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Register a new userStatistical variances in traffic data
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Added by
Milan Krbalek Ph.D.
Publication date
2006
fields
Physics
and research's language is
English
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We perform statistical analysis of the single-vehicle data measured on the Dutch freeway A9 and discussed in Ref. [2]. Using tools originating from the Random Matrix Theory we show that the significant changes in the statistics of the traffic data can be explained applying equilibrium statistical physics of interacting particles.
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We present a Bayesian dynamical inference method for characterizing cardiorespiratory (CR) dynamics in humans by inverse modelling from blood pressure time-series data. This new method is applicable to a broad range of stochastic dynamical models, and can be implemented without severe computational demands. A simple nonlinear dynamical model is found that describes a measured blood pressure time-series in the primary frequency band of the CR dynamics. The accuracy of the method is investigated using surrogate data with parameters close to the parameters inferred in the experiment. The connection of the inferred model to a well-known beat-to-beat model of the baroreflex is discussed.
In statistical data assimilation (SDA) and supervised machine learning (ML), we wish to transfer information from observations to a model of the processes underlying those observations. For SDA, the model consists of a set of differential equations that describe the dynamics of a physical system. For ML, the model is usually constructed using other strategies. In this paper, we develop a systematic formulation based on Monte Carlo sampling to achieve such information transfer. Following the derivation of an appropriate target distribution, we present the formulation based on the standard Metropolis-Hasting (MH) procedure and the Hamiltonian Monte Carlo (HMC) method for performing the high dimensional integrals that appear. To the extensive literature on MH and HMC, we add (1) an annealing method using a hyperparameter that governs the precision of the model to identify and explore the highest probability regions of phase space dominating those integrals, and (2) a strategy for initializing the state space search. The efficacy of the proposed formulation is demonstrated using a nonlinear dynamical model with chaotic solutions widely used in geophysics.
ROOT is an object-oriented C++ framework conceived in the high-energy physics (HEP) community, designed for storing and analyzing petabytes of data in an efficient way. Any instance of a C++ class can be stored into a ROOT file in a machine-independent compressed binary format. In ROOT the TTree object container is optimized for statistical data analysis over very large data sets by using vertical data storage techniques. These containers can span a large number of files on local disks, the web, or a number of different shared file systems. In order to analyze this data, the user can chose out of a wide set of mathematical and statistical functions, including linear algebra classes, numerical algorithms such as integration and minimization, and various methods for performing regression analysis (fitting). In particular, ROOT offers packages for complex data modeling and fitting, as well as multivariate classification based on machine learning techniques. A central piece in these analysis tools are the histogram classes which provide binning of one- and multi-dimensional data. Results can be saved in high-quality graphical formats like Postscript and PDF or in bitmap formats like JPG or GIF. The result can also be stored into ROOT macros that allow a full recreation and rework of the graphics. Users typically create their analysis macros step by step, making use of the interactive C++ interpreter CINT, while running over small data samples. Once the development is finished, they can run these macros at full compiled speed over large data sets, using on-the-fly compilation, or by creating a stand-alone batch program. Finally, if processing farms are available, the user can reduce the execution time of intrinsically parallel tasks - e.g. data mining in HEP - by using PROOF, which will take care of optimally distributing the work over the available resources in a transparent way.
Modern analysis of high energy physics (HEP) data needs advanced statistical tools to separate signal from background. A C++ package has been implemented to provide such tools for the HEP community. The package includes linear and quadratic discriminant analysis, decision trees, bump hunting (PRIM), boosting (AdaBoost), bagging and random forest algorithms, and interfaces to the standard backpropagation neural net and radial basis function neural net implemented in the Stuttgart Neural Network Simulator. Supplemental tools such as bootstrap, estimation of data moments, and a test of zero correlation between two variables with a joint elliptical distribution are also provided. The package offers a convenient set of tools for imposing requirements on input data and displaying output. Integrated in the BaBar computing environment, the package maintains a minimal set of external dependencies and therefore can be easily adapted to any other environment. It has been tested on many idealistic and realistic examples.
Self-similarity in the network traffic has been studied from several aspects: both at the user side and at the network side there are many sources of the long range dependence. Recently some dynamical origins are also identified: the TCP adaptive congestion avoidance algorithm itself can produce chaotic and long range dependent throughput behavior, if the loss rate is very high. In this paper we show that there is a close connection between the static and dynamic origins of self-similarity: parallel TCPs can generate the self-similarity themselves, they can introduce heavily fluctuations into the background traffic and produce high effective loss rate causing a long range dependent TCP flow, however, the dropped packet ratio is low.
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