arXiv research

Soft Actor-Critic is a state-of-the-art reinforcement learning algorithm for continuous action settings that is not applicable to discrete action settings. Many important settings involve discrete actions, however, and so here we derive an alternative version of the Soft Actor-Critic algorithm that is applicable to dis…

The study finds discrete subgroups with full limit sets in higher rank Lie groups.

To date, attribute discretization is typically performed by replacing the original set of continuous features with a transposed set of discrete ones. This paper provides support for a new idea that discretized features should often be used in addition to existing features and as such, datasets should be extended, and n…

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…

We present a definition of discrete channel surfaces in Lie sphere geometry, which reflects several properties for smooth channel surfaces. Various sets of data, defined at vertices, on edges or on faces, are associated with a discrete channel surface that may be used to reconstruct the underlying particular discrete L…

Alternative discrete Dirac mechanics using Dirac structures.

We study the limit set of discrete subgroups arising from Anosov representations. Specially we study the limit set of discrete groups arising from strictly convex real projective structures and Anosov representations from a finitely generated word hyperbolic group into a semisimple Lie group.

Study proves existence and convergence of discrete-time Kyle models with multiple insiders.

Proves hardness of semi-discrete optimal transport and proposes regularization methods.

We study robust stochastic optimization problems in the quasi-sure setting in discrete-time. The strategies in the multi-period-case are restricted to those taking values in a discrete set. The optimization problems under consideration are not concave. We provide conditions under which a maximizer exists. The class of …

We provide an action for gauge theories discretized on simplicial meshes, inspired by finite element methods. The action is discretely gauge invariant and we give a proof of consistency. A discrete Noether's theorem that can be applied to our setting, is also proved.

Study the limits of discrete DPPs to continuous DPPs as set size grows.

An important question that discrete approaches to quantum gravity must address is how continuum features of spacetime can be recovered from the discrete substructure. Here, we examine this question within the causal set approach to quantum gravity, where the substructure replacing the spacetime continuum is a locally f…

Develops deep jump learning for continuous treatment OPE.

Fully augmented links have dense volume densities but discrete in certain ranges.

Unique metric found for discrete curvature on spherical cone-metrics.

We study the set of critical exponents of discrete groups acting on regular trees. We prove that for every real number $δ$ between $0$ and $\frac{1}{2}\log q$, there is a discrete subgroup $Γ$ acting without inversion on a $(q+1)$-regular tree whose critical exponent is equal to $δ$. Explicit construction of edge-index…

Given a finite set of points in $\mathbb R^n$ and a radius parameter, we study the Čech, Delaunay-Čech, Delaunay (or Alpha), and Wrap complexes in the light of generalized discrete Morse theory. Establishing the Čech and Delaunay complexes as sublevel sets of generalized discrete Morse functions, we prove that the four…

A new graphical model for discrete data without parametric restrictions.

A new method reduces high-dimensional state space for dynamic choice models.

Bi-Lipschitz rigidity theorem for dense subgroups of algebraic groups.

Given a trivalent graph in the 3-dimensional Euclidean space, we call it a discrete surface because it has a tangent space at each vertex determined by its neighbor vertices. To abstract a continuum object hidden in the discrete surface, we introduce a subdivision method by applying the Goldberg-Coxeter subdivision and…

The paper studies singularities in discrete indefinite affine minimal surfaces.

A Clifford algebra model for M"obius geometry is presented. The notion of Ribaucour pairs of orthogonal systems in arbitrary dimensions is introduced, and the structure equations for adapted frames are derived. These equations are discretized and the geometry of the occuring discrete nets and sphere congruences is disc…

The paper proves convergence of discrete maps to Riemann mappings for polyhedral surfaces.

Neural nets replicate hedging payoffs for realistic discrete-time settings.

Any discrete differential manifold $M$ (finite set endowed with an algebraic differential calculus) can be represented by appropriate polyhedron ${\cal P}(M)$. This representation demonstrates the adequacy of the calculus of discrete differential manifolds and links this approach with that based on finitary substitutes…

We investigate the systematic mechanism for designing fast mixing Markov chain Monte Carlo algorithms to sample from discrete point processes under the Dobrushin uniqueness condition for Gibbs measures. Discrete point processes are defined as probability distributions $μ(S)\propto \exp(βf(S))$ over all subsets $S\in 2^…

Improves regression accuracy by using multiple discrete representations.

We begin by showing that commensurators of Zariski dense subgroups of isometry groups of symmetric spaces of non-compact type are discrete provided that the limit set on the Furstenberg boundary is not invariant under the action of a (virtual) simple factor. In particular for rank one or simple Lie groups, Zariski dens…

Discrete connections on abelian Lie groups bundles are studied.

A new diffusion model uses efficient conditional estimators for discrete data.

Study dynamics of automorphisms on cubic surfaces and their connection to Painlevé 6.

Maps discrete manifolds to partitions to define new manifolds.

This paper develops a discrete theory of real Riemann surfaces using quad-graphs and linear discretization.

Introduces flat discrete signatures for financial data analysis.

Smooth fractal trees via analytic generators, preserving combinatorial and geometric properties.

The paper uses MDM theory to analyze multifiltering functions on simplicial complexes.

Paper variates Navier-Stokes-Fourier system for thermodynamic consistency.

In this paper, we will give a rigorous construction of the exact discrete Lagrangian formulation associated to a continuous Lagrangian problem. Moreover, we work in the setting of Lie groupoids and Lie algebroids which is enough general to simultaneously cover several cases of interest in discrete and continuous descri…

New metrics produce discrete zero sets for nondegenerate harmonic forms.

Smooth knots in complex hyperbolic plane limit sets to chains or R-circles.

In this paper, we consider the problem of black box continuous submodular maximization where we only have access to the function values and no information about the derivatives is provided. For a monotone and continuous DR-submodular function, and subject to a bounded convex body constraint, we propose Black-box Contin…

BayesSum improves Bayesian quadrature for discrete domains, requiring fewer samples.

Faster sampling in discrete diffusion models with predetermined transition time.

The paper studies stability of discretized Anosov flows.

Develops combinatorial theory of vector bundles on simplicial complexes.

We propose a natural discretisation scheme for classical projective minimal surfaces. We follow the classical geometric characterisation and classification of projective minimal surfaces and introduce at each step canonical discrete models of the associated geometric notions and objects. Thus, we introduce discrete ana…