High order structure preserving explicit methods for solving linear-quadratic optimal control problems

[EN] We consider the numerical integration of linear-quadratic optimal control problems. This problem requires the solution of a boundary value problem: a non-autonomous matrix Riccati differential equation (RDE) with final conditions coupled with the state vector equation with initial conditions. The RDE has positive definite matrix solution and to numerically preserve this qualitative property we propose first to integrate this equation backward in time with a sufficiently accurate scheme. Then, this problem turns into an initial value problem, and we analyse splitting and Magnus integrators for the forward time integration which preserve the positive definite matrix solutions for the RDE. Duplicating the time as two new coordinates and using appropriate splitting methods, high order methods preserving the desired property can be obtained. The schemes make sequential computations and do not require the storrage of intermediate results, so the storage requirements are minimal. The proposed methods are also adapted for solving linear-quadratic N-player differential games. The performance of the splitting methods can be considerably improved if the system is a perturbation of an exactly solvable problem and the system is properly split. Some numerical examples illustrate the performance of the proposed methods.The author wishes to thank the University of California San Diego for its hospitality where part of this work was done. He also acknowledges the support of the Ministerio de Ciencia e Innovacion (Spain) under the coordinated project MTM2010-18246-C03. The author also acknowledges the suggestions by the referees to improve the presentation of this work.Blanes Zamora, S. (2015). High order structure preserving explicit methods for solving linear-quadratic optimal control problems. 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How Humans Differ from Other Animals in Their Levels of Morphological Variation

Animal species come in many shapes and sizes, as do the individuals and populations that make up each species. To us, humans might seem to show particularly high levels of morphological variation, but perhaps this perception is simply based on enhanced recognition of individual conspecifics relative to individual heterospecifics. We here more objectively ask how humans compare to other animals in terms of body size variation. We quantitatively compare levels of variation in body length (height) and mass within and among 99 human populations and 848 animal populations (210 species). We find that humans show low levels of within-population body height variation in comparison to body length variation in other animals. Humans do not, however, show distinctive levels of within-population body mass variation, nor of among-population body height or mass variation. These results are consistent with the idea that natural and sexual selection have reduced human height variation within populations, while maintaining it among populations. We therefore hypothesize that humans have evolved on a rugged adaptive landscape with strong selection for body height optima that differ among locations

Agent-Based Model of Therapeutic Adipose-Derived Stromal Cell Trafficking during Ischemia Predicts Ability To Roll on P-Selectin

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Genetic Control of a Central Pattern Generator: Rhythmic Oromotor Movement in Mice Is Controlled by a Major Locus near Atp1a2

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Personality psychology: Lexical approaches, assessment methods, and trait concepts reveal only half of the story—Why it is time for a paradigm shift

This article develops a comprehensive philosophy-of-science for personality psychology that goes far beyond the scope of the lexical approaches, assessment methods, and trait concepts that currently prevail. One of the field’s most important guiding scientific assumptions, the lexical hypothesis, is analysed from meta-theoretical viewpoints to reveal that it explicitly describes two sets of phenomena that must be clearly differentiated: 1) lexical repertoires and the representations that they encode and 2) the kinds of phenomena that are represented. Thus far, personality psychologists largely explored only the former, but have seriously neglected studying the latter. Meta-theoretical analyses of these different kinds of phenomena and their distinct natures, commonalities, differences, and interrelations reveal that personality psychology’s focus on lexical approaches, assessment methods, and trait concepts entails a) erroneous meta-theoretical assumptions about what the phenomena being studied actually are, and thus how they can be analysed and interpreted, b) that contemporary personality psychology is largely based on everyday psychological knowledge, and c) a fundamental circularity in the scientific explanations used in trait psychology. These findings seriously challenge the widespread assumptions about the causal and universal status of the phenomena described by prominent personality models. The current state of knowledge about the lexical hypothesis is reviewed, and implications for personality psychology are discussed. Ten desiderata for future research are outlined to overcome the current paradigmatic fixations that are substantially hampering intellectual innovation and progress in the field

Evaluation of appendicitis risk prediction models in adults with suspected appendicitis

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Indian cognitivism and the phenomenology of conceptualization

We perform conceptual acts throughout our daily lives; we are always judging others, guessing their intentions, agreeing or opposing their views and so on. These conceptual acts have phenomenological as well as formal richness. This paper attempts to correct the imbalance between the phenomenal and formal approaches to conceptualization by claiming that we need to shift from the usual dichotomies of cognitive science and epistemology such as the formal/empirical and the rationalist/ empiricist divides—to a view of conceptualization grounded in the Indian philosophical notion of “valid cognitio