A global optimization approach for generating efficient points for multiobjective concave fractional programs

In this article, we present a global optimization approach for generating efficient points for multiobjective concave fractional programming problems. The main work of the approach involves solving an instance of a concave multiplicative fractional program (W̄). Problem (W̄) is a global optimization problem for which no known algorithms are available. Therefore, to render the approach practical, we develop and validate a branch and bound algorithm for globally solving problem (W̄). To illustrate the performance of the global optimization approach, we use it to generate efficient points for a sample multiobjective concave fractional program. Copyright © 2006 John Wiley & Sons, Ltd.     

Psychotic functioning in adolescence: The perverse solution to survive

A psychotic breakdown in adolescence marks the emergence of a manifest aspect of a more complex process that has its origins in the patient's family pre‐history and in the patient's childhood story. This period of life is characterized by a sensorial explosion and adolescents will react differently according to the different resources they have at their disposal. Adolescents will attempt to create defensive solutions in order to face this decompensation on their own. In particular, polymorphously perverse behaviours can be utilized because of their specific characteristics in order to create a potent defence used to arrest a still more severe regression and at the same time providing the time necessary to safely navigate through a difficult and dangerous developmental phase. These solutions can be transitory or transform themselves into lasting defensive adaptations. These defensive modalities are very complex and articulated and can become fossilized in time, as, for example, in the case of a use of perverse defences against a breakdown. An analyst finding him/herself in these situations will find it difficult to differentiate in the diagnosis between a condition that is due to a perverse functioning used as a defence against decompensation, and a truly perverse structure that is beginning to emerge after puberty.     

Orientational high-entropy alloys

In high-entropy alloys (HEA), the configurational entropy arising from the presence of multiple elements, stabilizes a disordered solid solution in preference to the possible formation of compounds. In the current work, we identify cluster compounds (of the type AM₄X₈) as orientational analogues of HEA (as a first report on orientational high-entropy systems). In cluster compounds, orientational disorder increases the entropy and plays a role analogous to positional disorder in HEA. In the GaMo₄S₈ compound, at temperatures greater than 50 K, the entropic benefit more than makes up for the strain energy cost and stabilizes the disordered phase in preference to an orientationally ordered compound.     

Efficient atomic packing clusters and glass formation in ternary Al-based metallic glasses

In this article, we propose an efficient atomic packing cluster-based composition protocol to help design Al-based metallic glasses. Its validity is verified by some typical experimental data from the literatures. Furthermore, with this understanding, the Al–Ni–Y alloy system is re-evaluated. As a result, the best glass former Al₈₆Ni₉Y₅ in this system, with the critical thickness of about 500 µm, is successfully fabricated by wedge casting.     

MILL'S ARGUMENT FOR OTHER MINDS

Montesquieu's Considérations sur les causes de la grandeur des Romains et de leur décadence (1733/1734) is a methodological exercise in causal explanation on the meso-level applied to the subject of the military rise and fall of Rome. Rome is described as a system with contingent initial conditions that have a strong path-determining effect. Contingent and plastic initial configurations become highly determining in their subsequent operation, thanks to self-reinforcing feedback loops. Montesquieu's method seems influenced by the ruthless commitment to efficient causality and the reductionism of seventeenth-century mechanicist philosophy; but in contrast to these predecessors, he is more interested in dynamic processes than in unchangeable substances, and his use of efficient causality in the context of a system approach implies a form of holism that is lacking in his predecessors. The formal and conceptual analysis in this article is in many ways complementary with Paul Rahe's recent predominantly political analysis of the Considérations. At the same time, this article points to a problem in the works on the Enlightenment by Jonathan Israel: his account stresses a one-dimensional continuum consisting of Radical, Moderate and Counter-Enlightenment. This invites Israel to place the combined religious, political and philosophical views of each thinker on one of these three points. His scheme runs into trouble when a thinker with moderate religious and political views produces radical philosophical concepts. Montesquieu's Considérations is a case in point.     

Multiple Local Solutions and Geomin Rotation

In exploratory factor analysis, factor rotation is conducted to improve model interpretability. A promising and increasingly popular factor rotation method is geomin rotation. Geomin rotation, however, frequently encounters multiple local solutions. We report a simulation study that explores the frequency of local solutions in geomin rotation and the implications of such phenomena. The findings include: (1) multiple local solutions exist for geomin rotation in a variety of situations; (2) ? = .01 provides satisfactory rotated factor loadings in most situations; (3) 100 random starts appear sufficient to examine the multiple solution phenomenon; and (4) a population global solution may correspond to a sample local solution rather than the sample global solution.     

Degeneracy in Candecomp/Parafac explained for p × p × 2 arrays of rank p + 1 or higher

The Candecomp/Parafac (CP) model decomposes a three-way array into a prespecified number R of rank-1 arrays and a residual array, in which the sum of squares of the residual array is minimized. The practical use of CP is sometimes complicated by the occurrence of so-called degenerate solutions, in which some components are highly correlated in all three modes and the elements of these components become arbitrarily large. We consider the real-valued CP model in which p × p × 2 arrays of rank p + 1 or higher are decomposed into p rank-1 arrays and a residual array. It is shown that the CP objective function does not have a minimum in these cases, but an infimum. Moreover, any sequence of CP approximations, of which the objective value approaches the infimum, will become degenerate. This result extends Ten Berge, Kiers, & De Leeuw (1988), who consider a particular 2 × 2 × 2 array of rank 3. Request for reprints should be sent to Alwin Stegeman, Heijmans Institute of Psychological Research, University of Groningen, Grote Kruisstraat 2/1, 9712 TS Groningen, The Netherlands. The author is obliged to Jos ten Berge and Henk Kiers for helpful comments. Also, the author would like to thank the Associate Editor and the anonymous reviewers for many suggestions on how to improve the contents and the presentation of the paper.     

Statistical inference of minimum rank factor analysis

For any given number of factors, Minimum Rank Factor Analysis yields optimal communalities for an observed covariance matrix in the sense that the unexplained common variance with that number of factors is minimized, subject to the constraint that both the diagonal matrix of unique variances and the observed covariance matrix minus that diagonal matrix are positive semidefinite. As a result, it becomes possible to distinguish the explained common variance from the total common variance. The percentage of explained common variance is similar in meaning to the percentage of explained observed variance in Principal Component Analysis, but typically the former is much closer to 100 than the latter. So far, no statistical theory of MRFA has been developed. The present paper is a first start. It yields closed-form expressions for the asymptotic bias of the explained common variance, or, more precisely, of the unexplained common variance, under the assumption of multivariate normality. Also, the asymptotic variance of this bias is derived, and also the asymptotic covariance matrix of the unique variances that define a MRFA solution. The presented asymptotic statistical inference is based on a recently developed perturbation theory of semidefinite programming. A numerical example is also offered to demonstrate the accuracy of the expressions.This work was supported, in part, by grant DMS-0073770 from the National Science Foundation.     

Modification indices for the 2-PL and the nominal response model

In this paper, it is shown that various violations of the 2-PL model and the nominal response model can be evaluated using the Lagrange multiplier test or the equivalent efficient score test. The tests presented here focus on violation of local stochastic independence and insufficient capture of the form of the item characteristic curves. Primarily, the tests are item-oriented diagnostic tools, but taken together, they also serve the purpose of evaluation of global model fit. A useful feature of Lagrange multiplier statistics is that they are evaluated using maximum likelihood estimates of the null-model only, that is, the parameters of alternative models need not be estimated. As numerical examples, an application to real data and some power studies are presented.