945 resultados para Probability Distribution Function


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The ERS-1 Satellite was launched in July 1991 by the European Space Agency into a polar orbit at about 800 km, carrying a C-band scatterometer. A scatterometer measures the amount of backscatter microwave radiation reflected by small ripples on the ocean surface induced by sea-surface winds, and so provides instantaneous snap-shots of wind flow over large areas of the ocean surface, known as wind fields. Inherent in the physics of the observation process is an ambiguity in wind direction; the scatterometer cannot distinguish if the wind is blowing toward or away from the sensor device. This ambiguity implies that there is a one-to-many mapping between scatterometer data and wind direction. Current operational methods for wind field retrieval are based on the retrieval of wind vectors from satellite scatterometer data, followed by a disambiguation and filtering process that is reliant on numerical weather prediction models. The wind vectors are retrieved by the local inversion of a forward model, mapping scatterometer observations to wind vectors, and minimising a cost function in scatterometer measurement space. This thesis applies a pragmatic Bayesian solution to the problem. The likelihood is a combination of conditional probability distributions for the local wind vectors given the scatterometer data. The prior distribution is a vector Gaussian process that provides the geophysical consistency for the wind field. The wind vectors are retrieved directly from the scatterometer data by using mixture density networks, a principled method to model multi-modal conditional probability density functions. The complexity of the mapping and the structure of the conditional probability density function are investigated. A hybrid mixture density network, that incorporates the knowledge that the conditional probability distribution of the observation process is predominantly bi-modal, is developed. The optimal model, which generalises across a swathe of scatterometer readings, is better on key performance measures than the current operational model. Wind field retrieval is approached from three perspectives. The first is a non-autonomous method that confirms the validity of the model by retrieving the correct wind field 99% of the time from a test set of 575 wind fields. The second technique takes the maximum a posteriori probability wind field retrieved from the posterior distribution as the prediction. For the third technique, Markov Chain Monte Carlo (MCMC) techniques were employed to estimate the mass associated with significant modes of the posterior distribution, and make predictions based on the mode with the greatest mass associated with it. General methods for sampling from multi-modal distributions were benchmarked against a specific MCMC transition kernel designed for this problem. It was shown that the general methods were unsuitable for this application due to computational expense. On a test set of 100 wind fields the MAP estimate correctly retrieved 72 wind fields, whilst the sampling method correctly retrieved 73 wind fields.

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We present a stochastic agent-based model for the distribution of personal incomes in a developing economy. We start with the assumption that incomes are determined both by individual labour and by stochastic effects of trading and investment. The income from personal effort alone is distributed about a mean, while the income from trade, which may be positive or negative, is proportional to the trader's income. These assumptions lead to a Langevin model with multiplicative noise, from which we derive a Fokker-Planck (FP) equation for the income probability density function (IPDF) and its variation in time. We find that high earners have a power law income distribution while the low-income groups have a Levy IPDF. Comparing our analysis with the Indian survey data (obtained from the world bank website: http://go.worldbank.org/SWGZB45DN0) taken over many years we obtain a near-perfect data collapse onto our model's equilibrium IPDF. Using survey data to relate the IPDF to actual food consumption we define a poverty index (Sen A. K., Econometrica., 44 (1976) 219; Kakwani N. C., Econometrica, 48 (1980) 437), which is consistent with traditional indices, but independent of an arbitrarily chosen "poverty line" and therefore less susceptible to manipulation. Copyright © EPLA, 2010.

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An experimental method for characterizing the time-resolved phase noise of a fast switching tunable laser is discussed. The method experimentally determines a complementary cumulative distribution function of the laser's differential phase as a function of time after a switching event. A time resolved bit error rate of differential quadrature phase shift keying formatted data, calculated using the phase noise measurements, was fitted to an experimental time-resolved bit error rate measurement using a field programmable gate array, finding a good agreement between the time-resolved bit error rates.

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We find the probability distribution of the fluctuating parameters of a soliton propagating through a medium with additive noise. Our method is a modification of the instanton formalism (method of optimal fluctuation) based on a saddle-point approximation in the path integral. We first solve consistently a fundamental problem of soliton propagation within the framework of noisy nonlinear Schrödinger equation. We then consider model modifications due to in-line (filtering, amplitude and phase modulation) control. It is examined how control elements change the error probability in optical soliton transmission. Even though a weak noise is considered, we are interested here in probabilities of error-causing large fluctuations which are beyond perturbation theory. We describe in detail a new phenomenon of soliton collapse that occurs under the combined action of noise, filtering and amplitude modulation. © 2004 Elsevier B.V. All rights reserved.

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We introduce a general technique how to reveal in experiments of limited electrical bandwidth which is lower than the optical bandwidth of the optical signal under study, whether the statistical properties of the light source obey Gaussian distribution or mode correlations do exist. To do that one needs to perform measurements by decreasing the measurement bandwidth. We develop a simple model of bandwidth-limited measurements and predict universal laws how intensity probability density function and intensity auto-correlation function of ideal completely stochastic source of Gaussian statistics depend on limited measurement bandwidth and measurement noise level. Results of experimental investigation are in good agreement with model predictions. In particular, we reveal partial mode correlations in the radiation of quasi-CW Raman fibre laser.

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In the present paper we numerically study instrumental impact on statistical properties of quasi-CW Raman fiber laser using a simple model of multimode laser radiation. Effects, that have the most influence, are limited electrical bandwidth of measurement equipment and noise. To check this influence, we developed a simple model of the multimode quasi- CW generation with exponential statistics (i.e. uncorrelated modes). We found that the area near zero intensity in probability density function (PDF) is strongly affected by both factors, for example both lead to formation of a negative wing of intensity distribution. But far wing slope of PDF is not affected by noise and, for moderate mismatch between optical and electrical bandwidth, is only slightly affected by bandwidth limitation. The generation spectrum often becomes broader at higher power in experiments, so the spectral/electrical bandwidth mismatch factor increases over the power that can lead to artificial dependence of the PDF slope over the power. It was also found that both effects influence the ACF background level: noise impact decreases it, while limited bandwidth leads to its increase. © (2014) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

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Motivation: Within bioinformatics, the textual alignment of amino acid sequences has long dominated the determination of similarity between proteins, with all that implies for shared structure, function, and evolutionary descent. Despite the relative success of modern-day sequence alignment algorithms, so-called alignment-free approaches offer a complementary means of determining and expressing similarity, with potential benefits in certain key applications, such as regression analysis of protein structure-function studies, where alignment-base similarity has performed poorly. Results: Here, we offer a fresh, statistical physics-based perspective focusing on the question of alignment-free comparison, in the process adapting results from “first passage probability distribution” to summarize statistics of ensemble averaged amino acid propensity values. In this paper, we introduce and elaborate this approach.

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* This work was financially supported by RFBR-04-01-00858.

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* This work was financially supported by RFBR-04-01-00858.

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The aim of this paper is to establish some mixture distributions that arise in stochastic processes. Some basic functions associated with the probability mass function of the mixture distributions, such as k-th moments, characteristic function and factorial moments are computed. Further we obtain a three-term recurrence relation for each established mixture distribution.

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The method for the computation of the conditional probability density function for the nonlinear Schrödinger equation with additive noise is developed. We present in a constructive form the conditional probability density function in the limit of small noise and analytically derive it in a weakly nonlinear case. The general theory results are illustrated using fiber-optic communications as a particular, albeit practically very important, example.

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Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.

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MSC 2010: 42C40, 94A12

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The article analyzes the contribution of stochastic thermal fluctuations in the attachment times of the immature T-cell receptor TCR: peptide-major-histocompatibility-complex pMHC immunological synapse bond. The key question addressed here is the following: how does a synapse bond remain stabilized in the presence of high-frequency thermal noise that potentially equates to a strong detaching force? Focusing on the average time persistence of an immature synapse, we show that the high-frequency nodes accompanying large fluctuations are counterbalanced by low-frequency nodes that evolve over longer time periods, eventually leading to signaling of the immunological synapse bond primarily decided by nodes of the latter type. Our analysis shows that such a counterintuitive behavior could be easily explained from the fact that the survival probability distribution is governed by two distinct phases, corresponding to two separate time exponents, for the two different time regimes. The relatively shorter timescales correspond to the cohesion:adhesion induced immature bond formation whereas the larger time reciprocates the association:dissociation regime leading to TCR:pMHC signaling. From an estimate of the bond survival probability, we show that, at shorter timescales, this probability PΔ(τ) scales with time τ as a universal function of a rescaled noise amplitude DΔ2, such that PΔ(τ)∼τ-(ΔD+12),Δ being the distance from the mean intermembrane (T cell:Antigen Presenting Cell) separation distance. The crossover from this shorter to a longer time regime leads to a universality in the dynamics, at which point the survival probability shows a different power-law scaling compared to the one at shorter timescales. In biological terms, such a crossover indicates that the TCR:pMHC bond has a survival probability with a slower decay rate than the longer LFA-1:ICAM-1 bond justifying its stability.

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2000 Mathematics Subject Classification: 62G32, 62G05.