The spectrum of minimal defining sets of some Steiner systems

For a design D, define spec(D) = {\M\ \ M is a minimal defining set of D} to be the spectrum of minimal defining sets of D. In this note we give bounds on the size of an element in spec(D) when D is a Steiner system. We also show that the spectrum of minimal defining sets of the Steiner triple system given by the points and lines of PG(3,2) equals {16,17,18,19,20,21,22}, and point out some open questions concerning the Steiner triple systems associated with PG(n, 2) in general. (C) 2002 Elsevier Science B.V. All rights reserved.

A flaw in the use of minimal defining sets for secret sharing schemes

It is shown that in some cases it is possible to reconstruct a block design D uniquely from incomplete knowledge of a minimal defining set for D. This surprising result has implications for the use of minimal defining sets in secret sharing schemes.

Uma metodologia para modelagem e avaliação da dependabilidade de redes industriais sem fio

Ensuring the dependability requirements is essential for the industrial applications since faults may cause failures whose consequences result in economic losses, environmental damage or hurting people. Therefore, faced from the relevance of topic, this thesis proposes a methodology for the dependability evaluation of industrial wireless networks (WirelessHART, ISA100.11a, WIA-PA) on early design phase. However, the proposal can be easily adapted to maintenance and expansion stages of network. The proposal uses graph theory and fault tree formalism to create automatically an analytical model from a given wireless industrial network topology, where the dependability can be evaluated. The evaluation metrics supported are the reliability, availability, MTTF (mean time to failure), importance measures of devices, redundancy aspects and common cause failures. It must be emphasized that the proposal is independent of any tool to evaluate quantitatively the target metrics. However, due to validation issues it was used a tool widely accepted on academy for this purpose (SHARPE). In addition, an algorithm to generate the minimal cut sets, originally applied on graph theory, was adapted to fault tree formalism to guarantee the scalability of methodology in wireless industrial network environments (< 100 devices). Finally, the proposed methodology was validate from typical scenarios found in industrial environments, as star, line, cluster and mesh topologies. It was also evaluated scenarios with common cause failures and best practices to guide the design of an industrial wireless network. For guarantee scalability requirements, it was analyzed the performance of methodology in different scenarios where the results shown the applicability of proposal for networks typically found in industrial environments

Reliability evaluation of distribution systems considering automatic reclosers

This paper presents a new methodology to evaluate in a predictive way the reliability of distribution systems, considering the impact of automatic recloser switches. The developed algorithm is based on state enumeration techniques with Markovian models and on the minimal cut set theory. Some computational aspects related with the implementation of the proposed algorithm in typical distribution networks are also discussed. The description of the proposed approach is carried out using a sample test system. The results obtained with a typical configuration of a Brazilian system (EDP Bandeirante Energia S.A.) are presented and discussed.

Reliability analysis for hazard and operability studies

Fault tree analysis is used as a tool within hazard and operability (Hazop) studies. The present study proposes a new methodology for obtaining the exact TOP event probability of coherent fault trees. The technique uses a top-down approach similar to that of FATRAM. This new Fault Tree Disjoint Reduction Algorithm resolves all the intermediate events in the tree except OR gates with basic event inputs so that a near minimal cut sets expression is obtained. Then Bennetts' disjoint technique is applied and remaining OR gates are resolved. The technique has been found to be appropriate as an alternative to Monte Carlo simulation methods when rare events are countered and exact results are needed. The algorithm has been developed in FORTRAN 77 on the Perq workstation as an addition to the Aston Hazop package. The Perq graphical environment enabled a friendly user interface to be created. The total package takes as its input cause and symptom equations using Lihou's form of coding and produces both drawings of fault trees and the Boolean sum of products expression into which reliability data can be substituted directly.

Minimal anomaly-free chiral fermion sets and gauce coupling unification

We look for minimal chiral sets of fermions beyond the standard model that are anomaly free and, simultaneously, vectorlike particles with respect to color SU(3) and electromagnetic U(1). We then study whether the addition of such particles to the standard model particle content allows for the unification of gauge couplings at a high energy scale, above 5.0 x 10(15) GeV so as to be safely consistent with proton decay bounds. The possibility to have unification at the string scale is also considered. Inspired in grand unified theories, we also search for minimal chiral fermion sets that belong to SU(5) multiplets, restricted to representations up to dimension 50. It is shown that, in various cases, it is possible to achieve gauge unification provided that some of the extra fermions decouple at relatively high intermediate scales.

Doubling and Tripling Constructions for Defining Sets in Steiner Triple Systems

A minimal defining set of a Steiner triple system on a points (STS(v)) is a partial Steiner triple system contained in only this STS(v), and such that any of its proper subsets is contained in at least two distinct STS(v)s. We consider the standard doubling and tripling constructions for STS(2v + 1) and STS(3v) from STS(v) and show how minimal defining sets of an STS(v) gives rise to minimal defining sets in the larger systems. We use this to construct some new families of defining sets. For example, for Steiner triple systems on, 3" points; we construct minimal defining sets of volumes varying by as much as 7(n-/-).

On Solution Sets of Information Inequalities

We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce important properties of Bayesian networks, which is important within causal inference.

Effective atomic orbitals for fuzzy atoms

The method of extracting effective atomic orbitals and effective minimal basis sets from molecular wave function characterizing the state of an atom in a molecule is developed in the framework of the "fuzzy" atoms. In all cases studied, there were as many effective orbitals that have considerable occupation numbers as orbitals in the classical minimal basis. That is considered to be of high conceptual importance

Effective atomic orbitals for fuzzy atoms

The method of extracting effective atomic orbitals and effective minimal basis sets from molecular wave function characterizing the state of an atom in a molecule is developed in the framework of the "fuzzy" atoms. In all cases studied, there were as many effective orbitals that have considerable occupation numbers as orbitals in the classical minimal basis. That is considered to be of high conceptual importance

Exact Unification and Admissibility

A new hierarchy of "exact" unification types is introduced, motivated by the study of admissible rules for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by instantiation, but rather by inclusion over the corresponding sets of unified identities. Minimal complete sets of unifiers under this new preordering always have a smaller or equal cardinality than those provided by the standard instantiation preordering, and in significant cases a dramatic reduction may be observed. In particular, the classes of distributive lattices, idempotent semigroups, and MV-algebras, which all have nullary unification type, have unitary or finitary exact type. These results are obtained via an algebraic interpretation of exact unification, inspired by Ghilardi's algebraic approach to equational unification.

PC Points and their Application to Vector Optimization

AMS subject classification: 90C29, 90C48

Chaotic planar piecewise smooth vector fields with non-trivial minimal sets

In this paper some aspects on chaotic behavior and minimality in planar piecewise smooth vector fields theory are treated. The occurrence of non-deterministic chaos is observed and the concept of orientable minimality is introduced. Some relations between minimality and orientable minimality are also investigated and the existence of new kinds of non-trivial minimal sets in chaotic systems is observed. The approach is geometrical and involves the ordinary techniques of non-smooth systems.

Fast Algorithms Using Minimal Data Structures for Common Topological Relationships in Large, Irregularly-spaced Topographic Data Sets

Digital terrain models (DTM) typically contain large numbers of postings, from hundreds of thousands to billions. Many algorithms that run on DTMs require topological knowledge of the postings, such as finding nearest neighbors, finding the posting closest to a chosen location, etc. If the postings are arranged irregu- larly, topological information is costly to compute and to store. This paper offers a practical approach to organizing and searching irregularly-space data sets by presenting a collection of efficient algorithms (O(N),O(lgN)) that compute important topological relationships with only a simple supporting data structure. These relationships include finding the postings within a window, locating the posting nearest a point of interest, finding the neighborhood of postings nearest a point of interest, and ordering the neighborhood counter-clockwise. These algorithms depend only on two sorted arrays of two-element tuples, holding a planimetric coordinate and an integer identification number indicating which posting the coordinate belongs to. There is one array for each planimetric coordinate (eastings and northings). These two arrays cost minimal overhead to create and store but permit the data to remain arranged irregularly.