First-passage-time statistics for diffusion processes with an external random force

We present exact equations and expressions for the first-passage-time statistics of dynamical systems that are a combination of a diffusion process and a random external force modeled as dichotomous Markov noise. We prove that the mean first passage time for this system does not show any resonantlike behavior.

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.

Random diffusion and leverage effect in financial markets

We prove that Brownian market models with random diffusion coefficients provide an exact measure of the leverage effect [J-P. Bouchaud et al., Phys. Rev. Lett. 87, 228701 (2001)]. This empirical fact asserts that past returns are anticorrelated with future diffusion coefficient. Several models with random diffusion have been suggested but without a quantitative study of the leverage effect. Our analysis lets us to fully estimate all parameters involved and allows a deeper study of correlated random diffusion models that may have practical implications for many aspects of financial markets.

Self and cross-velocity correlation functions and diffusion coefficients in liquids: a molecular dynamics study of binary mixtures of soft spheres

Molecular dynamics simulation is applied to the study of the diffusion properties in binary liquid mixtures made up of soft-sphere particles with different sizes and masses. Self- and distinct velocity correlation functions and related diffusion coefficients have been calculated. Special attention has been paid to the dynamic cross correlations which have been computed through recently introduced relative mean molecular velocity correlation functions which are independent on the reference frame. The differences between the distinct velocity correlations and diffusion coefficients in different reference frames (mass-fixed, number-fixed, and solvent-fixed) are discussed.

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.

SEQUENTIAL EXTRACTION OF PHOSPHORUS BY MEHLICH-1 AND ION EXCHANGE RESIN FROM B HORIZONS OF FERRIC AND PERFERRIC LATOSOLS (OXISOLS)

In general, Latosols have low levels of available P, however, the influence of the parent material seems to be decisive in defining the pool and predominant form of P in these soils. This study evaluated P availability by extraction with Mehlich-1 (M-1) and Ion Exchange Resin (IER), from samples of B horizons of Ferric and Perferric Latosols developed from different parent materials. To this end, in addition to the physical and chemical characterization of soils, 10 sequential extractions were performed with M-1 and IER from samples of B horizons (depth between 0.8 and 1.0 m). Total contents of Ca, P, Fe, Al, and Ti were determined after digestion with nitric, hydrofluoric and perchloric acids. The effects of sequential P extractions on Fe oxides were also evaluated from the analyses of dithionite-citrate-bicarbonate and ammonium acid oxalate. The high similarity between contents of P accumulated after sequential extractions with M-1 and IER in soils developed on tuffite indicated a predominance of P-Ca. Higher contents of P after a single IER extraction show greater efficiency in P removal from highly weathered soils, as from the Latosols studied here. The P contents also show the high sensitivity of extractant M-1 in highly buffered soils. Furthermore, a single extraction with extractant M-1 or IER is not sufficient to estimate the amount of labile P in these soils.

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.

Exact temporal evolution for some non-linear diffusion process

Exact solutions to FokkerPlanck equations with nonlinear drift are considered. Applications of these exact solutions for concrete models are studied. We arrive at the conclusion that for certain drifts we obtain divergent moments (and infinite relaxation time) if the diffusion process can be extended without any obstacle to the whole space. But if we introduce a potential barrier that limits the diffusion process, moments converge with a finite relaxation time.

Diffusion Spectrum Imaging after stroke shows structural changes in the contra-lateral motor network correlating with functional recovery

There is growing interest in understanding the role of the non-injured contra-lateral hemisphere in stroke recovery. In the experimental field, histological evidence has been reported that structural changes occur in the contra-lateral connectivity and circuits during stroke recovery. In humans, some recent imaging studies indicated that contra-lateral sub-cortical pathways and functional and structural cortical networks are remodeling, after stroke. Structural changes in the contra-lateral networks, however, have never been correlated to clinical recovery in patients. To determine the importance of the contra-lateral structural changes in post-stroke recovery, we selected a population of patients with motor deficits after stroke affecting the motor cortex and/or sub-cortical motor white matter. We explored i) the presence of Generalized Fractional Anisotropy (GFA) changes indicating structural alterations in the motor network of patientsâeuro? contra-lateral hemisphere as well as their longitudinal evolution ii) the correlation of GFA changes with patientsâeuro? clinical scores, stroke size and demographics data iii) and a predictive model.

ROLES OF ACID-SENSING ION CHANNELS (ASICS) IN PERIPHERAL NEUROPEPTIDE SECRETION AND PAIN

Acid-sensing ion channels (ASICs) are non-voltage-gated sodium channels activated by an extracellular acidification. They are widely expressed in neurons of the central and peripheral nervous system. ASICs have a role in learning, the expression of fear, in neuronal death after cerebral ischemia, and in pain sensation. Tissue damage leads to the release of inflammatory mediators. There is a subpopulation of sensory neurons which are able to release the neuropeptides calcitonin gene-related peptide (CGRP) and substance P (SP). Neurogenic inflammation refers to the process whereby peripheral release of the neuropeptides CGRP and SP induces vasodilation and extravasation of plasma proteins, respectively. Our laboratory has previously shown that calcium-permeable homomeric ASIC1a channels are present in a majority of CGRP- or SP-expressing small diameter sensory neurons. In the first part of my thesis, we tested the hypothesis that a local acidification can produce an ASIC-mediated calcium-dependant neuropeptide secretion. We have first verified the co-expression of ASICs and CGRP/SP using immunochemistry and in-situ hybridization on dissociated rat dorsal root ganglion (DRG) neurons. We found that most CGRP/SP-positive neurons also expressed ASIC1a and ASIC3 subunits. Calcium imaging experiments with Fura-2 dye showed that an extracellular acidification can induce an increase of intracellular Ca2+ concentration, which is essential for secretion. This increase of intracellular Ca2+ concentration is, at least in some cells, ASIC-dependent, as it can be prevented by amiloride, an ASIC antagonist, and by Psalmotoxin (PcTx1), a specific ASIC1a antagonist. We identified a sub-population of neurons whose acid-induced Ca2+ entry was completely abolished by amiloride, an amiloride-resistant population which does not express ASICs, but rather another acid-sensing channel, possibly transient receptor potential vanilloïde 1 (TRPV1), and a population expressing both H+-gated channel types. Voltage-gated calcium channels (Cavs) may also mediate Ca2+ entry. Co-application of the Cavs inhibitors (ω-conotoxin MVIIC, Mibefradil and Nifedipine) reduced the Ca2+ increase in neurons expressing ASICs during an acidification to pH 6. This indicates that ASICs can depolarise the neuron and activate Cavs. Homomeric ASIC1a are Ca2+-permeable and allow a direct entry of Ca2+ into the cell; other ASICs mediate an indirect entry of Ca2+ by inducing a membrane depolarisation that activates Cavs. We showed with a secretion assay that CGRP secretion can be induced by extracellular acidification in cultured rat DRG neurons. Amiloride and PcTx1 were not able to inhibit the secretion at acidic pH, but BCTC, a TRPV1 inhibitor was able to decrease the secretion induced by an extracellular acidification in our in vitro secretion assay. In conclusion, these results show that in DRG neurons a mild extracellular acidification can induce a calcium-dependent neuropeptide secretion. Even if our data show that ASICs can mediate an increase of intracellular Ca2+ concentration, this appears not to be sufficient to trigger neuropeptide secretion. TRPV1, a calcium channel whose activation induces a sustained current - in contrary of ASICs - played in our experimental conditions a predominant role in neurosecretion. In the second part of my thesis, we focused on the role of ASICs in neuropathic pain. We used the spared nerve injury (SNI) model which consists in a nerve injury that induces symptoms of neuropathic pain such as mechanical allodynia. We have previously shown that the SNI model modifies ASIC currents in dissociated rat DRG neurons. We hypothesized that ASICs could play a role in the development of mechanical allodynia. The SNI model was performed on ASIC1a, -2, and -3 knock-out mice and wild type littermates. We measured mechanical allodynia on these mice with calibrated von Frey filaments. There were no differences between the wild-type and the ASIC1, or ASIC2 knockout mice. ASIC3 null mice were less sensitive than wild type mice at 21 day after SNI, indicating a role for ASIC3. Finally, to investigate other possible roles of ASICs in the perception of the environment, we measured the baseline heat responses. We used two different models; the tail flick model and the hot plate model. ASIC1a null mice showed increased thermal allodynia behaviour in the hot plate test at three different temperatures (49, 52, 55°C) compared to their wild type littermates. On the contrary, ASIC2 null mice showed reduced thermal allodynia behaviour in the hot plate test compared to their wild type littermates at the three same temperatures. We conclude that ASIC1a and ASIC2 in mice can play a role in temperature sensing. It is currently not understood how ASICs are involved in temperature sensing and what the reason for the opposed effects in the two knockout models is.

Determination of radionuclide levels in rainwater using ion exchange resin and gamma-spectrometry.

The evaluation of radioactivity accidentally released into the atmosphere involves determining the radioactivity levels of rainwater samples. Rainwater scavenges atmospheric airborne radioactivity in such a way that surface contamination can be deduced from rainfall rate and rainwater radioactivity content. For this purpose, rainwater is usually collected in large surface collectors and then measured by gamma-spectrometry after such treatments as evaporation or iron hydroxide precipitation. We found that collectors can be adapted to accept large surface (diameter 47mm) cartridges containing a strongly acidic resin (Dowex AG 88) which is able to quantitatively extract radioactivity from rainwater, even during heavy rainfall. The resin can then be measured by gamma-spectrometry. The detection limit is 0.1Bq per sample of resin (80g) for (137)Cs. Natural (7)Be and (210)Pb can also be measured and the activity ratio of both radionuclides is comparable with those obtained through iron hydroxide precipitation and air filter measurements. Occasionally (22)Na has also been measured above the detection limit. A comparison between the evaporation method and the resin method demonstrated that 2/3 of (7)Be can be lost during the evaporation process. The resin method is simple and highly efficient at extracting radioactivity. Because of these great advantages, we anticipate it could replace former rainwater determination methods. Moreover, it does not necessitate the transportation of large rainwater volumes to the laboratory.

A single point mutation in the pore region of the epithelial Na+ channel changes ion selectivity by modifying molecular sieving.

The epithelial Na+ channel (ENaC) belongs to a new class of channel proteins called the ENaC/DEG superfamily involved in epithelial Na+ transport, mechanotransduction, and neurotransmission. The role of ENaC in Na+ homeostasis and in the control of blood pressure has been demonstrated recently by the identification of mutations in ENaC beta and gamma subunits causing hypertension. The function of ENaC in Na+ reabsorption depends critically on its ability to discriminate between Na+ and other ions like K+ or Ca2+. ENaC is virtually impermeant to K+ ions, and the molecular basis for its high ionic selectivity is largely unknown. We have identified a conserved Ser residue in the second transmembrane domain of the ENaC alpha subunit (alphaS589), which when mutated allows larger ions such as K+, Rb+, Cs+, and divalent cations to pass through the channel. The relative ion permeability of each of the alphaS589 mutants is related inversely to the ionic radius of the permeant ion, indicating that alphaS589 mutations increase the molecular cutoff of the channel by modifying the pore geometry at the selectivity filter. Proper geometry of the pore is required to tightly accommodate Na+ and Li+ ions and to exclude larger cations. We provide evidence that ENaC discriminates between cations mainly on the basis of their size and the energy of dehydration.