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.

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.

Three essays on internationalization and firm entrepreneurial behavior

PAPER 1: A THEORY ON THE EFFECTS OF INTERNATIONALIZATION ON FIRM ENTREPRENEURIAL BEHAVIOR AND GROWTH Abstract This article addresses the relationship. Past findings reveal that the direct effects of internationalization on performance are mixed and inconclusive. Our framework integrates firm entrepreneurial behavior as a mediating force of the troublesome Drawing on the tension between the entrepreneurship literature and the organizational inertia theory, we argue that internationalization is key to minimizing the stifling effects of inertia and in engendering entrepreneurial behavior towards growth. We suggest that firms that internationalize at a young age and enjoy an intense degree of internationalization tend to become more entrepreneurial than do late and weakly internationalized firms. As a consequence, early and intense internationalizers experience superior growth. Aware of the inherent endogeneity of our propositions, we also discuss how consistent estimates can be obtained when testing the model empirically. PAPER 2: DOES INTERNATIONALIZATION MATTER FOR GROWTH? THE CASE OF SWISS SOFTWARE FIRMS. Abstract This paper seeks to address the issue of whether early and intense internationalization leads to superior firm growth. We revisit the hypotheses of previous studies within the emerging research domain of international entrepreneurship. Empirical analyses on the performance implications of internationalization have so far been limited and inconsistent. Our paper intends to make two contributions to the international entrepreneurship literature. First, we bring additional empirical evidence as to the inconclusive firm performance endogeneity in our causal model, using a sample of 103 Swiss international small and medium-sized enterprises (SMEs). On one hand, we find that the degree of internationalization significantly increases perceived firm growth (i.e., relative firm performance in a market); however, age at internationalization was unrelated to perceived firm growth. On the other hand, we reproduced the causal path of a highly cited study that showed how age at internationalization was significantly and negatively associated with objective firm growth (i.e., sales). Interestingly, our results support the study similar setting (OLS regression with comparable control variables); however, the effect for age at internationalization reverses when we correct for endogeneity. PAPER 3: EFFECT OF INTERNATIONALIZATION ON FIRM ENTREPRENEURIAL ORIENTATION AND PERFORMANCE: THE CASE OF SWISS SOFTWARE FIRMS. Abstract How does internationalization influence a firm orientation (EO) and is this related to firm growth? This paper inquires into the performance theorizing, we test a process model in which EO plays a mediating role in accounting for the relationship between internationalization and growth. We position this paper on the tension zone between the entrepreneurship literature and the organizational inertia theory. We lay out the argument that internationalization is source of opportunities that drives a firm and thus mitigates inertial pressure. Using a sample of Swiss software small and medium-sized enterprises (SMEs), we found that degree of internationalization (but not age of internationalization) increases EO, which subsequently increased firm growth.

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.