Theory for correlation functions of processes driven by external colored noise

We study steady-state correlation functions of nonlinear stochastic processes driven by external colored noise. We present a methodology that provides explicit expressions of correlation functions approximating simultaneously short- and long-time regimes. The non-Markov nature is reduced to an effective Markovian formulation, and the nonlinearities are treated systematically by means of double expansions in high and low frequencies. We also derive some exact expressions for the coefficients of these expansions for arbitrary noise by means of a generalization of projection-operator techniques.

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.

Ultrathin strut biodegradable polymer sirolimus-eluting stent versus durable polymer everolimus-eluting stent for percutaneous coronary revascularisation (BIOSCIENCE): a randomised, single-blind, non-inferiority trial.

BACKGROUND: Refinements in stent design affecting strut thickness, surface polymer, and drug release have improved clinical outcomes of drug-eluting stents. We aimed to compare the safety and efficacy of a novel, ultrathin strut cobalt-chromium stent releasing sirolimus from a biodegradable polymer with a thin strut durable polymer everolimus-eluting stent. METHODS: We did a randomised, single-blind, non-inferiority trial with minimum exclusion criteria at nine hospitals in Switzerland. We randomly assigned (1:1) patients aged 18 years or older with chronic stable coronary artery disease or acute coronary syndromes undergoing percutaneous coronary intervention to treatment with biodegradable polymer sirolimus-eluting stents or durable polymer everolimus-eluting stents. Randomisation was via a central web-based system and stratified by centre and presence of ST segment elevation myocardial infarction. Patients and outcome assessors were masked to treatment allocation, but treating physicians were not. The primary endpoint, target lesion failure, was a composite of cardiac death, target vessel myocardial infarction, and clinically-indicated target lesion revascularisation at 12 months. A margin of 3·5% was defined for non-inferiority of the biodegradable polymer sirolimus-eluting stent compared with the durable polymer everolimus-eluting stent. Analysis was by intention to treat. The trial is registered with ClinicalTrials.gov, number NCT01443104. FINDINGS: Between Feb 24, 2012, and May 22, 2013, we randomly assigned 2119 patients with 3139 lesions to treatment with sirolimus-eluting stents (1063 patients, 1594 lesions) or everolimus-eluting stents (1056 patients, 1545 lesions). 407 (19%) patients presented with ST-segment elevation myocardial infarction. Target lesion failure with biodegradable polymer sirolimus-eluting stents (69 cases; 6·5%) was non-inferior to durable polymer everolimus-eluting stents (70 cases; 6·6%) at 12 months (absolute risk difference -0·14%, upper limit of one-sided 95% CI 1·97%, p for non-inferiority <0·0004). No significant differences were noted in rates of definite stent thrombosis (9 [0·9%] vs 4 [0·4%], rate ratio [RR] 2·26, 95% CI 0·70-7·33, p=0·16). In pre-specified stratified analyses of the primary endpoint, biodegradable polymer sirolimus-eluting stents were associated with improved outcome compared with durable polymer everolimus-eluting stents in the subgroup of patients with ST-segment elevation myocardial infarction (7 [3·3%] vs 17 [8·7%], RR 0·38, 95% CI 0·16-0·91, p=0·024, p for interaction=0·014). INTERPRETATION: In a patient population with minimum exclusion criteria and high adherence to dual antiplatelet therapy, biodegradable polymer sirolimus-eluting stents were non-inferior to durable polymer everolimus-eluting stents for the combined safety and efficacy outcome target lesion failure at 12 months. The noted benefit in the subgroup of patients with ST-segment elevation myocardial infarction needs further study. FUNDING: Clinical Trials Unit, University of Bern, and Biotronik, Bülach, Switzerland.

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.

Ammonia volatilization and yield components after application of polymer-coated urea to maize

A form of increasing the efficiency of N fertilizer is by coating urea with polymers to reduce ammonia volatilization. The aim of this study was to evaluate the effect of polymer-coated urea on the control of ammonia volatilization, yield and nutritional characteristics of maize. The experiment was carried out during one maize growing cycle in 2009/10 on a Geric Ferralsol, inUberlândia, MG, Brazil. Nitrogen fertilizers were applied as topdressing on the soil surface in the following urea treatments: polymer-coated urea at rates of 45, 67.5 and 90 kg ha-1 N and one control treatment (no N), in randomized blocks with four replications. Nitrogen application had a favorable effect on N concentrations in leaves and grains, Soil Plant Analysis Development (SPAD) chlorophyll meter readings and on grain yield, where as coated urea had no effect on the volatilization rates, SPAD readings and N leaf and grain concentration, nor on grain yield in comparison to conventional fertilization.