arXiv research

The paper studies discrete sums of geometric Brownian motions in finance.

3D HQFT comparison proves state sum equals surgery.

Study optimal stopping and a non-zero-sum game with risk measures in discrete time.

Paper extends trigonometric summation formula with weights.

Log-concavity proven for multinomial likelihoods under specific constraints.

A system for federated learning with private data, adding discrete Gaussian noise and secure aggregation.

Gradient-based methods for games suffer from discrete update steps that cause drift, affecting performance.

Study of discrete period matrices on embedded graphs, relating to Riemann surfaces.

Study local differential privacy methods for estimating power sums of discrete distributions.

Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are …

Discretizing time series data introduces bias for decision-making models.

We consider two-player non-zero-sum stopping games in discrete time. Unlike Dynkin games, in our games the payoff of each player is revealed after both players stop. Moreover, each player can adjust her own stopping strategy according to the other player's action. In the first part of the paper, we consider the game wh…

Sum-Product Networks (SPNs) are a class of expressive yet tractable hierarchical graphical models. LearnSPN is a structure learning algorithm for SPNs that uses hierarchical co-clustering to simultaneously identifying similar entities and similar features. The original LearnSPN algorithm assumes that all the variables …

Paper proves method for calculating NML code length works for continuous models.

Study on convergence of Langevin dynamics for zero-sum games in probability distributions.

Non-elementary discrete subgroups of Sp(2,1) with complex trace are conjugate to U(2,1).

Study orbits of discrete lattice actions on the plane, derive new results for Veech surfaces.

We prove a discrete Gauss-Bonnet-Chern theorem which states where summing the curvature over all vertices of a finite graph G=(V,E) gives the Euler characteristic of G.

Lognormal random variables appear naturally in many engineering disciplines, including wireless communications, reliability theory, and finance. So, too, does the sum of (correlated) lognormal random variables. Unfortunately, no closed form probability distribution exists for such a sum, and it requires approximation. …

Partition functions for dimers on closed oriented surfaces are known to be alternating sums of Pfaffians of Kasteleyn matrices. In this paper, we obtain the formula for the coefficients in terms of discrete spin structures.

Bayesian optimization for expensive integrands achieves optimal performance.

A game theory study on optimal hiding and searching strategies in discrete locations.

Given a discrete group G and a spherical G-fusion category whose neutral component has invertible dimension, we use the state-sum method to construct a 3-dimensional Homotopy Quantum Field Theory (HQFT) with target the Eilenberg-MacLane space K(G,1).

Novel analysis of EFP for finite-sum problems in neural networks.

Study shows linear sample complexity for learning SPNs.

This thesis predicts the distribution of smoothed zeros of random sections on line bundles.

New scalar curvature defined from Ollivier-Ricci curvature for graphs.

Study mirror symmetry on manifolds with exceptional holonomy groups.

Study asymptotic expansion of graph Laplacian on discretized surfaces, relating spanning trees and cycle-rooted forests.

XSPNs combine SPNs and MEVMs for efficient inference in data with repeated parts.

Study of convergence of point-object configurations to a charged dust continuum.

We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price $π$ is given by the supremum over the prices of the American option under randomized models. T…

Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to …

New method reduces bias in estimating causal effects from discretized variables.

The functional determinant of an elliptic operator with positive, discrete spectrum may be defined as $e^{-Z'(0)}$, where $Z(s)$, the zeta function, is the sum $\sum_n^{\infty} λ_n^{-s}$ analytically continued to $s$ around the origin. In this paper $Z'(0)$ is calculated for the Laplace operator with Dirichlet boundary…

We consider the discretized version of a (continuous-time) two-factor model introduced by Benth and coauthors for the electricity markets. For this model, the underlying is the exponent of a sum of independent random variables. We provide and test an algorithm, which is based on the celebrated Foellmer-Schweizer decomp…

Develops a new quadrature method for Lebesgue integrals.

New method compresses non-Gaussian distributions exponentially.

We introduce the index i(v) = 1 - X(S(v)) for critical points of a locally injective function f on the vertex set V of a simple graph G=(V,E). Here S(v) = {w in E | (v,w) in E, f(w)-f(v)<0} is the subgraph of the unit sphere at v in G. It is the exit set of the gradient vector field. We prove that the sum of i(v) over …

Researchers prove inequalities for reaction-diffusion systems using a new curvature-dimension condition.

Computes a new metric quantity Y(M) for Riemannian 2d-manifolds.

We show that the Bregman divergence provides a rich framework to estimate unnormalized statistical models for continuous or discrete random variables, that is, models which do not integrate or sum to one, respectively. We prove that recent estimation methods such as noise-contrastive estimation, ratio matching, and sco…

A new algorithm for minimizing functions on Wasserstein space.

We extend risk measure stability conditions for coherent risk management.

New method estimates discrete distributions while protecting privacy.

We prove the existence of extremal, non-csc, Kähler metrics on certain unstable projectivised vector bundles $¶(E) \to M$ over a cscK-manifold $M$ with discrete holomorphic automorphism group, in certain adiabatic Kähler classes. In particular, the vector bundles $E \to M$ under consideration are assumed to split as a …

If $G$ is a finite group, is a function $f:G\to\mathbb C$ determined by its sums over all cosets of cyclic subgroups of $G$? In other words, is the Radon transform on $G$ injective? This inverse problem is a discrete analogue of asking whether a function on a compact Lie group is determined by its integrals over all ge…

Piecewise flat approximations for curvature in Euclidean and non-Euclidean spaces.