Processes models, environmental analyses, and cognitive architectures: Quo vadis quantum probability theory? (Commentary on Pothos and Busemeyer)

A lot of research in cognition and decision making suffers from a lack of formalism. The quantum probability program could help to improve this situation, but we wonder whether it would provide even more added value if its presumed focus on outcome models were complemented by process models that are, ideally, informed by ecological analyses and integrated into cognitive architectures.

Diffraction theory of Fresnel lenses encoded in low-resolution devices

A mathematical model that describes the behavior of low-resolution Fresnel lenses encoded in any low-resolution device (e.g., a spatial light modulator) is developed. The effects of low-resolution codification, such the appearance of new secondary lenses, are studied for a general case. General expressions for the phase of these lenses are developed, showing that each lens behaves as if it were encoded through all pixels of the low-resolution device. Simple expressions for the light distribution in the focal plane and its dependence on the encoded focal length are developed and commented on in detail. For a given codification device an optimum focal length is found for best lens performance. An optimization method for codification of a single lens with a short focal length is proposed.

Diffraction theory of optimized low-resolution Fresnel encoded lenses

A mathematical model describing the behavior of low-resolution Fresnel encoded lenses (LRFEL's) encoded in any low-resolution device (e.g., a spatial light modulator) has recently been developed. From this model, an LRFEL with a short focal length was optimized by our imposing the maximum intensity of light onto the optical axis. With this model, analytical expressions for the light-amplitude distribution, the diffraction efficiency, and the frequency response of the optimized LRFEL's are derived.

Contexts and typologies in the analysis of welfare state legitimacy : a social psychological approach to political opinion formation

This dissertation analyses public opinion towards the welfare state across 29 European countries. Based on an interdisciplinary approach combining social psychological, sociological, and public opinion approaches to political opinion formation, it investigates how social position and shared beliefs shape perceived legitimacy of welfare institutions, and how social contexts impact on the processes of opinion formation. Drawing on social representations theory, as well as socialization and self-interest approaches, the dissertation analyses the role of social position in lay support for institutional solidarity. Normative beliefs-defined as preferred views regarding the organisation of social relations-mediate the effect of social position on welfare support. In addition, drawing on public opinion literature, the dissertation analyses opinion formation as a function of country-level structural (e.g., level of social spending, unemployment) and ideological factors (e.g., level of meritocracy). The dissertation comprises two theoretical and four empirical chapters. Three of the empirical chapters use data from the European Social Survey 2008. Using multilevel and typological approaches, the dissertation contributes to welfare attitude literature by showing that normative beliefs, such as distrust or egalitarianism, function as underlying mechanisms that link social position to policy attitudes (Chapter 3), and that characteristics of the national contexts influence the processes of political opinion formation (Chapters 3 and 4). Chapter 5 proposes and predicts a typology of the relationship between attitudes towards solidarity and attitudes towards control, reflecting the two central domains of government intervention. Finally, Chapter 6 examines welfare support in the realm of action and social protest, using data from a survey on Spanish Indigados activists. The findings of this dissertation inform contemporary debates about welfare state legitimacy and retrenchment. - Cette thèse avait pour but d'analyser l'opinion publique envers l'Etat social dans 29 pays européens. Basée sur une approche interdisciplinaire qui combine des perspectives psycho-sociales, sociologiques et d'opinion publique sur la formation d'opinion politique, la thèse étudie comment la position sociale et les croyances partagées façonnent la légitimité perçue des institutions de l'Etat social, et comment les contextes sociaux influencent les processus de formation d'opinion. Basée sur la théorie des représentations sociales, ainsi qu'une approche de socialisation et d'intérêt propre, cette thèse analyse le rôle des positions sociales dans le soutien envers la solidarité institutionnelle. Les croyances normatives-définies comme les visions préférées de l'organisation des rapports sociaux-médiatisent l'effet de la position sociale sur le soutien pour l'Etat social. De plus, s'inspirant de la littérature sur l'opinion publique, la thèse analyse la formation d'opinion en fonction des facteurs structurels (ex. le taux de dépenses sociales, le chômage) et idéologiques (ex. le degré de méritocratie). Cette thèse est composée de deux chapitres théoriques et quatre chapitres empiriques. Trois chapitres empiriques utilisent des données provenant de l'enquête European Social Survey 2008. Appliquant des approches multi-niveux et typoloqiques, la thèse contribue à la littérature sur les attitudes envers l'Etat social en montrant que les croyances normatives, telles que la méfiance ou l'égalitarisme, fonctionnent comme des mécanismes sous-jacents qui relient la position sociale aux attitudes politiques (Chapitre 3), et que les caractéristiques des contextes nationaux influencent les processus de formation d'opinion politique (Chapitres 3 et 4). Le chapitre 5 propose et prédit une typologie sur le rapport entre les attitudes envers la solidarité et celles envers le contrôle, renvoyant à deux domaines centraux de régulation étatique. Enfin, le chapitre 6 examine le soutien à l'Etat social dans le domaine de l'action protestataire, utilisant des données d'une enquête menée auprès des militants espagnols du mouvement des Indignés. Les résultats de cette thèse apportent des éléments qui éclairent les débats contemporains sur la légitimité de l'Etat social et son démantèlement.

Vacuum decay in quantum field theory

We study the contribution to vacuum decay in field theory due to the interaction between the long- and short-wavelength modes of the field. The field model considered consists of a scalar field of mass M with a cubic term in the potential. The dynamics of the long-wavelength modes becomes diffusive in this interaction. The diffusive behavior is described by the reduced Wigner function that characterizes the state of the long-wavelength modes. This function is obtained from the whole Wigner function by integration of the degrees of freedom of the short-wavelength modes. The dynamical equation for the reduced Wigner function becomes a kind of Fokker-Planck equation which is solved with suitable boundary conditions enforcing an initial metastable vacuum state trapped in the potential well. As a result a finite activation rate is found, even at zero temperature, for the formation of true vacuum bubbles of size M-1. This effect makes a substantial contribution to the total decay rate.

Perturbations on domain walls and strings: A covariant theory

A covariant formalism is developed for describing perturbations on vacuum domain walls and strings. The treatment applies to arbitrary domain walls in (N+1)-dimensional flat spacetime, including the case of bubbles of a true vacuum nucleating in a false vacuum. Straight strings and planar walls in de Sitter space, as well as closed strings and walls nucleating during inflation, are also considered. Perturbations are represented by a scalar field defined on the unperturbed wall or string world sheet. In a number of interesting cases, this field has a tachyonic mass and a nonminimal coupling to the world-sheet curvature.

Perturbation theory for classical thermodynamic Green's functions

A systematic time-dependent perturbation scheme for classical canonical systems is developed based on a Wick's theorem for thermal averages of time-ordered products. The occurrence of the derivatives with respect to the canonical variables noted by Martin, Siggia, and Rose implies that two types of Green's functions have to be considered, the propagator and the response function. The diagrams resulting from Wick's theorem are "double graphs" analogous to those introduced by Dyson and also by Kawasaki, in which the response-function lines form a "tree structure" completed by propagator lines. The implication of a fluctuation-dissipation theorem on the self-energies is analyzed and compared with recent results by Deker and Haake.

On the Schoenberg transformations in data analysis: theory and illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A distance-based discriminant algorithm and a robust multidimensional centroid estimate illustrate the theory, closely connected to the Gaussian kernels of Machine Learning.

Dissipation, noise and vacuum decay in quantum field theory

We study the process of vacuum decay in quantum field theory focusing on the stochastic aspects of the interaction between long- and short-wavelength modes. This interaction results in a diffusive behavior of the reduced Wigner function describing the state of long-wavelength modes, and thereby to a finite activation rate even at zero temperature. This effect can make a substantial contribution to the total decay rate.

Microstates of a neutral black hole in M theory

We consider vacuum solutions in M theory of the form of a five-dimensional Kaluza-Klein black hole cross T6. In a certain limit, these include the five-dimensional neutral rotating black hole (cross T6). From a type-IIA standpoint, these solutions carry D0 and D6 charges. We show that there is a simple D-brane description which precisely reproduces the Hawking-Bekenstein entropy in the extremal limit, even though supersymmetry is completely broken.

Self-dynamic structure factor of dense liquids: Theory and simulation

The self-intermediate dynamic structure factor Fs(k,t) of liquid lithium near the melting temperature is calculated by molecular dynamics. The results are compared with the predictions of several theoretical approaches, paying special attention to the Lovesey model and the Wahnstrm and Sjgren mode-coupling theory. To this end the results for the Fs(k,t) second memory function predicted by both models are compared with the ones calculated from the simulations.

Quantitative Assessment of Soil Physical Quality in Northern China Based on S-theory

ABSTRACT Quantitative assessment of soil physical quality is of great importance for eco-environmental pollution and soil quality studies. In this paper, based on the S-theory, data from 16 collection sites in the Haihe River Basin in northern China were used, and the effects of soil particle size distribution and bulk density on three important indices of theS-theory were investigated on a regional scale. The relationships between unsaturated hydraulic conductivityKi at the inflection point and S values (S/hi) were also studied using two different types of fitting equations. The results showed that the polynomial equation was better than the linear equation for describing the relationships between -log Ki and -logS, and -log Kiand -log (S/hi)2; and clay content was the most important factor affecting the soil physical quality index (S). The variation in the S index according to soil clay content was able to be fitted using a double-linear-line approach, with decrease in the S index being much faster for clay content less than 20 %. In contrast, the bulk density index was found to be less important than clay content. The average S index was 0.077, indicating that soil physical quality in the Haihe River Basin was good.