scholarly journals Relative Entropies and Jensen Divergences in the Classical Limit

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
A. M. Kowalski ◽  
A. Plastino
Keyword(s):  
Time Series ◽  
Classical Limit ◽  
Probability Distributions ◽  
Numerical Techniques ◽  
The Road ◽  
Semiclassical Model ◽  
Probability Spaces

Metrics and distances in probability spaces have shown to be useful tools for physical purposes. Here we use this idea, with emphasis on Jensen Divergences and relative entropies, to investigate features of the road towards the classical limit. A well-known semiclassical model is used and recourse is made to numerical techniques, via the well-known Bandt and Pompe methodology, to extract probability distributions from the pertinent time-series associated with dynamical data.

scholarly journals Road Short-Term Travel Time Prediction Method Based on Flow Spatial Distribution and the Relations

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Mingjun Deng ◽  
Shiru Qu
Keyword(s):  
Time Series ◽  
Spatial Distribution ◽  
Travel Time ◽  
Nonparametric Regression ◽  
Nearest Neighbor ◽  
Nearest Neighbor Search ◽  
Short Term ◽  
Combination Model ◽  
The Road ◽  
Neighbor Search

There are many short-term road travel time forecasting studies based on time series, but indeed, road travel time not only relies on the historical travel time series, but also depends on the road and its adjacent sections history flow. However, few studies have considered that. This paper is based on the correlation of flow spatial distribution and the road travel time series, applying nearest neighbor and nonparametric regression method to build a forecasting model. In aspect of spatial nearest neighbor search, three different space distances are defined. In addition, two forecasting functions are introduced: one combines the forecasting value by mean weight and the other uses the reciprocal of nearest neighbors distance as combined weight. Three different distances are applied in nearest neighbor search, which apply to the two forecasting functions. For travel time series, the nearest neighbor and nonparametric regression are applied too. Then minimizing forecast error variance is utilized as an objective to establish the combination model. The empirical results show that the combination model can improve the forecast performance obviously. Besides, the experimental results of the evaluation for the computational complexity show that the proposed method can satisfy the real-time requirement.

scholarly journals Breakdown coefficients and scaling properties of rain fields

1998 ◽  
Vol 5 (2) ◽  
pp. 93-104 ◽  
Author(s):  
D. Harris ◽  
M. Menabde ◽  
A. Seed ◽  
G. Austin
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Power Law ◽  
Scale Parameter ◽  
Probability Distributions ◽  
Scaling Analysis ◽  
Scaling Properties ◽  
Power Law Exponent ◽  
Scale Similarity ◽  
Parameter Estimation Techniques

Abstract. The theory of scale similarity and breakdown coefficients is applied here to intermittent rainfall data consisting of time series and spatial rain fields. The probability distributions (pdf) of the logarithm of the breakdown coefficients are the principal descriptor used. Rain fields are distinguished as being either multiscaling or multiaffine depending on whether the pdfs of breakdown coefficients are scale similar or scale dependent, respectively. Parameter  estimation techniques are developed which are applicable to both multiscaling and multiaffine fields. The scale parameter (width), σ, of the pdfs of the log-breakdown coefficients is a measure of the intermittency of a field. For multiaffine fields, this scale parameter is found to increase with scale in a power-law fashion consistent with a bounded-cascade picture of rainfall modelling. The resulting power-law exponent, H, is indicative of the smoothness of the field. Some details of breakdown coefficient analysis are addressed and a theoretical link between this analysis and moment scaling analysis is also presented. Breakdown coefficient properties of cascades are also investigated in the context of parameter estimation for modelling purposes.

On the Probability Distribution of Mooring Line Tensions in a Directional Environment

2011 ◽  
Author(s):  
Jan Mathisen ◽  
Siril Okkenhaug ◽  
Kjell Larsen
Keyword(s):  
Time Series ◽  
Probability Distributions ◽  
Extreme Value Distribution ◽  
Line Tension ◽  
Extreme Value ◽  
Mooring Line ◽  
Large Set ◽  
Short Term ◽  
Reliability Method ◽  
Line Design

A joint probabilistic model of the metocean environment is assembled, taking account of wind, wave and current and their respective heading angles. Mooring line tensions are computed in the time domain, for a large set of short-term stationary conditions, intended to span the domain of metocean conditions that contribute significantly to the probabilities of high tensions. Weibull probability distributions are fitted to local tension maxima extracted from each time series. Long time series of 30 hours duration are used to reduce statistical uncertainty. Short-term, Gumbel extreme value distributions of line tension are derived from the maxima distributions. A response surface is fitted to the distribution parameters for line tension, to allow interpolation between the metocean conditions that have been explicitly analysed. A second order reliability method is applied to integrate the short-term tension distributions over the probability of the metocean conditions and obtain the annual extreme value distribution of line tension. Results are given for the most heavily loaded mooring line in two mooring systems: a mobile drilling unit and a production platform. The effects of different assumptions concerning the distribution of wave heading angles in simplified analysis for mooring line design are quantified by comparison with the detailed calculations.

scholarly journals Hydrological model calibration for derived flood frequency analysis using stochastic rainfall and probability distributions of peak flows

2014 ◽  
Vol 18 (1) ◽  
pp. 353-365 ◽  
Author(s):  
U. Haberlandt ◽  
I. Radtke
Keyword(s):  
Time Series ◽  
Frequency Analysis ◽  
Model Calibration ◽  
Hydrological Model ◽  
Probability Distributions ◽  
Flood Frequency ◽  
Rainfall Data ◽  
Flood Frequency Analysis ◽  
Peak Flows ◽  
Hourly Rainfall

Abstract. Derived flood frequency analysis allows the estimation of design floods with hydrological modeling for poorly observed basins considering change and taking into account flood protection measures. There are several possible choices regarding precipitation input, discharge output and consequently the calibration of the model. The objective of this study is to compare different calibration strategies for a hydrological model considering various types of rainfall input and runoff output data sets and to propose the most suitable approach. Event based and continuous, observed hourly rainfall data as well as disaggregated daily rainfall and stochastically generated hourly rainfall data are used as input for the model. As output, short hourly and longer daily continuous flow time series as well as probability distributions of annual maximum peak flow series are employed. The performance of the strategies is evaluated using the obtained different model parameter sets for continuous simulation of discharge in an independent validation period and by comparing the model derived flood frequency distributions with the observed one. The investigations are carried out for three mesoscale catchments in northern Germany with the hydrological model HEC-HMS (Hydrologic Engineering Center's Hydrologic Modeling System). The results show that (I) the same type of precipitation input data should be used for calibration and application of the hydrological model, (II) a model calibrated using a small sample of extreme values works quite well for the simulation of continuous time series with moderate length but not vice versa, and (III) the best performance with small uncertainty is obtained when stochastic precipitation data and the observed probability distribution of peak flows are used for model calibration. This outcome suggests to calibrate a hydrological model directly on probability distributions of observed peak flows using stochastic rainfall as input if its purpose is the application for derived flood frequency analysis.

scholarly journals Classical Chaos Described by a Density Matrix

Physics ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 739-746
Author(s):  
Andres Mauricio Kowalski ◽  
Angelo Plastino ◽  
Gaspar Gonzalez
Keyword(s):  
Density Matrix ◽  
Pure State ◽  
Classical Limit ◽  
Degrees Of Freedom ◽  
Temporal Evolution ◽  
Entropy Density ◽  
State Density ◽  
Unexpected Result ◽  
Semiclassical Model ◽  
Classical Chaos

In this paper, a reference to the semiclassical model, in which quantum degrees of freedom interact with classical ones, is considered. The classical limit of a maximum-entropy density matrix that describes the temporal evolution of such a system is analyzed. Here, it is analytically shown that, in the classical limit, it is possible to reproduce classical results. An example is classical chaos. This is done by means a pure-state density matrix, a rather unexpected result. It is shown that this is possible only if the quantum part of the system is in a special class of states.

scholarly journals Landscape-scale water balance monitoring with an iGrav superconducting gravimeter in a field enclosure

2017 ◽  
Vol 21 (6) ◽  
pp. 3167-3182 ◽  
Author(s):  
Andreas Güntner ◽  
Marvin Reich ◽  
Michal Mikolaj ◽  
Benjamin Creutzfeldt ◽  
Stephan Schroeder ◽  
...  
Keyword(s):  
Time Series ◽  
Water Balance ◽  
Water Storage ◽  
Superconducting Gravimeter ◽  
Landscape Scale ◽  
Temperate Climate ◽  
Water Balance Components ◽  
Climate Conditions ◽  
The Road ◽  
Field Deployment

Abstract. In spite of the fundamental role of the landscape water balance for the Earth's water and energy cycles, monitoring the water balance and its components beyond the point scale is notoriously difficult due to the multitude of flow and storage processes and their spatial heterogeneity. Here, we present the first field deployment of an iGrav superconducting gravimeter (SG) in a minimized enclosure for long-term integrative monitoring of water storage changes. Results of the field SG on a grassland site under wet–temperate climate conditions were compared to data provided by a nearby SG located in the controlled environment of an observatory building. The field system proves to provide gravity time series that are similarly precise as those of the observatory SG. At the same time, the field SG is more sensitive to hydrological variations than the observatory SG. We demonstrate that the gravity variations observed by the field setup are almost independent of the depth below the terrain surface where water storage changes occur (contrary to SGs in buildings), and thus the field SG system directly observes the total water storage change, i.e., the water balance, in its surroundings in an integrative way. We provide a framework to single out the water balance components actual evapotranspiration and lateral subsurface discharge from the gravity time series on annual to daily timescales. With about 99 and 85 % of the gravity signal due to local water storage changes originating within a radius of 4000 and 200 m around the instrument, respectively, this setup paves the road towards gravimetry as a continuous hydrological field-monitoring technique at the landscape scale.

scholarly journals Efficient Approximate Techniques for Integrating Stochastic Differential Equations

2006 ◽  
Vol 134 (10) ◽  
pp. 3006-3014 ◽  
Author(s):  
James A. Hansen ◽  
Cecile Penland
Keyword(s):  
Time Series ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Deterministic Model ◽  
Probability Distributions ◽  
Approximate Solutions ◽  
Integration Scheme ◽  
Time Step ◽  
Integration Schemes ◽  
Runge Kutta

Abstract The delicate (and computationally expensive) nature of stochastic numerical modeling naturally leads one to look for efficient and/or convenient methods for integrating stochastic differential equations. Concomitantly, one may wish to sensibly add stochastic terms to an existing deterministic model without having to rewrite that model. In this note, two possibilities in the context of the fourth-order Runge–Kutta (RK4) integration scheme are examined. The first approach entails a hybrid of deterministic and stochastic integration schemes. In these examples, the hybrid RK4 generates time series with the correct climatological probability distributions. However, it is doubtful that the resulting time series are approximate solutions to the stochastic equations at every time step. The second approach uses the standard RK4 integration method modified by appropriately scaling stochastic terms. This is shown to be a special case of the general stochastic Runge–Kutta schemes considered by Ruemelin and has global convergence of order one. Thus, it gives excellent results for cases in which real noise with small but finite correlation time is approximated as white. This restriction on the type of problems to which the stochastic RK4 can be applied is strongly compensated by its computational efficiency.

Parameterization of multifractal cascade models based on their breakdown coefficients

2020 ◽  
Author(s):  
César Aguilar Flores ◽  
Alin Andrei Carsteanu
Keyword(s):  
Time Series ◽  
Probability Distribution ◽  
Rainfall Intensity ◽  
Probability Distributions ◽  
Asymptotic Properties ◽  
Distribution Functions ◽  
Marginal Probability ◽  
Probability Distribution Functions ◽  
Marginal Probability Distribution ◽  
Cascade Models

<p>Breakdown coefficients of multifractal cascades have been shown, in various contexts, to be ergodic in their (marginal) probability distribution functions, however the necessary connection between the cascading process (or a tracer thereof, such as rainfall) and the breakdown coefficients of the measure generated by the cascade, was missing. This work presents a method of parameterization of certain types of multiplicative cascades, using the breakdown coefficients of the measures they generate. The method is based on asymptotic properties of the probability distributions of the breakdown coefficients in “dressed” cascades, as compared with the respective distributions of the cascading weights. An application to rainfall intensity time series is presented.</p>

scholarly journals Gamma-Divergence. An Introduction to New Divergence Family

2020 ◽  
Author(s):  
Leonardo Riveaud ◽  
Mateos Diego ◽  
Pedro Walter Lamberti
Keyword(s):  
Time Series ◽  
Probability Distribution ◽  
Real Time ◽  
Probability Distributions ◽  
Convexity Property ◽  
Weighted Probability

Divergences have become a very useful tool for measuring similarity (or dissimilarity) between probability distributions. Depending on the field of application, a more appropriate measure may be necessary. In this paper we introduce a family of divergences called γ-Divergences. They are based on the convexity property of the functions that generate them. We demonstrate that these divergences verify all the usually required properties, and we extend them to weighted probability distribution. In addition, we define a generalised entropy closely related to the γ-Divergences. Finally, we apply our findings to the analysis of simulated and real time series.

scholarly journals FOURIER ANALYSIS OF THE TRAFFIC FLOW INTENSITY

2021 ◽  
pp. 46-59
Author(s):  
M.G. Boyarshinov ◽  
◽  
A.S. Vavilin ◽  
A.G. Shumkov ◽  
◽  
...  
Keyword(s):  
Time Series ◽  
Fourier Series ◽  
Traffic Flow ◽  
Harmonic Functions ◽  
Traffic Flows ◽  
The Road ◽  
Flow Intensity ◽  
Software And Hardware ◽  
On The Road ◽  
Amplitude Characteristics

The relevance of this work is determined by the need to find modern ways to process the information about traffic flows for regulating and controlling the movement of transport and pedestrians, to reduce congestion, road accidents, etc. The object of study is a part of road with heavy two-way traffic, equipped with a software and hardware complex that allows to measure the characteristics of the transport flow. The subject of the study is the daily intensity of the cars flow during the week, from Monday to Sunday. The purpose of this study is to analyze the amplitudes, frequencies, and periods of harmonic functions obtained by decomposing the time series of road traffic intensities to identify the main patterns of traffic flow formation. As a theoretical and methodological approach, the decomposition of the function of the traffic flow intensity in the Fourier series with respect to harmonic functions is used. The approach developed by the authors using the fast Fourier transform procedure made it possible to determine the amplitude-frequency characteristics of the time series under consideration, which is a scientific novelty of the analysis. It is proposed to use the «period-amplitude» characteristics as physically more meaningful instead of the «frequency-amplitude» dependencies traditionally used for the analysis. The processing of data obtained from software and hardware complexes allowed us to determine dependences of the car flow intensity on the road of the Perm city at different averaging intervals, to describe the features of the motor transport movement on the road under consideration. As a result of the study, the amplitude-frequency characteristics of time series are obtained. It is shown that the individual harmonics of the Fourier series expansion of the traffic flow intensity, which exhibits the properties of a random function, duplicate the periodicity of the global, local, and intermediate extremes of the original function and have similar periods. The practical significance consists in the use of the decomposition of the function of the traffic flow intensity in the Fourier series of harmonic functions for predicting traffic flows, controlling the operation of traffic lights, monitoring the operation of equipment, as well as in the reconstruction, design and construction of roads and road objects. The study will continue in the direction of obtaining, processing and determining the «period-amplitude» characteristics for time series of traffic flow intensity for other road networks.

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