliations and diffeomorphism groups.

We prove extension theorems for several geometric properties such as asymptotic property C (APC), finite decomposition complexity (FDC), strict finite decomposition complexity (sFDC) which are weakenings of Gromov's finite asymptotic dimension (FAD). The context of all theorems is a finitely generated group $G$ with a …

Study generalizes property elicitation to imprecise probabilities.

Introduces bounded scale measure and generalizes property A.

Study cohomological and metric properties of non-Kähler complex manifolds.

The paper explores the twisted Rokhlin property in mapping class groups of surfaces.

The balance property is crucial for insurance pricing, ensuring total actuarial price equals loss. Maximum likelihood GLMs fulfill it, but Lindholm-Wüthrich suggests three methods, with constrained GLM being superior.

We prove some general results about quasi-actions on trees and define Property (QFA), which is analogous to Serre's Property (FA), but in the coarse setting. This property is shown to hold for a class of groups, including $SL(n,\Z)$ for $n\geq 3$. We also give a way of thinking about Property (QFA) by breaking it down …

We present examples of metric spaces that are not Riemannian manifolds nor dimensionally homogeneous that satisfy the Tetrahedral Property. In spite of that, Euclidean cones over metric spaces with small diameter do not satisfy this property. We extend Sormani's Tetrahedral Property to a less restrictive property and p…

The paper examines curvature properties of twistor spaces.

Study Finsler metric measure manifolds' concentration properties.

Paper proves naturally reductive property is inaudible for certain manifolds.

Hybrid clustering combines partitional and hierarchical clustering for computational effectiveness and versatility in cluster shape. In such clustering, a dissimilarity measure plays a crucial role in the hierarchical merging. The dissimilarity measure has great impact on the final clustering, and data-independent prop…

3-manifold groups have a property that allows them to act on quasi-trees.

The average shadowing property is considered for set-valued dynamical systems, generated by parameterized IFS, which are uniformly contracting, or conjugacy, or products of such ones. We also prove that if a continuous surjective IFS F on a compact metric space X has the aver- age shadowing property, then every point x…

Simplicial spheres have a weak Lefschetz property in characteristic 2.

A property, or statistical functional, is said to be elicitable if it minimizes expected loss for some loss function. The study of which properties are elicitable sheds light on the capabilities and limitations of point estimation and empirical risk minimization. While recent work asks which properties are elicitable, …

In this article, we survey recent developments in defining the quasi-local mass in general relativity. We discuss various approaches and the properties and applications of the different definitions. Among the expected properties, we focus on the rigidity property: for a surface in the Minkowski spacetime, one expects t…

Groups with hyperbolic properties don't have strong Property (T).

Paper proposes a method to design molecules with specific properties.

The paper tests properties of trees in graphical models using covariance queries.

Discussing rigidity properties of conics, inspired by billiards in ellipses.

Paper offers a framework for estimating symmetric properties efficiently.

The paper studies groups with proper actions on finite products of hyperbolic spaces.

The paper proves properties of strain tensors on surfaces with changing Gauss curvature.

Investigates maps and properties in spaces with negative dimensions and curvature.

Graph networks struggle with multi-task learning due to varying property loss surface curvatures.