Understanding the relationship between a search algorithm and the space of problems is a fundamental issue in the optimization field. In this paper, we lay the foundations to elaborate taxonomies of problems under est...
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Understanding the relationship between a search algorithm and the space of problems is a fundamental issue in the optimization field. In this paper, we lay the foundations to elaborate taxonomies of problems under estimation of distribution algorithms (EDAs). By using an infinite population model and assuming that the selection operator is based on the rank of the solutions, we group optimization problems according to the behavior of the EDA. Throughout the definition of an equivalence relation between functions it is possible to partition the space of problems in equivalence classes in which the algorithm has the same behavior. We show that only the probabilistic model is able to generate different partitions of the set of possible problems and hence, it predetermines the number of different behaviors that the algorithm can exhibit. As a natural consequence of our definitions, all the objective functions are in the same equivalence class when the algorithm does not impose restrictions to the probabilistic model. The taxonomy of problems, which is also valid for finite populations, is studied in depth for a simple EDA that considers independence among the variables of the problem. We provide the sufficient and necessary condition to decide the equivalence between functions and then we develop the operators to describe and count the members of a class. In addition, we show the intrinsic relation between univariate EDAs and the neighborhood system induced by the Hamming distance by proving that all the functions in the same class have the same number of local optima and that they are in the same ranking positions. Finally, we carry out numerical simulations in order to analyze the different behaviors that the algorithm can exhibit for the functions defined over the search space {0, 1}(3).
Contemporary psychiatry is becoming more biologically oriented in the attempt to elicit a biological rationale of mental diseases. Although mental disorders comprise mostly functional abnormalities, there is a substan...
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Contemporary psychiatry is becoming more biologically oriented in the attempt to elicit a biological rationale of mental diseases. Although mental disorders comprise mostly functional abnormalities, there is a substantial overlap between neurology and psychiatry in addressing cognitive disturbances. In schizophrenia, the presence of cognitive impairment prior to the onset of psychosis and early after its manifestation suggests that some neurocognitive abnormalities precede the onset of psychosis and may represent a trait marker. These cognitive alterations may arise from functional disconnectivity, as no significant brain damage has been found. In this review we aim to revise A.R. Luria's systematic approach used in the neuropsychological evaluation of cognitive functions, which was primarily applied in patients with neurological disorders and in the cognitive evaluation in schizophrenia and other related disorders. As proposed by Luria, cognitive processes, associated with higher cortical functions, may represent functional systems that are not localized in narrow, circumscribed areas of the brain, but occur among groups of concertedly working brain structures, each of which makes its own particular contribution to the organization of the functional system. Current developments in neuroscience provide evidence of functional connectivity in the brain. Therefore, Luria's approach may serve as a frame of reference for the analysis and interpretation of cognitive functions in general and their abnormalities in schizophrenia in particular. Having said that, modern technology, as well as experimental evidence, may help us to understand the brain better and lead us towards creating a new classification of cognitive functions. In schizophrenia research, multidisciplinary approaches must be utilized to address specific cognitive alterations. The relationships among the components of cognitive functions derived from the functional connectivity of the brain may provide an ins
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