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 linearizes Darboux transformations of discrete curves.
Geometric approach uses Bäcklund transformations to create integrable discrete analogs of surface nets.
New geometric transformations link discrete and continuous curve motions.
We study the dynamics of the discrete bicycle (Darboux, Backlund) transformation of polygons in n-dimensional Euclidean space. This transformation is a discretization of the continuous bicycle transformation, recently studied by Foote, Levi, and Tabachnikov. We prove that the respective monodromy is a Moebius transform…
Permutability of surface transforms yields discrete analogs.
A new method for discrete data normalizing flows using latent transformations.
New Bäcklund transformations for discrete pseudospherical surfaces of revolution are found.
New method solves discrete mKdV equation from curve motions.
Using a quaternionic calculus, the Christoffel, Darboux, Goursat, and spectral transformations for discrete isothermic nets are described, with their interrelations. The Darboux and spectral transformations are used to define discrete analogs for cmc-1 surfaces in hyperbolic space and to obtain a discrete version of Br…
A Darboux transformation for polarized space curves is introduced and its properties are studied, in particular, Bianchi permutability. Semi-discrete isothermic surfaces are described as sequences of Darboux transforms of polarized curves in the conformal n-sphere and their transformation theory is studied. Semi-discre…
New discrete models for constant mean curvature surfaces and tori.
The asymptotic lattices and their transformations are studied within the line geometry approach. It is shown that the discrete asymptotic nets are represented by isotropic congruences in the Plucker quadric. On the basis of the Lelieuvre-type representation of asymptotic lattices and of the discrete analog of the Mouta…
We introduce the Koenigs lattice, which is a new integrable reduction of the quadrilateral lattice (discrete conjugate net) and provides natural integrable discrete analogue of the Koenigs net. We construct the Darboux-type transformations of the Koenigs lattice and we show permutability of superpositions of such trans…
Bayesian model for discrete data with conditional transformations.
MODWST improves classification tasks with wavelet scattering.
Training of discrete latent variable models remains challenging because passing gradient information through discrete units is difficult. We propose a new class of smoothing transformations based on a mixture of two overlapping distributions, and show that the proposed transformation can be used for training binary lat…
We construct explicit solutions to the discrete motion of discrete plane curves that has been introduced by one of the authors recently. Explicit formulas in terms the function are presented. Transformation theory of the motions of both smooth and discrete curves is developed simultaneously.
Calculates affine transformations for specific homogeneous spaces.
We study Christoffel and Darboux transforms of discrete isothermic nets in 4-dimensional Euclidean space: definitions and basic properties are derived. Analogies with the smooth case are discussed and a definition for discrete Ribaucour congruences is given. Surfaces of constant mean curvature are special among all iso…
New methods create full discretized isothermic tori in Euclidean spaces.
Finding appropriate notions of discrete holomorphic maps and, more generally, conformal immersions of discrete Riemann surfaces into 3-space is an important problem of discrete differential geometry and computer visualization. We propose an approach to discrete conformality that is based on the concept of holomorphic l…
New representations for discrete surfaces derived from dual transforms.
Efficiently calculates Brazilian stock options with discrete dividends.
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. In this survey we discuss the following two fundamental Discretization Principles: the transformation group principle (smooth geometric objects and their discretizations are invar…
DNFS trains efficient samplers for discrete distributions using locally equivariant Transformers.
Skew parallelogram nets factorize, encompassing discrete differential geometry.
Weingarten transformations which, by definition, preserve the asymptotic lines on smooth surfaces have been studied extensively in classical differential geometry and also play an important role in connection with the modern geometric theory of integrable systems. Their natural discrete analogues have been investigated…
The paper connects quantum -symbols to tetrahedra volumes via discrete Fourier transforms.
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…
Discrete conjugate systems are quadrilateral nets with all planar faces. Discrete orthogonal systems are defined by the additional property of all faces being concircular. Their geometric properties allow one to consider them as proper discretization of conjugate, resp. orthogonal coordinate systems of classical differ…
Defines CAMC discrete nets and their properties.
New discrete curves defined in space forms with geometric properties.
We introduce (binary) Darboux transformation for general differential equation of the second order in two independent variables. We present a discrete version of the transformation for a 6-point difference scheme. The scheme is appropriate to solving a hyperbolic type initial-boundary value problem. We discuss several …
We find a normal form for two-input flat discrete-time systems.
Neural networks' feature geometry evolves like discrete Ricci flow.
Study identifies and analyzes three types of errors in learning Fourier operators.
Discrete linear Weingarten surfaces in space forms are characterized as special discrete -nets, a discrete analogue of Demoulin's -surfaces. It is shown that the Lie-geometric deformation of -nets descends to a Lawson transformation for discrete linear Weingarten surfaces, which coincides with the well-known L…
We propose a novel multilinear dynamical system (MLDS) in a transform domain, named -MLDS, to model tensor time series. With transformations applied to a tensor data, the latent multidimensional correlations among the frontal slices are built, and thus resulting in the computational independence in the tra…
We discuss results for the Ribaucour transformation of curves or of higher dimensional smooth and discrete submanifolds. In particular, a result for the reduction of the ambient dimension of a submanifold is proved and the notion of Ribaucour coordinates is derived using a Bianchi permutability result. Further, we disc…
A new model for time series using discrete latent states.
New invertible transformations improve flow-based generative models.
A new method trains discrete EBMs without sampling.
A method for vectorizing persistence diagrams simplifies topological data analysis.
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 …
The paper develops a computational method for efficient online filtering of diffusion processes.
Study preserves symplectic structure in forced discrete mechanical systems.
We extend the Fourier cosine method to discrete probability distributions, achieving faster convergence rates.
We consider the quasiconformal dilatation of projective transformations of the real projective plane. For non-affine transformations, the contour lines of dilatation form a hyperbolic pencil of circles, and these are the only circles that are mapped to circles. We apply this result to analyze the dilatation of the circ…