Continuous-time formulation of reaction-diffusion processes on heterogeneous metapopulations

We present the derivation of the continuous-time equations governing the limit dynamics of discrete-time reaction-diffusion processes defined on heterogeneous metapopulations. We show that, when a rigorous time limit is performed, the lack of an epidemic threshold in the spread of infections is not limited to metapopulations with a scale-free architecture, as it has been predicted from dynamical equations in which reaction and diffusion occur sequentially in time

Optimum pilot overhead in wireless communication: a unified treatment of continuous and block-fading channels

The optimization of the pilot overhead in wireless fading channels is investigated, and the dependence of this overhead on various system parameters of interest (e.g., fading rate, signal-to-noise ratio) is quantified. The achievable pilot-based spectral efficiency is expanded with respect to the fading rate about the no-fading point, which leads to an accurate order expansion for the pilot overhead. This expansion identifies that the pilot overhead, as well as the spectral efficiency penalty with respect to a reference system with genie-aided CSI (channel state information) at the receiver, depend on the square root of the normalized Doppler frequency. It is also shown that the widely-usedblock fading model is a special case of more accurate continuous fading models in terms of the achievable pilot-based spectral efficiency. Furthermore, it is established that the overhead optimization for multiantenna systems is effectively the same as for single-antenna systems with thenormalized Doppler frequency multiplied by the number of transmit antennas.

Late bloomer or language impaired? Screening the speech of a Spanish-English bilingual toddler for early signs of language impairment

This case study presents corpus data gathered from a Spanish-English bilingual child with expressive language delay. Longitudinal data on the child’s linguistic development was collected from the onset of productive speech at age 1;1 until age 4 over the course of 28 video-taped sessions with the child’s principal caregivers. A literature review focused on the relationship between language delay and persisting disorders—including a discussion of the frequent difficulty in distinguishing between the two at early stages of bilingual development—is followed by an analysis of the child’s productive development in 2 distinct phases. An attempt is made to assess the child’s speech at age 4 for preliminary signs of SLI and to consider techniques for identifying ‘at risk’ bilingual children (that is, those with productive language delay, poor oral fluency, and family history of language problems) based on samples of recorded and transcribed speech.

Solving higher-dimensional continuous time stochastic control problems by value function regression

The paper develops a method to solve higher-dimensional stochasticcontrol problems in continuous time. A finite difference typeapproximation scheme is used on a coarse grid of low discrepancypoints, while the value function at intermediate points is obtainedby regression. The stability properties of the method are discussed,and applications are given to test problems of up to 10 dimensions.Accurate solutions to these problems can be obtained on a personalcomputer.

Ignoring information in binary choice with continuous variables: When is less 'more'?

When can a single variable be more accurate in binary choice than multiple sources of information? We derive analytically the probability that a single variable (SV) will correctly predict one of two choices when both criterion and predictor are continuous variables. We further provide analogous derivations for multiple regression (MR) and equal weighting (EW) and specify the conditions under which the models differ in expected predictive ability. Key factors include variability in cue validities, intercorrelation between predictors, and the ratio of predictors to observations in MR. Theory and simulations are used to illustrate the differential effects of these factors. Results directly address why and when one-reason decision making can be more effective than analyses that use more information. We thus provide analytical backing to intriguing empirical results that, to date, have lacked theoretical justification. There are predictable conditions for which one should expect less to be more.

Continuous phase shift of sinusoidal signals using injection locked oscillators

This work presents an alternative to generate continuous phase shift of sinusoidal signals based on the use of super harmonic injection locked oscillators (ILO). The proposed circuit is a second harmonic ILO with varactor diodes as tuning elements. In the locking state, by changing the varactor bias, a phase shift instead of a frequency shift is observed at the oscillator output. By combining two of these circuits, relative phases up to 90 could be achieved. Two prototypes of the circuit have been implemented and tested, a hybrid version working in the range of 200-300 MHz and a multichip module (MCM) version covering the 900¿1000 MHz band.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

Continuous-time random-walk model for financial distributions

We apply the formalism of the continuous-time random walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time between successive jumps and the corresponding probability density for the magnitude of a jump. We have applied the formalism to data on the U.S. dollardeutsche mark future exchange, finding good agreement between theory and the observed data.

Continuous phase transition in a spin-glass model without time-reversal symmetry

We investigate the phase transition in a strongly disordered short-range three-spin interaction model characterized by the absence of time-reversal symmetry in the Hamiltonian. In the mean-field limit the model is well described by the Adam-Gibbs-DiMarzio scenario for the glass transition; however, in the short-range case this picture turns out to be modified. The model presents a finite temperature continuous phase transition characterized by a divergent spin-glass susceptibility and a negative specific-heat exponent. We expect the nature of the transition in this three-spin model to be the same as the transition in the Edwards-Anderson model in a magnetic field, with the advantage that the strong crossover effects present in the latter case are absent.

Non independent continuous-time random walks

The usual development of the continuous-time random walk (CTRW) assumes that jumps and time intervals are a two-dimensional set of independent and identically distributed random variables. In this paper, we address the theoretical setting of nonindependent CTRWs where consecutive jumps and/or time intervals are correlated. An exact solution to the problem is obtained for the special but relevant case in which the correlation solely depends on the signs of consecutive jumps. Even in this simple case, some interesting features arise, such as transitions from unimodal to bimodal distributions due to correlation. We also develop the necessary analytical techniques and approximations to handle more general situations that can appear in practice.

Parrondo-like behavior in continuous-time random walks with memory

The continuous-time random walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this paper we will show how the random combination of two different unbiased CTRWs can give rise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought of as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same as that of the Parrondo paradox in game theory.

Optimization of analytical methods for the assessment of the quality of fats and oils used in continuous deep fat frying

La aplicabilidad, repetibilidad y capacidad de diferentes métodos de análisis para discriminar muestras de aceites con diferentes grados de oxidación fueron evaluadas mediante aceites recogidos en procesos de fritura en continuo en varias empresas españolas. El objetivo de este trabajo fue encontrar métodos complementarios a la determinación del índice de acidez para el control de calidad rutinario de los aceites de fritura empleados en estas empresas. La optimización de la determinación de la constante dieléctrica conllevó una clara mejora de la variabilidad. No obstante, excepto en el caso del índice del ATB, el resto de métodos ensayados mostraron una menor variabilidad. La determinación del índice del ATB fue descartada ya que su sensibilidad fue insuficiente para discriminar entre aceites con diferente grado de oxidación. Los diferentes parámetros de alteración determinados en los aceites de fritura mostraron correlaciones significativas entre el índice de acidez y varios parámetros de oxidación diferentes, como la constante dieléctrica, el índice de p-anisidina, la absorción al ultravioleta y el contenido en polímeros de los triacilgliceroles. El índice de acidez solo evalúa la alteración hidrolítica, por lo que estos parámetros aportan información complementaria al evaluar la alteración termooxidativa.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.