Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Estimating slope and level change in N=1 designs

The current study proposes a new procedure for separately estimating slope change and level change between two adjacent phases in single-case designs. The procedure eliminates baseline trend from the whole data series prior to assessing treatment effectiveness. The steps necessary to obtain the estimates are presented in detail, explained, and illustrated. A simulation study is carried out to explore the bias and precision of the estimators and compare them to an analytical procedure matching the data simulation model. The experimental conditions include two data generation models, several degrees of serial dependence, trend, level and/or slope change. The results suggest that the level and slope change estimates provided by the procedure are unbiased for all levels of serial dependence tested and trend is effectively controlled for. The efficiency of the slope change estimator is acceptable, whereas the variance of the level change estimator may be problematic for highly negatively autocorrelated data series.

A comparison of mean phase difference and generalized least squares for analyzing single-case data

The present study focuses on single-case data analysis and specifically on two procedures for quantifying differences between baseline and treatment measurements The first technique tested is based on generalized least squares regression analysis and is compared to a proposed non-regression technique, which allows obtaining similar information. The comparison is carried out in the context of generated data representing a variety of patterns (i.e., independent measurements, different serial dependence underlying processes, constant or phase-specific autocorrelation and data variability, different types of trend, and slope and level change). The results suggest that the two techniques perform adequately for a wide range of conditions and researchers can use both of them with certain guarantees. The regression-based procedure offers more efficient estimates, whereas the proposed non-regression procedure is more sensitive to intervention effects. Considering current and previous findings, some tentative recommendations are offered to applied researchers in order to help choosing among the plurality of single-case data analysis techniques.

The Uncertain generalized probabilistic weighted average and its application in the theory of expertons

A new model for dealing with decision making under risk by considering subjective and objective information in the same formulation is here presented. The uncertain probabilistic weighted average (UPWA) is also presented. Its main advantage is that it unifies the probability and the weighted average in the same formulation and considering the degree of importance that each case has in the analysis. Moreover, it is able to deal with uncertain environments represented in the form of interval numbers. We study some of its main properties and particular cases. The applicability of the UPWA is also studied and it is seen that it is very broad because all the previous studies that use the probability or the weighted average can be revised with this new approach. Focus is placed on a multi-person decision making problem regarding the selection of strategies by using the theory of expertons.

A non-linear VAD for noisy environments

This paper deals with non-linear transformations for improving the performance of an entropy-based voice activity detector (VAD). The idea to use a non-linear transformation has already been applied in the field of speech linear prediction, or linear predictive coding (LPC), based on source separation techniques, where a score function is added to classical equations in order to take into account the true distribution of the signal. We explore the possibility of estimating the entropy of frames after calculating its score function, instead of using original frames. We observe that if the signal is clean, the estimated entropy is essentially the same; if the signal is noisy, however, the frames transformed using the score function may give entropy that is different in voiced frames as compared to nonvoiced ones. Experimental evidence is given to show that this fact enables voice activity detection under high noise, where the simple entropy method fails.

On the approximation of the subgrid scale for systems of equations

Postprint (published version)

On periodic solutions of 2-periodic Lyness difference equations

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.

Wave-height hazard analysis in Eastern Coast of Spain : Bayesian approach using generalized Pareto distribution

Standard practice of wave-height hazard analysis often pays little attention to the uncertainty of assessed return periods and occurrence probabilities. This fact favors the opinion that, when large events happen, the hazard assessment should change accordingly. However, uncertainty of the hazard estimates is normally able to hide the effect of those large events. This is illustrated using data from the Mediterranean coast of Spain, where the last years have been extremely disastrous. Thus, it is possible to compare the hazard assessment based on data previous to those years with the analysis including them. With our approach, no significant change is detected when the statistical uncertainty is taken into account. The hazard analysis is carried out with a standard model. Time-occurrence of events is assumed Poisson distributed. The wave-height of each event is modelled as a random variable which upper tail follows a Generalized Pareto Distribution (GPD). Moreover, wave-heights are assumed independent from event to event and also independent of their occurrence in time. A threshold for excesses is assessed empirically. The other three parameters (Poisson rate, shape and scale parameters of GPD) are jointly estimated using Bayes' theorem. Prior distribution accounts for physical features of ocean waves in the Mediterranean sea and experience with these phenomena. Posterior distribution of the parameters allows to obtain posterior distributions of other derived parameters like occurrence probabilities and return periods. Predictives are also available. Computations are carried out using the program BGPE v2.0

Integro-difference equations for interacting species and the Neolithic transition

We introduce a set of sequential integro-difference equations to analyze the dynamics of two interacting species. Firstly, we derive the speed of the fronts when a species invades a space previously occupied by a second species, and check its validity by means of numerical random-walk simulations. As an example, we consider the Neolithic transition: the predictions of the model are consistent with the archaeological data for the front speed, provided that the interaction parameter is low enough. Secondly, an equation for the coexistence time between the invasive and the invaded populations is obtained for the first time. It agrees well with the simulations, is consistent with observations of the Neolithic transition, and makes it possible to estimate the value of the interaction parameter between the incoming and the indigenous populations

Fronts from integrodifference equations and persistence effects on the Neolithic transition

We extend a previous model of the Neolithic transition in Europe [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)] by taking two effects into account: (i) we do not use the diffusion approximation (which corresponds to second-order Taylor expansions), and (ii) we take proper care of the fact that parents do not migrate away from their children (we refer to this as a time-order effect, in the sense that it implies that children grow up with their parents, before they become adults and can survive and migrate). We also derive a time-ordered, second-order equation, which we call the sequential reaction-diffusion equation, and use it to show that effect (ii) is the most important one, and that both of them should in general be taken into account to derive accurate results. As an example, we consider the Neolithic transition: the model predictions agree with the observed front speed, and the corrections relative to previous models are important (up to 70%)

BadiRate: Estimating Family Turnover Rates by Likelihood-Based Methods

Motivation: The comparative analysis of gene gain and loss rates is critical for understanding the role of natural selection and adaptation in shaping gene family sizes. Studying complete genome data from closely related species allows accurate estimation of gene family turnover rates. Current methods and software tools, however, are not well designed for dealing with certain kinds of functional elements, such as microRNAs or transcription factor binding sites. Results: Here, we describe BadiRate, a new software tool to estimate family turnover rates, as well as the number of elements in internal phylogenetic nodes, by likelihood-based methods and parsimony. It implements two stochastic population models, which provide the appropriate statistical framework for testing hypothesis, such as lineage-specific gene family expansions or contractions. We have assessed the accuracy of BadiRate by computer simulations, and have also illustrated its functionality by analyzing a representative empirical dataset.

BadiRate: estimating family turnover rates by likelihood-based methods

Motivation: The comparative analysis of gene gain and loss rates is critical for understanding the role of natural selection and adaptation in shaping gene family sizes. Studying complete genome data from closely related species allows accurate estimation of gene family turnover rates. Current methods and software tools, however, are not well designed for dealing with certain kinds of functional elements, such as microRNAs or transcription factor binding sites. Results: Here, we describe BadiRate, a new software tool to estimate family turnover rates, as well as the number of elements in internal phylogenetic nodes, by likelihood-based methods and parsimony. It implements two stochastic population models, which provide the appropriate statistical framework for testing hypothesis, such as lineage-specific gene family expansions or contractions. We have assessed the accuracy of BadiRate by computer simulations, and have also illustrated its functionality by analyzing a representative empirical dataset.

Generalized synchronization in directionally coupled systems with identical individual dynamics

A simple chaotic flow is presented, which when driven by an identical copy of itself, for certain initial conditions, is able to display generalized synchronization instead of identical synchronization. Being that the drive and the response are observed in exactly the same coordinate system, generalized synchronization is demonstrated by means of the auxiliary system approach and by the conditional Lyapunov spectrum. This is interpreted in terms of changes in the structure of the system stationary points, caused by the coupling, which modify its global behavior.

Determination of the components of the gyration tensor of quartz by oblique incidence transmission two-modulator generalized ellipsometry

The two independent components of the gyration tensor of quartz, g11 and g33, have been spectroscopically measured using a transmission two-modulator generalized ellipsometer. The method is used to determine the optical activity in crystals in directions other than the optic axis, where the linear birefringence is much larger than the optical activity.