Implicit optimality criterion for convex SIP problem with box constrained index set

We consider a convex problem of Semi-Infinite Programming (SIP) with multidimensional index set. In study of this problem we apply the approach suggested in [20] for convex SIP problems with one-dimensional index sets and based on the notions of immobile indices and their immobility orders. For the problem under consideration we formulate optimality conditions that are explicit and have the form of criterion. We compare this criterion with other known optimality conditions for SIP and show its efficiency in the convex case.

Categorical data clustering using a minimum message length criterion

Research on cluster analysis for categorical data continues to develop, new clustering algorithms being proposed. However, in this context, the determination of the number of clusters is rarely addressed. We propose a new approach in which clustering and the estimation of the number of clusters is done simultaneously for categorical data. We assume that the data originate from a finite mixture of multinomial distributions and use a minimum message length criterion (MML) to select the number of clusters (Wallace and Bolton, 1986). For this purpose, we implement an EM-type algorithm (Silvestre et al., 2008) based on the (Figueiredo and Jain, 2002) approach. The novelty of the approach rests on the integration of the model estimation and selection of the number of clusters in a single algorithm, rather than selecting this number based on a set of pre-estimated candidate models. The performance of our approach is compared with the use of Bayesian Information Criterion (BIC) (Schwarz, 1978) and Integrated Completed Likelihood (ICL) (Biernacki et al., 2000) using synthetic data. The obtained results illustrate the capacity of the proposed algorithm to attain the true number of cluster while outperforming BIC and ICL since it is faster, which is especially relevant when dealing with large data sets.

From "This is my body" to the Church in the twenty-first century: the Last Supper as the decisive moment and criterion of a renewed ecclesiology

Certains symptômes sont les indicateurs incontestés des très graves problèmes que connaît l’Église. S’ils existent aussi dans des confessions et des religions diverses, seuls seront examinés ici ceux qui concernent l’Église catholique. Parmi les plus significatifs figurent un fort déclin dans la participation à des activités religieuses comme les célébrations eucharistiques dominicales, surtout chez les jeunes, une pénurie presque catastrophique de prêtres ordonnés, une perte de prestige et d’influence de l’enseignement dispensé par l’Église. Ces symptômes varient en intensité selon les pays, mais les statistiques indiquent qu’ils se multiplient. Nombre de ces problèmes sont attribuables à l’extrême vélocité de changements qui surviennent partout et à l’apparente inaptitude de l’Église à s’adapter, en raison notamment de son attachement à la pensée néo-scolastique et à la tradition tridentine. Cette fidélité absolue à une tradition vieille de quatre cents ans l’empêche de se faire à un environnement en évolution rapide et radicale. Des changements appropriés s’imposent pratiquement partout dans l’Église. Or, pour que ceux-ci soient efficaces et respectueux de la nature propre de l’Église, la tradition est un guide qui ne suffit pas. S’appuyant sur les termes de l’encyclique Ecclesia de Eucharistia, « le moment décisif où elle (l’Église) a pris forme est certainement celui où a eu lieu l’institution de l’Eucharistie, dans la chambre à l’étage », la thèse présentée suit le plus près possible l’interprétation donnée aux paroles de Jésus, ceci est mon corps, telles qu’elles ont été prononcées la première fois. Selon cette évidence, il est permis d’affirmer que les caractéristiques définitoires de l’Église provenant de ces mots sont agape, unité, service. Tel doit être le principe directeur des changements. C’est sur une telle base que sont décrits les secteurs où les changements s’imposent ainsi que les aspects visés. Ces changements comprennent les points suivants : liturgie, sacrements, catéchèse, mystagogie, théologie, structure, gouvernance de l’Église et ses enseignements, évangélisation. Ces secteurs exigent des efforts sérieux dans la préparation des personnes touchées par ces changements et dans l’attention portée à l’exigence primordiale voulant qu’agape, unité et service soient les principes actifs et évidents régissant l’Église.

A Bayesian design criterion for locating the optimum point on a response surface

Most factorial experiments in industrial research form one stage in a sequence of experiments and so considerable prior knowledge is often available from earlier stages. A Bayesian A-optimality criterion is proposed for choosing designs, when each stage in experimentation consists of a small number of runs and the objective is to optimise a response. Simple formulae for the weights are developed, some examples of the use of the design criterion are given and general recommendations are made. (C) 2003 Elsevier B.V. All rights reserved.

The assessment of GCSE art: Criterion-referencing and cognitive abilities

In this paper Cognitive Abilities Test scores are compared directly with moderated GCSE scores awarded to the same group of pupils. For ease of interpretation the comparisons are presented in a graphical form. Whilst some provisional and tentative conclusions are drawn about the reliability of GCSE art, questions are raised about the general validity of criterion-referenced assessment in this area.

A hybridised evolutionary algorithm for multi-criterion minimum spanning tree problems

A hybridised and Knowledge-based Evolutionary Algorithm (KEA) is applied to the multi-criterion minimum spanning tree problems. Hybridisation is used across its three phases. In the first phase a deterministic single objective optimization algorithm finds the extreme points of the Pareto front. In the second phase a K-best approach finds the first neighbours of the extreme points, which serve as an elitist parent population to an evolutionary algorithm in the third phase. A knowledge-based mutation operator is applied in each generation to reproduce individuals that are at least as good as the unique parent. The advantages of KEA over previous algorithms include its speed (making it applicable to large real-world problems), its scalability to more than two criteria, and its ability to find both the supported and unsupported optimal solutions.

On translational superfluidity and the Landau criterion for Bose gases in the Gross-Pitaevski limit

The two-fluid and Landau criteria for superfluidity are compared for trapped Bose gases. While the two-fluid criterion predicts translational superfluidity, it is suggested, on the basis of the homogeneous Gross-Pitaevski limit, that a necessary part of Landau`s criterion, adequate for non-translationally invariant systems, does not hold for trapped Bose gases in the GP limit. As a consequence, if the compressibility is detected to be very large (infinite by experimental standards), the two-fluid criterion is seen to be the relevant one in case the system is a translational superfluid, while the Landau criterion is the relevant one if translational superfluidity is absent.

Entanglement degree measure and a criterion for sudden death as a phase transition in bipartite systems

We propose a method to compute the entanglement degree E of bipartite systems having dimension 2 x 2 and demonstrate that the partial transposition of density matrix, the Peres criterion, arise as a consequence Of Our method. Differently from other existing measures of entanglement, the one presented here makes possible the derivation of a criterion to verify if an arbitrary bipartite entanglement will suffers sudden death (SD) based only on the initial-state parameters. Our method also makes possible to characterize the SD as a dynamical quantum phase transition, with order parameter epsilon. having a universal critical exponent -1/2. (C) 2009 Elsevier Inc. All rights reserved.

A criterion for unitary similarity of upper triangular matrices in general position

Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A = [a(ij)] and B = [b(ij)] be upper triangular n x n matrices that are not similar to direct sums of square matrices of smaller sizes, or are in general position and have the same main diagonal. We prove that A and B are unitarily similar if and only if parallel to h(A(k))parallel to = parallel to h(B(k))parallel to for all h is an element of C vertical bar x vertical bar and k = 1, ..., n, where A(k) := [a(ij)](i.j=1)(k) and B(k) := [b(ij)](i.j=1)(k) are the leading principal k x k submatrices of A and B, and parallel to . parallel to is the Frobenius norm. (C) 2011 Elsevier Inc. All rights reserved.

Pair trading in Bovespa with a quantitative approach: cointegration, Ornstein-Uhlenbeck equation and Kelly criterion.

Pair trading is an old and well-known technique among traders. In this paper, we discuss an important element not commonly debated in Brazil: the cointegration between pairs, which would guarantee the spread stability. We run the Dickey-Fuller test to check cointegration, and then compare the results with non-cointegrated pairs. We found that the Sharpe ratio of cointegrated pairs is greater than the non-cointegrated. We also use the Ornstein-Uhlenbeck equation in order to calculate the half-life of the pairs. Again, this improves their performance. Last, we use the leverage suggested by Kelly Formula, once again improving the results.