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Rytis Kazakevicius; Julius Ruseckas
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Complex dynamical systems which are governed by anomalous diffusion often can be described by Langevin equations driven by L\'evy stable noise. In this article we generalize nonlinear stochastic differential equations driven by Gaussian noise and generating signals with 1/f power spectral density by replacing the Gaussian noise with a more general L\'evy stable noise. The equations with the Gaussian noise arise as a special case when the index of stability alpha=2. We expect that this...
Topics: Physics, Data Analysis, Statistics and Probability, Statistical Mechanics, Condensed Matter
Source: http://arxiv.org/abs/1403.0409
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Enrico Massa; Carlo Paolo Sasso; Giovanni Mana; Carlo Palmisano
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In 2011, a discrepancy between the values of the Planck constant measured by counting Si atoms and by comparing mechanical and electrical powers prompted a review, among others, of the measurement of the spacing of Si 28 {220} lattice planes, either to confirm the measured value and its uncertainty or to identify errors. This exercise confirmed the result of the previous measurement and yields the additional value $d_{220}=192014711.98(34)$ am having a reduced uncertainty.
Topics: Condensed Matter, Data Analysis, Statistics and Probability, Physics, Materials Science
Source: http://arxiv.org/abs/1503.06136
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Rinku Jacob; K. P. Harikrishnan; R. Misra; G. Ambika
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We undertake a preliminary numerical investigation to understand how the addition of white and colored noise to a time series affects the topology and structure of the underlying chaotic attractor. We use the methods and measures of recurrence networks generated from the time series for this analysis. We explicitly show that the addition of noise destroys the recurrence of trajectory points in the phase space. By using the results obtained from this analysis, we go on to analyse the light...
Topics: Nonlinear Sciences, Data Analysis, Statistics and Probability, Physics, Chaotic Dynamics,...
Source: http://arxiv.org/abs/1508.02724
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WenJie Xie; ZhiQiang Jiang; GaoFeng Gu; Xiong Xiong; WeiXing Zhou
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Many complex systems generate multifractal time series which are longrange crosscorrelated. Numerous methods have been proposed to characterize the multifractal nature of these longrange cross correlations. However, several important issues about these methods are not well understood and most methods consider only one moment order. We study the joint multifractal analysis based on partition function with two moment orders, which was initially invented to investigate fluid fields, and derive...
Topics: Data Analysis, Statistics and Probability, Quantitative Finance, Statistical Finance, Physics
Source: http://arxiv.org/abs/1509.05952
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Shintaro Mori; Masato Hisakado
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We describe a universality class of the transitions of a generalized P\'{o}lya urn by studying the asymptotic behavior of the normalized correlation function $C(t)$ using finitesize scaling analysis. $X(1),X(2),\cdots$ are the successive additions of a red (blue) ball [$X(t)=1\,(0)$] at stage $t$ and $C(t)\equiv \mbox{Cov}(X(1),X(t+1))/\mbox{Var}(X(1))$. Furthermore, $z(t)=\sum_{s=1}^{t}X(s)/t$ represents the successive proportions of red balls in an urn to which, at the $t+1$th stage, a red...
Topics: Statistical Mechanics, Condensed Matter, Data Analysis, Statistics and Probability, Physics
Source: http://arxiv.org/abs/1501.00764
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MinWoo Ahn; WooSung Jung
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Link prediction is a technique that uses the topological information in a given network to infer the missing links in it. Since past research on link prediction has primarily focused on enhancing performance for given empirical systems, negligible attention has been devoted to link prediction with regard to network models. In this paper, we thus apply link prediction to two network models: The WattsStrogatz (WS) model and Barab\'asiAlbert (BA) model. We attempt to gain a better understanding...
Topics: Physics and Society, Computing Research Repository, Social and Information Networks, Physics, Data...
Source: http://arxiv.org/abs/1503.02872
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Laetitia Loncan; Luis B. Almeida; José M. BioucasDias; Xavier Briottet; Jocelyn Chanussot; Nicolas Dobigeon; Sophie Fabre; Wenzhi Liao; Giorgio A. Licciardi; Miguel Simões; JeanYves Tourneret; Miguel A. Veganzones; Gemine Vivone; Qi Wei; Naoto Yokoya
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Pansharpening aims at fusing a panchromatic image with a multispectral one, to generate an image with the high spatial resolution of the former and the high spectral resolution of the latter. In the last decade, many algorithms have been presented in the literature for pansharpening using multispectral data. With the increasing availability of hyperspectral systems, these methods are now being adapted to hyperspectral images. In this work, we compare new pansharpening techniques designed for...
Topics: Data Analysis, Statistics and Probability, Statistics, Computer Vision and Pattern Recognition,...
Source: http://arxiv.org/abs/1504.04531
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PierreAntoine Thouvenin; Nicolas Dobigeon; JeanYves Tourneret
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Given a mixed hyperspectral data set, linear unmixing aims at estimating the reference spectral signatures composing the data  referred to as endmembers  their abundance fractions and their number. In practice, the identified endmembers can vary spectrally within a given image and can thus be construed as variable instances of reference endmembers. Ignoring this variability induces estimation errors that are propagated into the unmixing procedure. To address this issue, endmember variability...
Topics: Statistics, Physics, Data Analysis, Statistics and Probability, Methodology
Source: http://arxiv.org/abs/1502.01260
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Xuzhen Zhu; Hui Tian; Zheng Hu; Ping Zhang; Tao Zhou
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The explosive growth of information challenges people's capability in finding out items fitting to their own interests. Recommender systems provide an efficient solution by automatically push possibly relevant items to users according to their past preferences. Recommendation algorithms usually embody the causality from what having been collected to what should be recommended. In this article, we argue that in many cases, a user's interests are stable, and thus the previous and future...
Topics: Information Retrieval, Computing Research Repository, Physics, Data Analysis, Statistics and...
Source: http://arxiv.org/abs/1501.03577
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Yazan N. Billeh; Michael T. Schaub; Costas A. Anastassiou; Mauricio Barahona; Christof Koch
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Background: Current neuronal monitoring techniques, such as calcium imaging and multielectrode arrays, enable recordings of spiking activity from hundreds of neurons simultaneously. Of primary importance in systems neuroscience is the identification of cell assemblies: groups of neurons that cooperate in some form within the recorded population. New Method: We introduce a simple, integrated framework for the detection of cellassemblies from spiking data without a priori assumptions about the...
Topics: Physics, Data Analysis, Statistics and Probability, Quantitative Biology, Neurons and Cognition
Source: http://arxiv.org/abs/1411.2103
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Marco Cianciaruso; Thomas R. Bromley; Wojciech Roga; Rosario Lo Franco; Gerardo Adesso
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Quantum correlations in a composite system can be measured by resorting to a geometric approach, according to which the distance from the state of the system to a suitable set of classically correlated states is considered. Here we show that all distance functions, which respect natural assumptions of invariance under transposition, convexity, and contractivity under quantum channels, give rise to geometric quantifiers of quantum correlations which exhibit the peculiar freezing phenomenon,...
Topics: Quantum Physics, Data Analysis, Statistics and Probability, Physics, Statistical Mechanics,...
Source: http://arxiv.org/abs/1411.2978
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Araik Tamazian; Josef Ludescher; Armin Bunde
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We study the distribution $P(x;\alpha,L)$ of the relative trend $x$ in longterm correlated records of length $L$ that are characterized by a Hurstexponent $\alpha$ between 0.5 and 1.5 obtained by DFA2. The relative trend $x$ is the ratio between the strength of the trend $\Delta$ in the record measured by linear regression, and the standard deviation $\sigma$ around the regression line. We consider $L$ between 400 and 2200, which is the typical length scale of monthly local and annual...
Topics: Physics, Data Analysis, Statistics and Probability, Atmospheric and Oceanic Physics
Source: http://arxiv.org/abs/1411.3903
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Justin B. Kinney
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The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such approaches. Both have origins in statistical physics, but the relationship between them has remained unclear. Here I unify these two methods by showing that every maximum entropy...
Topics: Physics, Data Analysis, Statistics and Probability, Quantitative Biology, Statistics, Quantitative...
Source: http://arxiv.org/abs/1411.5371
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Aleksei Lokhov; Fyodor Tkachov
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The method of quasioptimal weights is applied to constructing (quasi)optimal criteria for various anomalous contributions in experimental spectra. Anomalies in the spectra could indicate physics beyond the Standard Model (additional interactions and neutrino flavours, Lorenz violation etc.). In particular the cumulative tritium $\beta$decay spectrum (for instance, in Troitsk$\nu$mass, Mainz Neutrino Mass and KATRIN experiments) is analysed using the derived special criteria. Using the...
Topics: Physics, Data Analysis, Statistics and Probability
Source: http://arxiv.org/abs/1411.6245
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Luca M. Ghiringhelli; Jan Vybiral; Sergey V. Levchenko; Claudia Draxl; Matthias Scheffler
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Statistical learning of materials properties or functions so far starts with a largely silent, nonchallenged step: the choice of the set of descriptive parameters (termed descriptor). However, when the scientific connection between the descriptor and the actuating mechanisms is unclear, causality of the learned descriptorproperty relation is uncertain. Thus, trustful prediction of new promising materials, identification of anomalies, and scientific advancement are doubtful. We analyse this...
Topics: Physics, Data Analysis, Statistics and Probability
Source: http://arxiv.org/abs/1411.7437
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Ruokuang Lin; Qianli D. Y. Ma; Chunhua Bian
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Human language, as a typical complex system, its organization and evolution is an attractive topic for both physical and cultural researchers. In this paper, we present the first exhaustive analysis of the text organization of human speech. Two important results are that: (i) the construction and organization of spoken language can be characterized as Zipf's law and Heaps' law, as observed in written texts; (ii) word frequency vs. rank distribution and the growth of distinct words with the...
Topics: Physics, Data Analysis, Statistics and Probability, Computing Research Repository, Computation and...
Source: http://arxiv.org/abs/1412.4846
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Stanisław H. Nowak; Aniouar Bjeoumikhov; Johannes von Borany; Josef Buchriegler; Frans Munnik; Marko Petric; Martin Radtke; Axel D. Renno; Uwe Reinholz; Oliver Scharf; Reiner Wedell
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The color Xray camera SLcam(R) is a fullfield, single photon detector providing scanning free, energy and spatially resolved Xray imaging. Spatial resolution is achieved with the use of polycapillary optics guiding Xray photons from small regions on a sample to distinct energy dispersive pixels on a CCD. Applying subpixel resolution, signals from individual capillary channels can be distinguished. Accordingly the SLcam(R) spatial resolution can be released from pixel size being confined...
Topics: Physics, Instrumentation and Methods for Astrophysics, Instrumentation and Detectors, Astrophysics,...
Source: http://arxiv.org/abs/1501.06825
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Konstantin Zuev; Marian Boguna; Ginestra Bianconi; Dmitri Krioukov
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All real networks are different, but many have some structural properties in common. There seems to be no consensus on what the most common properties are, but scalefree degree distributions, strong clustering, and community structure are frequently mentioned without question. Surprisingly, there exists no simple generative mechanism explaining all the three properties at once in growing networks. Here we show how latent network geometry coupled with preferential attachment of nodes to this...
Topics: Social and Information Networks, Applications, Physics and Society, Statistics, Physics, Computing...
Source: http://arxiv.org/abs/1501.06835
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We propose a new method to estimate the photometric redshift of galaxies by using the full galaxy image in each measured band. This method draws from the latest techniques and advances in machine learning, in particular Deep Neural Networks. We pass the entire multiband galaxy image into the machine learning architecture to obtain a redshift estimate that is competitive with the best existing standard machine learning techniques. The standard techniques estimate redshifts using postprocessed...
Topics: Data Analysis, Statistics and Probability, Cosmology and Nongalactic Astrophysics, Instrumentation...
Source: http://arxiv.org/abs/1504.07255
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H. V. Ribeiro; L. S. Costa; L. G. A. Alves; P. A. Santoro; S. Picoli; E. K. Lenzi; R. S. Mendes
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We report on an extensive characterization of the cracking noise produced by charcoal samples when dampened with ethanol. We argue that the evaporation of ethanol causes transient and irregularly distributed internal stresses that promote the fragmentation of the samples and mimic some situations found in mining processes. The results show that, in general, the most fundamental seismic laws ruling earthquakes (GutenbergRichter law, unified scaling law for the recurrence times, Omori's law,...
Topics: Geophysics, Materials Science, Data Analysis, Statistics and Probability, Statistical Mechanics,...
Source: http://arxiv.org/abs/1506.04981
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Lukasz Kusmierz; Ewa GudowskaNowak
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We consider diffusive motion of a particle performing a random walk with L\'evy distributed jump lengths and subject to resetting mechanism bringing the walker to an initial position at uniformly distributed times. In the limit of infinite number of steps and for long times, the process converges to a superdiffusive motion with replenishment. We derive formula for a mean first arrival time (MFAT) to a predefined target position reached by a meandering particle and analyze efficiency of the...
Topics: Mathematical Physics, Data Analysis, Statistics and Probability, Statistical Mechanics, Physics,...
Source: http://arxiv.org/abs/1508.03184
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Martin Gueuning; JeanCharles Delvenne; Renaud Lambiotte
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We study spreading on networks where the contact dynamics between the nodes is governed by a random process and where the intercontact time distribution may differ from the exponential. We consider a process of imperfect spreading, where transmission is successful with a determined probability at each contact. We first derive an expression for the intersuccess time distribution, determining the speed of the propagation, and then focus on a problem related to epidemic spreading, by estimating...
Topics: Social and Information Networks, Physics and Society, Computing Research Repository, Data Analysis,...
Source: http://arxiv.org/abs/1508.04006
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Christopher Granade; Joshua Combes; D. G. Cory
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In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. Stateoftheart Bayesian tomography solutions suffer from three problems: numerical intractability, a lack of informative prior distributions, and an inability to track timedependent processes. Here, we address all three problems. First, we use modern statistical methods, as pioneered by Husz\'ar and Houlsby and by Ferrie, to make Bayesian tomography...
Topics: Quantum Physics, Data Analysis, Statistics and Probability, Applications, Statistics, Physics
Source: http://arxiv.org/abs/1509.03770
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Z. Koohi Lai; S. Vasheghani Farahani; S. M. S. Movahed; G. R. Jafari
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The aim here is to study the concept of pairing multifractality between time series possessing nonGaussian distributions. The increasing number of rare events creates "criticality". We show how the pairing between two series is affected by rare events, which we call "coupled criticality". A method is proposed for studying the coupled criticality born out of the interaction between two series, using the bivariate multifractal random walk (BiMRW). This method allows studying...
Topics: Statistical Finance, Statistical Mechanics, Statistics, Condensed Matter, Quantitative Finance,...
Source: http://arxiv.org/abs/1510.03040
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Bing Wang; Xiuqing Wu; Changzhao Chen; Mengjun Hu; Xuanyan Cao
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The average velocity of selfpropelled particles in a twodimensional potential with colored noise is investigated. The current reversal phenomenon appear with changing x direction colored noise intensity. There exist optimal values of the parameters at which the average velocity takes its maximal value. The y direction noise and the selfpropelled angle noise have great effects on the x direction average velocity, but they can not induce x direction particles transport phenomenon themselves.
Topics: Statistical Mechanics, Condensed Matter, Physics, Nonlinear Sciences, Adaptation and...
Source: http://arxiv.org/abs/1512.06181
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Siddharth Maddali; Shlomo Ta'asan; Robert M. Suter
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The main focus of this paper is a nonparametric filtering technique for the estimation of interface geometry in bulk materials obtainable from modern imaging measurements. The filtering methodology relies on an assumed hierarchy of topological features present in a typical interface network, such as foam interfaces and grain boundary networks in polycrystalline materials. Each type of topological feature is treated in order of rank in the hierarchy, with the lowerlevel feature being filtered...
Topics: Data Analysis, Statistics and Probability, Materials Science, Condensed Matter, Physics
Source: http://arxiv.org/abs/1601.04699
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Xiaochao Wu; Weihua Deng; Eli Barkai
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Functionals of Brownian/nonBrownian motions have diverse applications and attracted a lot of interest of scientists. This paper focuses on deriving the forward and backward fractional FeynmanKac equations describing the distribution of the functionals of the space and time tempered anomalous diffusion, belonging to the continuous time random walk class. Several examples of the functionals are explicitly treated, including the occupation time in halfspace, the first passage time, the maximal...
Topics: Data Analysis, Statistics and Probability, Statistical Mechanics, Condensed Matter, Physics
Source: http://arxiv.org/abs/1602.00071
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Andrey Y. Lokhov; Nathan Lemons; Thomas C. McAndrew; Aric Hagberg; Scott Backhaus
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Cyberphysical systems are critical infrastructures that are crucial both to the reliable delivery of resources such as energy, and to the stable functioning of automatic and control architectures. These systems are composed of interdependent physical, control and communications networks described by disparate mathematical models creating scientific challenges that go well beyond the modeling and analysis of the individual networks. A key challenge in cyberphysical defense is a fast online...
Topics: Social and Information Networks, Data Analysis, Statistics and Probability, Applications, Physics,...
Source: http://arxiv.org/abs/1602.06604
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Enrico Guarnera; Eric VandenEijnden
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A method is proposed to identify target states that optimize a metastability index amongst a set of trial states and use these target states as milestones (or core sets) to build Markov State Models (MSMs). If the optimized metastability index is small, this automatically guarantees the accuracy of the MSM, in the sense that the transitions between the target milestones is indeed approximately Markovian. The method is simple to implement and use, it does not require that the dynamics on the...
Topics: Data Analysis, Statistics and Probability, Statistical Mechanics, Condensed Matter, Physics,...
Source: http://arxiv.org/abs/1605.01150
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Giona Casiraghi; Vahan Nanumyan; Ingo Scholtes; Frank Schweitzer
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Statistical ensembles of networks, i.e., probability spaces of all networks that are consistent with given aggregate statistics, have become instrumental in the analysis of complex networks. Their numerical and analytical study provides the foundation for the inference of topological patterns, the definition of networkanalytic measures, as well as for model selection and statistical hypothesis testing. Contributing to the foundation of these data analysis techniques, in this Letter we...
Topics: Physics and Society, Data Analysis, Statistics and Probability, Physics, Mathematics,...
Source: http://arxiv.org/abs/1607.02441
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Simon Christ; Bernard Sonnenschein; Lutz SchimanskyGeier
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We study complex networks of stochastic twostate units. Our aim is to model discrete stochastic excitable dynamics with a rest and an excited state. Both states are assumed to possess different waiting time distributions. The rest state is treated as an activation process with an exponentially distributed life time, whereas the latter in the excited state shall have a constant mean which may originate from any distribution. The activation rate of any single unit is determined by its neighbors...
Topics: Data Analysis, Statistics and Probability, Physics, Physics and Society
Source: http://arxiv.org/abs/1608.03120
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Afef Cherni; Emilie Chouzenoux; MarcAndré Delsuc
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NMR is a tool of choice for the measure of diffusion coefficients of species in solution. The DOSY experiment, a 2D implementation of this measure, has proven to be particularly useful for the study of complex mixtures, molecular interactions, polymers, etc. However, DOSY data analysis requires to resort to inverse Laplace transform, in particular for polydisperse samples. This is a known difficult numerical task, for which we present here a novel approach. A new algorithm based on a splitting...
Topics: Data Analysis, Statistics and Probability, Physics
Source: http://arxiv.org/abs/1608.07055
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Michael Bianco; Peter Gerstoft
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To provide constraints on their inversion, ocean sound speed profiles (SSPs) often are modeled using empirical orthogonal functions (EOFs). However, this regularization, which uses the leading order EOFs with a minimumenergy constraint on their coefficients, often yields low resolution SSP estimates. In this paper, it is shown that dictionary learning, a form of unsupervised machine learning, can improve SSP resolution by generating a dictionary of shape functions for sparse processing (e.g....
Topics: Atmospheric and Oceanic Physics, Data Analysis, Statistics and Probability, Physics, Mathematics,...
Source: http://arxiv.org/abs/1609.04840
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A new method for optimal sensor placement based on variable importance of machine learned models is proposed. With its simplicity, adaptivity, and low computational cost, the method offers many advantages over existing approaches. The new method is implemented on the flow over an airfoil equipped with a Coanda actuator. The analysis is based on flow field data obtained from 2D unsteady Reynolds averaged NavierStokes (URANS) simulations with different actuation conditions. The optimal sensor...
Topics: Data Analysis, Statistics and Probability, Fluid Dynamics, Physics
Source: http://arxiv.org/abs/1609.07885
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Sudipta Bera; Shuvojit Paul; Rajesh Singh; Dipanjan Ghosh; Avijit Kundu; Ayan Banerjee; R. Adhikari
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Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the OrnsteinUhlenbeck process and can be observed directly in experiment. Here we present Bayesian methods for inferring the parameters of this process, the trap stiffness and the particle diffusion coefficient, that use exact likelihoods and sufficient statistics...
Topics: Data Analysis, Statistics and Probability, Soft Condensed Matter, Condensed Matter, Physics
Source: http://arxiv.org/abs/1610.00315
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Wilhelm Braun; Rüdiger Thul
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Firstpassage time problems are ubiquitous across many fields of study including transport processes in semiconductors and biological synapses, evolutionary game theory and percolation. Despite their prominence, firstpassage time calculations have proven to be particularly challenging. Analytical results to date have often been obtained under strong conditions, leaving most of the exploration of firstpassage time problems to direct numerical computations. Here we present an analytical...
Topics: Physics, Quantitative Biology, Neurons and Cognition, Data Analysis, Statistics and Probability
Source: http://arxiv.org/abs/1701.00648
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Ashif Sikandar Iquebal; Satish Bukkapatnam; Arun Srinivasa
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We present an approach for realtime change detection in the transient phases of complex dynamical systems based on tracking the local phase and amplitude synchronization among the components of a univariate time series signal derived via Intrinsic Time scale Decomposition (ITD)a nonlinear, nonparametric analysis method. We investigate the properties of ITD components and show that the expected level of phase synchronization at a given change point may be enhanced by more than 4 folds when...
Topics: Physics, Data Analysis, Statistics and Probability
Source: http://arxiv.org/abs/1701.00610
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Jie Sun; Erik Bollt
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Optical flow refers to the visual motion observed between two consecutive images. Since the degree of freedom is typically much larger than the constraints imposed by the image observations, the straightforward formulation of optical flow inference is an illposed problem. By setting some type of additional "regularity" constraints, classical approaches formulate a wellposed optical flow inference problem in the form of a parameterized set of variational equations. In this work we...
Topics: Computer Vision and Pattern Recognition, Machine Learning, Data Analysis, Statistics and...
Source: http://arxiv.org/abs/1611.01230
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Silas G. T. Laycock
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In time domain astronomy, recurrent transients present a special problem: how to infer total populations from limited observations. Monitoring observations may give a biassed view of the underlying population due to limitations on observing time, visibility and instrumental sensitivity. A similar problem exists in the life sciences, where animal populations (such as migratory birds) or disease prevalence, must be estimated from sparse and incomplete data. The class of methods termed...
Topics: Biological Physics, Physics, Data Analysis, Statistics and Probability, Astrophysics, High Energy...
Source: http://arxiv.org/abs/1701.03801
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Consider the problem of modeling hysteresis for finitestate random walks using higherorder Markov chains. This Letter introduces a Bayesian framework to determine, from data, the number of prior states of recent history upon which a trajectory is statistically dependent. The general recommendation is to use leaveoneout cross validation, using an easilycomputable formula that is provided in closed form. Importantly, Bayes factors using flat model priors are biased in favor of toocomplex a...
Topics: Physics, Quantitative Methods, Learning, Data Analysis, Statistics and Probability, Computing...
Source: http://arxiv.org/abs/1702.06221
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G. Inglese; R. Olmi; S. Priori
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Let $\Omega_\epsilon$ be a metallic plate whose top inaccessible surface has been damaged by some chemical or mechanical agent. We heat the opposite side and collect a sequence of temperature maps $u^\epsilon$. Here, we construct a formal explicit approximation of the damage $\epsilon\theta$ by solving a nonlinear inverse problem for the heat equation in three steps: (i) smoothing of temperature maps, (ii) domain derivative of the temperature, (iii) thin plate approximation of the model and...
Topics: Physics, Data Analysis, Statistics and Probability, Instrumentation and Detectors
Source: http://arxiv.org/abs/1703.04551
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Vladimir Klinshov; Serhiy Yanchuk; Artur Stephan; Vladimir Nekorkin
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Phase response curve (PRC) is an extremely useful tool for studying the response of oscillatory systems, e.g. neurons, to sparse or weak stimulation. Here we develop a framework for studying the response to a series of pulses which are frequent or/and strong so that the standard PRC fails. We show that in this case, the phase shift caused by each pulse depends on the history of several previous pulses. We call the corresponding function which measures this shift the phase response function...
Topics: Physics, Data Analysis, Statistics and Probability, Chaotic Dynamics, Nonlinear Sciences,...
Source: http://arxiv.org/abs/1703.05611
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Luca Perotti; Daniel Vrinceanu; Daniel Bessis
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We present a new method to locate the starting points in time of an arbitrary number of (damped) delayed signals. For a finite data sequence, the method permits to first locate the starting point of the component with the longest delay, and then by iteration all the preceding ones. Numerical examples are given and noise sensitivity is tested for weak noise.
Topics: Physics, Data Analysis, Statistics and Probability
Source: http://arxiv.org/abs/1703.07001
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Ardeshir Mohammad Ebtehaj; Efi FoufoulaGeorgiou; Gilad Lerman; Rafael Luis Bras
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We demonstrate that the global fields of temperature, humidity and geopotential heights admit a nearly sparse representation in the wavelet domain, offering a viable path forward to explore new paradigms of sparsitypromoting data assimilation and compressive recovery of land surfaceatmospheric states from space. We illustrate this idea using retrieval products of the Atmospheric Infrared Sounder (AIRS) and Advanced Microwave Sounding Unit (AMSU) on board the Aqua satellite. The results reveal...
Topics: Physics, Data Analysis, Statistics and Probability
Source: http://arxiv.org/abs/1409.5068
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S. S. Melnik; O. V. Usatenko
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The goal of this paper is to develop an estimate for the entropy of random longrange correlated symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the highorder additive stationary ergodic Markov chain. Supposing that the correlations between random elements of the chain are weak we express the differential entropy of the sequence by means of the symbolic pair correlation function. We also examine an algorithm for estimating the differential entropy...
Topics: Physics, Data Analysis, Statistics and Probability, Statistical Mechanics, Disordered Systems and...
Source: http://arxiv.org/abs/1412.3692
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We introduce NIFTY, "Numerical Information Field Theory", a software package for the development of Bayesian signal inference algorithms that operate independently from any underlying spatial grid and its resolution. A large number of Bayesian and Maximum Entropy methods for 1D signal reconstruction, 2D imaging, as well as 3D tomography, appear formally similar, but one often finds individualized implementations that are neither flexible nor easily transferable. Signal inference in...
Topics: Physics, Data Analysis, Statistics and Probability, Astrophysics, Mathematics, Computing Research...
Source: http://arxiv.org/abs/1412.7160
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Gunnar Claussen; Alexander K. Hartmann; Satya N. Majumdar
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We study the convex hull of the set of points visited by a twodimensional random walker of T discrete time steps. Two natural observables that characterize the convex hull in two dimensions are its perimeter L and area A. While the mean perimeter and the mean area have been studied before, analytically and numerically, and exact results are known for large T (Brownian motion limit), little is known about the full distributions P(A) and P(L). In this paper, we provide numerical results for...
Topics: Statistical Mechanics, Condensed Matter, Data Analysis, Statistics and Probability, Physics
Source: http://arxiv.org/abs/1501.01041
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Ladislav Kristoufek
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In this note, we investigate possible relationships between the bivariate Hurst exponent $H_{xy}$ and an average of the separate Hurst exponents $\frac{1}{2}(H_x+H_y)$. We show that two cases are well theoretically founded. These are the cases when $H_{xy}=\frac{1}{2}(H_x+H_y)$ and $H_{xy} \frac{1}{2}(H_x+H_y)$ is not possible regardless of stationarity issues. Further discussion of the implications is provided as well together with a note on the finite sample effect.
Topics: Data Analysis, Statistics and Probability, Physics
Source: http://arxiv.org/abs/1501.02947
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Mark K. Transtrum; Benjamin Machta; Kevin Brown; Bryan C. Daniels; Christopher R. Myers; James P. Sethna
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Large scale models of physical phenomena demand the development of new statistical and computational tools in order to be effective. Many such models are `sloppy', i.e., exhibit behavior controlled by a relatively small number of parameter combinations. We review an information theoretic framework for analyzing sloppy models. This formalism is based on the Fisher Information Matrix, which we interpret as a Riemannian metric on a parameterized space of models. Distance in this space is a measure...
Topics: Statistical Mechanics, Quantitative Biology, Molecular Networks, Data Analysis, Statistics and...
Source: http://arxiv.org/abs/1501.07668
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Nico Reinke; André Fuchs; Wided Medjroubi; Pedro G. Lind; Matthias Wächter; Joachim Peinke
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We describe a simple stochastic method, socalled Langevin approach, which enables one to extract evolution equations of stochastic variables from a set of measurements. Our method is parameterfree and it is based on the nonlinear Langevin equation. Moreover, it can be applied not only to processes in time, but also to processes in scale, given that the data available shows ergodicity. This chapter introduces the mathematical foundations of the Langevin approach and describes how to implement...
Topics: Physics, Data Analysis, Statistics and Probability
Source: http://arxiv.org/abs/1502.05253