Related papers: Derangements and Generalizations: A Counting Note …

We introduce a theory of integration with respect to the fixed point index, offering a substantial improvement over previous approaches based on the Lefschetz number. This framework eliminates several restrictive assumptions -- such as the…

We present a common generalization of counting lattice points in rational polytopes and the enumeration of proper graph colorings, nowhere-zero flows on graphs, magic squares and graphs, antimagic squares and graphs, compositions of an…

In this survey article (which hitherto is an ongoing work-in-progress) we present the formulation of the induction and coinduction principles using the language and conventions of each of order theory, set theory, programming languages'…

This paper studies decision-making and statistical inference for two-sided matching markets via matrix completion. In contrast to the independent sampling assumed in classical matrix completion literature, the observed entries, which arise…

We investigate a general matrix factorization for deviance-based data losses, extending the ubiquitous singular value decomposition beyond squared error loss. While similar approaches have been explored before, our method leverages…

Sum-of-norms clustering is a convex optimization problem whose solution can be used for the clustering of multivariate data. We propose and study a localized version of this method, and show in particular that it can separate arbitrarily…

The problem of matching two sets of multiple elements, namely set-to-set matching, has received a great deal of attention in recent years. In particular, it has been reported that good experimental results can be obtained by preparing a…

We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…

Models such as the zero-inflated and zero-altered Poisson and zero-truncated binomial are well-established in modern regression analysis. We propose a super model that jointly and maximally unifies alteration, inflation, truncation and…

We consider the problem of exact low-rank matrix completion from a geometric viewpoint: given a partially filled matrix M, we keep the positions of specified and unspecified entries fixed, and study how the minimal completion rank depends…

For unconstrained control problems, a local convergence rate is established for an $hp$-method based on collocation at the Radau quadrature points in each mesh interval of the discretization. If the continuous problem has a sufficiently…

Given a text and a pattern over two types of symbols called constants and variables, the parameterized pattern matching problem is to find all occurrences of substrings of the text that the pattern matches by substituting a variable in the…

We overview results on the topic of Poisson approximation that are missed in existing surveys. The topic of Poisson approximation to the distribution of a sum of integer-valued random variables is presented as well. We do not restrict…

The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of…

The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact…

Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…

Matrix completion is a class of machine learning methods that concerns the prediction of missing entries in a partially observed matrix. This paper studies matrix completion for mixed data, i.e., data involving mixed types of variables…

We identify and study relevant structural parameters for the problem PerfMatch of counting perfect matchings in a given input graph $G$. These generalize the well-known tractable planar case, and they include the genus of $G$, its apex…

Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks. The study of its fundamental…

Counting perfect matchings has played a central role in the theory of counting problems. The permanent, corresponding to bipartite graphs, was shown to be #P-complete to compute exactly by Valiant (1979), and a fully polynomial randomized…