Related papers: Algorithmic Construction of Real Hyperfields from …
Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first…
This paper presents a novel enumerative biclustering algorithm to directly mine all maximal biclusters in mixed-attribute datasets (containing both numerical and categorical attributes), with or without missing values. The proposal is an…
Subspace codes and particularly constant dimension codes have attracted much attention in recent years due to their applications in random network coding. As a particular subclass of subspace codes, cyclic subspace codes have additional…
We show that a monic univariate polynomial over a field of characteristic zero, with $k$ distinct non-zero known roots, is determined by its $k$ proper leading coefficients by providing an explicit algorithm for computing the multiplicities…
Let $\mathrm{R}$ be a real closed field and $\mathrm{C}$ the algebraic closure of $\mathrm{R}$. We give an algorithm for computing a semi-algebraic basis for the first homology group, $\mathrm{H}_1(S,\mathbb{F})$, with coefficients in a…
Feature generation aims to generate new and meaningful features to create a discriminative representation space.A generated feature is meaningful when the generated feature is from a feature pair with inherent feature interaction. In the…
We provide lower estimates on the minimal number of generators of the profinite completion of free products of finite groups. In particular, we show that if C_1,...,C_n are finite cyclic groups then there exists a finite group G which is…
We develop a representation theoretic technique for detecting closed orbits that is applicable in all characteristics. Our technique is based on Kempf's theory of optimal subgroups and we make some improvements and simplify the theory from…
We focus on two aspects of cyclic orbit codes: invariants under equivalence and quasi-optimality. Regarding the first aspect, we establish a connection between the codewords of a cyclic orbit code and a certain linear set on the projective…
In intractable, undirected graphical models, an intuitive way of creating structured mean field approximations is to select an acyclic tractable subgraph. We show that the hardness of computing the objective function and gradient of the…
Optimizing an implicational base of a closure system consists in turning this implicational base into an equivalent one with premises and conclusions as small as possible. This task is known to be hard in general but tractable for a number…
Let C/K: F = 0 be a smooth plane quartic over a complete discrete valuation field K. In a previous paper the authors togetehr with Q. Liu give various characterizations of the reduction (i.e. non-hyperelliptic genus 3 curve, hyperelliptic…
In this paper, we find criteria for when cyclic cubic and cyclic quartic fields have well-rounded ideal lattices. We show that every cyclic cubic field has at least one well-rounded ideal. We also prove that there exist families of cyclic…
Hypergraphs, which use hyperedges to capture groupwise interactions among different entities, have gained increasing attention recently for their versatility in effectively modeling real-world networks. In this paper, we study the problem…
We propose an efficient method to compute a small set of integer-constrained cone singularities, which induce a rotationally seamless conformal parameterization with low distortion. Since the problem only involves discrete variables, i.e.,…
In this paper we show that every area minimizing cone C^{n-1} in R^n can be approximated by entirely smooth area minimizing hypersurfaces. This extensively uses hyperbolic unfoldings of such hypersurfaces and the resulting potential theory…
In this paper we present an algorithm for computing all algebraic intermediate subfields in a separably generated unirational field extension (which in particular includes the zero characteristic case). One of the main tools is Groebner…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
We provide new computations in bounded cohomology: A group is boundedly acyclic if its bounded cohomology with trivial real coefficients is zero in all positive degrees. We show that there exists a continuum of finitely generated…
It is well known that the ring of polynomial invariants of a reductive group is finitely generated. However, it is difficult to give strong upper bounds on the degrees of the generators, especially over fields of positive characteristic. In…