scholarly journals A New Characterization of Rain and Clouds: Results from a Statistical Inversion of Count Data

2007 ◽  
Vol 64 (6) ◽  
pp. 2012-2028 ◽  
Author(s):  
A. R. Jameson
Keyword(s):  
Count Data ◽  
Drop Size ◽  
Mean Value ◽  
Probability Density Functions ◽  
Density Functions ◽  
Mean Values ◽  
Precise Meaning ◽  
Statistical Heterogeneity ◽  
Single Set

Most variables in meteorology are statistically heterogeneous. The statistics of data from several different locations, then, can be thought of as an amalgamation of information contained in several contributing probability density functions (PDFs) having different sets of parameters, different parametric forms, and different mean values. The frequency distribution of such data, then, will often be multimodal. Usually, however, in order to achieve better sampling, measurements of these variables over an entire set of data gathered at widely disparate locations are processed as though the data were statistically homogeneous, that is, as though they were fully characterized by just one PDF and one single set of parameters having one mean value. Is there, instead, a better way of treating the data in a manner that is consistent with this statistical heterogeneity? This question is addressed here using a statistical inversion technique developed by Tarantola based upon Bayesian methodology. Two examples of disdrometer measurements in real rain, one 16 h and the other 3 min long, reveal the presence of multiple mean values of the counts at all the different drop sizes. In both cases the heterogeneous rain can be decomposed into five–seven statistically homogeneous components, each characterized by its own steady drop size distribution. Concepts such as stratiform versus convective rain can be given more precise meaning in terms of the contributions each component makes to the rain. Furthermore, this discovery permits the explicit inclusion of statistical heterogeneity into some analytic theories.

scholarly journals Some Illustrations of Information Geometry in Biology and Physics

2012 ◽  
pp. 287-315 ◽  
Author(s):  
C. T. J. Dodson
Keyword(s):  
Amino Acid ◽  
State Space ◽  
Information Geometry ◽  
Probability Density Functions ◽  
Density Functions ◽  
Binary Variables ◽  
Information Theoretic ◽  
Precise Meaning ◽  
Rate Processes ◽  
Intuitive Sense

Many real processes have stochastic features which seem to be representable in some intuitive sense as `close to Poisson’, `nearly random’, `nearly uniform’ or with binary variables `nearly independent’. Each of those particular reference states, defined by an equation, is unstable in the formal sense, but it is passed through or hovered about by the observed process. Information geometry gives precise meaning for nearness and neighbourhood in a state space of processes, naturally quantifying proximity of a process to a particular state via an information theoretic metric structure on smoothly parametrized families of probability density functions. We illustrate some aspects of the methodology through case studies: inhomogeneous statistical evolutionary rate processes for epidemics, amino acid spacings along protein chains, constrained disordering of crystals, distinguishing nearby signal distributions and testing pseudorandom number generators.

scholarly journals On the Detection of Statistical Heterogeneity in Rain Measurements

2018 ◽  
Vol 35 (7) ◽  
pp. 1399-1413 ◽  
Author(s):  
A. R. Jameson ◽  
M. L. Larsen ◽  
A. B. Kostinski
Keyword(s):  
Heuristic Method ◽  
Mean Value ◽  
Small Data ◽  
Wide Sense ◽  
Mean Values ◽  
Statistical Homogeneity ◽  
Second Moments ◽  
Statistical Heterogeneity ◽  
Rain Events ◽  
Global Mean

AbstractThe application of the Wiener–Khintchine theorem for translating a readily measured correlation function into the variance spectrum, important for scale analyses and for scaling transformations of data, requires that the data be wide-sense homogeneous (stationary), that is, that the first and second moments of the probability distribution of the variable are the same at all times (stationarity) or at all locations (homogeneity) over the entire observed domain. This work provides a heuristic method independent of statistical models for evaluating whether a set of data in rain is wide-sense stationary (WSS). The alternative, statistical heterogeneity, requires 1) that there be no single global mean value and/or 2) that the variance of the variable changes in the domain. Here, the number of global mean values is estimated using a Bayesian inversion approach, while changes in the variance are determined using record counting techniques. An index of statistical heterogeneity (IXH) is proposed for rain such that as its value approaches zero, the more likely the data are wide-sense stationary and the more acceptable is the use of the Wiener–Khintchine theorem. Numerical experiments as well as several examples in real rain demonstrate the potential of IXH to identify statistical homogeneity, heterogeneity, and statistical mixtures. In particular, the examples demonstrate that visual inspections of data alone are insufficient for determining whether they are wide-sense stationary. Furthermore, in this small data collection, statistical heterogeneity was associated with convective rain, while statistical homogeneity appeared in more stratiform or mixed rain events. These tentative associations, however, need further substantiation.

scholarly journals Statistical Properties of Rain Cells in the Padana Valley

2008 ◽  
Vol 25 (12) ◽  
pp. 2230-2244 ◽  
Author(s):  
Carlo Capsoni ◽  
Michele D’Amico ◽  
Paolo Locatelli
Keyword(s):  
Probability Density Functions ◽  
Statistical Properties ◽  
Morphological Properties ◽  
Density Functions ◽  
Large Collection ◽  
Rain Intensity ◽  
Daughter Cells ◽  
Experimental Station ◽  
Mother Cells

Abstract A large collection of radar reflectivity maps gathered from 1988 to 1992 at the Spino d’Adda experimental station, located in the Padana Valley, has been exploited to investigate the statistical properties of rain structures and their descriptors. The results of this analysis can be of interest for meteorological, hydrological, and telecommunication applications. The authors found that the isosuperficial diameter follows an exponential distribution; when the threshold of rain intensity is increased, disappearance is dominant over fragmentation; moreover, the number of “mother cells” that generate N “daughter cells” decreases exponentially with N. To give a complete but concise characterization of the geometrical, physical, and morphological properties of rain cells, a set of analytical descriptors has been introduced and statistically defined through their probability density functions and the centrality, dispersion, and excursion parameters. As a final point, comparative statistical analyses have been performed at different thresholds for every couple of descriptors introduced, which allowed the authors to highlight correlations between them.

Mean values and classes of harmonic functions

1984 ◽  
Vol 96 (3) ◽  
pp. 501-505 ◽  
Author(s):  
Thomas Ramsey ◽  
Yitzhak Weit
Keyword(s):  
Unit Circle ◽  
Harmonic Functions ◽  
Borel Measure ◽  
Mean Value ◽  
Finite Complex ◽  
Mean Values ◽  
Complex Borel Measure ◽  
Generalized Mean ◽  
Image Position

Let μ be a finite complex Borel measure supported on the unit circle.In this paper, we are concerned with the characterization of the sets of functions satisfying the generalized mean value equation of the form.and for all ξ ∈ , | ξ | = R for some fixed R > 0.

Stochastic Spiking-Bursting Excitability and Transition to Chaos in a Discrete-Time Neuron Model

2020 ◽  
Vol 30 (10) ◽  
pp. 2050153
Author(s):  
Irina Bashkirtseva ◽  
Venera Nasyrova ◽  
Lev Ryashko
Keyword(s):  
Neuron Model ◽  
Deterministic Model ◽  
Probability Density Functions ◽  
Phase Portraits ◽  
Mutual Arrangement ◽  
Density Functions ◽  
Stochastic Effects ◽  
Mean Values ◽  
Transition To Chaos ◽  
Relationship Of

The randomly forced Rulkov neuron model with the discontinuous 2D-map is considered. We study the phenomena of the stochastic excitement: (i) noise-induced spiking in the parametric zone where the equilibrium is a single attractor; (ii) stochastic generation of the spiking in bistability zone; (iii) noise-induced bursting in the parametric zone where the deterministic model exhibits the tonic spiking. These stochastic effects are investigated numerically by means of probability density functions and mean values of interspike (interburst) intervals. For the parametric study of these noise-induced transformations, we suggest an analytical approach taking into account the stochastic sensitivity of attractors and peculiarities of deterministic phase portraits. In this analysis, we study the mutual arrangement of confidence domains and superthreshold zones near deterministic attractors. This approach gives a prediction of the onset of the noise-induced excitement in the form of the transitions quiescence-spiking or spiking-bursting. A relationship of these phenomena with the order-chaos transformations are discussed.

scholarly journals Time-Dependent Probability Density Functions and Attractor Structure in Self-Organised Shear Flows

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 613 ◽  
Author(s):  
Quentin Jacquet ◽  
Eun-jin Kim ◽  
Rainer Hollerbach
Keyword(s):  
Probability Density ◽  
Shear Flows ◽  
Numerical Solutions ◽  
Planck Equation ◽  
Probability Density Functions ◽  
Time Dependent ◽  
Parameter Study ◽  
Density Functions ◽  
Stochastic Forcing ◽  
Mean Values

We report the time-evolution of Probability Density Functions (PDFs) in a toy model of self-organised shear flows, where the formation of shear flows is induced by a finite memory time of a stochastic forcing, manifested by the emergence of a bimodal PDF with the two peaks representing non-zero mean values of a shear flow. Using theoretical analyses of limiting cases, as well as numerical solutions of the full Fokker–Planck equation, we present a thorough parameter study of PDFs for different values of the correlation time and amplitude of stochastic forcing. From time-dependent PDFs, we calculate the information length ( L ), which is the total number of statistically different states that a system passes through in time and utilise it to understand the information geometry associated with the formation of bimodal or unimodal PDFs. We identify the difference between the relaxation and build-up of the shear gradient in view of information change and discuss the total information length ( L ∞ = L ( t → ∞ ) ) which maps out the underlying attractor structures, highlighting a unique property of L ∞ which depends on the trajectory/history of a PDF’s evolution.

Fatigue Lives of Metals up to Crack Initiation

1977 ◽  
Vol 99 (3) ◽  
pp. 212-214
Author(s):  
Chiaki Ihara ◽  
Akira Tsurui ◽  
Akito Igarashi
Keyword(s):  
Crack Initiation ◽  
Stochastic Model ◽  
Probability Density ◽  
Material Properties ◽  
Probability Density Functions ◽  
Tension Test ◽  
True Stress ◽  
Density Functions ◽  
Stress Strain ◽  
Mean Values

Recently a stochastic model for fatigue of metals has been proposed by two of the present authors. In this paper some parameters adopted in that model are related to the material properties obtained from the static true stress-strain tension test. On this basis, the probability density functions of lives up to crack initiation and their mean values are estimated.

scholarly journals Characterization of Brassica napus (Canola) Germplasm Based on Microsatellite Markers

2021 ◽  
pp. 1-7
Author(s):  
Muhammad Asif ◽  
Zinnia Mansoor ◽  
Syed Bilal Hussain ◽  
Muhammad Arshad ◽  
Muhammad Babar ◽  
...  
Keyword(s):  
Genetic Diversity ◽  
Brassica Napus ◽  
Ssr Markers ◽  
Mean Value ◽  
Oilseed Crop ◽  
Brassica Napus L ◽  
Mean Values ◽  
Allelic Differences ◽  
Breeding Programmes

Brassica napus L. is a major oilseed crop all over the world. The aim of this study was to investigate the genetic diversity of B. napus germplasm by using simple sequence repeats (SSR) markers. In the current study, ten SSR markers were used for studying genetic diversity of ten Brassica cultivars. Out of 110 total bands, 68 bands were polymorphic with 52.11% average polymorphism. Mean value of Nei’s genetic diversity and Polymorphism Information Content was 1.7, and 0.2630, respectively. These mean values show that there are moderate allelic differences between Brassica cultivars. The Nei’s genetic distance among various cultivars was 0.3281 and 0.125 which showed that germplasm of Brassica cultivars are different from each other, which is probably due to anthropogenic interventions and environmental factors. Thus, genetically different lines identified in this study could be employed in breeding programmes to develop higher-quality canola inbred varieties in future.

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