A novel framework on exact average symbol error probabilities of multihop transmission over amplify-and-forward relay fading channels

KAUST Repository

Yilmaz, Ferkan; Kucur, Oǧuz; Alouini, Mohamed-Slim

2010-01-01

In this paper, we propose an analytical framework on the exact computation of the average symbol error probabilities (ASEP) of multihop transmission over generalized fading channels when an arbitrary number of amplify-and-forward relays is used. Our approach relies on moment generating function (MGF) framework to obtain exact single integral expressions which can be easily computed by Gauss-Chebyshev Quadrature (GCQ) rule. As such, the derived results are a convenient tool to analyze the ASEP performance of multihop transmission over amplify-and-forward relay fading channels. Numerical and simulation results, performed to verify the correctness of the proposed formulation, are in perfect agreement. © 2010 IEEE.

A novel framework on exact average symbol error probabilities of multihop transmission over amplify-and-forward relay fading channels

KAUST Repository

Yilmaz, Ferkan

2010-09-01

In this paper, we propose an analytical framework on the exact computation of the average symbol error probabilities (ASEP) of multihop transmission over generalized fading channels when an arbitrary number of amplify-and-forward relays is used. Our approach relies on moment generating function (MGF) framework to obtain exact single integral expressions which can be easily computed by Gauss-Chebyshev Quadrature (GCQ) rule. As such, the derived results are a convenient tool to analyze the ASEP performance of multihop transmission over amplify-and-forward relay fading channels. Numerical and simulation results, performed to verify the correctness of the proposed formulation, are in perfect agreement. © 2010 IEEE.

Exact Symbol Error Probability of Cross-QAM in AWGN and Fading Channels

Directory of Open Access Journals (Sweden)

Zhang Xi-chun

2010-01-01

Full Text Available The exact symbol error probability (SEP performance of -ary cross quadrature amplitude modulation (QAM in additive white Gaussian noise (AWGN channel and fading channels, including Rayleigh, Nakagami-m, Rice, and Nakagami-q (Hoyt channels, is analyzed. The obtained closed-form SEP expressions contain a finite (in proportion to sum of single integrals with finite limits and an integrand composed of elementary (exponential, trigonometric, and/or power functions, thus readily enabling numerical evaluation. Particularly, Gaussian -function is a special case of these integrals and is included in the SEP expressions. Simple and very precise approximations, which contain only Gaussian -function for AWGN channel and contain three terms of the single integrals mentioned above for fading channels, respectively, are also given. The analytical expressions show excellent agreement with the simulation results, and numerical evaluation with the proposed expressions reveals that cross QAM can obtain at least 1.1 dB gain compared to rectangular QAM when SEP < 0.3 in all the considered channels.

Simultaneous feature selection and classification via Minimax Probability Machine

Directory of Open Access Journals (Sweden)

Liming Yang

2010-12-01

Full Text Available This paper presents a novel method for simultaneous feature selection and classification by incorporating a robust L1-norm into the objective function of Minimax Probability Machine (MPM. A fractional programming framework is derived by using a bound on the misclassification error involving the mean and covariance of the data. Furthermore, the problems are solved by the Quadratic Interpolation method. Experiments show that our methods can select fewer features to improve the generalization compared to MPM, which illustrates the effectiveness of the proposed algorithms.

Exact valence bond entanglement entropy and probability distribution in the XXX spin chain and the potts model.

Science.gov (United States)

Jacobsen, J L; Saleur, H

2008-02-29

We determine exactly the probability distribution of the number N_(c) of valence bonds connecting a subsystem of length L>1 to the rest of the system in the ground state of the XXX antiferromagnetic spin chain. This provides, in particular, the asymptotic behavior of the valence-bond entanglement entropy S_(VB)=N_(c)ln2=4ln2/pi(2)lnL disproving a recent conjecture that this should be related with the von Neumann entropy, and thus equal to 1/3lnL. Our results generalize to the Q-state Potts model.

Clinical Features in a Danish Population-Based Cohort of Probable Multiple System Atrophy Patients

DEFF Research Database (Denmark)

Starhof, Charlotte; Korbo, Lise; Lassen, Christina Funch

2016-01-01

Background: Multiple system atrophy (MSA) is a rare, sporadic and progressive neurodegenerative disorder. We aimed to describe the clinical features of Danish probable MSA patients, evaluate their initial response to dopaminergic therapy and examine mortality. Methods: From the Danish National...... the criteria for probable MSA. We recorded clinical features, examined differences by MSA subtype and used Kaplan-Meier survival analysis to examine mortality. Results: The mean age at onset of patients with probable MSA was 60.2 years (range 36-75 years) and mean time to wheelchair dependency was 4.7 years...

Exact probability function for bulk density and current in the asymmetric exclusion process

Science.gov (United States)

Depken, Martin; Stinchcombe, Robin

2005-03-01

We examine the asymmetric simple exclusion process with open boundaries, a paradigm of driven diffusive systems, having a nonequilibrium steady-state transition. We provide a full derivation and expanded discussion and digression on results previously reported briefly in M. Depken and R. Stinchcombe, Phys. Rev. Lett. 93, 040602 (2004). In particular we derive an exact form for the joint probability function for the bulk density and current, both for finite systems, and also in the thermodynamic limit. The resulting distribution is non-Gaussian, and while the fluctuations in the current are continuous at the continuous phase transitions, the density fluctuations are discontinuous. The derivations are done by using the standard operator algebraic techniques and by introducing a modified version of the original operator algebra. As a by-product of these considerations we also arrive at a very simple way of calculating the normalization constant appearing in the standard treatment with the operator algebra. Like the partition function in equilibrium systems, this normalization constant is shown to completely characterize the fluctuations, albeit in a very different manner.

Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension.

Science.gov (United States)

Simpson, Matthew J; Baker, Ruth E

2015-09-07

Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard non-growing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here.

Ensemble based system for whole-slide prostate cancer probability mapping using color texture features.

LENUS (Irish Health Repository)

DiFranco, Matthew D

2011-01-01

We present a tile-based approach for producing clinically relevant probability maps of prostatic carcinoma in histological sections from radical prostatectomy. Our methodology incorporates ensemble learning for feature selection and classification on expert-annotated images. Random forest feature selection performed over varying training sets provides a subset of generalized CIEL*a*b* co-occurrence texture features, while sample selection strategies with minimal constraints reduce training data requirements to achieve reliable results. Ensembles of classifiers are built using expert-annotated tiles from training images, and scores for the probability of cancer presence are calculated from the responses of each classifier in the ensemble. Spatial filtering of tile-based texture features prior to classification results in increased heat-map coherence as well as AUC values of 95% using ensembles of either random forests or support vector machines. Our approach is designed for adaptation to different imaging modalities, image features, and histological decision domains.

Exact asymptotics of probabilities of large deviations for Markov chains: the Laplace method

Energy Technology Data Exchange (ETDEWEB)

Fatalov, Vadim R [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

2011-08-31

We prove results on exact asymptotics as n{yields}{infinity} for the expectations E{sub a} exp{l_brace}-{theta}{Sigma}{sub k=0}{sup n-1}g(X{sub k}){r_brace} and probabilities P{sub a}{l_brace}(1/n {Sigma}{sub k=0}{sup n-1}g(X{sub k})=}1, is the corresponding random walk on R, g(x) is a positive continuous function satisfying certain conditions, and d>0, {theta}>0, a element of R are fixed numbers. Our results are obtained using a new method which is developed in this paper: the Laplace method for the occupation time of discrete-time Markov chains. For g(x) one can take |x|{sup p}, log (|x|{sup p}+1), p>0, |x| log (|x|+1), or e{sup {alpha}|x|}-1, 0<{alpha}<1/2, x element of R, for example. We give a detailed treatment of the case when g(x)=|x| using Bessel functions to make explicit calculations.

Semi-Local DFT Functionals with Exact-Exchange-Like Features: Beyond the AK13

Science.gov (United States)

Armiento, Rickard

The Armiento-Kümmel functional from 2013 (AK13) is a non-empirical semi-local exchange functional on generalized gradient approximation form (GGA) in Kohn-Sham (KS) density functional theory (DFT). Recent works have established that AK13 gives improved electronic-structure exchange features over other semi-local methods, with a qualitatively improved orbital description and band structure. For example, the Kohn-Sham band gap is greatly extended, as it is for exact exchange. This talk outlines recent efforts towards new exchange-correlation functionals based on, and extending, the AK13 design ideas. The aim is to improve the quantitative accuracy, the description of energetics, and to address other issues found with the original formulation. Swedish e-Science Research Centre (SeRC).

Audio Query by Example Using Similarity Measures between Probability Density Functions of Features

Directory of Open Access Journals (Sweden)

Marko Helén

2010-01-01

Full Text Available This paper proposes a query by example system for generic audio. We estimate the similarity of the example signal and the samples in the queried database by calculating the distance between the probability density functions (pdfs of their frame-wise acoustic features. Since the features are continuous valued, we propose to model them using Gaussian mixture models (GMMs or hidden Markov models (HMMs. The models parametrize each sample efficiently and retain sufficient information for similarity measurement. To measure the distance between the models, we apply a novel Euclidean distance, approximations of Kullback-Leibler divergence, and a cross-likelihood ratio test. The performance of the measures was tested in simulations where audio samples are automatically retrieved from a general audio database, based on the estimated similarity to a user-provided example. The simulations show that the distance between probability density functions is an accurate measure for similarity. Measures based on GMMs or HMMs are shown to produce better results than that of the existing methods based on simpler statistics or histograms of the features. A good performance with low computational cost is obtained with the proposed Euclidean distance.

Universality in exact quantum state population dynamics and control

International Nuclear Information System (INIS)

Wu, Lian-Ao; Segal, Dvira; Brumer, Paul; Egusquiza, Inigo L.

2010-01-01

We consider an exact population transition, defined as the probability of finding a state at a final time that is exactly equal to the probability of another state at the initial time. We prove that, given a Hamiltonian, there always exists a complete set of orthogonal states that can be employed as time-zero states for which this exact population transition occurs. The result is general: It holds for arbitrary systems, arbitrary pairs of initial and final states, and for any time interval. The proposition is illustrated with several analytic models. In particular, we demonstrate that in some cases, by tuning the control parameters, a complete transition might occur, where a target state, vacant at t=0, is fully populated at time τ.

Ruin probabilities

DEFF Research Database (Denmark)

Asmussen, Søren; Albrecher, Hansjörg

The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities......, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially...... updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber–Shiu functions and dependence....

Finding optimal exact reducts

KAUST Repository

AbouEisha, Hassan M.

2014-01-01

The problem of attribute reduction is an important problem related to feature selection and knowledge discovery. The problem of finding reducts with minimum cardinality is NP-hard. This paper suggests a new algorithm for finding exact reducts

Filtering a statistically exactly solvable test model for turbulent tracers from partial observations

International Nuclear Information System (INIS)

Gershgorin, B.; Majda, A.J.

2011-01-01

A statistically exactly solvable model for passive tracers is introduced as a test model for the authors' Nonlinear Extended Kalman Filter (NEKF) as well as other filtering algorithms. The model involves a Gaussian velocity field and a passive tracer governed by the advection-diffusion equation with an imposed mean gradient. The model has direct relevance to engineering problems such as the spread of pollutants in the air or contaminants in the water as well as climate change problems concerning the transport of greenhouse gases such as carbon dioxide with strongly intermittent probability distributions consistent with the actual observations of the atmosphere. One of the attractive properties of the model is the existence of the exact statistical solution. In particular, this unique feature of the model provides an opportunity to design and test fast and efficient algorithms for real-time data assimilation based on rigorous mathematical theory for a turbulence model problem with many active spatiotemporal scales. Here, we extensively study the performance of the NEKF which uses the exact first and second order nonlinear statistics without any approximations due to linearization. The role of partial and sparse observations, the frequency of observations and the observation noise strength in recovering the true signal, its spectrum, and fat tail probability distribution are the central issues discussed here. The results of our study provide useful guidelines for filtering realistic turbulent systems with passive tracers through partial observations.

[Choice between probability and value of alimentary reinforcement as means for revealing individual typological features of dog behavior].

Science.gov (United States)

Chilingarian, L I

2005-01-01

Individual typological features of behavior of dogs were investigated by the method of choice between the low-valuable food available constantly and food of high quality presented with low probability. Animals were subjected to instrumental conditioning with the same conditioned stimuli but different types of reinforcement. Depression of a white pedal was always reinforced with meat-bread-crumb mixture, depression of a black pedal was reinforced with two pieces of liver (with probabilities of 100, 40, 33, 20, or 0%). The choice of reinforcement depended on probability of valuable food and individual typological features of the nervous system of a dog. Decreasing the probability of the reinforcement value to 40-20% revealed differences in behavior of dogs. Dogs of the first group, presumably with the weak type of the nervous system, more frequently pressed the white pedal (always reinforced) than the black pedal thus "avoiding a situation of risk" to receive an empty cup. They displayed symptoms of neurosis: whimper, refusals of food or of the choice of reinforcement, and obtrusive movements. Dogs of the second group, presumably with the strong type of the nervous system, more frequently pressed the black pedal (more valuable food) for the low-probability reward until they obtained the valuable food. They did not show neurosis symptoms and were not afraid of "situation of risk". A decrease in probability of the valuable reinforcement increased a percentage of long-latency depressions of pedals. It can be probably suggested that this phenomenon was associated with increasing involvement of cognitive processes, when contributions of the assessments of probability and value of the reinforcement to decision making became approximately equal. Choice between the probability and value of alimentary reinforcement is a good method for revealing individual typological features of dogs.

The Sequential Probability Ratio Test: An efficient alternative to exact binomial testing for Clean Water Act 303(d) evaluation.

Science.gov (United States)

Chen, Connie; Gribble, Matthew O; Bartroff, Jay; Bay, Steven M; Goldstein, Larry

2017-05-01

The United States's Clean Water Act stipulates in section 303(d) that states must identify impaired water bodies for which total maximum daily loads (TMDLs) of pollution inputs into water bodies are developed. Decision-making procedures about how to list, or delist, water bodies as impaired, or not, per Clean Water Act 303(d) differ across states. In states such as California, whether or not a particular monitoring sample suggests that water quality is impaired can be regarded as a binary outcome variable, and California's current regulatory framework invokes a version of the exact binomial test to consolidate evidence across samples and assess whether the overall water body complies with the Clean Water Act. Here, we contrast the performance of California's exact binomial test with one potential alternative, the Sequential Probability Ratio Test (SPRT). The SPRT uses a sequential testing framework, testing samples as they become available and evaluating evidence as it emerges, rather than measuring all the samples and calculating a test statistic at the end of the data collection process. Through simulations and theoretical derivations, we demonstrate that the SPRT on average requires fewer samples to be measured to have comparable Type I and Type II error rates as the current fixed-sample binomial test. Policymakers might consider efficient alternatives such as SPRT to current procedure. Copyright © 2017 Elsevier Ltd. All rights reserved.

New results to BDD truncation method for efficient top event probability calculation

International Nuclear Information System (INIS)

Mo, Yuchang; Zhong, Farong; Zhao, Xiangfu; Yang, Quansheng; Cui, Gang

2012-01-01

A Binary Decision Diagram (BDD) is a graph-based data structure that calculates an exact top event probability (TEP). It has been a very difficult task to develop an efficient BDD algorithm that can solve a large problem since its memory consumption is very high. Recently, in order to solve a large reliability problem within limited computational resources, Jung presented an efficient method to maintain a small BDD size by a BDD truncation during a BDD calculation. In this paper, it is first identified that Jung's BDD truncation algorithm can be improved for a more practical use. Then, a more efficient truncation algorithm is proposed in this paper, which can generate truncated BDD with smaller size and approximate TEP with smaller truncation error. Empirical results showed this new algorithm uses slightly less running time and slightly more storage usage than Jung's algorithm. It was also found, that designing a truncation algorithm with ideal features for every possible fault tree is very difficult, if not impossible. The so-called ideal features of this paper would be that with the decrease of truncation limits, the size of truncated BDD converges to the size of exact BDD, but should never be larger than exact BDD.

Exactly solvable birth and death processes

International Nuclear Information System (INIS)

Sasaki, Ryu

2009-01-01

Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable 'matrix' quantum mechanics, which is recently proposed by Odake and the author [S. Odake and R. Sasaki, J. Math. Phys. 49, 053503 (2008)]. The (q-) Askey scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of q x (with x being the population) corresponding to the q-Racah polynomial.

Classification of Knee Joint Vibration Signals Using Bivariate Feature Distribution Estimation and Maximal Posterior Probability Decision Criterion

Directory of Open Access Journals (Sweden)

Fang Zheng

2013-04-01

Full Text Available Analysis of knee joint vibration or vibroarthrographic (VAG signals using signal processing and machine learning algorithms possesses high potential for the noninvasive detection of articular cartilage degeneration, which may reduce unnecessary exploratory surgery. Feature representation of knee joint VAG signals helps characterize the pathological condition of degenerative articular cartilages in the knee. This paper used the kernel-based probability density estimation method to model the distributions of the VAG signals recorded from healthy subjects and patients with knee joint disorders. The estimated densities of the VAG signals showed explicit distributions of the normal and abnormal signal groups, along with the corresponding contours in the bivariate feature space. The signal classifications were performed by using the Fisher’s linear discriminant analysis, support vector machine with polynomial kernels, and the maximal posterior probability decision criterion. The maximal posterior probability decision criterion was able to provide the total classification accuracy of 86.67% and the area (Az of 0.9096 under the receiver operating characteristics curve, which were superior to the results obtained by either the Fisher’s linear discriminant analysis (accuracy: 81.33%, Az: 0.8564 or the support vector machine with polynomial kernels (accuracy: 81.33%, Az: 0.8533. Such results demonstrated the merits of the bivariate feature distribution estimation and the superiority of the maximal posterior probability decision criterion for analysis of knee joint VAG signals.

Exact Solution of Mutator Model with Linear Fitness and Finite Genome Length

Science.gov (United States)

Saakian, David B.

2017-08-01

We considered the infinite population version of the mutator phenomenon in evolutionary dynamics, looking at the uni-directional mutations in the mutator-specific genes and linear selection. We solved exactly the model for the finite genome length case, looking at the quasispecies version of the phenomenon. We calculated the mutator probability both in the statics and dynamics. The exact solution is important for us because the mutator probability depends on the genome length in a highly non-trivial way.

Exact results on diffusion in a piecewise linear potential with a time-dependent sink

Energy Technology Data Exchange (ETDEWEB)

Diwaker, E-mail: diwakerphysics@gmail.com [Central University of Himachal Pradesh, School of Physical and Astronomical Sciences (India); Chakraborty, Aniruddha [Indian Institute of Technology Mandi (India)

2016-02-15

The Smoluchowski equation with a time-dependent sink term is solved exactly. In this method, knowing the probability distribution P(0, s) at the origin, allows deriving the probability distribution P(x, s) at all positions. Exact solutions of the Smoluchowski equation are also provided in different cases where the sink term has linear, constant, inverse, and exponential variation in time.

Probability in quantum mechanics

Directory of Open Access Journals (Sweden)

J. G. Gilson

1982-01-01

Full Text Available By using a fluid theory which is an alternative to quantum theory but from which the latter can be deduced exactly, the long-standing problem of how quantum mechanics is related to stochastic processes is studied. It can be seen how the Schrödinger probability density has a relationship to time spent on small sections of an orbit, just as the probability density has in some classical contexts.

Protein single-model quality assessment by feature-based probability density functions.

Science.gov (United States)

Cao, Renzhi; Cheng, Jianlin

2016-04-04

Protein quality assessment (QA) has played an important role in protein structure prediction. We developed a novel single-model quality assessment method-Qprob. Qprob calculates the absolute error for each protein feature value against the true quality scores (i.e. GDT-TS scores) of protein structural models, and uses them to estimate its probability density distribution for quality assessment. Qprob has been blindly tested on the 11th Critical Assessment of Techniques for Protein Structure Prediction (CASP11) as MULTICOM-NOVEL server. The official CASP result shows that Qprob ranks as one of the top single-model QA methods. In addition, Qprob makes contributions to our protein tertiary structure predictor MULTICOM, which is officially ranked 3rd out of 143 predictors. The good performance shows that Qprob is good at assessing the quality of models of hard targets. These results demonstrate that this new probability density distribution based method is effective for protein single-model quality assessment and is useful for protein structure prediction. The webserver of Qprob is available at: http://calla.rnet.missouri.edu/qprob/. The software is now freely available in the web server of Qprob.

Limiting values of large deviation probabilities of quadratic statistics

NARCIS (Netherlands)

Jeurnink, Gerardus A.M.; Kallenberg, W.C.M.

1990-01-01

Application of exact Bahadur efficiencies in testing theory or exact inaccuracy rates in estimation theory needs evaluation of large deviation probabilities. Because of the complexity of the expressions, frequently a local limit of the nonlocal measure is considered. Local limits of large deviation

Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics

International Nuclear Information System (INIS)

Niven, Robert K.

2005-01-01

The exact Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) entropies and probabilistic distributions are derived by the combinatorial method of Boltzmann, without Stirling's approximation. The new entropy measures are explicit functions of the probability and degeneracy of each state, and the total number of entities, N. By analysis of the cost of a 'binary decision', exact BE and FD statistics are shown to have profound consequences for the behaviour of quantum mechanical systems

Probability 1/e

Science.gov (United States)

Koo, Reginald; Jones, Martin L.

2011-01-01

Quite a number of interesting problems in probability feature an event with probability equal to 1/e. This article discusses three such problems and attempts to explain why this probability occurs with such frequency.

Development of a new model to evaluate the probability of automatic plant trips for pressurized water reactors

Energy Technology Data Exchange (ETDEWEB)

Shimada, Yoshio [Institute of Nuclear Safety System Inc., Mihama, Fukui (Japan); Kawai, Katsunori; Suzuki, Hiroshi [Mitsubishi Heavy Industries Ltd., Tokyo (Japan)

2001-09-01

In order to improve the reliability of plant operations for pressurized water reactors, a new fault tree model was developed to evaluate the probability of automatic plant trips. This model consists of fault trees for sixteen systems. It has the following features: (1) human errors and transmission line incidents are modeled by the existing data, (2) the repair of failed components is considered to calculate the failure probability of components, (3) uncertainty analysis is performed by an exact method. From the present results, it is confirmed that the obtained upper and lower bound values of the automatic plant trip probability are within the existing data bound in Japan. Thereby this model can be applicable to the prediction of plant performance and reliability. (author)

Exact combinatorial approach to finite coagulating systems

Science.gov (United States)

Fronczak, Agata; Chmiel, Anna; Fronczak, Piotr

2018-02-01

This paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, an exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters, and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.

Dynamical Response of Networks Under External Perturbations: Exact Results

Science.gov (United States)

Chinellato, David D.; Epstein, Irving R.; Braha, Dan; Bar-Yam, Yaneer; de Aguiar, Marcus A. M.

2015-04-01

We give exact statistical distributions for the dynamic response of influence networks subjected to external perturbations. We consider networks whose nodes have two internal states labeled 0 and 1. We let nodes be frozen in state 0, in state 1, and the remaining nodes change by adopting the state of a connected node with a fixed probability per time step. The frozen nodes can be interpreted as external perturbations to the subnetwork of free nodes. Analytically extending and to be smaller than 1 enables modeling the case of weak coupling. We solve the dynamical equations exactly for fully connected networks, obtaining the equilibrium distribution, transition probabilities between any two states and the characteristic time to equilibration. Our exact results are excellent approximations for other topologies, including random, regular lattice, scale-free and small world networks, when the numbers of fixed nodes are adjusted to take account of the effect of topology on coupling to the environment. This model can describe a variety of complex systems, from magnetic spins to social networks to population genetics, and was recently applied as a framework for early warning signals for real-world self-organized economic market crises.

Estimating the Probability of Wind Ramping Events: A Data-driven Approach

OpenAIRE

Wang, Cheng; Wei, Wei; Wang, Jianhui; Qiu, Feng

2016-01-01

This letter proposes a data-driven method for estimating the probability of wind ramping events without exploiting the exact probability distribution function (PDF) of wind power. Actual wind data validates the proposed method.

Model checking exact cost for attack scenarios

DEFF Research Database (Denmark)

Aslanyan, Zaruhi; Nielson, Flemming

2017-01-01

Attack trees constitute a powerful tool for modelling security threats. Many security analyses of attack trees can be seamlessly expressed as model checking of Markov Decision Processes obtained from the attack trees, thus reaping the benefits of a coherent framework and a mature tool support....... However, current model checking does not encompass the exact cost analysis of an attack, which is standard for attack trees. Our first contribution is the logic erPCTL with cost-related operators. The extended logic allows to analyse the probability of an event satisfying given cost bounds and to compute...... the exact cost of an event. Our second contribution is the model checking algorithm for erPCTL. Finally, we apply our framework to the analysis of attack trees....

Exactly soluble matrix models

International Nuclear Information System (INIS)

Raju Viswanathan, R.

1991-09-01

We study examples of one dimensional matrix models whose potentials possess an energy spectrum that can be explicitly determined. This allows for an exact solution in the continuum limit. Specifically, step-like potentials and the Morse potential are considered. The step-like potentials show no scaling behaviour and the Morse potential (which corresponds to a γ = -1 model) has the interesting feature that there are no quantum corrections to the scaling behaviour in the continuum limit. (author). 5 refs

Exact probability distribution function for the volatility of cumulative production

Science.gov (United States)

Zadourian, Rubina; Klümper, Andreas

2018-04-01

In this paper we study the volatility and its probability distribution function for the cumulative production based on the experience curve hypothesis. This work presents a generalization of the study of volatility in Lafond et al. (2017), which addressed the effects of normally distributed noise in the production process. Due to its wide applicability in industrial and technological activities we present here the mathematical foundation for an arbitrary distribution function of the process, which we expect will pave the future research on forecasting of the production process.

Disadvantage factors for square lattice cells using a collision probability method

International Nuclear Information System (INIS)

Raghav, H.P.

1976-01-01

The flux distribution in an infinite square lattice consisting of cylindrical fuel rods and moderator is calculated by using a collision probability method. Neutrons are assumed to be monoenergetic and the sources as well as scattering are assumed to be isotropic. Carlvik's method for the calculation of collision probability is used. The important features of the method are that the square boundary is treated exactly and the contribution of the surrounding cells is calculated explicitly. The method is programmed in a computer code CELLC. This carries out integration by Simpson's rule. The convergence and accuracy of CELLC is assessed by computing disadvantage factors for the well-known Thie lattices and comparing the results with Monte Carlo and other integral transport theory methods used elsewhere. It is demonstrated that it is not correct to apply the white boundary condition in the Wigner Seitz Cell for low pitch and low cross sections. (orig.) [de

Constructing exact symmetric informationally complete measurements from numerical solutions

Science.gov (United States)

Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne

2018-04-01

Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.

Probable Inference and Quantum Mechanics

International Nuclear Information System (INIS)

Grandy, W. T. Jr.

2009-01-01

In its current very successful interpretation the quantum theory is fundamentally statistical in nature. Although commonly viewed as a probability amplitude whose (complex) square is a probability, the wavefunction or state vector continues to defy consensus as to its exact meaning, primarily because it is not a physical observable. Rather than approach this problem directly, it is suggested that it is first necessary to clarify the precise role of probability theory in quantum mechanics, either as applied to, or as an intrinsic part of the quantum theory. When all is said and done the unsurprising conclusion is that quantum mechanics does not constitute a logic and probability unto itself, but adheres to the long-established rules of classical probability theory while providing a means within itself for calculating the relevant probabilities. In addition, the wavefunction is seen to be a description of the quantum state assigned by an observer based on definite information, such that the same state must be assigned by any other observer based on the same information, in much the same way that probabilities are assigned.

Exact outage analysis of incremental decode-and-forward opportunistic relaying

KAUST Repository

Tourki, Kamel; Yang, Hongchuan; Alouini, Mohamed-Slim

2010-01-01

In this paper, we investigate a dual-hop decode-andforward opportunistic relaying scheme where the selected relay chooses to cooperate only if the source-destination channel is of an unacceptable quality. In our study, we derive exact closed-form expression for the outage probability based on the exact statistics of each hop. Furthermore, we perform asymptotic analysis and we deduce the diversity order of the scheme. We validate our analysis by showing that performance simulation results coincide with our analytical results over different network architectures. © 2010 IEEE.

Exact outage analysis of incremental decode-and-forward opportunistic relaying

KAUST Repository

Tourki, Kamel

2010-11-01

In this paper, we investigate a dual-hop decode-andforward opportunistic relaying scheme where the selected relay chooses to cooperate only if the source-destination channel is of an unacceptable quality. In our study, we derive exact closed-form expression for the outage probability based on the exact statistics of each hop. Furthermore, we perform asymptotic analysis and we deduce the diversity order of the scheme. We validate our analysis by showing that performance simulation results coincide with our analytical results over different network architectures. © 2010 IEEE.

Quantum Probabilities as Behavioral Probabilities

Directory of Open Access Journals (Sweden)

Vyacheslav I. Yukalov

2017-03-01

Full Text Available We demonstrate that behavioral probabilities of human decision makers share many common features with quantum probabilities. This does not imply that humans are some quantum objects, but just shows that the mathematics of quantum theory is applicable to the description of human decision making. The applicability of quantum rules for describing decision making is connected with the nontrivial process of making decisions in the case of composite prospects under uncertainty. Such a process involves deliberations of a decision maker when making a choice. In addition to the evaluation of the utilities of considered prospects, real decision makers also appreciate their respective attractiveness. Therefore, human choice is not based solely on the utility of prospects, but includes the necessity of resolving the utility-attraction duality. In order to justify that human consciousness really functions similarly to the rules of quantum theory, we develop an approach defining human behavioral probabilities as the probabilities determined by quantum rules. We show that quantum behavioral probabilities of humans do not merely explain qualitatively how human decisions are made, but they predict quantitative values of the behavioral probabilities. Analyzing a large set of empirical data, we find good quantitative agreement between theoretical predictions and observed experimental data.

Recurrent formulas and some exact relations for radial integrals with Dirac and Schroedinger wave functions

International Nuclear Information System (INIS)

Shabaev, V.M.

1984-01-01

Some exact relations are derived for radial integrals with Dirac wave functions. These relations are used for calculating radial integrals in the case of the Coulomb field. The threedimensional harmonic oscillator is also considered and exact formulae for the dipole transition probabilities are obtained using general relations between matrix elements

Exact critical properties of two-dimensional polymer networks from conformal invariance

International Nuclear Information System (INIS)

Duplantier, B.

1988-03-01

An infinity of exact critical exponents for two-dimensional self-avoiding walks can be derived from conformal invariance and Coulomb gas techniques applied to the O(n) model and to the Potts model. They apply to polymer networks of any topology, for which a general scaling theory is given, valid in any dimension d. The infinite set of exponents has also been calculated to O(ε 2 ), for d=4-ε. The 2D study also includes other universality classes like the dense polymers, the Hamiltonian walks, the polymers at their θ-point. Exact correlation functions can be further given for Hamiltonian walks, and exact winding angle probability distributions for the self-avoiding walks

Finite-size scaling of survival probability in branching processes

OpenAIRE

Garcia-Millan, Rosalba; Font-Clos, Francesc; Corral, Alvaro

2014-01-01

Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We reveal the finite-size scaling law of the survival probability for a given branching process ruled by a probability distribution of the number of offspring per element whose standard deviation is finite, obtaining the exact scaling function as well as the critical exponents. Our findings prove the universal behavi...

Probability an introduction

CERN Document Server

Grimmett, Geoffrey

2014-01-01

Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains. A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit th...

Fitness Probability Distribution of Bit-Flip Mutation.

Science.gov (United States)

Chicano, Francisco; Sutton, Andrew M; Whitley, L Darrell; Alba, Enrique

2015-01-01

Bit-flip mutation is a common mutation operator for evolutionary algorithms applied to optimize functions over binary strings. In this paper, we develop results from the theory of landscapes and Krawtchouk polynomials to exactly compute the probability distribution of fitness values of a binary string undergoing uniform bit-flip mutation. We prove that this probability distribution can be expressed as a polynomial in p, the probability of flipping each bit. We analyze these polynomials and provide closed-form expressions for an easy linear problem (Onemax), and an NP-hard problem, MAX-SAT. We also discuss a connection of the results with runtime analysis.

Stochastic approximation Monte Carlo importance sampling for approximating exact conditional probabilities

KAUST Repository

Cheon, Sooyoung

2013-02-16

Importance sampling and Markov chain Monte Carlo methods have been used in exact inference for contingency tables for a long time, however, their performances are not always very satisfactory. In this paper, we propose a stochastic approximation Monte Carlo importance sampling (SAMCIS) method for tackling this problem. SAMCIS is a combination of adaptive Markov chain Monte Carlo and importance sampling, which employs the stochastic approximation Monte Carlo algorithm (Liang et al., J. Am. Stat. Assoc., 102(477):305-320, 2007) to draw samples from an enlarged reference set with a known Markov basis. Compared to the existing importance sampling and Markov chain Monte Carlo methods, SAMCIS has a few advantages, such as fast convergence, ergodicity, and the ability to achieve a desired proportion of valid tables. The numerical results indicate that SAMCIS can outperform the existing importance sampling and Markov chain Monte Carlo methods: It can produce much more accurate estimates in much shorter CPU time than the existing methods, especially for the tables with high degrees of freedom. © 2013 Springer Science+Business Media New York.

Stochastic approximation Monte Carlo importance sampling for approximating exact conditional probabilities

KAUST Repository

Cheon, Sooyoung; Liang, Faming; Chen, Yuguo; Yu, Kai

2013-01-01

Importance sampling and Markov chain Monte Carlo methods have been used in exact inference for contingency tables for a long time, however, their performances are not always very satisfactory. In this paper, we propose a stochastic approximation Monte Carlo importance sampling (SAMCIS) method for tackling this problem. SAMCIS is a combination of adaptive Markov chain Monte Carlo and importance sampling, which employs the stochastic approximation Monte Carlo algorithm (Liang et al., J. Am. Stat. Assoc., 102(477):305-320, 2007) to draw samples from an enlarged reference set with a known Markov basis. Compared to the existing importance sampling and Markov chain Monte Carlo methods, SAMCIS has a few advantages, such as fast convergence, ergodicity, and the ability to achieve a desired proportion of valid tables. The numerical results indicate that SAMCIS can outperform the existing importance sampling and Markov chain Monte Carlo methods: It can produce much more accurate estimates in much shorter CPU time than the existing methods, especially for the tables with high degrees of freedom. © 2013 Springer Science+Business Media New York.

Pade approximant calculations for neutron escape probability

International Nuclear Information System (INIS)

El Wakil, S.A.; Saad, E.A.; Hendi, A.A.

1984-07-01

The neutron escape probability from a non-multiplying slab containing internal source is defined in terms of a functional relation for the scattering function for the diffuse reflection problem. The Pade approximant technique is used to get numerical results which compare with exact results. (author)

LAMP-B: a Fortran program set for the lattice cell analysis by collision probability method

International Nuclear Information System (INIS)

Tsuchihashi, Keiichiro

1979-02-01

Nature of physical problem solved: LAMB-B solves an integral transport equation by the collision probability method for many variety of lattice cell geometries: spherical, plane and cylindrical lattice cell; square and hexagonal arrays of pin rods; annular clusters and square clusters. LAMP-B produces homogenized constants for multi and/or few group diffusion theory programs. Method of solution: LAMP-B performs an exact numerical integration to obtain the collision probabilities. Restrictions on the complexity of the problem: Not more than 68 group in the fast group calculation, and not more than 20 regions in the resonance integral calculation. Typical running time: It varies with the number of energy groups and the selection of the geometry. Unusual features of the program: Any or any combination of constituent subprograms can be used so that the partial use of this program is available. (author)

Exactly and quasi-exactly solvable 'discrete' quantum mechanics.

Science.gov (United States)

Sasaki, Ryu

2011-03-28

A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.

Observations of the interstellar ice grain feature in the Taurus molecular clouds

International Nuclear Information System (INIS)

Whittet, D.C.B.; Longmore, A.J.; Baines, D.W.T.; Evans, A.

1984-01-01

Although water ice was originally proposed as a major constituent of the interstellar grain population, the advent of infrared astronomy has shown that the expected absorption due to O-H stretching vibrations at 3 μm is illusive. Observations have in fact revealed that the carrier of this feature is apparently restricted to regions deep within dense molecular clouds. However, the exact carrier of this feature is still controversial, and many questions remain as to the conditions required for its appearance. The Taurus molecular clouds were selected for observations, in the form of a preliminary survey in the 2-4 μm window. It is concluded that the carrier of the 3μm absorption feature appears to reside in the general cloud medium and is probably amorphous water ice. (author)

Exactly soluble two-state quantum models with linear couplings

International Nuclear Information System (INIS)

Torosov, B T; Vitanov, N V

2008-01-01

A class of exact analytic solutions of the time-dependent Schroedinger equation is presented for a two-state quantum system coherently driven by a nonresonant external field. The coupling is a linear function of time with a finite duration and the detuning is constant. Four special models are considered in detail, namely the shark, double-shark, tent and zigzag models. The exact solution is derived by rotation of the Landau-Zener propagator at an angle of π/4 and is expressed in terms of Weber's parabolic cylinder function. Approximations for the transition probabilities are derived for all four models by using the asymptotics of the Weber function; these approximations demonstrate various effects of physical interest for each model

Conditional non-independence of radiographic image features and the derivation of post-test probabilities – A mammography BI-RADS example

International Nuclear Information System (INIS)

Benndorf, Matthias

2012-01-01

Bayes' theorem has proven to be one of the cornerstones in medical decision making. It allows for the derivation of post-test probabilities, which in case of a positive test result become positive predictive values. If several test results are observed successively Bayes' theorem may be used with assumed conditional independence of test results or with incorporated conditional dependencies. Herein it is examined whether radiographic image features should be considered conditionally independent diagnostic tests when post-test probabilities are to be derived. For this purpose the mammographic mass dataset from the UCI (University of California, Irvine) machine learning repository is analysed. It comprises the description of 961 (516 benign, 445 malignant) mammographic mass lesions according to the BI-RADS (Breast Imaging: Reporting and Data System) lexicon. Firstly, an exhaustive correlation matrix is presented for mammography BI-RADS features among benign and malignant lesions separately; correlation can be regarded as measure for conditional dependence. Secondly, it is shown that the derived positive predictive values for the conjunction of the two features “irregular shape” and “spiculated margin” differ significantly depending on whether conditional dependencies are incorporated into the decision process or not. It is concluded that radiographic image features should not generally be regarded as conditionally independent diagnostic tests.

Dysphonic Voice Pattern Analysis of Patients in Parkinson’s Disease Using Minimum Interclass Probability Risk Feature Selection and Bagging Ensemble Learning Methods

Directory of Open Access Journals (Sweden)

Yunfeng Wu

2017-01-01

Full Text Available Analysis of quantified voice patterns is useful in the detection and assessment of dysphonia and related phonation disorders. In this paper, we first study the linear correlations between 22 voice parameters of fundamental frequency variability, amplitude variations, and nonlinear measures. The highly correlated vocal parameters are combined by using the linear discriminant analysis method. Based on the probability density functions estimated by the Parzen-window technique, we propose an interclass probability risk (ICPR method to select the vocal parameters with small ICPR values as dominant features and compare with the modified Kullback-Leibler divergence (MKLD feature selection approach. The experimental results show that the generalized logistic regression analysis (GLRA, support vector machine (SVM, and Bagging ensemble algorithm input with the ICPR features can provide better classification results than the same classifiers with the MKLD selected features. The SVM is much better at distinguishing normal vocal patterns with a specificity of 0.8542. Among the three classification methods, the Bagging ensemble algorithm with ICPR features can identify 90.77% vocal patterns, with the highest sensitivity of 0.9796 and largest area value of 0.9558 under the receiver operating characteristic curve. The classification results demonstrate the effectiveness of our feature selection and pattern analysis methods for dysphonic voice detection and measurement.

Path probabilities of continuous time random walks

International Nuclear Information System (INIS)

Eule, Stephan; Friedrich, Rudolf

2014-01-01

Employing the path integral formulation of a broad class of anomalous diffusion processes, we derive the exact relations for the path probability densities of these processes. In particular, we obtain a closed analytical solution for the path probability distribution of a Continuous Time Random Walk (CTRW) process. This solution is given in terms of its waiting time distribution and short time propagator of the corresponding random walk as a solution of a Dyson equation. Applying our analytical solution we derive generalized Feynman–Kac formulae. (paper)

An exact solution of the extinction problem in supercritical multiplying systems

International Nuclear Information System (INIS)

Williams, M.M.R.

1979-01-01

Using the point model approximation and one-speed theory with no delayed neutrons a probability balance equation for neutrons by the backward method has been constructed. This probability gives the distribution of neutrons in a multiplying medium at a given time and also the distribution that a chain will have generated a specified number of neutrons before extinction. We consider the limit of this probability for super and subcritical systems for long times after the initial triggering neutron. This leads to the extinction probability and to the individual probabilities of neutron population. To obtain specific results we have used a variety of models for the neutron multiplicity in the fission process, ie Poisson, birth and death, geometric and binomial. Exact solutions for the extinction probability have been obtained and its sensitivity to various parameters examined. Finally, we use the 'quadratic approximation' and assess its accuracy; it is found to overestimate the extinction probability and to be useful only for multiplication factors near unity. (author)

Boundary conditions of the exact impulse wave function

International Nuclear Information System (INIS)

Gravielle, M.; Miraglia, J.E.

1997-01-01

The behavior of the exact impulse wave function is investigated at intermediate and high impact energies. Numerical details of the wave function and its perturbative potential are reported. We conclude that the impulse wave function does not tend to the proper Coulomb asymptotic limit. For electron capture, however, it is shown that the impulse wave function produces reliable probabilities even for intermediate velocities and symmetric collision systems. copyright 1997 The American Physical Society

Quasi-exact solvability

International Nuclear Information System (INIS)

Ushveridze, A.G.

1992-01-01

This paper reports that quasi-exactly solvable (QES) models realize principally new type of exact solvability in quantum physics. These models are distinguished by the fact that the Schrodinger equations for them can be solved exactly only for certain limited parts of the spectrum, but not for the whole spectrum. They occupy an intermediate position between the exactly the authors solvable (ES) models and all the others. The number of energy levels for which the spectral problems can be solved exactly refer below to as the order of QES model. From the mathematical point of view the existence of QES models is not surprising. Indeed, if the term exact solvability expresses the possibility of total explicit diagonalization of infinite Hamiltonian matrix, then the term quasi-exact solvability implies the situation when the Hamiltonian matrix can be reduced explicitly to the block-diagonal form with one of the appearing blocks being finite

Computer program determines exact two-sided tolerance limits for normal distributions

Science.gov (United States)

Friedman, H. A.; Webb, S. R.

1968-01-01

Computer program determines by numerical integration the exact statistical two-sided tolerance limits, when the proportion between the limits is at least a specified number. The program is limited to situations in which the underlying probability distribution for the population sampled is the normal distribution with unknown mean and variance.

ExactPack Documentation

Energy Technology Data Exchange (ETDEWEB)

Singleton, Robert Jr. [Los Alamos National Laboratory; Israel, Daniel M. [Los Alamos National Laboratory; Doebling, Scott William [Los Alamos National Laboratory; Woods, Charles Nathan [Los Alamos National Laboratory; Kaul, Ann [Los Alamos National Laboratory; Walter, John William Jr [Los Alamos National Laboratory; Rogers, Michael Lloyd [Los Alamos National Laboratory

2016-05-09

For code verification, one compares the code output against known exact solutions. There are many standard test problems used in this capacity, such as the Noh and Sedov problems. ExactPack is a utility that integrates many of these exact solution codes into a common API (application program interface), and can be used as a stand-alone code or as a python package. ExactPack consists of python driver scripts that access a library of exact solutions written in Fortran or Python. The spatial profiles of the relevant physical quantities, such as the density, fluid velocity, sound speed, or internal energy, are returned at a time specified by the user. The solution profiles can be viewed and examined by a command line interface or a graphical user interface, and a number of analysis tools and unit tests are also provided. We have documented the physics of each problem in the solution library, and provided complete documentation on how to extend the library to include additional exact solutions. ExactPack’s code architecture makes it easy to extend the solution-code library to include additional exact solutions in a robust, reliable, and maintainable manner.

Finding optimal exact reducts

KAUST Repository

AbouEisha, Hassan M.

2014-01-01

The problem of attribute reduction is an important problem related to feature selection and knowledge discovery. The problem of finding reducts with minimum cardinality is NP-hard. This paper suggests a new algorithm for finding exact reducts with minimum cardinality. This algorithm transforms the initial table to a decision table of a special kind, apply a set of simplification steps to this table, and use a dynamic programming algorithm to finish the construction of an optimal reduct. I present results of computer experiments for a collection of decision tables from UCIML Repository. For many of the experimented tables, the simplification steps solved the problem.

Exact time-dependent exchange-correlation potentials for strong-field electron dynamics

International Nuclear Information System (INIS)

Lein, Manfred; Kuemmel, Stephan

2005-01-01

By solving the time-dependent Schroedinger equation and inverting the time-dependent Kohn-Sham scheme we obtain the exact time-dependent exchange-correlation potential of density-functional theory for the strong-field dynamics of a correlated system. We demonstrate that essential features of the exact exchange-correlation potential can be related to derivative discontinuities in stationary density-functional theory. Incorporating the discontinuity in a time-dependent density-functional calculation greatly improves the description of the ionization process

Exact Turbulence Law in Collisionless Plasmas: Hybrid Simulations

Science.gov (United States)

Hellinger, P.; Verdini, A.; Landi, S.; Franci, L.; Matteini, L.

2017-12-01

An exact vectorial law for turbulence in homogeneous incompressible Hall-MHD is derived and tested in two-dimensional hybrid simulations of plasma turbulence. The simulations confirm the validity of the MHD exact law in the kinetic regime, the simulated turbulence exhibits a clear inertial range on large scales where the MHD cascade flux dominates. The simulation results also indicate that in the sub-ion range the cascade continues via the Hall term and that the total cascade rate tends to decrease at around the ion scales, especially in high-beta plasmas. This decrease is like owing to formation of non-thermal features, such as collisionless ion energization, that can not be retained in the Hall MHD approximation.

A first course in probability

CERN Document Server

Ross, Sheldon

2014-01-01

A First Course in Probability, Ninth Edition, features clear and intuitive explanations of the mathematics of probability theory, outstanding problem sets, and a variety of diverse examples and applications. This book is ideal for an upper-level undergraduate or graduate level introduction to probability for math, science, engineering and business students. It assumes a background in elementary calculus.

Analytic formulation of neutrino oscillation probability in constant matter

International Nuclear Information System (INIS)

Kimura, Keiichi; Takamura, Akira; Yokomakura, Hidekazu

2003-01-01

In this paper, based on the work (Kimura K et al 2002 Phys. Lett. B 537 86) we present the simple derivation of an exact and analytic formula for neutrino oscillation probability. We consider three flavour neutrino oscillations in matter with constant density

Exact Time-Dependent Exchange-Correlation Potential in Electron Scattering Processes

Science.gov (United States)

Suzuki, Yasumitsu; Lacombe, Lionel; Watanabe, Kazuyuki; Maitra, Neepa T.

2017-12-01

We identify peak and valley structures in the exact exchange-correlation potential of time-dependent density functional theory that are crucial for time-resolved electron scattering in a model one-dimensional system. These structures are completely missed by adiabatic approximations that, consequently, significantly underestimate the scattering probability. A recently proposed nonadiabatic approximation is shown to correctly capture the approach of the electron to the target when the initial Kohn-Sham state is chosen judiciously, and it is more accurate than standard adiabatic functionals but ultimately fails to accurately capture reflection. These results may explain the underestimation of scattering probabilities in some recent studies on molecules and surfaces.

Fingerprints of exceptional points in the survival probability of resonances in atomic spectra

International Nuclear Information System (INIS)

Cartarius, Holger; Moiseyev, Nimrod

2011-01-01

The unique time signature of the survival probability exactly at the exceptional point parameters is studied here for the hydrogen atom in strong static magnetic and electric fields. We show that indeed the survival probability S(t)=| | 2 decays exactly as |1-at| 2 e -Γ EP t/(ℎ/2π) , where Γ EP is associated with the decay rate at the exceptional point and a is a complex constant depending solely on the initial wave packet that populates exclusively the two almost degenerate states of the non-Hermitian Hamiltonian. This may open the possibility for a first experimental detection of exceptional points in a quantum system.

Fingerprints of exceptional points in the survival probability of resonances in atomic spectra

Science.gov (United States)

Cartarius, Holger; Moiseyev, Nimrod

2011-07-01

The unique time signature of the survival probability exactly at the exceptional point parameters is studied here for the hydrogen atom in strong static magnetic and electric fields. We show that indeed the survival probability S(t)=||2 decays exactly as |1-at|2e-ΓEPt/ℏ, where ΓEP is associated with the decay rate at the exceptional point and a is a complex constant depending solely on the initial wave packet that populates exclusively the two almost degenerate states of the non-Hermitian Hamiltonian. This may open the possibility for a first experimental detection of exceptional points in a quantum system.

Linear positivity and virtual probability

International Nuclear Information System (INIS)

Hartle, James B.

2004-01-01

We investigate the quantum theory of closed systems based on the linear positivity decoherence condition of Goldstein and Page. The objective of any quantum theory of a closed system, most generally the universe, is the prediction of probabilities for the individual members of sets of alternative coarse-grained histories of the system. Quantum interference between members of a set of alternative histories is an obstacle to assigning probabilities that are consistent with the rules of probability theory. A quantum theory of closed systems therefore requires two elements: (1) a condition specifying which sets of histories may be assigned probabilities and (2) a rule for those probabilities. The linear positivity condition of Goldstein and Page is the weakest of the general conditions proposed so far. Its general properties relating to exact probability sum rules, time neutrality, and conservation laws are explored. Its inconsistency with the usual notion of independent subsystems in quantum mechanics is reviewed. Its relation to the stronger condition of medium decoherence necessary for classicality is discussed. The linear positivity of histories in a number of simple model systems is investigated with the aim of exhibiting linearly positive sets of histories that are not decoherent. The utility of extending the notion of probability to include values outside the range of 0-1 is described. Alternatives with such virtual probabilities cannot be measured or recorded, but can be used in the intermediate steps of calculations of real probabilities. Extended probabilities give a simple and general way of formulating quantum theory. The various decoherence conditions are compared in terms of their utility for characterizing classicality and the role they might play in further generalizations of quantum mechanics

Quantum decay model with exact explicit analytical solution

Science.gov (United States)

Marchewka, Avi; Granot, Er'El

2009-01-01

A simple decay model is introduced. The model comprises a point potential well, which experiences an abrupt change. Due to the temporal variation, the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a fractional power law, which differs from perturbation quantum method predictions. At long times the decay includes oscillations with an envelope that decays algebraically. This is a model where the final state can be either continuous or localized, and that has an exact analytical solution.

Exact analytic solutions for Mikheyev-Smirnov-Wolfenstein level crossings

International Nuclear Information System (INIS)

Noetzold, D.

1987-01-01

An exact formula for the transition probability in level-crossing phenomena is derived for a general case, ranging from adiabatic to sudden crossings. This is done in the context of neutrino flavor oscillations for the Mikheyev-Smirnov-Wolfenstein (MSW) effect, where hitherto only numerical or approximate solutions were obtained. The matter density or level splitting is assumed to be governed by a hyperbolic-tangent function which, however, can change arbitrarily fast between two constant values. For example, in context of the MSW effect this furnishes a nice fit to the solar density determining the level crossing of solar neutrinos. In the quasiadiabatic limit the exact Landau-Zener factor can be read off, correcting some expressions obtained so far. Even in the opposite limit of a sudden level crossing a conversion is found, which can have far-reaching consequences for neutrino detection on Earth

Failure probability under parameter uncertainty.

Science.gov (United States)

Gerrard, R; Tsanakas, A

2011-05-01

In many problems of risk analysis, failure is equivalent to the event of a random risk factor exceeding a given threshold. Failure probabilities can be controlled if a decisionmaker is able to set the threshold at an appropriate level. This abstract situation applies, for example, to environmental risks with infrastructure controls; to supply chain risks with inventory controls; and to insurance solvency risks with capital controls. However, uncertainty around the distribution of the risk factor implies that parameter error will be present and the measures taken to control failure probabilities may not be effective. We show that parameter uncertainty increases the probability (understood as expected frequency) of failures. For a large class of loss distributions, arising from increasing transformations of location-scale families (including the log-normal, Weibull, and Pareto distributions), the article shows that failure probabilities can be exactly calculated, as they are independent of the true (but unknown) parameters. Hence it is possible to obtain an explicit measure of the effect of parameter uncertainty on failure probability. Failure probability can be controlled in two different ways: (1) by reducing the nominal required failure probability, depending on the size of the available data set, and (2) by modifying of the distribution itself that is used to calculate the risk control. Approach (1) corresponds to a frequentist/regulatory view of probability, while approach (2) is consistent with a Bayesian/personalistic view. We furthermore show that the two approaches are consistent in achieving the required failure probability. Finally, we briefly discuss the effects of data pooling and its systemic risk implications. © 2010 Society for Risk Analysis.

RePS: a sequence assembler that masks exact repeats identified from the shotgun data

DEFF Research Database (Denmark)

Wang, Jun; Wong, Gane Ka-Shu; Ni, Peixiang

2002-01-01

We describe a sequence assembler, RePS (repeat-masked Phrap with scaffolding), that explicitly identifies exact 20mer repeats from the shotgun data and removes them prior to the assembly. The established software is used to compute meaningful error probabilities for each base. Clone......-end-pairing information is used to construct scaffolds that order and orient the contigs. We show with real data for human and rice that reasonable assemblies are possible even at coverages of only 4x to 6x, despite having up to 42.2% in exact repeats. Udgivelsesdato: 2002-May...

Improved bounds on the epidemic threshold of exact SIS models on complex networks

KAUST Repository

Ruhi, Navid Azizan; Thrampoulidis, Christos; Hassibi, Babak

2017-01-01

The SIS (susceptible-infected-susceptible) epidemic model on an arbitrary network, without making approximations, is a 2n-state Markov chain with a unique absorbing state (the all-healthy state). This makes analysis of the SIS model and, in particular, determining the threshold of epidemic spread quite challenging. It has been shown that the exact marginal probabilities of infection can be upper bounded by an n-dimensional linear time-invariant system, a consequence of which is that the Markov chain is “fast-mixing” when the LTI system is stable, i.e. when equation (where β is the infection rate per link, δ is the recovery rate, and λmax(A) is the largest eigenvalue of the network's adjacency matrix). This well-known threshold has been recently shown not to be tight in several cases, such as in a star network. In this paper, we provide tighter upper bounds on the exact marginal probabilities of infection, by also taking pairwise infection probabilities into account. Based on this improved bound, we derive tighter eigenvalue conditions that guarantee fast mixing (i.e., logarithmic mixing time) of the chain. We demonstrate the improvement of the threshold condition by comparing the new bound with the known one on various networks with various epidemic parameters.

Improved bounds on the epidemic threshold of exact SIS models on complex networks

KAUST Repository

Ruhi, Navid Azizan

2017-01-05

The SIS (susceptible-infected-susceptible) epidemic model on an arbitrary network, without making approximations, is a 2n-state Markov chain with a unique absorbing state (the all-healthy state). This makes analysis of the SIS model and, in particular, determining the threshold of epidemic spread quite challenging. It has been shown that the exact marginal probabilities of infection can be upper bounded by an n-dimensional linear time-invariant system, a consequence of which is that the Markov chain is “fast-mixing” when the LTI system is stable, i.e. when equation (where β is the infection rate per link, δ is the recovery rate, and λmax(A) is the largest eigenvalue of the network\\'s adjacency matrix). This well-known threshold has been recently shown not to be tight in several cases, such as in a star network. In this paper, we provide tighter upper bounds on the exact marginal probabilities of infection, by also taking pairwise infection probabilities into account. Based on this improved bound, we derive tighter eigenvalue conditions that guarantee fast mixing (i.e., logarithmic mixing time) of the chain. We demonstrate the improvement of the threshold condition by comparing the new bound with the known one on various networks with various epidemic parameters.

Exact capture probability analysis of GSC receivers over i.n.d. Rayleigh fading channels

KAUST Repository

Nam, Sungsik; Yang, Hongchuan; Alouini, Mohamed-Slim; Kim, Dongin

2013-01-01

variates. With this motivation in mind, we first provide in this paper some new order statistics results in terms of both moment generating function (MGF) and probability density function (PDF) expressions under an i.n.d. assumption and then derive a new

Precise Propagation of Upper and Lower Probability Bounds in System P

OpenAIRE

Gilio, Angelo

2000-01-01

In this paper we consider the inference rules of System P in the framework of coherent imprecise probabilistic assessments. Exploiting our algorithms, we propagate the lower and upper probability bounds associated with the conditional assertions of a given knowledge base, automatically obtaining the precise probability bounds for the derived conclusions of the inference rules. This allows a more flexible and realistic use of System P in default reasoning and provides an exact illustration of ...

Construction and study of exact ground states for a class of quantum antiferromagnets

International Nuclear Information System (INIS)

Fannes, M.

1989-01-01

Techniques of quantum probability are used to construct the exact ground states for a class of quantum spin systems in one dimension. This class in particular contains the antiferromagnetic models introduced by various authors under the name of VBS-models. The construction permits a detailed study of these ground states. (A.C.A.S.) [pt

Exact milestoning

International Nuclear Information System (INIS)

Bello-Rivas, Juan M.; Elber, Ron

2015-01-01

A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of the new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MD simulations on the system studied

Interference-exact radiative transfer equation

DEFF Research Database (Denmark)

Partanen, Mikko; Haÿrynen, Teppo; Oksanen, Jani

2017-01-01

Maxwell's equations with stochastic or quantum optical source terms accounting for the quantum nature of light. We show that both the nonlocal wave and local particle features associated with interference and emission of propagating fields in stratified geometries can be fully captured by local damping...... and scattering coefficients derived from the recently introduced quantized fluctuational electrodynamics (QFED) framework. In addition to describing the nonlocal optical interference processes as local directionally resolved effects, this allows reformulating the well known and widely used radiative transfer...... equation (RTE) as a physically transparent interference-exact model that extends the useful range of computationally efficient and quantum optically accurate interference-aware optical models from simple structures to full optical devices....

Determining the nucleation rate from the dimer growth probability

NARCIS (Netherlands)

Ter Horst, J.H.; Kashchiev, D.

2005-01-01

A new method is proposed for the determination of the stationary one-component nucleation rate J with the help of data for the growth probability P2 of a dimer which is the smallest cluster of the nucleating phase. The method is based on an exact formula relating J and P2, and is readily applicable

Accelerating rejection-based simulation of biochemical reactions with bounded acceptance probability

Energy Technology Data Exchange (ETDEWEB)

Thanh, Vo Hong, E-mail: vo@cosbi.eu [The Microsoft Research - University of Trento Centre for Computational and Systems Biology, Piazza Manifattura 1, Rovereto 38068 (Italy); Priami, Corrado, E-mail: priami@cosbi.eu [The Microsoft Research - University of Trento Centre for Computational and Systems Biology, Piazza Manifattura 1, Rovereto 38068 (Italy); Department of Mathematics, University of Trento, Trento (Italy); Zunino, Roberto, E-mail: roberto.zunino@unitn.it [Department of Mathematics, University of Trento, Trento (Italy)

2016-06-14

Stochastic simulation of large biochemical reaction networks is often computationally expensive due to the disparate reaction rates and high variability of population of chemical species. An approach to accelerate the simulation is to allow multiple reaction firings before performing update by assuming that reaction propensities are changing of a negligible amount during a time interval. Species with small population in the firings of fast reactions significantly affect both performance and accuracy of this simulation approach. It is even worse when these small population species are involved in a large number of reactions. We present in this paper a new approximate algorithm to cope with this problem. It is based on bounding the acceptance probability of a reaction selected by the exact rejection-based simulation algorithm, which employs propensity bounds of reactions and the rejection-based mechanism to select next reaction firings. The reaction is ensured to be selected to fire with an acceptance rate greater than a predefined probability in which the selection becomes exact if the probability is set to one. Our new algorithm improves the computational cost for selecting the next reaction firing and reduces the updating the propensities of reactions.

Does really Born-Oppenheimer approximation break down in charge transfer processes? An exactly solvable model

International Nuclear Information System (INIS)

Kuznetsov, Alexander M.; Medvedev, Igor G.

2006-01-01

Effects of deviation from the Born-Oppenheimer approximation (BOA) on the non-adiabatic transition probability for the transfer of a quantum particle in condensed media are studied within an exactly solvable model. The particle and the medium are modeled by a set of harmonic oscillators. The dynamic interaction of the particle with a single local mode is treated explicitly without the use of BOA. Two particular situations (symmetric and non-symmetric systems) are considered. It is shown that the difference between the exact solution and the true BOA is negligibly small at realistic parameters of the model. However, the exact results differ considerably from those of the crude Condon approximation (CCA) which is usually considered in the literature as a reference point for BOA (Marcus-Hush-Dogonadze formula). It is shown that the exact rate constant can be smaller (symmetric system) or larger (non-symmetric one) than that obtained in CCA. The non-Condon effects are also studied

An Exact Solution of The Neutron Slowing Down Equation

Energy Technology Data Exchange (ETDEWEB)

Stefanovic, D [Boris Kidric Vinca Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)

1970-07-01

The slowing down equation for an infinite homogeneous monoatomic medium is solved exactly. The cross sections depend on neutron energy. The solution is given in analytical form within each of the lethargy intervals. This analytical form is the sum of probabilities which are given by the Green functions. The calculated collision density is compared with the one obtained by Bednarz and also with an approximate Wigner formula for the case of a resonance not wider than one collision interval. For the special case of hydrogen, the present solution reduces to Bethe's solution. (author)

Counterexamples in probability

CERN Document Server

Stoyanov, Jordan M

2013-01-01

While most mathematical examples illustrate the truth of a statement, counterexamples demonstrate a statement's falsity. Enjoyable topics of study, counterexamples are valuable tools for teaching and learning. The definitive book on the subject in regards to probability, this third edition features the author's revisions and corrections plus a substantial new appendix.

' "~w.ith ~a'~nd"Atypz'cal Features

African Journals Online (AJOL)

2006-09-11

}? While there have been reports of ' this syndrome from ' Ibadan,' the exact incidence 1\\_Iigeria is It probably rare but it is alsoylikely that 'some. cases are missed in chm', 'cal due to poor awareness -and constraints' '.

Height probabilities in the Abelian sandpile model on the generalized finite Bethe lattice

Science.gov (United States)

Chen, Haiyan; Zhang, Fuji

2013-08-01

In this paper, we study the sandpile model on the generalized finite Bethe lattice with a particular boundary condition. Using a combinatorial method, we give the exact expressions for all single-site probabilities and some two-site joint probabilities. As a by-product, we prove that the height probabilities of bulk vertices are all the same for the Bethe lattice with certain given boundary condition, which was found from numerical evidence by Grassberger and Manna ["Some more sandpiles," J. Phys. (France) 51, 1077-1098 (1990)], 10.1051/jphys:0199000510110107700 but without a proof.

An exact solution for quantum tunneling in a dissipative system

International Nuclear Information System (INIS)

Yu, L.H.

1996-01-01

Applying a technique developed recently for a harmonic oscillator coupled to a bath of harmonic oscillators, we present an exact solution for the tunneling problem in an Ohmic dissipative system with inverted harmonic potential. The result shows that while the dissipation tends to suppress the tunneling, the Brownian motion tends to enhance the tunneling. Whether the tunneling rate increases or not would then depend on the initial conditions. We give a specific formula to calculate the tunneling probability determined by various parameters and the initial conditions

Exact performance analysis of MIMO cognitive radio systems using transmit antenna selection

KAUST Repository

Tourki, Kamel

2014-03-01

We consider in this paper, a spectrum sharing cognitive radio system with a ratio selection scheme; where one out of N independent-and-identically- distributed transmit antennas is selected such that the ratio of the secondary transmitter (ST) to the secondary receiver (SR) channel gain to the interference from the ST to the primary receiver (PR) channel gain is maximized. Although previous works considered perfect, outdated, or partial channel state information at the transmitter, we stress that using such assumptions may lead to a feedback overhead for updating the SR with the ST-PR interference channel estimation. Considering only statistical knowledge of the ST-PR channel gain, we investigate a ratio selection scheme using a mean value (MV)-based power allocation strategy referred to as MV-based scheme. We first provide the exact statistics in terms of probability density function and cumulative distribution function of the secondary channel gain as well as of the interference channel gain. Furthermore, we derive exact cumulative density function of the received signal-to-noise ratio at the SR where the ST uses a power allocation based on instantaneous perfect channel state information (CSI) referred to as CSI-based scheme. These statistics are then used to derive exact closed form expressions of the outage probability, symbol error rate, and ergodic capacity of the secondary system when the interference channel from the primary transmitter (PT) to the SR is ignored. Furthermore, an asymptotical analysis is also carried out for the MV-based scheme as well as for the CSI-based scheme to derive the generalized diversity gain for each. Subsequently, we address the performance analysis based on exact statistics of the combined signal-to-interference-plus- noise ratio at the SR of the more challenging case; when the PT-SR interference channel is considered. Numerical results in a Rayleigh fading environment manifest that the MV-based scheme outperforms the CSI

Probability an introduction with statistical applications

CERN Document Server

Kinney, John J

2014-01-01

Praise for the First Edition""This is a well-written and impressively presented introduction to probability and statistics. The text throughout is highly readable, and the author makes liberal use of graphs and diagrams to clarify the theory.""  - The StatisticianThoroughly updated, Probability: An Introduction with Statistical Applications, Second Edition features a comprehensive exploration of statistical data analysis as an application of probability. The new edition provides an introduction to statistics with accessible coverage of reliability, acceptance sampling, confidence intervals, h

Fractal supersymmetric QM, Geometric Probability and the Riemann Hypothesis

CERN Document Server

Castro, C

2004-01-01

The Riemann's hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form $ s_n =1/2+i\\lambda_n $. Earlier work on the RH based on supersymmetric QM, whose potential was related to the Gauss-Jacobi theta series, allows to provide the proper framework to construct the well defined algorithm to compute the probability to find a zero (an infinity of zeros) in the critical line. Geometric probability theory furnishes the answer to the very difficult question whether the probability that the RH is true is indeed equal to unity or not. To test the validity of this geometric probabilistic framework to compute the probability if the RH is true, we apply it directly to the the hyperbolic sine function $ \\sinh (s) $ case which obeys a trivial analog of the RH (the HSRH). Its zeros are equally spaced in the imaginary axis $ s_n = 0 + i n \\pi $. The geometric probability to find a zero (and an infinity of zeros) in the imaginary axis is exactly unity. We proceed with a fractal supersymme...

Stationary Probability and First-Passage Time of Biased Random Walk

International Nuclear Information System (INIS)

Li Jing-Wen; Tang Shen-Li; Xu Xin-Ping

2016-01-01

In this paper, we consider the stationary probability and first-passage time of biased random walk on 1D chain, where at each step the walker moves to the left and right with probabilities p and q respectively (0 ⩽ p, q ⩽ 1, p + q = 1). We derive exact analytical results for the stationary probability and first-passage time as a function of p and q for the first time. Our results suggest that the first-passage time shows a double power-law F ∼ (N − 1) γ , where the exponent γ = 2 for N < |p − q| −1 and γ = 1 for N > |p − q| −1 . Our study sheds useful insights into the biased random-walk process. (paper)

Multifractals embedded in short time series: An unbiased estimation of probability moment

Science.gov (United States)

Qiu, Lu; Yang, Tianguang; Yin, Yanhua; Gu, Changgui; Yang, Huijie

2016-12-01

An exact estimation of probability moments is the base for several essential concepts, such as the multifractals, the Tsallis entropy, and the transfer entropy. By means of approximation theory we propose a new method called factorial-moment-based estimation of probability moments. Theoretical prediction and computational results show that it can provide us an unbiased estimation of the probability moments of continuous order. Calculations on probability redistribution model verify that it can extract exactly multifractal behaviors from several hundred recordings. Its powerfulness in monitoring evolution of scaling behaviors is exemplified by two empirical cases, i.e., the gait time series for fast, normal, and slow trials of a healthy volunteer, and the closing price series for Shanghai stock market. By using short time series with several hundred lengths, a comparison with the well-established tools displays significant advantages of its performance over the other methods. The factorial-moment-based estimation can evaluate correctly the scaling behaviors in a scale range about three generations wider than the multifractal detrended fluctuation analysis and the basic estimation. The estimation of partition function given by the wavelet transform modulus maxima has unacceptable fluctuations. Besides the scaling invariance focused in the present paper, the proposed factorial moment of continuous order can find its various uses, such as finding nonextensive behaviors of a complex system and reconstructing the causality relationship network between elements of a complex system.

Classic Problems of Probability

CERN Document Server

Gorroochurn, Prakash

2012-01-01

"A great book, one that I will certainly add to my personal library."—Paul J. Nahin, Professor Emeritus of Electrical Engineering, University of New Hampshire Classic Problems of Probability presents a lively account of the most intriguing aspects of statistics. The book features a large collection of more than thirty classic probability problems which have been carefully selected for their interesting history, the way they have shaped the field, and their counterintuitive nature. From Cardano's 1564 Games of Chance to Jacob Bernoulli's 1713 Golden Theorem to Parrondo's 1996 Perplexin

Joint probabilities and quantum cognition

International Nuclear Information System (INIS)

Acacio de Barros, J.

2012-01-01

In this paper we discuss the existence of joint probability distributions for quantumlike response computations in the brain. We do so by focusing on a contextual neural-oscillator model shown to reproduce the main features of behavioral stimulus-response theory. We then exhibit a simple example of contextual random variables not having a joint probability distribution, and describe how such variables can be obtained from neural oscillators, but not from a quantum observable algebra.

Joint probabilities and quantum cognition

Energy Technology Data Exchange (ETDEWEB)

Acacio de Barros, J. [Liberal Studies, 1600 Holloway Ave., San Francisco State University, San Francisco, CA 94132 (United States)

2012-12-18

In this paper we discuss the existence of joint probability distributions for quantumlike response computations in the brain. We do so by focusing on a contextual neural-oscillator model shown to reproduce the main features of behavioral stimulus-response theory. We then exhibit a simple example of contextual random variables not having a joint probability distribution, and describe how such variables can be obtained from neural oscillators, but not from a quantum observable algebra.

Comparison of approximate formulas for decision levels and detection limits for paired counting with the exact results

International Nuclear Information System (INIS)

Potter, W.E.

2005-01-01

The exact probability density function for paired counting can be expressed in terms of modified Bessel functions of integral order when the expected blank count is known. Exact decision levels and detection limits can be computed in a straightforward manner. For many applications perturbing half-integer corrections to Gaussian distributions yields satisfactory results for decision levels. When there is concern about the uncertainty for the expected value of the blank count, a way to bound the errors of both types using confidence intervals for the expected blank count is discussed. (author)

Advances in delimiting the Hilbert-Schmidt separability probability of real two-qubit systems

International Nuclear Information System (INIS)

Slater, Paul B

2010-01-01

We seek to derive the probability-expressed in terms of the Hilbert-Schmidt (Euclidean or flat) metric-that a generic (nine-dimensional) real two-qubit system is separable, by implementing the well-known Peres-Horodecki test on the partial transposes (PTs) of the associated 4 x 4 density matrices (ρ). But the full implementation of the test-requiring that the determinant of the PT be nonnegative for separability to hold-appears to be, at least presently, computationally intractable. So, we have previously implemented-using the auxiliary concept of a diagonal-entry-parameterized separability function (DESF)-the weaker implied test of nonnegativity of the six 2 x 2 principal minors of the PT. This yielded an exact upper bound on the separability probability of 1024/135π 2 ∼0.76854. Here, we piece together (reflection-symmetric) results obtained by requiring that each of the four 3 x 3 principal minors of the PT, in turn, be nonnegative, giving an improved/reduced upper bound of 22/35∼0.628571. Then, we conclude that a still further improved upper bound of 1129/2100∼0.537619 can be found by similarly piecing together the (reflection-symmetric) results of enforcing the simultaneous nonnegativity of certain pairs of the four 3 x 3 principal minors. Numerical simulations-as opposed to exact symbolic calculations-indicate, on the other hand, that the true probability is certainly less than 1/2 . Our analyses lead us to suggest a possible form for the true DESF, yielding a separability probability of 29/64∼0.453125, while the absolute separability probability of (6928-2205π)/(2 9/2 )∼0.0348338 provides the best exact lower bound established so far. In deriving our improved upper bounds, we rely repeatedly upon the use of certain integrals over cubes that arise. Finally, we apply an independence assumption to a pair of DESFs that comes close to reproducing our numerical estimate of the true separability function.

A methodology for the transfer of probabilities between accident severity categories

International Nuclear Information System (INIS)

Whitlow, J.D.; Neuhauser, K.S.

1991-01-01

A methodology has been developed which allows the accident probabilities associated with one accident-severity category scheme to be transferred to another severity category scheme. The methodology requires that the schemes use a common set of parameters to define the categories. The transfer of accident probabilities is based on the relationships between probability of occurrence and each of the parameters used to define the categories. Because of the lack of historical data describing accident environments in engineering terms, these relationships may be difficult to obtain directly for some parameters. Numerical models or experienced judgement are often needed to obtain the relationships. These relationships, even if they are not exact, allow the accident probability associated with any severity category to be distributed within that category in a manner consistent with accident experience, which in turn will allow the accident probability to be appropriately transferred to a different category scheme

Ruin probabilities with compounding assets for discrete time finite horizon problems, independent period claim sizes and general premium structure

NARCIS (Netherlands)

Kok, de A.G.

2003-01-01

In this paper we present fast and accurate approximations for the probability of ruin over a finite number of periods, assuming inhomogeneous independent claim size distributions and arbitrary premium income in subsequent periods. We develop exact recursive expressions for the non-ruin probabilities

Wave functions and two-electron probability distributions of the Hooke's-law atom and helium

International Nuclear Information System (INIS)

O'Neill, Darragh P.; Gill, Peter M. W.

2003-01-01

The Hooke's-law atom (hookium) provides an exactly soluble model for a two-electron atom in which the nuclear-electron Coulombic attraction has been replaced by a harmonic one. Starting from the known exact position-space wave function for the ground state of hookium, we present the momentum-space wave function. We also look at the intracules, two-electron probability distributions, for hookium in position, momentum, and phase space. These are compared with the Hartree-Fock results and the Coulomb holes (the difference between the exact and Hartree-Fock intracules) in position, momentum, and phase space are examined. We then compare these results with analogous results for the ground state of helium using a simple, explicitly correlated wave function

Stochastic processes crossing from ballistic to fractional diffusion with memory: exact results

Directory of Open Access Journals (Sweden)

V. Ilyin

2010-01-01

Full Text Available We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion at longer times. Using the standard non-Markovian diffusion equation we demonstrate how to choose the memory kernel to exactly respect the two different asymptotics of the diffusion process. Having done so we solve for the probability distribution function as a continuous function which evolves inside a ballistically expanding domain. This general solution agrees for long times with the probability distribution function obtained within the continuous random walk approach but it is much superior to this solution at shorter times where the effect of the ballistic regime is crucial.

Probability: A Matter of Life and Death

Science.gov (United States)

Hassani, Mehdi; Kippen, Rebecca; Mills, Terence

2016-01-01

Life tables are mathematical tables that document probabilities of dying and life expectancies at different ages in a society. Thus, the life table contains some essential features of the health of a population. Probability is often regarded as a difficult branch of mathematics. Life tables provide an interesting approach to introducing concepts…

Exact renormalization group equations: an introductory review

Science.gov (United States)

Bagnuls, C.; Bervillier, C.

2001-07-01

We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.

Non-singular string-cosmologies from exact conformal field theories

International Nuclear Information System (INIS)

Vega, H.J. de; Larsen, A.L.; Sanchez, N.

2001-01-01

Non-singular two and three dimensional string cosmologies are constructed using the exact conformal field theories corresponding to SO(2,1)/SO(1,1) and SO(2,2)/SO(2,1). All semi-classical curvature singularities are canceled in the exact theories for both of these cosets, but some new quantum curvature singularities emerge. However, considering different patches of the global manifolds, allows the construction of non-singular space-times with cosmological interpretation. In both two and three dimensions, we construct non-singular oscillating cosmologies, non-singular expanding and inflationary cosmologies including a de Sitter (exponential) stage with positive scalar curvature as well as non-singular contracting and deflationary cosmologies. Similarities between the two and three dimensional cases suggest a general picture for higher dimensional coset cosmologies: Anisotropy seems to be a generic unavoidable feature, cosmological singularities are generically avoided and it is possible to construct non-singular cosmologies where some spatial dimensions are experiencing inflation while the others experience deflation

Family of probability distributions derived from maximal entropy principle with scale invariant restrictions.

Science.gov (United States)

Sonnino, Giorgio; Steinbrecher, György; Cardinali, Alessandro; Sonnino, Alberto; Tlidi, Mustapha

2013-01-01

Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing the minimum entropy production and the maximum entropy principle under the scale invariance restrictions. The obtained probability distribution presents a singularity that has immediate physical interpretation in terms of the intermittency models. The derived reference probability distribution function is interpreted as time and ensemble average of the real physical one. A generic family of stochastic processes describing noise-driven intermittency, where the stationary density distribution coincides exactly with the one resulted from entropy maximization, is presented.

Probabilities of inherent shutdown of unprotected events in innovative liquid metal reactors

International Nuclear Information System (INIS)

Mueller, C.J.

1987-01-01

The uncertainty in predicting the effectiveness of inherent shutdown (ISD) in innovative designs results from three broad contributing areas of uncertainty: (1) the inability to exactly predict the frequency of ATWS events with potential to challenge the safety systems and require ISD; (2) the approximation of representing all such ATWS events by a selected set of ''generic scenarios''; and (3) the inability to exactly calculate the core response to the selected generic scenarios. In this summary, the methodology and associated results of work used to establish probabilities of failure of inherent shutdown of innovative LMRs to the unprotected loss-of-flow (LOF) accident are discussed

Energetics and performance of a microscopic heat engine based on exact calculations of work and heat distributions

International Nuclear Information System (INIS)

Chvosta, Petr; Holubec, Viktor; Ryabov, Artem; Einax, Mario; Maass, Philipp

2010-01-01

We investigate a microscopic motor based on an externally controlled two-level system. One cycle of the motor operation consists of two strokes. Within each stroke, the two-level system is in contact with a given thermal bath and its energy levels are driven at a constant rate. The time evolutions of the occupation probabilities of the two states are controlled by one rate equation and represent the system's response with respect to the external driving. We give the exact solution of the rate equation for the limit cycle and discuss the emerging thermodynamics: the work done on the environment, the heat exchanged with the baths, the entropy production, the motor's efficiency, and the power output. Furthermore we introduce an augmented stochastic process which reflects, at a given time, both the occupation probabilities for the two states and the time spent in the individual states during the previous evolution. The exact calculation of the evolution operator for the augmented process allows us to discuss in detail the probability density for the work performed during the limit cycle. In the strongly irreversible regime, the density exhibits important qualitative differences with respect to the more common Gaussian shape in the regime of weak irreversibility

Class of nonsingular exact solutions for Laplacian pattern formation

International Nuclear Information System (INIS)

Mineev-Weinstein, M.B.; Dawson, S.P.

1994-01-01

We present a class of exact solutions for the so-called Laplacian growth equation describing the zero-surface-tension limit of a variety of two-dimensional pattern formation problems. These solutions are free of finite-time singularities (cusps) for quite general initial conditions. They reproduce various features of viscous fingering observed in experiments and numerical simulations with surface tension, such as existence of stagnation points, screening, tip splitting, and coarsening. In certain cases the asymptotic interface consists of N separated moving Saffman-Taylor fingers

Exact cosmological solutions for MOG

International Nuclear Information System (INIS)

Roshan, Mahmood

2015-01-01

We find some new exact cosmological solutions for the covariant scalar-tensor-vector gravity theory, the so-called modified gravity (MOG). The exact solution of the vacuum field equations has been derived. Also, for non-vacuum cases we have found some exact solutions with the aid of the Noether symmetry approach. More specifically, the symmetry vector and also the Noether conserved quantity associated to the point-like Lagrangian of the theory have been found. Also we find the exact form of the generic vector field potential of this theory by considering the behavior of the relevant point-like Lagrangian under the infinitesimal generator of the Noether symmetry. Finally, we discuss the cosmological implications of the solutions. (orig.)

Exact scattering solutions in an energy sudden (ES) representation

International Nuclear Information System (INIS)

Chang, B.; Eno, L.; Rabitz, H.

1983-01-01

In this paper, we lay down the theoretical foundations for computing exact scattering wave functions in a reference frame which moves in unison with the system internal coordinates. In this frame the (internal) coordinates appear to be fixed and its adoption leads very naturally (in zeroth order) to the energy sudden (ES) approximation [and the related infinite order sudden (IOS) method]. For this reason we call the new representation for describing the exact dynamics of a many channel scattering problem, the ES representation. Exact scattering solutions are derived in both time dependent and time independent frameworks for the representation and many interesting results in these frames are established. It is shown, e.g., that in a time dependent frame the usual Schroedinger propagator factorizes into internal Hamiltonian, ES, and energy correcting propagators. We also show that in a time independent frame the full Green's functions can be similarly factorized. Another important feature of the new representation is that it forms a firm foundation for seeking corrections to the ES approximation. Thus, for example, the singularity which arises in conventional perturbative expansions of the full Green's functions (with the ES Green's function as the zeroth order solution) is avoided in the ES representation. Finally, a number of both time independent and time dependent ES correction schemes are suggested

The transition probability and the probability for the left-most particle's position of the q-totally asymmetric zero range process

Energy Technology Data Exchange (ETDEWEB)

Korhonen, Marko [Department of Mathematics and Statistics, University of Helsinki, FIN-00014 (Finland); Lee, Eunghyun [Centre de Recherches Mathématiques (CRM), Université de Montréal, Quebec H3C 3J7 (Canada)

2014-01-15

We treat the N-particle zero range process whose jumping rates satisfy a certain condition. This condition is required to use the Bethe ansatz and the resulting model is the q-boson model by Sasamoto and Wadati [“Exact results for one-dimensional totally asymmetric diffusion models,” J. Phys. A 31, 6057–6071 (1998)] or the q-totally asymmetric zero range process (TAZRP) by Borodin and Corwin [“Macdonald processes,” Probab. Theory Relat. Fields (to be published)]. We find the explicit formula of the transition probability of the q-TAZRP via the Bethe ansatz. By using the transition probability we find the probability distribution of the left-most particle's position at time t. To find the probability for the left-most particle's position we find a new identity corresponding to identity for the asymmetric simple exclusion process by Tracy and Widom [“Integral formulas for the asymmetric simple exclusion process,” Commun. Math. Phys. 279, 815–844 (2008)]. For the initial state that all particles occupy a single site, the probability distribution of the left-most particle's position at time t is represented by the contour integral of a determinant.

Quasi-exact solutions of nonlinear differential equations

OpenAIRE

Kudryashov, Nikolay A.; Kochanov, Mark B.

2014-01-01

The concept of quasi-exact solutions of nonlinear differential equations is introduced. Quasi-exact solution expands the idea of exact solution for additional values of parameters of differential equation. These solutions are approximate solutions of nonlinear differential equations but they are close to exact solutions. Quasi-exact solutions of the the Kuramoto--Sivashinsky, the Korteweg--de Vries--Burgers and the Kawahara equations are founded.

Probabilities the little numbers that rule our lives

CERN Document Server

Olofsson, Peter

2014-01-01

Praise for the First Edition"If there is anything you want to know, or remind yourself, about probabilities, then look no further than this comprehensive, yet wittily written and enjoyable, compendium of how to apply probability calculations in real-world situations."- Keith Devlin, Stanford University, National Public Radio's "Math Guy" and author of The Math Gene and The Unfinished GameFrom probable improbabilities to regular irregularities, Probabilities: The Little Numbers That Rule Our Lives, Second Edition investigates the often surprising effects of risk and chance in our lives. Featur

Knowing where is different from knowing what: Distinct response time profiles and accuracy effects for target location, orientation, and color probability.

Science.gov (United States)

Jabar, Syaheed B; Filipowicz, Alex; Anderson, Britt

2017-11-01

When a location is cued, targets appearing at that location are detected more quickly. When a target feature is cued, targets bearing that feature are detected more quickly. These attentional cueing effects are only superficially similar. More detailed analyses find distinct temporal and accuracy profiles for the two different types of cues. This pattern parallels work with probability manipulations, where both feature and spatial probability are known to affect detection accuracy and reaction times. However, little has been done by way of comparing these effects. Are probability manipulations on space and features distinct? In a series of five experiments, we systematically varied spatial probability and feature probability along two dimensions (orientation or color). In addition, we decomposed response times into initiation and movement components. Targets appearing at the probable location were reported more quickly and more accurately regardless of whether the report was based on orientation or color. On the other hand, when either color probability or orientation probability was manipulated, response time and accuracy improvements were specific for that probable feature dimension. Decomposition of the response time benefits demonstrated that spatial probability only affected initiation times, whereas manipulations of feature probability affected both initiation and movement times. As detection was made more difficult, the two effects further diverged, with spatial probability disproportionally affecting initiation times and feature probability disproportionately affecting accuracy. In conclusion, all manipulations of probability, whether spatial or featural, affect detection. However, only feature probability affects perceptual precision, and precision effects are specific to the probable attribute.

Selection of risk reduction portfolios under interval-valued probabilities

International Nuclear Information System (INIS)

Toppila, Antti; Salo, Ahti

2017-01-01

A central problem in risk management is that of identifying the optimal combination (or portfolio) of improvements that enhance the reliability of the system most through reducing failure event probabilities, subject to the availability of resources. This optimal portfolio can be sensitive with regard to epistemic uncertainties about the failure events' probabilities. In this paper, we develop an optimization model to support the allocation of resources to improvements that mitigate risks in coherent systems in which interval-valued probabilities defined by lower and upper bounds are employed to capture epistemic uncertainties. Decision recommendations are based on portfolio dominance: a resource allocation portfolio is dominated if there exists another portfolio that improves system reliability (i) at least as much for all feasible failure probabilities and (ii) strictly more for some feasible probabilities. Based on non-dominated portfolios, recommendations about improvements to implement are derived by inspecting in how many non-dominated portfolios a given improvement is contained. We present an exact method for computing the non-dominated portfolios. We also present an approximate method that simplifies the reliability function using total order interactions so that larger problem instances can be solved with reasonable computational effort. - Highlights: • Reliability allocation under epistemic uncertainty about probabilities. • Comparison of alternatives using dominance. • Computational methods for generating the non-dominated alternatives. • Deriving decision recommendations that are robust with respect to epistemic uncertainty.

The mean distance to the nth neighbour in a uniform distribution of random points: an application of probability theory

International Nuclear Information System (INIS)

Bhattacharyya, Pratip; Chakrabarti, Bikas K

2008-01-01

We study different ways of determining the mean distance (r n ) between a reference point and its nth neighbour among random points distributed with uniform density in a D-dimensional Euclidean space. First, we present a heuristic method; though this method provides only a crude mathematical result, it shows a simple way of estimating (r n ). Next, we describe two alternative means of deriving the exact expression of (r n ): we review the method using absolute probability and develop an alternative method using conditional probability. Finally, we obtain an approximation to (r n ) from the mean volume between the reference point and its nth neighbour and compare it with the heuristic and exact results

Introduction to probability and stochastic processes with applications

CERN Document Server

Castañ, Blanco; Arunachalam, Viswanathan; Dharmaraja, Selvamuthu

2012-01-01

An easily accessible, real-world approach to probability and stochastic processes Introduction to Probability and Stochastic Processes with Applications presents a clear, easy-to-understand treatment of probability and stochastic processes, providing readers with a solid foundation they can build upon throughout their careers. With an emphasis on applications in engineering, applied sciences, business and finance, statistics, mathematics, and operations research, the book features numerous real-world examples that illustrate how random phenomena occur in nature and how to use probabilistic t

Probability density of wave function of excited photoelectron: understanding XANES features

Czech Academy of Sciences Publication Activity Database

Šipr, Ondřej

2001-01-01

Roč. 8, - (2001), s. 232-234 ISSN 0909-0495 R&D Projects: GA ČR GA202/99/0404 Institutional research plan: CEZ:A02/98:Z1-010-914 Keywords : XANES * PED - probability density of wave function Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.519, year: 2001

Greedy solution of ill-posed problems: error bounds and exact inversion

International Nuclear Information System (INIS)

Denis, L; Lorenz, D A; Trede, D

2009-01-01

The orthogonal matching pursuit (OMP) is a greedy algorithm to solve sparse approximation problems. Sufficient conditions for exact recovery are known with and without noise. In this paper we investigate the applicability of the OMP for the solution of ill-posed inverse problems in general, and in particular for two deconvolution examples from mass spectrometry and digital holography, respectively. In sparse approximation problems one often has to deal with the problem of redundancy of a dictionary, i.e. the atoms are not linearly independent. However, one expects them to be approximatively orthogonal and this is quantified by the so-called incoherence. This idea cannot be transferred to ill-posed inverse problems since here the atoms are typically far from orthogonal. The ill-posedness of the operator probably causes the correlation of two distinct atoms to become huge, i.e. that two atoms look much alike. Therefore, one needs conditions which take the structure of the problem into account and work without the concept of coherence. In this paper we develop results for the exact recovery of the support of noisy signals. In the two examples, mass spectrometry and digital holography, we show that our results lead to practically relevant estimates such that one may check a priori if the experimental setup guarantees exact deconvolution with OMP. Especially in the example from digital holography, our analysis may be regarded as a first step to calculate the resolution power of droplet holography

Exact piecewise flat gravitational waves

NARCIS (Netherlands)

van de Meent, M.

2011-01-01

We generalize our previous linear result (van de Meent 2011 Class. Quantum Grav 28 075005) in obtaining gravitational waves from our piecewise flat model for gravity in 3+1 dimensions to exact piecewise flat configurations describing exact planar gravitational waves. We show explicitly how to

Exact solitary waves of the Fisher equation

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.

2005-01-01

New method is presented to search exact solutions of nonlinear differential equations. This approach is used to look for exact solutions of the Fisher equation. New exact solitary waves of the Fisher equation are given

Joint probability discrimination between stationary tissue and blood velocity signals

DEFF Research Database (Denmark)

Schlaikjer, Malene; Jensen, Jørgen Arendt

2001-01-01

before and after echo-canceling, and (b) the amplitude variations between samples in consecutive RF-signals before and after echo-canceling. The statistical discriminator was obtained by computing the probability density functions (PDFs) for each feature through histogram analysis of data....... This study presents a new statistical discriminator. Investigation of the RF-signals reveals that features can be derived that distinguish the segments of the signal, which do an do not carry information on the blood flow. In this study 4 features, have been determined: (a) the energy content in the segments....... The discrimination is performed by determining the joint probability of the features for the segment under investigation and choosing the segment type that is most likely. The method was tested on simulated data resembling RF-signals from the carotid artery....

Exact suppression of depolarisation by beam-beam interaction in an electron ring

International Nuclear Information System (INIS)

Buon, J.

1983-03-01

It is shown that depolarisation due to beam-beam interaction can be exactly suppressed in an electron storage ring. The necessary ''spin matching'' conditions to be fulfilled are derived for a planar ring. They depend on the ring optics, assumed linear, but not on the features of the beam-beam force, like intensity and non-linearity. Extension to a ring equipped with 90 0 spin rotators is straightorward

Failure Probability Estimation Using Asymptotic Sampling and Its Dependence upon the Selected Sampling Scheme

Directory of Open Access Journals (Sweden)

Martinásková Magdalena

2017-12-01

Full Text Available The article examines the use of Asymptotic Sampling (AS for the estimation of failure probability. The AS algorithm requires samples of multidimensional Gaussian random vectors, which may be obtained by many alternative means that influence the performance of the AS method. Several reliability problems (test functions have been selected in order to test AS with various sampling schemes: (i Monte Carlo designs; (ii LHS designs optimized using the Periodic Audze-Eglājs (PAE criterion; (iii designs prepared using Sobol’ sequences. All results are compared with the exact failure probability value.

Internal Medicine residents use heuristics to estimate disease probability

OpenAIRE

Phang, Sen Han; Ravani, Pietro; Schaefer, Jeffrey; Wright, Bruce; McLaughlin, Kevin

2015-01-01

Background: Training in Bayesian reasoning may have limited impact on accuracy of probability estimates. In this study, our goal was to explore whether residents previously exposed to Bayesian reasoning use heuristics rather than Bayesian reasoning to estimate disease probabilities. We predicted that if residents use heuristics then post-test probability estimates would be increased by non-discriminating clinical features or a high anchor for a target condition. Method: We randomized 55 In...

Quantum interference of probabilities and hidden variable theories

International Nuclear Information System (INIS)

Srinivas, M.D.

1984-01-01

One of the fundamental contributions of Louis de Broglie, which does not get cited often, has been his analysis of the basic difference between the calculus of the probabilities as predicted by quantum theory and the usual calculus of probabilities - the one employed by most mathematicians, in its standard axiomatised version due to Kolmogorov. This paper is basically devoted to a discussion of the 'quantum interference of probabilities', discovered by de Broglie. In particular, it is shown that it is this feature of the quantum theoretic probabilities which leads to some serious constraints on the possible 'hidden-variable formulations' of quantum mechanics, including the celebrated theorem of Bell. (Auth.)

Exact Heat Kernel on a Hypersphere and Its Applications in Kernel SVM

Directory of Open Access Journals (Sweden)

Chenchao Zhao

2018-01-01

Full Text Available Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector machine compared to other competing similarity measures. Specifically, the idea of using heat diffusion on a hypersphere to measure similarity has been previously proposed and tested by Lafferty and Lebanon [1], demonstrating promising results based on a heuristic heat kernel obtained from the zeroth order parametrix expansion; however, how well this heuristic kernel agrees with the exact hyperspherical heat kernel remains unknown. This paper presents a higher order parametrix expansion of the heat kernel on a unit hypersphere and discusses several problems associated with this expansion method. We then compare the heuristic kernel with an exact form of the heat kernel expressed in terms of a uniformly and absolutely convergent series in high-dimensional angular momentum eigenmodes. Being a natural measure of similarity between sample points dwelling on a hypersphere, the exact kernel often shows superior performance in kernel SVM classifications applied to text mining, tumor somatic mutation imputation, and stock market analysis.

Using Dynamic Geometry Software for Teaching Conditional Probability with Area-Proportional Venn Diagrams

Science.gov (United States)

Radakovic, Nenad; McDougall, Douglas

2012-01-01

This classroom note illustrates how dynamic visualization can be used to teach conditional probability and Bayes' theorem. There are two features of the visualization that make it an ideal pedagogical tool in probability instruction. The first feature is the use of area-proportional Venn diagrams that, along with showing qualitative relationships,…

Finite-size scaling of survival probability in branching processes.

Science.gov (United States)

Garcia-Millan, Rosalba; Font-Clos, Francesc; Corral, Álvaro

2015-04-01

Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We derive analytically the existence of finite-size scaling for the survival probability as a function of the control parameter and the maximum number of generations, obtaining the critical exponents as well as the exact scaling function, which is G(y)=2ye(y)/(e(y)-1), with y the rescaled distance to the critical point. Our findings are valid for any branching process of the Galton-Watson type, independently of the distribution of the number of offspring, provided its variance is finite. This proves the universal behavior of the finite-size effects in branching processes, including the universality of the metric factors. The direct relation to mean-field percolation is also discussed.

Dynamic encoding of speech sequence probability in human temporal cortex.

Science.gov (United States)

Leonard, Matthew K; Bouchard, Kristofer E; Tang, Claire; Chang, Edward F

2015-05-06

Sensory processing involves identification of stimulus features, but also integration with the surrounding sensory and cognitive context. Previous work in animals and humans has shown fine-scale sensitivity to context in the form of learned knowledge about the statistics of the sensory environment, including relative probabilities of discrete units in a stream of sequential auditory input. These statistics are a defining characteristic of one of the most important sequential signals humans encounter: speech. For speech, extensive exposure to a language tunes listeners to the statistics of sound sequences. To address how speech sequence statistics are neurally encoded, we used high-resolution direct cortical recordings from human lateral superior temporal cortex as subjects listened to words and nonwords with varying transition probabilities between sound segments. In addition to their sensitivity to acoustic features (including contextual features, such as coarticulation), we found that neural responses dynamically encoded the language-level probability of both preceding and upcoming speech sounds. Transition probability first negatively modulated neural responses, followed by positive modulation of neural responses, consistent with coordinated predictive and retrospective recognition processes, respectively. Furthermore, transition probability encoding was different for real English words compared with nonwords, providing evidence for online interactions with high-order linguistic knowledge. These results demonstrate that sensory processing of deeply learned stimuli involves integrating physical stimulus features with their contextual sequential structure. Despite not being consciously aware of phoneme sequence statistics, listeners use this information to process spoken input and to link low-level acoustic representations with linguistic information about word identity and meaning. Copyright © 2015 the authors 0270-6474/15/357203-12$15.00/0.

CONDITIONS FOR EXACT CAVALIERI ESTIMATION

Directory of Open Access Journals (Sweden)

Mónica Tinajero-Bravo

2014-03-01

Full Text Available Exact Cavalieri estimation amounts to zero variance estimation of an integral with systematic observations along a sampling axis. A sufficient condition is given, both in the continuous and the discrete cases, for exact Cavalieri sampling. The conclusions suggest improvements on the current stereological application of fractionator-type sampling.

Method to Calculate Accurate Top Event Probability in a Seismic PSA

Energy Technology Data Exchange (ETDEWEB)

Jung, Woo Sik [Sejong Univ., Seoul (Korea, Republic of)

2014-05-15

ACUBE(Advanced Cutset Upper Bound Estimator) calculates the top event probability and importance measures from cutsets by dividing cutsets into major and minor groups depending on the cutset probability, where the cutsets that have higher cutset probability are included in the major group and the others in minor cutsets, converting major cutsets into a Binary Decision Diagram (BDD). By applying the ACUBE algorithm to the seismic PSA cutsets, the accuracy of a top event probability and importance measures can be significantly improved. ACUBE works by dividing the cutsets into two groups (higher and lower cutset probability groups), calculating the top event probability and importance measures in each group, and combining the two results from the two groups. Here, ACUBE calculates the top event probability and importance measures of the higher cutset probability group exactly. On the other hand, ACUBE calculates these measures of the lower cutset probability group with an approximation such as MCUB. The ACUBE algorithm is useful for decreasing the conservatism that is caused by approximating the top event probability and importance measure calculations with given cutsets. By applying the ACUBE algorithm to the seismic PSA cutsets, the accuracy of a top event probability and importance measures can be significantly improved. This study shows that careful attention should be paid and an appropriate method be provided in order to avoid the significant overestimation of the top event probability calculation. Due to the strength of ACUBE that is explained in this study, the ACUBE became a vital tool for calculating more accurate CDF of the seismic PSA cutsets than the conventional probability calculation method.

Heart sounds analysis using probability assessment.

Science.gov (United States)

Plesinger, F; Viscor, I; Halamek, J; Jurco, J; Jurak, P

2017-07-31

This paper describes a method for automated discrimination of heart sounds recordings according to the Physionet Challenge 2016. The goal was to decide if the recording refers to normal or abnormal heart sounds or if it is not possible to decide (i.e. 'unsure' recordings). Heart sounds S1 and S2 are detected using amplitude envelopes in the band 15-90 Hz. The averaged shape of the S1/S2 pair is computed from amplitude envelopes in five different bands (15-90 Hz; 55-150 Hz; 100-250 Hz; 200-450 Hz; 400-800 Hz). A total of 53 features are extracted from the data. The largest group of features is extracted from the statistical properties of the averaged shapes; other features are extracted from the symmetry of averaged shapes, and the last group of features is independent of S1 and S2 detection. Generated features are processed using logical rules and probability assessment, a prototype of a new machine-learning method. The method was trained using 3155 records and tested on 1277 hidden records. It resulted in a training score of 0.903 (sensitivity 0.869, specificity 0.937) and a testing score of 0.841 (sensitivity 0.770, specificity 0.913). The revised method led to a test score of 0.853 in the follow-up phase of the challenge. The presented solution achieved 7th place out of 48 competing entries in the Physionet Challenge 2016 (official phase). In addition, the PROBAfind software for probability assessment was introduced.

Exact solutions for rotating charged dust

International Nuclear Information System (INIS)

Islam, J.N.

1984-01-01

Earlier work by the author on rotating charged dust is summarized. An incomplete class of exact solutions for differentially rotating charged dust in Newton-Maxwell theory for the equal mass and charge case that was found earlier is completed. A new global exact solution for cylindrically symmetric differentially rotating charged dust in Newton-Maxwell theory is presented. Lastly, a new exact solution for cylindrically symmetric rigidly rotating charged dust in general relativity is given. (author)

Eigenvalue ratio detection based on exact moments of smallest and largest eigenvalues

KAUST Repository

Shakir, Muhammad; Tang, Wuchen; Rao, Anlei; Imran, Muhammad Ali; Alouini, Mohamed-Slim

2011-01-01

Detection based on eigenvalues of received signal covariance matrix is currently one of the most effective solution for spectrum sensing problem in cognitive radios. However, the results of these schemes always depend on asymptotic assumptions since the close-formed expression of exact eigenvalues ratio distribution is exceptionally complex to compute in practice. In this paper, non-asymptotic spectrum sensing approach to approximate the extreme eigenvalues is introduced. In this context, the Gaussian approximation approach based on exact analytical moments of extreme eigenvalues is presented. In this approach, the extreme eigenvalues are considered as dependent Gaussian random variables such that the joint probability density function (PDF) is approximated by bivariate Gaussian distribution function for any number of cooperating secondary users and received samples. In this context, the definition of Copula is cited to analyze the extent of the dependency between the extreme eigenvalues. Later, the decision threshold based on the ratio of dependent Gaussian extreme eigenvalues is derived. The performance analysis of our newly proposed approach is compared with the already published asymptotic Tracy-Widom approximation approach. © 2011 ICST.

Bounding spectral gaps of Markov chains: a novel exact multi-decomposition technique

International Nuclear Information System (INIS)

Destainville, N

2003-01-01

We propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration, we successfully use this technique to evaluate the 'absorption time' of the 'Backgammon model', a paradigmatic model for glassy dynamics. We also discuss the application of this technique to the 'contingency table problem', a notoriously difficult problem from probability theory. The interest of this technique is that it connects spectral gaps, which are quantities related to dynamics, with static quantities, calculated at equilibrium

Common Frontiers of the Exact Sciences and the Humanities

Science.gov (United States)

Hiebert, Erwin N.

The physicist Franz Serafin Exner (1849-1926) was a prominent Austrian spokesman for the new developments that were coupled with turn-of-the-century experiments and theories related to entropy thermodynamics, the internally structured atom, quantum theory, and relativity. The Exner circle found its inspiration in the intellectual world of Ludwig Boltzmann and his teachers, colleagues, and students. Cross-discipline discussions on common and divergent frontiers of the exact sciences and the humanities meaningfully converged on the significance, comparison, and transfer of concepts such as the laws of nature, causality, probability, and chance. Oswald Spengler's Decline of the West, with its pessimistic, subjectivistic, and negative science-directed messages provided Exner with the opportunity to sharpen his support for the new scientific trends in physics - thus to champion the search for objective truth.

Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

Science.gov (United States)

Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.

2018-04-01

Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.

Consistent probabilities in loop quantum cosmology

International Nuclear Information System (INIS)

Craig, David A; Singh, Parampreet

2013-01-01

A fundamental issue for any quantum cosmological theory is to specify how probabilities can be assigned to various quantum events or sequences of events such as the occurrence of singularities or bounces. In previous work, we have demonstrated how this issue can be successfully addressed within the consistent histories approach to quantum theory for Wheeler–DeWitt-quantized cosmological models. In this work, we generalize that analysis to the exactly solvable loop quantization of a spatially flat, homogeneous and isotropic cosmology sourced with a massless, minimally coupled scalar field known as sLQC. We provide an explicit, rigorous and complete decoherent-histories formulation for this model and compute the probabilities for the occurrence of a quantum bounce versus a singularity. Using the scalar field as an emergent internal time, we show for generic states that the probability for a singularity to occur in this model is zero, and that of a bounce is unity, complementing earlier studies of the expectation values of the volume and matter density in this theory. We also show from the consistent histories point of view that all states in this model, whether quantum or classical, achieve arbitrarily large volume in the limit of infinite ‘past’ or ‘future’ scalar ‘time’, in the sense that the wave function evaluated at any arbitrary fixed value of the volume vanishes in that limit. Finally, we briefly discuss certain misconceptions concerning the utility of the consistent histories approach in these models. (paper)

Exact classical scaling formalism for nonreactive processes

International Nuclear Information System (INIS)

DePristo, A.E.

1981-01-01

A general nonreactive collision system is considered with internal molecular variables (p, r) and/or (I, theta) of arbitrary dimensions and relative translational variables (P, R) of three or less dimensions. We derive an exact classical scaling formalism which relates the collisional change in any function of molecular variables directly to the initial values of these variables. The collision dynamics is then described by an explicit function of the initial point in the internal molecular phase space, for a fixed point in the relative translational phase space. In other words, the systematic variation of the internal molecular properties (e.g., actions and average internal kinetic energies) is given as a function of the initial internal action-angle variables. A simple three term approximation to the exact formalism is derived, the natural variables of which are the internal action I and internal linear momenta p. For the final average internal kinetic energies T, the result is T-T/sup( 0 ) = α+βp/sup( 0 )+γI/sup( 0 ), where the superscripted ''0'' indicates the initial value. The parameters α, β, and γ in this scaling theory are directly related to the moments of the change in average internal kinetic energy. Utilizing a very limited number of input moments generated from classical trajectory calculations, the scaling can be used to predict the entire distribution of final internal variables as a function of initial internal actions and linear momenta. Initial examples for atom--collinear harmonic oscillator collision systems are presented in detail, with the scaling predictions (e.g., moments and quasiclassical histogram transition probabilities) being generally very good to excellent quantitatively

Exact Analysis of Intrinsic Qualitative Features of Phosphorelays using Mathematical Models

DEFF Research Database (Denmark)

Knudsen, Michael; Feliu, Elisenda; Wiuf, Carsten Henrik

2012-01-01

stable steady-state. Furthermore, we derive explicit functions relating stimulus to the response in any layer of a phosphorelay and show that a limited degree of ultrasensitivity in the bottom layer of a phosphorelay is an intrinsic feature which does not depend on any reaction rates or substrate amounts....... On the other hand, we show how adjusting reaction rates and substrate amounts may lead to higher degrees of ultrasensitivity in intermediate layers. The explicit formulas also enable us to prove how the response changes with alterations in stimulus, kinetic parameters, and substrate amounts. Aside from...

Criteria, Probability and Degree of Instability of Employment Taking into Account the Features of the Russian Labour Market

Directory of Open Access Journals (Sweden)

Vyacheslav Nikolaevich Bobkov

2017-09-01

Full Text Available The article reveals the issues of the global character of precarization and substantiates the criteria of precarious employment taking into account its special aspects in Russian Federation. The existing variability of approaches to the definition of precarious employment and the necessity to elaborate its optimal criteria in view of features of national labour have conditioned the relevance of the research. The paper involves international and Russian research on precarity and significantly uses the results of expert survey conducted by the authors in autumn 2016. The experts have considered groups of criteria based on: labour contract term, nature of labour relations, precarious terms of work. The experts also were asked to evaluate different forms of employment in which precarity may exert. As a result of the conducted research, we have elaborated the generalized criteria, which identify various forms of instability in labour market. The authors put forward a hypothesis that the criteria of the International Labour Organization (ILO need to be adapted to the Russian realities when determining unstable employment, and the phenomenon of precarious employment has to be defined from the point of view of the probabilistic nature of its various manifestations. Based on the results of the research, the authors have qualified the relevance of International Labour Organization’s (ILO criteria in the Russian context. We also have substantiated the probable character of precarious employment and defined probability of precarity exertion in the flexible forms of employment. The set of precarious employment criteria is specified in accordance with Russian context: we have clarified and complemented them, and defined the probability of precarity exertion in different forms of employment. The main result of the research is the structure of criterial standards, which identifies precarious employment.The conceptual issues and findings of the paper can be

Elements of probability and statistics an introduction to probability with De Finetti’s approach and to Bayesian statistics

CERN Document Server

Biagini, Francesca

2016-01-01

This book provides an introduction to elementary probability and to Bayesian statistics using de Finetti's subjectivist approach. One of the features of this approach is that it does not require the introduction of sample space – a non-intrinsic concept that makes the treatment of elementary probability unnecessarily complicate – but introduces as fundamental the concept of random numbers directly related to their interpretation in applications. Events become a particular case of random numbers and probability a particular case of expectation when it is applied to events. The subjective evaluation of expectation and of conditional expectation is based on an economic choice of an acceptable bet or penalty. The properties of expectation and conditional expectation are derived by applying a coherence criterion that the evaluation has to follow. The book is suitable for all introductory courses in probability and statistics for students in Mathematics, Informatics, Engineering, and Physics.

Spatial probability aids visual stimulus discrimination

Directory of Open Access Journals (Sweden)

Michael Druker

2010-08-01

Full Text Available We investigated whether the statistical predictability of a target's location would influence how quickly and accurately it was classified. Recent results have suggested that spatial probability can be a cue for the allocation of attention in visual search. One explanation for probability cuing is spatial repetition priming. In our two experiments we used probability distributions that were continuous across the display rather than relying on a few arbitrary screen locations. This produced fewer spatial repeats and allowed us to dissociate the effect of a high probability location from that of short-term spatial repetition. The task required participants to quickly judge the color of a single dot presented on a computer screen. In Experiment 1, targets were more probable in an off-center hotspot of high probability that gradually declined to a background rate. Targets garnered faster responses if they were near earlier target locations (priming and if they were near the high probability hotspot (probability cuing. In Experiment 2, target locations were chosen on three concentric circles around fixation. One circle contained 80% of targets. The value of this ring distribution is that it allowed for a spatially restricted high probability zone in which sequentially repeated trials were not likely to be physically close. Participant performance was sensitive to the high-probability circle in addition to the expected effects of eccentricity and the distance to recent targets. These two experiments suggest that inhomogeneities in spatial probability can be learned and used by participants on-line and without prompting as an aid for visual stimulus discrimination and that spatial repetition priming is not a sufficient explanation for this effect. Future models of attention should consider explicitly incorporating the probabilities of targets locations and features.

Exact string theory model of closed timelike curves and cosmological singularities

International Nuclear Information System (INIS)

Johnson, Clifford V.; Svendsen, Harald G.

2004-01-01

We study an exact model of string theory propagating in a space-time containing regions with closed timelike curves (CTCs) separated from a finite cosmological region bounded by a big bang and a big crunch. The model is an nontrivial embedding of the Taub-NUT geometry into heterotic string theory with a full conformal field theory (CFT) definition, discovered over a decade ago as a heterotic coset model. Having a CFT definition makes this an excellent laboratory for the study of the stringy fate of CTCs, the Taub cosmology, and the Milne/Misner-type chronology horizon which separates them. In an effort to uncover the role of stringy corrections to such geometries, we calculate the complete set of α ' corrections to the geometry. We observe that the key features of Taub-NUT persist in the exact theory, together with the emergence of a region of space with Euclidean signature bounded by timelike curvature singularities. Although such remarks are premature, their persistence in the exact geometry is suggestive that string theory is able to make physical sense of the Milne/Misner singularities and the CTCs, despite their pathological character in general relativity. This may also support the possibility that CTCs may be viable in some physical situations, and may be a natural ingredient in pre-big bang cosmological scenarios

Exact matrix treatment of statistical mechanical lattice model of adsorption induced gate opening in metal-organic frameworks

International Nuclear Information System (INIS)

Dunne, Lawrence J; Manos, George

2015-01-01

Here we present a statistical mechanical lattice model which is exactly solvable using a matrix method and allows treatment of adsorption induced gate opening structural transformations of metal-organic frameworks which are nanoporous materials with exceptional adsorption properties. Modelling of these structural changes presents a serious theoretical challenge when the solid and gas species are treated in an even handed way. This exactly solvable model complements other simulation based approaches. The methodology presented here highlights the competition between the potential for adsorption and the energy required for structural transition as a driving force for the features in the adsorption isotherms. (paper)

On exact solutions of scattering problems

International Nuclear Information System (INIS)

Nikishov, P.Yu.; Plekhanov, E.B.; Zakhariev, B.N.

1982-01-01

Examples illustrating the quality of the reconstruction of potentials from single-channel scattering data by using exactly solvable models are given. Simple exact solutions for multi-channel systems with non-degenerated resonance singularities of the scattering matrix are derived

On the probability of extinction of the Haiti cholera epidemic

Science.gov (United States)

Bertuzzo, Enrico; Finger, Flavio; Mari, Lorenzo; Gatto, Marino; Rinaldo, Andrea

2014-05-01

Nearly 3 years after its appearance in Haiti, cholera has already exacted more than 8,200 deaths and 670,000 reported cases and it is feared to become endemic. However, no clear evidence of a stable environmental reservoir of pathogenic Vibrio cholerae, the infective agent of the disease, has emerged so far, suggesting that the transmission cycle of the disease is being maintained by bacteria freshly shed by infected individuals. Thus in principle cholera could possibly be eradicated from Haiti. Here, we develop a framework for the estimation of the probability of extinction of the epidemic based on current epidemiological dynamics and health-care practice. Cholera spreading is modelled by an individual-based spatially-explicit stochastic model that accounts for the dynamics of susceptible, infected and recovered individuals hosted in different local communities connected through hydrologic and human mobility networks. Our results indicate that the probability that the epidemic goes extinct before the end of 2016 is of the order of 1%. This low probability of extinction highlights the need for more targeted and effective interventions to possibly stop cholera in Haiti.

Maximization of regional probabilities using Optimal Surface Graphs

DEFF Research Database (Denmark)

Arias Lorza, Andres M.; Van Engelen, Arna; Petersen, Jens

2018-01-01

Purpose: We present a segmentation method that maximizes regional probabilities enclosed by coupled surfaces using an Optimal Surface Graph (OSG) cut approach. This OSG cut determines the globally optimal solution given a graph constructed around an initial surface. While most methods for vessel...... wall segmentation only use edge information, we show that maximizing regional probabilities using an OSG improves the segmentation results. We applied this to automatically segment the vessel wall of the carotid artery in magnetic resonance images. Methods: First, voxel-wise regional probability maps...... were obtained using a Support Vector Machine classifier trained on local image features. Then, the OSG segments the regions which maximizes the regional probabilities considering smoothness and topological constraints. Results: The method was evaluated on 49 carotid arteries from 30 subjects...

Normal mammogram detection based on local probability difference transforms and support vector machines

International Nuclear Information System (INIS)

Chiracharit, W.; Kumhom, P.; Chamnongthai, K.; Sun, Y.; Delp, E.J.; Babbs, C.F

2007-01-01

Automatic detection of normal mammograms, as a ''first look'' for breast cancer, is a new approach to computer-aided diagnosis. This approach may be limited, however, by two main causes. The first problem is the presence of poorly separable ''crossed-distributions'' in which the correct classification depends upon the value of each feature. The second problem is overlap of the feature distributions that are extracted from digitized mammograms of normal and abnormal patients. Here we introduce a new Support Vector Machine (SVM) based method utilizing with the proposed uncrossing mapping and Local Probability Difference (LPD). Crossed-distribution feature pairs are identified and mapped into a new features that can be separated by a zero-hyperplane of the new axis. The probability density functions of the features of normal and abnormal mammograms are then sampled and the local probability difference functions are estimated to enhance the features. From 1,000 ground-truth-known mammograms, 250 normal and 250 abnormal cases, including spiculated lesions, circumscribed masses or microcalcifications, are used for training a support vector machine. The classification results tested with another 250 normal and 250 abnormal sets show improved testing performances with 90% sensitivity and 89% specificity. (author)

Exact extraction method for road rutting laser lines

Science.gov (United States)

Hong, Zhiming

2018-02-01

This paper analyzes the importance of asphalt pavement rutting detection in pavement maintenance and pavement administration in today's society, the shortcomings of the existing rutting detection methods are presented and a new rutting line-laser extraction method based on peak intensity characteristic and peak continuity is proposed. The intensity of peak characteristic is enhanced by a designed transverse mean filter, and an intensity map of peak characteristic based on peak intensity calculation for the whole road image is obtained to determine the seed point of the rutting laser line. Regarding the seed point as the starting point, the light-points of a rutting line-laser are extracted based on the features of peak continuity, which providing exact basic data for subsequent calculation of pavement rutting depths.

New Exact and Asymptotic Results of Dual-Branch MRC over Correlated Nakagami-m Fading Channels

KAUST Repository

Al-Quwaiee, Hessa

2015-05-01

We present in this paper a new performance analysis results of dual-branch maximal-ratio combining over correlated Nakagami-m fading channels with arbitrary fading parameter. In particular, we derive exact closed-form expressions of the outage probability, the average bit error rate, and the ergodic capacity in terms of the extended generalized bivariate Meijer G- function. Moreover, we also provide simple closed- form asymptotic expressions in the high signal-to- noise ratio regime of these three fundamental performance measures. © 2015 IEEE.

New Exact and Asymptotic Results of Dual-Branch MRC over Correlated Nakagami-m Fading Channels

KAUST Repository

Al-Quwaiee, Hessa; Alouini, Mohamed-Slim

2015-01-01

We present in this paper a new performance analysis results of dual-branch maximal-ratio combining over correlated Nakagami-m fading channels with arbitrary fading parameter. In particular, we derive exact closed-form expressions of the outage probability, the average bit error rate, and the ergodic capacity in terms of the extended generalized bivariate Meijer G- function. Moreover, we also provide simple closed- form asymptotic expressions in the high signal-to- noise ratio regime of these three fundamental performance measures. © 2015 IEEE.

Introduction to probability with statistical applications

CERN Document Server

Schay, Géza

2016-01-01

Now in its second edition, this textbook serves as an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. More classical examples such as Montmort's problem, the ballot problem, and Bertrand’s paradox are now included, along with applications such as the Maxwell-Boltzmann and Bose-Einstein distributions in physics. Key features in new edition: * 35 new exercises * Expanded section on the algebra of sets * Expanded chapters on probabilities to include more classical examples * New section on regression * Online instructors' manual containing solutions to all exercises

Bounding spectral gaps of Markov chains: a novel exact multi-decomposition technique

Energy Technology Data Exchange (ETDEWEB)

Destainville, N [Laboratoire de Physique Theorique - IRSAMC, CNRS/Universite Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 04 (France)

2003-04-04

We propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration, we successfully use this technique to evaluate the 'absorption time' of the 'Backgammon model', a paradigmatic model for glassy dynamics. We also discuss the application of this technique to the 'contingency table problem', a notoriously difficult problem from probability theory. The interest of this technique is that it connects spectral gaps, which are quantities related to dynamics, with static quantities, calculated at equilibrium.

Time measurement - technical importance of most exact clocks

International Nuclear Information System (INIS)

Goebel, E.O.; Riehle, F.

2004-01-01

The exactness of the best atomic clocks currently shows a temporal variation of 1 second in 30 million years. This means that we have reached the point of the most exact frequency and time measurement ever. In the past, there was a trend towards increasing the exactness in an increasingly fast sequence. Will this trend continue? And who will profit from it? This article is meant to give answers to these questions. This is done by presenting first the level reached currently with the best atomic clocks and describing the research activities running worldwide with the aim of achieving even more exact clocks. In the second part, we present examples of various areas of technical subjects and research in which the most exact clocks are being applied presently and even more exact ones will be needed in the future [de

Exact sampling hardness of Ising spin models

Science.gov (United States)

Fefferman, B.; Foss-Feig, M.; Gorshkov, A. V.

2017-09-01

We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of exact classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Leibniz International Proceedings in Informatics (Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.

Profiles of US and CT imaging features with a high probability of appendicitis

International Nuclear Information System (INIS)

Randen, A. van; Lameris, W.; Es, H.W. van; Hove, W. ten; Bouma, W.H.; Leeuwen, M.S. van; Keulen, E.M. van; Hulst, V.P.M. van der; Henneman, O.D.; Bossuyt, P.M.; Boermeester, M.A.; Stoker, J.

2010-01-01

To identify and evaluate profiles of US and CT features associated with acute appendicitis. Consecutive patients presenting with acute abdominal pain at the emergency department were invited to participate in this study. All patients underwent US and CT. Imaging features known to be associated with appendicitis, and an imaging diagnosis were prospectively recorded by two independent radiologists. A final diagnosis was assigned after 6 months. Associations between appendiceal imaging features and a final diagnosis of appendicitis were evaluated with logistic regression analysis. Appendicitis was assigned to 284 of 942 evaluated patients (30%). All evaluated features were associated with appendicitis. Imaging profiles were created after multivariable logistic regression analysis. Of 147 patients with a thickened appendix, local transducer tenderness and peri-appendiceal fat infiltration on US, 139 (95%) had appendicitis. On CT, 119 patients in whom the appendix was completely visualised, thickened, with peri-appendiceal fat infiltration and appendiceal enhancement, 114 had a final diagnosis of appendicitis (96%). When at least two of these essential features were present on US or CT, sensitivity was 92% (95% CI 89-96%) and 96% (95% CI 93-98%), respectively. Most patients with appendicitis can be categorised within a few imaging profiles on US and CT. When two of the essential features are present the diagnosis of appendicitis can be made accurately. (orig.)

Profiles of US and CT imaging features with a high probability of appendicitis

Energy Technology Data Exchange (ETDEWEB)

Randen, A. van; Lameris, W. [University of Amsterdam, Department of Radiology, Academic Medical Center, Amsterdam (Netherlands); University of Amsterdam, Department of Surgery, Academic Medical Center, Amsterdam (Netherlands); Es, H.W. van [St Antonius Hospital, Department of Radiology, Nieuwegein (Netherlands); Hove, W. ten; Bouma, W.H. [Gelre Hospitals, Department of Surgery, Apeldoorn (Netherlands); Leeuwen, M.S. van [University Medical Centre, Department of Radiology, Utrecht (Netherlands); Keulen, E.M. van [Tergooi Hospitals, Department of Radiology, Hilversum (Netherlands); Hulst, V.P.M. van der [Onze Lieve Vrouwe Gasthuis, Department of Radiology, Amsterdam (Netherlands); Henneman, O.D. [Bronovo Hospital, Department of Radiology, The Hague (Netherlands); Bossuyt, P.M. [University of Amsterdam, Department of Clinical Epidemiology, Biostatistics, and Bioinformatics, Academic Medical Center, Amsterdam (Netherlands); Boermeester, M.A. [University of Amsterdam, Department of Surgery, Academic Medical Center, Amsterdam (Netherlands); Stoker, J. [University of Amsterdam, Department of Radiology, Academic Medical Center, Amsterdam (Netherlands)

2010-07-15

To identify and evaluate profiles of US and CT features associated with acute appendicitis. Consecutive patients presenting with acute abdominal pain at the emergency department were invited to participate in this study. All patients underwent US and CT. Imaging features known to be associated with appendicitis, and an imaging diagnosis were prospectively recorded by two independent radiologists. A final diagnosis was assigned after 6 months. Associations between appendiceal imaging features and a final diagnosis of appendicitis were evaluated with logistic regression analysis. Appendicitis was assigned to 284 of 942 evaluated patients (30%). All evaluated features were associated with appendicitis. Imaging profiles were created after multivariable logistic regression analysis. Of 147 patients with a thickened appendix, local transducer tenderness and peri-appendiceal fat infiltration on US, 139 (95%) had appendicitis. On CT, 119 patients in whom the appendix was completely visualised, thickened, with peri-appendiceal fat infiltration and appendiceal enhancement, 114 had a final diagnosis of appendicitis (96%). When at least two of these essential features were present on US or CT, sensitivity was 92% (95% CI 89-96%) and 96% (95% CI 93-98%), respectively. Most patients with appendicitis can be categorised within a few imaging profiles on US and CT. When two of the essential features are present the diagnosis of appendicitis can be made accurately. (orig.)

Probability calculations for three-part mineral resource assessments

Science.gov (United States)

Ellefsen, Karl J.

2017-06-27

Three-part mineral resource assessment is a methodology for predicting, in a specified geographic region, both the number of undiscovered mineral deposits and the amount of mineral resources in those deposits. These predictions are based on probability calculations that are performed with computer software that is newly implemented. Compared to the previous implementation, the new implementation includes new features for the probability calculations themselves and for checks of those calculations. The development of the new implementation lead to a new understanding of the probability calculations, namely the assumptions inherent in the probability calculations. Several assumptions strongly affect the mineral resource predictions, so it is crucial that they are checked during an assessment. The evaluation of the new implementation leads to new findings about the probability calculations,namely findings regarding the precision of the computations,the computation time, and the sensitivity of the calculation results to the input.

The Probabilistic Convolution Tree: Efficient Exact Bayesian Inference for Faster LC-MS/MS Protein Inference

Science.gov (United States)

Serang, Oliver

2014-01-01

Exact Bayesian inference can sometimes be performed efficiently for special cases where a function has commutative and associative symmetry of its inputs (called “causal independence”). For this reason, it is desirable to exploit such symmetry on big data sets. Here we present a method to exploit a general form of this symmetry on probabilistic adder nodes by transforming those probabilistic adder nodes into a probabilistic convolution tree with which dynamic programming computes exact probabilities. A substantial speedup is demonstrated using an illustration example that can arise when identifying splice forms with bottom-up mass spectrometry-based proteomics. On this example, even state-of-the-art exact inference algorithms require a runtime more than exponential in the number of splice forms considered. By using the probabilistic convolution tree, we reduce the runtime to and the space to where is the number of variables joined by an additive or cardinal operator. This approach, which can also be used with junction tree inference, is applicable to graphs with arbitrary dependency on counting variables or cardinalities and can be used on diverse problems and fields like forward error correcting codes, elemental decomposition, and spectral demixing. The approach also trivially generalizes to multiple dimensions. PMID:24626234

New exact solutions of the mBBM equation

International Nuclear Information System (INIS)

Zhang Zhe; Li Desheng

2013-01-01

The enhanced modified simple equation method presented in this article is applied to construct the exact solutions of modified Benjamin-Bona-Mahoney equation. Some new exact solutions are derived by using this method. When some parameters are taken as special values, the solitary wave solutions can be got from the exact solutions. It is shown that the method introduced in this paper has general significance in searching for exact solutions to the nonlinear evolution equations. (authors)

Exact discretization of Schrödinger equation

Energy Technology Data Exchange (ETDEWEB)

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2016-01-08

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

Exact discretization of Schrödinger equation

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2016-01-01

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

Harmonic oscillator in heat bath: Exact simulation of time-lapse-recorded data and exact analytical benchmark statistics

DEFF Research Database (Denmark)

Nørrelykke, Simon F; Flyvbjerg, Henrik

2011-01-01

The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...

Endoscopic ultrasound features of chronic pancreatitis

DEFF Research Database (Denmark)

Rana, Surinder Singh; Vilmann, Peter

2015-01-01

As endoscopic ultrasound (EUS) is the most sensitive imaging modality for diagnosing pancreatic disorders, it can demonstrate subtle alterations in the pancreatic parenchymal and ductal structure even before traditional imaging and functional testing demonstrate any abnormality. In spite...... of this fact and abundant literature, the exact role of EUS in the diagnosis of chronic pancreatitis (CP) is still not established. The EUS features to diagnose CP have evolved over a period from a pure qualitative approach to more advanced and complicated scoring systems incorporating multiple parenchymal...... to define the exact role of these criteria. The measurement of strain ratio using quantitative EUS elastography and thus allowing quantification of pancreatic fibrosis seems to be a promising new technique....

An extended car-following model considering random safety distance with different probabilities

Science.gov (United States)

Wang, Jufeng; Sun, Fengxin; Cheng, Rongjun; Ge, Hongxia; Wei, Qi

2018-02-01

Because of the difference in vehicle type or driving skill, the driving strategy is not exactly the same. The driving speeds of the different vehicles may be different for the same headway. Since the optimal velocity function is just determined by the safety distance besides the maximum velocity and headway, an extended car-following model accounting for random safety distance with different probabilities is proposed in this paper. The linear stable condition for this extended traffic model is obtained by using linear stability theory. Numerical simulations are carried out to explore the complex phenomenon resulting from multiple safety distance in the optimal velocity function. The cases of multiple types of safety distances selected with different probabilities are presented. Numerical results show that the traffic flow with multiple safety distances with different probabilities will be more unstable than that with single type of safety distance, and will result in more stop-and-go phenomena.

Internal Medicine residents use heuristics to estimate disease probability.

Science.gov (United States)

Phang, Sen Han; Ravani, Pietro; Schaefer, Jeffrey; Wright, Bruce; McLaughlin, Kevin

2015-01-01

Training in Bayesian reasoning may have limited impact on accuracy of probability estimates. In this study, our goal was to explore whether residents previously exposed to Bayesian reasoning use heuristics rather than Bayesian reasoning to estimate disease probabilities. We predicted that if residents use heuristics then post-test probability estimates would be increased by non-discriminating clinical features or a high anchor for a target condition. We randomized 55 Internal Medicine residents to different versions of four clinical vignettes and asked them to estimate probabilities of target conditions. We manipulated the clinical data for each vignette to be consistent with either 1) using a representative heuristic, by adding non-discriminating prototypical clinical features of the target condition, or 2) using anchoring with adjustment heuristic, by providing a high or low anchor for the target condition. When presented with additional non-discriminating data the odds of diagnosing the target condition were increased (odds ratio (OR) 2.83, 95% confidence interval [1.30, 6.15], p = 0.009). Similarly, the odds of diagnosing the target condition were increased when a high anchor preceded the vignette (OR 2.04, [1.09, 3.81], p = 0.025). Our findings suggest that despite previous exposure to the use of Bayesian reasoning, residents use heuristics, such as the representative heuristic and anchoring with adjustment, to estimate probabilities. Potential reasons for attribute substitution include the relative cognitive ease of heuristics vs. Bayesian reasoning or perhaps residents in their clinical practice use gist traces rather than precise probability estimates when diagnosing.

Ruin probabilities with compounding assets for discrete time finite horizon problem, independent period claim sizes and general premium structure

NARCIS (Netherlands)

Kok, de A.G.

2003-01-01

In this paper, we present fast and accurate approximations for the probability of ruin over a finite number of periods, assuming inhomogeneous independent claim size distributions and arbitrary premium income in subsequent periods. We develop exact recursive expressions for the non-ruin

Qubit-qutrit separability-probability ratios

International Nuclear Information System (INIS)

Slater, Paul B.

2005-01-01

Paralleling our recent computationally intensive (quasi-Monte Carlo) work for the case N=4 (e-print quant-ph/0308037), we undertake the task for N=6 of computing to high numerical accuracy, the formulas of Sommers and Zyczkowski (e-print quant-ph/0304041) for the (N 2 -1)-dimensional volume and (N 2 -2)-dimensional hyperarea of the (separable and nonseparable) NxN density matrices, based on the Bures (minimal monotone) metric--and also their analogous formulas (e-print quant-ph/0302197) for the (nonmonotone) flat Hilbert-Schmidt metric. With the same seven 10 9 well-distributed ('low-discrepancy') sample points, we estimate the unknown volumes and hyperareas based on five additional (monotone) metrics of interest, including the Kubo-Mori and Wigner-Yanase. Further, we estimate all of these seven volume and seven hyperarea (unknown) quantities when restricted to the separable density matrices. The ratios of separable volumes (hyperareas) to separable plus nonseparable volumes (hyperareas) yield estimates of the separability probabilities of generically rank-6 (rank-5) density matrices. The (rank-6) separability probabilities obtained based on the 35-dimensional volumes appear to be--independently of the metric (each of the seven inducing Haar measure) employed--twice as large as those (rank-5 ones) based on the 34-dimensional hyperareas. (An additional estimate--33.9982--of the ratio of the rank-6 Hilbert-Schmidt separability probability to the rank-4 one is quite clearly close to integral too.) The doubling relationship also appears to hold for the N=4 case for the Hilbert-Schmidt metric, but not the others. We fit simple exact formulas to our estimates of the Hilbert-Schmidt separable volumes and hyperareas in both the N=4 and N=6 cases

Profiles of US and CT imaging features with a high probability of appendicitis

NARCIS (Netherlands)

van Randen, A.; Laméris, W.; van Es, H.W.; ten Hove, W.; Bouma, W.H.; van Leeuwen, M.S.; van Keulen, E.M.; van der Hulst, V.P.M.; Henneman, O.D.; Bossuyt, P.M.; Boermeester, M.A.; Stoker, J.

2010-01-01

To identify and evaluate profiles of US and CT features associated with acute appendicitis. Consecutive patients presenting with acute abdominal pain at the emergency department were invited to participate in this study. All patients underwent US and CT. Imaging features known to be associated with

Algorithms for the extension of precise and imprecise conditional probability assessments: an implementation with maple V

Directory of Open Access Journals (Sweden)

Veronica Biazzo

2000-05-01

Full Text Available In this paper, we illustrate an implementation with Maple V of some procedures which allow to exactly propagate precise and imprecise probability assessments. The extension of imprecise assessments is based on a suitable generalization of the concept of coherence of de Finetti. The procedures described are supported by some examples and relevant cases.

Advanced features of the fault tree solver FTREX

International Nuclear Information System (INIS)

Jung, Woo Sik; Han, Sang Hoon; Ha, Jae Joo

2005-01-01

This paper presents advanced features of a fault tree solver FTREX (Fault Tree Reliability Evaluation eXpert). Fault tree analysis is one of the most commonly used methods for the safety analysis of industrial systems especially for the probabilistic safety analysis (PSA) of nuclear power plants. Fault trees are solved by the classical Boolean algebra, conventional Binary Decision Diagram (BDD) algorithm, coherent BDD algorithm, and Bayesian networks. FTREX could optionally solve fault trees by the conventional BDD algorithm or the coherent BDD algorithm and could convert the fault trees into the form of the Bayesian networks. The algorithm based on the classical Boolean algebra solves a fault tree and generates MCSs. The conventional BDD algorithm generates a BDD structure of the top event and calculates the exact top event probability. The BDD structure is a factorized form of the prime implicants. The MCSs of the top event could be extracted by reducing the prime implicants in the BDD structure. The coherent BDD algorithm is developed to overcome the shortcomings of the conventional BDD algorithm such as the huge memory requirements and a long run time

Exact analysis of discrete data

CERN Document Server

Hirji, Karim F

2005-01-01

Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...

Exact, almost and delayed fault detection

DEFF Research Database (Denmark)

Niemann, Hans Henrik; Saberi, Ali; Stoorvogel, Anton A.

1999-01-01

Considers the problem of fault detection and isolation while using zero or almost zero threshold. A number of different fault detection and isolation problems using exact or almost exact disturbance decoupling are formulated. Solvability conditions are given for the formulated design problems....... The l-step delayed fault detection problem is also considered for discrete-time systems....

Exact solutions, numerical relativity and gravitational radiation

International Nuclear Information System (INIS)

Winicour, J.

1986-01-01

In recent years, there has emerged a new use for exact solutions to Einstein's equation as checks on the accuracy of numerical relativity codes. Much has already been written about codes based upon the space-like Cauchy problem. In the case of two Killing vectors, a numerical characteristic initial value formulation based upon two intersecting families of null hypersurfaces has successfully evolved the Schwarzschild and the colliding plane wave vacuum solutions. Here the author discusses, in the context of exact solutions, numerical studies of gravitational radiation based upon the null cone initial value problem. Every stage of progress in the null cone approach has been associated with exact solutions in some sense. He begins by briefly recapping this history. Then he presents two new examples illustrating how exact solutions can be useful

Perturbation of an exact strong gravity solution

International Nuclear Information System (INIS)

Baran, S.A.

1982-10-01

Perturbations of an exact strong gravity solution are investigated. It is shown, by using the new multipole expansions previously presented, that this exact and static spherically symmetric solution is stable under odd parity perturbations. (author)

Probabilities of inherent shutdown of unprotected events in innovative liquid metal reactors

International Nuclear Information System (INIS)

Mueller, C.J.; Wade, D.C.

1988-01-01

The uncertainty in predicting the effectiveness of inherent shutdown in innovative liquid metal cooled reactors with metallic fuel results from three broad contributing areas of uncertainty: (1) the inability to exactly predict the frequency of ATWS events with potential to challenge the safety systems and require inherent shutdown; (2) the approximation of representing all such events by a selected set of ''generic scenarios''; and (3) the inability to exactly calculate the core response to the selected generic scenarios. This paper discusses the work being done to address each of these contributing areas, identifies the design and research approaches being used at Argonne National Laboratory to reducing the key contributions to uncertainties in inherent shutdown, and presents results. The conditional probabilities (given ATWS initiation) of achieving temperatures capable of defeating inherent shutdown are shown to range from /approximately/0.1% to negligible for current designs

MRI features associated with acute appendicitis

Energy Technology Data Exchange (ETDEWEB)

Leeuwenburgh, Marjolein M.N. [University of Amsterdam, Department of Surgery, Academic Medical Center, Amsterdam (Netherlands); University of Amsterdam, Department of Radiology, Academic Medical Center, Amsterdam (Netherlands); Academic Medical Center, Department of Radiology (G1-223.1), Amsterdam (Netherlands); Jensch, Sebastiaan [Sint Lucas Andreas Hospital, Department of Radiology, Amsterdam (Netherlands); Gratama, Jan W.C. [Gelre Hospitals, Department of Radiology, Apeldoorn (Netherlands); Spilt, Aart [Kennemer Gasthuis, Department of Radiology, Haarlem (Netherlands); Wiarda, Bart M. [Alkmaar Medical Center, Department of Radiology, Alkmaar (Netherlands); Es, H.W. van [Sint Antonius Hospital, Department of Radiology, Nieuwegein (Netherlands); Cobben, Lodewijk P.J. [Haaglanden Medical Center, Department of Radiology, Leidschendam (Netherlands); Bossuyt, Patrick M.M. [University of Amsterdam, Department of Clinical Epidemiology, Academic Medical Center, Amsterdam (Netherlands); Boermeester, Marja A. [University of Amsterdam, Department of Surgery, Academic Medical Center, Amsterdam (Netherlands); Stoker, Jaap [University of Amsterdam, Department of Radiology, Academic Medical Center, Amsterdam (Netherlands); Collaboration: on behalf of the OPTIMAP study group

2014-01-15

To identify MRI features associated with appendicitis. Features expected to be associated with appendicitis were recorded in consensus by two expert radiologists on 223 abdominal MRIs in patients with suspected appendicitis. Nine MRI features were studied: appendix diameter >7 mm, appendicolith, peri-appendiceal fat infiltration, peri-appendiceal fluid, absence of gas in the appendix, appendiceal wall destruction, restricted diffusion of the appendiceal wall, lumen or focal fluid collections. Appendicitis was assigned as the final diagnosis in 117/223 patients. Associations between imaging features and appendicitis were evaluated with logistic regression analysis. All investigated features were significantly associated with appendicitis in univariate analysis. Combinations of two and three features were associated with a probability of appendicitis of 88 % and 92 %, respectively. In patients without any of the nine features, appendicitis was present in 2 % of cases. After multivariate analysis, only an appendix diameter >7 mm, peri-appendiceal fat infiltration and restricted diffusion of the appendiceal wall were significantly associated with appendicitis. The probability of appendicitis was 96 % in their presence and 2 % in their absence. An appendix diameter >7 mm, peri-appendiceal fat infiltration and restricted diffusion of the appendiceal wall have the strongest association with appendicitis on MRI. (orig.)

MRI features associated with acute appendicitis

International Nuclear Information System (INIS)

Leeuwenburgh, Marjolein M.N.; Jensch, Sebastiaan; Gratama, Jan W.C.; Spilt, Aart; Wiarda, Bart M.; Es, H.W. van; Cobben, Lodewijk P.J.; Bossuyt, Patrick M.M.; Boermeester, Marja A.; Stoker, Jaap

2014-01-01

To identify MRI features associated with appendicitis. Features expected to be associated with appendicitis were recorded in consensus by two expert radiologists on 223 abdominal MRIs in patients with suspected appendicitis. Nine MRI features were studied: appendix diameter >7 mm, appendicolith, peri-appendiceal fat infiltration, peri-appendiceal fluid, absence of gas in the appendix, appendiceal wall destruction, restricted diffusion of the appendiceal wall, lumen or focal fluid collections. Appendicitis was assigned as the final diagnosis in 117/223 patients. Associations between imaging features and appendicitis were evaluated with logistic regression analysis. All investigated features were significantly associated with appendicitis in univariate analysis. Combinations of two and three features were associated with a probability of appendicitis of 88 % and 92 %, respectively. In patients without any of the nine features, appendicitis was present in 2 % of cases. After multivariate analysis, only an appendix diameter >7 mm, peri-appendiceal fat infiltration and restricted diffusion of the appendiceal wall were significantly associated with appendicitis. The probability of appendicitis was 96 % in their presence and 2 % in their absence. An appendix diameter >7 mm, peri-appendiceal fat infiltration and restricted diffusion of the appendiceal wall have the strongest association with appendicitis on MRI. (orig.)

Analytic results for asymmetric random walk with exponential transition probabilities

International Nuclear Information System (INIS)

Gutkowicz-Krusin, D.; Procaccia, I.; Ross, J.

1978-01-01

We present here exact analytic results for a random walk on a one-dimensional lattice with asymmetric, exponentially distributed jump probabilities. We derive the generating functions of such a walk for a perfect lattice and for a lattice with absorbing boundaries. We obtain solutions for some interesting moment properties, such as mean first passage time, drift velocity, dispersion, and branching ratio for absorption. The symmetric exponential walk is solved as a special case. The scaling of the mean first passage time with the size of the system for the exponentially distributed walk is determined by the symmetry and is independent of the range

Computing Moment-Based Probability Tables for Self-Shielding Calculations in Lattice Codes

International Nuclear Information System (INIS)

Hebert, Alain; Coste, Mireille

2002-01-01

As part of the self-shielding model used in the APOLLO2 lattice code, probability tables are required to compute self-shielded cross sections for coarse energy groups (typically with 99 or 172 groups). This paper describes the replacement of the multiband tables (typically with 51 subgroups) with moment-based tables in release 2.5 of APOLLO2. An improved Ribon method is proposed to compute moment-based probability tables, allowing important savings in CPU resources while maintaining the accuracy of the self-shielding algorithm. Finally, a validation is presented where the absorption rates obtained with each of these techniques are compared with exact values obtained using a fine-group elastic slowing-down calculation in the resolved energy domain. Other results, relative to the Rowland's benchmark and to three assembly production cases, are also presented

Classes of exact Einstein Maxwell solutions

Science.gov (United States)

Komathiraj, K.; Maharaj, S. D.

2007-12-01

We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.

Exact optics - III. Schwarzschild's spectrograph camera revised

Science.gov (United States)

Willstrop, R. V.

2004-03-01

Karl Schwarzschild identified a system of two mirrors, each defined by conic sections, free of third-order spherical aberration, coma and astigmatism, and with a flat focal surface. He considered it impractical, because the field was too restricted. This system was rediscovered as a quadratic approximation to one of Lynden-Bell's `exact optics' designs which have wider fields. Thus the `exact optics' version has a moderate but useful field, with excellent definition, suitable for a spectrograph camera. The mirrors are strongly aspheric in both the Schwarzschild design and the exact optics version.

Parabolic features and the erosion rate on Venus

Science.gov (United States)

Strom, Robert G.

1993-01-01

The impact cratering record on Venus consists of 919 craters covering 98 percent of the surface. These craters are remarkably well preserved, and most show pristine structures including fresh ejecta blankets. Only 35 craters (3.8 percent) have had their ejecta blankets embayed by lava and most of these occur in the Atla-Beta Regio region; an area thought to be recently active. parabolic features are associated with 66 of the 919 craters. These craters range in size from 6 to 105 km diameter. The parabolic features are thought to be the result of the deposition of fine-grained ejecta by winds in the dense venusian atmosphere. The deposits cover about 9 percent of the surface and none appear to be embayed by younger volcanic materials. However, there appears to be a paucity of these deposits in the Atla-Beta Regio region, and this may be due to the more recent volcanism in this area of Venus. Since parabolic features are probably fine-grain, wind-deposited ejecta, then all impact craters on Venus probably had these deposits at some time in the past. The older deposits have probably been either eroded or buried by eolian processes. Therefore, the present population of these features is probably associated with the most recent impact craters on the planet. Furthermore, the size/frequency distribution of craters with parabolic features is virtually identical to that of the total crater population. This suggests that there has been little loss of small parabolic features compared to large ones, otherwise there should be a significant and systematic paucity of craters with parabolic features with decreasing size compared to the total crater population. Whatever is erasing the parabolic features apparently does so uniformly regardless of the areal extent of the deposit. The lifetime of parabolic features and the eolian erosion rate on Venus can be estimated from the average age of the surface and the present population of parabolic features.

Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

Science.gov (United States)

Simpson, Matthew J

2015-01-01

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).

Generalized Probability-Probability Plots

NARCIS (Netherlands)

Mushkudiani, N.A.; Einmahl, J.H.J.

2004-01-01

We introduce generalized Probability-Probability (P-P) plots in order to study the one-sample goodness-of-fit problem and the two-sample problem, for real valued data.These plots, that are constructed by indexing with the class of closed intervals, globally preserve the properties of classical P-P

Exact and approximate multiple diffraction calculations

International Nuclear Information System (INIS)

Alexander, Y.; Wallace, S.J.; Sparrow, D.A.

1976-08-01

A three-body potential scattering problem is solved in the fixed scatterer model exactly and approximately to test the validity of commonly used assumptions of multiple scattering calculations. The model problem involves two-body amplitudes that show diffraction-like differential scattering similar to high energy hadron-nucleon amplitudes. The exact fixed scatterer calculations are compared to Glauber approximation, eikonal-expansion results and a noneikonal approximation

Exact Performance Analysis of Dual-Hop Semi-Blind AF Relaying over Arbitrary Nakagami-m Fading Channels

KAUST Repository

Xia, Minghua

2011-10-01

Relay transmission is promising for future wireless systems due to its significant cooperative diversity gain. The performance of dual-hop semi-blind amplify-and-forward (AF) relaying systems was extensively investigated, for transmissions over Rayleigh fading channels or Nakagami- fading channels with integer fading parameter. For the general Nakagami- fading with arbitrary values, the exact closed-form system performance analysis is more challenging. In this paper, we explicitly derive the moment generation function (MGF), probability density function (PDF) and moments of the end-to-end signal-to-noise ratio (SNR) over arbitrary Nakagami- fading channels with semi-blind AF relay. With these results, the system performance evaluation in terms of outage probability, average symbol error probability, ergodic capacity and diversity order, is conducted. The analysis developed in this paper applies to any semi-blind AF relaying systems with fixed relay gain, and two major strategies for computing the relay gain are compared in terms of system performance. All analytical results are corroborated by simulation results and they are shown to be efficient tools to evaluate system performance.

Exact Performance Analysis of Dual-Hop Semi-Blind AF Relaying over Arbitrary Nakagami-m Fading Channels

KAUST Repository

Xia, Minghua; Xing, Chengwen; Wu, Yik-Chung; Aissa, Sonia

2011-01-01

Relay transmission is promising for future wireless systems due to its significant cooperative diversity gain. The performance of dual-hop semi-blind amplify-and-forward (AF) relaying systems was extensively investigated, for transmissions over Rayleigh fading channels or Nakagami-𝑚 fading channels with integer fading parameter. For the general Nakagami-𝑚 fading with arbitrary 𝑚 values, the exact closed-form system performance analysis is more challenging. In this paper, we explicitly derive the moment generation function (MGF), probability density function (PDF) and moments of the end-to-end signal-to-noise ratio (SNR) over arbitrary Nakagami-𝑚 fading channels with semi-blind AF relay. With these results, the system performance evaluation in terms of outage probability, average symbol error probability, ergodic capacity and diversity order, is conducted. The analysis developed in this paper applies to any semi-blind AF relaying systems with fixed relay gain, and two major strategies for computing the relay gain are compared in terms of system performance. All analytical results are corroborated by simulation results and they are shown to be efficient tools to evaluate system performance.

Probability, random variables, and random processes theory and signal processing applications

CERN Document Server

Shynk, John J

2012-01-01

Probability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. It is intended for first-year graduate students who have some familiarity with probability and random variables, though not necessarily of random processes and systems that operate on random signals. It is also appropriate for advanced undergraduate students who have a strong mathematical background. The book has the following features: Several app

Probability Aggregates in Probability Answer Set Programming

OpenAIRE

Saad, Emad

2013-01-01

Probability answer set programming is a declarative programming that has been shown effective for representing and reasoning about a variety of probability reasoning tasks. However, the lack of probability aggregates, e.g. {\\em expected values}, in the language of disjunctive hybrid probability logic programs (DHPP) disallows the natural and concise representation of many interesting problems. In this paper, we extend DHPP to allow arbitrary probability aggregates. We introduce two types of p...

Exact solutions for a system of nonlinear plasma fluid equations

International Nuclear Information System (INIS)

Prahovic, M.G.; Hazeltine, R.D.; Morrison, P.J.

1991-04-01

A method is presented for constructing exact solutions to a system of nonlinear plasma fluid equations that combines the physics of reduced magnetohydrodynamics and the electrostatic drift-wave description of the Charney-Hasegawa-Mima equation. The system has nonlinearities that take the form of Poisson brackets involving the fluid field variables. The method relies on modifying a class of simple equilibrium solutions, but no approximations are made. A distinguishing feature is that the original nonlinear problem is reduced to the solution of two linear partial differential equations, one fourth-order and the other first-order. The first-order equation has Hamiltonian characteristics and is easily integrated, supplying information about the general structure of solutions. 6 refs

Incidental learning of probability information is differentially affected by the type of visual working memory representation.

Science.gov (United States)

van Lamsweerde, Amanda E; Beck, Melissa R

2015-12-01

In this study, we investigated whether the ability to learn probability information is affected by the type of representation held in visual working memory. Across 4 experiments, participants detected changes to displays of coloured shapes. While participants detected changes in 1 dimension (e.g., colour), a feature from a second, nonchanging dimension (e.g., shape) predicted which object was most likely to change. In Experiments 1 and 3, items could be grouped by similarity in the changing dimension across items (e.g., colours and shapes were repeated in the display), while in Experiments 2 and 4 items could not be grouped by similarity (all features were unique). Probability information from the predictive dimension was learned and used to increase performance, but only when all of the features within a display were unique (Experiments 2 and 4). When it was possible to group by feature similarity in the changing dimension (e.g., 2 blue objects appeared within an array), participants were unable to learn probability information and use it to improve performance (Experiments 1 and 3). The results suggest that probability information can be learned in a dimension that is not explicitly task-relevant, but only when the probability information is represented with the changing dimension in visual working memory. (c) 2015 APA, all rights reserved).

Random trees between two walls: exact partition function

International Nuclear Information System (INIS)

Bouttier, J; Di Francesco, P; Guitter, E

2003-01-01

We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labelled by integers representing their position in the target space, with the solid-on-solid constraint that adjacent vertices have labels differing by ±1. A non-trivial partition function is obtained whenever the target space is bounded by walls. We concentrate on the two cases where the target space is (i) the half-line bounded by a wall at the origin or (ii) a segment bounded by two walls at a finite distance. The general solution has a soliton-like structure involving elliptic functions. We derive the corresponding continuum scaling limit which takes the remarkable form of the Weierstrass p function with constrained periods. These results are used to analyse the probability for an evolving population spreading in one dimension to attain the boundary of a given domain with the geometry of the target (i) or (ii). They also translate, via suitable bijections, into generating functions for bounded planar graphs

Probability density function modeling of scalar mixing from concentrated sources in turbulent channel flow

OpenAIRE

Bakosi, J.; Franzese, P.; Boybeyi, Z.

2010-01-01

Dispersion of a passive scalar from concentrated sources in fully developed turbulent channel flow is studied with the probability density function (PDF) method. The joint PDF of velocity, turbulent frequency and scalar concentration is represented by a large number of Lagrangian particles. A stochastic near-wall PDF model combines the generalized Langevin model of Haworth & Pope with Durbin's method of elliptic relaxation to provide a mathematically exact treatment of convective and viscous ...

Probability, Statistics, and Stochastic Processes

CERN Document Server

Olofsson, Peter

2012-01-01

This book provides a unique and balanced approach to probability, statistics, and stochastic processes.   Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area.  The Second Edition features new coverage of analysis of variance (ANOVA), consistency and efficiency of estimators, asymptotic theory for maximum likelihood estimators, empirical distribution function and the Kolmogorov-Smirnov test, general linear models, multiple comparisons, Markov chain Monte Carlo (MCMC), Brownian motion, martingales, and

Exact and approximate formulas for neutrino mixing and oscillations with non-standard interactions

International Nuclear Information System (INIS)

Meloni, Davide; Ohlsson, Tommy; Zhang, He

2009-01-01

We present, both exactly and approximately, a complete set of mappings between the vacuum (or fundamental) leptonic mixing parameters and the effective ones in matter with non-standard neutrino interaction (NSI) effects included. Within the three-flavor neutrino framework and a constant matter density profile, a full set of sum rules is established, which enables us to reconstruct the moduli of the effective leptonic mixing matrix elements, in terms of the vacuum mixing parameters in order to reproduce the neutrino oscillation probabilities for future long-baseline experiments. Very compact, but quite accurate, approximate mappings are obtained based on series expansions in the neutrino mass hierarchy parameter η ≡ Δm 2 21 /Δm 2 31 , the vacuum leptonic mixing parameter s 13 ≡ sin θ 13 , and the NSI parameters ε αβ . A detailed numerical analysis about how the NSIs affect the smallest leptonic mixing angle θ 13 , the deviation of the leptonic mixing angle θ 23 from its maximal mixing value, and the transition probabilities useful for future experiments are performed using our analytical results.

Feature-Learning-Based Printed Circuit Board Inspection via Speeded-Up Robust Features and Random Forest

Directory of Open Access Journals (Sweden)

Eun Hye Yuk

2018-06-01

Full Text Available With the coming of the 4th industrial revolution era, manufacturers produce high-tech products. As the production process is refined, inspection technologies become more important. Specifically, the inspection of a printed circuit board (PCB, which is an indispensable part of electronic products, is an essential step to improve the quality of the process and yield. Image processing techniques are utilized for inspection, but there are limitations because the backgrounds of images are different and the kinds of defects increase. In order to overcome these limitations, methods based on machine learning have been used recently. These methods can inspect without a normal image by learning fault patterns. Therefore, this paper proposes a method can detect various types of defects using machine learning. The proposed method first extracts features through speeded-up robust features (SURF, then learns the fault pattern and calculates probabilities. After that, we generate a weighted kernel density estimation (WKDE map weighted by the probabilities to consider the density of the features. Because the probability of the WKDE map can detect an area where the defects are concentrated, it improves the performance of the inspection. To verify the proposed method, we apply the method to PCB images and confirm the performance of the method.

Exact solutions in three-dimensional gravity

CERN Document Server

Garcia-Diaz, Alberto A

2017-01-01

A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravit...

Exact gravitational quasinormal frequencies of topological black holes

International Nuclear Information System (INIS)

Birmingham, Danny; Mokhtari, Susan

2006-01-01

We compute the exact gravitational quasinormal frequencies for massless topological black holes in d-dimensional anti-de Sitter space. Using the gauge invariant formalism for gravitational perturbations derived by Kodama and Ishibashi, we show that in all cases the scalar, vector, and tensor modes can be reduced to a simple scalar field equation. This equation is exactly solvable in terms of hypergeometric functions, thus allowing an exact analytic determination of the gravitational quasinormal frequencies

Matrix elements and transition probabilities of interaction of electromagnetic field with a hydrogen-like atom

International Nuclear Information System (INIS)

Rajput, B.S.

1977-01-01

Using the reduced expansions of second quantized electromagnetic vector potential operator in terms of irreducible representations of Pioncare group in the interaction Hamiltonian, the exact matrix elements of interaction of electromagnetic field with a hydrogenic atom have been derived and the contributions of transitions for different combinations of angular momentum quantum numbers to the transition probabilities of various lines in Lyman-, Balmer-, and Paschen-series have been computed. (author)

Classical many-body theory with retarded interactions: Dynamical irreversibility and determinism without probabilities

Energy Technology Data Exchange (ETDEWEB)

Zakharov, A.Yu., E-mail: Anatoly.Zakharov@novsu.ru; Zakharov, M.A., E-mail: ma_zakharov@list.ru

2016-01-28

The exact equations of motion for microscopic density of classical many-body system with account of inter-particle retarded interactions is derived. It is shown that interactions retardation leads to irreversible behavior of many-body systems. - Highlights: • A new form of equation of motion of classical many-body system is proposed. • Interactions retardation as one of the mechanisms of many-body system irreversibility. • Irreversibility and determinism without probabilities. • The possible way to microscopic foundation of thermodynamics.

Quaternionic formulation of the exact parity model

Energy Technology Data Exchange (ETDEWEB)

Brumby, S.P.; Foot, R.; Volkas, R.R.

1996-02-28

The exact parity model (EPM) is a simple extension of the standard model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In the paper it is shown that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory. 13 refs.

Quaternionic formulation of the exact parity model

International Nuclear Information System (INIS)

Brumby, S.P.; Foot, R.; Volkas, R.R.

1996-01-01

The exact parity model (EPM) is a simple extension of the standard model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In the paper it is shown that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory. 13 refs

Exact Kantowski-Sachs and Bianchi types I and III cosmological models with a conformally invariant scalar field

International Nuclear Information System (INIS)

Accioly, A.J.

1985-01-01

Exact solutions of the Einstein-Conformally Invariant Scalar Field Equations are obtained for Kantowski-Sachs and Bianchi types I and III cosmologies. The presence of the conformally invariant scalar field is responsible for some interesting features of the solutions. In particular it is found that the Bianchi I model is consistent with the big-bang theory of cosmology. (Author) [pt

Risk estimation using probability machines

Science.gov (United States)

2014-01-01

Background Logistic regression has been the de facto, and often the only, model used in the description and analysis of relationships between a binary outcome and observed features. It is widely used to obtain the conditional probabilities of the outcome given predictors, as well as predictor effect size estimates using conditional odds ratios. Results We show how statistical learning machines for binary outcomes, provably consistent for the nonparametric regression problem, can be used to provide both consistent conditional probability estimation and conditional effect size estimates. Effect size estimates from learning machines leverage our understanding of counterfactual arguments central to the interpretation of such estimates. We show that, if the data generating model is logistic, we can recover accurate probability predictions and effect size estimates with nearly the same efficiency as a correct logistic model, both for main effects and interactions. We also propose a method using learning machines to scan for possible interaction effects quickly and efficiently. Simulations using random forest probability machines are presented. Conclusions The models we propose make no assumptions about the data structure, and capture the patterns in the data by just specifying the predictors involved and not any particular model structure. So they do not run the same risks of model mis-specification and the resultant estimation biases as a logistic model. This methodology, which we call a “risk machine”, will share properties from the statistical machine that it is derived from. PMID:24581306

Exact soliton solutions of the generalized Gross-Pitaevskii equation based on expansion method

Directory of Open Access Journals (Sweden)

Ying Wang

2014-06-01

Full Text Available We give a more generalized treatment of the 1D generalized Gross-Pitaevskii equation (GGPE with variable term coefficients. External harmonic trapping potential is fully considered and the nonlinear interaction term is of arbitrary polytropic index of superfluid wave function. We also eliminate the interdependence between variable coefficients of the equation terms avoiding the restrictions that occur in some other works. The exact soliton solutions of the GGPE are obtained through the delicate combined utilization of modified lens-type transformation and F-expansion method with dominant features like soliton type properties highlighted.

The exact wavefunction factorization of a vibronic coupling system

International Nuclear Information System (INIS)

Chiang, Ying-Chih; Klaiman, Shachar; Otto, Frank; Cederbaum, Lorenz S.

2014-01-01

We investigate the exact wavefunction as a single product of electronic and nuclear wavefunction for a model conical intersection system. Exact factorized spiky potentials and nodeless nuclear wavefunctions are found. The exact factorized potential preserves the symmetry breaking effect when the coupling mode is present. Additionally nodeless wavefunctions are found to be closely related to the adiabatic nuclear eigenfunctions. This phenomenon holds even for the regime where the non-adiabatic coupling is relevant, and sheds light on the relation between the exact wavefunction factorization and the adiabatic approximation

Grading system to categorize breast MRI using BI-RADS 5th edition: a statistical study of non-mass enhancement descriptors in terms of probability of malignancy.

Science.gov (United States)

Asada, Tatsunori; Yamada, Takayuki; Kanemaki, Yoshihide; Fujiwara, Keishi; Okamoto, Satoko; Nakajima, Yasuo

2018-03-01

To analyze the association of breast non-mass enhancement descriptors in the BI-RADS 5th edition with malignancy, and to establish a grading system and categorization of descriptors. This study was approved by our institutional review board. A total of 213 patients were enrolled. Breast MRI was performed with a 1.5-T MRI scanner using a 16-channel breast radiofrequency coil. Two radiologists determined internal enhancement and distribution of non-mass enhancement by consensus. Corresponding pathologic diagnoses were obtained by either biopsy or surgery. The probability of malignancy by descriptor was analyzed using Fisher's exact test and multivariate logistic regression analysis. The probability of malignancy by category was analyzed using Fisher's exact and multi-group comparison tests. One hundred seventy-eight lesions were malignant. Multivariate model analysis showed that internal enhancement (homogeneous vs others, p probability of malignancy (p < 0.0001). The three-grade criteria and categorization by sum-up grades of descriptors appear valid for non-mass enhancement.

Exact folded-band chaotic oscillator.

Science.gov (United States)

Corron, Ned J; Blakely, Jonathan N

2012-06-01

An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.

Dissociation between exact and approximate addition in developmental dyslexia.

Science.gov (United States)

Yang, Xiujie; Meng, Xiangzhi

2016-09-01

Previous research has suggested that number sense and language are involved in number representation and calculation, in which number sense supports approximate arithmetic, and language permits exact enumeration and calculation. Meanwhile, individuals with dyslexia have a core deficit in phonological processing. Based on these findings, we thus hypothesized that children with dyslexia may exhibit exact calculation impairment while doing mental arithmetic. The reaction time and accuracy while doing exact and approximate addition with symbolic Arabic digits and non-symbolic visual arrays of dots were compared between typically developing children and children with dyslexia. Reaction time analyses did not reveal any differences across two groups of children, the accuracies, interestingly, revealed a distinction of approximation and exact addition across two groups of children. Specifically, two groups of children had no differences in approximation. Children with dyslexia, however, had significantly lower accuracy in exact addition in both symbolic and non-symbolic tasks than that of typically developing children. Moreover, linguistic performances were selectively associated with exact calculation across individuals. These results suggested that children with dyslexia have a mental arithmetic deficit specifically in the realm of exact calculation, while their approximation ability is relatively intact. Copyright © 2016 Elsevier Ltd. All rights reserved.

Transition probabilities for two-photon H (1з–2з) and He (1 1з–2 1з ...

Indian Academy of Sciences (India)

Transition amplitudes and transition probabilities for the two-photon 1-2 transition in the hydrogen atom and 11-21 transition in helium atom have been calculated using a partialclosure approach. The dominant term is calculated exactly and the remaining sum over intermediate states is calculated using a mean ...

Construction of exact constants of motion and effective models for many-body localized systems

Science.gov (United States)

Goihl, M.; Gluza, M.; Krumnow, C.; Eisert, J.

2018-04-01

One of the defining features of many-body localization is the presence of many quasilocal conserved quantities. These constants of motion constitute a cornerstone to an intuitive understanding of much of the phenomenology of many-body localized systems arising from effective Hamiltonians. They may be seen as local magnetization operators smeared out by a quasilocal unitary. However, accurately identifying such constants of motion remains a challenging problem. Current numerical constructions often capture the conserved operators only approximately, thus restricting a conclusive understanding of many-body localization. In this work, we use methods from the theory of quantum many-body systems out of equilibrium to establish an alternative approach for finding a complete set of exact constants of motion which are in addition guaranteed to represent Pauli-z operators. By this we are able to construct and investigate the proposed effective Hamiltonian using exact diagonalization. Hence, our work provides an important tool expected to further boost inquiries into the breakdown of transport due to quenched disorder.

Case series of probable sporadic Creutzfeldt-Jakob disease from Eastern India

Directory of Open Access Journals (Sweden)

Atanu Biswas

2013-01-01

Full Text Available Background: Creutzfeldt-Jakob disease is a rapidly progressive, fatal, transmissible neurodegenerative disorder caused by prion protein. It is still considered rare in countries like India. This is probably due to nonavailability of autopsy studies in majority of the center. The recent European diagnostic criterion for sporadic CJD (sCJD is useful for making an early diagnosis. Objective: To report a series of patients of probable sCJD from a neurology institute of eastern India. Materials and Methods: Patients of rapidly developing dementia fulfilling the diagnostic criteria for sCJD were included. All were investigated in detail to find out any possible treatable cause including electroencephalography (EEG, magnetic resonance imaging (MRI of brain, and cerebrospinal fluid analysis. Results: A total 10 patients of probable sCJD diagnosed using the European diagnostic criterion between December 2011 and January 2013. The clinical features are consistent with other reported series. While 60% of patients had the classical EEG findings, 100% had typical MRI features. Eight patients died within a mean duration of 4.56 months from the disease onset. Conclusions: The clinical features are similar to other reported series. Our observation raises question about the prevalence of this disease in India which needs more elaborate studies.

Negative probability in the framework of combined probability

OpenAIRE

Burgin, Mark

2013-01-01

Negative probability has found diverse applications in theoretical physics. Thus, construction of sound and rigorous mathematical foundations for negative probability is important for physics. There are different axiomatizations of conventional probability. So, it is natural that negative probability also has different axiomatic frameworks. In the previous publications (Burgin, 2009; 2010), negative probability was mathematically formalized and rigorously interpreted in the context of extende...

Internal versus external features in triggering the brain waveforms for conjunction and feature faces in recognition.

Science.gov (United States)

Nie, Aiqing; Jiang, Jingguo; Fu, Qiao

2014-08-20

Previous research has found that conjunction faces (whose internal features, e.g. eyes, nose, and mouth, and external features, e.g. hairstyle and ears, are from separate studied faces) and feature faces (partial features of these are studied) can produce higher false alarms than both old and new faces (i.e. those that are exactly the same as the studied faces and those that have not been previously presented) in recognition. The event-related potentials (ERPs) that relate to conjunction and feature faces at recognition, however, have not been described as yet; in addition, the contributions of different facial features toward ERPs have not been differentiated. To address these issues, the present study compared the ERPs elicited by old faces, conjunction faces (the internal and the external features were from two studied faces), old internal feature faces (whose internal features were studied), and old external feature faces (whose external features were studied) with those of new faces separately. The results showed that old faces not only elicited an early familiarity-related FN400, but a more anterior distributed late old/new effect that reflected recollection. Conjunction faces evoked similar late brain waveforms as old internal feature faces, but not to old external feature faces. These results suggest that, at recognition, old faces hold higher familiarity than compound faces in the profiles of ERPs and internal facial features are more crucial than external ones in triggering the brain waveforms that are characterized as reflecting the result of familiarity.

Are Haar-like Rectangular Features for Biometric Recognition Reducible?

DEFF Research Database (Denmark)

Nasrollahi, Kamal; Moeslund, Thomas B.

2013-01-01

Biometric recognition is still a very difficult task in real-world scenarios wherein unforeseen changes in degradations factors like noise, occlusion, blurriness and illumination can drastically affect the extracted features from the biometric signals. Very recently Haar-like rectangular features...... which have usually been used for object detection were introduced for biometric recognition resulting in systems that are robust against most of the mentioned degradations [9]. The problem with these features is that one can define many different such features for a given biometric signal...... and it is not clear whether all of these features are required for the actual recognition or not. This is exactly what we are dealing with in this paper: How can an initial set of Haar-like rectangular features, that have been used for biometric recognition, be reduced to a set of most influential features...

Performance Analysis of Secrecy Outage Probability for AF-Based Partial Relay Selection with Outdated Channel Estimates

Directory of Open Access Journals (Sweden)

Kyu-Sung Hwang

2017-01-01

Full Text Available We study the secrecy outage probability of the amplify-and-forward (AF relaying protocol, which consists of one source, one destination, multiple relays, and multiple eavesdroppers. In this system, the aim is to transmit the confidential messages from a source to a destination via the selected relay in presence of eavesdroppers. Moreover, partial relay selection scheme is utilized for relay selection based on outdated channel state information where only neighboring channel information (source-relays is available and passive eavesdroppers are considered where a transmitter does not have any knowledge of eavesdroppers’ channels. Specifically, we offer the exact secrecy outage probability of the proposed system in a one-integral form as well as providing the asymptotic secrecy outage probability in a closed-form. Numerical examples are given to verify our provided analytical results for different system conditions.

Exact Solutions for Einstein's Hyperbolic Geometric Flow

International Nuclear Information System (INIS)

He Chunlei

2008-01-01

In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow

A Class of Quasi-exact Solutions of Rabi Hamiltonian

International Nuclear Information System (INIS)

Pan Feng; Yao Youkun; Xie Mingxia; Han Wenjuan; Draayer, J.P.

2007-01-01

A class of quasi-exact solutions of the Rabi Hamiltonian, which describes a two-level atom interacting with a single-mode radiation field via a dipole interaction without the rotating-wave approximation, are obtained by using a wavefunction ansatz. Exact solutions for part of the spectrum are obtained when the atom-field coupling strength and the field frequency satisfy certain relations. As an example, the lowest exact energy level and the corresponding atom-field entanglement at the quasi-exactly solvable point are calculated and compared to results from the Jaynes-Cummings and counter-rotating cases of the Rabi Hamiltonian.

Abelian 2-form gauge theory: special features

International Nuclear Information System (INIS)

Malik, R P

2003-01-01

It is shown that the four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory provides an example of (i) a class of field theoretical models for the Hodge theory, and (ii) a possible candidate for the quasi-topological field theory (q-TFT). Despite many striking similarities with some of the key topological features of the two (1 + 1)-dimensional (2D) free Abelian (and self-interacting non-Abelian) gauge theories, it turns out that the 4D free Abelian 2-form gauge theory is not an exact TFT. To corroborate this conclusion, some of the key issues are discussed. In particular, it is shown that the (anti-)BRST and (anti-)co-BRST invariant quantities of the 4D 2-form Abelian gauge theory obey recursion relations that are reminiscent of the exact TFTs but the Lagrangian density of this theory is not found to be able to be expressed as the sum of (anti-)BRST and (anti-)co-BRST exact quantities as is the case with the topological 2D free Abelian (and self-interacting non-Abelian) gauge theories

Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

Directory of Open Access Journals (Sweden)

Matthew J Simpson

Full Text Available Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i the rate at which the domain elongates, (ii the diffusivity associated with the spreading density profile, (iii the reaction rate, and (iv the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t.

Tuned by experience: How orientation probability modulates early perceptual processing.

Science.gov (United States)

Jabar, Syaheed B; Filipowicz, Alex; Anderson, Britt

2017-09-01

Probable stimuli are more often and more quickly detected. While stimulus probability is known to affect decision-making, it can also be explained as a perceptual phenomenon. Using spatial gratings, we have previously shown that probable orientations are also more precisely estimated, even while participants remained naive to the manipulation. We conducted an electrophysiological study to investigate the effect that probability has on perception and visual-evoked potentials. In line with previous studies on oddballs and stimulus prevalence, low-probability orientations were associated with a greater late positive 'P300' component which might be related to either surprise or decision-making. However, the early 'C1' component, thought to reflect V1 processing, was dampened for high-probability orientations while later P1 and N1 components were unaffected. Exploratory analyses revealed a participant-level correlation between C1 and P300 amplitudes, suggesting a link between perceptual processing and decision-making. We discuss how these probability effects could be indicative of sharpening of neurons preferring the probable orientations, due either to perceptual learning, or to feature-based attention. Copyright © 2017 Elsevier Ltd. All rights reserved.

Gravity and count probabilities in an expanding universe

Science.gov (United States)

Bouchet, Francois R.; Hernquist, Lars

1992-01-01

The time evolution of nonlinear clustering on large scales in cold dark matter, hot dark matter, and white noise models of the universe is investigated using N-body simulations performed with a tree code. Count probabilities in cubic cells are determined as functions of the cell size and the clustering state (redshift), and comparisons are made with various theoretical models. We isolate the features that appear to be the result of gravitational instability, those that depend on the initial conditions, and those that are likely a consequence of numerical limitations. More specifically, we study the development of skewness, kurtosis, and the fifth moment in relation to variance, the dependence of the void probability on time as well as on sparseness of sampling, and the overall shape of the count probability distribution. Implications of our results for theoretical and observational studies are discussed.

Outage Probability Analysis in Power-Beacon Assisted Energy Harvesting Cognitive Relay Wireless Networks

Directory of Open Access Journals (Sweden)

Ngoc Phuc Le

2017-01-01

Full Text Available We study the performance of the secondary relay system in a power-beacon (PB assisted energy harvesting cognitive relay wireless network. In our system model, a secondary source node and a relay node first harvest energy from distributed PBs. Then, the source node transmits its data to the destination node with the help of the relay node. Also, fading coefficients of the links from the PBs to the source node and relay node are assumed independent but not necessarily identically distributed (i.n.i.d Nakagami-m random variables. We derive exact expressions for the power outage probability and the channel outage probability. Based on that, we analyze the total outage probability of the secondary relay system. Asymptotic analysis is also performed, which provides insights into the system behavior. Moreover, we evaluate impacts of the primary network on the performance of the secondary network with respect to the tolerant interference threshold at the primary receiver as well as the interference introduced by the primary transmitter at the secondary source and relay nodes. Simulation results are provided to validate the analysis.

Extremal black holes as exact string solutions

International Nuclear Information System (INIS)

Horowitz, G.T.; Tseytlin, A.A.

1994-01-01

We show that the leading order solution describing an extremal electrically charged black hole in string theory is, in fact, an exact solution to all orders in α' when interpreted in a Kaluza-Klein fashion. This follows from the observation that it can be obtained via dimensional reduction from a five-dimensional background which is proved to be an exact string solution

Quasi exact solution of the Rabi Hamiltonian

CERN Document Server

Koç, R; Tuetuencueler, H

2002-01-01

A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for eigenstates and eigenvalues in terms of orthogonal polynomials. It is also demonstrated that the Rabi system, in a particular case, coincides with the quasi exactly solvable Poeschl-Teller potential.

Criteria for exact qudit universality

International Nuclear Information System (INIS)

Brennen, Gavin K.; O'Leary, Dianne P.; Bullock, Stephen S.

2005-01-01

We describe criteria for implementation of quantum computation in qudits. A qudit is a d-dimensional system whose Hilbert space is spanned by states vertical bar 0>, vertical bar 1>, ..., vertical bar d-1>. An important earlier work [A. Muthukrishnan and C.R. Stroud, Jr., Phys. Rev. A 62, 052309 (2000)] describes how to exactly simulate an arbitrary unitary on multiple qudits using a 2d-1 parameter family of single qudit and two qudit gates. That technique is based on the spectral decomposition of unitaries. Here we generalize this argument to show that exact universality follows given a discrete set of single qudit Hamiltonians and one two-qudit Hamiltonian. The technique is related to the QR-matrix decomposition of numerical linear algebra. We consider a generic physical system in which the single qudit Hamiltonians are a small collection of H jk x =(ℎ/2π)Ω(vertical bar k> jk y =(ℎ/2π)Ω(i vertical bar k> jk x,y are allowed Hamiltonians. One qudit exact universality follows iff this graph is connected, and complete universality results if the two-qudit Hamiltonian H=(ℎ/2π)Ω vertical bar d-1,d-1> 87 Rb and construct an optimal gate sequence using Raman laser pulses

Exact theory of freeze-out

Science.gov (United States)

Cannoni, Mirco

2015-03-01

We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature . The point , which coincides with the stationary point of the equation for the quantity , is where the maximum departure of the WIMPs abundance from the thermal value is reached. For each mass and total annihilation cross section , the temperature and the actual WIMPs abundance are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval . The matching of the two abundances at is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1-2 % in the case of -wave and -wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics.

Quasitraces on exact C*-algebras are traces

DEFF Research Database (Denmark)

Haagerup, Uffe

2014-01-01

It is shown that all 2-quasitraces on a unital exact C ∗   -algebra are traces. As consequences one gets: (1) Every stably finite exact unital C ∗   -algebra has a tracial state, and (2) if an AW ∗   -factor of type II 1   is generated (as an AW ∗   -algebra) by an exact C ∗   -subalgebra, then i......, then it is a von Neumann II 1   -factor. This is a partial solution to a well known problem of Kaplansky. The present result was used by Blackadar, Kumjian and Rørdam to prove that RR(A)=0  for every simple non-commutative torus of any dimension...

Exact analytical thermodynamic expressions for a Brownian heat engine

Science.gov (United States)

Taye, Mesfin Asfaw

2015-09-01

The nonequilibrium thermodynamics feature of a Brownian motor operating between two different heat baths is explored as a function of time t . Using the Gibbs entropy and Schnakenberg microscopic stochastic approach, we find exact closed form expressions for the free energy, the rate of entropy production, and the rate of entropy flow from the system to the outside. We show that when the system is out of equilibrium, it constantly produces entropy and at the same time extracts entropy out of the system. Its entropy production and extraction rates decrease in time and saturate to a constant value. In the long time limit, the rate of entropy production balances the rate of entropy extraction, and at equilibrium both entropy production and extraction rates become zero. Furthermore, via the present model, many thermodynamic theories can be checked.

Sufficient Statistics for Divergence and the Probability of Misclassification

Science.gov (United States)

Quirein, J.

1972-01-01

One particular aspect is considered of the feature selection problem which results from the transformation x=Bz, where B is a k by n matrix of rank k and k is or = to n. It is shown that in general, such a transformation results in a loss of information. In terms of the divergence, this is equivalent to the fact that the average divergence computed using the variable x is less than or equal to the average divergence computed using the variable z. A loss of information in terms of the probability of misclassification is shown to be equivalent to the fact that the probability of misclassification computed using variable x is greater than or equal to the probability of misclassification computed using variable z. First, the necessary facts relating k-dimensional and n-dimensional integrals are derived. Then the mentioned results about the divergence and probability of misclassification are derived. Finally it is shown that if no information is lost (in x = Bz) as measured by the divergence, then no information is lost as measured by the probability of misclassification.

New exact solutions of the Dirac equation. 11

International Nuclear Information System (INIS)

Bagrov, V.G.; Noskov, M.D.

1984-01-01

Investigations into determining new exact solutions of relativistic wave equations started in another paper were continued. Exact solutions of the Dirac, Klein-Gordon equations and classical relativistic equations of motion in four new types of external electromagnetic fields were found

Exact solitary waves of the Korteveg - de Vries - Burgers equation

OpenAIRE

Kudryashov, N. A.

2004-01-01

New approach is presented to search exact solutions of nonlinear differential equations. This method is used to look for exact solutions of the Korteveg -- de Vries -- Burgers equation. New exact solitary waves of the Korteveg -- de Vries -- Burgers equation are found.

Probability representations of a class of two-way diffusions

Energy Technology Data Exchange (ETDEWEB)

Clifford, P.; Green, N.J.P. [Department of Statistics, University of Oxford, Oxford (United Kingdom); Feng, J.F. [COGS, Sussex University, Brighton (United Kingdom); Wei, G. [Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong (China)

2002-07-19

There has been little progress in the analysis of two-way diffusion in the last few decades due to the difficulties brought by the interface section similar to a free boundary condition. In this paper, however, the equivalent probability model is considered and the interface section is precisely described by an integral equation. The solution of two-way diffusion is then expressed in an integral form with the integrand being the solution of a classical first passage time model and the solution of a one-dimensional integral equation which is relatively easier to solve. The exact expression of the two-way diffusion enables us to find the explicit solution of the model with infinite horizontal boundaries and without drifting. (author)

Analysis of Conserved Structural Features of Selenoprotein K | Al ...

African Journals Online (AJOL)

Selenium plays important roles in human health and these roles may be exerted through its presence in selenoproteins. Among the 25 selenoproteins in human is selenoprotein K (SelK) whose exact function is still unclear. Here, we investigated the conserved structural features of SelK using bioinformatics as an approach ...

Exact Wigner surmise type evaluation of the spacing distribution in the bulk of the scaled random matrix ensembles

International Nuclear Information System (INIS)

Forrester, P.J.; Witte, N.S.

2000-01-01

Random matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices respectively. We show that the probability density function for the corresponding spacings between consecutive eigenvalues can be written exactly in the Wigner surmise type form a(s) e-b(s) for a simply related to a Painleve transcendent and b its anti-derivative. A formula consisting of the sum of two such terms is given for the symplectic case (Hermitian matrices with real quaternion elements)

Polygons of differential equations for finding exact solutions

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.; Demina, Maria V.

2007-01-01

A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of polygons corresponding to nonlinear differential equations. It allows one to express exact solutions of the equation studied through solutions of another equation using properties of the basic equation itself. The ideas of power geometry are used and developed. Our approach has a pictorial interpretation, which is illustrative and effective. The method can be also applied for finding transformations between solutions of differential equations. To demonstrate the method application exact solutions of several equations are found. These equations are: the Korteveg-de Vries-Burgers equation, the generalized Kuramoto-Sivashinsky equation, the fourth-order nonlinear evolution equation, the fifth-order Korteveg-de Vries equation, the fifth-order modified Korteveg-de Vries equation and the sixth-order nonlinear evolution equation describing turbulent processes. Some new exact solutions of nonlinear evolution equations are given

Quantum return probability of a system of N non-interacting lattice fermions

Science.gov (United States)

Krapivsky, P. L.; Luck, J. M.; Mallick, K.

2018-02-01

We consider N non-interacting fermions performing continuous-time quantum walks on a one-dimensional lattice. The system is launched from a most compact configuration where the fermions occupy neighboring sites. We calculate exactly the quantum return probability (sometimes referred to as the Loschmidt echo) of observing the very same compact state at a later time t. Remarkably, this probability depends on the parity of the fermion number—it decays as a power of time for even N, while for odd N it exhibits periodic oscillations modulated by a decaying power law. The exponent also slightly depends on the parity of N, and is roughly twice smaller than what it would be in the continuum limit. We also consider the same problem, and obtain similar results, in the presence of an impenetrable wall at the origin constraining the particles to remain on the positive half-line. We derive closed-form expressions for the amplitudes of the power-law decay of the return probability in all cases. The key point in the derivation is the use of Mehta integrals, which are limiting cases of the Selberg integral.

A generalization of the quantum Rabi model: exact solution and spectral structure

International Nuclear Information System (INIS)

Eckle, Hans-Peter; Johannesson, Henrik

2017-01-01

We consider a generalization of the quantum Rabi model where the two-level system and the single-mode cavity oscillator are coupled by an additional Stark-like term. By adapting a method recently introduced by Braak (2011 Phys. Rev. Lett . 107 100401), we solve the model exactly. The low-lying spectrum in the experimentally relevant ultrastrong and deep strong regimes of the Rabi coupling is found to exhibit two striking features absent from the original quantum Rabi model: avoided level crossings for states of the same parity and an anomalously rapid onset of two-fold near-degenerate levels as the Rabi coupling increases. (paper)

Construction of exact solutions for the Stern-Gerlach effect

International Nuclear Information System (INIS)

Diaz Bulnes, J.; Oliveira, I.S.

2001-01-01

We obtain exact solutions for the Schroedinger-Pauli matrix equation for a neutral particle of spin 1/2 in a magnetic field with a field gradient. The analytical wave functions are written on the symmetry plane Y = 0, which contains the incident and splitted beams, in terms of the Airy functions. The time-evolution of the probability, |Ψ+| 2 and |Ψ-| 2 , and the eigenenergies are calculated. The include a small contribution from the field gradient, α, proportional to (α ℎ) 2/3 , which amount to equal energy displacements on both magnetic levels. The results are generalized for spin S = 3/2, and in this case we found that the m = ±1/2 and m = ±3/2 magnetic sublevels are unequally splitted by the field gradient, being the difference in energy of the order 0.4 MHz. Replacing real experimental parameters we obtained a spatial splitting of the spin up and spin down states of the order Δz ≅4 mm, in accordance to a real Stern-Gerlach experiment. (author)

Features and prevalence of patients with probable adult attention deficit hyperactivity disorder who request treatment for cocaine use disorders.

Science.gov (United States)

Pérez de Los Cobos, José; Siñol, Núria; Puerta, Carmen; Cantillano, Vanessa; López Zurita, Cristina; Trujols, Joan

2011-01-30

To characterize those patients with probable adult attention deficit hyperactivity disorder (ADHD) who ask for treatment of cocaine use disorders; to estimate the prevalence of probable adult ADHD among these patients. This is a cross-sectional and multi-center study performed at outpatient resources of 12 addiction treatment centers in Spain. Participants were treatment-seeking primary cocaine abusers recruited consecutively at one center and through convenience sampling at the other centers. Assessments included semi-structured clinical interview focused on Diagnostic and Statistical Manual of Mental Disorders, fourth edition (DSM-IV) ADHD criteria adapted to adulthood, and the Wender-Utah Rating Scale (WURS) for screening childhood history of ADHD according to patients. Probable adult ADHD was diagnosed when patients met DSM-IV criteria of ADHD in adulthood and scored WURS>32. All participants were diagnosed with current cocaine dependence (n=190) or abuse (n=15). Patients with probable adult ADHD, compared with patients having no lifetime ADHD, were more frequently male, reported higher impulsivity, and began to use nicotine, alcohol, cannabis, or cocaine earlier. Before starting the current treatment, patients with probable adult ADHD also showed higher cocaine craving for the previous day, less frequent cocaine abstinence throughout the previous week, and higher use of cocaine and tobacco during the previous month. Impulsivity and male gender were the only independent risk factors of probable adult ADHD in a logistic regression analysis. The prevalence of probable adult ADHD was 20.5% in the sub-sample of patients consecutively recruited (n=78). A diagnosis of probable adult ADHD strongly distinguishes among treatment-seeking cocaine primary abusers regarding past and current key aspects of their addictive disorder; one-fifth of these patients present with probable adult ADHD. Copyright © 2009 Elsevier Ireland Ltd. All rights reserved.

ELIPGRID-PC: A PC program for calculating hot spot probabilities

International Nuclear Information System (INIS)

Davidson, J.R.

1994-10-01

ELIPGRID-PC, a new personal computer program has been developed to provide easy access to Singer's 1972 ELIPGRID algorithm for hot-spot detection probabilities. Three features of the program are the ability to determine: (1) the grid size required for specified conditions, (2) the smallest hot spot that can be sampled with a given probability, and (3) the approximate grid size resulting from specified conditions and sampling cost. ELIPGRID-PC also provides probability of hit versus cost data for graphing with spread-sheets or graphics software. The program has been successfully tested using Singer's published ELIPGRID results. An apparent error in the original ELIPGRID code has been uncovered and an appropriate modification incorporated into the new program

INDEFINITE COPOSITIVE MATRICES WITH EXACTLY ONE POSITIVE EIGENVALUE OR EXACTLY ONE NEGATIVE EIGENVALUE

NARCIS (Netherlands)

Jargalsaikhan, Bolor

Checking copositivity of a matrix is a co-NP-complete problem. This paper studies copositive matrices with certain spectral properties. It shows that an indefinite matrix with exactly one positive eigenvalue is copositive if and only if the matrix is nonnegative. Moreover, it shows that finding out

Probability

CERN Document Server

Shiryaev, A N

1996-01-01

This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, ergodic theory, weak convergence of probability measures, stationary stochastic processes, and the Kalman-Bucy filter Many examples are discussed in detail, and there are a large number of exercises The book is accessible to advanced undergraduates and can be used as a text for self-study This new edition contains substantial revisions and updated references The reader will find a deeper study of topics such as the distance between probability measures, metrization of weak convergence, and contiguity of probability measures Proofs for a number of some important results which were merely stated in the first edition have been added The author included new material on the probability of large deviations, and on the central limit theorem for sums of dependent random variables

The Interplay of Population Size and Mutation Probability in the (1+λ) EA on OneMax

DEFF Research Database (Denmark)

Gießen, Christian; Witt, Carsten

2017-01-01

The ((Formula presented.)) EA with mutation probability c / n, where (Formula presented.) is an arbitrary constant, is studied for the classical OneMax function. Its expected optimization time is analyzed exactly (up to lower order terms) as a function of c and (Formula presented.). It turns out...... that 1 / n is the only optimal mutation probability if (Formula presented.), which is the cut-off point for linear speed-up. However, if (Formula presented.) is above this cut-off point then the standard mutation probability 1 / n is no longer the only optimal choice. Instead, the expected number...... of generations is (up to lower order terms) independent of c, irrespectively of it being less than 1 or greater. The theoretical results are obtained by a careful study of order statistics of the binomial distribution and variable drift theorems for upper and lower bounds. Experimental supplements shed light...

Clan structure analysis and rapidity gap probability

International Nuclear Information System (INIS)

Lupia, S.; Giovannini, A.; Ugoccioni, R.

1995-01-01

Clan structure analysis in rapidity intervals is generalized from negative binomial multiplicity distribution to the wide class of compound Poisson distributions. The link of generalized clan structure analysis with correlation functions is also established. These theoretical results are then applied to minimum bias events and evidentiate new interesting features, which can be inspiring and useful in order to discuss data on rapidity gap probability at TEVATRON and HERA. (orig.)

Clan structure analysis and rapidity gap probability

Energy Technology Data Exchange (ETDEWEB)

Lupia, S. [Turin Univ. (Italy). Ist. di Fisica Teorica]|[Istituto Nazionale di Fisica Nucleare, Turin (Italy); Giovannini, A. [Turin Univ. (Italy). Ist. di Fisica Teorica]|[Istituto Nazionale di Fisica Nucleare, Turin (Italy); Ugoccioni, R. [Turin Univ. (Italy). Ist. di Fisica Teorica]|[Istituto Nazionale di Fisica Nucleare, Turin (Italy)

1995-03-01

Clan structure analysis in rapidity intervals is generalized from negative binomial multiplicity distribution to the wide class of compound Poisson distributions. The link of generalized clan structure analysis with correlation functions is also established. These theoretical results are then applied to minimum bias events and evidentiate new interesting features, which can be inspiring and useful in order to discuss data on rapidity gap probability at TEVATRON and HERA. (orig.)

Statistical Feature Recognition for Multidimensional Solar Imagery

Science.gov (United States)

Turmon, Michael; Jones, Harrison P.; Malanushenko, Olena V.; Pap, Judit M.

2010-04-01

A maximum a posteriori (MAP) technique is developed to identify solar features in cotemporal and cospatial images of line-of-sight magnetic flux, continuum intensity, and equivalent width observed with the NASA/National Solar Observatory (NSO) Spectromagnetograph (SPM). The technique facilitates human understanding of patterns in large data sets and enables systematic studies of feature characteristics for comparison with models and observations of long-term solar activity and variability. The method uses Bayes’ rule to compute the posterior probability of any feature segmentation of a trio of observed images from per-pixel, class-conditional probabilities derived from independently-segmented training images. Simulated annealing is used to find the most likely segmentation. New algorithms for computing class-conditional probabilities from three-dimensional Gaussian mixture models and interpolated histogram densities are described and compared. A new extension to the spatial smoothing in the Bayesian prior model is introduced, which can incorporate a spatial dependence such as center-to-limb variation. How the spatial scale of training segmentations affects the results is discussed, and a new method for statistical separation of quiet Sun and quiet network is presented.

Analytic progress on exact lattice chiral symmetry

International Nuclear Information System (INIS)

Kikukawa, Y.

2002-01-01

Theoretical issues of exact chiral symmetry on the lattice are discussed and related recent works are reviewed. For chiral theories, the construction with exact gauge invariance is reconsidered from the point of view of domain wall fermion. The issue in the construction of electroweak theory is also discussed. For vector-like theories, we discuss unitarity (positivity), Hamiltonian approach, and several generalizations of the Ginsparg-Wilson relation (algebraic and odd-dimensional)

Quantifying seining detection probability for fishes of Great Plains sand‐bed rivers

Science.gov (United States)

Mollenhauer, Robert; Logue, Daniel R.; Brewer, Shannon K.

2018-01-01

Species detection error (i.e., imperfect and variable detection probability) is an essential consideration when investigators map distributions and interpret habitat associations. When fish detection error that is due to highly variable instream environments needs to be addressed, sand‐bed streams of the Great Plains represent a unique challenge. We quantified seining detection probability for diminutive Great Plains fishes across a range of sampling conditions in two sand‐bed rivers in Oklahoma. Imperfect detection resulted in underestimates of species occurrence using naïve estimates, particularly for less common fishes. Seining detection probability also varied among fishes and across sampling conditions. We observed a quadratic relationship between water depth and detection probability, in which the exact nature of the relationship was species‐specific and dependent on water clarity. Similarly, the direction of the relationship between water clarity and detection probability was species‐specific and dependent on differences in water depth. The relationship between water temperature and detection probability was also species dependent, where both the magnitude and direction of the relationship varied among fishes. We showed how ignoring detection error confounded an underlying relationship between species occurrence and water depth. Despite imperfect and heterogeneous detection, our results support that determining species absence can be accomplished with two to six spatially replicated seine hauls per 200‐m reach under average sampling conditions; however, required effort would be higher under certain conditions. Detection probability was low for the Arkansas River Shiner Notropis girardi, which is federally listed as threatened, and more than 10 seine hauls per 200‐m reach would be required to assess presence across sampling conditions. Our model allows scientists to estimate sampling effort to confidently assess species occurrence, which

Exact vacuum polarization in 1 + 1 dimensional finite nuclei

International Nuclear Information System (INIS)

Ferree, T.C.

1992-01-01

There is considerable interest in the use of renormalizable quantum field theories to describe nuclear structure. In particular, theories which employ hadronic degrees of freedom are used widely and lead to efficient models which allow self-consistent solutions of the many-body problem. An interesting feature inherent to relativistic field theories (like QHD) is the presence of an infinite sea of negative energy fermion (nucleon) states, which interact dynamically with positive energy fermions via other fields. Such interactions give rise to, for example, vacuum polarization effects, in which virtual particle-antiparticle pairs interact with positive energy valence nucleons as well as with each other, and can significantly influence the ground and excited states of nuclear systems. Several authors have addressed this question in various approximations for finite nuclei, mostly based on extensions of results derived for a uniform system of nucleons. Some attempts have also been made to include vacuum effects in finite systems exactly, but the presence of a vector potential can be problematic when working in a spectral representation. In this paper, the author presents a computational method by which vacuum polarization effects in finite nuclei can be calculated exactly in the RHA by employing matrix diagonalization methods in a discrete Fourier representation of the Dirac equation, and an approximate method for including deep negative energy states based on a derivative expansion of the effective action. This efficient approach is shown to provide well-behaved vacuum polarization densities which remain so even in the presence of strong vector potential

Exact Optimum Design of Segmented Thermoelectric Generators

Directory of Open Access Journals (Sweden)

M. Zare

2016-01-01

Full Text Available A considerable difference between experimental and theoretical results has been observed in the studies of segmented thermoelectric generators (STEGs. Because of simplicity, the approximate methods are widely used for design and optimization of the STEGs. This study is focused on employment of exact method for design and optimization of STEGs and comparison of exact and approximate results. Thus, using new highly efficient thermoelectric materials, four STEGs are proposed to operate in the temperature range of 300 to 1300 kelvins. The proposed STEGs are optimally designed to achieve maximum efficiency. Design and performance characteristics of the optimized generators including maximum conversion efficiency and length of elements are calculated through both exact and approximate methods. The comparison indicates that the approximate method can cause a difference up to 20% in calculation of some design characteristics despite its appropriate results in efficiency calculation. The results also show that the maximum theoretical efficiency of 23.08% is achievable using the new proposed STEGs. Compatibility factor of the selected materials for the proposed STEGs is also calculated using both exact and approximate methods. The comparison indicates a negligible difference in calculation of compatibility factor, despite the considerable difference in calculation of reduced efficiency (temperature independence efficiency.

EDISON-WMW: Exact Dynamic Programing Solution of the Wilcoxon–Mann–Whitney Test

Directory of Open Access Journals (Sweden)

Alexander Marx

2016-02-01

Full Text Available In many research disciplines, hypothesis tests are applied to evaluate whether findings are statistically significant or could be explained by chance. The Wilcoxon–Mann–Whitney (WMW test is among the most popular hypothesis tests in medicine and life science to analyze if two groups of samples are equally distributed. This nonparametric statistical homogeneity test is commonly applied in molecular diagnosis. Generally, the solution of the WMW test takes a high combinatorial effort for large sample cohorts containing a significant number of ties. Hence, P value is frequently approximated by a normal distribution. We developed EDISON-WMW, a new approach to calculate the exact permutation of the two-tailed unpaired WMW test without any corrections required and allowing for ties. The method relies on dynamic programing to solve the combinatorial problem of the WMW test efficiently. Beyond a straightforward implementation of the algorithm, we presented different optimization strategies and developed a parallel solution. Using our program, the exact P value for large cohorts containing more than 1000 samples with ties can be calculated within minutes. We demonstrate the performance of this novel approach on randomly-generated data, benchmark it against 13 other commonly-applied approaches and moreover evaluate molecular biomarkers for lung carcinoma and chronic obstructive pulmonary disease (COPD. We found that approximated P values were generally higher than the exact solution provided by EDISON-WMW. Importantly, the algorithm can also be applied to high-throughput omics datasets, where hundreds or thousands of features are included. To provide easy access to the multi-threaded version of EDISON-WMW, a web-based solution of our algorithm is freely available at http://www.ccb.uni-saarland.de/software/wtest/.

Interfrontal encephalocele: a rare feature of forehead in hydrocephalic myelomeningocele patients. Clinical feature, probable mechanisms, and management.

Science.gov (United States)

Nejat, Farideh; Kamali, Shahab; El Khashab, Mostafa

2013-08-01

Myelomeningocele is a complex central nervous system malformation mostly associated with other neural and extraneural anomalies. A rare special feature of the forehead and skull was observed in myelomeningocele. Here, we present several patients with myelomeningocele, severe hydrocephalus, and interfrontal encephalocele accompanied by metopic suture widening and abnormally shaped frontal bones. Five children with this feature were enrolled in this series. The age, sex, location of myelomeningocele sac, neurological deficits, hydrocephalus and history of shunt surgery, and follow-up period were evaluated. Patients were aged from 1 to 12 months (mean, 6 months). All patients were male. Most sacs were located in lumbar and lumbosacral areas. Neurological deficits varying from only sphincter problem to paraplegia were found in all patients. Hydrocephalus was found in all children that needed a shunt procedure. Asymptomatic Chiari malformation, interfrontal encephalocele, and corpus callosum agenesis were evident in five, five, and three patients, respectively. Anterior fontanel anomalies known as interfrontal encephalocele associated with myelomeningocele have been reported before. The patients have an open metopic suture extending widely to the nasal radix producing hypertelorism accompanied by interfrontal herniation of frontal lobes. The associated hydrocephalus exaggerates the anomaly. Treatment of accompanying hydrocephalus is advised to decrease the severity of frontal lobe herniation. Some patients may need frontal bone reconstruction surgery to provide cosmetic correction at the place of the midline frontal bone defect.

Exact traveling wave solutions of the Boussinesq equation

International Nuclear Information System (INIS)

Ding Shuangshuang; Zhao Xiqiang

2006-01-01

The repeated homogeneous balance method is used to construct exact traveling wave solutions of the Boussinesq equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions of the Boussinesq equation are successfully obtained

Exact models for isotropic matter

Science.gov (United States)

Thirukkanesh, S.; Maharaj, S. D.

2006-04-01

We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently, we can find an explicit exact solution to the Einstein-Maxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously, including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series, we show that the series terminate and there exist two linearly independent solutions. Consequently, it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.

Generalized exact holographic mapping with wavelets

Science.gov (United States)

Lee, Ching Hua

2017-12-01

The idea of renormalization and scale invariance is pervasive across disciplines. It has not only drawn numerous surprising connections between physical systems under the guise of holographic duality, but has also inspired the development of wavelet theory now widely used in signal processing. Synergizing on these two developments, we describe in this paper a generalized exact holographic mapping that maps a generic N -dimensional lattice system to a (N +1 )-dimensional holographic dual, with the emergent dimension representing scale. In previous works, this was achieved via the iterations of the simplest of all unitary mappings, the Haar mapping, which fails to preserve the form of most Hamiltonians. By taking advantage of the full generality of biorthogonal wavelets, our new generalized holographic mapping framework is able to preserve the form of a large class of lattice Hamiltonians. By explicitly separating features that are fundamentally associated with the physical system from those that are basis specific, we also obtain a clearer understanding of how the resultant bulk geometry arises. For instance, the number of nonvanishing moments of the high-pass wavelet filter is revealed to be proportional to the radius of the dual anti-de Sitter space geometry. We conclude by proposing modifications to the mapping for systems with generic Fermi pockets.

Outage probability of dual-hop partial relay selection with feedback delay in the presence of interference

KAUST Repository

Al-Qahtani, Fawaz S.

2011-09-01

In this paper, we investigate the outage performance of a dual-hop relaying systems with partial relay selection and feedback delay. The analysis considers the case of Rayleigh fading channels when the relaying station as well as the destination undergo mutually independent interfering signals. Particularly, we derive the cumulative distribution function (c.d.f.) of a new type of random variable involving sum of multiple independent exponential random variables, based on which, we present closed-form expressions for the exact outage probability of a fixed amplify-and-forward (AF) and decode-and-forward (DF) relaying protocols. Numerical results are provided to illustrate the joint effect of the delayed feedback and co-channel interference on the outage probability. © 2011 IEEE.

Exactly energy conserving semi-implicit particle in cell formulation

International Nuclear Information System (INIS)

Lapenta, Giovanni

2017-01-01

We report a new particle in cell (PIC) method based on the semi-implicit approach. The novelty of the new method is that unlike any of its semi-implicit predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. Recent research has presented fully implicit methods where energy conservation is obtained as part of a non-linear iteration procedure. The new method (referred to as Energy Conserving Semi-Implicit Method, ECSIM), instead, does not require any non-linear iteration and its computational cycle is similar to that of explicit PIC. The properties of the new method are: i) it conserves energy exactly to round-off for any time step or grid spacing; ii) it is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency and allowing the user to select any desired time step; iii) it eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length; iv) the particle mover has a computational complexity identical to that of the explicit PIC, only the field solver has an increased computational cost. The new ECSIM is tested in a number of benchmarks where accuracy and computational performance are tested. - Highlights: • We present a new fully energy conserving semi-implicit particle in cell (PIC) method based on the implicit moment method (IMM). The new method is called Energy Conserving Implicit Moment Method (ECIMM). • The novelty of the new method is that unlike any of its predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. • The new method is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency. • The new method eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length. • These

Exactly energy conserving semi-implicit particle in cell formulation

Energy Technology Data Exchange (ETDEWEB)

Lapenta, Giovanni, E-mail: giovanni.lapenta@kuleuven.be

2017-04-01

We report a new particle in cell (PIC) method based on the semi-implicit approach. The novelty of the new method is that unlike any of its semi-implicit predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. Recent research has presented fully implicit methods where energy conservation is obtained as part of a non-linear iteration procedure. The new method (referred to as Energy Conserving Semi-Implicit Method, ECSIM), instead, does not require any non-linear iteration and its computational cycle is similar to that of explicit PIC. The properties of the new method are: i) it conserves energy exactly to round-off for any time step or grid spacing; ii) it is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency and allowing the user to select any desired time step; iii) it eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length; iv) the particle mover has a computational complexity identical to that of the explicit PIC, only the field solver has an increased computational cost. The new ECSIM is tested in a number of benchmarks where accuracy and computational performance are tested. - Highlights: • We present a new fully energy conserving semi-implicit particle in cell (PIC) method based on the implicit moment method (IMM). The new method is called Energy Conserving Implicit Moment Method (ECIMM). • The novelty of the new method is that unlike any of its predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. • The new method is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency. • The new method eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length. • These

Joint probability distributions and fluctuation theorems

International Nuclear Information System (INIS)

García-García, Reinaldo; Kolton, Alejandro B; Domínguez, Daniel; Lecomte, Vivien

2012-01-01

We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady state by using joint probability distribution symmetries of different entropy production decompositions. The analytical approach is applied to diverse problems such as the description of the fluctuations induced by experimental errors, for unveiling symmetries of correlation functions appearing in fluctuation–dissipation relations recently generalized to non-equilibrium steady states, and also for mapping averages between different trajectory-based dynamical ensembles. Many known fluctuation theorems arise as special instances of our approach for particular twofold decompositions of the total entropy production. As a complement, we also briefly review and synthesize the variety of fluctuation theorems applying to stochastic dynamics of both continuous systems described by a Langevin dynamics and discrete systems obeying a Markov dynamics, emphasizing how these results emerge from distinct symmetries of the dynamical entropy of the trajectory followed by the system. For Langevin dynamics, we embed the 'dual dynamics' with a physical meaning, and for Markov systems we show how the fluctuation theorems translate into symmetries of modified evolution operators

Integrable perturbed magnetic fields in toroidal geometry: An exact analytical flux surface label for large aspect ratio

Energy Technology Data Exchange (ETDEWEB)

Kallinikos, N.; Isliker, H.; Vlahos, L.; Meletlidou, E. [Department of Physics, Aristotle University of Thessaloniki, GR-54124 Thessaloniki (Greece)

2014-06-15

An analytical description of magnetic islands is presented for the typical case of a single perturbation mode introduced to tokamak plasma equilibrium in the large aspect ratio approximation. Following the Hamiltonian structure directly in terms of toroidal coordinates, the well known integrability of this system is exploited, laying out a precise and practical way for determining the island topology features, as required in various applications, through an analytical and exact flux surface label.

Integrable perturbed magnetic fields in toroidal geometry: An exact analytical flux surface label for large aspect ratio

Science.gov (United States)

Kallinikos, N.; Isliker, H.; Vlahos, L.; Meletlidou, E.

2014-06-01

An analytical description of magnetic islands is presented for the typical case of a single perturbation mode introduced to tokamak plasma equilibrium in the large aspect ratio approximation. Following the Hamiltonian structure directly in terms of toroidal coordinates, the well known integrability of this system is exploited, laying out a precise and practical way for determining the island topology features, as required in various applications, through an analytical and exact flux surface label.

Integrable perturbed magnetic fields in toroidal geometry: An exact analytical flux surface label for large aspect ratio

International Nuclear Information System (INIS)

Kallinikos, N.; Isliker, H.; Vlahos, L.; Meletlidou, E.

2014-01-01

An analytical description of magnetic islands is presented for the typical case of a single perturbation mode introduced to tokamak plasma equilibrium in the large aspect ratio approximation. Following the Hamiltonian structure directly in terms of toroidal coordinates, the well known integrability of this system is exploited, laying out a precise and practical way for determining the island topology features, as required in various applications, through an analytical and exact flux surface label

Scaling Qualitative Probability

OpenAIRE

Burgin, Mark

2017-01-01

There are different approaches to qualitative probability, which includes subjective probability. We developed a representation of qualitative probability based on relational systems, which allows modeling uncertainty by probability structures and is more coherent than existing approaches. This setting makes it possible proving that any comparative probability is induced by some probability structure (Theorem 2.1), that classical probability is a probability structure (Theorem 2.2) and that i...

Symmetries and exact solutions of the nondiagonal Einstein-Rosen metrics

International Nuclear Information System (INIS)

Goyal, N; Gupta, R K

2012-01-01

We seek exact solutions of the nondiagonal Einstein-Rosen metrics. The method of Lie symmetry of differential equations is utilized to obtain new exact solutions of Einstein vacuum equations obtained from the nondiagonal Einstein-Rosen metric. Four cases arise depending on the nature of the Lie symmetry generator. In all cases, we find reductions in terms of ordinary differential equations and exact solutions of the nonlinear system of partial differential equations (PDEs) are derived. For this purpose, first we check the Painlevé property and then corresponding to the nonlinear system of PDEs, symmetries and exact solutions are obtained.

Exact solution for the generalized Telegraph Fisher's equation

International Nuclear Information System (INIS)

Abdusalam, H.A.; Fahmy, E.S.

2009-01-01

In this paper, we applied the factorization scheme for the generalized Telegraph Fisher's equation and an exact particular solution has been found. The exact particular solution for the generalized Fisher's equation was obtained as a particular case of the generalized Telegraph Fisher's equation and the two-parameter solution can be obtained when n=2.

Exact solution of the hidden Markov processes

Science.gov (United States)

Saakian, David B.

2017-11-01

We write a master equation for the distributions related to hidden Markov processes (HMPs) and solve it using a functional equation. Thus the solution of HMPs is mapped exactly to the solution of the functional equation. For a general case the latter can be solved only numerically. We derive an exact expression for the entropy of HMPs. Our expression for the entropy is an alternative to the ones given before by the solution of integral equations. The exact solution is possible because actually the model can be considered as a generalized random walk on a one-dimensional strip. While we give the solution for the two second-order matrices, our solution can be easily generalized for the L values of the Markov process and M values of observables: We should be able to solve a system of L functional equations in the space of dimension M -1 .

Dissipative motion perturbation theory and exact solutions

International Nuclear Information System (INIS)

Lodder, J.J.

1976-06-01

Dissipative motion of classical and quantum systems is described. In particular, attention is paid to systems coupled to the radiation field. A dissipative equation of motion for a particle in an arbitrary potential coupled to the radiation field is derived by means of perturbation theory. The usual divrgencies associated with the radiation field are eliminated by the application of a theory of generalized functions. This theory is developed as a subject in its own right and is presented independently. The introduction of classical zero-point energy makes the classical equa tion of motion for the phase density formally the same as its quantum counterpart. In particular, it is shown that the classical zero-point energy prevents the collapse of a classical H-atom and gives rise to a classical ground state. For systems with a quadratic Hamiltoian, the equation of motion can be solved exactly, even in the continuum limit for the radiation field, by means of the new generalized functions. Classically, the Fokker-Planck equation is found without any approximations, and quantum mechanically, the only approximation is the neglect of the change in the ground state caused by the interaction. The derivation is valid even for strong damping and arbitrarily short times. There is no transient time. For harmonic oscillators complete equivalence is shown to exist between quantum mechanics and classical mechanics with zero-point energy. A discussion of the derivation of the Pauli equation is given and perturbation theory is compared with the exact derivation. The exactly solvable models are used to calculate the Langevin force of the radiation field. The result is that the classical Langevin force is exactly delta-correlated, while the quantum Langevin force is not delta-correlated at all. The fluctuation-dissipation theorem is shown to be an exact consequence of the solution to the equations of motion

Exact Theory of Compressible Fluid Turbulence

Science.gov (United States)

Drivas, Theodore; Eyink, Gregory

2017-11-01

We obtain exact results for compressible turbulence with any equation of state, using coarse-graining/filtering. We find two mechanisms of turbulent kinetic energy dissipation: scale-local energy cascade and ``pressure-work defect'', or pressure-work at viscous scales exceeding that in the inertial-range. Planar shocks in an ideal gas dissipate all kinetic energy by pressure-work defect, but the effect is omitted by standard LES modeling of pressure-dilatation. We also obtain a novel inverse cascade of thermodynamic entropy, injected by microscopic entropy production, cascaded upscale, and removed by large-scale cooling. This nonlinear process is missed by the Kovasznay linear mode decomposition, treating entropy as a passive scalar. For small Mach number we recover the incompressible ``negentropy cascade'' predicted by Obukhov. We derive exact Kolmogorov 4/5th-type laws for energy and entropy cascades, constraining scaling exponents of velocity, density, and internal energy to sub-Kolmogorov values. Although precise exponents and detailed physics are Mach-dependent, our exact results hold at all Mach numbers. Flow realizations at infinite Reynolds are ``dissipative weak solutions'' of compressible Euler equations, similarly as Onsager proposed for incompressible turbulence.

Exact Cover Problem in Milton Babbitt's All-partition Array

OpenAIRE

Bemman, Brian; Meredith, David

2015-01-01

One aspect of analyzing Milton Babbitt’s (1916–2011) all- partition arrays requires finding a sequence of distinct, non-overlapping aggregate regions that completely and exactly covers an irregular matrix of pitch class integers. This is an example of the so-called exact cover problem. Given a set, A, and a collection of distinct subsets of this set, S, then a subset of S is an exact cover of A if it exhaustively and exclu- sively partitions A. We provide a backtracking algorithm for solving ...

Exact theory of freeze-out

International Nuclear Information System (INIS)

Cannoni, Mirco

2015-01-01

We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature x * = m χ /T * . The point x., which coincides with the stationary point of the equation for the quantity Δ = Y-Y 0 , is where the maximum departure of the WIMPs abundance Y from the thermal value Y 0 is reached. For each mass m χ and total annihilation cross section left angle σ ann υ r right angle, the temperature x * and the actual WIMPs abundance Y(x * ) are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval x ≥ x * . The matching of the two abundances at x * is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1.2 % in the case of S-wave and P-wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics. (orig.)

An novel frequent probability pattern mining algorithm based on circuit simulation method in uncertain biological networks

Science.gov (United States)

2014-01-01

Background Motif mining has always been a hot research topic in bioinformatics. Most of current research on biological networks focuses on exact motif mining. However, due to the inevitable experimental error and noisy data, biological network data represented as the probability model could better reflect the authenticity and biological significance, therefore, it is more biological meaningful to discover probability motif in uncertain biological networks. One of the key steps in probability motif mining is frequent pattern discovery which is usually based on the possible world model having a relatively high computational complexity. Methods In this paper, we present a novel method for detecting frequent probability patterns based on circuit simulation in the uncertain biological networks. First, the partition based efficient search is applied to the non-tree like subgraph mining where the probability of occurrence in random networks is small. Then, an algorithm of probability isomorphic based on circuit simulation is proposed. The probability isomorphic combines the analysis of circuit topology structure with related physical properties of voltage in order to evaluate the probability isomorphism between probability subgraphs. The circuit simulation based probability isomorphic can avoid using traditional possible world model. Finally, based on the algorithm of probability subgraph isomorphism, two-step hierarchical clustering method is used to cluster subgraphs, and discover frequent probability patterns from the clusters. Results The experiment results on data sets of the Protein-Protein Interaction (PPI) networks and the transcriptional regulatory networks of E. coli and S. cerevisiae show that the proposed method can efficiently discover the frequent probability subgraphs. The discovered subgraphs in our study contain all probability motifs reported in the experiments published in other related papers. Conclusions The algorithm of probability graph isomorphism

Poster - 18: New features in EGSnrc for photon cross sections

Energy Technology Data Exchange (ETDEWEB)

Ali, Elsayed; Mainegra-Hing, Ernesto; Rogers, David W.O. [The Ottawa Hospital Cancer Centre, National Research Council Canada, Carleton University (Canada)

2016-08-15

Purpose: To implement two new features in the EGSnrc Monte Carlo system. The first is an option to account for photonuclear attenuation, which can contribute a few percent to the total cross section at the higher end of the energy range of interest to medical physics. The second is an option to use exact NIST XCOM photon cross sections. Methods: For the first feature, the photonuclear total cross sections are generated from the IAEA evaluated data. In the current, first-order implementation, after a photonuclear event, there is no energy deposition or secondary particle generation. The implementation is validated against deterministic calculations and experimental measurements of transmission signals. For the second feature, before this work, if the user explicitly requested XCOM photon cross sections, EGSnrc still used its own internal incoherent scattering cross sections. These differ by up to 2% from XCOM data between 30 keV and 40 MeV. After this work, exact XCOM incoherent scattering cross sections are an available option. Minor interpolation artifacts in pair and triplet XCOM cross sections are also addressed. The default for photon cross section in EGSnrc is XCOM except for the new incoherent scattering cross sections, which have to be explicitly requested. The photonuclear, incoherent, pair and triplet data from this work are available for elements and compounds for photon energies from 1 keV to 100 GeV. Results: Both features are implemented and validated in EGSnrc.Conclusions: The two features are part of the standard EGSnrc distribution as of version 4.2.3.2.

Occupation probabilities and fluctuations in the asymmetric simple inclusion process

Science.gov (United States)

Reuveni, Shlomi; Hirschberg, Ori; Eliazar, Iddo; Yechiali, Uri

2014-04-01

The asymmetric simple inclusion process (ASIP), a lattice-gas model of unidirectional transport and aggregation, was recently proposed as an "inclusion" counterpart of the asymmetric simple exclusion process. In this paper we present an exact closed-form expression for the probability that a given number of particles occupies a given set of consecutive lattice sites. Our results are expressed in terms of the entries of Catalan's trapezoids—number arrays which generalize Catalan's numbers and Catalan's triangle. We further prove that the ASIP is asymptotically governed by the following: (i) an inverse square-root law of occupation, (ii) a square-root law of fluctuation, and (iii) a Rayleigh law for the distribution of interexit times. The universality of these results is discussed.

Exact work

International Nuclear Information System (INIS)

Zeger, J.

1993-01-01

Organized criminals also tried to illegally transfer nuclear material through Austria. Two important questions have to be answered after the material is sized by police authorities: What is the composition of the material and where does it come from? By application of a broad range of analytical techniques, which were developed or refined by our experts, it is possible to measure the exact amount and isotopic composition of uranium and plutonium in any kind of samples. The criminalistic application is only a byproduct of the large scale work on controlling the peaceful application of nuclear energy, which is done in contract with the IAEA in the context of the 'Network of Analytical Laboratories'

Exact solution of nonsteady thermal boundary layer equation

International Nuclear Information System (INIS)

Dorfman, A.S.

1995-01-01

There are only a few exact solutions of the thermal boundary layer equation. Most of them are derived for a specific surface temperature distribution. The first exact solution of the steady-state boundary layer equation was given for a plate with constant surface temperature and free-stream velocity. The same problem for a plate with polynomial surface temperature distribution was solved by Chapmen and Rubesin. Levy gave the exact solution for the case of a power law distribution of both surface temperature and free-stream velocity. The exact solution of the steady-state boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution was given by the author in two forms: of series and of the integral with an influence function of unheated zone. A similar solution of the nonsteady thermal boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution is presented here. In this case, the coefficients of series depend on time, and in the limit t → ∞ they become the constant coefficients of a similar solution published before. This solution, unlike the one presented here, does not satisfy the initial conditions at t = 0, and, hence, can be used only in time after the beginning of the process. The solution in the form of a series becomes a closed-form exact solution for polynomial surface temperature and a power law free-stream velocity distribution. 7 refs., 2 figs

The exact distributions of F(IS under partial asexuality in small finite populations with mutation.

Directory of Open Access Journals (Sweden)

Solenn Stoeckel

Full Text Available Reproductive systems like partial asexuality participate to shape the evolution of genetic diversity within populations, which is often quantified by the inbreeding coefficient F IS. Understanding how those mating systems impact the possible distributions of F IS values in theoretical populations helps to unravel forces shaping the evolution of real populations. We proposed a population genetics model based on genotypic states in a finite population with mutation. For populations with less than 400 individuals, we assessed the impact of the rates of asexuality on the full exact distributions of F IS, the probabilities of positive and negative F IS, the probabilities of fixation and the probabilities to observe changes in the sign of F IS over one generation. After an infinite number of generations, we distinguished three main patterns of effects of the rates of asexuality on genetic diversity that also varied according to the interactions of mutation and genetic drift. Even rare asexual events in mainly sexual populations impacted the balance between negative and positive F IS and the occurrence of extreme values. It also drastically modified the probability to change the sign of F IS value at one locus over one generation. When mutation prevailed over genetic drift, increasing rates of asexuality continuously increased the variance of F IS that reached its highest value in fully asexual populations. In consequence, even ancient asexual populations showed the entire F IS spectrum, including strong positive F IS. The prevalence of heterozygous loci only occurred in full asexual populations when genetic drift dominated.

An exact fermion-pair to boson mapping

International Nuclear Information System (INIS)

Johnson, C.W.

1993-01-01

I derive in a novel fashion exact formulas for the calculation of general matrix elements, including the overlap (norm) matrix, between states constructed from fermion pairs. Mapping the fermion pairs to bosons, I show how to construct finite and exact (in the sense of preserving matrix elements) boson representations of the norm operator and one- and two-fermion operators. This may lead to a microscopic basis for the Interacting Boson Model, as well as new truncation schemes for the nuclear shell model

The exact mass-gaps of the principal chiral models

CERN Document Server

Hollowood, Timothy J

1994-01-01

An exact expression for the mass-gap, the ratio of the physical particle mass to the $\\Lambda$-parameter, is found for the principal chiral sigma models associated to all the classical Lie algebras. The calculation is based on a comparison of the free-energy in the presence of a source coupling to a conserved charge of the theory computed in two ways: via the thermodynamic Bethe Ansatz from the exact scattering matrix and directly in perturbation theory. The calculation provides a non-trivial test of the form of the exact scattering matrix.

Spatiotemporal Features for Asynchronous Event-based Data

Directory of Open Access Journals (Sweden)

Xavier eLagorce

2015-02-01

Full Text Available Bio-inspired asynchronous event-based vision sensors are currently introducing a paradigm shift in visual information processing. These new sensors rely on a stimulus-driven principle of light acquisition similar to biological retinas. They are event-driven and fully asynchronous, thereby reducing redundancy and encoding exact times of input signal changes, leading to a very precise temporal resolution. Approaches for higher-level computer vision often rely on the realiable detection of features in visual frames, but similar definitions of features for the novel dynamic and event-based visual input representation of silicon retinas have so far been lacking. This article addresses the problem of learning and recognizing features for event-based vision sensors, which capture properties of truly spatiotemporal volumes of sparse visual event information. A novel computational architecture for learning and encoding spatiotemporal features is introduced based on a set of predictive recurrent reservoir networks, competing via winner-take-all selection. Features are learned in an unsupervised manner from real-world input recorded with event-based vision sensors. It is shown that the networks in the architecture learn distinct and task-specific dynamic visual features, and can predict their trajectories over time.

An Exact Solution of the Binary Singular Problem

Directory of Open Access Journals (Sweden)

Baiqing Sun

2014-01-01

Full Text Available Singularity problem exists in various branches of applied mathematics. Such ordinary differential equations accompany singular coefficients. In this paper, by using the properties of reproducing kernel, the exact solution expressions of dual singular problem are given in the reproducing kernel space and studied, also for a class of singular problem. For the binary equation of singular points, I put it into the singular problem first, and then reuse some excellent properties which are applied to solve the method of solving differential equations for its exact solution expression of binary singular integral equation in reproducing kernel space, and then obtain its approximate solution through the evaluation of exact solutions. Numerical examples will show the effectiveness of this method.

Introduction to probability and statistics for ecosystem managers simulation and resampling

CERN Document Server

Haas, Timothy C

2013-01-01

Explores computer-intensive probability and statistics for ecosystem management decision making Simulation is an accessible way to explain probability and stochastic model behavior to beginners. This book introduces probability and statistics to future and practicing ecosystem managers by providing a comprehensive treatment of these two areas. The author presents a self-contained introduction for individuals involved in monitoring, assessing, and managing ecosystems and features intuitive, simulation-based explanations of probabilistic and statistical concepts. Mathematical programming details are provided for estimating ecosystem model parameters with Minimum Distance, a robust and computer-intensive method. The majority of examples illustrate how probability and statistics can be applied to ecosystem management challenges. There are over 50 exercises - making this book suitable for a lecture course in a natural resource and/or wildlife management department, or as the main text in a program of self-stud...

Exact extreme-value statistics at mixed-order transitions.

Science.gov (United States)

Bar, Amir; Majumdar, Satya N; Schehr, Grégory; Mukamel, David

2016-05-01

We study extreme-value statistics for spatially extended models exhibiting mixed-order phase transitions (MOT). These are phase transitions that exhibit features common to both first-order (discontinuity of the order parameter) and second-order (diverging correlation length) transitions. We consider here the truncated inverse distance squared Ising model, which is a prototypical model exhibiting MOT, and study analytically the extreme-value statistics of the domain lengths The lengths of the domains are identically distributed random variables except for the global constraint that their sum equals the total system size L. In addition, the number of such domains is also a fluctuating variable, and not fixed. In the paramagnetic phase, we show that the distribution of the largest domain length l_{max} converges, in the large L limit, to a Gumbel distribution. However, at the critical point (for a certain range of parameters) and in the ferromagnetic phase, we show that the fluctuations of l_{max} are governed by novel distributions, which we compute exactly. Our main analytical results are verified by numerical simulations.

Exact solutions of a nonpolynomially nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Parwani, R.; Tan, H.S.

2007-01-01

A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurrence of higher-derivative nonlinear terms at all orders. Here we construct some exact solutions to that equation in 1+1 dimensions. On the half-line, the solutions resemble (exponentially damped) Bloch waves even though no external periodic potential is included. The solutions are nonperturbative as they do not reduce to solutions of the linear theory in the limit that the nonlinearity parameter vanishes. An intriguing feature of the solutions is their infinite degeneracy: for a given energy, there exists a very large arbitrariness in the normalisable wavefunctions. We also consider solutions to a q-deformed version of the nonlinear equation and discuss a natural discretisation implied by the nonpolynomiality. Finally, we contrast the properties of our solutions with other solutions of nonlinear Schrodinger equations in the literature and suggest some possible applications of our results in the domains of low-energy and high-energy physics

Exact soliton-like solutions of perturbed phi4-equation

International Nuclear Information System (INIS)

Gonzalez, J.A.

1986-05-01

Exact soliton-like solutions of damped, driven phi 4 -equation are found. The exact expressions for the velocities of solitons are given. It is non-perturbatively proved that the perturbed phi 4 -equation has stable kink-like solutions of a new type. (author)

Inverse Schroedinger equation and the exact wave function

International Nuclear Information System (INIS)

Nakatsuji, Hiroshi

2002-01-01

Using the inverse of the Hamiltonian, we introduce the inverse Schroedinger equation (ISE) that is equivalent to the ordinary Schroedinger equation (SE). The ISE has the variational principle and the H-square group of equations as the SE has. When we use a positive Hamiltonian, shifting the energy origin, the inverse energy becomes monotonic and we further have the inverse Ritz variational principle and cross-H-square equations. The concepts of the SE and the ISE are combined to generalize the theory for calculating the exact wave function that is a common eigenfunction of the SE and ISE. The Krylov sequence is extended to include the inverse Hamiltonian, and the complete Krylov sequence is introduced. The iterative configuration interaction (ICI) theory is generalized to cover both the SE and ISE concepts and four different computational methods of calculating the exact wave function are presented in both analytical and matrix representations. The exact wave-function theory based on the inverse Hamiltonian can be applied to systems that have singularities in the Hamiltonian. The generalized ICI theory is applied to the hydrogen atom, giving the exact solution without any singularity problem

Propagation of nuclear data uncertainty: Exact or with covariances

Directory of Open Access Journals (Sweden)

van Veen D.

2010-10-01

Full Text Available Two distinct methods of propagation for basic nuclear data uncertainties to large scale systems will be presented and compared. The “Total Monte Carlo” method is using a statistical ensemble of nuclear data libraries randomly generated by means of a Monte Carlo approach with the TALYS system. These libraries are then directly used in a large number of reactor calculations (for instance with MCNP after which the exact probability distribution for the reactor parameter is obtained. The second method makes use of available covariance files and can be done in a single reactor calculation (by using the perturbation method. In this exercise, both methods are using consistent sets of data files, which implies that covariance files used in the second method are directly obtained from the randomly generated nuclear data libraries from the first method. This is a unique and straightforward comparison allowing to directly apprehend advantages and drawbacks of each method. Comparisons for different reactions and criticality-safety benchmarks from 19F to actinides will be presented. We can thus conclude whether current methods for using covariance data are good enough or not.

Toward a generalized probability theory: conditional probabilities

International Nuclear Information System (INIS)

Cassinelli, G.

1979-01-01

The main mathematical object of interest in the quantum logic approach to the foundations of quantum mechanics is the orthomodular lattice and a set of probability measures, or states, defined by the lattice. This mathematical structure is studied per se, independently from the intuitive or physical motivation of its definition, as a generalized probability theory. It is thought that the building-up of such a probability theory could eventually throw light on the mathematical structure of Hilbert-space quantum mechanics as a particular concrete model of the generalized theory. (Auth.)

Exact theory of freeze-out

Energy Technology Data Exchange (ETDEWEB)

Cannoni, Mirco [Universidad de Huelva, Departamento de Fisica Aplicada, Facultad de Ciencias Experimentales, Huelva (Spain)

2015-03-01

We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature x{sub *} = m{sub χ}/T{sub *}. The point x., which coincides with the stationary point of the equation for the quantity Δ = Y-Y{sub 0}, is where the maximum departure of the WIMPs abundance Y from the thermal value Y{sub 0} is reached. For each mass m{sub χ} and total annihilation cross section left angle σ{sub ann}υ{sub r} right angle, the temperature x{sub *} and the actual WIMPs abundance Y(x{sub *}) are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval x ≥ x{sub *}. The matching of the two abundances at x{sub *} is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1.2 % in the case of S-wave and P-wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics. (orig.)

Automatic Attraction of Visual Attention by Supraletter Features of Former Target Strings

Directory of Open Access Journals (Sweden)

Søren eKyllingsbæk

2014-11-01

Full Text Available Observers were trained to search for a particular horizontal string of 3 capital letters presented among similar strings consisting of exactly the same letters in different orders. The training was followed by a test in which the observers searched for a new target that was identical to one of the former distractors. The new distractor set consisted of the remaining former distractors plus the former target. On each trial, three letter-strings were displayed, which included the target string with a probability of .5. In Experiment 1, the strings were centered at different locations on the circumference of an imaginary circle around the fixation point. The training phase of Experiment 2 was similar, but in the test phase of the experiment, the strings were located in a vertical array centered on fixation, and in target-present arrays, the target always appeared at fixation. In both experiments, performance (d’ degraded on trials in which former targets were present, suggesting that the former targets automatically drew processing resources away from the current targets. Apparently, the two experiments showed automatic attraction of visual attention by supraletter features of former target strings.

Exactly marginal deformations from exceptional generalised geometry

Energy Technology Data Exchange (ETDEWEB)

Ashmore, Anthony [Merton College, University of Oxford,Merton Street, Oxford, OX1 4JD (United Kingdom); Mathematical Institute, University of Oxford,Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG (United Kingdom); Gabella, Maxime [Institute for Advanced Study,Einstein Drive, Princeton, NJ 08540 (United States); Graña, Mariana [Institut de Physique Théorique, CEA/Saclay,91191 Gif-sur-Yvette (France); Petrini, Michela [Sorbonne Université, UPMC Paris 05, UMR 7589, LPTHE,75005 Paris (France); Waldram, Daniel [Department of Physics, Imperial College London,Prince Consort Road, London, SW7 2AZ (United Kingdom)

2017-01-27

We apply exceptional generalised geometry to the study of exactly marginal deformations of N=1 SCFTs that are dual to generic AdS{sub 5} flux backgrounds in type IIB or eleven-dimensional supergravity. In the gauge theory, marginal deformations are parametrised by the space of chiral primary operators of conformal dimension three, while exactly marginal deformations correspond to quotienting this space by the complexified global symmetry group. We show how the supergravity analysis gives a geometric interpretation of the gauge theory results. The marginal deformations arise from deformations of generalised structures that solve moment maps for the generalised diffeomorphism group and have the correct charge under the generalised Reeb vector, generating the R-symmetry. If this is the only symmetry of the background, all marginal deformations are exactly marginal. If the background possesses extra isometries, there are obstructions that come from fixed points of the moment maps. The exactly marginal deformations are then given by a further quotient by these extra isometries. Our analysis holds for any N=2 AdS{sub 5} flux background. Focussing on the particular case of type IIB Sasaki-Einstein backgrounds we recover the result that marginal deformations correspond to perturbing the solution by three-form flux at first order. In various explicit examples, we show that our expression for the three-form flux matches those in the literature and the obstruction conditions match the one-loop beta functions of the dual SCFT.

Exact solutions of nonlinear differential equations using continued fractions

International Nuclear Information System (INIS)

Ditto, W.L.; Pickett, T.J.

1990-01-01

The continued-fraction conversion method (J. Math. Phys. (N.Y.), 29, 1761 (1988)) is used to generate a homologous family of exact solutions to the Lane-Emden equation φ(r) '' + 2φ(r)'/r + αφ(r) p = 0, for p=5. An exact solution is also obtained for a generalization of the Lane-Emden equation of the form -φ '' (r) -2φ(r)'/r + αφ(r) 2p+1 + λφ(r) 4p+1 = 0 for arbitrary α, γ and p. A condition is established for the generation of exact solutions from the method

Exact Lattice Supersymmetry

Energy Technology Data Exchange (ETDEWEB)

Catterall, Simon; Kaplan, David B.; Unsal, Mithat

2009-03-31

We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.

Universal features of multiplicity distributions

International Nuclear Information System (INIS)

Balantekin, A.B.; Washington Univ., Seattle, WA

1994-01-01

Universal features of multiplicity distributions are studied and combinants, certain linear combinations of ratios of probabilities, are introduced. It is argued that they can be a useful tool in analyzing multiplicity distributions of hadrons emitted in high energy collisions and large scale structure of galaxy distributions

Upper bounds on minimum cardinality of exact and approximate reducts

KAUST Repository

Chikalov, Igor

2010-01-01

In the paper, we consider the notions of exact and approximate decision reducts for binary decision tables. We present upper bounds on minimum cardinality of exact and approximate reducts depending on the number of rows (objects) in the decision table. We show that the bound for exact reducts is unimprovable in the general case, and the bound for approximate reducts is almost unimprovable in the general case. © 2010 Springer-Verlag Berlin Heidelberg.

Electron transfer dynamics: Zusman equation versus exact theory

International Nuclear Information System (INIS)

Shi Qiang; Chen Liping; Nan Guangjun; Xu Ruixue; Yan Yijing

2009-01-01

The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations.

Exact solutions of some nonlinear partial differential equations using ...

Indian Academy of Sciences (India)

The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm ...

Topological order in an exactly solvable 3D spin model

International Nuclear Information System (INIS)

Bravyi, Sergey; Leemhuis, Bernhard; Terhal, Barbara M.

2011-01-01

Research highlights: RHtriangle We study exactly solvable spin model with six-qubit nearest neighbor interactions on a 3D face centered cubic lattice. RHtriangle The ground space of the model exhibits topological quantum order. RHtriangle Elementary excitations can be geometrically described as the corners of rectangular-shaped membranes. RHtriangle The ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. RHtriangle Logical operators acting on the encoded qubits are described in terms of closed strings and closed membranes. - Abstract: We study a 3D generalization of the toric code model introduced recently by Chamon. This is an exactly solvable spin model with six-qubit nearest-neighbor interactions on an FCC lattice whose ground space exhibits topological quantum order. The elementary excitations of this model which we call monopoles can be geometrically described as the corners of rectangular-shaped membranes. We prove that the creation of an isolated monopole separated from other monopoles by a distance R requires an operator acting on Ω(R 2 ) qubits. Composite particles that consist of two monopoles (dipoles) and four monopoles (quadrupoles) can be described as end-points of strings. The peculiar feature of the model is that dipole-type strings are rigid, that is, such strings must be aligned with face-diagonals of the lattice. For periodic boundary conditions the ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. We describe a complete set of logical operators acting on the encoded qubits in terms of closed strings and closed membranes.

Quantum probability measures and tomographic probability densities

NARCIS (Netherlands)

Amosov, GG; Man'ko, [No Value

2004-01-01

Using a simple relation of the Dirac delta-function to generalized the theta-function, the relationship between the tomographic probability approach and the quantum probability measure approach with the description of quantum states is discussed. The quantum state tomogram expressed in terms of the

Impulsive synchronization of Markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach.

Science.gov (United States)

Chandrasekar, A; Rakkiyappan, R; Cao, Jinde

2015-10-01

This paper studies the impulsive synchronization of Markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach. The array of neural networks are coupled in a random fashion which is governed by Bernoulli random variable. The aim of this paper is to obtain the synchronization criteria, which is suitable for both exactly known and partly unknown transition probabilities such that the coupled neural network is synchronized with mixed time-delay. The considered impulsive effects can be synchronized at partly unknown transition probabilities. Besides, a multiple integral approach is also proposed to strengthen the Markovian jumping randomly coupled neural networks with partly unknown transition probabilities. By making use of Kronecker product and some useful integral inequalities, a novel Lyapunov-Krasovskii functional was designed for handling the coupled neural network with mixed delay and then impulsive synchronization criteria are solvable in a set of linear matrix inequalities. Finally, numerical examples are presented to illustrate the effectiveness and advantages of the theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Exact Cover Problem in Milton Babbitt's All-partition Array

DEFF Research Database (Denmark)

Bemman, Brian; Meredith, David

2015-01-01

One aspect of analyzing Milton Babbitt’s (1916–2011) all- partition arrays requires finding a sequence of distinct, non-overlapping aggregate regions that completely and exactly covers an irregular matrix of pitch class integers. This is an example of the so-called exact cover problem. Given a set...

A class of exact solutions to the Einstein field equations

International Nuclear Information System (INIS)

Goyal, Nisha; Gupta, R K

2012-01-01

The Einstein-Rosen metric is considered and a class of new exact solutions of the field equations for stationary axisymmetric Einstein-Maxwell fields is obtained. The Lie classical approach is applied to obtain exact solutions. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of Einstein-Maxwell equations. (paper)

Mathematics of epidemics on networks from exact to approximate models

CERN Document Server

Kiss, István Z; Simon, Péter L

2017-01-01

This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate...

Exactly and completely integrable nonlinear dynamical systems

International Nuclear Information System (INIS)

Leznov, A.N.; Savel'ev, M.V.

1987-01-01

The survey is devoted to a consitent exposition of the group-algebraic methods for the integration of systems of nonlinear partial differential equations possessing a nontrivial internal symmetry algebra. Samples of exactly and completely integrable wave and evolution equations are considered in detail, including generalized (periodic and finite nonperiodic Toda lattice, nonlinear Schroedinger, Korteweg-de Vries, Lotka-Volterra equations, etc.) For exactly integrable systems the general solutions of the Cauchy and Goursat problems are given in an explicit form, while for completely integrable systems an effective method for the construction of their soliton solutions is developed. Application of the developed methods to a differential geometry problem of classification of the integrable manifolds embeddings is discussed. For exactly integrable systems the supersymmetric extensions are constructed. By the example of the generalized Toda lattice a quantization scheme is developed. It includes an explicit derivation of the corresponding Heisenberg operators and their desription in terms of the quantum algebras of the Hopf type. Among multidimensional systems the four-dimensional self-dual Yang-Mills equations are investigated most attentively with a goal of constructing their general solutions

Stochastic epidemic-type model with enhanced connectivity: exact solution

International Nuclear Information System (INIS)

Williams, H T; Mazilu, I; Mazilu, D A

2012-01-01

We present an exact analytical solution to a one-dimensional model of the susceptible–infected–recovered (SIR) epidemic type, with infection rates dependent on nearest-neighbor occupations. We use a quantum mechanical approach, transforming the master equation via a quantum spin operator formulation. We calculate exactly the time-dependent density of infected, recovered and susceptible populations for random initial conditions. Our results compare well with those of previous work, validating the model as a useful tool for additional and extended studies in this important area. Our model also provides exact solutions for the n-point correlation functions, and can be extended to more complex epidemic-type models

Maps on statistical manifolds exactly reduced from the Perron-Frobenius equations for solvable chaotic maps

Science.gov (United States)

Goto, Shin-itiro; Umeno, Ken

2018-03-01

Maps on a parameter space for expressing distribution functions are exactly derived from the Perron-Frobenius equations for a generalized Boole transform family. Here the generalized Boole transform family is a one-parameter family of maps, where it is defined on a subset of the real line and its probability distribution function is the Cauchy distribution with some parameters. With this reduction, some relations between the statistical picture and the orbital one are shown. From the viewpoint of information geometry, the parameter space can be identified with a statistical manifold, and then it is shown that the derived maps can be characterized. Also, with an induced symplectic structure from a statistical structure, symplectic and information geometric aspects of the derived maps are discussed.

COVAL, Compound Probability Distribution for Function of Probability Distribution

International Nuclear Information System (INIS)

Astolfi, M.; Elbaz, J.

1979-01-01

1 - Nature of the physical problem solved: Computation of the probability distribution of a function of variables, given the probability distribution of the variables themselves. 'COVAL' has been applied to reliability analysis of a structure subject to random loads. 2 - Method of solution: Numerical transformation of probability distributions

Energy vs. density on paths toward exact density functionals

DEFF Research Database (Denmark)

Kepp, Kasper Planeta

2018-01-01

Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a “path”. Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness...

Exact Synthesis of Reversible Circuits Using A* Algorithm

Science.gov (United States)

Datta, K.; Rathi, G. K.; Sengupta, I.; Rahaman, H.

2015-06-01

With the growing emphasis on low-power design methodologies, and the result that theoretical zero power dissipation is possible only if computations are information lossless, design and synthesis of reversible logic circuits have become very important in recent years. Reversible logic circuits are also important in the context of quantum computing, where the basic operations are reversible in nature. Several synthesis methodologies for reversible circuits have been reported. Some of these methods are termed as exact, where the motivation is to get the minimum-gate realization for a given reversible function. These methods are computationally very intensive, and are able to synthesize only very small functions. There are other methods based on function transformations or higher-level representation of functions like binary decision diagrams or exclusive-or sum-of-products, that are able to handle much larger circuits without any guarantee of optimality or near-optimality. Design of exact synthesis algorithms is interesting in this context, because they set some kind of benchmarks against which other methods can be compared. This paper proposes an exact synthesis approach based on an iterative deepening version of the A* algorithm using the multiple-control Toffoli gate library. Experimental results are presented with comparisons with other exact and some heuristic based synthesis approaches.

Exact braneworld cosmology induced from bulk black holes

International Nuclear Information System (INIS)

Gregory, James P; Padilla, Antonio

2002-01-01

We use a new, exact approach in calculating the energy density measured by an observer living on a brane embedded in a charged black-hole spacetime. We find that the bulk Weyl tensor gives rise to nonlinear terms in the energy density and pressure in the FRW equations for the brane. Remarkably, these take exactly the same form as the 'unconventional' terms found in the cosmology of branes embedded in pure AdS, with extra matter living on the brane. Black-hole-driven cosmologies have the benefit that there is no ambiguity in splitting the braneworld energy momentum into tension and additional matter. We propose a new, enlarged relationship between the two descriptions of braneworld cosmology. We also study the exact thermodynamics of the field theory and present a generalized Cardy-Verlinde formula in this set-up

On Probability Leakage

OpenAIRE

Briggs, William M.

2012-01-01

The probability leakage of model M with respect to evidence E is defined. Probability leakage is a kind of model error. It occurs when M implies that events $y$, which are impossible given E, have positive probability. Leakage does not imply model falsification. Models with probability leakage cannot be calibrated empirically. Regression models, which are ubiquitous in statistical practice, often evince probability leakage.

An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice

International Nuclear Information System (INIS)

Bezzola, Andri; Bales, Benjamin B.; Alkire, Richard C.; Petzold, Linda R.

2014-01-01

We present an exact and efficient algorithm for reaction–diffusion–nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands

An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice

Energy Technology Data Exchange (ETDEWEB)

Bezzola, Andri, E-mail: andri.bezzola@gmail.com [Mechanical Engineering Department, University of California, Santa Barbara, CA 93106 (United States); Bales, Benjamin B., E-mail: bbbales2@gmail.com [Mechanical Engineering Department, University of California, Santa Barbara, CA 93106 (United States); Alkire, Richard C., E-mail: r-alkire@uiuc.edu [Department of Chemical Engineering, University of Illinois, Urbana, IL 61801 (United States); Petzold, Linda R., E-mail: petzold@engineering.ucsb.edu [Mechanical Engineering Department and Computer Science Department, University of California, Santa Barbara, CA 93106 (United States)

2014-01-01

We present an exact and efficient algorithm for reaction–diffusion–nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands.

When is quasi-linear theory exact. [particle acceleration

Science.gov (United States)

Jones, F. C.; Birmingham, T. J.

1975-01-01

We use the cumulant expansion technique of Kubo (1962, 1963) to derive an integrodifferential equation for the average one-particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the equation for this function degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory only for this limited class of fluctuations.

Exact Lagrangian caps and non-uniruled Lagrangian submanifolds

Science.gov (United States)

Dimitroglou Rizell, Georgios

2015-04-01

We make the elementary observation that the Lagrangian submanifolds of C n , n≥3, constructed by Ekholm, Eliashberg, Murphy and Smith are non-uniruled and, moreover, have infinite relative Gromov width. The construction of these submanifolds involve exact Lagrangian caps, which obviously are non-uniruled in themselves. This property is also used to show that if a Legendrian submanifold inside a contactisation admits an exact Lagrangian cap, then its Chekanov-Eliashberg algebra is acyclic.

Attentional Selection of Feature Conjunctions Is Accomplished by Parallel and Independent Selection of Single Features.

Science.gov (United States)

Andersen, Søren K; Müller, Matthias M; Hillyard, Steven A

2015-07-08

Experiments that study feature-based attention have often examined situations in which selection is based on a single feature (e.g., the color red). However, in more complex situations relevant stimuli may not be set apart from other stimuli by a single defining property but by a specific combination of features. Here, we examined sustained attentional selection of stimuli defined by conjunctions of color and orientation. Human observers attended to one out of four concurrently presented superimposed fields of randomly moving horizontal or vertical bars of red or blue color to detect brief intervals of coherent motion. Selective stimulus processing in early visual cortex was assessed by recordings of steady-state visual evoked potentials (SSVEPs) elicited by each of the flickering fields of stimuli. We directly contrasted attentional selection of single features and feature conjunctions and found that SSVEP amplitudes on conditions in which selection was based on a single feature only (color or orientation) exactly predicted the magnitude of attentional enhancement of SSVEPs when attending to a conjunction of both features. Furthermore, enhanced SSVEP amplitudes elicited by attended stimuli were accompanied by equivalent reductions of SSVEP amplitudes elicited by unattended stimuli in all cases. We conclude that attentional selection of a feature-conjunction stimulus is accomplished by the parallel and independent facilitation of its constituent feature dimensions in early visual cortex. The ability to perceive the world is limited by the brain's processing capacity. Attention affords adaptive behavior by selectively prioritizing processing of relevant stimuli based on their features (location, color, orientation, etc.). We found that attentional mechanisms for selection of different features belonging to the same object operate independently and in parallel: concurrent attentional selection of two stimulus features is simply the sum of attending to each of those

Exact rebinning methods for three-dimensional PET.

Science.gov (United States)

Liu, X; Defrise, M; Michel, C; Sibomana, M; Comtat, C; Kinahan, P; Townsend, D

1999-08-01

The high computational cost of data processing in volume PET imaging is still hindering the routine application of this successful technique, especially in the case of dynamic studies. This paper describes two new algorithms based on an exact rebinning equation, which can be applied to accelerate the processing of three-dimensional (3-D) PET data. The first algorithm, FOREPROJ, is a fast-forward projection algorithm that allows calculation of the 3-D attenuation correction factors (ACF's) directly from a two-dimensional (2-D) transmission scan, without first reconstructing the attenuation map and then performing a 3-D forward projection. The use of FOREPROJ speeds up the estimation of the 3-D ACF's by more than a factor five. The second algorithm, FOREX, is a rebinning algorithm that is also more than five times faster, compared to the standard reprojection algorithm (3DRP) and does not suffer from the image distortions generated by the even faster approximate Fourier rebinning (FORE) method at large axial apertures. However, FOREX is probably not required by most existing scanners, as the axial apertures are not large enough to show improvements over FORE with clinical data. Both algorithms have been implemented and applied to data simulated for a scanner with a large axial aperture (30 degrees), and also to data acquired with the ECAT HR and the ECAT HR+ scanners. Results demonstrate the excellent accuracy achieved by these algorithms and the important speedup when the sinogram sizes are powers of two.

Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations

CERN Document Server

Verde, Licia; Heavens, Alan F; Jimenez, Raul; Matarrese, Sabino

2013-01-01

We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non- Gaussianity estimation from Cosmic Microwave Background maps and the halo mass function where we obtain analytical expressions. We also provide analytic approximations and their range of validity. For the Cosmic Microwave Background we give a fast way to compute the PDF which is valid up to 7{\\sigma} for fNL values (both true and sampled) not ruled out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.

Exact Relativistic `Antigravity' Propulsion

Science.gov (United States)

Felber, Franklin S.

2006-01-01

The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.

Lattice sigma models with exact supersymmetry

International Nuclear Information System (INIS)

Simon Catterall; Sofiane Ghadab

2004-01-01

We show how to construct lattice sigma models in one, two and four dimensions which exhibit an exact fermionic symmetry. These models are discretized and twisted versions of conventional supersymmetric sigma models with N=2 supersymmetry. The fermionic symmetry corresponds to a scalar BRST charge built from the original supercharges. The lattice theories possess local actions and exhibit no fermion doubling. In the two and four dimensional theories we show that these lattice theories are invariant under additional discrete symmetries. We argue that the presence of these exact symmetries ensures that no fine tuning is required to achieve N=2 supersymmetry in the continuum limit. As a concrete example we show preliminary numerical results from a simulation of the O(3) supersymmetric sigma model in two dimensions. (author)

Quantitative estimation of the human error probability during soft control operations

International Nuclear Information System (INIS)

Lee, Seung Jun; Kim, Jaewhan; Jung, Wondea

2013-01-01

Highlights: ► An HRA method to evaluate execution HEP for soft control operations was proposed. ► The soft control tasks were analyzed and design-related influencing factors were identified. ► An application to evaluate the effects of soft controls was performed. - Abstract: In this work, a method was proposed for quantifying human errors that can occur during operation executions using soft controls. Soft controls of advanced main control rooms have totally different features from conventional controls, and thus they may have different human error modes and occurrence probabilities. It is important to identify the human error modes and quantify the error probability for evaluating the reliability of the system and preventing errors. This work suggests an evaluation framework for quantifying the execution error probability using soft controls. In the application result, it was observed that the human error probabilities of soft controls showed both positive and negative results compared to the conventional controls according to the design quality of advanced main control rooms

Benchmarking GW against exact diagonalization for semiempirical models

DEFF Research Database (Denmark)

Kaasbjerg, Kristen; Thygesen, Kristian Sommer

2010-01-01

We calculate ground-state total energies and single-particle excitation energies of seven pi-conjugated molecules described with the semiempirical Pariser-Parr-Pople model using self-consistent many-body perturbation theory at the GW level and exact diagonalization. For the total energies GW capt...... (Hubbard models) where correlation effects dominate over screening/relaxation effects. Finally we illustrate the important role of the derivative discontinuity of the true exchange-correlation functional by computing the exact Kohn-Sham levels of benzene....

Exactly solvable energy-dependent potentials

International Nuclear Information System (INIS)

Garcia-Martinez, J.; Garcia-Ravelo, J.; Pena, J.J.; Schulze-Halberg, A.

2009-01-01

We introduce a method for constructing exactly-solvable Schroedinger equations with energy-dependent potentials. Our method is based on converting a general linear differential equation of second order into a Schroedinger equation with energy-dependent potential. Particular examples presented here include harmonic oscillator, Coulomb and Morse potentials with various types of energy dependence.

New exact travelling wave solutions for the Ostrovsky equation

International Nuclear Information System (INIS)

Kangalgil, Figen; Ayaz, Fatma

2008-01-01

In this Letter, auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation. In order to illustrate the validity and the advantages of the method we choose the Ostrovsky equation. As a result, many new and more general exact solutions have been obtained for the equation

An exact power series formula of the outage probability with noise and interference over generalized fading channels

KAUST Repository

Rached, Nadhir B.

2016-12-24

In this paper, we develop a generalized momentbased approach for the evaluation of the outage probability (OP) in the presence of co-channel interference and additive white Gaussian noise. The proposed method allows the evaluation of the OP of the signal-to-interference-plus-noise ratio by a power series expansion in the threshold value. Its main advantage is that it does not require a particular distribution for the interference channels. The only necessary ingredients are a power series expansion for the cumulative distribution function of the desired user power and the cross-moments of the interferers\\' powers. These requirements are easily met in many practical fading models, for which the OP might not be obtained in closed-form expression. For a sake of illustration, we consider the application of our method to the Rician fading environment. Under this setting, we carry out a convergence study of the proposed power series and corroborate the validity of our method for different values of fading parameters and various numbers of co-channel interferers.

Exact Symbol Error Probability of Square M-QAM Signaling over Generalized Fading Channels subject to Additive Generalized Gaussian Noise

KAUST Repository

Soury, Hamza

2013-07-01

This paper considers the average symbol error probability of square Quadrature Amplitude Modulation (QAM) coherent signaling over flat fading channels subject to additive generalized Gaussian noise. More specifically, a generic closedform expression in terms of the Fox H function and the bivariate Fox H function is offered for the extended generalized-K fading case. Simplifications for some special fading distributions such as generalized-K fading, Nakagami-m fading, and Rayleigh fading and special additive noise distributions such as Gaussian and Laplacian noise are then presented. Finally, the mathematical formalism is illustrated by some numerical examples verified by computer based simulations for a variety of fading and additive noise parameters.

Quantum probabilities as Dempster-Shafer probabilities in the lattice of subspaces

International Nuclear Information System (INIS)

Vourdas, A.

2014-01-01

The orthocomplemented modular lattice of subspaces L[H(d)], of a quantum system with d-dimensional Hilbert space H(d), is considered. A generalized additivity relation which holds for Kolmogorov probabilities is violated by quantum probabilities in the full lattice L[H(d)] (it is only valid within the Boolean subalgebras of L[H(d)]). This suggests the use of more general (than Kolmogorov) probability theories, and here the Dempster-Shafer probability theory is adopted. An operator D(H 1 ,H 2 ), which quantifies deviations from Kolmogorov probability theory is introduced, and it is shown to be intimately related to the commutator of the projectors P(H 1 ),P(H 2 ), to the subspaces H 1 , H 2 . As an application, it is shown that the proof of the inequalities of Clauser, Horne, Shimony, and Holt for a system of two spin 1/2 particles is valid for Kolmogorov probabilities, but it is not valid for Dempster-Shafer probabilities. The violation of these inequalities in experiments supports the interpretation of quantum probabilities as Dempster-Shafer probabilities

Exact solutions for some discrete models of the Boltzmann equation

International Nuclear Information System (INIS)

Cabannes, H.; Hong Tiem, D.

1987-01-01

For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models [fr

Exact Algorithms for Solving Stochastic Games

DEFF Research Database (Denmark)

Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels

2012-01-01

Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....

Feature-level domain adaptation

DEFF Research Database (Denmark)

Kouw, Wouter M.; Van Der Maaten, Laurens J P; Krijthe, Jesse H.

2016-01-01

-level domain adaptation (flda), that models the dependence between the two domains by means of a feature-level transfer model that is trained to describe the transfer from source to target domain. Subsequently, we train a domain-adapted classifier by minimizing the expected loss under the resulting transfer...... modeled via a dropout distribution, which allows the classiffier to adapt to differences in the marginal probability of features in the source and the target domain. Our experiments on several real-world problems show that flda performs on par with state-of-the-art domainadaptation techniques.......Domain adaptation is the supervised learning setting in which the training and test data are sampled from different distributions: training data is sampled from a source domain, whilst test data is sampled from a target domain. This paper proposes and studies an approach, called feature...

Exact goodness-of-fit tests for Markov chains.

Science.gov (United States)

Besag, J; Mondal, D

2013-06-01

Goodness-of-fit tests are useful in assessing whether a statistical model is consistent with available data. However, the usual χ² asymptotics often fail, either because of the paucity of the data or because a nonstandard test statistic is of interest. In this article, we describe exact goodness-of-fit tests for first- and higher order Markov chains, with particular attention given to time-reversible ones. The tests are obtained by conditioning on the sufficient statistics for the transition probabilities and are implemented by simple Monte Carlo sampling or by Markov chain Monte Carlo. They apply both to single and to multiple sequences and allow a free choice of test statistic. Three examples are given. The first concerns multiple sequences of dry and wet January days for the years 1948-1983 at Snoqualmie Falls, Washington State, and suggests that standard analysis may be misleading. The second one is for a four-state DNA sequence and lends support to the original conclusion that a second-order Markov chain provides an adequate fit to the data. The last one is six-state atomistic data arising in molecular conformational dynamics simulation of solvated alanine dipeptide and points to strong evidence against a first-order reversible Markov chain at 6 picosecond time steps. © 2013, The International Biometric Society.

PROBABILITY SURVEYS , CONDITIONAL PROBABILITIES AND ECOLOGICAL RISK ASSESSMENT

Science.gov (United States)

We show that probability-based environmental resource monitoring programs, such as the U.S. Environmental Protection Agency's (U.S. EPA) Environmental Monitoring and Assessment Program, and conditional probability analysis can serve as a basis for estimating ecological risk over ...

Probability-Based Recognition Framework for Underwater Landmarks Using Sonar Images †.

Science.gov (United States)

Lee, Yeongjun; Choi, Jinwoo; Ko, Nak Yong; Choi, Hyun-Taek

2017-08-24

This paper proposes a probability-based framework for recognizing underwater landmarks using sonar images. Current recognition methods use a single image, which does not provide reliable results because of weaknesses of the sonar image such as unstable acoustic source, many speckle noises, low resolution images, single channel image, and so on. However, using consecutive sonar images, if the status-i.e., the existence and identity (or name)-of an object is continuously evaluated by a stochastic method, the result of the recognition method is available for calculating the uncertainty, and it is more suitable for various applications. Our proposed framework consists of three steps: (1) candidate selection, (2) continuity evaluation, and (3) Bayesian feature estimation. Two probability methods-particle filtering and Bayesian feature estimation-are used to repeatedly estimate the continuity and feature of objects in consecutive images. Thus, the status of the object is repeatedly predicted and updated by a stochastic method. Furthermore, we develop an artificial landmark to increase detectability by an imaging sonar, which we apply to the characteristics of acoustic waves, such as instability and reflection depending on the roughness of the reflector surface. The proposed method is verified by conducting basin experiments, and the results are presented.

Integrated reporting and board features

Directory of Open Access Journals (Sweden)

Rares HURGHIS

2017-02-01

Full Text Available In the last two decades the concept of sustainability reporting gained more importance in the companies’ annual reports, a trend which is embedded also in integrated reporting. Issuing an integrated report became a necessity, because the report explains to the investors how the organization creates value over time. The governance structure, more exactly the board of directors, decides whether or not the company will issue an integrated report. Thus, are there certain features of the board that might influence the issue of an integrated report? Do the companies which issue an integrated report have certain features of the governance structure? Looking for an answer to these questions, we seek for any possible correlations between a disclosure index and the corporate governance structure characteristics, on a sample from the companies participating at the International Integrated Reporting Council Examples Database. The results highlight that only the size of the board influences the extent to which the issued integrated report is in accordance with the International Framework.

A Semi-Continuous State-Transition Probability HMM-Based Voice Activity Detector

Directory of Open Access Journals (Sweden)

H. Othman

2007-02-01

Full Text Available We introduce an efficient hidden Markov model-based voice activity detection (VAD algorithm with time-variant state-transition probabilities in the underlying Markov chain. The transition probabilities vary in an exponential charge/discharge scheme and are softly merged with state conditional likelihood into a final VAD decision. Working in the domain of ITU-T G.729 parameters, with no additional cost for feature extraction, the proposed algorithm significantly outperforms G.729 Annex B VAD while providing a balanced tradeoff between clipping and false detection errors. The performance compares very favorably with the adaptive multirate VAD, option 2 (AMR2.

A Semi-Continuous State-Transition Probability HMM-Based Voice Activity Detector

Directory of Open Access Journals (Sweden)

Othman H

2007-01-01

Full Text Available We introduce an efficient hidden Markov model-based voice activity detection (VAD algorithm with time-variant state-transition probabilities in the underlying Markov chain. The transition probabilities vary in an exponential charge/discharge scheme and are softly merged with state conditional likelihood into a final VAD decision. Working in the domain of ITU-T G.729 parameters, with no additional cost for feature extraction, the proposed algorithm significantly outperforms G.729 Annex B VAD while providing a balanced tradeoff between clipping and false detection errors. The performance compares very favorably with the adaptive multirate VAD, option 2 (AMR2.

The asymptotic and exact Fisher information matrices of a vector ARMA process

NARCIS (Netherlands)

Klein, A.; Melard, G.; Saidi, A.

2008-01-01

The exact Fisher information matrix of a Gaussian vector autoregressive-moving average (VARMA) process has been considered for a time series of length N in relation to the exact maximum likelihood estimation method. In this paper it is shown that the Gaussian exact Fisher information matrix

Exact 2-point function in Hermitian matrix model

International Nuclear Information System (INIS)

Morozov, A.; Shakirov, Sh.

2009-01-01

J. Harer and D. Zagier have found a strikingly simple generating function [1,2] for exact (all-genera) 1-point correlators in the Gaussian Hermitian matrix model. In this paper we generalize their result to 2-point correlators, using Toda integrability of the model. Remarkably, this exact 2-point correlation function turns out to be an elementary function - arctangent. Relation to the standard 2-point resolvents is pointed out. Some attempts of generalization to 3-point and higher functions are described.

Exact solutions in string-motivated scalar-field cosmology

International Nuclear Information System (INIS)

Oezer, M.; Taha, M.O.

1992-01-01

Two exact cosmological solutions to a scalar-field potential motivated by six-dimensional (6D) Einstein-Maxwell theory are given. The resulting pure scalar-field cosmology is free of singularity and causality problems but conserves entropy. These solutions are then extended into exact cosmological solutions for a decaying scalar field with an approximate two-loop 4D string potential. The resulting cosmology is, for both solutions, free of cosmological problems and close to the standard cosmology of the radiation era

Land use and land cover classification for rural residential areas in China using soft-probability cascading of multifeatures

Science.gov (United States)

Zhang, Bin; Liu, Yueyan; Zhang, Zuyu; Shen, Yonglin

2017-10-01

A multifeature soft-probability cascading scheme to solve the problem of land use and land cover (LULC) classification using high-spatial-resolution images to map rural residential areas in China is proposed. The proposed method is used to build midlevel LULC features. Local features are frequently considered as low-level feature descriptors in a midlevel feature learning method. However, spectral and textural features, which are very effective low-level features, are neglected. The acquisition of the dictionary of sparse coding is unsupervised, and this phenomenon reduces the discriminative power of the midlevel feature. Thus, we propose to learn supervised features based on sparse coding, a support vector machine (SVM) classifier, and a conditional random field (CRF) model to utilize the different effective low-level features and improve the discriminability of midlevel feature descriptors. First, three kinds of typical low-level features, namely, dense scale-invariant feature transform, gray-level co-occurrence matrix, and spectral features, are extracted separately. Second, combined with sparse coding and the SVM classifier, the probabilities of the different LULC classes are inferred to build supervised feature descriptors. Finally, the CRF model, which consists of two parts: unary potential and pairwise potential, is employed to construct an LULC classification map. Experimental results show that the proposed classification scheme can achieve impressive performance when the total accuracy reached about 87%.

Linear orbit parameters for the exact equations of motion

International Nuclear Information System (INIS)

Parzen, G.

1995-01-01

This paper defines the beta function and other linear orbit parameters using the exact equations of motion. The β, α and ψ functions are redefined using the exact equations. Expressions are found for the transfer matrix and the emittance. The differential equations for η = x/β 1/2 is found. New relationships between α, β, ψ and ν are derived

Fast and Exact Fiber Surfaces for Tetrahedral Meshes.

Science.gov (United States)

Klacansky, Pavol; Tierny, Julien; Carr, Hamish; Zhao Geng

2017-07-01

Isosurfaces are fundamental geometrical objects for the analysis and visualization of volumetric scalar fields. Recent work has generalized them to bivariate volumetric fields with fiber surfaces, the pre-image of polygons in range space. However, the existing algorithm for their computation is approximate, and is limited to closed polygons. Moreover, its runtime performance does not allow instantaneous updates of the fiber surfaces upon user edits of the polygons. Overall, these limitations prevent a reliable and interactive exploration of the space of fiber surfaces. This paper introduces the first algorithm for the exact computation of fiber surfaces in tetrahedral meshes. It assumes no restriction on the topology of the input polygon, handles degenerate cases and better captures sharp features induced by polygon bends. The algorithm also allows visualization of individual fibers on the output surface, better illustrating their relationship with data features in range space. To enable truly interactive exploration sessions, we further improve the runtime performance of this algorithm. In particular, we show that it is trivially parallelizable and that it scales nearly linearly with the number of cores. Further, we study acceleration data-structures both in geometrical domain and range space and we show how to generalize interval trees used in isosurface extraction to fiber surface extraction. Experiments demonstrate the superiority of our algorithm over previous work, both in terms of accuracy and running time, with up to two orders of magnitude speedups. This improvement enables interactive edits of range polygons with instantaneous updates of the fiber surface for exploration purpose. A VTK-based reference implementation is provided as additional material to reproduce our results.

Fuzziness and Foundations of Exact and Inexact Sciences

CERN Document Server

Dompere, Kofi Kissi

2013-01-01

The monograph is an examination of the fuzzy rational foundations of the structure of exact and inexact sciences over the epistemological space which is distinguished from the ontological space. It is thus concerned with the demarcation problem. It examines exact science and its critique of inexact science. The role of fuzzy rationality in these examinations is presented. The driving force of the discussions is the nature of the information that connects the cognitive relational structure of the epistemological space to the ontological space for knowing. The knowing action is undertaken by decision-choice agents who must process information to derive exact-inexact or true-false conclusions. The information processing is done with a paradigm and laws of thought that constitute the input-output machine. The nature of the paradigm selected depends on the nature of the information structure that is taken as input of the thought processing. Generally, the information structure received from the ontological space i...

Symmetry and exact solutions of nonlinear spinor equations

International Nuclear Information System (INIS)

Fushchich, W.I.; Zhdanov, R.Z.

1989-01-01

This review is devoted to the application of algebraic-theoretical methods to the problem of constructing exact solutions of the many-dimensional nonlinear systems of partial differential equations for spinor, vector and scalar fields widely used in quantum field theory. Large classes of nonlinear spinor equations invariant under the Poincare group P(1, 3), Weyl group (i.e. Poincare group supplemented by a group of scale transformations), and the conformal group C(1, 3) are described. Ansaetze invariant under the Poincare and the Weyl groups are constructed. Using these we reduce the Poincare-invariant nonlinear Dirac equations to systems of ordinary differential equations and construct large families of exact solutions of the nonlinear Dirac-Heisenberg equation depending on arbitrary parameters and functions. In a similar way we have obtained new families of exact solutions of the nonlinear Maxwell-Dirac and Klein-Gordon-Dirac equations. The obtained solutions can be used for quantization of nonlinear equations. (orig.)

Fast Exact Euclidean Distance (FEED) Transformation

NARCIS (Netherlands)

Schouten, Theo; Kittler, J.; van den Broek, Egon; Petrou, M.; Nixon, M.

2004-01-01

Fast Exact Euclidean Distance (FEED) transformation is introduced, starting from the inverse of the distance transformation. The prohibitive computational cost of a naive implementation of traditional Euclidean Distance Transformation, is tackled by three operations: restriction of both the number

Exact Results in Non-Supersymmetric Large N Orientifold Field Theories

CERN Document Server

Armoni, Adi; Veneziano, Gabriele

2003-01-01

We consider non-supersymmetric large N orientifold field theories. Specifically, we discuss a gauge theory with a Dirac fermion in the anti-symmetric tensor representation. We argue that, at large N and in a large part of its bosonic sector, this theory is non-perturbatively equivalent to N=1 SYM, so that exact results established in the latter (parent) theory also hold in the daughter orientifold theory. In particular, the non-supersymmetric theory has an exactly calculable bifermion condensate, exactly degenerate parity doublets, and a vanishing cosmological constant (all this to leading order in 1/N).

On nonlinear differential equation with exact solutions having various pole orders

International Nuclear Information System (INIS)

Kudryashov, N.A.

2015-01-01

We consider a nonlinear ordinary differential equation having solutions with various movable pole order on the complex plane. We show that the pole order of exact solution is determined by values of parameters of the equation. Exact solutions in the form of the solitary waves for the second order nonlinear differential equation are found taking into account the method of the logistic function. Exact solutions of differential equations are discussed and analyzed

Error Probability of Binary and -ary Signals with Spatial Diversity in Nakagami- (Hoyt Fading Channels

Directory of Open Access Journals (Sweden)

Duong Trung Q

2007-01-01

Full Text Available We analyze the exact average symbol error probability (SEP of binary and -ary signals with spatial diversity in Nakagami- (Hoyt fading channels. The maximal-ratio combining and orthogonal space-time block coding are considered as diversity techniques for single-input multiple-output and multiple-input multiple-output systems, respectively. We obtain the average SEP in terms of the Lauricella multivariate hypergeometric function . The analysis is verified by comparing with Monte Carlo simulations and we further show that our general SEP expressions particularize to the previously known results for Rayleigh ( = 1 and single-input single-output (SISO Nakagami- cases.

Probability an introduction

CERN Document Server

Goldberg, Samuel

1960-01-01

Excellent basic text covers set theory, probability theory for finite sample spaces, binomial theorem, probability distributions, means, standard deviations, probability function of binomial distribution, more. Includes 360 problems with answers for half.

Exact approaches for scaffolding

OpenAIRE

Weller, Mathias; Chateau, Annie; Giroudeau, Rodolphe

2015-01-01

This paper presents new structural and algorithmic results around the scaffolding problem, which occurs prominently in next generation sequencing. The problem can be formalized as an optimization problem on a special graph, the "scaffold graph". We prove that the problem is polynomial if this graph is a tree by providing a dynamic programming algorithm for this case. This algorithm serves as a basis to deduce an exact algorithm for general graphs using a tree decomposition of the input. We ex...

Analysis of Probability of Non-zero Secrecy Capacity for Multi-hop Networks in Presence of Hardware Impairments over Nakagami-m Fading Channels

Directory of Open Access Journals (Sweden)

T.-T. Phu

2016-12-01

Full Text Available In this paper, we evaluate probability of non-zero secrecy capacity of multi-hop relay networks over Nakagami-m fading channels in presence of hardware impairments. In the considered protocol, a source attempts to transmit its data to a destination by using multi-hop randomize-and-forward (RF strategy. The data transmitted by the source and relays are overheard by an eavesdropper. For performance evaluation, we derive exact expressions of probability of non-zero secrecy capacity (PoNSC, which are expressed by sums of infinite series of exponential functions and exponential integral functions. We then perform Monte Carlo simulations to verify the theoretical analysis.

Exact boundary controllability of nodal profile for quasilinear hyperbolic systems

CERN Document Server

Li, Tatsien; Gu, Qilong

2016-01-01

This book provides a comprehensive overview of the exact boundary controllability of nodal profile, a new kind of exact boundary controllability stimulated by some practical applications. This kind of controllability is useful in practice as it does not require any precisely given final state to be attained at a suitable time t=T by means of boundary controls, instead it requires the state to exactly fit any given demand (profile) on one or more nodes after a suitable time t=T by means of boundary controls. In this book we present a general discussion of this kind of controllability for general 1-D first order quasilinear hyperbolic systems and for general 1-D quasilinear wave equations on an interval as well as on a tree-like network using a modular-structure construtive method, suggested in LI Tatsien's monograph "Controllability and Observability for Quasilinear Hyperbolic Systems"(2010), and we establish a complete theory on the local exact boundary controllability of nodal profile for 1-D quasilinear hyp...

Outage probability of dual-hop FSO fixed gain relay transmission systems

KAUST Repository

Zedini, Emna

2016-12-24

In this paper, we analyze the end-to-end performance of dual-hop free-space optical (FSO) fixed gain relaying systems in the presence of atmospheric turbulence as well as pointing errors. More specifically, an exact closed-form expression for the outage probability is presented in terms of the bivariate Fox\\'s H function that accounts for both heterodyne detection as well as intensity modulation with direct detection. At high signal-to-noise ratio (SNR) regime, we provide very tight asymptotic result for this performance metric in terms of simple elementary functions. By using dual-hop FSO relaying, we demonstrate a better system performance as compared to the single FSO link. Numerical and Monte-Carlo simulation results are provided to verify the accuracy of the newly proposed results, and a perfect agreement is observed.

arXiv Integrable flows between exact CFTs

CERN Document Server

Georgiou, George

2017-11-14

We explicitly construct families of integrable σ-model actions smoothly inter-polating between exact CFTs. In the ultraviolet the theory is the direct product of two current algebras at levels k$_{1}$ and k$_{2}$. In the infrared and for the case of two deformation matrices the CFT involves a coset CFT, whereas for a single matrix deformation it is given by the ultraviolet direct product theories but at levels k$_{1}$ and k$_{2}$ − k$_{1}$. For isotropic deformations we demonstrate integrability. In this case we also compute the exact beta-function for the deformation parameters using gravitational methods. This is shown to coincide with previous results obtained using perturbation theory and non-perturbative symmetries.

Exact computation of the 9-j symbols

International Nuclear Information System (INIS)

Lai Shantao; Chiu Jingnan

1992-01-01

A useful algebraic formula for the 9-j symbol has been rewritten for convenient use on a computer. A simple FORTRAN program for the exact computation of 9-j symbols has been written for the VAX with VMS version V5,4-1 according to this formula. The results agree with the approximate values in existing literature. Some specific values of 9-j symbols needed for the intensity and alignments of three-photon nonresonant transitions are tabulated. Approximate 9-j symbol values beyond the limitation of the computer can also be computed by this program. The computer code of the exact computation of 3-j, 6-j and 9-j symbols are available through electronic mail upon request. (orig.)

Exact deconstruction of the 6D (2,0) theory

Science.gov (United States)

Hayling, J.; Papageorgakis, C.; Pomoni, E.; Rodríguez-Gómez, D.

2017-06-01

The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T 2, starting from a four-dimensional N=2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: in the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D N=2 quiver to the "half-BPS" limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S 4 to the (2,0) partition function on S 4 × T 2. In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.

Exact deconstruction of the 6D (2,0) theory

International Nuclear Information System (INIS)

Hayling, J.; Papageorgakis, C.; Pomoni, E.; Rodriguez-Gomez, D.

2017-06-01

The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T 2 , starting from a four-dimensional N=2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: In the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D N=2 quiver to the ''half-BPS'' limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S 4 to the (2,0) partition function on S 4 x T 2 . In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.

Exact Stiffness for Beams on Kerr-Type Foundation: The Virtual Force Approach

Directory of Open Access Journals (Sweden)

Suchart Limkatanyu

2013-01-01

Full Text Available This paper alternatively derives the exact element stiffness equation for a beam on Kerr-type foundation. The shear coupling between the individual Winkler-spring components and the peripheral discontinuity at the boundaries between the loaded and the unloaded soil surfaces are taken into account in this proposed model. The element flexibility matrix is derived based on the virtual force principle and forms the core of the exact element stiffness matrix. The sixth-order governing differential compatibility of the problem is revealed using the virtual force principle and solved analytically to obtain the exact force interpolation functions. The matrix virtual force equation is employed to obtain the exact element flexibility matrix based on the exact force interpolation functions. The so-called “natural” element stiffness matrix is obtained by inverting the exact element flexibility matrix. One numerical example is utilized to confirm the accuracy and the efficiency of the proposed beam element on Kerr-type foundation and to show a more realistic distribution of interactive foundation force.

Novel correlations in two dimensions: Some exact solutions

International Nuclear Information System (INIS)

Murthy, M.V.; Bhaduri, R.K.; Sen, D.

1996-01-01

We construct a new many-body Hamiltonian with two- and three-body interactions in two space dimensions and obtain its exact many-body ground state for an arbitrary number of particles. This ground state has a novel pairwise correlation. A class of exact solutions for the excited states is also found. These excited states display an energy spectrum similar to the Calogero-Sutherland model in one dimension. The model reduces to an analog of the well-known trigonometric Sutherland model when projected on to a circular ring. copyright 1996 The American Physical Society

Exact results for integrable asymptotically-free field theories

CERN Document Server

Evans, J M; Evans, Jonathan M; Hollowood, Timothy J

1995-01-01

An account is given of a technique for testing the equivalence between an exact factorizable S-matrix and an asymptotically-free Lagrangian field theory in two space-time dimensions. The method provides a way of resolving CDD ambiguities in the S-matrix and it also allows for an exact determination of the physical mass in terms of the Lambda parameter of perturbation theory. The results for various specific examples are summarized. (To appear in the Proceedings of the Conference on Recent Developments in Quantum Field Theory and Statistical Mechanics, ICTP, Trieste, Easter 1995).

Superthermal photon bunching in terms of simple probability distributions

Science.gov (United States)

Lettau, T.; Leymann, H. A. M.; Melcher, B.; Wiersig, J.

2018-05-01

We analyze the second-order photon autocorrelation function g(2 ) with respect to the photon probability distribution and discuss the generic features of a distribution that results in superthermal photon bunching [g(2 )(0 ) >2 ]. Superthermal photon bunching has been reported for a number of optical microcavity systems that exhibit processes such as superradiance or mode competition. We show that a superthermal photon number distribution cannot be constructed from the principle of maximum entropy if only the intensity and the second-order autocorrelation are given. However, for bimodal systems, an unbiased superthermal distribution can be constructed from second-order correlations and the intensities alone. Our findings suggest modeling superthermal single-mode distributions by a mixture of a thermal and a lasinglike state and thus reveal a generic mechanism in the photon probability distribution responsible for creating superthermal photon bunching. We relate our general considerations to a physical system, i.e., a (single-emitter) bimodal laser, and show that its statistics can be approximated and understood within our proposed model. Furthermore, the excellent agreement of the statistics of the bimodal laser and our model reveals that the bimodal laser is an ideal source of bunched photons, in the sense that it can generate statistics that contain no other features but the superthermal bunching.

Some new exact solitary wave solutions of the van der Waals model arising in nature

Science.gov (United States)

Bibi, Sadaf; Ahmed, Naveed; Khan, Umar; Mohyud-Din, Syed Tauseef

2018-06-01

This work proposes two well-known methods, namely, Exponential rational function method (ERFM) and Generalized Kudryashov method (GKM) to seek new exact solutions of the van der Waals normal form for the fluidized granular matter, linked with natural phenomena and industrial applications. New soliton solutions such as kink, periodic and solitary wave solutions are established coupled with 2D and 3D graphical patterns for clarity of physical features. Our comparison reveals that the said methods excel several existing methods. The worked-out solutions show that the suggested methods are simple and reliable as compared to many other approaches which tackle nonlinear equations stemming from applied sciences.

Accelerating exact schedulability analysis for fixed-priority pre-emptive scheduling

NARCIS (Netherlands)

Hang, Y.; Jiale, Z.; Keskin, U.; Bril, R.J.

2010-01-01

The schedulability analysis for fixed-priority preemptive scheduling (FPPS) plays a significant role in the real-time systems domain. The so-called Hyperplanes Exact Test (HET) [1] is an example of an exact schedulability test for FPPS. In this paper, we aim at improving the efficiency of HET by

Novel acoustic features for speech emotion recognition

Institute of Scientific and Technical Information of China (English)

ROH; Yong-Wan; KIM; Dong-Ju; LEE; Woo-Seok; HONG; Kwang-Seok

2009-01-01

This paper focuses on acoustic features that effectively improve the recognition of emotion in human speech.The novel features in this paper are based on spectral-based entropy parameters such as fast Fourier transform(FFT) spectral entropy,delta FFT spectral entropy,Mel-frequency filter bank(MFB) spectral entropy,and Delta MFB spectral entropy.Spectral-based entropy features are simple.They reflect frequency characteristic and changing characteristic in frequency of speech.We implement an emotion rejection module using the probability distribution of recognized-scores and rejected-scores.This reduces the false recognition rate to improve overall performance.Recognized-scores and rejected-scores refer to probabilities of recognized and rejected emotion recognition results,respectively.These scores are first obtained from a pattern recognition procedure.The pattern recognition phase uses the Gaussian mixture model(GMM).We classify the four emotional states as anger,sadness,happiness and neutrality.The proposed method is evaluated using 45 sentences in each emotion for 30 subjects,15 males and 15 females.Experimental results show that the proposed method is superior to the existing emotion recognition methods based on GMM using energy,Zero Crossing Rate(ZCR),linear prediction coefficient(LPC),and pitch parameters.We demonstrate the effectiveness of the proposed approach.One of the proposed features,combined MFB and delta MFB spectral entropy improves performance approximately 10% compared to the existing feature parameters for speech emotion recognition methods.We demonstrate a 4% performance improvement in the applied emotion rejection with low confidence score.

Novel acoustic features for speech emotion recognition

Institute of Scientific and Technical Information of China (English)

ROH Yong-Wan; KIM Dong-Ju; LEE Woo-Seok; HONG Kwang-Seok

2009-01-01

This paper focuses on acoustic features that effectively improve the recognition of emotion in human speech. The novel features in this paper are based on spectral-based entropy parameters such as fast Fourier transform (FFT) spectral entropy, delta FFT spectral entropy, Mel-frequency filter bank (MFB)spectral entropy, and Delta MFB spectral entropy. Spectral-based entropy features are simple. They reflect frequency characteristic and changing characteristic in frequency of speech. We implement an emotion rejection module using the probability distribution of recognized-scores and rejected-scores.This reduces the false recognition rate to improve overall performance. Recognized-scores and rejected-scores refer to probabilities of recognized and rejected emotion recognition results, respectively.These scores are first obtained from a pattern recognition procedure. The pattern recognition phase uses the Gaussian mixture model (GMM). We classify the four emotional states as anger, sadness,happiness and neutrality. The proposed method is evaluated using 45 sentences in each emotion for 30 subjects, 15 males and 15 females. Experimental results show that the proposed method is superior to the existing emotion recognition methods based on GMM using energy, Zero Crossing Rate (ZCR),linear prediction coefficient (LPC), and pitch parameters. We demonstrate the effectiveness of the proposed approach. One of the proposed features, combined MFB and delta MFB spectral entropy improves performance approximately 10% compared to the existing feature parameters for speech emotion recognition methods. We demonstrate a 4% performance improvement in the applied emotion rejection with low confidence score.

Exact WKB analysis and cluster algebras

International Nuclear Information System (INIS)

Iwaki, Kohei; Nakanishi, Tomoki

2014-01-01

We develop the mutation theory in the exact WKB analysis using the framework of cluster algebras. Under a continuous deformation of the potential of the Schrödinger equation on a compact Riemann surface, the Stokes graph may change the topology. We call this phenomenon the mutation of Stokes graphs. Along the mutation of Stokes graphs, the Voros symbols, which are monodromy data of the equation, also mutate due to the Stokes phenomenon. We show that the Voros symbols mutate as variables of a cluster algebra with surface realization. As an application, we obtain the identities of Stokes automorphisms associated with periods of cluster algebras. The paper also includes an extensive introduction of the exact WKB analysis and the surface realization of cluster algebras for nonexperts. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Cluster algebras in mathematical physics’. (paper)

Clinical features and natural history of von Hippel-Lindau disease.

Science.gov (United States)

Maher, E R; Yates, J R; Harries, R; Benjamin, C; Harris, R; Moore, A T; Ferguson-Smith, M A

1990-11-01

The clinical features, age at onset and survival of 152 patients with von Hippel-Lindau disease were studied. Mean age at onset was 26.3 years and 97 per cent of patients had presented by aged 60 years. Retinal angioma was the first manifestation in 65 patients (43 per cent), followed by cerebellar haemangioblastoma (n = 60, 39 per cent) and renal cell carcinoma (n = 15, 10 per cent). Overall, 89 patients (59 per cent) developed a cerebellar haemangioblastoma, 89 (59 per cent) a retinal angioma, 43 (28 per cent) renal cell carcinoma, 20 (13 per cent) spinal haemangioblastoma and 11 (7 per cent) a phaeochromocytoma. Renal, pancreatic and epididymal cysts were frequent findings but their exact incidence was not accurately assessed. Mean age at diagnosis of renal cell carcinoma (44.0 +/- 10.9 years) was significantly older than that for cerebellar haemangioblastoma (29.0 +/- 10.0 years) and retinal angioma (25.4 +/- 12.7 years). The probability of a patient with von Hippel-Lindan disease developing a cerebellar haemangioblastoma, retinal angioma or renal cell carcinoma by age 60 years was 0.84, 0.7 and 0.69, respectively. A comprehensive screening protocol for affected patients and at-risk relatives is presented, based on detailed analysis of age at onset data for each of the major complications. Median actuarial survival was 49 years, with renal cell carcinoma the leading cause of death.

Simple and compact expressions for neutrino oscillation probabilities in matter

International Nuclear Information System (INIS)

Minakata, Hisakazu; Parke, Stephen J.

2016-01-01

We reformulate perturbation theory for neutrino oscillations in matter with an expansion parameter related to the ratio of the solar to the atmospheric Δm"2 scales. Unlike previous works, we use a renormalized basis in which certain first-order effects are taken into account in the zeroth-order Hamiltonian. We show that the new framework has an exceptional feature that leads to the neutrino oscillation probability in matter with the same structure as in vacuum to first order in the expansion parameter. It facilitates immediate physical interpretation of the formulas, and makes the expressions for the neutrino oscillation probabilities extremely simple and compact. We find, for example, that the ν_e disappearance probability at this order is of a simple two-flavor form with an appropriately identified mixing angle and Δm"2. More generally, all the oscillation probabilities can be written in the universal form with the channel-discrimination coefficient of 0, ±1 or simple functions of θ_2_3. Despite their simple forms they include all order effects of θ_1_3 and all order effects of the matter potential, to first order in our expansion parameter.

Camera-Model Identification Using Markovian Transition Probability Matrix

Science.gov (United States)

Xu, Guanshuo; Gao, Shang; Shi, Yun Qing; Hu, Ruimin; Su, Wei

Detecting the (brands and) models of digital cameras from given digital images has become a popular research topic in the field of digital forensics. As most of images are JPEG compressed before they are output from cameras, we propose to use an effective image statistical model to characterize the difference JPEG 2-D arrays of Y and Cb components from the JPEG images taken by various camera models. Specifically, the transition probability matrices derived from four different directional Markov processes applied to the image difference JPEG 2-D arrays are used to identify statistical difference caused by image formation pipelines inside different camera models. All elements of the transition probability matrices, after a thresholding technique, are directly used as features for classification purpose. Multi-class support vector machines (SVM) are used as the classification tool. The effectiveness of our proposed statistical model is demonstrated by large-scale experimental results.

Exact simulation of conditioned Wright-Fisher models.

Science.gov (United States)

Zhao, Lei; Lascoux, Martin; Waxman, David

2014-12-21

Forward and backward simulations play an increasing role in population genetics, in particular when inferring the relative importance of evolutionary forces. It is therefore important to develop fast and accurate simulation methods for general population genetics models. Here we present an exact simulation method that generates trajectories of an allele׳s frequency in a finite population, as described by a general Wright-Fisher model. The method generates conditioned trajectories that start from a known frequency at a known time, and which achieve a specific final frequency at a known final time. The simulation method applies irrespective of the smallness of the probability of the transition between the initial and final states, because it is not based on rejection of trajectories. We illustrate the method on several different populations where a Wright-Fisher model (or related) applies, namely (i) a locus with 2 alleles, that is subject to selection and mutation; (ii) a locus with 3 alleles, that is subject to selection; (iii) a locus in a metapopulation consisting of two subpopulations of finite size, that are subject to selection and migration. The simulation method allows the generation of conditioned trajectories that can be used for the purposes of visualisation, the estimation of summary statistics, and the development/testing of new inferential methods. The simulated trajectories provide a very simple approach to estimating quantities that cannot easily be expressed in terms of the transition matrix, and can be applied to finite Markov chains other than the Wright-Fisher model. Copyright © 2014 Elsevier Ltd. All rights reserved.

On estimating probability of presence from use-availability or presence-background data.

Science.gov (United States)

Phillips, Steven J; Elith, Jane

2013-06-01

A fundamental ecological modeling task is to estimate the probability that a species is present in (or uses) a site, conditional on environmental variables. For many species, available data consist of "presence" data (locations where the species [or evidence of it] has been observed), together with "background" data, a random sample of available environmental conditions. Recently published papers disagree on whether probability of presence is identifiable from such presence-background data alone. This paper aims to resolve the disagreement, demonstrating that additional information is required. We defined seven simulated species representing various simple shapes of response to environmental variables (constant, linear, convex, unimodal, S-shaped) and ran five logistic model-fitting methods using 1000 presence samples and 10 000 background samples; the simulations were repeated 100 times. The experiment revealed a stark contrast between two groups of methods: those based on a strong assumption that species' true probability of presence exactly matches a given parametric form had highly variable predictions and much larger RMS error than methods that take population prevalence (the fraction of sites in which the species is present) as an additional parameter. For six species, the former group grossly under- or overestimated probability of presence. The cause was not model structure or choice of link function, because all methods were logistic with linear and, where necessary, quadratic terms. Rather, the experiment demonstrates that an estimate of prevalence is not just helpful, but is necessary (except in special cases) for identifying probability of presence. We therefore advise against use of methods that rely on the strong assumption, due to Lele and Keim (recently advocated by Royle et al.) and Lancaster and Imbens. The methods are fragile, and their strong assumption is unlikely to be true in practice. We emphasize, however, that we are not arguing against

Processing and Probability Analysis of Pulsed Terahertz NDE of Corrosion under Shuttle Tile Data

Science.gov (United States)

Anastasi, Robert F.; Madaras, Eric I.; Seebo, Jeffrey P.; Ely, Thomas M.

2009-01-01

This paper examines data processing and probability analysis of pulsed terahertz NDE scans of corrosion defects under a Shuttle tile. Pulsed terahertz data collected from an aluminum plate with fabricated corrosion defects and covered with a Shuttle tile is presented. The corrosion defects imaged were fabricated by electrochemically etching areas of various diameter and depth in the plate. In this work, the aluminum plate echo signal is located in the terahertz time-of-flight data and a threshold is applied to produce a binary image of sample features. Feature location and area are examined and identified as corrosion through comparison with the known defect layout. The results are tabulated with hit, miss, or false call information for a probability of detection analysis that is used to identify an optimal processing threshold.

Fully automatized renal parenchyma volumetry using a support vector machine based recognition system for subject-specific probability map generation in native MR volume data

Science.gov (United States)

Gloger, Oliver; Tönnies, Klaus; Mensel, Birger; Völzke, Henry

2015-11-01

In epidemiological studies as well as in clinical practice the amount of produced medical image data strongly increased in the last decade. In this context organ segmentation in MR volume data gained increasing attention for medical applications. Especially in large-scale population-based studies organ volumetry is highly relevant requiring exact organ segmentation. Since manual segmentation is time-consuming and prone to reader variability, large-scale studies need automatized methods to perform organ segmentation. Fully automatic organ segmentation in native MR image data has proven to be a very challenging task. Imaging artifacts as well as inter- and intrasubject MR-intensity differences complicate the application of supervised learning strategies. Thus, we propose a modularized framework of a two-stepped probabilistic approach that generates subject-specific probability maps for renal parenchyma tissue, which are refined subsequently by using several, extended segmentation strategies. We present a three class-based support vector machine recognition system that incorporates Fourier descriptors as shape features to recognize and segment characteristic parenchyma parts. Probabilistic methods use the segmented characteristic parenchyma parts to generate high quality subject-specific parenchyma probability maps. Several refinement strategies including a final shape-based 3D level set segmentation technique are used in subsequent processing modules to segment renal parenchyma. Furthermore, our framework recognizes and excludes renal cysts from parenchymal volume, which is important to analyze renal functions. Volume errors and Dice coefficients show that our presented framework outperforms existing approaches.

Fully automatized renal parenchyma volumetry using a support vector machine based recognition system for subject-specific probability map generation in native MR volume data

International Nuclear Information System (INIS)

Gloger, Oliver; Völzke, Henry; Tönnies, Klaus; Mensel, Birger

2015-01-01

In epidemiological studies as well as in clinical practice the amount of produced medical image data strongly increased in the last decade. In this context organ segmentation in MR volume data gained increasing attention for medical applications. Especially in large-scale population-based studies organ volumetry is highly relevant requiring exact organ segmentation. Since manual segmentation is time-consuming and prone to reader variability, large-scale studies need automatized methods to perform organ segmentation. Fully automatic organ segmentation in native MR image data has proven to be a very challenging task. Imaging artifacts as well as inter- and intrasubject MR-intensity differences complicate the application of supervised learning strategies. Thus, we propose a modularized framework of a two-stepped probabilistic approach that generates subject-specific probability maps for renal parenchyma tissue, which are refined subsequently by using several, extended segmentation strategies. We present a three class-based support vector machine recognition system that incorporates Fourier descriptors as shape features to recognize and segment characteristic parenchyma parts. Probabilistic methods use the segmented characteristic parenchyma parts to generate high quality subject-specific parenchyma probability maps. Several refinement strategies including a final shape-based 3D level set segmentation technique are used in subsequent processing modules to segment renal parenchyma. Furthermore, our framework recognizes and excludes renal cysts from parenchymal volume, which is important to analyze renal functions. Volume errors and Dice coefficients show that our presented framework outperforms existing approaches. (paper)

Exact solutions to the Mo-Papas and Landau-Lifshitz equations

Science.gov (United States)

Rivera, R.; Villarroel, D.

2002-10-01

Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics.

Exact solutions to the Mo-Papas and Landau-Lifshitz equations

International Nuclear Information System (INIS)

Rivera, R.; Villarroel, D.

2002-01-01

Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics

Exact axially symmetric galactic dynamos

Science.gov (United States)

Henriksen, R. N.; Woodfinden, A.; Irwin, J. A.

2018-05-01

We give a selection of exact dynamos in axial symmetry on a galactic scale. These include some steady examples, at least one of which is wholly analytic in terms of simple functions and has been discussed elsewhere. Most solutions are found in terms of special functions, such as associated Lagrange or hypergeometric functions. They may be considered exact in the sense that they are known to any desired accuracy in principle. The new aspect developed here is to present scale-invariant solutions with zero resistivity that are self-similar in time. The time dependence is either a power law or an exponential factor, but since the geometry of the solution is self-similar in time we do not need to fix a time to study it. Several examples are discussed. Our results demonstrate (without the need to invoke any other mechanisms) X-shaped magnetic fields and (axially symmetric) magnetic spiral arms (both of which are well observed and documented) and predict reversing rotation measures in galaxy haloes (now observed in the CHANG-ES sample) as well as the fact that planar magnetic spirals are lifted into the galactic halo.

Foundations of probability

International Nuclear Information System (INIS)

Fraassen, B.C. van

1979-01-01

The interpretation of probabilities in physical theories are considered, whether quantum or classical. The following points are discussed 1) the functions P(μ, Q) in terms of which states and propositions can be represented, are classical (Kolmogoroff) probabilities, formally speaking, 2) these probabilities are generally interpreted as themselves conditional, and the conditions are mutually incompatible where the observables are maximal and 3) testing of the theory typically takes the form of confronting the expectation values of observable Q calculated with probability measures P(μ, Q) for states μ; hence, of comparing the probabilities P(μ, Q)(E) with the frequencies of occurrence of the corresponding events. It seems that even the interpretation of quantum mechanics, in so far as it concerns what the theory says about the empirical (i.e. actual, observable) phenomena, deals with the confrontation of classical probability measures with observable frequencies. This confrontation is studied. (Auth./C.F.)

Exact deconstruction of the 6D (2,0) theory

Energy Technology Data Exchange (ETDEWEB)

Hayling, J.; Papageorgakis, C. [Queen Mary Univ. of London (United Kingdom). CRST and School of Physics and Astronomy; Pomoni, E. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group; Rodriguez-Gomez, D. [Oviedo Univ. (Spain). Dept. of Physics

2017-06-15

The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T{sup 2}, starting from a four-dimensional N=2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: In the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D N=2 quiver to the ''half-BPS'' limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S{sup 4} to the (2,0) partition function on S{sup 4} x T{sup 2}. In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.

XI Symposium on Probability and Stochastic Processes

CERN Document Server

Pardo, Juan; Rivero, Víctor; Bravo, Gerónimo

2015-01-01

This volume features lecture notes and a collection of contributed articles from the XI Symposium on Probability and Stochastic Processes, held at CIMAT Mexico in September 2013. Since the symposium was part of the activities organized in Mexico to celebrate the International Year of Statistics, the program included topics from the interface between statistics and stochastic processes. The book starts with notes from the mini-course given by Louigi Addario-Berry with an accessible description of some features of the multiplicative coalescent and its connection with random graphs and minimum spanning trees. It includes a number of exercises and a section on unanswered questions. Further contributions provide the reader with a broad perspective on the state-of-the art of active areas of research. Contributions by: Louigi Addario-Berry Octavio Arizmendi Fabrice Baudoin Jochen Blath Loïc Chaumont J. Armando Domínguez-Molina Bjarki Eldon Shui Feng Tulio Gaxiola Adrián González Casanova Evgueni Gordienko Daniel...

New exact wave solutions for Hirota equation

Indian Academy of Sciences (India)

2Department of Engineering Sciences, Faculty of Technology and Engineering,. University ... of nonlinear partial differential equations (NPDEs) in mathematical physics. Keywords. ... This method has been successfully applied to obtain exact.

Collective fluctuations in magnetized plasma: Transition probability approach

International Nuclear Information System (INIS)

Sosenko, P.P.

1997-01-01

Statistical plasma electrodynamics is elaborated with special emphasis on the transition probability approach and quasi-particles, and on modern applications to magnetized plasmas. Fluctuation spectra in the magnetized plasma are calculated in the range of low frequencies (with respect to the cyclotron one), and the conditions for the transition from incoherent to collective fluctuations are established. The role of finite-Larmor-radius effects and particle polarization drift in such a transition is explained. The ion collective features in fluctuation spectra are studied. 63 refs., 30 figs

Non-Archimedean Probability

NARCIS (Netherlands)

Benci, Vieri; Horsten, Leon; Wenmackers, Sylvia

We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample space are measurable and only the empty set gets assigned

TVT-Exact and midurethral sling (SLING-IUFT) operative procedures: a randomized study.

Science.gov (United States)

Aniuliene, Rosita; Aniulis, Povilas; Skaudickas, Darijus

2015-01-01

The aim of the study is to compare results, effectiveness and complications of TVT exact and midurethral sling (SLING-IUFT) operations in the treatment of female stress urinary incontinence (SUI). A single center nonblind, randomized study of women with SUI who were randomized to TVT-Exact and SLING-IUFT was performed by one surgeon from April 2009 to April 2011. SUI was diagnosed on coughing and Valsalva test and urodynamics (cystometry and uroflowmetry) were assessed before operation and 1 year after surgery. This was a prospective randomized study. The follow up period was 12 months. 76 patients were operated using the TVT-Exact operation and 78 patients - using the SLING-IUFT operation. There was no statistically significant differences between groups for BMI, parity, menopausal status and prolapsed stage (no patients had cystocele greater than stage II). Mean operative time was significantly shorter in the SLING-IUFT group (19 ± 5.6 min.) compared with the TVT-Exact group (27 ± 7.1 min.). There were statistically significant differences in the effectiveness of both procedures: TVT-Exact - at 94.5% and SLING-IUFT - at 61.2% after one year. Hospital stay was statistically significantly shorter in the SLING-IUFT group (1. 2 ± 0.5 days) compared with the TVT-Exact group (3.5 ± 1.5 days). Statistically significantly fewer complications occurred in the SLING-IUFT group. the TVT-Exact and SLING-IUFT operations are both effective for surgical treatment of female stress urinary incontinence. The SLING-IUFT involved a shorter operation time and lower complications rate., the TVT-Exact procedure had statistically significantly more complications than the SLING-IUFT operation, but a higher effectiveness.

Exact solutions to quadratic gravity

Czech Academy of Sciences Publication Activity Database

Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

2017-01-01

Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025

Exact solutions to quadratic gravity

Czech Academy of Sciences Publication Activity Database

Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

2017-01-01

Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025

Exact nonparametric confidence bands for the survivor function.

Science.gov (United States)

Matthews, David

2013-10-12

A method to produce exact simultaneous confidence bands for the empirical cumulative distribution function that was first described by Owen, and subsequently corrected by Jager and Wellner, is the starting point for deriving exact nonparametric confidence bands for the survivor function of any positive random variable. We invert a nonparametric likelihood test of uniformity, constructed from the Kaplan-Meier estimator of the survivor function, to obtain simultaneous lower and upper bands for the function of interest with specified global confidence level. The method involves calculating a null distribution and associated critical value for each observed sample configuration. However, Noe recursions and the Van Wijngaarden-Decker-Brent root-finding algorithm provide the necessary tools for efficient computation of these exact bounds. Various aspects of the effect of right censoring on these exact bands are investigated, using as illustrations two observational studies of survival experience among non-Hodgkin's lymphoma patients and a much larger group of subjects with advanced lung cancer enrolled in trials within the North Central Cancer Treatment Group. Monte Carlo simulations confirm the merits of the proposed method of deriving simultaneous interval estimates of the survivor function across the entire range of the observed sample. This research was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. It was begun while the author was visiting the Department of Statistics, University of Auckland, and completed during a subsequent sojourn at the Medical Research Council Biostatistics Unit in Cambridge. The support of both institutions, in addition to that of NSERC and the University of Waterloo, is greatly appreciated.

Handbook of probability

CERN Document Server

Florescu, Ionut

2013-01-01

THE COMPLETE COLLECTION NECESSARY FOR A CONCRETE UNDERSTANDING OF PROBABILITY Written in a clear, accessible, and comprehensive manner, the Handbook of Probability presents the fundamentals of probability with an emphasis on the balance of theory, application, and methodology. Utilizing basic examples throughout, the handbook expertly transitions between concepts and practice to allow readers an inclusive introduction to the field of probability. The book provides a useful format with self-contained chapters, allowing the reader easy and quick reference. Each chapter includes an introductio

Probability-1

CERN Document Server

Shiryaev, Albert N

2016-01-01

This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, the measure-theoretic foundations of probability theory, weak convergence of probability measures, and the central limit theorem. Many examples are discussed in detail, and there are a large number of exercises. The book is accessible to advanced undergraduates and can be used as a text for independent study. To accommodate the greatly expanded material in the third edition of Probability, the book is now divided into two volumes. This first volume contains updated references and substantial revisions of the first three chapters of the second edition. In particular, new material has been added on generating functions, the inclusion-exclusion principle, theorems on monotonic classes (relying on a detailed treatment of “π-λ” systems), and the fundamental theorems of mathematical statistics.

Probability Machines: Consistent Probability Estimation Using Nonparametric Learning Machines

Science.gov (United States)

Malley, J. D.; Kruppa, J.; Dasgupta, A.; Malley, K. G.; Ziegler, A.

2011-01-01

Summary Background Most machine learning approaches only provide a classification for binary responses. However, probabilities are required for risk estimation using individual patient characteristics. It has been shown recently that every statistical learning machine known to be consistent for a nonparametric regression problem is a probability machine that is provably consistent for this estimation problem. Objectives The aim of this paper is to show how random forests and nearest neighbors can be used for consistent estimation of individual probabilities. Methods Two random forest algorithms and two nearest neighbor algorithms are described in detail for estimation of individual probabilities. We discuss the consistency of random forests, nearest neighbors and other learning machines in detail. We conduct a simulation study to illustrate the validity of the methods. We exemplify the algorithms by analyzing two well-known data sets on the diagnosis of appendicitis and the diagnosis of diabetes in Pima Indians. Results Simulations demonstrate the validity of the method. With the real data application, we show the accuracy and practicality of this approach. We provide sample code from R packages in which the probability estimation is already available. This means that all calculations can be performed using existing software. Conclusions Random forest algorithms as well as nearest neighbor approaches are valid machine learning methods for estimating individual probabilities for binary responses. Freely available implementations are available in R and may be used for applications. PMID:21915433

Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions

Directory of Open Access Journals (Sweden)

Armando Martínez-Pérez

2017-10-01

Full Text Available We define a finite-differences derivative operation, on a non uniformly spaced partition, which has the exponential function as an exact eigenvector. We discuss some properties of this operator and we propose a definition for the components of a finite-differences momentum operator. This allows us to perform exact discrete calculations.

Exact Boundary Controllability of Electromagnetic Fields in a General Region

International Nuclear Information System (INIS)

Eller, M. M.; Masters, J. E.

2002-01-01

We prove exact controllability for Maxwell's system with variable coefficients in a bounded domain by a current flux in the boundary. The proof relies on a duality argument which reduces the proof of exact controllability to the proof of continuous observability for the homogeneous adjoint system. There is no geometric restriction imposed on the domain

New Exact Solutions for (1 + 1)-Dimensional Dispersion-Less System

International Nuclear Information System (INIS)

Naranmandula; Hu Jianguo; Bao Gang; Tubuxin

2008-01-01

Using improved homogeneous balance method, we obtain complex function form new exact solutions for the (1+1)-dimensional dispersion-less system, and from the exact solutions we derive real function form solution of the field u. Based on this real function form solution, we find some new interesting coherent structures by selecting arbitrary functions appropriately

An Exact Confidence Region in Multivariate Calibration

OpenAIRE

Mathew, Thomas; Kasala, Subramanyam

1994-01-01

In the multivariate calibration problem using a multivariate linear model, an exact confidence region is constructed. It is shown that the region is always nonempty and is invariant under nonsingular transformations.

Exact geodesic distances in FLRW spacetimes

Science.gov (United States)

Cunningham, William J.; Rideout, David; Halverson, James; Krioukov, Dmitri

2017-11-01

Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3 +1 )-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.

A unified form of exact-MSR codes via product-matrix frameworks

KAUST Repository

Lin, Sian Jheng

2015-02-01

Regenerating codes represent a class of block codes applicable for distributed storage systems. The [n, k, d] regenerating code has data recovery capability while possessing arbitrary k out of n code fragments, and supports the capability for code fragment regeneration through the use of other arbitrary d fragments, for k ≤ d ≤ n - 1. Minimum storage regenerating (MSR) codes are a subset of regenerating codes containing the minimal size of each code fragment. The first explicit construction of MSR codes that can perform exact regeneration (named exact-MSR codes) for d ≥ 2k - 2 has been presented via a product-matrix framework. This paper addresses some of the practical issues on the construction of exact-MSR codes. The major contributions of this paper include as follows. A new product-matrix framework is proposed to directly include all feasible exact-MSR codes for d ≥ 2k - 2. The mechanism for a systematic version of exact-MSR code is proposed to minimize the computational complexities for the process of message-symbol remapping. Two practical forms of encoding matrices are presented to reduce the size of the finite field.

A unified form of exact-MSR codes via product-matrix frameworks

KAUST Repository

Lin, Sian Jheng; Chung, Weiho; Han, Yunghsiangsam; Al-Naffouri, Tareq Y.

2015-01-01

Regenerating codes represent a class of block codes applicable for distributed storage systems. The [n, k, d] regenerating code has data recovery capability while possessing arbitrary k out of n code fragments, and supports the capability for code fragment regeneration through the use of other arbitrary d fragments, for k ≤ d ≤ n - 1. Minimum storage regenerating (MSR) codes are a subset of regenerating codes containing the minimal size of each code fragment. The first explicit construction of MSR codes that can perform exact regeneration (named exact-MSR codes) for d ≥ 2k - 2 has been presented via a product-matrix framework. This paper addresses some of the practical issues on the construction of exact-MSR codes. The major contributions of this paper include as follows. A new product-matrix framework is proposed to directly include all feasible exact-MSR codes for d ≥ 2k - 2. The mechanism for a systematic version of exact-MSR code is proposed to minimize the computational complexities for the process of message-symbol remapping. Two practical forms of encoding matrices are presented to reduce the size of the finite field.

Exact analytic solutions generated from stipulated Morse and trigonometric Scarf potentials

International Nuclear Information System (INIS)

Saikia, N; Ahmed, S A S

2011-01-01

The extended transformation method has been applied to the exactly solvable stipulated Morse potential and trigonometric Scarf potential, to generate a set of exactly solvable quantum systems (QSs) in any chosen dimension. Bound state solutions of the exactly solvable potentials are given. The generated QSs are generally of Sturmian form. We also report a system case-specific regrouping technique to convert a Sturmian QS to a normal QS. A second-order application of the transformation method is given. The normalizability of the generated QSs is generally given in Sturmian form.

Exact ground and excited states of an antiferromagnetic quantum spin model

International Nuclear Information System (INIS)

Bose, I.

1989-08-01

A quasi-one-dimensional spin model which consists of a chain of octahedra of spins has been suggested for which a certain parameter regime of the Hamiltonian, the ground state, can be written down exactly. The ground state is highly degenerate and can be other than a singlet. Also, several excited states can be constructed exactly. The ground state is a local RVB state for which resonance is confined to rings of spins. Some exact numerical results for an octahedron of spins have also been reported. (author). 16 refs, 2 figs, 1 tab

Invariant properties between stroke features in handwriting

NARCIS (Netherlands)

Teulings, H L; Schomaker, L R

A handwriting pattern is considered as a sequence of ballistic strokes. Replications of a pattern may be generated from a single, higher-level memory representation, acting as a motor program. Therefore, those stroke features which show the most invariant pattern are probably related to the

Corollary from the Exact Expression for Enthalpy of Vaporization

OpenAIRE

A. A. Sobko

2011-01-01

A problem on determining effective volumes for atoms and molecules becomes actual due to rapidly developing nanotechnologies. In the present study an exact expression for enthalpy of vaporization is obtained, from which an exact expression is derived for effective volumes of atoms and molecules, and under certain assumptions on the form of an atom (molecule) it is possible to find their linear dimensions. The accuracy is only determined by the accuracy of measurements of thermodynamic paramet...

Exact penalty results for mathematical programs with vanishing constraints

Czech Academy of Sciences Publication Activity Database

Hoheisel, T.; Kanzow, Ch.; Outrata, Jiří

2010-01-01

Roč. 72, č. 5 (2010), s. 2514-2526 ISSN 0362-546X R&D Projects: GA AV ČR IAA100750802 Institutional research plan: CEZ:AV0Z10750506 Keywords : Mathematical programs with vanishing constraints * Mathematical programs with equilibrium constraints * Exact penalization * Calmness * Subdifferential calculus * Limiting normal cone Subject RIV: BA - General Mathematics Impact factor: 1.279, year: 2010 http://library.utia.cas.cz/separaty/2010/MTR/outrata-exact penalty results for mathematical programs with vanishing constraints.pdf

Exact non-Markovian master equations for multiple qubit systems: Quantum-trajectory approach

Science.gov (United States)

Chen, Yusui; You, J. Q.; Yu, Ting

2014-11-01

A wide class of exact master equations for a multiple qubit system can be explicitly constructed by using the corresponding exact non-Markovian quantum-state diffusion equations. These exact master equations arise naturally from the quantum decoherence dynamics of qubit system as a quantum memory coupled to a collective colored noisy source. The exact master equations are also important in optimal quantum control, quantum dissipation, and quantum thermodynamics. In this paper, we show that the exact non-Markovian master equation for a dissipative N -qubit system can be derived explicitly from the statistical average of the corresponding non-Markovian quantum trajectories. We illustrated our general formulation by an explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This multiple qubit master equation offers an accurate time evolution of quantum systems in various domains, and paves the way to investigate the memory effect of an open system in a non-Markovian regime without any approximation.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions.

Science.gov (United States)

Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H

2015-07-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

Exact Slater integrals

International Nuclear Information System (INIS)

Golden, L.B.

1968-01-01

In atomic structure calculations, one has to evaluate the Slater integrals. In the present program, the authors evaluate exactly the Slater integral when hydrogenic wave functions are used for the bound-state orbitals. When hydrogenic wave functions are used, the Slater integrals involve integrands which can be written in the form of a product of an exponential, exp(ax) and a known analytic polynomial function, f(x). By repeated partial integration such an integral can be expressed in terms of a finite series involving the exponential, the polynomial function and its derivatives. PL/1-FORMAC has a built-in subroutine that will analytically find the derivatives of any multinomial. Thus, the finite series and hence the Slater integral can be evaluated analytically. (Auth.)

Decision making generalized by a cumulative probability weighting function

Science.gov (United States)

dos Santos, Lindomar Soares; Destefano, Natália; Martinez, Alexandre Souto

2018-01-01

Typical examples of intertemporal decision making involve situations in which individuals must choose between a smaller reward, but more immediate, and a larger one, delivered later. Analogously, probabilistic decision making involves choices between options whose consequences differ in relation to their probability of receiving. In Economics, the expected utility theory (EUT) and the discounted utility theory (DUT) are traditionally accepted normative models for describing, respectively, probabilistic and intertemporal decision making. A large number of experiments confirmed that the linearity assumed by the EUT does not explain some observed behaviors, as nonlinear preference, risk-seeking and loss aversion. That observation led to the development of new theoretical models, called non-expected utility theories (NEUT), which include a nonlinear transformation of the probability scale. An essential feature of the so-called preference function of these theories is that the probabilities are transformed by decision weights by means of a (cumulative) probability weighting function, w(p) . We obtain in this article a generalized function for the probabilistic discount process. This function has as particular cases mathematical forms already consecrated in the literature, including discount models that consider effects of psychophysical perception. We also propose a new generalized function for the functional form of w. The limiting cases of this function encompass some parametric forms already proposed in the literature. Far beyond a mere generalization, our function allows the interpretation of probabilistic decision making theories based on the assumption that individuals behave similarly in the face of probabilities and delays and is supported by phenomenological models.

Exactly soluble dynamics of (p,q) string near macroscopic fundamental strings

International Nuclear Information System (INIS)

Bak, Dongsu; Rey, Soojong; Yee, Houng

2004-01-01

We study dynamics of type-IIB bound-state of a Dirichlet string and n fundamental strings in the background of N fundamental strings. Because of supergravity potential, the bound-state string is pulled to the background fundamental strings, whose motion is described by open string rolling radion field. The string coupling can be made controllably weak and, in the limit 1 2 st n 2 st N, the bound-state energy involved is small compared to the string scale. We thus propose rolling dynamics of open string radion in this system as an exactly solvable analog for rolling dynamics of open string tachyon in decaying D-brane. The dynamics bears a novel feature that the worldsheet electric field increases monotonically to the critical value as the bound-state string falls into the background string. Close to the background string, D string constituent inside the bound-state string decouples from fundamental string constituents. (author)

Constructing diagnostic likelihood: clinical decisions using subjective versus statistical probability.

Science.gov (United States)

Kinnear, John; Jackson, Ruth

2017-07-01

Although physicians are highly trained in the application of evidence-based medicine, and are assumed to make rational decisions, there is evidence that their decision making is prone to biases. One of the biases that has been shown to affect accuracy of judgements is that of representativeness and base-rate neglect, where the saliency of a person's features leads to overestimation of their likelihood of belonging to a group. This results in the substitution of 'subjective' probability for statistical probability. This study examines clinicians' propensity to make estimations of subjective probability when presented with clinical information that is considered typical of a medical condition. The strength of the representativeness bias is tested by presenting choices in textual and graphic form. Understanding of statistical probability is also tested by omitting all clinical information. For the questions that included clinical information, 46.7% and 45.5% of clinicians made judgements of statistical probability, respectively. Where the question omitted clinical information, 79.9% of clinicians made a judgement consistent with statistical probability. There was a statistically significant difference in responses to the questions with and without representativeness information (χ2 (1, n=254)=54.45, pprobability. One of the causes for this representativeness bias may be the way clinical medicine is taught where stereotypic presentations are emphasised in diagnostic decision making. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/.

Janus-faced probability

CERN Document Server

Rocchi, Paolo

2014-01-01

The problem of probability interpretation was long overlooked before exploding in the 20th century, when the frequentist and subjectivist schools formalized two conflicting conceptions of probability. Beyond the radical followers of the two schools, a circle of pluralist thinkers tends to reconcile the opposing concepts. The author uses two theorems in order to prove that the various interpretations of probability do not come into opposition and can be used in different contexts. The goal here is to clarify the multifold nature of probability by means of a purely mathematical approach and to show how philosophical arguments can only serve to deepen actual intellectual contrasts. The book can be considered as one of the most important contributions in the analysis of probability interpretation in the last 10-15 years.

Survival probability of a local excitation in a non-Markovian environment: Survival collapse, Zeno and anti-Zeno effects

International Nuclear Information System (INIS)

Rufeil-Fiori, E.; Pastawski, H.M.

2009-01-01

The decay dynamics of a local excitation interacting with a non-Markovian environment, modeled by a semi-infinite tight-binding chain, is exactly evaluated. We identify distinctive regimes for the dynamics. Sequentially: (i) early quadratic decay of the initial-state survival probability, up to a spreading time t S , (ii) exponential decay described by a self-consistent Fermi Golden Rule, and (iii) asymptotic behavior governed by quantum diffusion through the return processes, leading to an inverse power law decay. At this last cross-over time t R a survival collapse becomes possible. This could reduce the survival probability by several orders of magnitude. The cross-over times t S and t R allow to assess the range of applicability of the Fermi Golden Rule and give the conditions for the observation of the Zeno and anti-Zeno effect.

Exactly solvable models in many-body theory

CERN Document Server

March, N H

2016-01-01

The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed.The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments.

Coalescent: an open-source and scalable framework for exact calculations in coalescent theory

Science.gov (United States)

2012-01-01

Background Currently, there is no open-source, cross-platform and scalable framework for coalescent analysis in population genetics. There is no scalable GUI based user application either. Such a framework and application would not only drive the creation of more complex and realistic models but also make them truly accessible. Results As a first attempt, we built a framework and user application for the domain of exact calculations in coalescent analysis. The framework provides an API with the concepts of model, data, statistic, phylogeny, gene tree and recursion. Infinite-alleles and infinite-sites models are considered. It defines pluggable computations such as counting and listing all the ancestral configurations and genealogies and computing the exact probability of data. It can visualize a gene tree, trace and visualize the internals of the recursion algorithm for further improvement and attach dynamically a number of output processors. The user application defines jobs in a plug-in like manner so that they can be activated, deactivated, installed or uninstalled on demand. Multiple jobs can be run and their inputs edited. Job inputs are persisted across restarts and running jobs can be cancelled where applicable. Conclusions Coalescent theory plays an increasingly important role in analysing molecular population genetic data. Models involved are mathematically difficult and computationally challenging. An open-source, scalable framework that lets users immediately take advantage of the progress made by others will enable exploration of yet more difficult and realistic models. As models become more complex and mathematically less tractable, the need for an integrated computational approach is obvious. Object oriented designs, though has upfront costs, are practical now and can provide such an integrated approach. PMID:23033878

Coalescent: an open-source and scalable framework for exact calculations in coalescent theory

Directory of Open Access Journals (Sweden)

Tewari Susanta

2012-10-01

Full Text Available Abstract Background Currently, there is no open-source, cross-platform and scalable framework for coalescent analysis in population genetics. There is no scalable GUI based user application either. Such a framework and application would not only drive the creation of more complex and realistic models but also make them truly accessible. Results As a first attempt, we built a framework and user application for the domain of exact calculations in coalescent analysis. The framework provides an API with the concepts of model, data, statistic, phylogeny, gene tree and recursion. Infinite-alleles and infinite-sites models are considered. It defines pluggable computations such as counting and listing all the ancestral configurations and genealogies and computing the exact probability of data. It can visualize a gene tree, trace and visualize the internals of the recursion algorithm for further improvement and attach dynamically a number of output processors. The user application defines jobs in a plug-in like manner so that they can be activated, deactivated, installed or uninstalled on demand. Multiple jobs can be run and their inputs edited. Job inputs are persisted across restarts and running jobs can be cancelled where applicable. Conclusions Coalescent theory plays an increasingly important role in analysing molecular population genetic data. Models involved are mathematically difficult and computationally challenging. An open-source, scalable framework that lets users immediately take advantage of the progress made by others will enable exploration of yet more difficult and realistic models. As models become more complex and mathematically less tractable, the need for an integrated computational approach is obvious. Object oriented designs, though has upfront costs, are practical now and can provide such an integrated approach.

Analysis of thin plates with holes by using exact geometrical representation within XFEM.

Science.gov (United States)

Perumal, Logah; Tso, C P; Leng, Lim Thong

2016-05-01

This paper presents analysis of thin plates with holes within the context of XFEM. New integration techniques are developed for exact geometrical representation of the holes. Numerical and exact integration techniques are presented, with some limitations for the exact integration technique. Simulation results show that the proposed techniques help to reduce the solution error, due to the exact geometrical representation of the holes and utilization of appropriate quadrature rules. Discussion on minimum order of integration order needed to achieve good accuracy and convergence for the techniques presented in this work is also included.

Exactness of supersymmetric WKB method for translational shape invariant potentials

International Nuclear Information System (INIS)

Cheng, K M; Leung, P T; Pang, C S

2003-01-01

By examining the generic form of the superpotential of translational shape invariant potentials (TSIPs), we explicitly show the exactness of the lowest order supersymmetric WKB (SWKB) formula for TSIPs. Remarkably, our method applies to both unbroken and broken supersymmetric systems. We also demonstrate the equivalence of one-parameter and multi-parameter TSIPs, thus establishing the exactness of the SWKB formula for all TSIPs

Exactness of supersymmetric WKB method for translational shape invariant potentials

CERN Document Server

Cheng, K M; Pang, C S

2003-01-01

By examining the generic form of the superpotential of translational shape invariant potentials (TSIPs), we explicitly show the exactness of the lowest order supersymmetric WKB (SWKB) formula for TSIPs. Remarkably, our method applies to both unbroken and broken supersymmetric systems. We also demonstrate the equivalence of one-parameter and multi-parameter TSIPs, thus establishing the exactness of the SWKB formula for all TSIPs.

Investigating decision rules with a new experimental design: the EXACT paradigm

Science.gov (United States)

Biscione, Valerio; Harris, Christopher M.

2015-01-01

In the decision-making field, it is important to distinguish between the perceptual process (how information is collected) and the decision rule (the strategy governing decision-making). We propose a new paradigm, called EXogenous ACcumulation Task (EXACT) to disentangle these two components. The paradigm consists of showing a horizontal gauge that represents the probability of receiving a reward at time t and increases with time. The participant is asked to press a button when they want to request a reward. Thus, the perceptual mechanism is hard-coded and does not need to be inferred from the data. Based on this paradigm, we compared four decision rules (Bayes Risk, Reward Rate, Reward/Accuracy, and Modified Reward Rate) and found that participants appeared to behave according to the Modified Reward Rate. We propose a new way of analysing the data by using the accuracy of responses, which can only be inferred in classic RT tasks. Our analysis suggests that several experimental findings such as RT distribution and its relationship with experimental conditions, usually deemed to be the result of a rise-to-threshold process, may be simply explained by the effect of the decision rule employed. PMID:26578916

Interpretations of probability

CERN Document Server

Khrennikov, Andrei

2009-01-01

This is the first fundamental book devoted to non-Kolmogorov probability models. It provides a mathematical theory of negative probabilities, with numerous applications to quantum physics, information theory, complexity, biology and psychology. The book also presents an interesting model of cognitive information reality with flows of information probabilities, describing the process of thinking, social, and psychological phenomena.

Exact solution for a non-Markovian dissipative quantum dynamics.

Science.gov (United States)

Ferialdi, Luca; Bassi, Angelo

2012-04-27

We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions

Science.gov (United States)

Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.

2015-01-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256

Probability distribution of magnetization in the one-dimensional Ising model: effects of boundary conditions

Energy Technology Data Exchange (ETDEWEB)

Antal, T [Physics Department, Simon Fraser University, Burnaby, BC V5A 1S6 (Canada); Droz, M [Departement de Physique Theorique, Universite de Geneve, CH 1211 Geneva 4 (Switzerland); Racz, Z [Institute for Theoretical Physics, Eoetvoes University, 1117 Budapest, Pazmany setany 1/a (Hungary)

2004-02-06

Finite-size scaling functions are investigated both for the mean-square magnetization fluctuations and for the probability distribution of the magnetization in the one-dimensional Ising model. The scaling functions are evaluated in the limit of the temperature going to zero (T {yields} 0), the size of the system going to infinity (N {yields} {infinity}) while N[1 - tanh(J/k{sub B}T)] is kept finite (J being the nearest neighbour coupling). Exact calculations using various boundary conditions (periodic, antiperiodic, free, block) demonstrate explicitly how the scaling functions depend on the boundary conditions. We also show that the block (small part of a large system) magnetization distribution results are identical to those obtained for free boundary conditions.

Camera trap placement and the potential for bias due to trails and other features.

Science.gov (United States)

Kolowski, Joseph M; Forrester, Tavis D

2017-01-01

Camera trapping has become an increasingly widespread tool for wildlife ecologists, with large numbers of studies relying on photo capture rates or presence/absence information. It is increasingly clear that camera placement can directly impact this kind of data, yet these biases are poorly understood. We used a paired camera design to investigate the effect of small-scale habitat features on species richness estimates, and capture rate and detection probability of several mammal species in the Shenandoah Valley of Virginia, USA. Cameras were deployed at either log features or on game trails with a paired camera at a nearby random location. Overall capture rates were significantly higher at trail and log cameras compared to their paired random cameras, and some species showed capture rates as much as 9.7 times greater at feature-based cameras. We recorded more species at both log (17) and trail features (15) than at their paired control cameras (13 and 12 species, respectively), yet richness estimates were indistinguishable after 659 and 385 camera nights of survey effort, respectively. We detected significant increases (ranging from 11-33%) in detection probability for five species resulting from the presence of game trails. For six species detection probability was also influenced by the presence of a log feature. This bias was most pronounced for the three rodents investigated, where in all cases detection probability was substantially higher (24.9-38.2%) at log cameras. Our results indicate that small-scale factors, including the presence of game trails and other features, can have significant impacts on species detection when camera traps are employed. Significant biases may result if the presence and quality of these features are not documented and either incorporated into analytical procedures, or controlled for in study design.

Exact coefficients for higher dimensional operators with sixteen supersymmetries

Energy Technology Data Exchange (ETDEWEB)

Chen, Wei-Ming [Department of Physics and Astronomy, National Taiwan University,Taipei 10617, Taiwan, R.O.C. (China); Huang, Yu-tin [Department of Physics and Astronomy, National Taiwan University,Taipei 10617, Taiwan, R.O.C. (China); School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Wen, Congkao [INFN Sezione di Roma “Tor Vergata' ,Via della Ricerca Scientifica, 00133 Roma (Italy)

2015-09-15

We consider constraints on higher-dimensional operators for supersymmetric effective field theories. In four dimensions with maximal supersymmetry and SU(4) R-symmetry, we demonstrate that the coefficients of abelian operators F{sup n} with MHV helicity configurations must satisfy a recursion relation, and are completely determined by that of F{sup 4}. As the F{sup 4} coefficient is known to be one-loop exact, this allows us to derive exact coefficients for all such operators. We also argue that the results are consistent with the SL(2,Z) duality symmetry. Breaking SU(4) to Sp(4), in anticipation for the Coulomb branch effective action, we again find an infinite class of operators whose coefficients are determined exactly. We also consider three-dimensional N=8 as well as six-dimensional N=(2,0),(1,0) and (1,1) theories. In all cases, we demonstrate that the coefficient of dimension-six operator must be proportional to the square of that of dimension-four.

Quantile selection procedure and assoiated distribution of ratios of order statistics from a restricted family of probability distributions

International Nuclear Information System (INIS)

Gupta, S.S.; Panchapakesan, S.

1975-01-01

A quantile selection procedure in reliability problems pertaining to a restricted family of probability distributions is discussed. This family is assumed to be star-ordered with respect to the standard normal distribution folded at the origin. Motivation for this formulation of the problem is described. Both exact and asymptotic results dealing with the distribution of the maximum of ratios of order statistics from such a family are obtained and tables of the appropriate constants, percentiles of this statistic, are given in order to facilitate the use of the selection procedure

Exact results relating spin-orbit interactions in two-dimensional strongly correlated systems

Science.gov (United States)

Kucska, Nóra; Gulácsi, Zsolt

2018-06-01

A 2D square, two-bands, strongly correlated and non-integrable system is analysed exactly in the presence of many-body spin-orbit interactions via the method of Positive Semidefinite Operators. The deduced exact ground states in the high concentration limit are strongly entangled, and given by the spin-orbit coupling are ferromagnetic and present an enhanced carrier mobility, which substantially differs for different spin projections. The described state emerges in a restricted parameter space region, which however is clearly accessible experimentally. The exact solutions are provided via the solution of a matching system of equations containing 74 coupled, non-linear and complex algebraic equations. In our knowledge, other exact results for 2D interacting systems with spin-orbit interactions are not present in the literature.

A New Self-Constrained Inversion Method of Potential Fields Based on Probability Tomography

Science.gov (United States)

Sun, S.; Chen, C.; WANG, H.; Wang, Q.

2014-12-01

The self-constrained inversion method of potential fields uses a priori information self-extracted from potential field data. Differing from external a priori information, the self-extracted information are generally parameters derived exclusively from the analysis of the gravity and magnetic data (Paoletti et al., 2013). Here we develop a new self-constrained inversion method based on probability tomography. Probability tomography doesn't need any priori information, as well as large inversion matrix operations. Moreover, its result can describe the sources, especially the distribution of which is complex and irregular, entirely and clearly. Therefore, we attempt to use the a priori information extracted from the probability tomography results to constrain the inversion for physical properties. The magnetic anomaly data was taken as an example in this work. The probability tomography result of magnetic total field anomaly(ΔΤ) shows a smoother distribution than the anomalous source and cannot display the source edges exactly. However, the gradients of ΔΤ are with higher resolution than ΔΤ in their own direction, and this characteristic is also presented in their probability tomography results. So we use some rules to combine the probability tomography results of ∂ΔΤ⁄∂x, ∂ΔΤ⁄∂y and ∂ΔΤ⁄∂z into a new result which is used for extracting a priori information, and then incorporate the information into the model objective function as spatial weighting functions to invert the final magnetic susceptibility. Some magnetic synthetic examples incorporated with and without a priori information extracted from the probability tomography results were made to do comparison, results of which show that the former are more concentrated and with higher resolution of the source body edges. This method is finally applied in an iron mine in China with field measured ΔΤ data and performs well. ReferencesPaoletti, V., Ialongo, S., Florio, G., Fedi, M

Euclidean shortest paths exact or approximate algorithms

CERN Document Server

Li, Fajie

2014-01-01

This book reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. The coverage includes mathematical proofs for many of the given statements.

On exactly soluble model in quantum electrodynamics

International Nuclear Information System (INIS)

Bogolubov, N.N.; Shumovsky, A.S.; Fam Le Kien

1984-01-01

Equations of motion describing the dynamics of three-level atom of ladder type interacting with two modes of quantized radiation field are solved exactly. Evolution of level population and photon rumbers under different unitial conditions is irvestigated

Comments on exact quantization conditions and non-perturbative topological strings

International Nuclear Information System (INIS)

Hatsuda, Yasuyuki

2015-12-01

We give some remarks on exact quantization conditions associated with quantized mirror curves of local Calabi-Yau threefolds, conjectured in arXiv:1410.3382. It is shown that they characterize a non-perturbative completion of the refined topological strings in the Nekrasov-Shatashvili limit. We find that the quantization conditions enjoy an exact S-dual invariance. We also discuss Borel summability of the semi-classical spectrum.

Quasi-exact solvability and entropies of the one-dimensional regularised Calogero model

Science.gov (United States)

Pont, Federico M.; Osenda, Omar; Serra, Pablo

2018-05-01

The Calogero model can be regularised through the introduction of a cutoff parameter which removes the divergence in the interaction term. In this work we show that the one-dimensional two-particle regularised Calogero model is quasi-exactly solvable and that for certain values of the Hamiltonian parameters the eigenfunctions can be written in terms of Heun’s confluent polynomials. These eigenfunctions are such that the reduced density matrix of the two-particle density operator can be obtained exactly as well as its entanglement spectrum. We found that the number of non-zero eigenvalues of the reduced density matrix is finite in these cases. The limits for the cutoff distance going to zero (Calogero) and infinity are analysed and all the previously obtained results for the Calogero model are reproduced. Once the exact eigenfunctions are obtained, the exact von Neumann and Rényi entanglement entropies are studied to characterise the physical traits of the model. The quasi-exactly solvable character of the model is assessed studying the numerically calculated Rényi entropy and entanglement spectrum for the whole parameter space.

Exact simulation of max-stable processes.

Science.gov (United States)

Dombry, Clément; Engelke, Sebastian; Oesting, Marco

2016-06-01

Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes their simulation difficult. Algorithms based on finite approximations are often inexact and computationally inefficient. We present a new algorithm for exact simulation of a max-stable process at a finite number of locations. It relies on the idea of simulating only the extremal functions, that is, those functions in the construction of a max-stable process that effectively contribute to the pointwise maximum. We further generalize the algorithm by Dieker & Mikosch (2015) for Brown-Resnick processes and use it for exact simulation via the spectral measure. We study the complexity of both algorithms, prove that our new approach via extremal functions is always more efficient, and provide closed-form expressions for their implementation that cover most popular models for max-stable processes and multivariate extreme value distributions. For simulation on dense grids, an adaptive design of the extremal function algorithm is proposed.

New explicit and exact solutions of the Benney–Kawahara–Lin equation

International Nuclear Information System (INIS)

Yuan-Xi, Xie

2009-01-01

In this paper, we present a combination method of constructing the explicit and exact solutions of nonlinear partial differential equations. And as an illustrative example, we apply the method to the Benney–Kawahara–Lin equation and derive its many explicit and exact solutions which are all new solutions. (general)

DYNAMIC FEATURE SELECTION FOR WEB USER IDENTIFICATION ON LINGUISTIC AND STYLISTIC FEATURES OF ONLINE TEXTS

Directory of Open Access Journals (Sweden)

A. A. Vorobeva

2017-01-01

Full Text Available The paper deals with identification and authentication of web users participating in the Internet information processes (based on features of online texts.In digital forensics web user identification based on various linguistic features can be used to discover identity of individuals, criminals or terrorists using the Internet to commit cybercrimes. Internet could be used as a tool in different types of cybercrimes (fraud and identity theft, harassment and anonymous threats, terrorist or extremist statements, distribution of illegal content and information warfare. Linguistic identification of web users is a kind of biometric identification, it can be used to narrow down the suspects, identify a criminal and prosecute him. Feature set includes various linguistic and stylistic features extracted from online texts. We propose dynamic feature selection for each web user identification task. Selection is based on calculating Manhattan distance to k-nearest neighbors (Relief-f algorithm. This approach improves the identification accuracy and minimizes the number of features. Experiments were carried out on several datasets with different level of class imbalance. Experiment results showed that features relevance varies in different set of web users (probable authors of some text; features selection for each set of web users improves identification accuracy by 4% at the average that is approximately 1% higher than with the use of static set of features. The proposed approach is most effective for a small number of training samples (messages per user.

A new auxiliary equation and exact travelling wave solutions of nonlinear equations

International Nuclear Information System (INIS)

Sirendaoreji

2006-01-01

A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations

Improving Ranking Using Quantum Probability

OpenAIRE

Melucci, Massimo

2011-01-01

The paper shows that ranking information units by quantum probability differs from ranking them by classical probability provided the same data used for parameter estimation. As probability of detection (also known as recall or power) and probability of false alarm (also known as fallout or size) measure the quality of ranking, we point out and show that ranking by quantum probability yields higher probability of detection than ranking by classical probability provided a given probability of ...

Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory

Science.gov (United States)

Gould, Tim; Kronik, Leeor; Pittalis, Stefano

2018-05-01

By studying the lowest excitations of an exactly solvable one-dimensional soft-Coulomb molecular model, we show that components of Kohn-Sham ensembles can be used to describe charge transfer processes. Furthermore, we compute the approximate excitation energies obtained by using the exact ensemble densities in the recently formulated ensemble Hartree-exchange theory [T. Gould and S. Pittalis, Phys. Rev. Lett. 119, 243001 (2017)]. Remarkably, our results show that triplet excitations are accurately reproduced across a dissociation curve in all cases tested, even in systems where ground state energies are poor due to strong static correlations. Singlet excitations exhibit larger deviations from exact results but are still reproduced semi-quantitatively.

Identifying relevant feature-action associations for grasping unmodelled objects

DEFF Research Database (Denmark)

Thomsen, Mikkel Tang; Kraft, Dirk; Krüger, Norbert

2015-01-01

content. The method is provided with a large and structured set of visual features, motivated by the visual hierarchy in primates and finds relevant feature action associations automatically. We apply our method in a simulated environment on three different object sets for the case of grasp affordance...... learning. For box objects, we achieve a 0.90 success probability, 0.80 for round objects and up to 0.75 for open objects, when presented with novel objects. In this work, we in particular demonstrate the effect of choosing appropriate feature representations. We demonstrate a significant performance...

Asymptotically exact solution of a local copper-oxide model

International Nuclear Information System (INIS)

Zhang Guangming; Yu Lu.

1994-03-01

We present an asymptotically exact solution of a local copper-oxide model abstracted from the multi-band models. The phase diagram is obtained through the renormalization-group analysis of the partition function. In the strong coupling regime, we find an exactly solved line, which crosses the quantum critical point of the mixed valence regime separating two different Fermi-liquid (FL) phases. At this critical point, a many-particle resonance is formed near the chemical potential, and a marginal-FL spectrum can be derived for the spin and charge susceptibilities. (author). 15 refs, 1 fig

String propagation in an exact four-dimensional black hole background

International Nuclear Information System (INIS)

Mahapatra, S.

1997-01-01

We study string propagation in an exact, stringy, four-dimensional dyonic black hole background. The exact solutions in terms of elliptic functions describing string configurations in the J=0 limit are obtained by solving the string equations of motion and constraints. By using the covariant formalism, we also investigate the propagation of physical perturbations along the string in the given curved background. copyright 1997 The American Physical Society

Compiling Relational Bayesian Networks for Exact Inference

DEFF Research Database (Denmark)

Jaeger, Manfred; Chavira, Mark; Darwiche, Adnan

2004-01-01

We describe a system for exact inference with relational Bayesian networks as defined in the publicly available \\primula\\ tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evaluating...

Exact results for Wilson loops in arbitrary representations

Energy Technology Data Exchange (ETDEWEB)

Fiol, Bartomeu; Torrents, Genís [Departament de Física Fonamental i Institut de Ciències del Cosmos, Universitat de Barcelona,Martí i Franquès 1, 08028 Barcelona, Catalonia (Spain)

2014-01-08

We compute the exact vacuum expectation value of 1/2 BPS circular Wilson loops of N=4 U(N) super Yang-Mills in arbitrary irreducible representations. By localization arguments, the computation reduces to evaluating certain integrals in a Gaussian matrix model, which we do using the method of orthogonal polynomials. Our results are particularly simple for Wilson loops in antisymmetric representations; in this case, we observe that the final answers admit an expansion where the coefficients are positive integers, and can be written in terms of sums over skew Young diagrams. As an application of our results, we use them to discuss the exact Bremsstrahlung functions associated to the corresponding heavy probes.

A conditionally exactly solvable generalization of the inverse square root potential

Energy Technology Data Exchange (ETDEWEB)

Ishkhanyan, A.M., E-mail: aishkhanyan@gmail.com [Institute for Physical Research, NAS of Armenia, Ashtarak 0203 (Armenia); Armenian State Pedagogical University, Yerevan 0010 (Armenia); Institute of Physics and Technology, National Research Tomsk Polytechnic University, Tomsk 634050 (Russian Federation)

2016-11-25

We present a conditionally exactly solvable singular potential for the one-dimensional Schrödinger equation which involves the exactly solvable inverse square root potential. Each of the two fundamental solutions that compose the general solution of the problem is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. Discussing the bound-state wave functions vanishing both at infinity and in the origin, we derive the exact equation for the energy spectrum which is written using two Hermite functions of non-integer order. In specific auxiliary variables this equation becomes a mathematical equation that does not refer to a specific physical context discussed. In the two-dimensional space of these auxiliary variables the roots of this equation draw a countable infinite set of open curves with hyperbolic asymptotes. We present an analytic description of these curves by a transcendental algebraic equation for the involved variables. The intersections of the curves thus constructed with a certain cubic curve provide a highly accurate description of the energy spectrum. - Highlights: • We present a conditionally exactly solvable singular potential for 1D Schrödinger equation. • Each of the two fundamental solutions is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. • The exact equation for the energy spectrum is written using two Hermite functions that do not reduce to polynomials.

Calculating the Probability of Returning a Loan with Binary Probability Models

Directory of Open Access Journals (Sweden)

Julian Vasilev

2014-12-01

Full Text Available The purpose of this article is to give a new approach in calculating the probability of returning a loan. A lot of factors affect the value of the probability. In this article by using statistical and econometric models some influencing factors are proved. The main approach is concerned with applying probit and logit models in loan management institutions. A new aspect of the credit risk analysis is given. Calculating the probability of returning a loan is a difficult task. We assume that specific data fields concerning the contract (month of signing, year of signing, given sum and data fields concerning the borrower of the loan (month of birth, year of birth (age, gender, region, where he/she lives may be independent variables in a binary logistics model with a dependent variable “the probability of returning a loan”. It is proved that the month of signing a contract, the year of signing a contract, the gender and the age of the loan owner do not affect the probability of returning a loan. It is proved that the probability of returning a loan depends on the sum of contract, the remoteness of the loan owner and the month of birth. The probability of returning a loan increases with the increase of the given sum, decreases with the proximity of the customer, increases for people born in the beginning of the year and decreases for people born at the end of the year.

Exact EGB models for spherical static perfect fluids

Energy Technology Data Exchange (ETDEWEB)

Hansraj, Sudan; Chilambwe, Brian; Maharaj, Sunil D. [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Private Bag 54001, Durban (South Africa)

2015-06-15

We obtain a new exact solution to the field equations for a 5-dimensional spherically symmetric static distribution in the Einstein-Gauss-Bonnet modified theory of gravity. By using a transformation, the study is reduced to the analysis of a single second order nonlinear differential equation. In general the condition of pressure isotropy produces a first order differential equation which is an Abel equation of the second kind. An exact solution is found. The solution is examined for physical admissibility. In particular a set of constants is found which ensures that a pressure-free hypersurface exists which defines the boundary of the distribution. Additionally the isotropic pressure and the energy density are shown to be positive within the radius of the sphere. The adiabatic sound-speed criterion is also satisfied within the fluid ensuring a subluminal sound speed. Furthermore, the weak, strong and dominant conditions hold throughout the distribution. On setting the Gauss-Bonnet coupling to zero, an exact solution for 5-dimensional perfect fluids in the standard Einstein theory is obtained. Plots of the dynamical quantities for the Gauss-Bonnet and the Einstein case reveal that the pressure is unaffected, while the energy density increases under the influence of the Gauss-Bonnet term. (orig.)

An exactly solvable model for first- and second-order transitions

International Nuclear Information System (INIS)

Klushin, L I; Skvortsov, A M; Gorbunov, A A

1998-01-01

The possibility of an exact analytical description of first-order and second-order transitions is demonstrated using a specific microscopic model. Predictions using the exactly calculated partition function are compared with those based on the Landau and Yang-Lee approaches. The model employed is an adsorbed polymer chain with an arbitrary number of links and an external force applied to its end, for which the variation of the partition function with the adsorption interaction parameter and the magnitude of the applied force is calculated. In the thermodynamic limit, the system has one isotropic and two anisotropic, ordered phases, each of which is characterized by two order parameters and between which first-order and second-order transitions occur and a bicritical point exists. The Landau free energy is found exactly as a function of each order parameter separately and, near the bicritical point, as a function of both of them simultaneously. An exact analytical formula is found for the distribution of the complex zeros of the partition function in first-order and second-order phase transitions. Hypotheses concerning the way in which the free energy and the positions of the complex zeros scale with the number of particles N in the system are verified. (reviews of topical problems)

On the Possibility of Assigning Probabilities to Singular Cases, or: Probability Is Subjective Too!

Directory of Open Access Journals (Sweden)

Mark R. Crovelli

2009-06-01

Full Text Available Both Ludwig von Mises and Richard von Mises claimed that numerical probability could not be legitimately applied to singular cases. This paper challenges this aspect of the von Mises brothers’ theory of probability. It is argued that their denial that numerical probability could be applied to singular cases was based solely upon Richard von Mises’ exceptionally restrictive definition of probability. This paper challenges Richard von Mises’ definition of probability by arguing that the definition of probability necessarily depends upon whether the world is governed by time-invariant causal laws. It is argued that if the world is governed by time-invariant causal laws, a subjective definition of probability must be adopted. It is further argued that both the nature of human action and the relative frequency method for calculating numerical probabilities both presuppose that the world is indeed governed by time-invariant causal laws. It is finally argued that the subjective definition of probability undercuts the von Mises claim that numerical probability cannot legitimately be applied to singular, non-replicable cases.

Statistical Identification of Composed Visual Features Indicating High Likelihood of Grasp Success

DEFF Research Database (Denmark)

Thomsen, Mikkel Tang; Bodenhagen, Leon; Krüger, Norbert

2013-01-01

configurations of three 3D surface features that predict grasping actions with a high success probability. The strategy is based on first computing spatial relations between visual entities and secondly, exploring the cross-space of these relational feature space and grasping actions. The data foundation...... for identifying such indicative feature constellations is generated in a simulated environment wherein visual features are extracted and a large amount of grasping actions are evaluated through dynamic simulation. Based on the identified feature constellations, we validate by applying the acquired knowledge...

Exactly solvable position dependent mass schroedinger equation

International Nuclear Information System (INIS)

Koc, R.; Tuetuencueler, H.; Koercuek, E.

2002-01-01

Exact solution of the Schrodinger equation with a variable mass is presented. We have derived general expressions for the eigenstates and eigenvalues of the position dependent mass systems. We provide supersymmetric and Lie algebraic methods to discuss the position dependent mass systems

Compiling Relational Bayesian Networks for Exact Inference

DEFF Research Database (Denmark)

Jaeger, Manfred; Darwiche, Adnan; Chavira, Mark

2006-01-01

We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available PRIMULA tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference...

Invariant Handwriting Features Useful in Cursive-Script Recognition

NARCIS (Netherlands)

Teulings, Hans-leo L; Schomaker, L R; Impedovo, S.

1994-01-01

A handwriting pattern is considered as a sequence of ballistic strokes. Replications of a pattern may be generated from a single, higher-level memory representation, acting as a motor program. Therefore, those stroke features which show the most invariant pattern are probably related to the

Exact results and open questions in first principle functional RG

International Nuclear Information System (INIS)

Le Doussal, Pierre

2010-01-01

Some aspects of the functional RG (FRG) approach to pinned elastic manifolds (of internal dimension d) at finite temperature T > 0 are reviewed and reexamined in this much expanded version of Le Doussal (2006) . The particle limit d = 0 provides a test for the theory: there the FRG is equivalent to the decaying Burgers equation, with viscosity ν ∼ T-both being formally irrelevant. An outstanding question in FRG, i.e. how temperature regularizes the otherwise singular flow of T = 0 FRG, maps to the viscous layer regularization of inertial range Burgers turbulence (i.e. to the construction of the inviscid limit). Analogy between Kolmogorov scaling and FRG cumulant scaling is discussed. First, multi-loop FRG corrections are examined and the direct loop expansion at T > 0 is shown to fail already in d = 0, a hierarchy of ERG equations being then required (introduced in Balents and Le Doussal (2005) ). Next we prove that the FRG function R(u) and higher cumulants defined from the field theory can be obtained for any d from moments of a renormalized potential defined in an sliding harmonic well. This allows to measure the fixed point function R(u) in numerics and experiments. In d = 0 the beta function (of the inviscid limit) is obtained from first principles to four loop. For Sinai model (uncorrelated Burgers initial velocities) the ERG hierarchy can be solved and the exact function R(u) is obtained. Connections to exact solutions for the statistics of shocks in Burgers and to ballistic aggregation are detailed. A relation is established between the size distribution of shocks and the one for droplets. A droplet solution to the ERG functional hierarchy is found for any d, and the form of R(u) in the thermal boundary layer is related to droplet probabilities. These being known for the d = 0 Sinai model the function R(u) is obtained there at any T. Consistency of the ε=4-d expansion in one and two loop FRG is studied from first principles, and connected to shock and

PLNoise: a package for exact numerical simulation of power-law noises

Science.gov (United States)

Milotti, Edoardo

2006-08-01

in C: The Art of Scientific Computing, second ed., Cambridge Univ. Press, Cambridge, 1992, pp. 274-290]. Notice that ranlib requires a pair of routines from the linear algebra package LINPACK, and that the distribution of ranlib includes the C source of these routines, in case LINPACK is not installed on the target machine. Nature of problem: Exact generation of different types of Gaussian colored noise. Solution method: Random superposition of relaxation processes [E. Milotti, Phys. Rev. E 72 (2005) 056701]. Unusual features: The algorithm is theoretically guaranteed to be exact, and unlike all other existing generators it can generate samples with uneven spacing. Additional comments: The program requires an initialization step; for some parameter sets this may become rather heavy. Running time: Running time varies widely with different input parameters, however in a test run like the one in Section 4 in this work, the generation routine took on average about 7 ms for each sample.

An exact approach for studying cargo transport by an ensemble of molecular motors

International Nuclear Information System (INIS)

Materassi, Donatello; Roychowdhury, Subhrajit; Hays, Thomas; Salapaka, Murti

2013-01-01

Intracellular transport is crucial for many cellular processes where a large fraction of the cargo is transferred by motor-proteins over a network of microtubules. Malfunctions in the transport mechanism underlie a number of medical maladies. Existing methods for studying how motor-proteins coordinate the transfer of a shared cargo over a microtubule are either analytical or are based on Monte-Carlo simulations. Approaches that yield analytical results, while providing unique insights into transport mechanism, make simplifying assumptions, where a detailed characterization of important transport modalities is difficult to reach. On the other hand, Monte-Carlo based simulations can incorporate detailed characteristics of the transport mechanism; however, the quality of the results depend on the number and quality of simulation runs used in arriving at results. Here, for example, it is difficult to simulate and study rare-events that can trigger abnormalities in transport. In this article, a semi-analytical methodology that determines the probability distribution function of motor-protein behavior in an exact manner is developed. The method utilizes a finite-dimensional projection of the underlying infinite-dimensional Markov model, which retains the Markov property, and enables the detailed and exact determination of motor configurations, from which meaningful inferences on transport characteristics of the original model can be derived. Under this novel probabilistic approach new insights about the mechanisms of action of these proteins are found, suggesting hypothesis about their behavior and driving the design and realization of new experiments. The advantages provided in accuracy and efficiency make it possible to detect rare events in the motor protein dynamics, that could otherwise pass undetected using standard simulation methods. In this respect, the model has allowed to provide a possible explanation for possible mechanisms under which motor proteins could

A BEHAVIORAL-APPROACH TO LINEAR EXACT MODELING

NARCIS (Netherlands)

ANTOULAS, AC; WILLEMS, JC

1993-01-01

The behavioral approach to system theory provides a parameter-free framework for the study of the general problem of linear exact modeling and recursive modeling. The main contribution of this paper is the solution of the (continuous-time) polynomial-exponential time series modeling problem. Both

Naive Bayesian classifiers for multinomial features: a theoretical analysis

CSIR Research Space (South Africa)

Van Dyk, E

2007-11-01

Full Text Available The authors investigate the use of naive Bayesian classifiers for multinomial feature spaces and derive error estimates for these classifiers. The error analysis is done by developing a mathematical model to estimate the probability density...

Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients

Directory of Open Access Journals (Sweden)

Peng Jiang

2013-01-01

Full Text Available The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.

Too good to be true: the role of online reviews’ features in probability to buy

NARCIS (Netherlands)

Maslowska, E.; Malthouse, E.C.; Bernritter, S.F.

2017-01-01

Online consumer reviews are broadly believed to be a necessary and powerful marketing tool, and as such they have attracted considerable attention from both marketers and academics. However, previous research has not sufficiently focused on the effects of various review features on sales but rather

A Novel Virtual Node Hexahedral Element with Exact Integration and Octree Meshing

Directory of Open Access Journals (Sweden)

Logah Perumal

2016-01-01

Full Text Available The method presented in this work is a 3-dimensional polyhedral finite element (3D PFEM based on virtual node method. Novel virtual node polyhedral elements (termed as VPHE are developed here, particularly virtual node hexahedral element (termed as VHE. Stiffness matrices of these polyhedral elements consist of simple polynomials. Thus, a new algorithm is introduced in this paper, which enables exact integration of monomials without a need for high number of integration points and weights. The number of nodes for VHE elements is not restricted, as opposed to the conventional hexahedral elements. This feature enables formulation of transition elements (termed as T-VHE which are useful to adaptive computation. Performances of the new VHE elements in solid mechanics and conductive heat transfer phenomena are examined through numerical simulations. The new T-VHE elements are utilized in octree mesh. The VHE elements are found to produce good results and T-VHE elements help to reduce number of global nodes for the analysis.

The Problem of Understanding of Nature in Exact Science

Directory of Open Access Journals (Sweden)

Leo Näpinen

2014-10-01

Full Text Available In this short inquiry I would like to defend the statement that exact science deals with the explanation of models, but not with the understanding (comprehending of nature. By the word ‘nature’ I mean nature as physis (as a self-moving and self-developing living organism to which humans also belong, not nature as natura naturata (as a nonevolving creature created by someone or something. The Estonian philosopher of science Rein Vihalemm (2008 has shown with his conception of phi-science (φ-science that exact science is itself an idealized model or theoretical object derived from Galilean mathematical physics.

Quasi-exact solvability of the one-dimensional Holstein model

International Nuclear Information System (INIS)

Pan Feng; Dai Lianrong; Draayer, J P

2006-01-01

The one-dimensional Holstein model of spinless fermions interacting with dispersionless phonons is solved by using a Bethe ansatz in analogue to that for the one-dimensional spinless Fermi-Hubbard model. Excitation energies and the corresponding wavefunctions of the model are determined by a set of partial differential equations. It is shown that the model is, at least, quasi-exactly solvable for the two-site case, when the phonon frequency, the electron-phonon coupling strength and the hopping integral satisfy certain relations. As examples, some quasi-exact solutions of the model for the two-site case are derived. (letter to the editor)

Disease clusters, exact distributions of maxima, and P-values.

Science.gov (United States)

Grimson, R C

1993-10-01

This paper presents combinatorial (exact) methods that are useful in the analysis of disease cluster data obtained from small environments, such as buildings and neighbourhoods. Maxwell-Boltzmann and Fermi-Dirac occupancy models are compared in terms of appropriateness of representation of disease incidence patterns (space and/or time) in these environments. The methods are illustrated by a statistical analysis of the incidence pattern of bone fractures in a setting wherein fracture clustering was alleged to be occurring. One of the methodological results derived in this paper is the exact distribution of the maximum cell frequency in occupancy models.

Clock Math — a System for Solving SLEs Exactly

Directory of Open Access Journals (Sweden)

Jakub Hladík

2013-01-01

Full Text Available In this paper, we present a GPU-accelerated hybrid system that solves ill-conditioned systems of linear equations exactly. Exactly means without rounding errors due to using integer arithmetics. First, we scale floating-point numbers up to integers, then we solve dozens of SLEs within different modular arithmetics and then we assemble sub-solutions back using the Chinese remainder theorem. This approach effectively bypasses current CPU floating-point limitations. The system is capable of solving Hilbert’s matrix without losing a single bit of precision, and with a significant speedup compared to existing CPU solvers.

Exact solution of matricial Φ23 quantum field theory

Science.gov (United States)

Grosse, Harald; Sako, Akifumi; Wulkenhaar, Raimar

2017-12-01

We apply a recently developed method to exactly solve the Φ3 matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a multi-punctured 2-sphere. We show how Ward-Takahashi identities and Schwinger-Dyson equations lead in a special large- N limit to integral equations that we solve exactly for all correlation functions. The solved model arises from noncommutative field theory in a special limit of strong deformation parameter. The limit defines ordinary 2D Schwinger functions which, however, do not satisfy reflection positivity.

Probability in physics

CERN Document Server

Hemmo, Meir

2012-01-01

What is the role and meaning of probability in physical theory, in particular in two of the most successful theories of our age, quantum physics and statistical mechanics? Laws once conceived as universal and deterministic, such as Newton‘s laws of motion, or the second law of thermodynamics, are replaced in these theories by inherently probabilistic laws. This collection of essays by some of the world‘s foremost experts presents an in-depth analysis of the meaning of probability in contemporary physics. Among the questions addressed are: How are probabilities defined? Are they objective or subjective? What is their  explanatory value? What are the differences between quantum and classical probabilities? The result is an informative and thought-provoking book for the scientifically inquisitive. 

Buffer Management and Hybrid Probability Choice Routing for Packet Delivery in Opportunistic Networks

Directory of Open Access Journals (Sweden)

Daru Pan

2012-01-01

Full Text Available Due to the features of long connection delays, frequent network partitions, and topology unsteadiness, the design of opportunistic networks faces the challenge of how to effectively deliver data based only on occasional encountering of nodes, where the conventional routing schemes do not work properly. This paper proposes a hybrid probability choice routing protocol with buffer management for opportunistic networks. A delivery probability function is set up based on continuous encounter duration time, which is used for selecting a better node to relay packets. By combining the buffer management utility and the delivery probability, a total utility is used to decide whether the packet should be kept in the buffer or be directly transmitted to the encountering node. Simulation results show that the proposed routing outperforms the existing one in terms of the delivery rate and the average delay.

Exact Tests for Two-Way Contingency Tables with Structural Zeros

Directory of Open Access Journals (Sweden)

Luke J. West

2008-11-01

Full Text Available Fisher's exact test, named for Sir Ronald Aylmer Fisher, tests contingency tables for homogeneity of proportion. This paper discusses a generalization of Fisher's exact test for the case where some of the table entries are constrained to be zero. The resulting test is useful for assessing cases where the null hypothesis of conditional multinomial distribution is suspected to be false. The test is implemented in the form of a new R package, aylmer.

MRI features of placenta accreta

International Nuclear Information System (INIS)

Cao Manrui; Du Mu; Huang Yi; Liu Bingguang; Zhang Fangjing; Guo Jimin; Zhu Zhijun

2012-01-01

Objective: To investigate the MRI features of placenta accreta. Methods: From Apr 2009 to Jun 2011, 15 patients with placenta accrete received MRI examination. In them, placenta accreta was diagnosed based on clinical manifestations or postoperative histopathology. The MR features of placenta accreta in them (study group) were retrospectively analyzed and compared with those in 15 pregnant women without placenta accreta (control group) with Fisher exact test. Results: In the 15 patients with placenta accreta,uterine bulging and (or) a focal outward contour bulge was detected in 14 patients; heterogeneous signal intensity in the placenta was detected in 15 patients; dark intraplacental bands on T 2 -weighted images was detected in 15 patients; and increased subplacental vascularity was detected in 11 patients on T 1 - weighted images. In the study group, 14 patients showed at least three of the above four features, and in all of them uterine bulging and (or) a focal outward contour bulge, heterogeneous signal intensity in the placenta and dark intraplacental bands on T 2 -weighted images were detected; one patient showed heterogeneous signal intensity in the placenta, dark intraplacental bands on T 2 -weighted images and increased subplacental vascularity. In the control group,none patient had three of the above features.Uterine bulging and (or) a focal outward contour bulge, heterogeneous signal intensity in the placenta, dark intraplacental bands on T 2 -weighted images and increased subplacental vascularity were detected in 3, 6, 3 and 4 patients (P=0.000, 0.001, 0.000 and 0.027), respectively. Conclusions: The main MRI features of placenta accreta are uterine bulging and (or) a focal outward contour bulge, heterogeneous signal intensity in the placenta and dark intraplacental bands on T 2 -weighted images Besides, increased subplacental vascularity also could provide useful information for the diagnosis of placenta accreta. (authors)

Screening Analysis of Criticality Features, Events, and Processes for License Application

International Nuclear Information System (INIS)

J.A. McClure

2004-01-01

This report documents the screening analysis of postclosure criticality features, events, and processes. It addresses the probability of criticality events resulting from degradation processes as well as disruptive events (i.e., seismic, rock fall, and igneous). Probability evaluations are performed utilizing the configuration generator described in ''Configuration Generator Model'', a component of the methodology from ''Disposal Criticality Analysis Methodology Topical Report''. The total probability per package of criticality is compared against the regulatory probability criterion for inclusion of events established in 10 CFR 63.114(d) (consider only events that have at least one chance in 10,000 of occurring over 10,000 years). The total probability of criticality accounts for the evaluation of identified potential critical configurations of all baselined commercial and U.S. Department of Energy spent nuclear fuel waste form and waste package combinations, both internal and external to the waste packages. This criticality screening analysis utilizes available information for the 21-Pressurized Water Reactor Absorber Plate, 12-Pressurized Water Reactor Absorber Plate, 44-Boiling Water Reactor Absorber Plate, 24-Boiling Water Reactor Absorber Plate, and the 5-Defense High-Level Radioactive Waste/U.S. Department of Energy Short waste package types. Where defensible, assumptions have been made for the evaluation of the following waste package types in order to perform a complete criticality screening analysis: 21-Pressurized Water Reactor Control Rod, 5-Defense High-Level Radioactive Waste/U.S. Department of Energy Long, and 2-Multi-Canister Overpack/2-Defense High-Level Radioactive Waste package types. The inputs used to establish probabilities for this analysis report are based on information and data generated for the Total System Performance Assessment for the License Application, where available. This analysis report determines whether criticality is to be

Exact collisional moments for plasma fluid theories

Science.gov (United States)

Pfefferle, David; Hirvijoki, Eero; Lingam, Manasvi

2017-10-01

The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of the distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities, and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas, that relies on the Chapman-Enskog method, as well as to deriving collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer rate.

Exact solitary and periodic wave solutions for a generalized nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Sun Chengfeng; Gao Hongjun

2009-01-01

The generalized nonlinear Schroedinger equation (GNLS) iu t + u xx + β | u | 2 u + γ | u | 4 u + iα (| u | 2 u) x + iτ(| u | 2 ) x u = 0 is studied. Using the bifurcation of travelling waves of this equation, some exact solitary wave solutions were obtained in [Wang W, Sun J,Chen G, Bifurcation, Exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schroedinger equation. Int J Bifucat Chaos 2005:3295-305.]. In this paper, more explicit exact solitary wave solutions and some new smooth periodic wave solutions are obtained.

Probability on graphs random processes on graphs and lattices

CERN Document Server

Grimmett, Geoffrey

2018-01-01

This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.

Exact Results on Quantum Interference and Magnetoconductance in Variable-Range Hopping

Science.gov (United States)

Lin, Yeong-Lieh; Nori, Franco

1997-03-01

We study quantum interference effects on the transition strength for strongly localized electrons hopping on 2D square and 3D cubic lattices in a magnetic field B. In 2D, we obtain closed-form expressions for the tunneling probability between two arbitrary sites by exactly summing the corresponding phase factors of all directed paths connecting them. An analytic expression for the magnetoconductance, as an explicit function of the magnetic flux, is derived. A positive MC is clearly observed when turning on the magnetic field. When the strength of B reaches a certain value, which is inversely proportional to twice the hopping length, the MC is increased by a factor of two compared to that at zero field. The periodicity in the flux of the MC is found to be equal to hc/2e. In the experimentally important 3D case, we show how the interference patterns and the small-B behavior of the magnetoconductance vary according to the orientation of B. Furthermore, for a 3D sample, the effect on the low-flux MC due to the randomness of the angles between the hopping direction and the orientation of B is examined analytically.(Y.-L. Lin and F. Nori, Phys. Rev. Lett. 76), 4580 (1996); Phys. Rev. B 53, 15543 (1996).

Exact renormalization group as a scheme for calculations

International Nuclear Information System (INIS)

Mack, G.

1985-10-01

In this lecture I report on recent work to use exact renormalization group methods to construct a scheme for calculations in quantum field theory and classical statistical mechanics on the continuum. (orig./HSI)

AESS: Accelerated Exact Stochastic Simulation

Science.gov (United States)

Jenkins, David D.; Peterson, Gregory D.

2011-12-01

The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution

New types of exact solutions for a breaking soliton equation

International Nuclear Information System (INIS)

Mei Jianqin; Zhang Hongqing

2004-01-01

In this paper based on a system of Riccati equations, we present a newly generally projective Riccati equation expansion method and its algorithm, which can be used to construct more new exact solutions of nonlinear differential equations in mathematical physics. A typical breaking soliton equation is chosen to illustrate our algorithm such that more families of new exact solutions are obtained, which contain soliton-like solutions and periodic solutions. This algorithm can also be applied to other nonlinear differential equations