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PubMed2000

Hartree-fock approximation for inverse many-body problems

A new method is presented to reconstruct the potential of a quantum mechanical many-body system from observational data, combining a nonparametric Bayesian approach with a Hartree-Fock approximation. A priori information is implemented as a stochastic process, defined on the space of potentials. The method is computationally feasible and provides a general framework to treat inverse problems for quantum mechanical many-body systems.

Journal Article↗

PubMed2000

Exit-time approach to epsilon-entropy.

An efficient approach to the calculation of the epsilon-entropy is proposed. The method is based on the idea of looking at the information content of a string of data, by analyzing the signal only at the instants when the fluctuations are larger than a certain threshold epsilon, i.e., by looking at the exit-time statistics. The practical and theoretical advantages of our method with respect to the usual one are shown by the examples of a deterministic map and a self-affine stochastic process.

Journal Article↗

PubMed2001

Leverage effect in financial markets: the retarded volatility model.

We investigate quantitatively the so-called "leverage effect," which corresponds to a negative correlation between past returns and future volatility. For individual stocks this correlation is moderate and decays over 50 days, while for stock indices it is much stronger but decays faster. For individual stocks the magnitude of this correlation has a universal value that can be rationalized in terms of a new "retarded" model which interpolates between a purely additive and a purely multiplicative stochastic process. For stock indices a specific amplification phenomenon seems to be necessary to account for the observed amplitude of the effect.

Journal Article↗

PubMed2002

Optimizing searches via rare events.

Randomized search algorithms for hard combinatorial problems exhibit a large variability of performances. We study the different types of rare events which occur in such out-of-equilibrium stochastic processes and we show how they cooperate in determining the final distribution of running times. As a by-product of our analysis we show how search algorithms are optimized by random restarts.

Journal Article↗

PubMed2003

Phase control of directed diffusion in a symmetric optical lattice.

We demonstrate the phenomenon of directed diffusion in a symmetric periodic potential. This has been realized with cold atoms in a one-dimensional dissipative optical lattice. The stochastic process of optical pumping leads to a diffusive dynamics of the atoms through the periodic structure, while a zero-mean force which breaks the temporal symmetry of the system is applied by phase modulating one of the lattice beams. The atoms are set into directed motion as a result of the breaking of the temporal symmetry of the system.

Journal Article↗

PubMed2003

Binary N-step Markov chains and long-range correlated systems.

A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In our model, the conditional probability that the ith symbol in the chain equals zero (or unity) is a linear function of the number of unities among the preceding N symbols. The correlation and distribution functions as well as the variance of number of symbols in the words of arbitrary length L are obtained analytically and numerically. If the persistent correlations are not extremely strong, the variance is shown to be nonlinearly dependent on L. A self-similarity of the studied stochastic process is revealed. The applicability of the developed theory to the coarse-grained written and DNA texts is discussed.

Bacillus subtilis↗

PubMed2004

Generalized randomly amplified linear system driven by gaussian noises: extreme heavy tail and algebraic correlation decay in plasma turbulence.

The extreme heavy tail and the power-law decay of the turbulent flux correlation observed in hot magnetically confined plasmas are modeled by a system of coupled Langevin equations describing a continuous time linear randomly amplified stochastic process where the amplification factor is driven by a superposition of colored noises which, in a suitable limit, generate a fractional Brownian motion. An exact analytical formula for the power-law tail exponent beta is derived. The extremely small value of the heavy tail exponent and the power-law distribution of laminar times also found experimentally are obtained, in a robust manner, for a wide range of input values, as a consequence of the (asymptotic) self-similarity property of the noise spectrum. As a by-product, a new representation of the persistent fractional Brownian motion is obtained.

Journal Article↗

PubMed2004

Noise-induced macroscopic bifurcations in globally coupled chaotic units.

Large populations of globally coupled identical maps subjected to independent additive noise are shown to undergo qualitative changes as the features of the stochastic process are varied. We show that, for strong coupling, the collective dynamics can be described in terms of a few effective macroscopic degrees of freedom, whose deterministic equations of motion are systematically derived through an order parameter expansion.

Journal Article↗

PubMed2004

Maximum Renyi entropy principle for systems with power-law Hamiltonians.

The Renyi distribution ensuring the maximum of Renyi entropy is investigated for a particular case of a power-law Hamiltonian. Both Lagrange parameters alpha and beta can be eliminated. It is found that beta does not depend on a Renyi parameter q and can be expressed in terms of an exponent kappa of the power-law Hamiltonian and an average energy U. The Renyi entropy for the resulting Renyi distribution reaches its maximal value at q=1/(1+kappa) that can be considered as the most probable value of q when we have no additional information on the behavior of the stochastic process. The Renyi distribution for such q becomes a power-law distribution with the exponent -(kappa+1). When q=1/(1+kappa)+epsilon (0<epsilon<<1) there appears a horizontal head part of the Renyi distribution that precedes the power-law part. Such a picture corresponds to some observed phenomena.

Journal Article↗

PubMed2005

Fluctuation-regularized front propagation dynamics in reaction-diffusion systems.

We introduce and study a new class of fronts in finite particle-number reaction-diffusion systems, corresponding to propagating up a reaction-rate gradient. We show that these systems have no traditional mean-field limit, as the nature of the long-time front solution in the stochastic process differs essentially from that obtained by solving the mean-field deterministic reaction-diffusion equations. Instead, one can incorporate some aspects of the fluctuations via introducing a density cutoff. Using this method, we derive analytic expressions for the front velocity dependence on bulk particle density and show self-consistently why this cutoff approach can get the correct leading-order physics.

Biological Evolution↗

PubMed2005

Simulating nonequilibrium quantum fields with stochastic quantization techniques.

We present lattice simulations of nonequilibrium quantum fields in Minkowskian space-time. Starting from a nonthermal initial state, the real-time quantum ensemble in (3 + 1) dimensions is constructed by a stochastic process in an additional (5th) "Langevin-time." For the example of a self-interacting scalar field, we show how to resolve apparent unstable Langevin dynamics and compare our quantum results with those obtained in classical field theory. Such a direct simulation method is crucial for our understanding of collision experiments of heavy nuclei or other nonequilibrium phenomena in strongly coupled quantum many-body systems.

Journal Article↗

PubMed2006

Universality in solar flare and earthquake occurrence.

Earthquakes and solar flares are phenomena involving huge and rapid releases of energy characterized by complex temporal occurrence. By analyzing available experimental catalogs, we show that the stochastic processes underlying these apparently different phenomena have universal properties. Namely, both problems exhibit the same distributions of sizes, interoccurrence times, and the same temporal clustering: We find after flare sequences with power law temporal correlations as the Omori law for seismic sequences. The observed universality suggests a common approach to the interpretation of both phenomena in terms of the same driving physical mechanism.

Journal Article↗

PubMed2003

Isolation of a crystal matrix protein associated with calcium oxalate precipitation in vacuoles of specialized cells.

The formation of calcium (Ca) oxalate crystals is considered to be a high-capacity mechanism for regulating Ca in many plants. Ca oxalate precipitation is not a stochastic process, suggesting the involvement of specific biochemical and cellular mechanisms. Microautoradiography of water lettuce (Pistia stratiotes) tissue exposed to 3H-glutamate showed incorporation into developing crystals, indicating potential acidic proteins associated with the crystals. Dissolution of crystals leaves behind a crystal-shaped matrix "ghost" that is capable of precipitation of Ca oxalate in the original crystal morphology. To assess whether this matrix has a protein component, purified crystals were isolated and analyzed for internal protein. Polyacrylamide gel electrophoresis revealed the presence of one major polypeptide of about 55 kD and two minor species of 60 and 63 kD. Amino acid analysis indicates the matrix protein is relatively high in acidic amino acids, a feature consistent with its solubility in formic acid but not at neutral pH. 45Ca-binding assays demonstrated the matrix protein has a strong affinity for Ca. Immunocytochemical localization using antibody raised to the isolated protein showed that the matrix protein is specific to crystal-forming cells. Within the vacuole, the surface and internal structures of two morphologically distinct Ca oxalate crystals, raphide and druse, were labeled by the antimatrix protein serum, as were the surfaces of isolated crystals. These results demonstrate that a specific Ca-binding protein exists as an integral component of Ca oxalate crystals, which holds important implications with respect to regulation of crystal formation.

Amino Acids↗

PubMed2001

A model for the generation of synthetic intramuscular EMG signals to test decomposition algorithms.

As more and more intramuscular electromyogram (EMG) decomposition programs are being developed, there is a growing need for evaluating and comparing their performances. One way to achieve this goal is to generate synthetic EMG signals having known features. Features of interest are: the number of channels acquired (number of detection surfaces), the number of detected motor unit action potential (MUAP) trains, their time-varying firing rates, the degree of shape similarity among MUAPs belonging to the same motor unit (MU) or to different MUs, the degree of MUAP superposition, the MU activation intervals, the amount and type of additive noise. A model is proposed to generate one or more channels of intramuscular EMG starting from a library of real MUAPs represented in a 16-dimensional space using their Associated Hermite expansion. The MUAP shapes, regularity of repetition rate, degree of superposition, activation intervals, etc. may be time variable and are described quantitatively by a number of parameters which define a stochastic process (the model) with known statistical features. The desired amount of noise may be added to the synthetic signal which may then be processed by the decomposition algorithm under test to evaluate its capability of recovering the signal features.

Action Potentials↗

PubMed2001

Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm.

The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain magnetic resonance (MR) images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogram-based model, the FM has an intrinsic limitation--no spatial information is taken into account. This causes the FM model to work only on well-defined images with low levels of noise; unfortunately, this is often not the the case due to artifacts such as partial volume effect and bias field distortion. Under these conditions, FM model-based methods produce unreliable results. In this paper, we propose a novel hidden Markov random field (HMRF) model, which is a stochastic process generated by a MRF whose state sequence cannot be observed directly but which can be indirectly estimated through observations. Mathematically, it can be shown that the FM model is a degenerate version of the HMRF model. The advantage of the HMRF model derives from the way in which the spatial information is encoded through the mutual influences of neighboring sites. Although MRF modeling has been employed in MR image segmentation by other researchers, most reported methods are limited to using MRF as a general prior in an FM model-based approach. To fit the HMRF model, an EM algorithm is used. We show that by incorporating both the HMRF model and the EM algorithm into a HMRF-EM framework, an accurate and robust segmentation can be achieved. More importantly, the HMRF-EM framework can easily be combined with other techniques. As an example, we show how the bias field correction algorithm of Guillemaud and Brady (1997) can be incorporated into this framework to achieve a three-dimensional fully automated approach for brain MR image segmentation.

Algorithms↗

PubMed2003

Assessment of muscle fatigue during biking.

The analysis of the surface myoelectric signal recorded while a muscle is performing a sustained contraction is a valuable tool for assessing the progression of localized fatigue. It is well known that the modifications of the spectral content of the myoelectric signal are mainly related to changes in the interstitial fluid pH, which, in turn, affect the membrane excitability of the active muscle fibers. This paper describes the effects of muscle fatigue on the surface myoelectric signal recorded from three thigh and leg muscles during biking, on a population consisting of 22 young healthy volunteers. The purpose of this study was to obtain normative data relative to an exercise protocol mild enough to be applicable, in the future, to pathological subjects as well. Each subject was asked to exercise 30 min on a cycloergometer at a constant velocity and against a constant torque. While subjects were biking, the surface myoelectric signal was recorded from the rectus femoris, the biceps femoris, and the gastrocnemius muscles. In this study, we considered two different aspects of muscle fatigue: first, the localized muscle fatigue as shown by the decrement of the instantaneous frequency of the myoelectric signal during the exercise; second, the modifications of the muscle ON-OFF timing, which could be explained as a strategy for increasing endurance by modifying the role of different muscles during the exercise. The first aspect was studied by obtaining the spectral characteristics of the signals by means of bilinear time-frequency transforms and by applying an original estimator of the instantaneous frequency of stochastic processes based on cross time-frequency transforms. Our results demonstrated that none of the subjects showed significant signs of localized muscle fatigue, since the decrement of the instantaneous frequency during the exercise was always lower than 5% of its initial value. Muscle ON-OFF timing was obtained by applying to the raw myoelectric signal a double threshold statistical detector to identify the time intervals during which the observed muscles were active. This demonstrated that the subjective feeling of fatigue each subject reported during the exercise did not cause a change of the activation strategy of the observed muscles. It is concluded that the experimental protocol herein described and the signal processing procedures adopted are appropriate for monitoring different effects of muscle fatigue during biking. Moreover, data obtained from our sample population can be considered as a reference for studying the manifestations of muscle fatigue in pathological subjects asked to follow a similar experimental protocol.

Adaptation, Physiological↗

PubMed2002

Surface-related phase noise in SAW resonators.

With the advent of nanotechnologies, electronic devices are shrinking in thickness and width to reduce mass and, thereby, increase frequency and spe Lithographic approaches are capable of creating metal connections with thickness and lateral dimensions down to about 20 nm, approaching the molecular scale. As a result, the dimensions of outer particles are comparable with, or even larger than, those of active or passive regions in electronics devices. Therefore, directing our attention toward the effect of surface fluctuations is of practical significance. In fact, electronic device surface-related phenomena have already received more and more attention as device size decreases. In connection with surface phase noise, selection of a suitable device with high surface sensitivity is important. In this paper, high Q-value surface acoustic wave resonators were employed because of their strong sensitivity to surface perturbation. Phase noise in SAW resonators related to surface particle motion has been examined both theoretically and experimentally. This kind of noise has been studied from the point of view of a stochastic process resulting from particle molecular adsorption and desorption. Experimental results suggest that some volatile vapors can change flicker noise 1/f and random walk noise 1/f2. An analysis has been made indicating that these effects are not associated with Q value variation, but are generated by the change in the dynamic rate of adsorption and desorption of surface particles. Research on particle motion above the device substrate might explain the differences observed from the model based only on the substrate itself. Results might lead to a better understanding of the phase noise mechanism in micro-electronic devices and help us to build oscillators with improved performance.

Acoustics↗

PubMed1994

Melanogenesis during the anagen-catagen-telogen transformation of the murine hair cycle.

Melanin synthesis of follicular melanocytes is strictly coupled to the growth stage of the hair cycle (anagen), ceases during follicle regression (catagen), and is absent throughout the resting stage (telogen). Having previously characterized the expression and activity of melanogenesis-related proteins during the telogen-anagen transition of the murine hair cycle (JID 96:172, 1991), we here report a biophysical and biochemical analysis of follicular melanogenesis during the anagen-catagen-telogen transformation of the C57 BL-6 mouse hair cycle. Tyrosinase activity and concentration as well as dopachrome tautomerase activity were compared with melanin synthesis, as measured by electron paramagnetic resonance spectroscopy (EPR). The visible changes in skin color and the histologically appreciable switch-off of melanin formation during the anagen-catagen transformation were accompanied by a steep decline in 1) the melanin-associated EPR signal of full-thickness mouse skin, 2) tyrosinase and dopachrome tautomerase activities, and 3) the skin concentration of 80-85-kD melanogenesis related protein and 66-68-kD tyrosinase protein. Telogen skin displayed a minimum of the EPR amplitude as well as of tyrosinase and dopachrome tautomerase activity detected. By EPR, only eumelanin was identified during all hair cycle stages. The gradual switch-off of melanogenesis during anagen VI started with an unexpectedly early decline of the EPR melanin signal, followed by dopachrome tautomerase activity and the concentration of 80-85-kD melanogenesis related protein. The initiation of catagen was characterized by a significant and rapid decrease in activity and concentration of tyrosinase, and was accompanied by a second drop in dopachrome tautomerase activity. Together, these biochemical and biophysical parameters of follicular melanogenesis serve as novel and differential markers for the imminent termination of anagen and the development of catagen. They also show that the switch-off of melanogenesis during the anagen-catagen-telogen transition is a stochastic process commencing already in mid anagen VI.

Animals↗