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.
A simpler edge-based discretization method without dual volumes.
The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The 3-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The 4-dimensional Ric is the Einstein tensor for such spacetimes. More recently the Ric was used by Hamilton to define a non-li…
Geometric sampling of networks using curvature measures.
The Hodge decomposition provides a very powerful mathematical method for the analysis of 2D and 3D vector fields. It states roughly that any vector field can be -orthogonally decomposed into a curl-free, divergence-free, and a harmonic field. The harmonic field itself can be further decomposed into three component…
This paper establishes the consistency of spectral approaches to data clustering. We consider clustering of point clouds obtained as samples of a ground-truth measure. A graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points they connect. We investigate the…
Maximum a posteriori (MAP) inference is a fundamental computational paradigm for statistical inference. In the setting of graphical models, MAP inference entails solving a combinatorial optimization problem to find the most likely configuration of the discrete-valued model. Linear programming (LP) relaxations in the Sh…
Develops methods to analyze feature-outcome associations in subpopulations.
We define the distance between edges of graphs and study the coarse Ricci curvature on edges. We consider the Laplacian on edges based on the Jost-Horak's definition of the Laplacian on simplicial complexes. As one of our main results, we obtain an estimate of the first non-zero eigenvalue of the Laplacian by the Ricci…
Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set filtrations and edge-based filtrations. We present three novel applications: th…
Wiki-CS dataset benchmarks Graph Neural Networks using Wikipedia articles.
Edge augmentation connects disconnected graphs by elevating eigenvalues.
We propose a DTCWT ScatterNet Convolutional Neural Network (DTSCNN) formed by replacing the first few layers of a CNN network with a parametric log based DTCWT ScatterNet. The ScatterNet extracts edge based invariant representations that are used by the later layers of the CNN to learn high-level features. This improve…
Graph rewiring method alleviates over-squashing in GNNs.
A new graph neural network tackles oversmoothing and generalization issues.
We consider point clouds obtained as random samples of a measure on a Euclidean domain. A graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points they connect. Our goal is to develop mathematical tools needed to study the consistency, as the number of availa…
Deep RL predicts equipment maintenance from sensor data.
New framework detects directional influence in multivariate time series.
Proposes a co-hub node model for multiview graph learning.
Generative model uses recurrent neural networks to predict graph edges.
Study fragility in global financial indices using network analysis.
Causal inference improves heterophilic graph learning.
This paper studies large-scale dynamical networks where the current state of the system is a linear transformation of the previous state, contaminated by a multivariate Gaussian noise. Examples include stock markets, human brains and gene regulatory networks. We introduce a transition matrix to describe the evolution, …
A typical census of 3-manifolds contains all manifolds (under various constraints) that can be triangulated with at most n tetrahedra. Al- though censuses are useful resources for mathematicians, constructing them is difficult: the best algorithms to date have not gone beyond n = 12. The underlying algorithms essential…
A neural network speeds up bond-associated peridynamics simulations.
The paper clusters hypergraphs to find diverse and experienced groups based on past experiences.
Advanced GNNs improve molecular generation models.
New discrete models for constant mean curvature surfaces and tori.
Simple constructions of semi-discrete and discrete surfaces using Jacobi elliptic functions.
The study classifies singularities in discrete improper affine spheres.
Our aim in this paper is to provide a theory of discrete Riemann surfaces based on quadrilateral cellular decompositions of Riemann surfaces together with their complex structure encoded by complex weights. Previous work, in particular of Mercat, mainly focused on real weights corresponding to quadrilateral cells havin…
New method solves discrete mKdV equation from curve motions.
We introduce the discrete Einstein metrics as critical points of discrete energy on triangulated 3-manifolds, and study them by discrete curvature flow of second (fourth) order. We also study the convergence of the discrete curvature flow. Discrete curvature flow of second order is an analogue of smooth Ricci flow.
This paper explores geometric insights into discrete R-congruences and their envelopes.
Permutability of surface transforms yields discrete analogs.
Paper proposes a multi-phase pruning pipeline for deep ensemble learning on IIoT devices.
New representations for discrete surfaces derived from dual transforms.
In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric conditio…
Study on discrete surfaces with constant principal curvature for nanocarbon applications.
We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms the function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete …
New method linearizes Darboux transformations of discrete curves.
The paper introduces discrete Dirac structures for mechanics, simplifying dynamics.
We obtain a unified theory of discrete minimal surfaces based on discrete holomorphic quadratic differentials via a Weierstrass representation. Our discrete holomorphic quadratic differential are invariant under Möbius transformations. They can be obtained from discrete harmonic functions in the sense of the cotangent …
Paper proposes a new generative model for discrete distributions using flows on submanifolds.
In this paper, we introduce a parameterized discrete curvature (-curvature) for piecewise linear metrics on polyhedral surfaces, which is a generalization of the classical discrete curvature. A discrete uniformization theorem is established for the parameterized discrete curvature, which generalizes the discrete uni…
Formula derived for discrete improper affine spheres.
Discretization of curves is an ancient topic. Even discretization of curves with an eye toward differential geometry is over a century old. However there is no general theory or methodology in the literature, despite the ubiquitous use of discrete curves in mathematics and science. There are conflicting definitions of …
We define discrete flat surfaces in hyperbolic 3-space from the perspective of discrete integrable systems and prove properties that justify the definition. We show how these surfaces correspond to previously defined discrete constant mean curvature 1 surfaces in hyperbolic 3-space, and we also describe discrete focal …
Study proposes Local Linear Encoding for better feature discretization.