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.
Study of discrete period matrices on embedded graphs, relating to Riemann surfaces.
The stability and robustness of compact schemes for parabolic PDEs are analyzed.
We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for Weingarten's formula, the Ricci curvature and the Codazzi-Mainardi equations. For ma…
Survey on matrix hydrodynamics, a 2D fluid model.
This paper develops a discrete theory of real Riemann surfaces using quad-graphs and linear discretization.
Matrix completion is one of the key problems in signal processing and machine learning. In recent years, deep-learning-based models have achieved state-of-the-art results in matrix completion. Nevertheless, they suffer from two drawbacks: (i) they can not be extended easily to rows or columns unseen during training; an…
Derives a Hamiltonian model for 3D axially symmetric magnetohydrodynamics.
Data-dependent hashing has recently attracted attention due to being able to support efficient retrieval and storage of high-dimensional data such as documents, images, and videos. In this paper, we propose a novel learning-based hashing method called "Supervised Discrete Hashing with Relaxation" (SDHR) based on "Super…
DNFS trains efficient samplers for discrete distributions using locally equivariant Transformers.
New method decomposes corrupted data matrices into sparse and low-rank components.
Open problem: Establishing bounds for Cayley-table completion to discover discrete algorithmic axioms.
We define Discrete Quasi-Einstein metrics (DQE-metrics) as the critical points of discrete total curvature functional on triangulated 3-manifolds. We study DQE-metrics by introducing some combinatorial curvature flows. We prove that these flows produce solutions which converge to discrete quasi-Einstein metrics when th…
A new neural approach for generating origin-destination matrices in ABMs.
In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes baskets of arbitrary type and extends portfolio analysis to the complex variable domain. This allows us for simultaneous a…
We revisit the theory of Discrete Exterior Calculus (DEC) in 2D for general triangulations, relying only on Vector Calculus and Matrix Algebra. We present DEC numerical solutions of the Poisson equation and compare them against those found using the Finite Element Method with linear elements (FEML).
New matrix ensembles better match deep neural network spectral densities.
New method preserves MHD equations on sphere without costly matrix exponentials.
We study the problem of learning a distribution from samples, when the underlying distribution is a mixture of product distributions over discrete domains. This problem is motivated by several practical applications such as crowd-sourcing, recommendation systems, and learning Boolean functions. The existing solutions e…
We consider the problem of estimating the transition rate matrix of a continuous-time Markov chain from a finite-duration realisation of this process. We approach this problem in an imprecise probabilistic framework, using a set of prior distributions on the unknown transition rate matrix. The resulting estimator is a …
Supervised cross-modal hashing has gained increasing research interest on large-scale retrieval task owning to its satisfactory performance and efficiency. However, it still has some challenging issues to be further studied: 1) most of them fail to well preserve the semantic correlations in hash codes because of the la…
New method improves reliability of recommender systems in face of fake accounts and manipulation.
Generalized Precision Matrix for scalable estimation of nonparametric Markov networks.
We consider the problem of matrix completion on an matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the problem can be reformulated as a binary convex optimization problem. We design Opt…
The discrete Nahm equations, a system of matrix valued difference equations, arose in the work of Braam and Austin on half-integral mass hyperbolic monopoles. We show that the discrete Nahm equations are completely integrable in a natural sense: to any solution we can associate a spectral curve and a holomorphic line-b…
In this paper, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD. The main motivation is that a lower tubal rank tensor can be obtained by usin…
Study finds weak solutions for complex map flows with optimal lifespan.
We recall the theory of linear discrete Riemann surfaces and show how to use it in order to interpret a surface embedded in R^3 as a discrete Riemann surface and compute its basis of holomorphic forms on it. We present numerical examples, recovering known results to test the numerics and giving the yet unknown period m…
We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix of indicator variables on the vertices of a graph reflects the conditional indepe…
Positive-curvature metrics on trees identified for specific configurations.
MOB-dS uses permutation to correct for dependency in discrete survival data.
A Bayesian Boolean Matrix Factorization for cancer genomics
Existence and uniqueness of discrete Einstein metrics on trees proven.
High-dimensional inference for sparse spectral precision matrices
A new method for unfolding histograms without matrix inversion.
This paper gives new concentration inequalities for the spectral norm of a wide class of matrix martingales in continuous time. These results extend previously established Freedman and Bernstein inequalities for series of random matrices to the class of continuous time processes. Our analysis relies on a new supermarti…
LEAPS samples discrete distributions via CTMCs and locally equivariant networks.
We derive a numerical method for Darcy flow, hence also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedr…
We study the problem of computing the matrix exponential of a block triangular matrix in a peculiar way: Block column by block column, from left to right. The need for such an evaluation scheme arises naturally in the context of option pricing in polynomial diffusion models. In this setting a discretization process pro…
This work accelerates constrained sampling using large deviation principles.
A new graph neural network framework captures long-range interactions efficiently.
Paper introduces OMD for ordered state transitions in SSMs.
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…
We use the explicit relation between genus filtrated -loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich--Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces (discrete volumes), to express Gaussian means…
New method describes entanglement of straight lines in 3D space.
We present an intriguing discovery related to Random Fourier Features: in Gaussian kernel approximation, replacing the random Gaussian matrix by a properly scaled random orthogonal matrix significantly decreases kernel approximation error. We call this technique Orthogonal Random Features (ORF), and provide theoretical…
New finite element method for complex forms in any dimension.
There are certain families of words and word sequences (words in the generators of a two-generator group) that arise frequently in the Teichm{ü}ller theory of hyperbolic three-manifolds and Kleinian and Fuchsian groups and in the discreteness problem for two generator matrix groups. We survey some of the families of su…
Many applications, such as text modelling, high-throughput sequencing, and recommender systems, require analysing sparse, high-dimensional, and overdispersed discrete (count-valued or binary) data. Although probabilistic matrix factorisation and linear/nonlinear latent factor models have enjoyed great success in modell…