Free inertial processes driven by Gaussian noise: Probability distributions, anomalous diffusion and fractal behavior

We study the motion of an unbound particle under the influence of a random force modeled as Gaussian colored noise with an arbitrary correlation function. We derive exact equations for the joint and marginal probability density functions and find the associated solutions. We analyze in detail anomalous diffusion behaviors along with the fractal structure of the trajectories of the particle and explore possible connections between dynamical exponents of the variance and the fractal dimension of the trajectories.

Modelling diffusion of innovations in a social network

A simple model of diffusion of innovations in a social network with upgrading costs is introduced. Agents are characterized by a single real variable, their technological level. According to local information, agents decide whether to upgrade their level or not, balancing their possible benefit with the upgrading cost. A critical point where technological avalanches display a power-law behavior is also found. This critical point is characterized by a macroscopic observable that turns out to optimize technological growth in the stationary state. Analytical results supporting our findings are found for the globally coupled case.

Stationary states and phase diagram for a model of the Gunn effect under realistic boundary conditions

A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to study the classical unipolar drift-diffusion model for the Gunn effect. The analysis of its stationary solutions reveals the presence of bistability and hysteresis for a certain range of contact parameters. Several types of Gunn effect are predicted to occur in the model, when no stable stationary solution exists, depending on the value of the parameters of the injecting contact appearing in the boundary condition. In this way, the critical role played by contacts in the Gunn effect is clearly established.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

Characterization of alternatively spliced products and tissue-specific isoforms of USP28 and USP25

Background: The ubiquitin-dependent protein degradation pathway is essential for the proteolysis of intracellular proteins and peptides. Deubiquitinating enzymes constitute a complex protein family involved in a multitude of cellular processes. The ubiquitin-specific proteases (UBP) are a group of enzymes whose predicted function is to reverse the ubiquitinating reaction by removing ubiquitin from a large variety of substrates. We have lately reported the characterization of human USP25, a specific-ubiquitin protease gene at 21q11.2, with a specific pattern of expression in murine fetal brains and adult testis. Results: Database homology searches at the DNA and protein levels and cDNA library screenings led to the identification of a new UBP member in the human genome, named USP28, at 11q23. This novel gene showed preferential expression in heart and muscle. Moreover, cDNA, expressed sequence tag and RT-PCR analyses provided evidence for alternatively spliced products and tissue-specific isoforms. Concerning function, USP25 overexpression in Down syndrome fetal brains was shown by real-time PCR. Conclusions: On the basis of the genomic and protein sequence as well as the functional data, USP28 and USP25 establish a new subfamily of deubiquitinating enzymes. Both genes have alternatively spliced exons that could generate protein isoforms with distinct tissue-specific activity. The overexpression of USP25 in Down syndrome fetal brains supports the gene-dosage effects suggested for other UBP members related to aneuploidy syndromes.

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.

Diffusion of passive scalars under stochastic convection

The diffusion of passive scalars convected by turbulent flows is addressed here. A practical procedure to obtain stochastic velocity fields with well¿defined energy spectrum functions is also presented. Analytical results are derived, based on the use of stochastic differential equations, where the basic hypothesis involved refers to a rapidly decaying turbulence. These predictions are favorable compared with direct computer simulations of stochastic differential equations containing multiplicative space¿time correlated noise.

Congenital ataxia and hemiplegic migraine with cerebral edema associated with a novel gain of function mutation in the calcium channel CACNA1A.

Mutations in the CACNA1A gene, encoding the α1 subunit of the voltage-gated calcium channel CaV2.1 (P/Q-type), have been associated with three neurological phenotypes: familial and sporadic hemiplegic migraine type 1 (FHM1, SHM1), episodic ataxia type 2 (EA2), and spinocerebellar ataxia type 6 (SCA6). We report a child with congenital ataxia, abnormal eye movements and developmental delay who presented severe attacks of hemiplegic migraine triggered by minor head traumas and associated with hemispheric swelling and seizures. Progressive cerebellar atrophy was also observed. Remission of the attacks was obtained with acetazolamide. A de novo 3bp deletion was found in heterozygosity causing loss of a phenylalanine residue at position 1502, in one of the critical transmembrane domains of the protein contributing to the inner part of the pore. We characterized the electrophysiology of this mutant in a Xenopus oocyte in vitro system and showed that it causes gain of function of the channel. The mutant CaV2.1 activates at lower voltage threshold than the wild type. These findings provide further evidence of this molecular mechanism as causative of FHM1 and expand the phenotypic spectrum of CACNA1A mutations with a child exhibiting severe SHM1 and non-episodic ataxia of congenital onset.

On Ito's formula for elliptic diffusion processes

Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83-109] prove an extension of Ito's formula for F(Xt, t), where F(x, t) has a locally square-integrable derivative in x that satisfies a mild continuity condition in t and X is a one-dimensional diffusion process such that the law of Xt has a density satisfying certain properties. This formula was expressed using quadratic covariation. Following the ideas of Eisenbaum [Potential Anal. 13 (2000) 303-328] concerning Brownian motion, we show that one can re-express this formula using integration over space and time with respect to local times in place of quadratic covariation. We also show that when the function F has a locally integrable derivative in t, we can avoid the mild continuity condition in t for the derivative of F in x.

Prospective and retrospective motion correction in diffusion magnetic resonance imaging of the human brain.

Diffusion-weighting in magnetic resonance imaging (MRI) increases the sensitivity to molecular Brownian motion, providing insight in the micro-environment of the underlying tissue types and structures. At the same time, the diffusion weighting renders the scans sensitive to other motion, including bulk patient motion. Typically, several image volumes are needed to extract diffusion information, inducing also inter-volume motion susceptibility. Bulk motion is more likely during long acquisitions, as they appear in diffusion tensor, diffusion spectrum and q-ball imaging. Image registration methods are successfully used to correct for bulk motion in other MRI time series, but their performance in diffusion-weighted MRI is limited since diffusion weighting introduces strong signal and contrast changes between serial image volumes. In this work, we combine the capability of free induction decay (FID) navigators, providing information on object motion, with image registration methodology to prospectively--or optionally retrospectively--correct for motion in diffusion imaging of the human brain. Eight healthy subjects were instructed to perform small-scale voluntary head motion during clinical diffusion tensor imaging acquisitions. The implemented motion detection based on FID navigator signals is processed in real-time and provided an excellent detection performance of voluntary motion patterns even at a sub-millimetre scale (sensitivity≥92%, specificity>98%). Motion detection triggered an additional image volume acquisition with b=0 s/mm2 which was subsequently co-registered to a reference volume. In the prospective correction scenario, the calculated motion-parameters were applied to perform a real-time update of the gradient coordinate system to correct for the head movement. Quantitative analysis revealed that the motion correction implementation is capable to correct head motion in diffusion-weighted MRI to a level comparable to scans without voluntary head motion. The results indicate the potential of this method to improve image quality in diffusion-weighted MRI, a concept that can also be applied when highest diffusion weightings are performed.

Training referential communicative skills to individuals with autism spectrum disorder: a pilot study

Summary. The present study reports the effects of referential communication training in individuals formally diagnosed with autism spectrum disorder (ASD). Participants were 20 children with ASD (M age = 14.3 yr., SD = 4.2; 6 girls, 14 boys) in the role of speakers and 20 control children, who acted as listeners. They were all enrolled in mainstream compulsory education. Inclusion/exclusion criteria were defined according to the clinical diagnosis of ASD, the presence or absence of additional or associated disability, previous training in referential communication, and any drug treatment. Speakers were randomly assigned to one of two groups (trained vs untrained). Linguistic age, cognitive level, and autistic symptoms were analyzed, respectively, with the Peabody Picture Vocabulary Test (PPVT), the Wechsler Intelligence Scale (WISCR or WAISIII), and the Autistic Behavior Checklist (ABC). Communicative abilities were analyzed through two indexes related to message complexity and self-regulation. The trained group was trained in referential communication tasks (task analysis, role taking, and task evaluation), while the untrained group took part in a communicative game but without any specific communicative training. The results showed that the complexity of emitted messages had improved statistically significantly in the trained group as an effect of training. Ecological referential communication is shown to be an appropriate paradigm for studying the communicative process and its products and could be used to develop and implement a training program focused on those skills in which individuals with ASD are most deficient.

Activities of fosfomycin, tigecycline, colistin, and gentamicin against extended-spectrum-β-lactamase-producing Escherichia coli in a foreign-body infection model.

Limited antimicrobial agents are available for the treatment of implant-associated infections caused by fluoroquinolone-resistant Gram-negative bacilli. We compared the activities of fosfomycin, tigecycline, colistin, and gentamicin (alone and in combination) against a CTX-M15-producing strain of Escherichia coli (Bj HDE-1) in vitro and in a foreign-body infection model. The MIC and the minimal bactericidal concentration in logarithmic phase (MBC(log)) and stationary phase (MBC(stat)) were 0.12, 0.12, and 8 μg/ml for fosfomycin, 0.25, 32, and 32 μg/ml for tigecycline, 0.25, 0.5, and 2 μg/ml for colistin, and 2, 8, and 16 μg/ml for gentamicin, respectively. In time-kill studies, colistin showed concentration-dependent activity, but regrowth occurred after 24 h. Fosfomycin demonstrated rapid bactericidal activity at the MIC, and no regrowth occurred. Synergistic activity between fosfomycin and colistin in vitro was observed, with no detectable bacterial counts after 6 h. In animal studies, fosfomycin reduced planktonic counts by 4 log(10) CFU/ml, whereas in combination with colistin, tigecycline, or gentamicin, it reduced counts by >6 log(10) CFU/ml. Fosfomycin was the only single agent which was able to eradicate E. coli biofilms (cure rate, 17% of implanted, infected cages). In combination, colistin plus tigecycline (50%) and fosfomycin plus gentamicin (42%) cured significantly more infected cages than colistin plus gentamicin (33%) or fosfomycin plus tigecycline (25%) (P < 0.05). The combination of fosfomycin plus colistin showed the highest cure rate (67%), which was significantly better than that of fosfomycin alone (P < 0.05). In conclusion, the combination of fosfomycin plus colistin is a promising treatment option for implant-associated infections caused by fluoroquinolone-resistant Gram-negative bacilli.

An operator formulation of the multiscale finite-volume method with correction function

The multiscale finite-volume (MSFV) method has been derived to efficiently solve large problems with spatially varying coefficients. The fine-scale problem is subdivided into local problems that can be solved separately and are coupled by a global problem. This algorithm, in consequence, shares some characteristics with two-level domain decomposition (DD) methods. However, the MSFV algorithm is different in that it incorporates a flux reconstruction step, which delivers a fine-scale mass conservative flux field without the need for iterating. This is achieved by the use of two overlapping coarse grids. The recently introduced correction function allows for a consistent handling of source terms, which makes the MSFV method a flexible algorithm that is applicable to a wide spectrum of problems. It is demonstrated that the MSFV operator, used to compute an approximate pressure solution, can be equivalently constructed by writing the Schur complement with a tangential approximation of a single-cell overlapping grid and incorporation of appropriate coarse-scale mass-balance equations.

Effect of drift on segregation in two-component diffusion-limited aggregation

An effect of drift is investigated on the segregation pattern in diffusion-limited aggregation (DLA) with two components (A and B species). The sticking probability PAB (=PBA) between the different species is introduced into the DLA model with drift, where the sticking probability PAA (=PBB) between the same species equals 1. By using computer simulation it is found that the drift has an important effect on not only the morphology but also the segregation pattern. Under the drift and the small sticking probability, a characteristic pattern appears where elongated clusters of A species and of B species are periodically dispersed. The period decreases with increasing drift. The periodic structure of the deposits is characterized by an autocorrelation function. The shape of the cluster consisting of only A species (or B species) shows a vertically elongated filamentlike structure. Each cluster becomes vertically longer with decreasing sticking probability PAB. The segregation pattern is distinctly different from that with no drift and a small sticking probability PAA. The effect of the concentration on the segregation pattern is also shown.