Probability Distribution Of Size Research Articles

Efficient algorithms for 2D area management and online task placement on runtime reconfigurable FPGAs

Partial Runtime Reconfigurable (PRTR) FPGAs allow HW tasks to be placed and removed dynamically at runtime. We make two contributions in this paper. First, we present an efficient algorithm for finding the complete set of Maximal Empty Rectangles on a 2D PRTR FPGA. We also present a HW implementation of the algorithm with negligible runtime overhead. Second, we present an efficient online deadline-constrained task placement algorithm for minimizing area fragmentation on the FPGA by using an area fragmentation metric that takes into account probability distribution of sizes of future task arrivals as well as the time axis. The techniques presented in this paper are useful in an operating system for runtime reconfigurable FPGAs to manage the HW resources on the FPGA when HW tasks that arrive and finish dynamically at runtime.

Driven particle in a random landscape: Disorder correlator, avalanche distribution, and extreme value statistics of records

We review how the renormalized force correlator Delta(micro) , the function computed in the functional renormalization-group (RG) field theory, can be measured directly in numerics and experiments on the dynamics of elastic manifolds in the presence of pinning disorder. We show how this function can be computed analytically for a particle dragged through a one-dimensional random-force landscape. The limit of small velocity allows one to access the critical behavior at the depinning transition. For uncorrelated forces one finds three universality classes, corresponding to the three extreme value statistics, Gumbel, Weibull, and Fréchet. For each class we obtain analytically the universal function Delta(micro) , the corrections to the critical force, and the joint probability distribution of avalanche sizes s and waiting times w . We find P(s)=P(w) for all three cases. All results are checked numerically. For a Brownian force landscape, known as the Alessandro, Beatrice, Bertotti, and Montorsi (ABBM) model, avalanche distributions and Delta(micro) can be computed for any velocity. For two-dimensional disorder, we perform large-scale numerical simulations to calculate the renormalized force correlator tensor Delta_{ij}(micro[over ]) , and to extract the anisotropic scaling exponents zeta_{x}>zeta_{y} . We also show how the Middleton theorem is violated. Our results are relevant for the record statistics of random sequences with linear trends, as encountered, e.g., in some models of global warming. We give the joint distribution of the time s between two successive records and their difference in value w .

An Improved OPA Model and Blackout Risk Assessment

The ORNL-PSerc-Alaska (OPA) model is a blackout model proposed by researchers at Oak Ridge National Laboratory (ORNL), Power System Engineering Research Center of Wisconsin University (PSerc), and Alaska University (Alaska). Although the OPA model is a landmark study, it has two limitations. First, there is a significant difference between simulation and practice in transmission line outage and update; and second, the simulation of cascading failure and the probability distribution of blackout size are in general not accurate enough. Hence, an improved OPA model is proposed in this paper to address these limitations. The proposed model contains two layers of iteration. The inner iteration describes the fast dynamics of the system and considers the influence of power flow, dispatching, automation, relay protection, and so on. The outer iteration describes the slow overall system evolution and is concerned with the update of the power grid, operation modes and planning. Such a model can be applied to practical large-scale systems. Furthermore, based on the Value at Risk (VaR) and Conditional Value at Risk (CVaR), two new complementary blackout risk indices are defined, which reveal critical characteristics of blackouts and are used to evaluate security levels of power systems. The effectiveness of the improved OPA model is verified by the simulations concerning the Northeast Power Grid of China.

Probabilistic analysis of a genealogical model of animal group patterns

Many social animals live in stable groups, and it has been argued that kinship plays a major role in their group formation process. In this study we present the mathematical analysis of a recent model which uses kinship as a main factor to explain observed group patterns in a finite sample of individuals. We describe the average number of groups and the probability distribution of group sizes predicted by this model. Our method is based on the study of recursive equations underlying these quantities. We obtain asymptotic equivalents for probability distributions and moments as the sample size increases, and we exhibit power-law behaviours. Computer simulations are also utilized to measure the extent to which the asymptotic approximation can be applied with confidence.

Modelling of the grain size probability distribution in polycrystalline nanomaterials

Abstract Theoretical analyses have always resulted in nanomaterials’ grain size probability distribution being of varied form: approximately either lognormal, Rayleigh, normal, Weibull, etc. The isotropic Hillert’s model of grain growth which is more suitable for soap froth has been frequently used to establish these distributions with the hope of approximating experimental observations. Observed grain growth in nanomaterials shows departures from the Hillert’s model. In the present paper, the probability distribution of grain size in nanomaterials is dealt with. Use is made of a modified model of grain growth in polycrystalline nanomaterials developed recently by the authors. The modified model accounts for grain growth caused by curvature driven grain boundary migration and grain rotation-coalescence mechanisms. Since the grain size in the aggregate is random, the stochastic counterpart of the expression governing the incremental change in individual grain size is obtained by the addition of two fluctuation terms. The integro-differential equation governing the development of the probability density function of the grain size is obtained which is the generalised Fokker–Planck–Kolmogorov equation. Numerical solution to the integro-differential equation is obtained. Results from analytical modelling of grain size probability distribution in polycrystalline nanomaterials are different if the effect of grain rotation-coalescence mechanism on grain growth process is taken into account and, further, due to the addition of the fluctuation terms. Results also depend on the nature of the fluctuation term, which is a material property as the fluctuation in grain sizes varies from one material to another. It is shown that many of the major attributes of grain growth, such as self similarity (probability density approaching a stationary one), can be predicted by the solution of the Fokker–Planck–Kolmogorov equation.

Preparation and characterization of carbon pillared clay material

Carbon pillared clay material was prepared from montmorillonite modified by C19H42BrN and C10H16ClN. SEM, FT-IR, XRD, N2 adsorption-desorption, thermal-gravimetric analysis and differential scanning calorimetry were employed to characterize the pore structure and test the effect of surfactant. The results show that organic modifier combines with montmorillonite particles by covalent bond and ion embedded. The microstructure of carbon pillared material looks like needle slice. The most probable pore size distribution is about 1.7 nm. The clay material slice mainly consists of two-dimensional aperture supported by a carbonization pillar. The high-temperature stability of carbon pillared clay is improved.

Informational analysis of the grinding process of granular material using a multi-ribbon blender

AbstractA new concept of investigation on granular material grinding process using a multi-ribbon blender is demonstrated. A new approach of mathematical description of this process is presented using the Shannon’s entropy definition for random processes. The analysis of experiments was carried out employing the probability size distribution variation with the time of grinding process. The investigations reported in this work provide useful insight into the granular material grinding process. Moreover, the proposed informational description may be used to quantify the progress of this process whose importance in plant design and process optimisation, according to other experimental works, appears to be underestimated.

Finite-size effects on the statistics of extreme events in the BTW model

The BTW Abelian sandpile model is a prominent example of systems showing self-organised criticality (SOC) in the infinite size limit. We study finite-size effects with special focus on the statistics of extreme events, i.e., of particularly large avalanches. Not only the avalanche size probability distribution, but also the mutual independence of large avalanches in the critical state is affected by finite-size effects. Instead of a Poissonian recurrencetime distribution, in the finite system we find a repulsion of extreme events that depends on the avalanche size and not on the respective probability. The dependence of these effects on the system size is investigated and some data collapse is found. Our results imply that SOC is an unsuitable mechanism for the explanation of extreme events which occur in clusters.

Statistical estimation of stratospheric particle size distribution by combining optical modelling and lidar scattering measurements

Abstract. A method for estimating the stratospheric particle size distribution from multiwavelength lidar measurements is presented. It is based on matching measured and model-simulated backscatter coefficients. The lidar backscatter coefficients measured at the three commonly used wavelengths 355, 532 and 1064 nm are compared to a precomputed look-up table of model-calculated values. The optical model assumes that particles are spherical and that their size distribution is unimodal. This inverse problem is not trivial because the optical model is highly non-linear with a strong sensitivity to the size distribution parameters in some cases. The errors in the lidar backscatter coefficients are explicitly taken into account in the estimation. The method takes advantage of the statistical properties of the possible solution cluster to identify the most probable size distribution parameters. In order to discard model-simulated outliers resulting from the strong non-linearity of the model, solutions farther than one standard deviation of the median values of the solution cluster are filtered out, because the most probable solution is expected to be in the densest part of the cluster. Within the filtered solution cluster, the estimation algorithm minimizes a cost function of the misfit between measurements and model simulations. Two validation cases are presented on Polar Stratospheric Cloud (PSC) events detected above the ALOMAR observatory (69° N – Norway). A first validation is performed against optical particle counter measurements carried out in January 1996. In non-depolarizing regions of the cloud (i.e. spherical particles), the parameters of an unimodal size distribution and those of the optically dominant mode of a bimodal size distribution are quite successfully retrieved, especially for the median radius and the geometrical standard deviation. As expected, the algorithm performs poorly when solid particles drive the backscatter coefficient. A small bias is identified in modelling the refractive index when compared to previous works that inferred PSC type Ib refractive indices. The accuracy of the size distribution retrieval is improved when the refractive index is set to the value inferred in the reference paper. Our results are then compared to values retrieved with another similar method that does not account for the effect of the measurements errors and the non-linearity of the optical model on the likelihood of the solution. The case considered is a liquid PSC observed over northern Scandinavia on January 2005. An excellent agreement is found between the two methods when our algorithm is applied without any statistical filtering of the solution cluster. However, the solution for the geometrical standard deviation appears to be rather unlikely with a value close to unity (σ≈1.04). When our algorithm is applied with solution filtering, a more realistic value of the standard deviation (σ≈1.27) is found. This highlights the importance of taking into account the non linearity of the model together with the lidar errors, when estimating particle size distribution parameters from lidar measurements.

Scaling and memory effect in volatility return interval of the Chinese stock market

We investigate the probability distribution of the volatility return intervals τ for the Chinese stock market. We rescale both the probability distribution P q ( τ ) and the volatility return intervals τ as P q ( τ ) = 1 / τ ¯ f ( τ / τ ¯ ) to obtain a uniform scaling curve for different threshold value q . The scaling curve can be well fitted by the stretched exponential function f ( x ) ∼ e − α x γ , which suggests memory exists in τ . To demonstrate the memory effect, we investigate the conditional probability distribution P q ( τ | τ 0 ) , the mean conditional interval 〈 τ | τ 0 〉 and the cumulative probability distribution of the cluster size of τ . The results show clear clustering effect. We further investigate the persistence probability distribution P ± ( t ) and find that P − ( t ) decays by a power law with the exponent far different from the value 0.5 for the random walk, which further confirms long memory exists in τ . The scaling and long memory effect of τ for the Chinese stock market are similar to those obtained from the United States and the Japanese financial markets.

Effects of Vertex Activity and Self-organized Criticality Behavior on a Weighted Evolving Network

Effects of vertex activity have been analyzed on a weighted evolving network. The network is characterized by the probability distribution of vertex strength, each edge weight and evolution of the strength of vertices with different vertex activities. The model exhibits self-organized criticality behavior. The probability distribution of avalanche size for different network sizes is also shown. In addition, there is a power law relation between the size and the duration of an avalanche and the average of avalanche size has been studied for different vertex activities.

Criticality in Two-Variable Earthquake Model on a Random Graph

A two-variable earthquake model on a quenched random graph is established here. It can be seen as a generalization of the OFC models. We numerically study the critical behavior of the model when the system is nonconservative: the result indicates that the model exhibits self-organized criticality deep within the nonconservative regime. The probability distribution for avalanche size obeys finite size scaling. We compare our model with the model introduced by Stefano Lise and Maya Paczuski [Phys. Rev. Lett. 88 (2002) 228301], it is proved that they are not in the same universality class.

Temporal evolution of the domain structure in a Poisson-Voronoi nucleation and growth transformation: Results for one and three dimensions

The distribution of spatial domain structures originated during one- and three-dimensional Poisson-Voronoi transformations are computed analytically extending the recently obtained results for the two-dimensional case. The presented method gives a full description of the developed microstructure and is valid for tessellations of any dimensionality. The temporal and spatial dependences of the domain structure are completely discriminated and separated, showing the existence of geometric configurations independent of time. A single computation of the probability distribution of these geometric configurations allows us to calculate the total free-boundary and size probability distributions at any desired time. The obtained results show full agreement with stochastic simulations and reproduce completely the previously existing partial results. A discussion about the potential applications of the method to the calculation of other geometrical properties and the characteristics of the final static structure leading to a Gamma distribution of sizes is also presented.

Long-Term Effect of the n-1 Criterion on Cascading Line Outages in an Evolving Power Transmission Grid

Cascading transmission line outages contribute to widespread blackouts. Engineers respond to the risk of cascading line outages by applying policies such as the n-1 criterion and upgrading lines involved in recent cascading outages. The transmission grid slowly evolves as these policies are applied to maintain reliability while the load grows. We suggest how to assess the long-term effect of these policies on the risk of cascading line outages by simulating both the cascading and the slow evolution of the transmission grid. The long-term effects of these policies on the probability distribution of outage size and the grid utilization are computed for the IEEE 118-bus test system. The results show complex system self-organization of an evolving transmission grid.

A Performance Modeling of Connectivity in Vehicular Ad Hoc Networks

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, we study the statistical properties of the connectivity of Vehicular <emphasis emphasistype="italic">Ad hoc</emphasis> NETworks (VANETs) with user mobility. It is assumed that the nodes travel along a multilane highway that allows vehicles to pass each other. The nodes arrive at the highway through one of the traffic entry points according to a Poisson process and then travel in the same direction according to a user mobility model until they reach their exit points. The nodes on the highway may be able to communicate with each other. We derive the probability distribution of the node population size on the highway and the node's location distribution. Then, we determine the mean cluster size and the probability that the nodes will form a single cluster. The analysis of this paper also applies to any path in a network of highways, as well as to two-way traffic. The numerical results show the significance of mobility on the connectivity of VANETs. We also present simulation results that confirm the accuracy of the analysis. The results of this paper may be used to study the routing algorithms, throughput, or delay in VANETs. </para>

A self-adapting herding model: The agent judge-abilities influence the dynamic behaviors

We propose a self-adapting herding model, in which the financial markets consist of agent clusters with different sizes and market desires. The ratio of successful exchange and merger depends on the volatility of the market and the market desires of the agent clusters. The desires are assigned in term of the wealth of the agent clusters when they merge. After an exchange, the beneficial cluster’s desire keeps on the same, the losing one’s desire is altered which is correlative with the agent judge-ability. A parameter R is given to all agents to denote the judge-ability. The numerical calculation shows that the dynamic behaviors of the market are influenced distinctly by R , which includes the exponential magnitudes of the probability distribution of sizes of the agent clusters and the volatility autocorrelation of the returns, the intensity and frequency of the volatility.

OIL SPILL RISK ANALYSIS FOR CAPE WIND ENERGY PROJECT

ABSTRACT The oil spill risk associated with an offshore wind farm was analyzed. This paper describes the methodology employed to determine the probability that a spill would occur, as well as the size probability distribution of potential spills, including worst-case discharge scenarios from the facility. Spills from vessels transiting surrounding waters due to collisions, allisions, and groundings were also evaluated. The analysis involved: evaluating events that might cause damage to the electric service platform (ESP) and wind turbine generators (WTG) components of the wind farm; analysis of the probability of each of these events occurring; analysis of the probability that these events cause damage to the ESP/WTGs; and estimation of the probability of the events causing damage sufficient to cause an oil spill. Data were aggregated for all spill causes to determine the overall probability distribution function of spill volumes. Probability size distributions for all spill causes were coupled with the probability of spill occurrence to provide an overall function to predict the probability of a particular spill of a certain volume occurring over 5, 10, and 30 years.

Multifractal analysis as a tool for validating a rainfall model

AbstractA multifractal analysis was carried out in order to validate the simulation of hourly rainfall records of a local climate model for the Iberian Peninsula. Observed and simulated hourly rainfall data from four locations in Andalusia (southern Spain) were used to carry out the study. In order to detect the influence of the length of the data series on the results, two different sizes were used for the real data: 4 years, and 20 years. The results show that algebraic tails are required to fit the probability distribution of extreme rain event sizes, and rain and dry event durations for both kinds of rainfall data. Similar results are found for the extreme rain event sizes and dry event durations fits when the real and synthetic data are considered. Nevertheless, some differences appear in the cases of rain event durations. The detection of the presence of a first‐order multifractal phase transition associated with a critical moment in the empirical moment scaling exponent function and the results of the extreme rain event sizes fits, reveal that real rainfall is a self‐organized criticality (SOC) process. That behaviour is less evident in the simulated rainfall series. The same ‘synoptic maximum’ value was found for each place with both types of rainfall data. A time clustering analysis was carried out applying the count‐based periodogram and the Fano factor methods. Some periodicities have been detected in the periodograms, especially for the longest real rainfall data series. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Development at the wildland–urban interface and the mitigation of forest-fire risk

This work addresses the impacts of development at the wildland-urban interface on forest fires that spread to human habitats. Catastrophic fires in the western United States and elsewhere make these impacts a matter of urgency for decision makers, scientists, and the general public. Using a simple fire-spread model, along with housing and vegetation data, we show that fire size probability distributions can be strongly modified by the density and flammability of houses. We highlight a sharp transition zone in the parameter space of vegetation flammability and house density. Many actual fire landscapes in the United States appear to have spreading properties close to this transition. Thus, the density and flammability of buildings should be taken into account when assessing fire risk at the wildland-urban interface. Moreover, our results highlight ways for regulation at this interface to help mitigate fire risk.

Average-Case Performance Analysis Of Online Non-Clairvoyant Scheduling Of Parallel Tasks With Precedence Constraints

We evaluate the average-case performance of three approximation algorithms for online non-clairvoyant scheduling of parallel tasks with precedence constraints. We show that for a class of wide task graphs, when task sizes are uniformly distributed in the range [1₀C], the online non-clairvoyant scheduling algorithm LL-SIMPLE has an asymptotic average-case performance bound of M/(M-(3-(1 + 1/C)C+1)C-1), where M is the number of processors. For uniform probability distributions of task sizes, we present numerical and simulation data to demonstrate the accuracy of our general asymptotic average-case performance bound. We also report extensive experimental results on the average-case performance of online non-clairvoyant scheduling algorithms LL-GREEDY and LS. Algorithm LL-GREEDY has better performance than LL-SIMPLE using an improved algorithm to schedule independent tasks in the same level. Algorithm LS produces even better schedules due to a break of boundaries among levels.