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.

Einfluss von L-Carnitin-supplementierter total parenteraler Ernährung (TPE) auf die postoperative Fett- und Stickstoff-Utilisation [Effect of L-carnitine supplemented total parenteral nutrition on postoperative lipid and nitrogen utilization].

During episodes of trauma carnitine-free total parenteral nutrition (TPN) may result in a reduction of the total body carnitine pool, leading to a diminished rate of fat oxidation. Sixteen patients undergoing esophagectomy were equally and randomly divided and received isonitrogenous (0.2 gN/kg.day) and isocaloric (35 kcal/kg.day TPN over 11 days without and with L-carnitine supplementation (12 mg/kg.day). Compared with healthy controls, the total body carnitine pool was significantly reduced in both groups prior to the operation. Without supplementation carnitine concentrations were maintained, while daily provision of carnitine resulted in an elevation of total carnitine mainly due to an increase of the free fraction. Without supplementation the cumulative urinary carnitine losses were 11.5 +/- 6.3 mmol corresponding to 15.5% +/- 8.5% of the estimated total body carnitine pool. Patients receiving carnitine revealed a positive carnitine balance in the immediate postoperative phase, 11.1% +/- 19.0% of the infused carnitine being retained. After 11 days of treatment comparable values for respiratory quotient, plasma triglycerides, free fatty acids, ketone bodies, and cumulative nitrogen balance were observed. It is concluded that in the patient population studied here carnitine supplementation during postoperative TPN did not improve fat oxidation or nitrogen balance.

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.

Portal glucose infusion in the mouse induces hypoglycemia: evidence that the hepatoportal glucose sensor stimulates glucose utilization.

To analyze the role of the murine hepatoportal glucose sensor in the control of whole-body glucose metabolism, we infused glucose at a rate corresponding to the endogenous glucose production rate through the portal vein of conscious mice (Po-mice) that were fasted for 6 h. Mice infused with glucose at the same rate through the femoral vein (Fe-mice) and mice infused with a saline solution (Sal-mice) were used as controls. In Po-mice, hypoglycemia progressively developed until glucose levels dropped to a nadir of 2.3 +/- 0.1 mmol/l, whereas in Fe-mice, glycemia rapidly and transiently developed, and glucose levels increased to 7.7 +/- 0.6 mmol/l before progressively returning to fasting glycemic levels. Plasma insulin levels were similar in both Po- and Fe-mice during and at the end of the infusion periods (21.2 +/- 2.2 vs. 25.7 +/- 0.9 microU/ml, respectively, at 180 min of infusion). The whole-body glucose turnover rate was significantly higher in Po-mice than in Fe-mice (45.9 +/- 3.8 vs. 37.7 +/- 2.0 mg x kg(-1) x min)-1), respectively) and in Sal-mice (24.4 +/- 1.8 mg x kg(-1) x min(-1)). Somatostatin co-infusion with glucose in Po-mice prevented hypoglycemia without modifying the plasma insulin profile. Finally, tissue glucose clearance, which was determined after injecting 14C-2-deoxyglucose, increased to a higher level in Po-mice versus Fe-mice in the heart, brown adipose tissue, and the soleus muscle. Our data show that stimulation of the hepatoportal glucose sensor induced hypoglycemia and increased glucose utilization by a combination of insulin-dependent and insulin-independent or -sensitizing mechanisms. Furthermore, activation of the glucose sensor and/or transmission of its signal to target tissues can be blocked by somatostatin.