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.
New method improves graph neural networks by considering different types of relations in sampling.
TaRP predicts missing relations in KGs using type and instance-level info.
New method for learning on heterogeneous graphs without meta-paths.
Legendre transformations link related integrable hierarchies.
In the present work, the integrable bi-Hamiltonian hierarchies related to compatible nonlocal Poisson brackets of hydrodynamic type are effectively constructed. For achieving this aim, first of all, the problem on the canonical form of a special type for compatible nonlocal Poisson brackets of hydrodynamic type is solv…
Nodes in a multiplex network are connected by multiple types of relations. However, most existing network embedding methods assume that only a single type of relation exists between nodes. Even for those that consider the multiplexity of a network, they overlook node attributes, resort to node labels for training, and …
This paper aims at the problem of link pattern prediction in collections of objects connected by multiple relation types, where each type may play a distinct role. While common link analysis models are limited to single-type link prediction, we attempt here to capture the correlations among different relation types and…
Extends A-type coefficient polynomials to B-type setting, introducing new invariants.
We explore a Pluecker-type relation which occurs naturally in the study of maximally supersymmetric solutions of certain supergravity theories. This relation generalises at the same time the classical Pluecker relation and the Jacobi identity for a metric Lie algebra and coincides with the Jacobi identity of a metric n…
The paper explores various surgery equivalence relations on 3-manifolds.
Study proves existence of Kähler-Einstein metrics and Ricci flat Kähler metrics in 4-manifolds.
Advances combinatorial complexes for better modeling of hierarchical and set-type relations.
Study relates Finsler structures to Clifford bundles for flat metrics.
We define a Weyl-type curvature tensor of -type to provide a characterization for Finsler metrics of constant flag curvature. This Weyl-type curvature tensor is projective invariant only to projective factors that are Hamel functions. Based on this aspect we construct new families of projectively related Finsler…
In this paper we consider all possible generalizations of the B-type Hecke algebras, namely the cyclotomic and what we call 'generalized', and we construct Markov traces on each of them, so as to obtain all possible different levels of homfly-pt analogues in the solid torus related to the (Hecke) algebras of B-type.
A mass-type invariant for smooth metric measure spaces and its relation with the fractional Yamabe problem
The paper explores gaps in curvature-related metrics and rigidity.
Two results on end spaces of infinite type surfaces, answering questions about their topology and equivalence.
Study relates Gaussian curvature signs to cuspidal edge types and geometric invariants.
The success of recommender systems in modern online platforms is inseparable from the accurate capture of users' personal tastes. In everyday life, large amounts of user feedback data are created along with user-item online interactions in a variety of ways, such as browsing, purchasing, and sharing. These multiple typ…
Many researchers both in academia and industry have long been interested in the stock market. Numerous approaches were developed to accurately predict future trends in stock prices. Recently, there has been a growing interest in utilizing graph-structured data in computer science research communities. Methods that use …
In~\cite{Kim} the author generalized the Conway algebra and constructed the invariant valued in the generalized Conway algebra defined by applying two skein relations to crossings, which is called a generalized Conway type invariant. The generalized Conway type invariant is a generalization of Homflypt polynomial. In t…
The paper proves finite topological type theorems for open manifolds with non-negative Ricci curvature and almost maximal local rewinding volume.
The paper derives new Gauss-Bonnet formulas for frontal bundles over surfaces with boundary.
This paper focuses on a traditional relation extraction task in the context of limited annotated data and a narrow knowledge domain. We explore this task with a clinical corpus consisting of 200 breast cancer follow-up treatment letters in which 16 distinct types of relations are annotated. We experiment with an approa…
In this paper we describe how to define the circle packing (cp) type(either cp parabolic or cp hyperbolic) of a Riemann surface of class , and study the relation between this type and the conformal type of the surface.
We present an analysis of the problem of identifying biological context and associating it with biochemical events in biomedical texts. This constitutes a non-trivial, inter-sentential relation extraction task. We focus on biological context as descriptions of the species, tissue type and cell type that are associated …
We establish in this note some Cauchy-Schwarz-type inequalities on compact Kähler manifolds, which generalize the classical Khovanskii-Teissier inequalities to higher-dimensional cases. Our proof is to make full use of the mixed Hodge-Riemann bilinear relations due to Dinh and Nguyn. A proportionality p…
Real projective surfaces with Hitchin holonomy can be related via grafting.
The study extends knot theory to knotoids using two approaches.
Paper constructs a HOMFLYPT-type invariant for pseudo links.
Let be a non-negative self-adjoint Laplace type operator acting on sections of a hermitian vector bundle over a closed Riemannian manifold. In this paper we review the close relations between various -related coefficients such as the mollified spectral counting coefficients, the heat trace coefficients, the reso…
Delta finite-type invariants are defined analogously to finite-type invariants, using delta moves instead of crossing changes. We show that they are closely related to the lower central series of the commutator subgroup of the pure braid group.
Study geometric step options with jumps, deriving pricing equations and characterizations.
The paper defines a new equivalence relation for knot projections and finds an infinite number of distinct classes.
We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray transforms of lower order coefficients. We also give two different boundary determinat…
We study a generalized functional related to the pullback metrics (3). We derive the first variation formula which yield stationary maps. We introduce the stress-energy tensor which is naturally linked to conservation law and yield monotonicity formula via the coarea formula and comparison theorem in Riemannian geometr…
In this paper we present an overview of the connection between completely integrable systems and the background geometry of the flow. This relation is better seen when using a group-based concept of moving frame introduced by Fels and Olver in [Acta Appl. Math. 51 (1998), 161-213; 55 (1999), 127-208]. The paper discuss…
We study two types of preconditioners and preconditioned stochastic gradient descent (SGD) methods in a unified framework. We call the first one the Newton type due to its close relationship to the Newton method, and the second one the Fisher type as its preconditioner is closely related to the inverse of Fisher inform…
For singular corank 1 surfaces in we introduce a distinguished normal vector called the axial vector. Using this vector and the curvature parabola we define a new type of curvature called the axial curvature, which generalizes the singular curvature for frontal type singularities. We then study contact pr…
We determine a particular class of Roter type warped product manifolds. We show that every manifold of that class admits a geodesic mapping onto a some Roter type warped product manifold. Moreover, both geodesically related manifolds are pseudosymmetric of constant type.
Proposes a new method for predicting missing relations in knowledge graphs.
This paper extends geometric structure theory to infinite type structures.
When can one 3-manifold be transformed to another by a finite sequence of Dehn surgeries which are restricted to preserve the first homology of the manifolds ? What is the resulting equivalence relation on 3-manifolds ? What if the surgery circle is further restricted to lie more deeply in the lower central series of t…
We explain how to relate the problem of finding a mirror manifold for a Calabi-Yau manifold to the problem of characterizing the rational homotopy types of closed Kähler manifolds.
In this paper, we present a Lichnerowicz type estimate and (higher order) Buser type estimates for the magnetic Laplacian on a closed Riemannian manifold with a magnetic potential. These results relate eigenvalues, magnetic fields, Ricci curvature, and Cheeger type constants.
In the present paper we study the rigidity of 2-step Carnot groups, or equivalently, of graded 2-step nilpotent Lie algebras. We prove the alternative that depending on bi-dimensions of the algebra, the Lie algebra structure makes it either always of infinite type or generically rigid, and we specify the bi-dimensions …
Defines a new tensor related to special geometric spaces.