scholarly journals Efficient Algorithms on the Family Associated to an Implicational System

2004 ◽  
Vol Vol. 6 no. 2 ◽  
Author(s):  
Karell Bertet ◽  
Mirabelle Nebut
Keyword(s):  
Closure Operator ◽  
Efficient Algorithms ◽  
Minimal Size ◽  
Closure Operators ◽  
New Approach ◽  
The Family ◽  
Finite Set ◽  
International Audience ◽  
Moore Family

International audience An implication system (IS) on a finite set S is a set of rules called Σ -implications of the kind A →_Σ B, with A,B ⊆ S. A subset X ⊆ S satisfies A →_Σ B when ''A ⊆ X implies B ⊆ X'' holds, so ISs can be used to describe constraints on sets of elements, such as dependency or causality. ISs are formally closely linked to the well known notions of closure operators and Moore families. This paper focuses on their algorithmic aspects. A number of problems issued from an IS Σ (e.g. is it minimal, is a given implication entailed by the system) can be reduced to the computation of closures φ _Σ (X), where φ _Σ is the closure operator associated to Σ . We propose a new approach to compute such closures, based on the characterization of the direct-optimal IS Σ _do which has the following properties: \beginenumerate ıtemit is equivalent to Σ ıtemφ _Σ _do(X) (thus φ _Σ (X)) can be computed by a single scanning of Σ _do-implications ıtemit is of minimal size with respect to ISs satisfying 1. and 2. \endenumerate We give algorithms that compute Σ _do, and from Σ _do closures φ _Σ (X) and the Moore family associated to φ _Σ .

scholarly journals A symbolic projection of Langton's Ant

2003 ◽  
Vol DMTCS Proceedings vol. AB,... (Proceedings) ◽  
Author(s):  
Anahi Gajardo
Keyword(s):  
Point Of View ◽  
Algebraic Characterization ◽  
Transition Rule ◽  
Regular Graphs ◽  
New Approach ◽  
The Family ◽  
International Audience ◽  
Topological Dynamical Systems

International audience The Langton's ant is studied from the point of view of topological dynamical systems. A new approach which associate a subshift to the system is proposed.The transition rule is generalized to the family of bi-regular graphs $\Gamma(k,d)$ and the dependence of the dynamical system on $k$ and $d$ is analyzed. A classification of the $\Gamma (k,d)$ graphs based on the dynamical properties of the subshift is established. Also a hierarchy is defined on the graphs through the subset relation of the respective subshifts. The analysis are worked out by establishing an algebraic characterization of the forbidden words of the subshift.

scholarly journals Characterization of Infinite LSP Words and Endomorphisms Preserving the LSP Property

2019 ◽  
Vol 30 (01) ◽  
pp. 171-196 ◽  
Author(s):  
Gwenaël Richomme
Keyword(s):  
Infinite Words ◽  
Infinite Word ◽  
The Family ◽  
Finite Set ◽  
Special Factors

Answering a question of G. Fici, we give an [Formula: see text]-adic characterization of the family of infinite LSP words, that is, the family of infinite words having all their left special factors as prefixes. More precisely we provide a finite set of morphisms [Formula: see text] and an automaton [Formula: see text] such that an infinite word is LSP if and only if it is [Formula: see text]-adic and one of its directive words is recognizable by [Formula: see text]. Then we characterize the endomorphisms that preserve the property of being LSP for infinite words. This allows us to prove that there exists no set [Formula: see text] of endomorphisms for which the set of infinite LSP words corresponds to the set of [Formula: see text]-adic words. This implies that an automaton is required no matter which set of morphisms is used.

Structure and properties of strong prefix codes of pictures

2015 ◽  
Vol 27 (2) ◽  
pp. 123-142 ◽  
Author(s):  
MARCELLA ANSELMO ◽  
DORA GIAMMARRESI ◽  
MARIA MADONIA
Keyword(s):  
Polynomial Time ◽  
Complete Characterization ◽  
Structure And Properties ◽  
Minimal Size ◽  
Prefix Code ◽  
Decoding Algorithm ◽  
Prefix Codes ◽  
The Family ◽  
Definition Of

A setX⊆ Σ** of pictures is a code if every picture over Σ is tilable in at most one way with pictures inX. The definition ofstrong prefix codeis introduced. The family of finite strong prefix codes is decidable and it has a polynomial time decoding algorithm. Maximality for finite strong prefix codes is also studied and related to the notion of completeness. We prove that any finite strong prefix code can be embedded in a unique maximal strong prefix code that has minimal size and cardinality. A complete characterization of the structure of maximal finite strong prefix codes completes the paper.

scholarly journals The topology of θω-open sets

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5369-5377 ◽  
Author(s):  
Ghour Al ◽  
Bayan Irshedat
Keyword(s):  
Topological Space ◽  
Closure Operator ◽  
Sufficient Conditions ◽  
Topological Spaces ◽  
Product Theorem ◽  
Closure Operators ◽  
Separation Axiom ◽  
New Class

We define the ??-closure operator as a new topological operator. We show that ??-closure of a subset of a topological space is strictly between its usual closure and its ?-closure. Moreover, we give several sufficient conditions for the equivalence between ??-closure and usual closure operators, and between ??-closure and ?-closure operators. Also, we use the ??-closure operator to introduce ??-open sets as a new class of sets and we prove that this class of sets lies strictly between the class of open sets and the class of ?-open sets. We investigate ??-open sets, in particular, we obtain a product theorem and several mapping theorems. Moreover, we introduce ?-T2 as a new separation axiom by utilizing ?-open sets, we prove that the class of !-T2 is strictly between the class of T2 topological spaces and the class of T1 topological spaces. We study relationship between ?-T2 and ?-regularity. As main results of this paper, we give a characterization of ?-T2 via ??-closure and we give characterizations of ?-regularity via ??-closure and via ??-open sets.

scholarly journals Secure frameproof codes through biclique covers

2012 ◽  
Vol Vol. 14 no. 2 (Graph Theory) ◽  
Author(s):  
Hossein Hajiabolhassan ◽  
Farokhlagha Moazami
Keyword(s):  
Binary Code ◽  
Minimum Size ◽  
The Family ◽  
Frameproof Code ◽  
Finite Set ◽  
International Audience ◽  
Frameproof Codes ◽  
Kneser Graphs ◽  
Cover Free Families ◽  
Element Set

Graph Theory International audience For a binary code Γ of length v, a v-word w produces by a set of codewords {w1,...,wr}⊆Γ if for all i=1,...,v, we have wi∈{w1i,...,wri} . We call a code r-secure frameproof of size t if |Γ|=t and for any v-word that is produced by two sets C1 and C2 of size at most r then the intersection of these sets is nonempty. A d-biclique cover of size v of a graph G is a collection of v-complete bipartite subgraphs of G such that each edge of G belongs to at least d of these complete bipartite subgraphs. In this paper, we show that for t≥2r, an r-secure frameproof code of size t and length v exists if and only if there exists a 1-biclique cover of size v for the Kneser graph KG(t,r) whose vertices are all r-subsets of a t-element set and two r-subsets are adjacent if their intersection is empty. Then we investigate some connection between the minimum size of d-biclique covers of Kneser graphs and cover-free families, where an (r,w;d) cover-free family is a family of subsets of a finite set such that the intersection of any r members of the family contains at least d elements that are not in the union of any other w members. Also, we present an upper bound for 1-biclique covering number of Kneser graphs.

scholarly journals Improved inclusion-exclusion identities via closure operators

2000 ◽  
Vol Vol. 4 no. 1 ◽  
Author(s):  
Klaus Dohmen
Keyword(s):  
Closure Operator ◽  
Chromatic Polynomial ◽  
Finite Family ◽  
Exclusion Principle ◽  
Closure Operators ◽  
Base Property ◽  
Power Set ◽  
International Audience ◽  
Broken Circuit

International audience Let (A_v)_v ∈ V be a finite family of sets. We establish an improved inclusion-exclusion identity for each closure operator on the power set of V having the unique base property. The result generalizes three improvements of the inclusion-exclusion principle as well as Whitney's broken circuit theorem on the chromatic polynomial of a graph.

scholarly journals A new approach to ψ-continuity

2009 ◽  
Vol 42 (1) ◽  
pp. 107-117
Author(s):  
Małgorzata Terepeta
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
New Approach ◽  
Density Topology ◽  
The Family ◽  
Real Anal ◽  
Fixed Function

Abstract Let Tψ be a ψ-density topology for a fixed function ψ. For any topological space X with the topology τ we will consider the family C (X, ℝψ) of all continuous functions f from (X, τ) into (ℝ, Tψ). The main aim of this paper is to investigate when C (X, ℝψ) is a ring. This article is based on the results achieved by M. Knox [A characterization of rings of density continuous functions, Real Anal. Exchange 31 (2005), 165-177].

Prothrombin Metz : Purification and Characterization of a Variant of Human Prothrombin

1979 ◽  
Author(s):  
M Ribieto ◽  
J Elion ◽  
D Labie ◽  
F Josso
Keyword(s):  
Molecular Weight ◽  
Gel Electrophoresis ◽  
Polyacrylamide Gel Electrophoresis ◽  
Factor Xa ◽  
Polyacrylamide Gel ◽  
Cleavage Pattern ◽  
Purification And Characterization ◽  
Double Immunodiffusion ◽  
The Family

For the purification of the abnormal prothrombin (Pt Metz), advantage has been taken of the existence in the family of three siblings who, being double heterozygotes for Pt Metz and a hypoprothrombinemia, have no normal Pt. Purification procedures included barium citrate adsorption and chromatography on DEAE Sephadex as for normal Pt. As opposed to some other variants (Pt Barcelona and Madrid), Pt Metz elutes as a single symetrical peak. By SDS polyacrylamide gel electrophoresis, this material is homogeneous and appears to have the same molecular weight as normal Pt. Comigration of normal and abnormal Pt in the absence of SDS, shows a double band suggesting an abnormal charge for the variant. Pt Metz exhibits an identity reaction with the control by double immunodiffusion. Upon activation by factor Xa, Pt Metz can generate amydolytic activity on Bz-Phe-Val-Arg-pNa (S2160), but only a very low clotting activity. Clear abnormalities are observed in the cleavage pattern of Pt Metz when monitored by SDS gel electrophoresis. The main feature are the accumulation of prethrombin l (Pl) and the appearance of abnormal intermediates migrating faster than Pl.

scholarly journals Sustainability Investigation of Vehicles’ CO2 Emission in Hungary

2021 ◽  
Vol 13 (15) ◽  
pp. 8237
Author(s):  
István Árpád ◽  
Judit T. Kiss ◽  
Gábor Bellér ◽  
Dénes Kocsis
Keyword(s):  
Energy Efficiency ◽  
Co2 Emissions ◽  
Energy Supply ◽  
Internal Combustion Engines ◽  
Combustion Engines ◽  
The European Union ◽  
New Approach ◽  
Technology System ◽  
Low Co2

The regulation of vehicular CO2 emissions determines the permissible emissions of vehicles in units of g CO2/km. However, these values only partially provide adequate information because they characterize only the vehicle but not the emission of the associated energy supply technology system. The energy needed for the motion of vehicles is generated in several ways by the energy industry, depending on how the vehicles are driven. These methods of energy generation consist of different series of energy source conversions, where the last technological step is the vehicle itself, and the result is the motion. In addition, sustainability characterization of vehicles cannot be determined by the vehicle’s CO2 emissions alone because it is a more complex notion. The new approach investigates the entire energy technology system associated with the generation of motion, which of course includes the vehicle. The total CO2 emissions and the resulting energy efficiency have been determined. For this, it was necessary to systematize (collect) the energy supply technology lines of the vehicles. The emission results are not given in g CO2/km but in g CO2/J, which is defined in the paper. This new method is complementary to the European Union regulative one, but it allows more complex evaluations of sustainability. The calculations were performed based on Hungarian data. Finally, using the resulting energy efficiency values, the emission results were evaluated by constructing a sustainability matrix similar to the risk matrix. If only the vehicle is investigated, low CO2 emissions can be achieved with vehicles using internal combustion engines. However, taking into consideration present technologies, in terms of sustainability, the spread of electric-only vehicles using renewable energies can result in improvement in the future. This proposal was supported by the combined analysis of the energy-specific CO2 emissions and the energy efficiency of vehicles with different power-driven systems.

Sign in / Sign up

Export Citation Format

Share Document