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.
Internal Lagrangians derived from variational principles.
Clarifies relation between Pfaffian fibrations and relative algebroids.
New internal symmetry found for Lie pair algebra.
Extended symmetries and anomalies in compactified 6d SCFTs on various internal manifolds.
The geometrical theory of partial differential equations in the absolute sense, without any additional structures, is developed. In particular the symmetries need not preserve the hierarchy of independent and dependent variables. The order of derivatives can be changed and the article is devoted to the higher--order in…
We exploit the symmetry concepts developed in the companion review of this article to introduce a stochastic version of link reversal symmetry, which leads to an improved understanding of the reciprocity of directed networks. We apply our formalism to the international trade network and show that a strong embedding in …
Transformers reduce redundancy by focusing on invariant relational quantities.
Synthetic theory defines orbifolds as microlinear types with finite identifications.
New approach to Lagrangian systems using intrinsic geometry.
We scan for massive type IIA SU(3)-structure compactifications of the type AdS4 x CP3 with internal symmetry group SO(4). This group acts on CP3 with cohomogeneity one, so that one would expect new non-homogeneous solutions. We find however that all such solutions enhance their symmetry group to Sp(2) and form, in fact…
We introduce defects, with internal gauge symmetries, on a knot and Seifert surface to a knot into the combinatorial construction of finite gauge-group Dijkgraaf-Witten theory. The appropriate initial data for the construction are certain three object categories, with coefficients satisfying a partially degenerate cocy…
The article provides a modest survey of the absolute theory of general systems of (partial) differential equations. The equations are relieved of all additional structures and subject to quite arbitrary change of the variables. An abstract mathematical theory in the Bourbaki sense with its own concepts and technical to…
In this paper, from the viewpoint of completeness of Marsden-Weinstein reduction, we illustrate how to give the definitions of a controlled Hamiltonian (CH) system and a reducible controlled Hamiltonian system with symmetry; and how to describe the dynamics of a CH system and the controlled Hamiltonian equivalence; as …
This foreword discusses the contributions of Bolyai, Gauss, and Lobachevsky to non-Euclidean geometry.
Survey of recent developments in symmetric reductions and controls for Hamiltonian systems.
This thesis is divided into four chapters. The first chapter discusses the relationship between stacks on a site and groupoids internal to the site. It includes a rigorous proof of the folklore result that there is an equivalence between the bicategory of internal groupoids and the bicategory of geometric stacks. The s…
Symmetry in neural networks affects generalization, as shown by CLT and RG transformations.
New method constructs geometric flat outputs for robotic systems using symmetry.
While the fundamental object in Riemannian geometry is a metric, closed string theories call for us to put a two-form gauge field and a scalar dilaton on an equal footing with the metric. Here we propose a novel differential geometry which treats the three objects in a unified manner, manifests not only diffeomorphism …
We revisit the backgrounds of type IIB on manifolds with -structure and discuss two sets of solutions arising from internal geometries that are complex and symplectic respectively. Both can be realized in terms of generalized complex geometry. We identify a map which relates the complex and symplectic supersymme…
For For a given PDE system, or an exterior differential system possessing a Lie group of internal symmetries the orbit reduction procedure is introduced. It is proved that the solutions of the reduced exterior differential system are in one-to-one correspondence with the moduli space of regular solutions of the prolong…
We give a complete and explicit description of the kinematical data of higher gauge theory on principal 2-bundles with the string 2-group model of Schommer-Pries as structure 2-group. We start with a self-contained review of the weak 2-category Bibun of Lie groupoids, bibundles and bibundle morphisms. We then construct…
Lie groupoids generalize Lie groups with multiplication defined for certain pairs.
We define and examine the notion of a Killing section of a Riemannian Lie algebroid as a natural generalisation of a Killing vector field. We show that the various expression for a vector field to be Killing naturally generalise to the setting of Lie algebroids. As an application we examine the internal symmetries of a…
Mapper and Ball Mapper tools for complex data analysis.
In this paper, we first give the regular point reduction and the two types of Hamilton-Jacobi equation for a regular controlled Hamiltonian (RCH) system with symmetry and momentum map on the generalization of a semidirect product Lie group. Next, as an application of the theoretical results, we consider the underwater …
We study supersymmetric probe M5-branes in the AdS_4 solution that arises from M5-branes wrapped on a hyperbolic 3-manifold M_3. This amounts to introducing internal defects within the framework of the 3d-3d correspondence. The BPS condition for a probe M5-brane extending along all of AdS_4 requires it to wrap a surfac…
New findings on neural network identifiability using affine symmetries.
A group, defined as set with associative multiplication and inverse, is a natural structure describing the symmetry of a space. The concept of group generalizes to group objects internal to other categories than sets. But there are yet more general objects that can still be thought of as groups in many ways, such as qu…
In this article we give the realization of the Klein's Program for geometrical structures (Riemannian spaces and fiber bundles with connection) with arbitrary variable curvature within the framework of infinite deformed groups. These groups generalize gauge groups to the case of nontrivial action on the base space of b…
We relate a Chaplygin type system to a Cartan decomposition of a real semi-simple Lie group. The resulting system is described in terms of the structure theory associated to the Cartan decomposition. It is shown to possess a preserved measure and when internal symmetries are present these are factored out via a process…
This paper is devoted to the problem of choosing the most suitable model of a geometrical system for describing the real crystallographic space. It has been shown that all 230 crystallographic groups used to describe the crystalline structures in a Euclidean space can be presented by elliptic motions in the closed spac…
A n n-body system is a labelled collection of n point masses in Euclidean space, and their congruence and internal symmetry properties involve a rich mathematical structure which is investigated in the framework of equivariant Riemannian geometry. Some basic concepts are n-configuration, configuration space, internal s…
Model predicts internal fraud in retail banking is cyclical and influenced by corruption.
Humans are capable of building holistic representations for images at various levels, from local objects, to pairwise relations, to global structures. The interpretation of structures involves reasoning over repetition and symmetry of the objects in the image. In this paper, we present the Program-Guided Image Manipula…
The article treats the geometrical theory of partial differential equations in the absolute sense, i.e., without any additional structures and especially without any preferred choice of independent and dependent variables. The equations are subject to arbitrary transformations of variables in the widest possible sense.…
The 1950's foundational literature on rational mechanics exhibits two somewhat distinct paradigms to the representation of continuous distributions of defects in solids. In one paradigm, the fundamental objects are geometric structures on the body manifold, e.g., an affine connection and a Riemannian metric, which repr…
Neural networks learn task-specific features, influenced by nonlinearity.
Examines international taxation's impact on Georgian businesses.
Study presents a method to induce a generalized neural network from joint group invariant functions.
Optimized execution model using interbank and internal liquidity.
This study assesses how economic shocks affect the efficiency and robustness of international pesticide trade networks.
SPTN uses invertible transformations to improve sum-product networks.
We study supersymmetric AdS backgrounds of eleven-dimensional or type II supergravity preserving supersymmetries using generalised geometry. We show that a large class correspond precisely to spaces admitting a generalised structure with a weak integrability condition, which we cal…
Paper introduces Modular Jets for diagnosing model decompositions in pipelines.
There are few papers about the international trade of flowers, so it is believed that this paper, with this topic, could be an important contribution to the international scientific community. It is intended to analyze if the international trade flowers tendencies and policies are adapted to the actual world global con…
Spain uses DEA to select international markets for exports.
Improved speech recognition model with better performance.