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Under reasonable assumptions, a group action on a module extends to the minimal free resolutions of the module. Explicit descriptions of these actions can lead to a better understanding of free resolutions by providing, for example,…
In this paper we de ne conditional random elds in reproducing kernel Hilbert spaces and show connections to Gaussian Process classi cation. More speci cally, we prove decomposition results for undirected graphical models and we give…
A scalable graphical method is presented for selecting, and partitioning datasets for the training phase of a classification task. For the heuristic, a clustering algorithm is required to get its computation cost in a reasonable proportion…
A geometric method for obtaining an infinite family of Cayley digraphs of constant density on finite Abelian groups is presented. The method works for any given degree and it is based on consecutive dilates of a minimum distance diagram…
This paper concerns the computation and identification of the (homological) Conley index over the integers, in the context of discrete dynamical systems generated by continuous maps. We discuss the significance with respect to nonlinear…
Kernelization is a general theoretical framework for preprocessing instances of NP-hard problems into (generally smaller) instances with bounded size, via the repeated application of data reduction rules. For the fundamental Max Cut…
We investigate optimal expansions of Kakeya sequences for the representation of real numbers. Expansions of Kakeya sequences generalize the expansions in non-integer bases and they display analogous redundancy phenomena. In this paper, we…
We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite…
We conservatively extend classical elementary differential calculus to the Cartesian closed category of convergence spaces. By specializing results about the convergence space representation of directed graphs, we use Cayley graphs to…
We study the problem of language identification in the limit, where given a sequence of examples from a target language, the goal of the learner is to output a sequence of guesses for the target language such that all the guesses beyond…
Representations that can compactly and effectively capture temporal evolution of semantic content are important to machine learning algorithms that operate on multi-variate time-series data. We investigate such representations motivated by…
Shape-based regularization has proven to be a useful method for delineating objects within noisy images where one has prior knowledge of the shape of the targeted object. When a collection of possible shapes is available, the specification…
This is an expository article on recent developments in the theory of group relaxations in integer programming from an algebraic perspective.
This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a method to identify finite generators, demonstrated through…
This paper describes a method for compiling a constraint-based grammar into a potentially more efficient form for processing. This method takes dependent disjunctions within a constraint formula and factors them into non-interacting groups…
In $\mathbb R^d$, it is well-known that cumulants provide an alternative to moments that can achieve the same goals with numerous benefits such as lower variance estimators. In this paper we extend cumulants to reproducing kernel Hilbert…
Different linearizations have been proposed to cast dependency parsing as sequence labeling and solve the task as: (i) a head selection problem, (ii) finding a representation of the token arcs as bracket strings, or (iii) associating…
We introduce the concept of regular expression characteristics as a unified way to concisely express bounds on time-series constraints. This allows us not only to define time-series constraints in a compositional way, but also to deal with…
In this article, we study higher Nil $K$-groups via binary complexes. More particularly, we exhibit an explicit form of generators of higher Nil $K$-groups in terms of binary complexes.
There has been some work in the literature on limit theorems for the trace of commutators for compact Lie groups. We revisit this from the perspective of combinatorial representation theory.