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.
Paper explores limits of distributed dislocations in geometric and constitutive paradigms.
Unified theory for curved shell deformations with elastic and inelastic components.
In this work we apply the Poincare-Cartan formalism of the Classical Field Theory to study the systems of balance equations (balance systems). We introduce the partial k-jet bundles of the configurational bundle and study their basic properties: partial Cartan structure, prolongation of vector fields, etc. A constituti…
Over 50 million scholarly articles have been published: they constitute a unique repository of knowledge. In particular, one may infer from them relations between scientific concepts, such as synonyms and hyponyms. Artificial neural networks have been recently explored for relation extraction. In this work, we continue…
These notes constitute a sort of Crash Course in Optimal Transport Theory. The different features of the problem of Monge-Kantorovitch are treated, starting from convex duality issues. The main properties of space of probability measures endowed with the distances induced by optimal transport are detailed. The ke…
We analyzed multifractal properties of 5-minute stock returns from a period of over two years for 100 highly capitalized American companies. The two sources: fat-tailed probability distributions and nonlinear temporal correlations, vitally contribute to the observed multifractal dynamics of the returns. For majority of…
Factorable surfaces, i.e. graphs associated with the product of two functions of one variable, constitute a wide class of surfaces. Such surfaces in the pseudo-Galilean space with zero Gaussian and mean curvature were obtained in [1]. In this study, we provide new classification results relating to the factorable surfa…
Extracts biological context from biomedical texts to associate with events.
A framework detects where constitutive models fail in elastography, improving clinical interpretation.
TANNs integrate thermodynamics into ANN models for accurate, consistent predictions.
The Hessian Topology is a subject having interesting relations with several areas, for instance, differential geometry, implicit differential equations, analysis and singularity theory. In this article we study the problem of realization of a real plane curve as the Hessian curve of a smooth function. The plane curves …
Using very weak criteria for what may constitute a noncommutative geometry, I show that a pseudo-Riemannian manifold can only be smoothly deformed into noncommutative geometries if certain geometric obstructions vanish. These obstructions can be expressed as a system of partial differential equations relating the metri…
Automated framework generates mechanical models via deep reinforcement learning.
We prove short time existence and uniqueness of the Laplacian flow starting at an arbitrary closed -structure. We establish long time existence and convergence of the Laplacian flow starting near a torsion-free -structure. We analyze the limit map of the Laplacian flow in relation to the moduli space of torsi…
Paper explores how text generation quality and diversity metrics relate to distribution fitting.
A hybrid method combines model-based and data-driven approaches for multiscale constitutive responses.
The paper introduces austere and arid submanifolds in Hilbert spaces.
We present a variational formulation of electrodynamics using de Rham even and odd differential forms. Our formulation relies on a variational principle more complete than the Hamilton principle and thus leads to field equations with external sources and permits the derivation of the constitutive relations. We interpre…
We formulate the laws governing the dynamics of a crystalline solid in which a continuous distribution of dislocations is present. Our formulation is based on new differential geometric concepts, which in particular relate to Lie groups. We then consider the static case, which describes crystalline bodies in equilibriu…
Starting from suitable tableaux over finite dimensional Lie algebras, we provide a scheme for producing involutive linear Pfaffian systems related to various classes of submanifolds in homogeneous spaces which constitute integrable systems. These include isothermic surfaces, Willmore surfaces, and other classical solit…
We prove that the torsion of any closed space curve which bounds a simply connected locally convex surface vanishes at least 4 times. This answers a question of Rosenberg related to a problem of Yau on characterizing the boundary of positively curved disks in Euclidean space. Furthermore, our result generalizes the 4 v…
Study on materials with disclinations, limiting their size.
Given a linearly ordered set I, every surjective map p: A --> I endows the set A with a structure of set of preferences by "replacing" the elements of I with their inverse images via p considered as "balloons" (sets endowed with an equivalence relation), lifting the linear order on A, and "agglutinating" this structure…
We consider the generalized Kahler structures (g,J_+,J_-) that arise on a hyperkahler manifold (M,g,I,J,K) when we choose J_+ and J_- from the twistor space of M. We find a relation between semichiral and arctic superfields which can be used to determine the generalized Kahler potential for hyperkahler manifolds whose …
Kernelized PCovR reveals structure-property relations in chemistry and materials.
Predict player lifetime value based on engagement metrics.
Researchers solve Yamabe problems for specific operators, finding both uniqueness and nonuniqueness.
New algorithm clusters sparse data effectively.
Optimal transport for vector Gaussian mixtures improves efficiency and structure preservation.
Machine Learning community is recently exploring the implications of bias and fairness with respect to the AI applications. The definition of fairness for such applications varies based on their domain of application. The policies governing the use of such machine learning system in a given context are defined by the c…
Performance of investment managers are evaluated in comparison with benchmarks, such as financial indices. Due to the operational constraint that most professional databases do not track the change of constitution of benchmark portfolios, standard tests of performance suffer from the "look-ahead benchmark bias," when t…
Principal binets generalize curvature line surfaces to square lattices and are a discrete integrable system.
We prove that a group obtained as a quotient of the free product of finitely many cubulable groups by a finite set of relators satisfying the classical --small cancellation condition is cubulable. This yields a new large class of relatively hyperbolic groups that can be cubulated, and constitutes the first ins…
We review the Burghelea conjecture, which constitutes a full computation of the periodic cyclic homology of complex group rings, and its relation to the algebraic Baum-Connes conjecture. The Burghelea conjecture implies the Bass conjecture. We state two conjectures about groups of finite asymptotic dimension, which tog…
We introduce the Γ-extension of the spectrum of the Laplacian of a Riemannian orbifold, where Γis a finitely generated discrete group. This extension, called the Γ-spectrum, is the union of the Laplace spectra of the Γ-sectors of the orbifold, and hence constitutes a Riemannian invariant that is directly related to the…
This study classifies quadric surfaces in 3-sphere as Weingarten surfaces.
In this paper we introduce the notion of exact links, which constitute a broad class of high dimensional links.
New flatness measure for deep networks invariant to scaling.
In the spirit of Klein's Erlangen Program, we investigate the geometric and algebraic structure of fundamental line complexes and the underlying privileged discrete integrable system for the minors of a matrix which constitute associated Plücker coordinates. Particular emphasis is put on the restriction to Lie circle g…
Elasticity images map biomechanical properties of soft tissues to aid in the detection and diagnosis of pathological states. In particular, quasi-static ultrasonic (US) elastography techniques use force-displacement measurements acquired during an US scan to parameterize the spatio-temporal stress-strain behavior. Curr…
A natural occurrence of shift equivalence in a purely algebraic setting constitutes the subject matter of the following short exposition.
This work proposes a hybrid method for error detection in noisy Knowledge Graphs.
Shot-Noise processes constitute a useful tool in various areas, in particular in finance. They allow to model abrupt changes in a more flexible way than processes with jumps and hence are an ideal tool for modelling stock prices, credit portfolio risk, systemic risk, or electricity markets. Here we consider a general f…
In this work we show that the systems of balance equations (balance systems) of continuum thermodynamics occupy a natural place in the variational bicomplex formalism. We apply the vertical homotopy decomposition to get a local splitting (in a convenient domain) of a general balance system as the sum of a Lagrangian pa…
Majorizing measures control sequential complexities for online learning.
Discussing the need for explainable AI in various fields.
The high pay packages of U.S. CEOs have raised serious concerns about what would constitute a fair pay.
The study examines necessary conditions for Mabuchi solitons on Fano manifolds and their relation to Ding stability.