Operator ordering in quantum radiative processes

In this work we reexamine quantum electrodynamics of atomic electrons in the Coulomb gauge in the dipole approximation and calculate the shift of atomic energy levels in the context of Dalibard, Dupont-Roc and Cohen-Tannoudji formalism by considering the variation rates of physical observable. We then analyze the physical interpretation of the ordering of operators in the dipole approximation interaction Hamiltonian in terms of field fluctuations and self-reaction of atomic electrons, discussing the arbitrariness in the statistical functions in second-order bound-state perturbation theory. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Dressed-state approach to a simple radiating atom

We consider a system consisting of an atom in the dipole approximation, coupled to the electromagnetic field. Using recently introduced renormalized coordinates and dressed states, we give a non-perturbative solution to the atom radiation process. From this formalism a non-exponential decay law naturally emerges. However, at least for low frequencies and weak coupling, there is only a very small, practically non-detectable, deviation from a purely exponential decay, in agreement with all previous results in the literature. (c) 2005 Elsevier B.V. All rights reserved.

Optical third harmonic generation in the magnetic semiconductor EuSe

Third harmonic generation (THG) has been studied in europium selenide EuSe in the vicinity of the band gap at 2.1-2.6 eV and at higher energies up to 3.7 eV. EuSe is amagnetic semiconductor crystalizing in centrosymmetric structure of rock-salt type with the point group m3m. For this symmetry the crystallographic and magnetic-field-induced THG nonlinearities are allowed in the electric-dipole approximation. Using temperature, magnetic field, and rotational anisotropy measurements, the crystallographic and magnetic-field-induced contributions to THG were unambiguously separated. Strong resonant magnetic-field-induced THG signals were measured at energies in the range of 2.1-2.6 eV and 3.1-3.6 eV for which we assign to transitions from 4 f(7) to 4 f(6)5d(1) bands, namely involving 5d(t(2g)) and 5d(e(g)) states.

Frequency-domain source localization shows state-dependent diazepam effects in 47-channel EEG

The topic of this study was to evaluate state-dependent effects of diazepam on the frequency characteristics of 47-channel spontaneous EEG maps. A novel method, the FFT-Dipole-Approximation (Lehmann and Michel, 1990), was used to study effects on the strength and the topography of the maps in the different frequency bands. Map topography was characterized by the 3-dimensional location of the equivalent dipole source and map strength was defined as the spatial standard deviation (the Global Field Power) of the maps of each frequency point. The Global Field Power can be considered as a measure of the amount of energy produced by the system, while the source location gives an estimate of the center of gravity of all sources in the brain that were active at a certain frequency. State-dependency was studied by evaluating the drug effects before and after a continuous performance task of 25 min duration. Clear interactions between drug (diazepam vs. placebo) and time after drug intake (before and after the task) were found, especially in the inferior-superior location of the dipole sources. It supports the hypothesis that diazepam, like other drugs, has different effects on brain functions depending on the momentary functional state of the brain. In addition to the drug effects, clearly different source locations and Global Field Power were found for the different frequency bands, replicating earlier reports (Michel et al., 1992).

Affective attitudes to face images associated with intracerebral EEG source location before face viewing

We investigated whether different, personality-related affective attitudes are associated with different brain electric field (EEG) sources before any emotional challenge (stimulus exposure). A 27-channel EEG was recorded in 15 subjects during eyes-closed resting. After recording, subjects rated 32 images of human faces for affective appeal. The subjects in the first (i.e., most negative) and fourth (i.e., most positive) quartile of general affective attitude were further analyzed. The EEG data (mean=25±4.8 s/subject) were subjected to frequency-domain model dipole source analysis (FFT-Dipole-Approximation), resulting in 3-dimensional intracerebral source locations and strengths for the delta–theta, alpha, and beta EEG frequency band, and for the full range (1.5–30 Hz) band. Subjects with negative attitude (compared to those with positive attitude) showed the following source locations: more inferior for all frequency bands, more anterior for the delta–theta band, more posterior and more right for the alpha, beta and 1.5–30 Hz bands. One year later, the subjects were asked to rate the face images again. The rating scores for the same face images were highly correlated for all subjects, and original and retest affective mean attitude was highly correlated across subjects. The present results show that subjects with different affective attitudes to face images had different active, cerebral, neural populations in a task-free condition prior to viewing the images. We conclude that the brain functional state which implements affective attitude towards face images as a personality feature exists without elicitors, as a continuously present, dynamic feature of brain functioning.

Brain electric correlates of strong belief in paranormal phenomena: intracerebral EEG source and regional Omega complexity analyses

The neurocognitive processes underlying the formation and maintenance of paranormal beliefs are important for understanding schizotypal ideation. Behavioral studies indicated that both schizotypal and paranormal ideation are based on an overreliance on the right hemisphere, whose coarse rather than focussed semantic processing may favor the emergence of 'loose' and 'uncommon' associations. To elucidate the electrophysiological basis of these behavioral observations, 35-channel resting EEG was recorded in pre-screened female strong believers and disbelievers during resting baseline. EEG data were subjected to FFT-Dipole-Approximation analysis, a reference-free frequency-domain dipole source modeling, and Regional (hemispheric) Omega Complexity analysis, a linear approach estimating the complexity of the trajectories of momentary EEG map series in state space. Compared to disbelievers, believers showed: more right-located sources of the beta2 band (18.5-21 Hz, excitatory activity); reduced interhemispheric differences in Omega complexity values; higher scores on the Magical Ideation scale; more general negative affect; and more hypnagogic-like reveries after a 4-min eyes-closed resting period. Thus, subjects differing in their declared paranormal belief displayed different active, cerebral neural populations during resting, task-free conditions. As hypothesized, believers showed relatively higher right hemispheric activation and reduced hemispheric asymmetry of functional complexity. These markers may constitute the neurophysiological basis for paranormal and schizotypal ideation.

Smell and taste of chewing gum affect frequency domain EEG source localizations

We investigated brain electric field signatures of subjective feelings after chewing regular gum or gum base without flavor. 19-channel eyes-closed EEG from 20 healthy males before and after 5 minutes of chewing the two gum types in random sequence was source modeled in the frequency domain using the FFT-Dipole-Approximation. 3-dimensional brain locations and strengths (Global Field Power, GFP) of the equivalent sources of five frequency bands were computed as changes from pre-chewing baseline. Gum types differed (ANOVA) in pre-post changes of source locations for the alpha-2 band (to anterior and right after regular gum, opposite after gum base) and beta-2 band (to anterior and inferior after regular gum, opposite after gum base), and of GFP for delta-theta, alpha-2 and beta-1 (regular gum: increase, gum base: decrease). Subjective feeling changed to more positive values after regular gum than gum base (ANOVA).—Thus, chewing gum with and without taste-smell activates different brain neuronal populations.

A fuzzy decision tree-based duration model for Standard Yorùbá text-to-speech synthesis

In this paper, we present syllable-based duration modelling in the context of a prosody model for Standard Yorùbá (SY) text-to-speech (TTS) synthesis applications. Our prosody model is conceptualised around a modular holistic framework. This framework is implemented using the Relational Tree (R-Tree) techniques. An important feature of our R-Tree framework is its flexibility in that it facilitates the independent implementation of the different dimensions of prosody, i.e. duration, intonation, and intensity, using different techniques and their subsequent integration. We applied the Fuzzy Decision Tree (FDT) technique to model the duration dimension. In order to evaluate the effectiveness of FDT in duration modelling, we have also developed a Classification And Regression Tree (CART) based duration model using the same speech data. Each of these models was integrated into our R-Tree based prosody model. We performed both quantitative (i.e. Root Mean Square Error (RMSE) and Correlation (Corr)) and qualitative (i.e. intelligibility and naturalness) evaluations on the two duration models. The results show that CART models the training data more accurately than FDT. The FDT model, however, shows a better ability to extrapolate from the training data since it achieved a better accuracy for the test data set. Our qualitative evaluation results show that our FDT model produces synthesised speech that is perceived to be more natural than our CART model. In addition, we also observed that the expressiveness of FDT is much better than that of CART. That is because the representation in FDT is not restricted to a set of piece-wise or discrete constant approximation. We, therefore, conclude that the FDT approach is a practical approach for duration modelling in SY TTS applications. © 2006 Elsevier Ltd. All rights reserved.

Optimal threshold policies for admission control in communication networks via discrete parameter stochastic approximation

The problem of admission control of packets in communication networks is studied in the continuous time queueing framework under different classes of service and delayed information feedback. We develop and use a variant of a simulation based two timescale simultaneous perturbation stochastic approximation (SPSA) algorithm for finding an optimal feedback policy within the class of threshold type policies. Even though SPSA has originally been designed for continuous parameter optimization, its variant for the discrete parameter case is seen to work well. We give a proof of the hypothesis needed to show convergence of the algorithm on our setting along with a sketch of the convergence analysis. Extensive numerical experiments with the algorithm are illustrated for different parameter specifications. In particular, we study the effect of feedback delays on the system performance.

A fully discrete C-0 interior penalty Galerkin approximation of the extended Fisher-Kolmogorov equation

A fully discrete C-0 interior penalty finite element method is proposed and analyzed for the Extended Fisher-Kolmogorov (EFK) equation u(t) + gamma Delta(2)u - Delta u + u(3) - u = 0 with appropriate initial and boundary conditions, where gamma is a positive constant. We derive a regularity estimate for the solution u of the EFK equation that is explicit in gamma and as a consequence we derive a priori error estimates that are robust in gamma. (C) 2013 Elsevier B.V. All rights reserved.

Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

Logic-Based Outer Approximation for the Design of Discrete-Continuous Dynamic Systems with Implicit Discontinuities

We address the optimization of discrete-continuous dynamic optimization problems using a disjunctive multistage modeling framework, with implicit discontinuities, which increases the problem complexity since the number of continuous phases and discrete events is not known a-priori. After setting a fixed alternative sequence of modes, we convert the infinite-dimensional continuous mixed-logic dynamic (MLDO) problem into a finite dimensional discretized GDP problem by orthogonal collocation on finite elements. We use the Logic-based Outer Approximation algorithm to fully exploit the structure of the GDP representation of the problem. This modelling framework is illustrated with an optimization problem with implicit discontinuities (diver problem).

Logic-Based Outer-Approximation Algorithm for Solving Discrete-Continuous Dynamic Optimization Problems

We present an extension of the logic outer-approximation algorithm for dealing with disjunctive discrete-continuous optimal control problems whose dynamic behavior is modeled in terms of differential-algebraic equations. Although the proposed algorithm can be applied to a wide variety of discrete-continuous optimal control problems, we are mainly interested in problems where disjunctions are also present. Disjunctions are included to take into account only certain parts of the underlying model which become relevant under some processing conditions. By doing so the numerical robustness of the optimization algorithm improves since those parts of the model that are not active are discarded leading to a reduced size problem and avoiding potential model singularities. We test the proposed algorithm using three examples of different complex dynamic behavior. In all the case studies the number of iterations and the computational effort required to obtain the optimal solutions is modest and the solutions are relatively easy to find.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.