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A classical result of MacMahon states that inversion number and major index have the same distribution over permutations of a given multiset. In this work we prove a strengthening of this theorem originally conjectured by Haglund. Our…
A method for designing variational principles for the dynamics of a possibly dissipative and non-conservatively forced chain of particles is demonstrated. Some qualitative features of the formulation are discussed.
We give a simple, generic conformal prediction method for sequential prediction that achieves target empirical coverage guarantees against adversarially chosen data. It is computationally lightweight -- comparable to split conformal…
Several theorems about the equivalence of familiar theories of reverse mathematics with certain well-ordering principles have been proved by recursion-theoretic and combinatorial methods (Friedman, Marcone, Montalban et al.) and with…
The aim of this paper is to generalize the Core Inverse to arbitrary vector spaces using finite potent endomorphisms. As an application, the core partial order is studied in the set of finite potent endomorphisms (of index lesser or equal…
The power-expected-posterior (PEP) prior is an objective prior for Gaussian linear models, which leads to consistent model selection inference, under the M-closed scenario, and tends to favor parsimonious models. Recently, two new forms of…
We propose a method for the resummation of divergent perturbative expansions in quantum electrodynamics and related field theories. The method is based on a nonlinear sequence transformation and uses as input data only the numerical values…
Learning disentangled representations without supervision or inductive biases, often leads to non-interpretable or undesirable representations. On the other hand, strict supervision requires detailed knowledge of the true generative…
The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate.…
The size and complexity of software and hardware systems have significantly increased in the past years. As a result, it is harder to guarantee their correct behavior. One of the most successful methods for automated verification of…
We established order-preserving versions of the basic principles of functional analysis such as Hahn-Banach, Banach-Steinhaus, open mapping and Banach-Alaoglu theorems.
We give a principled method for decomposing the predictive uncertainty of a model into aleatoric and epistemic components with explicit semantics relating them to the real-world data distribution. While many works in the literature have…
We consider an extension of the setting of label ranking, in which the learner is allowed to make predictions in the form of partial instead of total orders. Predictions of that kind are interpreted as a partial abstention: If the learner…
We pursue various restricted variable generalizations of the Chevalley-Warning theorem for low degree polynomial systems over a finite field. Our first such result involves variables restricted to Cartesian products of the Vandermonde…
The simple L\'evy Poisson process and scaled forms are explicitly constructed from partial sums of independent and identically distributed random variables and from sums of non-stationary independent random variables. For the latter, the…
Conventional prior for Variational Auto-Encoder (VAE) is a Gaussian distribution. Recent works demonstrated that choice of prior distribution affects learning capacity of VAE models. We propose a general technique…
Similar to the generalized extreme value (GEV) family, the generalized extreme value distributions under power normalization are introduced by Roudsari (1999) and Barakat et al. (2013). In this article, we study the asymptotic behavior of…
This paper deals with an improvement of the "a-priori stability bounds" on the variation of the action variables and on the stability time obtained from a given Birkhoff normal form around the elliptic equilibrium point of an Hamiltonian…
This paper first makes an attempt to investigate the partial information near optimal control of systems governed by forward-backward stochastic differential equations with observation noise under the assumption of a convex control domain.…
A combinatorial study of multiple $q$-integrals is developed. This includes a $q$-volume of a convex polytope, which depends upon the order of $q$-integration. A multiple $q$-integral over an order polytope of a poset is interpreted as a…