Linear least squares estimation of the first order moving average parameter

We propose an iterative procedure to minimize the sum of squares function which avoids the nonlinear nature of estimating the first order moving average parameter and provides a closed form of the estimator. The asymptotic properties of the method are discussed and the consistency of the linear least squares estimator is proved for the invertible case. We perform various Monte Carlo experiments in order to compare the sample properties of the linear least squares estimator with its nonlinear counterpart for the conditional and unconditional cases. Some examples are also discussed

Diffusion in spatially and temporarily inhomogeneous media

In this paper we consider diffusion of a passive substance C in a temporarily and spatially inhomogeneous two-dimensional medium. As a realization for the latter we choose a phase-separating medium consisting of two substances A and B, whose dynamics is determined by the Cahn-Hilliard equation. Assuming different diffusion coefficients of C in A and B, we find that the variance of the distribution function of the said substance grows less than linearly in time. We derive a simple identity for the variance using a probabilistic ansatz and are then able to identify the interface between A and B as the main cause for this nonlinear dependence. We argue that, finally, for very large times the here temporarily dependent diffusion "constant" goes like t-1/3 to a constant asymptotic value D¿. The latter is calculated approximately by employing the effective-medium approximation and by fitting the simulation data to the said time dependence.

Inertial effects on reactive particles advected by turbulence

We study the problem of the advection of passive particles with inertia in a two-dimensional, synthetic, and stationary turbulent flow. The asymptotic analytical result and numerical simulations show the importance of inertial bias in collecting the particles preferentially in certain regions of the flow, depending on their density relative to that of the flow. We also study how these aggregates are affected when a simple chemical reaction mechanism is introduced through a Eulerian scheme. We find that inertia can be responsible for maintaining a stationary concentration pattern even under nonfavorable reactive conditions or destroying it under favorable ones.

Dynamics of sweeping through an instability: Passage-time statistics for colored noise

A calculation of passage-time statistics is reported for the laser switch-on problem, under the influence of colored noise, when the net gain is continuously swept from below to above threshold. Cases of fast and slow sweeping are considered. In the weak-noise limit, asymptotic results are given for small and large correlation times of the noise. The mean first passage time increases with the correlation time of the noise. This effect is more important for fast sweeping than for slow sweeping.

State-to-state reaction probabilities within the quantum transition state framework

Rigorous quantum dynamics calculations of reaction rates and initial state-selected reaction probabilities of polyatomic reactions can be efficiently performed within the quantum transition state concept employing flux correlation functions and wave packet propagation utilizing the multi-configurational time-dependent Hartree approach. Here, analytical formulas and a numerical scheme extending this approach to the calculation of state-to-state reaction probabilities are presented. The formulas derived facilitate the use of three different dividing surfaces: two dividing surfaces located in the product and reactant asymptotic region facilitate full state resolution while a third dividing surface placed in the transition state region can be used to define an additional flux operator. The eigenstates of the corresponding thermal flux operator then correspond to vibrational states of the activated complex. Transforming these states to reactant and product coordinates and propagating them into the respective asymptotic region, the full scattering matrix can be obtained. To illustrate the new approach, test calculations study the D + H2(ν, j) → HD(ν′, j′) + H reaction for J = 0.

Dynamics of transient pattern formation in nematic liquid crystals

We analyze the dynamics of a transient pattern formation in the Fréedericksz transition corresponding to a twist geometry. We present a calculation of the time-dependent structure factor based on a dynamical model which incorporates consistently the coupling of the director field with the velocity flow and also the effect of fluctuations. The appearance and development of a characteristic periodicity is described in terms of the time dependence of the maximum of the structure factor. We find a well-defined time for the appearance of the pattern and a subsequent stage of pattern development in which the characteristic periodicity tends to an asymptotic value.

Heated Optical Fiber for Distributed Soil-Moisture Measurements: A Lysimeter Experiment

An Actively Heated Fiber Optics (AHFO) method to estimate soil moisture is tested and the analysis technique improved on. The measurements were performed in a lysimeter uniformly packed with loam soil with variable water content profiles. In the first meter of the soil profi le, 30 m of fiber optic cable were installed in a 12 loops coil. The metal sheath armoring the fiber cable was used as an electrical resistance heater to generate a heat pulse, and the soil response was monitored with a Distributed Temperature Sensing (DTS) system. We study the cooling following three continuous heat pulses of 120 s at 36 W m(-1) by means of long-time approximation of radial heat conduction. The soil volumetric water contents were then inferred from the estimated thermal conductivities through a specifically calibrated model relating thermal conductivity and volumetric water content. To use the pre-asymptotic data we employed a time correction that allowed the volumetric water content to be estimated with a precision of 0.01-0.035 (m(3) m(-3)). A comparison of the AHFO measurements with soil-moisture measurements obtained with calibrated capacitance-based probes gave good agreement for wetter soils [discrepancy between the two methods was less than 0.04 (m(3) m(-3))]. In the shallow drier soils, the AHFO method underestimated the volumetric water content due to the longertime required for the temperature increment to become asymptotic in less thermally conductive media [discrepancy between the two methods was larger than 0.1 (m(3) m(-3))]. The present work suggests that future applications of the AHFO method should include longer heat pulses, that longer heating and cooling events are analyzed, and, temperature increments ideally be measured with higher frequency.

Robust accelerated failure time regression

Robust estimators for accelerated failure time models with asymmetric (or symmetric) error distribution and censored observations are proposed. It is assumed that the error model belongs to a log-location-scale family of distributions and that the mean response is the parameter of interest. Since scale is a main component of mean, scale is not treated as a nuisance parameter. A three steps procedure is proposed. In the first step, an initial high breakdown point S estimate is computed. In the second step, observations that are unlikely under the estimated model are rejected or down weighted. Finally, a weighted maximum likelihood estimate is computed. To define the estimates, functions of censored residuals are replaced by their estimated conditional expectation given that the response is larger than the observed censored value. The rejection rule in the second step is based on an adaptive cut-off that, asymptotically, does not reject any observation when the data are generat ed according to the model. Therefore, the final estimate attains full efficiency at the model, with respect to the maximum likelihood estimate, while maintaining the breakdown point of the initial estimator. Asymptotic results are provided. The new procedure is evaluated with the help of Monte Carlo simulations. Two examples with real data are discussed.

Multivariate prediction

The problem of prediction is considered in a multidimensional setting. Extending an idea presented by Barndorff-Nielsen and Cox, a predictive density for a multivariate random variable of interest is proposed. This density has the form of an estimative density plus a correction term. It gives simultaneous prediction regions with coverage error of smaller asymptotic order than the estimative density. A simulation study is also presented showing the magnitude of the improvement with respect to the estimative method.

Power variation of some integral fractional processes

We consider the asymptotic behaviour of the realized power variation of processes of the form ¿t0usdBHs, where BH is a fractional Brownian motion with Hurst parameter H E(0,1), and u is a process with finite q-variation, q<1/(1¿H). We establish the stable convergence of the corresponding fluctuations. These results provide new statistical tools to study and detect the long-memory effect and the Hurst parameter.

An AdS/QCD model from tachyon condensation: II

A simple holographic model is presented and analyzed that describes chiral symmetry breaking and the physics of the meson sector in QCD. This is a bottom-up model that incorporates string theory ingredients like tachyon condensation which is expected to be the main manifestation of chiral symmetry breaking in the holographic context. As a model for glue the Kuperstein-Sonnenschein background is used. The structure of the flavor vacuum is analyzed in the quenched approximation. Chiral symmetry breaking is shown at zero temperature. Above the deconfinement transition chiral symmetry is restored. A complete holographic renormalization is performed and the chiral condensate is calculated for different quark masses both at zero and non-zero temperatures. The 0++, 0¿+, 1++, 1¿¿ meson trajectories are analyzed and their masses and decay constants are computed. The asymptotic trajectories are linear. The model has one phenomenological parameter beyond those of QCD that affects the 1++, 0¿+ sectors. Fitting this parameter we obtain very good agreement with data. The model improves in several ways the popular hard-wall and soft wall bottom-up models.

OCP effects in catalan cliticization

In Catalan, sequences of sibilants are never pronounced as such. In most contexts all varieties coincide in the «strategies» used to avoid these sequences, namely epenthesis or deletion. Variation is only found in the domain of pronominal clitics (but not with other types of clitics). One source of variation is accounted for by decomposing a general constraint into two specific ones, which implies partial constraint reranking. The other source of variation, which involves a case of apparent opacity, is explained through an Output-Output constraint that makes reference to paradigmatic relations.

Efficient total variation algorithm for fetal brain MRI reconstruction.

Fetal MRI reconstruction aims at finding a high-resolution image given a small set of low-resolution images. It is usually modeled as an inverse problem where the regularization term plays a central role in the reconstruction quality. Literature has considered several regularization terms s.a. Dirichlet/Laplacian energy, Total Variation (TV)- based energies and more recently non-local means. Although TV energies are quite attractive because of their ability in edge preservation, standard explicit steepest gradient techniques have been applied to optimize fetal-based TV energies. The main contribution of this work lies in the introduction of a well-posed TV algorithm from the point of view of convex optimization. Specifically, our proposed TV optimization algorithm or fetal reconstruction is optimal w.r.t. the asymptotic and iterative convergence speeds O(1/n2) and O(1/√ε), while existing techniques are in O(1/n2) and O(1/√ε). We apply our algorithm to (1) clinical newborn data, considered as ground truth, and (2) clinical fetal acquisitions. Our algorithm compares favorably with the literature in terms of speed and accuracy.

Short-time dynamics of colloidal suspensions in confined geometries

We analyze the short-time dynamical behavior of a colloidal suspension in a confined geometry. We analyze the relevant dynamical response of the solvent, and derive the temporal behavior of the velocity autocorrelation function, which exhibits an asymptotic negative algebraic decay. We are able to compare quantitatively with theoretical expressions, and analyze the effects of confinement on the diffusive behavior of the suspension.

Adsorption of glyphosate in chilean soils and its relationship with unoccupied phosphate binding sites

The objective of this work was to investigate glyphosate adsorption by soils and its relationship with unoccupied binding sites for phosphate adsorption. Soil samples of three Chilean soils series - Valdivia (Andisol), Clarillo (Inceptisol) and Chicureo (Vertisol) - were incubated with different herbicide concentrations. Glyphosate remaining in solution was determined by adjusting a HPLC method with a UV detector. Experimental maximum adsorption capacity were 15,000, 14,300 and 4,700 mg g¹ for Valdivia, Clarillo, and Chicureo soils, respectively. Linear, Freundlich, and Langmuir models were used to describe glyphosate adsorption. Isotherms describing glyphosate adsorption differed among soils. Maximum adjusted adsorption capacity with the Langmuir model was 231,884, 17,874 and 5,670 mg g-1 for Valdivia, Clarillo, and Chicureo soils, respectively. Glyphosate adsorption on the Valdivia soil showed a linear behavior at the range of concentrations used and none of the adjusted models became asymptotic. The high glyphosate adsorption capacity of the Valdivia soil was probably a result of its high exchangeable Al, extractable Fe, and alophan and imogolite clay type. Adsorption was very much related to phosphate dynamics in the Valdivia soil, which showed the larger unoccupied phosphate binding sites. However relationship between unoccupied phosphate binding sites and glyphosate adsorption in the other two soils (Clarillo and Chicureo) was not clear.