Search results for "Computation Theory & Mathematics"
showing 10 items of 332 documents
Languages associated with saturated formations of groups
2013
International audience; In a previous paper, the authors have shown that Eilenberg's variety theorem can be extended to more general structures, called formations. In this paper, we give a general method to describe the languages corresponding to saturated formations of groups, which are widely studied in group theory. We recover in this way a number of known results about the languages corresponding to the classes of nilpotent groups, soluble groups and supersoluble groups. Our method also applies to new examples, like the class of groups having a Sylow tower.; Dans un article précédent, les auteurs avaient montré comment étendre le théorème des variétés d'Eilenberg à des structures plus g…
Regularity and h-polynomials of toric ideals of graphs
2020
For all integers 4 ≤ r ≤ d 4 \leq r \leq d , we show that there exists a finite simple graph G = G r , d G= G_{r,d} with toric ideal I G ⊂ R I_G \subset R such that R / I G R/I_G has (Castelnuovo–Mumford) regularity r r and h h -polynomial of degree d d . To achieve this goal, we identify a family of graphs such that the graded Betti numbers of the associated toric ideal agree with its initial ideal, and, furthermore, that this initial ideal has linear quotients. As a corollary, we can recover a result of Hibi, Higashitani, Kimura, and O’Keefe that compares the depth and dimension of toric ideals of graphs.
In the Shadows of a hypergraph: looking for associated primes of powers of squarefree monomial ideals
2018
The aim of this paper is to study the associated primes of powers of square-free monomial ideals. Each square-free monomial ideal corresponds uniquely to a finite simple hypergraph via the cover ideal construction, and vice versa. Let H be a finite simple hypergraph and J(H) the cover ideal of H. We define the shadows of hypergraph, H, described as a collection of smaller hypergraphs related to H under some conditions. We then investigate how the shadows of H preserve information about the associated primes of the powers of J(H). Finally, we apply our findings on shadows to study the persistence property of square-free monomial ideals and construct some examples exhibiting failure of contai…
An Efficient Algorithm for Helly Property Recognition in a Linear Hypergraph
2001
International audience; In this article we characterize bipartite graphs whose associated neighborhood hypergraphs have the Helly property. We examine incidence graphs both hypergraphs and linear hypergraphs and we give a polynomial algorithm to recognize if a linear hypergraph has the Helly property.
Steiner configurations ideals: Containment and colouring
2021
Given a homogeneous ideal I&sube
Defining Interaction Design Patterns to Extract Knowledge from Big Data
2018
[EN] The Big Data domain offers valuable opportunities to gain valuable knowledge. The User Interface (UI), the place where the user interacts to extract knowledge from data, must be adapted to address the domain complexities. Designing UIs for Big Data becomes a challenge that involves identifying and designing the user-data interaction implicated in the knowledge extraction. To design such an interaction, one widely used approach is design patterns. Design Patterns describe solutions to common interaction design problems. This paper proposes a set of patterns to design UIs aimed at extracting knowledge from the Big Data systems data conceptual schemas. As a practical example, we apply the…
Codimensions of star-algebras and low exponential growth
2020
In this paper we prove that if A is any algebra with involution * satisfying a non-trivial polynomial identity, then its sequence of *-codimensions is eventually non-decreasing. Furthermore, by making use of the *-exponent we reconstruct the only two *-algebras, up to T*-equivalence, generating varieties of almost polynomial growth. As a third result we characterize the varieties of algebras with involution whose exponential growth is bounded by 2.
A data aggregation strategy based on wavelet for the internet of things
2017
The advent of emerging information and communication technologies, such as RFID, small size sensors and sensor networks, has made accessible a huge amount of information that requires sophisticated and efficient search algorithms to support queries on that data. In this paper we focus on the problem of aggregating data collected from these devices to efficiently support queries, inferences or statistics on them. In general, data aggregation techniques are necessary to efficiently collect information in a compact and cost-effective way. Some current solutions try to meet the above criteria, by exploiting different data aggregation techniques, for instance BitVector or Q_Digest. In this manus…
From Nowhere to Everywhere
2017
International audience; This paper presents a synthetic view of a variety of projects built upon an Erasmuss Mundus Master Course. It highlights double degree programs, European credits transfer, joint PhDs, research collaborations as well as few other related European projects going from Thematic Networks to another Erasmus Mundus Course.
Minimal Forbidden Factors of Circular Words
2017
Minimal forbidden factors are a useful tool for investigating properties of words and languages. Two factorial languages are distinct if and only if they have different (antifactorial) sets of minimal forbidden factors. There exist algorithms for computing the minimal forbidden factors of a word, as well as of a regular factorial language. Conversely, Crochemore et al.ÃÂ [IPL, 1998] gave an algorithm that, given the trie recognizing a finite antifactorial language M, computes a DFA of the language having M as set of minimal forbidden factors. In the same paper, they showed that the obtained DFA is minimal if the input trie recognizes the minimal forbidden factors of a single word. We gener…