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Closed-form generating functions for counting one-face rooted hypermaps with a known number of darts by number of vertices and edges is found, using matrix integral expressions relating to the reduced density operator of a bipartite quantum…

We aim to reconstruct a monoid scheme $X$ from the category of quasi-coherent sheaves over it. This is much in the vein of Gabriel's original reconstruction theorem. Under some finiteness condition on a monoid schemes $X$, we show that the…

This paper discusses the split feasibility problem with polynomials. The sets are semi-algebraic, defined by polynomial inequalities. They can be either convex or nonconvex, either feasible or infeasible. We give semidefinite relaxations…

In this paper, we consider the problem of feature reconstruction from incomplete x-ray CT data. Such problems occurs, e.g., as a result of dose reduction in the context medical imaging. Since image reconstruction from incomplete data is a…

The present note considers a certain family of sums indexed by the set of fixed length compositions of a given number. The sums in question cannot be realized as weighted compositions. However they can be be related to the hypergeometric…

The results presented in this paper are refinements of some results presented in a previous paper. Three such refined results are presented. The first one relaxes one of the basic hypotheses assumed in the previous paper, and thus extends…

Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain. Typical examples include undersampled magnetic resonance…

The inverse problem of X-tray transforms considers reconstructing functions from some data that are easier to measure, which is typically the integral of that function along geodesics. We prove that if the domain has a foliation structure,…

It was recently shown that under mild assumptions second-order conformally superintegrable systems can be encoded in a $(0,3)$-tensor, called structure tensor. For abundant systems, this approach led to algebraic integrability conditions…

The main challenge for fine-grained few-shot image classification is to learn feature representations with higher inter-class and lower intra-class variations, with a mere few labelled samples. Conventional few-shot learning methods however…

The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the second in a series of papers in…

We describe an algorithm to decompose rational functions from which we determine the poset of groups fixing these functions.

Recovery of signals with elements defined on the nodes of a graph, from compressive measurements is an important problem, which can arise in various domains such as sensor networks, image reconstruction and group testing. In some scenarios,…

We show that various properties of unipotent elements in a reductive group over the complex numbers can be recovered purely in terms of the affine Weyl group of the dual group.

Most existing learning-based methods for solving imaging inverse problems can be roughly divided into two classes: iterative algorithms, such as plug-and-play and diffusion methods leveraging pretrained denoisers, and unrolled architectures…

We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…

A class of bilinear permutation polynomials over a finite field of characteristic 2 was constructed in a recursive manner recently which involved some other constructions as special cases. We determine the compositional inverses of them…

Piecewise affine functions are widely used to approximate nonlinear and discontinuous functions. However, most, if not all existing models only deal with fitting continuous functions. In this paper, we investigate the problem of fitting a…

A generally intelligent learner should generalize to more complex tasks than it has previously encountered, but the two common paradigms in machine learning -- either training a separate learner per task or training a single learner for all…

We refine and advance the study of the local structure of idempotent finite algebras started in [A.Bulatov, The Graph of a Relational Structure and Constraint Satisfaction Problems, LICS, 2004]. We introduce a graph-like structure on an…