Related papers: Counting Matchings via Capacity Preserving Operato…
Friedland's Lower Matching Conjecture asserts that if $G$ is a $d$--regular bipartite graph on $v(G)=2n$ vertices, and $m_k(G)$ denotes the number of matchings of size $k$, then $$m_k(G)\geq {n \choose…
We analyze modular invariance drawing inspiration from tauberian theorems. Given a modular invariant partition function with a positive spectral density, we derive lower and upper bounds on the number of operators within a given energy…
Clustering with most objective functions is NP-Hard, even to approximate well in the worst case. Recently, there has been work on exploring different notions of stability which lend structure to the problem. The notion of stability,…
In this paper, we provide new theoretical results on the generalization properties of learning algorithms for multiclass classification problems. The originality of our work is that we propose to use the confusion matrix of a classifier as…
The capacity of a deterministic multiple-input multiple-output (MIMO) channel under the peak and average power constraints is investigated. For the identity channel matrix, the approach of Shamai et al. is generalized to the higher…
We show that linear differential operators with polynomial coefficients over a field of characteristic zero can be multiplied in quasi-optimal time. This answers an open question raised by van der Hoeven.
Stable matching is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal paper by Gale and Shapley. In this paper, we provide a new upper bound on…
A method to compute guaranteed lower bounds to the eigenvalues of the Maxwell system in two or three space dimensions is proposed as a generalization of the method of Liu and Oishi [SIAM J. Numer. Anal., 51, 2013] for the Laplace operator.…
We introduce an S.o.S hierarchy of lower bounds for a polynomial optimization problem whose constraint is expressed as a matrix polynomial semidefinite inequality. Our approach involves utilizing a penalty function framework to directly…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…
We present new deterministic algorithms for several cases of the maximum rank matrix completion problem (for short matrix completion), i.e. the problem of assigning values to the variables in a given symbolic matrix as to maximize the…
We study algorithms for solving parity, mean-payoff and energy games. We propose a systematic framework, which we call Fast value iteration, for describing, comparing, and proving correctness of such algorithms. The approach is based on…
This paper introduces a unified framework for stable matching, which nests the traditional definition of stable matching in finite markets and the continuum definition of stable matching from Azevedo and Leshno (2016) as special cases.…
Stable matching theory is the foundation of centralized clearinghouses worldwide, from school choice programs to medical residency allocations. However, incorporating complex distributional goals-such as multi-dimensional diversity quotas…
The celebrated Brascamp-Lieb (BL) inequalities (and their extensions) are an important mathematical tool, unifying and generalizing numerous inequalities in analysis, convex geometry and information theory. While their structural theory is…
The complexity of computing the solutions of a system of multivariate polynomial equations by means of Groebner bases computations is upper bounded by a function of the solving degree. In this paper, we discuss how to rigorously estimate…
A finitely generated quadratic module or preordering in the real polynomial ring is called stable, if it admits a certain degree bound on the sums of squares in the representation of polynomials. Stability, first defined explicitly by…
In this paper we further develop the ideas from Geometric Function Theory initially introduced in [arXiv:2206.13206], to derive capacity estimate in metastability for arbitrary configurations. The novelty of this paper is twofold. First,…
The capacity of completely positive operators and the Brascamp--Lieb constant can both be interpreted in terms of unconstrained geometric programming up to an additional minimisation over a compact group. We shine light on this perspective…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…