Bivariate copulas on the exponentially weighted moving average control chart
Sasigarn Kuvattana
2016-10-01
Full Text Available This paper proposes four types of copulas on the Exponentially Weighted Moving Average (EWMA control chart when observations are from an exponential distribution using a Monte Carlo simulation approach. The performance of the control chart is based on the Average Run Length (ARL which is compared for each copula. Copula functions for specifying dependence between random variables are used and measured by Kendall’s tau. The results show that the Normal copula can be used for almost all shifts.
Enhancing the performance of exponentially weighted moving average charts: discussion
Abbas, N.; Riaz, M.; Does, R.J.M.M.
2015-01-01
Abbas et al. (Abbas N, Riaz M, Does RJMM. Enhancing the performance of EWMA charts. Quality and Reliability Engineering International 2011; 27(6):821-833) proposed the use of signaling schemes with exponentially weighted moving average charts (named as 2/2 and modified − 2/3 schemes) for their impro
An Exponentially Weighted Moving Average Control Chart for Bernoulli Data
Spliid, Henrik
2010-01-01
We consider a production process in which units are produced in a sequential manner. The units can, for example, be manufactured items or services, provided to clients. Each unit produced can be a failure with probability p or a success (non-failure) with probability (1-p). A novel exponentially...
Detecting the start of an influenza outbreak using exponentially weighted moving average charts
Coory Michael
2010-06-01
Full Text Available Abstract Background Influenza viruses cause seasonal outbreaks in temperate climates, usually during winter and early spring, and are endemic in tropical climates. The severity and length of influenza outbreaks vary from year to year. Quick and reliable detection of the start of an outbreak is needed to promote public health measures. Methods We propose the use of an exponentially weighted moving average (EWMA control chart of laboratory confirmed influenza counts to detect the start and end of influenza outbreaks. Results The chart is shown to provide timely signals in an example application with seven years of data from Victoria, Australia. Conclusions The EWMA control chart could be applied in other applications to quickly detect influenza outbreaks.
Aamir Saghir
2015-12-01
Full Text Available The geometric-Poisson exponentially weighted moving average (EWMA chart has been shown to be more effective than the Poisson EWMA chart in monitoring the number of defects in the production processes. In these applications, it is assumed that the process parameters are known or have been accurately estimated. However, in practice, the process parameters are rarely known and must be estimated from reference sample to construct the geometric-Poisson EWMA chart. The performance of the given chart, due to variability in the parameter estimation, might differ from known parameters’ case. This article explored the effect of estimated parameters on the conditional and marginal performance of the geometric-Poisson EWMA chart. The run length characteristics are calculated using a Markov chain approach and the effect of estimation on the performance of the given chart is shown to be significant. Recommendations about the proposer choice of sample size, smoothing constant, and dispersion parameter are made. Results of this study highlight the practical implications of estimation error, and to offer advice to practitioners when constructing/analyzing a phase-I sample.
Michele Scagliarini
2016-06-01
Full Text Available Exponentially weighted moving average (EWMA control charts have been successfully used in recent years in several areas of healthcare. Most of these applications have concentrated on the problem of detecting shifts in the mean level of a process. The EWMA chart for monitoring the variability has received, in general, less attention than its counterpart for the mean, although equally important and, to the best of our knowledge, it has never been used in the healthcare framework. In this work, EWMA control charts were applied retrospectively for monitoring the mean and variability of a hospital organizational performance indicator. The aim was to determine whether EWMA control charts can be used as a comprehensive approach for assessing the steady-state behaviour of the process and for early detection of changes indicating either improvement or deterioration in the performance of healthcare organizations. The results showed that the EWMA control schemes generate easy-to-read data displays that reflect process performance allowing a continuous monitoring and prompt detection of changes in process performance. Currently, hospital managers are designing an operating room dashboard which also includes the EWMA control charts.
Zaman, B.; Riaz, M.; Abbas, N.; Does, R.J.M.M.
2015-01-01
Shewhart, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) charts are famous statistical tools, to handle special causes and to bring the process back in statistical control. Shewhart charts are useful to detect large shifts, whereas EWMA and CUSUM are more sensitive for smal
Karin KANDANANOND
2010-12-01
Full Text Available The objective of this research is to select the appropriate control charts for detecting a shift in the autocorrelated observations. The autocorrelated processes were characterized using AR (1 and IMA (1, 1 for stationary and non-stationary processes respectively. A process model was simulated to achieve the response, the average run length (ARL. The empirical analysis was conducted to quantify the impacts of critical factors e.g., AR coefficient (f, MA coefficient (q, types of charts and shift sizes on the ARL. The results showed that the exponentially weighted moving average (EWMA was the most appropriate control chart to monitor AR (1 and IMA (1, 1 processes because of its sensitivity. For non-stationary case, the ARL at positive q was significantly higher than the one at negative q when a shift size was small. If the performance of the statistical process control under stationary and non-stationary disturbances is correctly characterized, practitioners will have guidelines for achieving the highest possible performance potential when deploying SPC.
Weighted exponential polynomial approximation
邓冠铁
2003-01-01
A necessary and sufficient condition for completeness of systems of exponentials with a weightin Lp is established and a quantitative relation between the weight and the system of exponential in Lp isobtained by using a generalization of Malliavin's uniqueness theorem about Watson's problem.
Using exponentially weighted moving average algorithm to defend against DDoS attacks
Machaka, P
2016-11-01
Full Text Available ) the effect, on detection-rate, of the alarm threshold α, tuning parameter; (2) the effect, on detection rate, of the EWMA weighting factor β, tuning parameter; (3) the trade-off between detection rate and the false positive rate; (4) the trade-off between... improves. It can be seen that there is a trade-off between detection rate and false positive rate. B. The effect of the EWMA factor (β) In this section we seek to investigate the effect of the value of the EWMA factor (β) on the detection rate...
Estimation and variable selection with exponential weights
Arias-Castro, Ery; Lounici, Karim
2014-01-01
In the context of a linear model with a sparse coefficient vector, exponential weights methods have been shown to be achieve oracle inequalities for denoising/prediction. We show that such methods also succeed at variable selection and estimation under the near minimum condition on the design matrix, instead of much stronger assumptions required by other methods such as the Lasso or the Dantzig Selector. The same analysis yields consistency results for Bayesian methods and BIC-type variable s...
Exponential convergence rates for weighted sums in noncommutative probability space
Choi, Byoung Jin; Ji, Un Cig
2016-11-01
We study exponential convergence rates for weighted sums of successive independent random variables in a noncommutative probability space of which the weights are in a von Neumann algebra. Then we prove a noncommutative extension of the result for the exponential convergence rate by Baum, Katz and Read. As applications, we first study a large deviation type inequality for weighted sums in a noncommutative probability space, and secondly we study exponential convergence rates for weighted free additive convolution sums of probability measures.
Variable Selection with Exponential Weights and $l_0$-Penalization
Arias-Castro, Ery; Lounici, Karim
2012-01-01
In the context of a linear model with a sparse coefficient vector, exponential weights methods have been shown to be achieve oracle inequalities for prediction. We show that such methods also succeed at variable selection and estimation under the necessary identifiability condition on the design matrix, instead of much stronger assumptions required by other methods such as the Lasso or the Dantzig Selector. The same analysis yields consistency results for Bayesian methods and BIC-type variabl...
Evolution of Weighted Networks with Exponential Aging of Sites
XU Xin-Jian; WU Zhi-Xi; WANG Ying-Hai
2005-01-01
@@ We study the growth of weighted networks with exponential aging of sites. Each new vertex of the network is connected to some old vertices with proportional (i) to the strength of the old vertex and (ii) to e-ατ, where τ is the age of the old vertex and α is a positive constant. As soon as the preferential attachment is moditied by such factors, the interesting quantities of the produced network (the vertex degree, vertex strength, clustering coefficient and average path length) will be significantly transformed.
Collective Prediction of Individual Mobility Traces with Exponential Weights
Hawelka, Bartosz; Kazakopoulos, Pavlos; Beinat, Euro
2015-01-01
We present and test a sequential learning algorithm for the short-term prediction of human mobility. This novel approach pairs the Exponential Weights forecaster with a very large ensemble of experts. The experts are individual sequence prediction algorithms constructed from the mobility traces of 10 million roaming mobile phone users in a European country. Average prediction accuracy is significantly higher than that of individual sequence prediction algorithms, namely constant order Markov models derived from the user's own data, that have been shown to achieve high accuracy in previous studies of human mobility prediction. The algorithm uses only time stamped location data, and accuracy depends on the completeness of the expert ensemble, which should contain redundant records of typical mobility patterns. The proposed algorithm is applicable to the prediction of any sufficiently large dataset of sequences.
Holographic Lifshitz fermions and exponentially suppressed spectral weight
Kim, Youngshin
2016-01-01
One of the unusual features of Lifshitz holography is the presence of a tunneling barrier that arises from the bulk geometry for probes carrying large transverse momentum. This leads to a decoupling of the horizon from the boundary, and in particular gives rise to an exponential suppression of spectral weight in the large transverse momentum limit. We compute the spin-1/2 holographic Green's function and show that this suppression has the same origin as in the scalar case. We furthermore demonstrate that the suppression factor is universal in the $\\hat\\omega\\to0$ limit where $\\hat\\omega=\\omega/|\\vec k|^z$. In particular, it depends only on $\\hat\\omega$ and the critical exponent $z$, and is independent of scaling dimension and spin.
Ding Jun YAO; Rong Ming WANG
2008-01-01
The authors consider two discrete-time insurance risk models. Two moving average risk models are introduced to model the surplus process, and the probabilities of ruin are examined in models with a constant interest force. Exponential bounds for ruin probabilities of an infinite time horizon are derived by the martingale method.
Lin, Meng; Yu, Xiaoduo; Chen, Yan; Ouyang, Han; Zhou, Chunwu [Chinese Academy of Medical Sciences, Department of Diagnostic Radiology, Cancer Institute and Hospital, Peking Union Medical College, Beijing (China); Wu, Bing; Zheng, Dandan [GE MR Research China, Beijing (China)
2017-06-15
To investigate the potential of various metrics derived from mono-exponential model (MEM), bi-exponential model (BEM) and stretched exponential model (SEM)-based diffusion-weighted imaging (DWI) in diagnosing and differentiating the pathological subtypes and grades of uterine cervical carcinoma. 71 newly diagnosed patients with cervical carcinoma (50 cases of squamous cell carcinoma [SCC] and 21 cases of adenocarcinoma [AC]) and 32 healthy volunteers received DWI with multiple b values. The apparent diffusion coefficient (ADC), pure molecular diffusion (D), pseudo-diffusion coefficient (D*), perfusion fraction (f), water molecular diffusion heterogeneity index (alpha), and distributed diffusion coefficient (DDC) were calculated and compared between tumour and normal cervix, among different pathological subtypes and grades. All of the parameters were significantly lower in cervical carcinoma than normal cervical stroma except alpha. SCC showed lower ADC, D, f and DDC values and higher D* value than AC; D and DDC values of SCC and ADC and D values of AC were lower in the poorly differentiated group than those in the well-moderately differentiated group. Compared with MEM, diffusion parameters from BEM and SEM may offer additional information in cervical carcinoma diagnosis, predicting pathological tumour subtypes and grades, while f and D showed promising significance. (orig.)
常志远; 孙金生
2016-01-01
为解决指数加权平滑(EWMA)控制图惯性问题而提出的自适应EWMA(adaptive EWMA, AEWMA)控制图的统计特性已经被广泛研究,但AEWMA控制图经济特性的研究却从未见有成果发表。针对该问题,在考虑Taguchi损失函数的基础上,给出了AEWMA控制图经济统计设计的模型。提出了一种在偏移区间上对AEWMA控制图进行优化设计的方法,用该方法优化设计的AEWMA控制图与针对固定偏移优化设计的EWMA控制图进行了比较。结果表明该方法设计的AEWMA控制图仍然保持其解决EWMA控制图惯性问题的特性, AEWMA控制图的经济特性同样优于EWMA控制图。分析了AEWMA控制图经济统计设计的参数灵敏度,总结了AEWMA控制图的参数变化与损失、平均链长以及最优参数组合之间的关系。%The statistical properties of adaptive exponentially weighted moving average (AEWMA) control chart, which is proposed to deal with the inertia problem of EWMA control chart, have been thoroughly investigated by many authors. However, the research results on economic properties of AEWMA control chart have never been reported in the publica-tions. In this paper, an economic-statistical design model based on Taguchi loss function is proposed for AEWMA control chart. The optimal algorithm based on the range of shift is developed for economic-statistical design of AEWMA chart. The effectiveness of the optimal algorithm is validated by the comparison between AEWMA chart and EWMA chart. The comparison results show that the designed AEWMA chart is still able to deal with the inertia problem of EWMA chart, and the economic properties of AEWMA chart outperforms the EWMA chart. Finally, the sensitivity analysis of AEWMA chart is performed, and the relationship between parameter changes and cost, average run length and optimal decision variables of AEWMA chart are summarized respectively.
Daniel Albiero
2012-03-01
Full Text Available Conceitos de qualidade cada vez mais se tornam essenciais para a sobrevivência da empresa agrícola, pois a importância do aprimoramento das operações agrícolas se faz necessária para a obtenção de resultados viáveis economicamente, ambientamente e socialmente. Uma das dimensões da qualidade é conseguir de conformidade, ou seja, a garantia de execução exata do que foi planejado para atender aos requisitos dos clientes em relação a um determinado produto ou serviço. Os objetivos deste trabalho são avaliar a distribuição longitudinal entre sementes de uma semeadora de anel interno rotativo, e propor a utilização da metodologia estatística da Média Móvel Exponencialmente Ponderada (MMEP como alternativa para o controle de qualidade da semeadura, quando não há normalidade da distribuição dos dados. Os resultados demonstraram que a MMEP é adequada para a avaliação da qualidade da distribuição longitudinal de sementes, pois concordou com os dados apresentados na estatística descritiva, o que lhe credencia para avaliação de distribuições não normais.Quality concepts are essentials for survivor of agricultural companies, therefore, the importancy of improvement of agricultural process is necessary for to get results economically, environmentally and socially viables. One quality dimension is to get a compliance quality, ie, ensure the exact execution than was planned. The subject of this paper is evaluable at longitudinal distribution between seed of a internal ring seeder. The subject of this paper is to evaluate at longitudinal distribution between seed distributed for a internal ring seeder and to propose the use of statistical methodology exponentially weighted moving average (MMEP like alternative for the quality control of seeders, when there is not normality in data. The results showed that the MMEP is adequate for quality evaluation of longitudinal distribution between seeds, as agreed with the data of
Heritability of body weight: moving beyond genetics.
Russo, P; Lauria, F; Siani, A
2010-12-01
Obesity is a complex disease, arising from the interaction between several genetic and environmental factors. Until recently, the genetic basis of complex diseases in general, and of obesity in particular, were poorly characterized. While the relatively rare monogenic and syndromic forms of obesity clearly recognize a genetic origin, the actual worldwide epidemics of obesity represent a challenge for the identification of the genetic factors involved, being likely the effect of several loci each having a subtle influence on the phenotypic expression. Progress in DNA analysis techniques and in computational tools, and the increasing level of characterization of the variability of the human genome has recently allowed to study comprehensively the association between genetic variants and obesity. To date, well-conducted and powered genome-wide association studies allowed to consistently identify genomic regions - lying on different chromosomes and affecting different metabolic pathways - influencing the predisposition to the accumulation of body fat, ultimately leading to overweight and obesity. However, the population attributable risk for obesity linked to the most statistically significant loci, like FTO and MC4R, remains discouragingly low, explaining only small fractions of the overall variance of body weight. In the last few years, the role of the complex interaction between genetic determinants and environmental factors in the rapid global increase of obesity has been further challenged by the entry of new players, that is the transcriptional and post-transcriptional regulation, summarized under the emerging discipline of epigenetics. The key challenge now is to move from the identification of causal genes and variants to the integration of different "omics" disciplines, finally allowing the molecular understanding of obesity and related conditions. Copyright © 2010 Elsevier B.V. All rights reserved.
Ma, Xiao; Zheng, Wei-Fan; Jiang, Bao-Shan; Zhang, Ji-Ye
2016-10-01
With the development of traffic systems, some issues such as traffic jams become more and more serious. Efficient traffic flow theory is needed to guide the overall controlling, organizing and management of traffic systems. On the basis of the cellular automata model and the traffic flow model with look-ahead potential, a new cellular automata traffic flow model with negative exponential weighted look-ahead potential is presented in this paper. By introducing the negative exponential weighting coefficient into the look-ahead potential and endowing the potential of vehicles closer to the driver with a greater coefficient, the modeling process is more suitable for the driver’s random decision-making process which is based on the traffic environment that the driver is facing. The fundamental diagrams for different weighting parameters are obtained by using numerical simulations which show that the negative exponential weighting coefficient has an obvious effect on high density traffic flux. The complex high density non-linear traffic behavior is also reproduced by numerical simulations. Project supported by the National Natural Science Foundation of China (Grant Nos. 11572264, 11172247, 11402214, and 61373009).
Exponential stability of time-delay systems via new weighted integral inequalities
Hien, L. V.; Trinh, H.
2015-01-01
In this paper, new weighted integral inequalities (WIIs) are first derived by refining the Jensen single and double inequalities. It is shown that the newly derived inequalities in this paper encompass both the Jensen inequality and its most recent improvements based on Wirtinger integral inequality. The potential capability of the proposed WIIs is demonstrated through applications in exponential stability analysis for some classes of time-delay systems in the framework of linear matrix inequ...
Zeros and logarithmic asymptotics of Sobolev orthogonal polynomials for exponential weights
Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.
2009-12-01
We obtain the (contracted) weak zero asymptotics for orthogonal polynomials with respect to Sobolev inner products with exponential weights in the real semiaxis, of the form , with [gamma]>0, which include as particular cases the counterparts of the so-called Freud (i.e., when [phi] has a polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) weights. In addition, the boundness of the distance of the zeros of these Sobolev orthogonal polynomials to the convex hull of the support and, as a consequence, a result on logarithmic asymptotics are derived.
Winfield, Jessica M.; Collins, David J.; Morgan, Veronica A.; DeSouza, Nandita M. [The Royal Marsden NHS Foundation Trust, MRI Unit, Sutton, Surrey (United Kingdom); The Institute of Cancer Research, Cancer Research UK Cancer Imaging Centre, Division of Radiotherapy and Imaging, London (United Kingdom); Orton, Matthew R. [The Institute of Cancer Research, Cancer Research UK Cancer Imaging Centre, Division of Radiotherapy and Imaging, London (United Kingdom); Ind, Thomas E.J. [The Royal Marsden NHS Foundation Trust, Gynaecology Unit, London (United Kingdom); Attygalle, Ayoma; Hazell, Steve [The Royal Marsden NHS Foundation Trust, Department of Histopathology, London (United Kingdom)
2017-02-15
Assessment of empirical diffusion-weighted MRI (DW-MRI) models in cervical tumours to investigate whether fitted parameters distinguish between types and grades of tumours. Forty-two patients (24 squamous cell carcinomas, 14 well/moderately differentiated, 10 poorly differentiated; 15 adenocarcinomas, 13 well/moderately differentiated, two poorly differentiated; three rare types) were imaged at 3 T using nine b-values (0 to 800 s mm{sup -2}). Mono-exponential, stretched exponential, kurtosis, statistical, and bi-exponential models were fitted. Model preference was assessed using Bayesian Information Criterion analysis. Differences in fitted parameters between tumour types/grades and correlation between fitted parameters were assessed using two-way analysis of variance and Pearson's linear correlation coefficient, respectively. Non-mono-exponential models were preferred by 83 % of tumours with bi-exponential and stretched exponential models preferred by the largest numbers of tumours. Apparent diffusion coefficient (ADC) and diffusion coefficients from non-mono-exponential models were significantly lower in poorly differentiated tumours than well/moderately differentiated tumours. α (stretched exponential), K (kurtosis), f and D* (bi-exponential) were significantly different between tumour types. Strong correlation was observed between ADC and diffusion coefficients from other models. Non-mono-exponential models were preferred to the mono-exponential model in DW-MRI data from cervical tumours. Parameters of non-mono-exponential models showed significant differences between types and grades of tumours. (orig.)
LI Qiang; WU Jianxin; SUN Yan
2009-01-01
Dynamic optimization of electromechanical coupling system is a significant engineering problem in the field of mechatronics. The performance improvement of electromechanical equipment depends on the system design parameters. Aiming at the spindle unit of refitted machine tool for solid rocket, the vibration acceleration of tool is taken as objective function, and the electromechanical system design parameters are appointed as design variables. Dynamic optimization model is set up by adopting Lagrange-Maxwell equations, Park transform and electromechanical system energy equations. In the procedure of seeking high efficient optimization method, exponential function is adopted to be the weight function of particle swarm optimization algorithm. Exponential inertia weight particle swarm algorithm(EPSA), is formed and applied to solve the dynamic optimization problem of electromechanical system. The probability density function of EPSA is presented and used to perform convergence analysis. After calculation, the optimized design parameters of the spindle unit are obtained in limited time period. The vibration acceleration of the tool has been decreased greatly by the optimized design parameters. The research job in the paper reveals that the problem of dynamic optimization of electromechanical system can be solved by the method of combining system dynamic analysis with reformed swarm particle optimization. Such kind of method can be applied in the design of robots, NC machine, and other electromechanical equipments.
On Asymptotic Regimes of Orthogonal Polynomials with Complex Varying Quartic Exponential Weight
Bertola, Marco; Tovbis, Alexander
2016-12-01
We study the asymptotics of recurrence coefficients for monic orthogonal polynomials π_n(z) with the quartic exponential weight exp [-N (1/2 z^2 + 1/4 t z^4)], where tin C and Nin{N}, Nto ∞. Our goal is to describe these asymptotic behaviors globally for tin C in different regions. We also describe the ''breaking'' curves separating these regions, and discuss their special (critical) points. All these pieces of information combined provide the global asymptotic ''phase portrait'' of the recurrence coefficients of π_n(z), which was studied numerically in [Constr. Approx. 41 (2015), 529-587, arXiv:1108.0321]. The main goal of the present paper is to provide a rigorous framework for the global asymptotic portrait through the nonlinear steepest descent analysis (with the g-function mechanism) of the corresponding Riemann-Hilbert problem (RHP) and the continuation in the parameter space principle. The latter allows to extend the nonlinear steepest descent analysis from some parts of the complex t-plane to all noncritical values of t. We also provide explicit solutions for recurrence coefficients in terms of the Riemann theta functions. The leading order behaviour of the recurrence coefficients in the full scaling neighbourhoods the critical points (double and triple scaling limits) was obtained in [Constr. Approx. 41 (2015), 529-587, arXiv:1108.0321] and [Asymptotics of complex orthogonal polynomials on the cross with varying quartic weight: critical point behaviour and the second Painlevé transcendents, in preparation].
Gardner, Don E.
The merits of double exponential smoothing are discussed relative to other types of pattern-based enrollment forecasting methods. The difficulties associated with selecting an appropriate weight factor are discussed, and their potential effects on prediction results are illustrated. Two methods for objectively selecting the "best" weight…
Tan, K. L.; Chong, Z. L.; Khoo, M. B. C.; Teoh, W. L.; Teh, S. Y.
2017-09-01
Quality control is crucial in a wide variety of fields, as it can help to satisfy customers’ needs and requirements by enhancing and improving the products and services to a superior quality level. The EWMA median chart was proposed as a useful alternative to the EWMA \\bar{X} chart because the median-type chart is robust against contamination, outliers or small deviation from the normality assumption compared to the traditional \\bar{X}-type chart. To provide a complete understanding of the run-length distribution, the percentiles of the run-length distribution should be investigated rather than depending solely on the average run length (ARL) performance measure. This is because interpretation depending on the ARL alone can be misleading, as the process mean shifts change according to the skewness and shape of the run-length distribution, varying from almost symmetric when the magnitude of the mean shift is large, to highly right-skewed when the process is in-control (IC) or slightly out-of-control (OOC). Before computing the percentiles of the run-length distribution, optimal parameters of the EWMA median chart will be obtained by minimizing the OOC ARL, while retaining the IC ARL at a desired value.
A robust Phase I exponentially weighted moving average chart for dispersion
Zwetsloot, I.M.; Schoonhoven, M.; Does, R.J.M.M.
2015-01-01
A Phase I estimator of the dispersion should be efficient under in-control data and robust against contaminations. Most estimation methods proposed in the literature are either efficient or robust against either sustained shifts or scattered disturbances. In this article, we propose a new estimation
Mixed exponentially weighted moving average-cumulative sum charts for process monitoring
Abbas, N.; Riaz, M.; Does, R.J.M.M.
2013-01-01
The control chart is a very popular tool of statistical process control. It is used to determine the existence of special cause variation to remove it so that the process may be brought in statistical control. Shewhart-type control charts are sensitive for large disturbances in the process, whereas
Sakai R
2010-01-01
Full Text Available Let , and let be an even function. In this paper, we consider the exponential-type weights , and the orthonormal polynomials of degree with respect to . So, we obtain a certain differential equation of higher order with respect to and we estimate the higher-order derivatives of and the coefficients of the higher-order Hermite-Fejér interpolation polynomial based at the zeros of .
Zhu, Ke; 10.1214/11-AOS895
2012-01-01
This paper investigates the asymptotic theory of the quasi-maximum exponential likelihood estimators (QMELE) for ARMA--GARCH models. Under only a fractional moment condition, the strong consistency and the asymptotic normality of the global self-weighted QMELE are obtained. Based on this self-weighted QMELE, the local QMELE is showed to be asymptotically normal for the ARMA model with GARCH (finite variance) and IGARCH errors. A formal comparison of two estimators is given for some cases. A simulation study is carried out to assess the performance of these estimators, and a real example on the world crude oil price is given.
LongShuyao; HuDe'an
2003-01-01
The meshless method is a new numerical technique presented in recent years .It uses the moving least square (MLS) approximation as a shape function . The smoothness of the MLS approximation is determined by that of the basic function and of the weight function, and is mainly determined by that of the weight function. Therefore, the weight function greatly affects the accuracy of results obtained. Different kinds of weight functions, such as the spline function, the Gauss function and so on, are proposed recently by many researchers. In the present work, the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method. The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed. Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and a in Gauss and exponential weight functions are in the range of reasonable values, respectively, and the higher the smoothness of the weight function, the better the features of the solutions.
Positioning of Weight Bias: Moving towards Social Justice
Alberga, Angela S.; Kassan, Anusha; Sesma-Vazquez, Monica
2016-01-01
Weight bias is a form of stigma with detrimental effects on the health and wellness of individuals with large bodies. Researchers from various disciplines have recognized weight bias as an important topic for public health and for professional practice. To date, researchers from various areas have approached weight bias from independent perspectives and from differing theoretical orientations. In this paper, we examined the similarities and differences between three perspectives (i.e., weight-centric, non-weight-centric (health-centric), and health at every size) used to understand weight bias and approach weight bias research with regard to (a) language about people with large bodies, (b) theoretical position, (c) identified consequences of weight bias, and (d) identified influences on weight-based social inequity. We suggest that, despite differences, each perspective acknowledges the negative influences that position weight as being within individual control and the negative consequences of weight bias. We call for recognition and discussion of weight bias as a social justice issue in order to change the discourse and professional practices extended towards individuals with large bodies. We advocate for an emphasis on social justice as a uniting framework for interdisciplinary research on weight bias.
Positioning of Weight Bias: Moving towards Social Justice
Sarah Nutter
2016-01-01
Full Text Available Weight bias is a form of stigma with detrimental effects on the health and wellness of individuals with large bodies. Researchers from various disciplines have recognized weight bias as an important topic for public health and for professional practice. To date, researchers from various areas have approached weight bias from independent perspectives and from differing theoretical orientations. In this paper, we examined the similarities and differences between three perspectives (i.e., weight-centric, non-weight-centric (health-centric, and health at every size used to understand weight bias and approach weight bias research with regard to (a language about people with large bodies, (b theoretical position, (c identified consequences of weight bias, and (d identified influences on weight-based social inequity. We suggest that, despite differences, each perspective acknowledges the negative influences that position weight as being within individual control and the negative consequences of weight bias. We call for recognition and discussion of weight bias as a social justice issue in order to change the discourse and professional practices extended towards individuals with large bodies. We advocate for an emphasis on social justice as a uniting framework for interdisciplinary research on weight bias.
MOVE! multidisciplinary programs: Challenges and resources for weight management treatment in VHA.
Rosenberger, Patricia H; Ruser, Christopher; Kashaf, Susan
2011-12-01
The MOVE! program has been a successful weight management and physical activity initiative from the Veteran's Health Administration. While it embraces a multicomponent approach to weight management, local facilities have primarily focused on the implementation of delivery of MOVE! educational materials to groups or individuals. We discuss additional MOVE!-related weight management efforts within VHA that reflect treatment strategies beyond delivery of these educational materials. First, we present a case study that highlights the special challenges associated with the Veteran overweight/obese population. Second, we describe the implementation of our local, multidisciplinary, individualized weight management clinic as an example of on-the-ground provision of a higher treatment intensity program as part of MOVE!'s multicomponent model. Third, we present program outcomes and consider challenges to program sustainability.
Yong Ping LIU; Chun Yuan SONG
2014-01-01
In this paper, we study the sharp Jackson inequality for the best approximation of f ∈L2,κ(Rd) by a subspace E2κ(σ) (SE2κ(σ)), which is a subspace of entire functions of exponential type (spherical exponential type) at most σ. Here L2,κ(Rd) denotes the space of all d-variate functions f endowed with the L2-norm with the weight vκ(x)=? ξ∈R+|(ξ, x)|2κ (ξ), which is defined by a positive subsystem R+ of a finite root system R ⊂ Rd and a function κ(ξ) : R → R+ invariant under the reflection group G(R) generated by R. In the case G(R)=Zd2 , we get some exact results. Moreover, the deviation of best approximation by the subspace E2κ(σ) (SE2κ(σ)) of some class of the smooth functions in the space L2,κ(Rd) is obtained.
Features of Discontinuous Galerkin Algorithms in Gkeyll, and Exponentially-Weighted Basis Functions
Hammett, G. W.; Hakim, A.; Shi, E. L.
2016-10-01
There are various versions of Discontinuous Galerkin (DG) algorithms that have interesting features that could help with challenging problems of higher-dimensional kinetic problems (such as edge turbulence in tokamaks and stellarators). We are developing the gyrokinetic code Gkeyll based on DG methods. Higher-order methods do more FLOPS to extract more information per byte, thus reducing memory and communication costs (which are a bottleneck for exascale computing). The inner product norm can be chosen to preserve energy conservation with non-polynomial basis functions (such as Maxwellian-weighted bases), which alternatively can be viewed as a Petrov-Galerkin method. This allows a full- F code to benefit from similar Gaussian quadrature employed in popular δf continuum gyrokinetic codes. We show some tests for a 1D Spitzer-Härm heat flux problem, which requires good resolution for the tail. For two velocity dimensions, this approach could lead to a factor of 10 or more speedup. Supported by the Max-Planck/Princeton Center for Plasma Physics, the SciDAC Center for the Study of Plasma Microturbulence, and DOE Contract DE-AC02-09CH11466.
Jansen, Rob T P; Laeven, Mark; Kardol, Wim
2002-06-01
The analytical processes in clinical laboratories should be considered to be non-stationary, non-ergodic and probably non-stochastic processes. Both the process mean and the process standard deviation vary. The variation can be different at different levels of concentration. This behavior is shown in five examples of different analytical systems: alkaline phosphatase on the Hitachi 911 analyzer (Roche), vitamin B12 on the Access analyzer (Beckman), prothrombin time and activated partial thromboplastin time on the STA Compact analyzer (Roche) and PO2 on the ABL 520 analyzer (Radiometer). A model is proposed to assess the status of a process. An exponentially weighted moving average and standard deviation was used to estimate process mean and standard deviation. Process means were estimated overall and for each control level. The process standard deviation was estimated in terms of within-run standard deviation. Limits were defined in accordance with state of the art- or biological variance-derived cut-offs. The examples given are real, not simulated, data. Individual control sample results were normalized to a target value and target standard deviation. The normalized values were used in the exponentially weighted algorithm. The weighting factor was based on a process time constant, which was estimated from the period between two calibration or maintenance procedures. The proposed system was compared with Westgard rules. The Westgard rules perform well, despite the underlying presumption of ergodicity. This is mainly caused by the introduction of the starting rule of 12s, which proves essential to prevent a large number of rule violations. The probability of reporting a test result with an analytical error that exceeds the total allowable error was calculated for the proposed system as well as for the Westgard rules. The proposed method performed better. The proposed algorithm was implemented in a computer program running on computers to which the analyzers were
EURO-USD PREDICTION APPLICATION USING WEIGHTED MOVING AVERAGE ON MOBILE DEVICE
Afan Galih Salman
2014-01-01
Full Text Available Investments in foreign exchange (forex promise lucrative profits, thus inviting a lot of attention for researcher sand traders to create a system or indicator in trading. All indicators or system is reliable and has proven hat can bring profit for traders. Basically all indicator are reliable and tested which able to bring some profit to traders. Ironically there are many trader fail to gain the profit and became bankrupt. It because they has no well money management and good mentality in trading. Therefore in this study is focused on technical analysis by using weighted moving average which will be implemented on the mobile device so that it can give predictions on the price of the EURO-USD currency pair. The results is the weighted moving average was not quite accurate in determining the price of a currency especially during sideways price but it so accurate when they have strong price trend or large-scale. weighted moving average becomes really easy to apply when using 2 or more weighted moving average and able to give facility in analyzing movement of currency with the counterpart of EURO-USD by means of mobile medium.
Gary Black
2011-01-01
Full Text Available Many real-world processes generate autocorrelated and/or Weibull data. In such cases, the independence and/or normality assumptions underlying the Shewhart and EWMA control charts are invalid. Although data transformations exist, such tools would not normally be understood or employed by naive practitioners. Thus, the question arises, “What are the effects on robustness whenever these charts are used in such applications?” Consequently, this paper examines and compares the performance of these two control charts when the problem (the model is subjected to autocorrelated and/or Weibull data. A variety of conditions are investigated related to the magnitudes of various parameters related to the process shift, the autocorrelation coefficient and the Weibull shape parameter. Results indicate that the EWMA chart outperforms the Shewhart in 62% of the cases, particularly those cases with low to moderate autocorrelation effects. The Shewhart chart outperforms the EWMA chart in 35% of the cases, particularly those cases with high autocorrelation and zero or high process shift effects.
A RED modified weighted moving average for soft real-time application
Domanśka Joanna
2014-09-01
Full Text Available The popularity of TCP/IP has resulted in an increase in usage of best-effort networks for real-time communication. Much effort has been spent to ensure quality of service for soft real-time traffic over IP networks. The Internet Engineering Task Force has proposed some architecture components, such as Active Queue Management (AQM. The paper investigates the influence of the weighted moving average on packet waiting time reduction for an AQM mechanism: the RED algorithm. The proposed method for computing the average queue length is based on a difference equation (a recursive equation. Depending on a particular optimality criterion, proper parameters of the modified weighted moving average function can be chosen. This change will allow reducing the number of violations of timing constraints and better use of this mechanism for soft real-time transmissions. The optimization problem is solved through simulations performed in OMNeT++ and later verified experimentally on a Linux implementation
Sisto, Alessandro
2011-01-01
Using ultrafilter techniques we show that in any partition of $\\mathbb{N}$ into 2 cells there is one cell containing infinitely many exponential triples, i.e. triples of the kind $a,b,a^b$ (with $a,b>1$). Also, we will show that any multiplicative $IP^*$ set is an "exponential $IP$ set", the analogue of an $IP$ set with respect to exponentiation.
Sensory re-weighting in human postural control during moving-scene perturbations.
Mahboobin, Arash; Loughlin, Patrick J; Redfern, Mark S; Sparto, Patrick J
2005-11-01
The aim of the current study was to further investigate a recently proposed "sensory re-weighting" hypothesis, by evoking anterior-posterior (AP) body sway using visual stimuli during sway-referencing of the support surface. Twelve healthy adults participated in this study. Subjects stood on the platform while looking at a visual scene that encompassed the full horizontal field of view. A sequence of scene movements was presented to the subjects consisting of multiple visual push/pull perturbations; in between the first two push/pull sequences, the scene either moved randomly or was stationary. The peak-squared velocity of AP center-of-pressure (COP) was computed within a 6 s window following each push and pull. The peak-squared velocity was lowest for the push/pull sequence immediately following the random moving scene. These results are consistent with the sensory re-weighting hypothesis, wherein the sensory integration process reduced the contribution of visual sensory input during the random moving scene interval. We also found evidence of habituation to moving scene perturbations with repeated exposure.
Cercueil, Jean-Pierre [University of Burgundy, INSERM U866, BP 87900, Dijon (France); CHU (University Hospital), Department of Radiology, BP 77908, Dijon (France); Petit, Jean-Michel [University of Burgundy, INSERM U866, BP 87900, Dijon (France); CHU (University Hospital), Department of Endocrinology, Diabetology, and Metabolic Diseases, BP 77908, Dijon (France); Nougaret, Stephanie; Pierredon-Foulongne, Marie-Ange; Schembri, Valentina; Delhom, Elisabeth; Guiu, Boris [St-Eloi University Hospital, Department of Radiology, Montpellier (France); Soyer, Philippe [Hopital 1 Lariboisiere, Assistance Publique Hopitaux de Paris, Department of Body and Interventional Imaging, Paris Cedex 10 (France); Fohlen, Audrey [University Hospital, Department of Radiology, Caen (France); Schmidt, Sabine; Denys, Alban [Centre Hospitalier Universitaire Vaudois, Department of Radiology, Lausanne (Switzerland); Aho, Serge [CHU (University Hospital), Department of Biostatistics, BP 77908, Dijon (France)
2015-06-01
To determine whether a mono-, bi- or tri-exponential model best fits the intravoxel incoherent motion (IVIM) diffusion-weighted imaging (DWI) signal of normal livers. The pilot and validation studies were conducted in 38 and 36 patients with normal livers, respectively. The DWI sequence was performed using single-shot echoplanar imaging with 11 (pilot study) and 16 (validation study) b values. In each study, data from all patients were used to model the IVIM signal of normal liver. Diffusion coefficients (D{sub i} ± standard deviations) and their fractions (f{sub i} ± standard deviations) were determined from each model. The models were compared using the extra sum-of-squares test and information criteria. The tri-exponential model provided a better fit than both the bi- and mono-exponential models. The tri-exponential IVIM model determined three diffusion compartments: a slow (D{sub 1} = 1.35 ± 0.03 x 10{sup -3} mm{sup 2}/s; f{sub 1} = 72.7 ± 0.9 %), a fast (D{sub 2} = 26.50 ± 2.49 x 10{sup -3} mm{sup 2}/s; f{sub 2} = 13.7 ± 0.6 %) and a very fast (D{sub 3} = 404.00 ± 43.7 x 10{sup -3} mm{sup 2}/s; f{sub 3} = 13.5 ± 0.8 %) diffusion compartment [results from the validation study]. The very fast compartment contributed to the IVIM signal only for b values ≤15 s/mm{sup 2} The tri-exponential model provided the best fit for IVIM signal decay in the liver over the 0-800 s/mm{sup 2} range. In IVIM analysis of normal liver, a third very fast (pseudo)diffusion component might be relevant. (orig.)
Higgins, Diana M; Buta, Eugenia; Dorflinger, Lindsey; Heapy, Alicia A; Ruser, Christopher B; Goulet, Joseph L; Masheb, Robin M
2016-07-01
The MOVE!23, a questionnaire to assess weight-related domains in veterans, was examined. Factor analysis of Perceived Contributors to Weight Change revealed three factors (psychosocial, eating behavior, and medical) that were positively correlated with body mass index, and psychiatric and medical comorbidity (p's MOVE!23 Perceived Contributors to Weight Change subscale is a reliable and valid measure that is associated with body mass index and may assist in tailoring treatments according to gender and comorbidity.
Spot Weight Adaptation for Moving Target in Spot Scanning Proton Therapy
Paul eMorel
2015-05-01
Full Text Available Purpose: This study describes a real-time spot weight adaptation method in spot-scanning proton therapy for moving target or moving patient, so that the resultant dose distribution closely matches the planned dose distribution. Materials and Methods: The method proposed in this study adapts the weight (MU of the delivering pencil beam to that of the target spot it will actually hit during patient/target motion. The target spot a certain delivering pencil beam may hit relies on patient monitoring and/or motion modeling using four-dimensional (4D CT. After the adapted delivery, the required total weight (MU for this target spot is then subtracted from the planned value. With continuous patient motion and continuous spot scanning, the planned doses to all target spots will eventually be all fulfilled. In a proof-of-principle test, a lung case was presented with realistic temporal and motion parameters; the resultant dose distribution using spot weight adaptation was compared to that without using this method. The impact of the real-time patient/target position tracking or prediction was also investigated.Results: For moderate motion (i.e., mean amplitude 0.5 cm, D95% to the planning target volume (PTV was only 81.5% of the prescription (RX dose; with spot weight adaptation PTV D95% achieves 97.7%RX. For large motion amplitude (i.e., 1.5 cm, without spot weight adaptation PTV D95% is only 42.9% of RX; with spot weight adaptation, PTV D95% achieves 97.7%RX. Larger errors in patient/target position tracking or prediction led to worse final target coverage; an error of 3mm or smaller in patient/target position tracking is preferred. Conclusion: The proposed spot weight adaptation method was able to deliver the planned dose distribution and maintain target coverage when patient motion was involved. The successful implementation of this method would rely on accurate monitoring or prediction of patient/target motion.
Node 1 and PMA-1 are moved for weight and center of gravity determination
1998-01-01
Node 1, the first U.S. element for the International Space Station, and Pressurized Mating Adapter-1 (PMA-1) continue with prelaunch preparation activities at KSC's Space Station Processing Facility. Node 1 is a connecting passageway to the living and working areas of the space station. The node and PMA-1 are being moved to an element rotation stand, or test stand, where they will undergo an interim weight and center of gravity determination. The final determination is planned to be performed prior to transporting Node 1 to the launch pad. Node 1 is scheduled to fly on STS-88.
Sergey K. Sekatskii
2015-01-01
Full Text Available Integral equalities involving integrals of the logarithm of the Riemann ς-function with exponential weight functions are introduced, and it is shown that an infinite number of them are equivalent to the Riemann hypothesis. Some of these equalities are tested numerically. The possible contribution of the Riemann function zeroes nonlying on the critical line is rigorously estimated and shown to be extremely small, in particular, smaller than nine milliards of decimals for the maximal possible weight function exp(−2πt. We also show how certain Fourier transforms of the logarithm of the Riemann zeta-function taken along the real (demiaxis are expressible via elementary functions plus logarithm of the gamma-function and definite integrals thereof, as well as certain sums over trivial and nontrivial Riemann function zeroes.
Om Prakash
2011-06-01
Full Text Available The present paper is concerned with the study of MHD free convective flow of a visco-elastic (Kuvshinski type dusty gas through a porous medium induced by the motion of a semi-infinite flat plate under the influence of radiative heat transfer moving with velocity decreasing exponentially with time. The expressions for velocity distribution of a dusty gas and dust particles, concentration profile and temperature field are obtained. The effect of Schmidt number (Sc, Magnetic field parameter (M and Radiation parameter (N on velocity distribution of dusty gas and dust particles, concentration and temperature distribution are discussed graphically.
The exponential rank of nonarchimedean exponential fields
Kuhlmann, Franz-Viktor; Kuhlmann, Salma
2000-01-01
For an exponential on a nonarchimedean ordered field, we introduce the notion of the exponential rank, in analogy to the rank of the field. This gives information about the growth rate of the exponential, and about the convex valuations on the field which are compatible with the exponential. We give several characterizations of these valuations, using maps induced by the exponential on the value group of the natural valuation and on the rank of the field. Finally, we construct exponential fie...
Factors that influence excessive gestational weight gain: moving beyond assessment and counselling.
Campbell, Emily E; Dworatzek, Paula D N; Penava, Debbie; de Vrijer, Barbra; Gilliland, Jason; Matthews, June I; Seabrook, Jamie A
2016-11-01
One in four Canadian adults is obese, and more women are entering pregnancy with a higher body mass index (BMI) than in the past. Pregnant women who are overweight or obese have a higher risk of pregnancy-related complications than women of normal weight. Gestational weight gain (GWG) is also associated with childhood obesity. Although the factors influencing weight gain during pregnancy are multifaceted, little is known about the social inequality of GWG. This review will address some of the socioeconomic factors and maternal characteristics influencing weight gain and the impact that excessive GWG has on health outcomes such as post-partum weight retention. The effects of an overweight or obese pre-pregnancy BMI on GWG and neonatal outcomes will also be addressed. The timing of weight gain is also important, as recommendations now include trimester-specific guidelines. While not conclusive, preliminary evidence suggests that excessive weight gain during the first trimester is most detrimental.
尹伟; 严威; 缪柏其
2012-01-01
The genenralized exponential predictor models for exchange rate forecasting based on weighted loss function is proposed.This method construct some exponential predictors through different smoothing parameters firstly, and then the weighted loss function based on absolute loss and square loss was proposed to select vaxiable,under which we combine exponential predictors to construct genneralized predictor model.At last compare with some existing methods,the models we proposed improves forecast precision.%本文提出在加权损失函数下构建汇率预测的广义指数预报因子模型。该方法首先选取有限个不同滑动参数构造指数预报因子，同时基于绝对值损失和平方损失的提出加权损失函数作为变量筛选的准则，然后在该准则下将指数预报因子进行线性组合，建立汇率预报的广义指数预报因子模型。本文最后用英镑／美元单周汇率数据与文献中的一些已有方法做比较，实证分析表明本文提出的方法在汇率预测效果上有较大改进。
Extended Poisson Exponential Distribution
Anum Fatima
2015-09-01
Full Text Available A new mixture of Modified Exponential (ME and Poisson distribution has been introduced in this paper. Taking the Maximum of Modified Exponential random variable when the sample size follows a zero truncated Poisson distribution we have derived the new distribution, named as Extended Poisson Exponential distribution. This distribution possesses increasing and decreasing failure rates. The Poisson-Exponential, Modified Exponential and Exponential distributions are special cases of this distribution. We have also investigated some mathematical properties of the distribution along with Information entropies and Order statistics of the distribution. The estimation of parameters has been obtained using the Maximum Likelihood Estimation procedure. Finally we have illustrated a real data application of our distribution.
Exponential Dowling structures
Ehrenborg, Richard
2010-01-01
The notion of exponential Dowling structures is introduced, generalizing Stanley's original theory of exponential structures. Enumerative theory is developed to determine the M\\"obius function of exponential Dowling structures, including a restriction of these structures to elements whose types satisfy a semigroup condition. Stanley's study of permutations associated with exponential structures leads to a similar vein of study for exponential Dowling structures. In particular, for the extended r-divisible partition lattice we show the M\\"obius function is, up to a sign, the number of permutations in the symmetric group on rn+k elements having descent set {r, 2r, ..., nr}. Using Wachs' original EL-labeling of the r-divisible partition lattice, the extended r-divisible partition lattice is shown to be EL-shellable.
Fletcher Carol E
2011-09-01
Full Text Available Abstract Background In January 2006, Veterans Affairs (VA disseminated the MOVE!® Weight Management Program to VA medical centers to address the high prevalence of overweight/obesity. In its second year, MOVE! implementation varied widely across facilities. The objective of this study was to understand contextual factors that facilitated or impeded implementation of MOVE! in VA medical centers in the second year after its dissemination. Methods We used an embedded mixed methods cross-sectional study design. Qualitative and quantitative data were collected simultaneously with the primary purpose to explore contextual factors most likely to influence MOVE! implementation effectiveness at five purposively selected facilities. Facilities were selected to maximize variation with respect to participation in MOVE! by candidate Veterans. Semi-structured phone interviews were conducted with 24 staff across the five facilities. Quantitative responses were elicited followed by open-ended questions. The quantitative measures were adapted from a published implementation model. Qualitative analysis was conducted using rigorous content analysis methods. Results Qualitative and quantitative data converged to strengthen findings that point to several recommendations. Management support can help increase visibility of the program, commit needed resources, and communicate the importance of implementation efforts. Establishing a receptive implementation climate can be accomplished by emphasizing the important role that weight management may have in reducing incidence and severity of obesity-related chronic conditions. Coalescing highly functioning multi-disciplinary teams was an essential step for more effective implementation of MOVE!. In some situations, local champions can overcome challenging barriers in facilities that lack sufficient management support. Conclusions Key organizational factors at local VA medical centers were strongly associated with MOVE
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
Exponential smoothing for financial time series data forecasting
Kuzhda, Tetyana Ivanivna
2014-05-01
Full Text Available The article begins with the formulation for predictive learning called exponential smoothing forecasting. The exponential smoothing is commonly applied to financial markets such as stock or bond, foreign exchange, insurance, credit, primary and secondary markets. The exponential smoothing models are useful in providing the valuable decision information for investors. Simple and double exponential smoothing models are two basic types of exponential smoothing method. The simple exponential smoothing method is suitable for financial time series forecasting for the specified time period. The simple exponential smoothing weights past observations with exponentially decreasing weights to forecast future values. The double exponential smoothing is a refinement of the simple exponential smoothing model but adds another component which takes into account any trend in the data. The double exponential smoothing is designed to address this type of data series by taking into account any trend in the data. Measurement of the forecast accuracy is described in this article. Finally, the quantitative value of the price per common share forecast using simple exponential smoothing is calculated. The applied recommendations concerning determination of the price per common share forecast using double exponential smoothing are shown in the article.
Methods of Fast Exponentiation
Mohammed A. Maitah
2010-01-01
Full Text Available Problem statement: Modular exponentiation constitutes the basis of many well-known and widely used public key cryptosystems. Approach: A fast portable modular exponentiation algorithm considerably enhanced the speed and applicability of these systems, also an efficient implementation of this algorithm was the key to high performance of such system. Results: In this study, two main approaches for solving this problem were proposed. The proposed approaches involved calculations without usage of extra operational memory for saving constants and calculations with usage of preliminary calculated constants. Conclusion/Recommendations: The estimation of complexity of the speedup and effectiveness of proposed approaches for the data were presented.
Exponential Polynomial Approximation with Unrestricted Upper Density
Xiang Dong YANG
2011-01-01
We take a new approach to obtaining necessary and sufficient conditions for the incompleteness of exponential polynomials in Lp/α, where Lp/α is the weighted Banach space of complex continuous functions f defined on the real axis (R)satisfying (∫+∞/-∞|f(t)|pe-α(t)dt)1/p, 1 < p < ∞, and α(t) is a nonnegative continuous function defined on the real axis (R). In this paper, the upper density of the sequence which forms the exponential polynomials is not required to be finite. In the study of weighted polynomial approximation, consideration of the case is new.
彭雯佳; 陆建平; 王鹤; 陈士跃; 金爱国; 王敏杰
2012-01-01
目的:以单侧大脑前循环动脉不同程度狭窄的患者为研究对象,比较DWI的拉伸指数模型、单指数模型的各参数值在左、右半球之间的差异.方法:对申请头颈部动脉CTA检查的患者,在无MRI检查禁忌及患者知情同意的情况下行单指数和拉伸指数模型的扩散加权检查.采用的b值序列是:0、5、10、20、50、100、200、400、600、1000、1500、2000、3000 s/mm2,通过工作站计算表观扩散系数(ADC)值、分布扩散系数(DDC)值和α值三个参数.根据颈内动脉系统是否狭窄及狭窄程度将患者分为A(无狭窄)、B(轻、中度狭窄)、C(重度狭窄或闭塞)三组,统计各组左右两侧大脑中动脉供血区的各参数值,运用非参数秩和检验法比较两侧值的组间差异及组内差异.结果:进入统计分析的患者共39例,其中A组11例,B组13例,C组15例.经统计学检验发现,ADC值、DDC值的左右侧差值及左右侧比值的对数值的各组间比较、C组的组内比较差异均有统计学意义(P＜0.05)；B组DDC值的左右侧差值及左右侧比值的对数值的组内比较差异均有统计学意义(P＜0.05)；B组ADC值的左右侧差值比较差异无统计学意义(P＞0.05),左右侧比值的对数值的比较差异有统计学意义(P＜0.05).α值的上述差异均无统计学意义(P＞0.05).结论:运用多b值DWI技术定量分析大脑前循环狭窄时,单指数模型的ADC值和拉伸指数模型的DDC值在无动脉狭窄和狭窄者之间的差异均有明显体现,而DDC值对不同程度狭窄者之间的差异更敏感.%Objective:To compare the differences of parameters of diffusion weighted imaging (DWI) with both stretched-exponential and mono-exponential model between left and right cerebral hemisphere in patients with unilateral ar-teriostenosis. Methods: Patients who underwent head-neck CTA scan in our hospital and had no MR imaging contraindication and signed the informed consent were included in our
Uniform Exponential Growth in Algebras /
Briggs, Christopher Alan
2013-01-01
We consider uniform exponential growth in algebras. We give conditions for the uniform exponential growth of descending-filtered algebras and prove that an N-graded algebra has uniform exponential growth if it has exponential growth. We use this to prove that Golod- Shafarevich algebras and group algebras of Golod- Shafarevich groups have uniform exponential growth. We prove that the twisted Laurent extension of a free commutative polynomial algebra with respect to an endomorphism with some e...
Estimating exponential scheduling preferences
Hjorth, Katrine; Börjesson, Maria; Engelson, Leonid
time by maximising expected total utility over the day, their departure times are conditional on rates of utility derived at these locations. For forecasting and economic evaluation of planning alternatives, it is desirable to have simple forms of utility rates with few parameters. Several forms...... the travel time is random, Noland and Small (1995) suggested using expected utility theory to derive the reduced form of expected travel time cost that includes the cost of TTV. For the α-β-γ formulation of scheduling preferences and exponential or uniform distribution of travel time, Noland and Small (1995....... The purpose of this paper is to explore how well these scheduling preferences explain behaviour, compared to other possible scheduling models, and whether empirical estimation of the more complex exponential scheduling preferences is feasible. We use data from a stated preference survey conducted among car...
Estimating exponential scheduling preferences
Hjorth, Katrine; Börjesson, Maria; Engelson, Leonid
time by maximising expected total utility over the day, their departure times are conditional on rates of utility derived at these locations. For forecasting and economic evaluation of planning alternatives, it is desirable to have simple forms of utility rates with few parameters. Several forms...... the travel time is random, Noland and Small (1995) suggested using expected utility theory to derive the reduced form of expected travel time cost that includes the cost of TTV. For the α-β-γ formulation of scheduling preferences and exponential or uniform distribution of travel time, Noland and Small (1995....... The purpose of this paper is to explore how well these scheduling preferences explain behaviour, compared to other possible scheduling models, and whether empirical estimation of the more complex exponential scheduling preferences is feasible. We use data from a stated preference survey conducted among car...
Exponential random graph models
Fronczak, Agata
2012-01-01
Nowadays, exponential random graphs (ERGs) are among the most widely-studied network models. Different analytical and numerical techniques for ERG have been developed that resulted in the well-established theory with true predictive power. An excellent basic discussion of exponential random graphs addressed to social science students and researchers is given in [Anderson et al., 1999][Robins et al., 2007]. This essay is intentionally designed to be more theoretical in comparison with the well-known primers just mentioned. Given the interdisciplinary character of the new emerging science of complex networks, the essay aims to give a contribution upon which network scientists and practitioners, who represent different research areas, could build a common area of understanding.
Possibilistic Exponential Fuzzy Clustering
Kiatichai Treerattanapitak; Chuleerat Jaruskulchai
2013-01-01
Generally,abnormal points (noise and outliers) cause cluster analysis to produce low accuracy especially in fuzzy clustering.These data not only stay in clusters but also deviate the centroids from their true positions.Traditional fuzzy clustering like Fuzzy C-Means (FCM) always assigns data to all clusters which is not reasonable in some circumstances.By reformulating objective function in exponential equation,the algorithm aggressively selects data into the clusters.However noisy data and outliers cannot be properly handled by clustering process therefore they are forced to be included in a cluster because of a general probabilistic constraint that the sum of the membership degrees across all clusters is one.In order to improve this weakness,possibilistic approach relaxes this condition to improve membership assignment.Nevertheless,possibilistic clustering algorithms generally suffer from coincident clusters because their membership equations ignore the distance to other clusters.Although there are some possibilistic clustering approaches that do not generate coincident clusters,most of them require the right combination of multiple parameters for the algorithms to work.In this paper,we theoretically study Possibilistic Exponential Fuzzy Clustering (PXFCM) that integrates possibilistic approach with exponential fuzzy clustering.PXFCM has only one parameter and not only partitions the data but also filters noisy data or detects them as outliers.The comprehensive experiments show that PXFCM produces high accuracy in both clustering results and outlier detection without generating coincident problems.
Paul Keriann H
2013-02-01
Full Text Available Abstract Background Few lifestyle interventions have successfully prevented excessive gestational weight gain. Understanding the program processes through which successful interventions achieve outcomes is important for the design of effective programs. The objective of this study was to evaluate the effect of the quantity and quality of participation in a healthy lifestyle intervention on risk of excessive gestational weight gain. Findings Pregnant women (N = 179 received five newsletters about weight, nutrition, and exercise plus postcards on which they were asked to set related goals and return to investigators. The quantity of participation (dose was defined as low for returning few or some vs. high for many postcards (N = 89, 49.7%. Quality of participation was low for setting few vs. high for some or many appropriate goals (N = 92, 51.4%. Fisher’s exact tests and multivariate logistic regression were used to analyze the effect of participation variables on the proportion with excessive weight gain. Quantity and quality of participation alone were each not significantly associated with excessive gestational weight gain, while quality of participation among those with high-levels of participation approached significance (p = 0.07. The odds of gaining excessively was decreased when women had both a high quantity and quality of participation (OR = 0.04, 95% CI = 0.005, 0.30. Conclusions Both quantity and quality of participation are important program process measures in evaluations of lifestyle interventions to promote healthy weight gain during pregnancy.
柴华; 梁彦刚; 唐国金
2014-01-01
Under the early warning of two passive satellite-borne sensors,the exponential weighted recursive least square method was applied to the burnout states estimation of ballistic targets.Due to the weighting factor can characterize the local quasi-linearity of the boost phase trajectory of the target,so to some extent the dilemma that generic polynomial cannot handle the whole boost phase of the target can be overcome.Through a dynamic analysis,the kinematic characteristics of boost phase target along the orientation of vertical surface were explored.On that basis,a novel boost phase motion model is proposed,which is more accurate than traditional planar motion model.Simulation results show that the proposed approach is superior to the traditional ones.%在双星预警条件下，将指数加权递归最小二乘算法应用于目标关机点状态估计问题中。通过引入加权因子对目标助推段运动的局部拟线性特性进行描述，从而在一定程度上克服了一般的线性多项式模型难以准确刻画整个助推段运动的难题。通过对助推段目标动力学特性的分析，考察了目标在垂直射面方向上的运动特性。在此基础上，提出了一种更为准确的助推段运动模型。仿真算例表明，所提出的关机点状态估计方法相对于传统的方法具有一定的优越性。
陈松灿; 蔡骏
2001-01-01
Wang和陈等利用各自提出的二值指数双向联想记忆模型（eBAM）及其改进型eBAM（IeBAM），分别构造了由多个eBAM和IeBAM组成的多重eBAM（Multi-eBAM）和多重IeBAM（Multi-IeBAM）的信念组合模型，使之可模拟多个专家的表决.该文在此基础上，借助陈提出的多值eBAM（MVeBAM）,提出了多重多值eBAM（Multi-MVeBAM），对Multi-eBAM和Multi-IeBAM进行了两方面的推广：一是将二值表示推广到多值表示，以此可以处理现实中的多值数据；二是将原有模型中具有同等权威度的各专家推广到各具不同的权威度的专家，以此模拟更实际的表决情形.文中借助能量函数证明了所提模型的渐近稳定性，以保证其实际可用.计算机模拟证实了模型的可行性.%Wang and Chen, together with their coworkers, adopted their binary exponential bidirectional associative memory(eBAM) and improved eBAM(IeBAM) to build their multiple eBAM(Multi-eBAM) and multiple IeBAM(Multi-IeBAM) belief combination models respectively composed of eBAM and IeBAM to mimic the voting of many experts. In this paper, on the basis of their models and with the use of Chen multivalued eBAM(MVeBAM), a new multiple weighted MVeBAM(Multi-WMVeBAM) model is presented which extends both Multi-eBAM and Multi-IeBAM in two aspects: one is the extension from binary to multivalued data format , the other is to apply different weights to all experts so that the proposed model can mimic a voting process in practice. By defining an energy function, the stability of the Multi-WMVeBAM in synchronous and asynchronous updating modes is proven which ensures its applicability in the real world. Finally computer simulations confirm its feasiblity.
Kuhlmann, Salma
1999-01-01
Model theoretic algebra has witnessed remarkable progress in the last few years. It has found profound applications in other areas of mathematics, notably in algebraic geometry and in singularity theory. Since Wilkie's results on the o-minimality of the expansion of the reals by the exponential function, and most recently even by all Pfaffian functions, the study of o-minimal expansions of the reals has become a fascinating topic. The quest for analogies between the semi-algebraic case and the o-minimal case has set a direction to this research. Through the Artin-Schreier Theory of real closed
El-Bachir Yallaoui
2012-06-01
Full Text Available In this article, we introduce a new class of analytic functions of the unit disc $mathbf{D}$ namely the Exponential Cauchy Transforms $mathbf{{K}_{e}}$ defined by f(z= {displaystyleint_{mathbf{T}}} expleft[ Kleft( xzight ight] dmu(x where $Kleft( zight =left( 1-zight ^{-1}$ is classical Cauchy kernel and $mu(x$ is a complex Borel measures and $x$ belongs to the unit circle $mathbf{T}$ . We use Laguerre polynomials to explore the coefficients of the Taylor expansions of the kernel and Peron's formula to study the asymptotic behavior of the Taylor coefficients. Finally we investigate relationships between our new class $mathbf{{K}_{e}}$, the classical Cauchy space $mathbf{K}$ and the Hardy spaces $H^{p}$.
Iyer-Biswas, Srividya; Wright, Charles; Henry, Jon; Burov, Stas; Lin, Yihan; Crosson, Sean; Dinner, Aaron; Scherer, Norbert
2013-03-01
The interplay between growth and division of cells is has been studied in the context of exponential growth of bacterial cells (in suitable conditions) for decades. However, bulk culture studies obscure phenomena that manifest in single cells over many generations. We introduce a unique technology combining microfluidics, single-cell imaging, and quantitative analysis. This enables us to track the growth of single Caulobacter crescentus stalked cells over hundreds of generations. The statistics that we extract indicate a size thresholding mechanism for cell division and a non-trivial scaling collapse of division time distributions at different temperatures. In this talk I shall discuss these observations and a stochastic model of growth and division that captures all our observations with no free parameters.
Bataille, Veronique
2013-11-01
There are many observations regarding the behaviour of melanoma which points away from sunshine as the main cause of this tumour. Incidence data shows that the increase is mostly seen for thin melanomas which cannot be attributed to sun exposure but increasing screening over the last 20 years. Melanoma behaves in a similar fashion all over the world regarding age of onset, gender differences and histological subtypes. An excess of naevi is the strongest risk factor for melanoma and their appearance and involution throughout life, and the differences in naevus distribution according to gender is giving us a lot of clues about melanoma biology. Melanoma like all cancers is a complex disease with the involvement of many common and low penetrance genes many of them involved in pigmentation and naevogenesis but these only explain a very small portion of melanoma susceptibility. Genes involved in melanocyte differentiation early on in embryogenesis are also becoming relevant for melanoma initiation and progression. Reduced senescence and longevity as well as body weight and energy expenditure are also relevant for melanoma susceptibility. These observations with links between melanoma and non-sun related phenotypes as well as gene discoveries should help to assess the relative contribution of genetic and environmental factors in its causation.
Fermi, Enrico
The Patent contains an extremely detailed description of an atomic pile employing natural uranium as fissile material and graphite as moderator. It starts with the discussion of the theory of the intervening phenomena, in particular the evaluation of the reproduction or multiplication factor, K, that is the ratio of the number of fast neutrons produced in one generation by the fissions to the original number of fast neutrons, in a system of infinite size. The possibility of having a self-maintaining chain reaction in a system of finite size depends both on the facts that K is greater than unity and the overall size of the system is sufficiently large to minimize the percentage of neutrons escaping from the system. After the description of a possible realization of such a pile (with many detailed drawings), the various kinds of neutron losses in a pile are depicted. Particularly relevant is the reported "invention" of the exponential experiment: since theoretical calculations can determine whether or not a chain reaction will occur in a give system, but can be invalidated by uncertainties in the parameters of the problem, an experimental test of the pile is proposed, aimed at ascertaining if the pile under construction would be divergent (i.e. with a neutron multiplication factor K greater than 1) by making measurements on a smaller pile. The idea is to measure, by a detector containing an indium foil, the exponential decrease of the neutron density along the length of a column of uranium-graphite lattice, where a neutron source is placed near its base. Such an exponential decrease is greater or less than that expected due to leakage, according to whether the K factor is less or greater than 1, so that this experiment is able to test the criticality of the pile, its accuracy increasing with the size of the column. In order to perform this measure a mathematical description of the effect of neutron production, diffusion, and absorption on the neutron density in the
On exponentiable soft topological spaces
Ghasem Mirhosseinkhani
2016-11-01
Full Text Available An object $X$ of a category $mathbf{C}$ with finite limits is called exponentiable if the functor $-times X:mathbf{C}rightarrow mathbf{C}$ has a right adjoint. There are many characterizations of the exponentiable spaces in the category $mathbf{Top}$ of topological spaces. Here, we study the exponentiable objects in the category $mathbf{STop}$ of soft topological spaces which is a generalization of the category $mathbf{Top}$. We investigate the exponentiability problem and give a characterization of exponentiable soft spaces. Also wegive the definition of exponential topology on the lattice of soft open sets of a soft space and present some characterizations of it.
Ahmad Mamandi
2011-01-01
Full Text Available In this study, the nonlinear vibrations analysis of an inclined pinned-pinned self-weight Timoshenko beam made of linear, homogenous and isotropic material with a constant cross section and finite length subjected to a traveling mass/force with constant velocity is investigated. The nonlinear coupled partial differential equations of motion for the rotation of warped cross section, longitudinal and transverse displacements are derived using the Hamilton's principle. These nonlinear coupled PDEs are solved by applying the Galerkin's method to obtain dynamic responses of the beam. The dynamic magnification factor and normalized time histories of mid-point of the beam are obtained for various load velocity ratios and the outcome results have been compared to the results with those obtained from linear solution. The influence of the large deflections caused by a stretching effect due to the beam's fixed ends is captured. It was seen that existence of quadratic-cubic nonlinear terms in the nonlinear governing coupled PDEs of motion causes stiffening (hardening behavior of the dynamic responses of the self-weight beam under the act of a traveling mass as well as equivalent concentrated moving force. Furthermore, in a case where the object leaves the beam, its planar motion path is derived and the targeting accuracy is investigated and compared with those from the rigid solution assumption.
Expectation Propagation for Exponential Families
Seeger, Matthias
2005-01-01
This is a tutorial describing the Expectation Propagation (EP) algorithm for a general exponential family. Our focus is on simplicity of exposition. Although the overhead of translating a specific model into its exponential family representation can be considerable, many apparent complications of EP can simply be sidestepped by working in this canonical representation.
Multivariate Matrix-Exponential Distributions
Bladt, Mogens; Nielsen, Bo Friis
2010-01-01
-exponential distributions. We prove a characterization that states that a distribution is an MVME distribution if and only if all non-negative, non-null linear combinations of the coordinates have a univariate matrix-exponential distribution. This theorem is analog to a well-known characterization theorem...
Is Radioactive Decay Really Exponential?
Aston, Philip J
2012-01-01
Radioactive decay of an unstable isotope is widely believed to be exponential. This view is supported by experiments on rapidly decaying isotopes but is more difficult to verify for slowly decaying isotopes. The decay of 14C can be calibrated over a period of 12,550 years by comparing radiocarbon dates with dates obtained from dendrochronology. It is well known that this approach shows that radiocarbon dates of over 3,000 years are in error, which is generally attributed to past variation in atmospheric levels of 14C. We note that predicted atmospheric variation (assuming exponential decay) does not agree with results from modelling, and that theoretical quantum mechanics does not predict exact exponential decay. We give mathematical arguments that non-exponential decay should be expected for slowly decaying isotopes and explore the consequences of non-exponential decay. We propose an experimental test of this prediction of non-exponential decay for 14C. If confirmed, a foundation stone of current dating meth...
Universality in stochastic exponential growth.
Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R
2014-07-11
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
Exponential Expansion in Evolutionary Economics
Frederiksen, Peter; Jagtfelt, Tue
2013-01-01
concepts are described in detail. Taken together it provides the rudimentary aspects of an economic system within an analytical perspective. It is argued that the main dynamic processes of the evolutionary perspective can be reduced to these four concepts. The model and concepts are evaluated in the light...... of Thomas Kuhn’s notion of scientific paradigms and criteria for a good theory (1977, 1996). The paper thus aims to augment and assimilate the fragmented and scattered body of concepts presently residing within the field of evolutionary economics, by presenting an intuitive framework, applicable within...... to this problem is proposed in the form of a model of exponential expansion. The model outlines the overall structure and function of the economy as exponential expansion. The pictographic model describes four axiomatic concepts and their exponential nature. The interactive, directional, emerging and expanding...
On the role of exponential splines in image interpolation.
Kirshner, Hagai; Porat, Moshe
2009-10-01
A Sobolev reproducing-kernel Hilbert space approach to image interpolation is introduced. The underlying kernels are exponential functions and are related to stochastic autoregressive image modeling. The corresponding image interpolants can be implemented effectively using compactly-supported exponential B-splines. A tight l(2) upper-bound on the interpolation error is then derived, suggesting that the proposed exponential functions are optimal in this regard. Experimental results indicate that the proposed interpolation approach with properly-tuned, signal-dependent weights outperforms currently available polynomial B-spline models of comparable order. Furthermore, a unified approach to image interpolation by ideal and nonideal sampling procedures is derived, suggesting that the proposed exponential kernels may have a significant role in image modeling as well. Our conclusion is that the proposed Sobolev-based approach could be instrumental and a preferred alternative in many interpolation tasks.
Phenomenology of stochastic exponential growth
Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya
2017-06-01
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.
Bilateral matrix-exponential distributions
Bladt, Mogens; Esparza, Luz Judith R; Nielsen, Bo Friis
2012-01-01
In this article we define the classes of bilateral and multivariate bilateral matrix-exponential distributions. These distributions have support on the entire real space and have rational moment-generating functions. These distributions extend the class of bilateral phasetype distributions of [1]...
Exponential convergence rate in entropy
Mu-Fa Chen
2007-01-01
The exponential convergence rate in entropy is studied for symmetric forms, with a specia! attention to the Markov chain with a state space having two points only. Some upper and lower bounds of the rate are obtained and five examples with precise or qualitatively exact estimates are presented.
Linear or Exponential Number Lines
Stafford, Pat
2011-01-01
Having decided to spend some time looking at one's understanding of numbers, the author was inspired by "Alex's Adventures in Numberland," by Alex Bellos to look at one's innate appreciation of number. Bellos quotes research studies suggesting that an individual's natural appreciation of numbers is more likely to be exponential rather than linear,…
Limit laws for exponential families
Balkema, August A.; Klüppelberg, Claudia; Resnick, Sidney I.
1999-01-01
For a real random variable [math] with distribution function [math] , define ¶ [math] ¶ The distribution [math] generates a natural exponential family of distribution functions [math] , where ¶ [math] ¶ We study the asymptotic behaviour of the distribution functions [math] as [math] increases to [math] . If [math] then [math] pointwise on [math] . It may still be possible to obtain a non-degenerate weak limit law [math] by choosing suitable scaling and centring constants [math] an...
Limit laws for exponential families
Balkema, August A.; Klüppelberg, Claudia; Resnick, Sidney I.
1999-01-01
For a real random variable [math] with distribution function [math] , define ¶ [math] ¶ The distribution [math] generates a natural exponential family of distribution functions [math] , where ¶ [math] ¶ We study the asymptotic behaviour of the distribution functions [math] as [math] increases to [math] . If [math] then [math] pointwise on [math] . It may still be possible to obtain a non-degenerate weak limit law [math] by choosing suitable scaling and centring constants [math] an...
Wararit PANICHKITKOSOLKUL
2012-09-01
Full Text Available Guttman and Tiao [1], and Chang [2] showed that the effect of outliers may cause serious bias in estimating autocorrelations, partial correlations, and autoregressive moving average parameters (cited in Chang et al. [3]. This paper presents a modified weighted symmetric estimator for a Gaussian first-order autoregressive AR(1 model with additive outliers. We apply the recursive median adjustment based on an exponentially weighted moving average (EWMA to the weighted symmetric estimator of Park and Fuller [4]. We consider the following estimators: the weighted symmetric estimator (, the recursive mean adjusted weighted symmetric estimator ( proposed by Niwitpong [5], the recursive median adjusted weighted symmetric estimator ( proposed by Panichkitkosolkul [6], and the weighted symmetric estimator using adjusted recursive median based on EWMA (. Using Monte Carlo simulations, we compare the mean square error (MSE of estimators. Simulation results have shown that the proposed estimator, , provides a MSE lower than those of , and for almost all situations.
An exponentiation method for XML element retrieval.
Wichaiwong, Tanakorn
2014-01-01
XML document is now widely used for modelling and storing structured documents. The structure is very rich and carries important information about contents and their relationships, for example, e-Commerce. XML data-centric collections require query terms allowing users to specify constraints on the document structure; mapping structure queries and assigning the weight are significant for the set of possibly relevant documents with respect to structural conditions. In this paper, we present an extension to the MEXIR search system that supports the combination of structural and content queries in the form of content-and-structure queries, which we call the Exponentiation function. It has been shown the structural information improve the effectiveness of the search system up to 52.60% over the baseline BM25 at MAP.
Circuit design and exponential stabilization of memristive neural networks.
Wen, Shiping; Huang, Tingwen; Zeng, Zhigang; Chen, Yiran; Li, Peng
2015-03-01
This paper addresses the problem of circuit design and global exponential stabilization of memristive neural networks with time-varying delays and general activation functions. Based on the Lyapunov-Krasovskii functional method and free weighting matrix technique, a delay-dependent criteria for the global exponential stability and stabilization of memristive neural networks are derived in form of linear matrix inequalities (LMIs). Two numerical examples are elaborated to illustrate the characteristics of the results. It is noteworthy that the traditional assumptions on the boundness of the derivative of the time-varying delays are removed.
Cosmological evolution in exponential gravity
Bamba, Kazuharu; Geng, Chao-Qiang; Lee, Chung-Chi, E-mail: bamba@phys.nthu.edu.tw, E-mail: geng@phys.nthu.edu.tw, E-mail: g9522545@oz.nthu.edu.tw [Department of Physics, National Tsing Hua University, Hsinchu, Taiwan (China)
2010-08-01
We explore the cosmological evolution in the exponential gravity f(R) = R+c{sub 1}(1−e{sup −c{sub 2}R}) (c{sub 1,2} = constant). We summarize various viability conditions and explicitly demonstrate that the late-time cosmic acceleration following the matter-dominated stage can be realized. We also study the equation of state for dark energy and confirm that the crossing of the phantom divide from the phantom phase to the non-phantom (quintessence) one can occur. Furthermore, we illustrate that the cosmological horizon entropy globally increases with time.
Cosmological evolution in exponential gravity
Bamba, Kazuharu; Lee, Chung-Chi
2010-01-01
We explore the cosmological evolution in the exponential gravity $f(R)=R +c_1 \\left(1-e^{- c_2 R} \\right)$ ($c_{1, 2} = \\mathrm{constant}$). We summarize various viability conditions and explicitly demonstrate that the late-time cosmic acceleration following the matter-dominated stage can be realized. We also study the equation of state for dark energy and confirm that the crossing of the phantom divide from the phantom phase to the non-phantom (quintessence) one can occur. Furthermore, we illustrate that the cosmological horizon entropy globally increases with time.
Rajchakit, G; Saravanakumar, R; Ahn, Choon Ki; Karimi, Hamid Reza
2017-02-01
This article examines the exponential stability analysis problem of generalized neural networks (GNNs) including interval time-varying delayed states. A new improved exponential stability criterion is presented by establishing a proper Lyapunov-Krasovskii functional (LKF) and employing new analysis theory. The improved reciprocally convex combination (RCC) and weighted integral inequality (WII) techniques are utilized to obtain new sufficient conditions to ascertain the exponential stability result of such delayed GNNs. The superiority of the obtained results is clearly demonstrated by numerical examples.
On uniform exponential growth for solvable groups
Breuillard, Emmanuel
2006-01-01
Using a theorem of J. Groves we give a ping-pong proof of Osin's uniform exponential growth for solvable groups. We discuss slow exponential growth and show that this phenomenon disappears as one passes to a finite index subgroup.
Teaching about Exponential Growth in Social Studies.
Allen, Rodney F.; LaHart, David E.
1984-01-01
Characteristics of exponential growth which should be taught in social studies classes are listed, and learning activities dealing with exponential growth which can be used in secondary social studies classes are provided. (RM)
Notes on the Stochastic Exponential and Logarithm
Larsson, Martin; Ruf, Johannes
2017-01-01
Stochastic exponentials are defined for semimartingales on stochastic intervals, and stochastic logarithms are defined for nonnegative semimartingales, up to the first time the semimartingale hits zero continuously. In the case of (nonnegative) local supermartingales, these two stochastic transformations are inverse to each other. The reciprocal of a stochastic exponential is again a stochastic exponential on a stochastic interval.
王翠巧; 邓冠铁
2015-01-01
将 Malliavin 关于一元解析函数唯一性的结果推广到多元情形，利用所得结果得到了多元复指数系不完备的充分必要条件及其闭包的特征。%In this paper,Malliavin’s uniqueness theorem on analytic functions of one complex variable is generalized to analytic functions of several complex variables,and this is used to obtain a necessary and sufficient condition of incompleteness of complex exponential system and to give a characteristic of its closure.
Robertson, Stanley L
2016-01-01
Magnetic Eternally Collapsing Objects (MECO) have been proposed as the central engines of galactic black hole candidates (GBHC) and supermassive active galactic nuclei (AGN). Previous work has shown that their luminosities and spectral and timing characteristics are in good agreement with observations. These features and the formation of jets are generated primarily by the interactions of accretion disks with an intrinsically magnetic central MECO. The interaction of accretion disks with the anchored magnetic fields of the central objects permits a unified description of properties for GBHC, AGN, neutron stars in low mass x-ray binaries and dwarf novae systems. The previously published MECO models have been based on a quasistatic Schwarzschild metric of General Relativity; however, the only essential feature of this metric is its ability to produce extreme gravitational redshifts. For reasons discussed in this article, an alternative development based on a quasistatic exponential metric is considered here.
Observational Constraints on Exponential Gravity
Yang, Louis; Luo, Ling-Wei; Geng, Chao-Qiang
2010-01-01
We study the observational constraints on the exponential gravity model of f(R)=-beta*Rs(1-e^(-R/Rs)). We use the latest observational data including Supernova Cosmology Project (SCP) Union2 compilation, Two-Degree Field Galaxy Redshift Survey (2dFGRS), Sloan Digital Sky Survey Data Release 7 (SDSS DR7) and Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP7) in our analysis. From these observations, we obtain a lower bound on the model parameter beta at 1.27 (95% CL) but no appreciable upper bound. The constraint on the present matter density parameter is 0.245< Omega_m^0<0.311 (95% CL). We also find out the best-fit value of model parameters on several cases.
UCB Algorithm for Exponential Distributions
Jouini, Wassim
2012-01-01
We introduce in this paper a new algorithm for Multi-Armed Bandit (MAB) problems. A machine learning paradigm popular within Cognitive Network related topics (e.g., Spectrum Sensing and Allocation). We focus on the case where the rewards are exponentially distributed, which is common when dealing with Rayleigh fading channels. This strategy, named Multiplicative Upper Confidence Bound (MUCB), associates a utility index to every available arm, and then selects the arm with the highest index. For every arm, the associated index is equal to the product of a multiplicative factor by the sample mean of the rewards collected by this arm. We show that the MUCB policy has a low complexity and is order optimal.
PARAMETER ESTIMATION OF EXPONENTIAL DISTRIBUTION
XU Haiyan; FEI Heliang
2005-01-01
Because of the importance of grouped data, many scholars have been devoted to the study of this kind of data. But, few documents have been concerned with the threshold parameter. In this paper, we assume that the threshold parameter is smaller than the first observing point. Then, on the basis of the two-parameter exponential distribution, the maximum likelihood estimations of both parameters are given, the sufficient and necessary conditions for their existence and uniqueness are argued, and the asymptotic properties of the estimations are also presented, according to which approximate confidence intervals of the parameters are derived. At the same time, the estimation of the parameters is generalized, and some methods are introduced to get explicit expressions of these generalized estimations. Also, a special case where the first failure time of the units is observed is considered.
Yang Dai; YunZe Cai; Xiao-Ming Xu
2009-01-01
Exponential estimates and sufficient conditions for the exponential synchronization of complex dynamical networks with bounded time-varying delays are given in terms of linear matrix inequalities (LMIs). A generalized complex networks model involving both neutral delays and retarded ones is presented. The exponential synchronization problem of the complex networks is converted equivalently into the exponential stability problem of a group of uncorrelated delay functional differential equations with mixed time-varying delays. By utilizing the free weighting matrix technique, a less conservative delay-dependent synchronization criterion is derived. An illustrative example is provided to demonstrate the effectiveness of the proposed method.
Recursive Least Squares Estimator with Multiple Exponential Windows in Vector Autoregression
Hong-zhi An; Zhi-guo Li
2002-01-01
In the parameter tracking of time-varying systems, the ordinary method is weighted least squares with the rectangular window or the exponential window. In this paper we propose a new kind of sliding window called the multiple exponential window, and then use it to fit time-varying Gaussian vector autoregressive models. The asymptotic bias and covariance of the estimator of the parameter for time-invariant models are also derived. Simulation results show that the multiple exponential windows have better parameter tracking effect than rectangular windows and exponential ones.
Nonlinear Schrodinger elliptic systems involving exponential critical growth in R^2
Francisco S. B. Albuquerque Albuquerque
2014-02-01
Full Text Available This article concerns the existence and multiplicity of solutions for elliptic systems with weights, and nonlinearities having exponential critical growth. Our approach is based on the Trudinger-Moser inequality and on a minimax theorem.
徐宝; 姜玉秋; 滕飞; 宋立新
2012-01-01
For exponential model c(x, n)θ-ve-T(x)/θ, we dealt with the Bayes estimator and admissible estimator of scale parameter θ under a new loss-weighted p, q symmetric entropy loss L(θ,d) = θp/pδp+δq/qθq-2(p,q＞0) which deduced from entropy that related to theory of information. The general and exact form of the Bayes estimator were obtained. The admissibility and inadmissibility of a class of linear estimators of the form cT(X) + d were studied. The invariance of the two estimators was proved using the theorem integral transform.%在由信息论中的熵演绎出的一种新损失-加权p,q对称熵损失L(θ,δ)=θp/pδp+δq/qθq -2(p,q＞0)下,研究了一类指数分布模型c(x,n)θ-ve-T(x)/θ的参数θ的Bayes估计的一般形式与精确形式,讨论了参数θ的形如cT(X)+d的一类估计的可容许性与不可容许性,并应用积分变换定理证明了参数θ的Bayes估计与可容许估计具有不变性.
Exponential Stabilization of Underactuated Vehicles
Pettersen, K.Y.
1996-12-31
Underactuated vehicles are vehicles with fewer independent control actuators than degrees of freedom to be controlled. Such vehicles may be used in inspection of sub-sea cables, inspection and maintenance of offshore oil drilling platforms, and similar. This doctoral thesis discusses feedback stabilization of underactuated vehicles. The main objective has been to further develop methods from stabilization of nonholonomic systems to arrive at methods that are applicable to underactuated vehicles. A nonlinear model including both dynamics and kinematics is used to describe the vehicles, which may be surface vessels, spacecraft or autonomous underwater vehicles (AUVs). It is shown that for a certain class of underactuated vehicles the stabilization problem is not solvable by linear control theory. A new stability result for a class of homogeneous time-varying systems is derived and shown to be an important tool for developing continuous periodic time-varying feedback laws that stabilize underactuated vehicles without involving cancellation of dynamics. For position and orientation control of a surface vessel without side thruster a new continuous periodic feedback law is proposed that does not cancel any dynamics, and that exponentially stabilizes the origin of the underactuated surface vessel. A further issue considered is the stabilization of the attitude of an AUV. Finally, the thesis discusses stabilization of both position and attitude of an underactuated AUV. 55 refs., 28 figs.
Theory, computation, and application of exponential splines
Mccartin, B. J.
1981-01-01
A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.
Guo Yan
2007-01-01
@@ China has already become the world's largest manufacturer of cement,copper and steel.Chinese producers have moved onto the world stage and dominated the global consumer market from textiles to electronics with amazing speed and efficiency.
Generalized exponential input-to-state stability of nonlinear systems with time delay
Sun, Fenglan; Gao, Lingxia; Zhu, Wei; Liu, Feng
2017-03-01
This paper studies the general input-to-state stability problem of the nonlinear delay systems. By employing Lypaunov-Razumikhin technique, several general input-to-state stability concepts, that is generalized globally exponential integral input-to-state stability (GGE-iISS), generalized globally integral exponential integral input-to-state stability (GGIE-iISS), and eλt-weighted generalized globally integral exponential integral input-to-state stability (eλt-weighted GGIE-iISS) are studied. An example is given to illustrate the correctness of the obtained theoretical results.
Generalised Exponential Families and Associated Entropy Functions
Jan Naudts
2008-07-01
Full Text Available A generalised notion of exponential families is introduced. It is based on the variational principle, borrowed from statistical physics. It is shown that inequivalent generalised entropy functions lead to distinct generalised exponential families. The well-known result that the inequality of CramÃ‚Â´er and Rao becomes an equality in the case of an exponential family can be generalised. However, this requires the introduction of escort probabilities.
Exponential Observers for Lotka-Volterra Systems
Dr. V. Sundarapandian
2011-03-01
Full Text Available This paper solves the exponential observer design problem for Lotka-Volterra systems. Explicitly, Sundarapandian’s theorem (2002 for observer design for exponential observer design is used to solve the nonlinear observer design problem for 2-species, 3-species and 4-species Lotka-Volterra systems. Numerical examples are provided to illustrate the effectiveness of the proposed exponential observer design for the Lotka-Volterra systems.
On the exponentials of some structured matrices
Ramakrishna, Viswanath; Costa, F [Department of Mathematical Sciences and Center for Signals, Systems and Communications, University of Texas at Dallas, PO Box 830688, Richardson, TX 75083 (United States)
2004-12-03
This paper provides explicit techniques to compute the exponentials of a variety of structured 4 x 4 matrices. The procedures are fully algorithmic and can be used to find the desired exponentials in closed form. With one exception, they require no spectral information about the matrix being exponentiated. They rely on a mixture of Lie theory and one particular Clifford algebra isomorphism. These can be extended, in some cases, to higher dimensions when combined with techniques such as Givens rotations.
The Matrix exponential, Dynamic Systems and Control
Poulsen, Niels Kjølstad
2004-01-01
The matrix exponential can be found in various connections in analysis and control of dynamic systems. In this short note we are going to list a few examples. The matrix exponential usably pops up in connection to the sampling process, whatever it is in a deterministic or a stochastic setting...
The Ronkin number of an exponential sum
Silipo, James
2011-01-01
We give an intrinsic estimate of the number of connected components of the complementary set to the amoeba of an exponential sum with real spectrum improving the result of Forsberg, Passare and Tsikh in the polynomial case and that of Ronkin in the exponential one.
The Matrix exponential, Dynamic Systems and Control
Poulsen, Niels Kjølstad
2004-01-01
The matrix exponential can be found in various connections in analysis and control of dynamic systems. In this short note we are going to list a few examples. The matrix exponential usably pops up in connection to the sampling process, whatever it is in a deterministic or a stochastic setting...
On level-transitivity and exponential growth
Klimann, Ines
2016-01-01
We prove that if the group generated by a Mealy automaton acts level-transitively on a regular rooted tree, then the semigroup generated by the dual automaton has exponential growth, hence giving a decision procedure of exponential growth for a restricted family of automaton semigroups.
q-exponentials on quantum spaces
Wachter, H. [Ludwig-Maximilians-Universitaet, Sektion Physik, Muenchen (Germany)
2004-10-01
We present explicit formulae for q-exponentials on quantum spaces which could be of particular importance in physics, i.e. the q-deformed Minkowski space and the q-deformed Euclidean space with two, three or four dimensions. Furthermore, these formulae can be viewed as 2-, 3- or 4-dimensional analogues of the well-known q-exponential function. (orig.)
Weighted approximation with varying weight
Totik, Vilmos
1994-01-01
A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.
Berthelot, Geoffroy; Len, Stéphane; Hellard, Philippe; Tafflet, Muriel; Guillaume, Marion; Vollmer, Jean-Claude; Gager, Bruno; Quinquis, Laurent; Marc, Andy; Toussaint, Jean-François
2012-08-01
The physiological parameters characterizing human capacities (the ability to move, reproduce or perform tasks) evolve with ageing: performance is limited at birth, increases to a maximum and then decreases back to zero at the day of death. Physical and intellectual skills follow such a pattern. Here, we investigate the development of sport and chess performances during the lifetime at two different scales: the individual athletes' careers and the world record by age class in 25 Olympic sports events and in grandmaster chess players. For all data sets, a biphasic development of growth and decline is described by a simple model that accounts for 91.7% of the variance at the individual level and 98.5% of the variance at the species one. The age of performance peak is computed at 26.1 years old for the events studied (26.0 years old for track and field, 21.0 years old for swimming and 31.4 years old for chess). The two processes (growth and decline) are exponential and start at age zero. Both were previously demonstrated to happen in other human and non-human biological functions that evolve with age. They occur at the individual and species levels with a similar pattern, suggesting a scale invariance property.
Comparing exponential and exponentiated models of drug demand in cocaine users.
Strickland, Justin C; Lile, Joshua A; Rush, Craig R; Stoops, William W
2016-12-01
Drug purchase tasks provide rapid and efficient measurement of drug demand. Zero values (i.e., prices with zero consumption) present a quantitative challenge when using exponential demand models that exponentiated models may resolve. We aimed to replicate and advance the utility of using an exponentiated model by demonstrating construct validity (i.e., association with real-world drug use) and generalizability across drug commodities. Participants (N = 40 cocaine-using adults) completed Cocaine, Alcohol, and Cigarette Purchase Tasks evaluating hypothetical consumption across changes in price. Exponentiated and exponential models were fit to these data using different treatments of zero consumption values, including retaining zeros or replacing them with 0.1, 0.01, or 0.001. Excellent model fits were observed with the exponentiated model. Means and precision fluctuated with different replacement values when using the exponential model but were consistent for the exponentiated model. The exponentiated model provided the strongest correlation between derived demand intensity (Q0) and self-reported free consumption in all instances (Cocaine r = .88; Alcohol r = .97; Cigarette r = .91). Cocaine demand elasticity was positively correlated with alcohol and cigarette elasticity. Exponentiated parameters were associated with real-world drug use (e.g., weekly cocaine use) whereas these correlations were less consistent for exponential parameters. Our findings show that selection of zero replacement values affects demand parameters and their association with drug-use outcomes when using the exponential model but not the exponentiated model. This work supports the adoption of the exponentiated demand model by replicating improved fit and consistency and demonstrating construct validity and generalizability. (PsycINFO Database Record (c) 2016 APA, all rights reserved).
Global exponential stability of Hopfield-type neural network and its applications
梁学斌; 吴立德
1995-01-01
If the matrix measure of connection weight of Hopfield-type continuous feedback neural network is less than the reciprocal of maximal product of resistance and gain constants, then the network system is globally and exponentially stable. The above reciprocal is a sharp upper bound of matrix measure of connection weight which guarantees that the above conclusion holds. The above result answers partially the open problem proposed by Vidyasagar recently, i. e whether neural network with "nearly" symmetric connection weight can exhibit limit cycles. The relation between the network time constant and the global exponential convergence rate is pointed out, and application to optimization computation of our results is also given.
A nanostructured surface increases friction exponentially at the solid-gas interface
Phani, Arindam; Hawk, J E; Prashanthi, Kovur; Thundat, Thomas
2016-01-01
According to Stokes' law, a moving solid surface experiences dissipation that is linearly related to its velocity and the viscosity of the medium. This linear dependence on viscosity forms the basis for many characterization techniques for liquids. Unlike viscosities of different liquids, viscosities of gases vary only in a narrow range which limits their use as an effective characterization parameter using moving structures. Here we report experimental results of dissipation showing exponential dependence on viscosity for oscillating surfaces modified with nanostructures. The surface nanostructures alter solid-gas interplay greatly, amplifying the dissipation response exponentially for even minute variations in viscosity. Nanostructured resonator thus allows discrimination of otherwise narrow range of gaseous viscosity making it an ideal detection parameter for analysis. We attribute the observed exponential enhancement to the stochastic nature of interactions of many coupled nanostructures with the gas medi...
An Exponential Bound for Cox Regression☆
Kosorok, M. R.
2012-01-01
We present an asymptotic exponential bound for the deviation of the survival function estimator of the Cox model. We show that the bound holds even when the proportional hazards assumption does not hold. PMID:23565013
An Exponential Bound for Cox Regression.
Goldberg, Y; Kosorok, M R
2012-07-01
We present an asymptotic exponential bound for the deviation of the survival function estimator of the Cox model. We show that the bound holds even when the proportional hazards assumption does not hold.
When economic growth is less than exponential
Groth, Christian; Koch, Karl-Josef; Steger, Thomas
2010-01-01
This paper argues that growth theory needs a more general notion of "regularity" than that of exponential growth. We suggest that paths along which the rate of decline of the growth rate is proportional to the growth rate itself deserve attention. This opens up for considering a richer set of par......) serves as illustration that a continuum of "regular" growth processes fill the whole range between exponential growth and complete stagnation....
When economic growth is less than exponential
Groth, Christian; Koch, Karl-Josef; Steger, Thomas M.
2009-01-01
This paper argues that growth theory needs a more general notion of “regularity” than that of exponential growth. We suggest that paths along which the rate of decline of the growth rate is proportional to the growth rate itself deserve attention. This opens up for considering a richer set of parameter combinations than in standard growth models. And it avoids the usual oversimplistic dichotomy of either exponential growth or stagnation. Allowing zero population growth in three ...
Continued Fraction Algorithm for Matrix Exponentials
无
2001-01-01
A recursive rational algorithm for matrix exponentials was obtained by making use of the generalized inverse of a matrix in this paper. On the basis of the n-th convergence of Thiele-type continued fraction expansion, a new type of the generalized inverse matrix-valued Padé approximant (GMPA) for matrix exponentials was defined and its remainder formula was proved. The results of this paper were illustrated by some examples.
Bachoc, Christine; Cohen, Gerard; Sole, Patrick; Tchamkerten, Aslan
2010-01-01
The maximum size of a binary code is studied as a function of its length N, minimum distance D, and minimum codeword weight W. This function B(N,D,W) is first characterized in terms of its exponential growth rate in the limit as N tends to infinity for fixed d=D/N and w=W/N. The exponential growth rate of B(N,D,W) is shown to be equal to the exponential growth rate of A(N,D) for w <= 1/2, and equal to the exponential growth rate of A(N,D,W) for 1/2< w <= 1. Second, analytic and numerical upper bounds on B(N,D,W) are derived using the semidefinite programming (SDP) method. These bounds yield a non-asymptotic improvement of the second Johnson bound and are tight for certain values of the parameters.
Local Exponential Methods: a domain decomposition approach to exponential time integration of PDEs
Bonaventura, Luca
2015-01-01
A local approach to the time integration of PDEs by exponential methods is proposed, motivated by theoretical estimates by A.Iserles on the decay of off-diagonal terms in the exponentials of sparse matrices. An overlapping domain decomposition technique is outlined, that allows to replace the computation of a global exponential matrix by a number of independent and easily parallelizable local problems. Advantages and potential problems of the proposed technique are discussed. Numerical experiments on simple, yet relevant model problems show that the resulting method allows to increase computational efficiency with respect to standard implementations of exponential methods.
2006-01-01
[figure removed for brevity, see original site] Context image for PIA03289 Moving Downhill This narrow canyon is part of Coprates Chasma. On the east side of the canyon a landslide is visible. The southern wall of the canyon is marked by bright and dark streaks where dust has slid down the cliff face. Image information: VIS instrument. Latitude -10.5N, Longitude 264.8E. 17 meter/pixel resolution. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
Leman Tomak
2015-01-01
Full Text Available Time-weighted graphs are used to detect small shifts in statistical process control. The aim of this study is to evaluate the inclination of the acetabular component with CUmulative SUM (CUSUM chart, Moving Average (MA chart, and Exponentially Weighted Moving Average (EWMA chart. The data were obtained directly from thirty patients who had undergone total hip replacement surgery at Ondokuz Mayis University, Faculty of Medicine. The inclination of the acetabular component of these people, after total hip replacement, was evaluated. CUSUM chart, Moving Average chart, and Exponentially Weighted Moving Average were used to evaluate the quality control process of acetabular component inclination. MINITAB Statistical Software 15.0 was used to generate these control charts. The assessment done with time-weighted charts revealed that the acetabular inclination angles were settled within control limits and the process was under control. It was determined that the change within the control limits had a random pattern. As a result of this study it has been obtained that time-weighted quality control charts which are used mostly in the field of industry can also be used in the field of medicine. It has provided us with a faster visual decision.
ESTIMATION ACCURACY OF EXPONENTIAL DISTRIBUTION PARAMETERS
muhammad zahid rashid
2011-04-01
Full Text Available The exponential distribution is commonly used to model the behavior of units that have a constant failure rate. The two-parameter exponential distribution provides a simple but nevertheless useful model for the analysis of lifetimes, especially when investigating reliability of technical equipment.This paper is concerned with estimation of parameters of the two parameter (location and scale exponential distribution. We used the least squares method (LSM, relative least squares method (RELS, ridge regression method (RR, moment estimators (ME, modified moment estimators (MME, maximum likelihood estimators (MLE and modified maximum likelihood estimators (MMLE. We used the mean square error MSE, and total deviation TD, as measurement for the comparison between these methods. We determined the best method for estimation using different values for the parameters and different sample sizes
Modeling aftershocks as a stretched exponential relaxation
Mignan, A.
2015-11-01
The decay rate of aftershocks has been modeled as a power law since the pioneering work of Omori in the late nineteenth century. Although other expressions have been proposed in recent decades to describe the temporal behavior of aftershocks, the number of model comparisons remains limited. After reviewing the aftershock models published from the late nineteenth century until today, I solely compare the power law, pure exponential and stretched exponential expressions defined in their simplest forms. By applying statistical methods recommended recently in applied mathematics, I show that all aftershock sequences tested in three regional earthquake catalogs (Southern and Northern California, Taiwan) and with three declustering techniques (nearest-neighbor, second-order moment, window methods) follow a stretched exponential instead of a power law. These results infer that aftershocks are due to a simple relaxation process, in accordance with most other relaxation processes observed in Nature.
Unification modulo a partial theory of exponentiation
Kapur, Deepak; Narendran, Paliath; 10.4204/EPTCS.42.2
2010-01-01
Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) plays an important role in a large number of key agreement protocols. In our earlier work, we gave many decidability as well as undecidability results for multiple equational theories, involving various properties of modular exponentiation. Here, we consider a partial subtheory focussing only on exponentiation and multiplication operators. Two main results are proved. The first result is positive, namely, that the unification problem for the above theory (in which no additional property is assumed of the multiplication operators) is decidable. The second result is negative: if we assume that the two multiplication operators belong to two different abelian groups, then the unification problem becomes undecidable.
ESTIMATION ACCURACY OF EXPONENTIAL DISTRIBUTION PARAMETERS
muhammad zahid rashid
2011-04-01
Full Text Available The exponential distribution is commonly used to model the behavior of units that have a constant failure rate. The two-parameter exponential distribution provides a simple but nevertheless useful model for the analysis of lifetimes, especially when investigating reliability of technical equipment.This paper is concerned with estimation of parameters of the two parameter (location and scale exponential distribution. We used the least squares method (LSM, relative least squares method (RELS, ridge regression method (RR, moment estimators (ME, modified moment estimators (MME, maximum likelihood estimators (MLE and modified maximum likelihood estimators (MMLE. We used the mean square error MSE, and total deviation TD, as measurement for the comparison between these methods. We determined the best method for estimation using different values for the parameters and different sample sizes
When Economic Growth is Less than Exponential
Groth, Christian; Koch, Karl-Josef; Steger, Thomas M.
This paper argues that growth theory needs a more general notion of "regularity" than that of exponential growth. We suggest that paths along which the rate of decline of the growth rate is proportional to the growth rate itself deserve attention. This opens up for considering a richer set...... of parameter combinations than in standard growth models. And it avoids the usual oversimplistic dichotomy of either exponential growth or stagnation. Allowing zero population growth in three different growth models (the Jones R&D-based model, a learning-by-doing model, and an embodied technical change model......) serve as illustrations that a continuum of "regular" growth processes fill the whole range between exponential growth and complete stagnation....
The technological singularity and exponential medicine
Iraj Nabipour
2016-01-01
Full Text Available The "technological singularity" is forecasted to occur in 2045. It is a point when non-biological intelligence becomes more intelligent than humans and each generation of intelligent machines re-designs itself smarter. Beyond this point, there is a symbiosis between machines and humans. This co-existence will produce incredible impacts on medicine that its sparkles could be seen in healthcare industry and the future medicine since 2025. Ray Kurzweil, the great futurist, suggested that three revolutions in science and technology consisting genetic and molecular science, nanotechnology, and robotic (artificial intelligence provided an exponential growth rate for medicine. The "exponential medicine" is going to create more disruptive technologies in healthcare industry. The exponential medicine shifts the paradigm of medical philosophy and produces significant impacts on the healthcare system and patient-physician relationship.
Metastability of exponentially perturbed Markov chains
陈大岳; 冯建峰; 钱敏平
1996-01-01
A family of irreducible Markov chains on a finite state space is considered as an exponential perturbation of a reducible Markov chain. This is a generalization of the Freidlin-Wentzell theory, motivated by studies of stochastic Ising models, neural network and simulated annealing. It is shown that the metastability is a universal feature for this wide class of Markov chains. The metastable states are simply those recurrent states of the reducible Markov chain. Higher level attractors, related attractive basins and their pyramidal structure are analysed. The logarithmic asymptotics of the hitting time of various sets are estimated. The hitting time over its mean converges in law to the unit exponential distribution.
Exponential Operators, Dobinski Relations and Summability
Blasiak, P; Horzela, A; Penson, K A; Solomon, A I
2005-01-01
We investigate properties of exponential operators preserving the particle number using combinatorial methods developed in order to solve the boson normal ordering problem. In particular, we apply generalized Dobinski relations and methods of multivariate Bell polynomials which enable us to understand the meaning of perturbation-like expansions of exponential operators. Such expansions, obtained as formal power series, are everywhere divergent but the Pade summation method is shown to give results which very well agree with exact solutions got for simplified quantum models of the one mode bosonic systems.
Exponential Data Fitting and its Applications
Pereyra, Victor
2010-01-01
Real and complex exponential data fitting is an important activity in many different areas of science and engineering, ranging from Nuclear Magnetic Resonance Spectroscopy and Lattice Quantum Chromodynamics to Electrical and Chemical Engineering, Vision and Robotics. The most commonly used norm in the approximation by linear combinations of exponentials is the l2 norm (sum of squares of residuals), in which case one obtains a nonlinear separable least squares problem. A number of different methods have been proposed through the years to solve these types of problems and new applications appear
Nonuniform exponential dichotomies and Lyapunov functions
Barreira, Luis; Dragičević, Davor; Valls, Claudia
2017-05-01
For the nonautonomous dynamics defined by a sequence of bounded linear operators acting on an arbitrary Hilbert space, we obtain a characterization of the notion of a nonuniform exponential dichotomy in terms of quadratic Lyapunov sequences. We emphasize that, in sharp contrast with previous results, we consider the general case of possibly noninvertible linear operators, thus requiring only the invertibility along the unstable direction. As an application, we give a simple proof of the robustness of a nonuniform exponential dichotomy under sufficiently small linear perturbations.
Phani Y.
2013-05-01
Full Text Available In this paper we make an attempt to construct a new three parameter linear model, we call this new model as Arc Tan-Exponential Type distribution, by applying Stereographic Projection or equivalently Bilinear transformation on Wrapped Exponential distribution, Probability density and cumulative distribution functions of this new model are presented and their graphs are plotted for various values of parameters.
Ellis, Amy B.; Ozgur, Zekiye; Kulow, Torrey; Dogan, Muhammed F.; Amidon, Joel
2016-01-01
This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students' initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students' thinking and learning over time in relation to a set of tasks…
Hyperbolic neighborhoods as organizers of finite-time exponential stretching
Balasuriya, Sanjeeva; Ouellette, Nicholas
2016-11-01
Hyperbolic points and their unsteady generalization, hyperbolic trajectories, drive the exponential stretching that is the hallmark of nonlinear and chaotic flow. Typical experimental and observational velocity data is unsteady and available only over a finite time interval, and in such situations hyperbolic trajectories will move around in the flow, and may lose their hyperbolicity at times. Here we introduce a way to determine their region of influence, which we term a hyperbolic neighborhood, which marks fluid elements whose dynamics are instantaneously dominated by the hyperbolic trajectory. We establish, using both theoretical arguments and numerical verification from model and experimental data, that the hyperbolic neighborhoods profoundly impact Lagrangian stretching experienced by fluid elements. In particular, we show that fluid elements traversing a flow experience exponential boosts in stretching while within these time-varying regions, that greater residence time within hyperbolic neighborhoods is directly correlated to larger Finite-Time Lyapunov Exponent (FTLE) values, and that FTLE diagnostics are reliable only when the hyperbolic neighborhoods have a geometrical structure which is regular in a specific sense. Future Fellowship Grant FT130100484 from the Australian Research Council (SB), and a Terman Faculty Fellowship from Stanford University (NO).
Arima model and exponential smoothing method: A comparison
Wan Ahmad, Wan Kamarul Ariffin; Ahmad, Sabri
2013-04-01
This study shows the comparison between Autoregressive Moving Average (ARIMA) model and Exponential Smoothing Method in making a prediction. The comparison is focused on the ability of both methods in making the forecasts with the different number of data sources and the different length of forecasting period. For this purpose, the data from The Price of Crude Palm Oil (RM/tonne), Exchange Rates of Ringgit Malaysia (RM) in comparison to Great Britain Pound (GBP) and also The Price of SMR 20 Rubber Type (cents/kg) with three different time series are used in the comparison process. Then, forecasting accuracy of each model is measured by examinethe prediction error that producedby using Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE), and Mean Absolute deviation (MAD). The study shows that the ARIMA model can produce a better prediction for the long-term forecasting with limited data sources, butcannot produce a better prediction for time series with a narrow range of one point to another as in the time series for Exchange Rates. On the contrary, Exponential Smoothing Method can produce a better forecasting for Exchange Rates that has a narrow range of one point to another for its time series, while itcannot produce a better prediction for a longer forecasting period.
On exponential growth [of gas breakdown
McAllister, Iain Wilson
1991-01-01
The agreement obtained between measured breakdown voltages and predicted breakdown values is frequently used as a means of assessing the validity of the theory/model in question. However, owing to the mathematical nature of exponential growth, it is easy to formulate a criterion that provides...
Intersection of the Exponential and Logarithmic Curves
Boukas, Andreas; Valahas, Theodoros
2009-01-01
The study of the number of intersection points of y = a[superscript x] and y = log[subscript a]x can be an interesting topic to present in a single-variable calculus class. In this article, the authors present a classroom presentation outline involving the basic algebra and the elementary calculus of the exponential and logarithmic functions. The…
When Economic Growth is Less than Exponential
Groth, Christian; Koch, Karl-Josef; Steger, Thomas M.
This paper argues that growth theory needs a more general notion of "regularity" than that of exponential growth. We suggest that paths along which the rate of decline of the growth rate is proportional to the growth rate itself deserve attention. This opens up for considering a richer set...
Exponential lifetime improvement in topological quantum memories
Bardyn, Charles-Edouard; Karzig, Torsten
2016-09-01
We propose a simple yet efficient mechanism for passive error correction in topological quantum memories. Our scheme relies on driven-dissipative ancilla systems which couple to local excitations (anyons) and make them "sink" in energy, with no required interaction among ancillae or anyons. Through this process, anyons created by some thermal environment end up trapped in potential "trenches" that they themselves generate, which can be interpreted as a "memory foam" for anyons. This self-trapping mechanism provides an energy barrier for anyon propagation and removes entropy from the memory by favoring anyon recombination over anyon separation (responsible for memory errors). We demonstrate that our scheme leads to an exponential increase of the memory-coherence time with system size L , up to an upper bound Lmax, which can increase exponentially with Δ /T , where T is the temperature and Δ is some energy scale defined by potential trenches. This results in a double exponential increase of the memory time with Δ /T , which greatly improves over the Arrhenius (single-exponential) scaling found in typical quantum memories.
Couplings and Asymptotic Exponentiality of Exit Times
Brassesco, S.; Olivieri, E.; Vares, M. E.
1998-10-01
The goal of this note is simply to call attention to the resulting simplification in the proof of asymptotic exponentiality of exit times in the Freidlin-Wentzell regime (as proved by F. Martinelli et al.) by using the coupling proposed by T. Lindvall and C. Rogers.
A Simple Mechanical Experiment on Exponential Growth
McGrew, Ralph
2015-01-01
With a rod, cord, pulleys, and slotted masses, students can observe and graph exponential growth in the cord tension over a factor of increase as large as several hundred. This experiment is adaptable for use either in algebra-based or calculus-based physics courses, fitting naturally with the study of sliding friction. Significant parts of the…
Exponentially tapered Josephson flux-flow oscillator
Benabdallah, A.; Caputo, J. G.; Scott, Alwyn C.
1996-01-01
We introduce an exponentially tapered Josephson flux-flow oscillator that is tuned by applying a bias current to the larger end of the junction. Numerical and analytical studies show that above a threshold level of bias current the static solution becomes unstable and gives rise to a train of flu......, and (iv) better impedance matching to a load....
Functional Regression for General Exponential Families
Dou, Wei; Zhou, Harrison H
2010-01-01
The paper derives a minimax lower bound for rates of convergence for an infinite-dimensional parameter in an exponential family model. An estimator that achieves the optimal rate is constructed by maximum likelihood on finite-dimensional approximations with parameter dimension that grows with sample size.
Generalized approach to non-exponential relaxation
R M Pickup; R Cywinski; C Pappas; P Fouquet; B Farago; P Falus
2008-11-01
Non-exponential relaxation is a universal feature of systems as diverse as glasses, spin glasses, earthquakes, financial markets and the universe. Complex relaxation results from hierarchically constrained dynamics with the strength of the constraints being directly related to the form of the relaxation, which changes from a simple exponential to a stretched exponential and a power law by increasing the constraints in the system. A global and unified approach to non-exponentiality was first achieved by Weron and was further generalized by Brouers and Sotolongo-Costa, who applied the concept of non-extensive entropy introduced by Tsallis to the relaxation of disordered systems. These concepts are now confronted with experimental results on the classical metallic spin glasses CuMn, AuFe and the insulating system EuSrS. The revisited data have also be complemented by new results on several compositions of the classical CuMn spin glass and on systems, like CoGa and CuCo, the magnetic behaviour of which is believed to arise from magnetic clusters and should be characteristic for superparamagnetism.
Claudia Marcelloni
2006-01-01
The Big-Wheel TGC-1 being moved against the Barrel Muon Spectrometer. The 216 trigger chambers are supported by a thin structure of 22 m diameter and 0.4 m thickness, weighting 44 tons and supported on two rails.
A nanostructured surface increases friction exponentially at the solid-gas interface
Phani, Arindam; Putkaradze, Vakhtang; Hawk, John E.; Prashanthi, Kovur; Thundat, Thomas
2016-09-01
According to Stokes’ law, a moving solid surface experiences viscous drag that is linearly related to its velocity and the viscosity of the medium. The viscous interactions result in dissipation that is known to scale as the square root of the kinematic viscosity times the density of the gas. We observed that when an oscillating surface is modified with nanostructures, the experimentally measured dissipation shows an exponential dependence on kinematic viscosity. The surface nanostructures alter solid-gas interplay greatly, amplifying the dissipation response exponentially for even minute variations in viscosity. Nanostructured resonator thus allows discrimination of otherwise narrow range of gaseous viscosity making dissipation an ideal parameter for analysis of a gaseous media. We attribute the observed exponential enhancement to the stochastic nature of interactions of many coupled nanostructures with the gas media.
Modified Binary Exponential Backoff Algorithm to Minimize Mobiles Communication Time
Ibrahim Sayed Ahmad
2014-02-01
Full Text Available the field of Wireless Local Area Networks (LANs is expanding rapidly as a result of advances in digital communications, portable computers, and semiconductor technology. The early adopters of this technology have primarily been vertical application that places a premium on the mobility offered by such systems. Binary Exponential Backoff (BEB refers to a collision resolution mechanism used in random access MAC protocols. This algorithm is used in Ethernet (IEEE 802.3 wired LANs. In Ethernet networks, this algorithm is commonly used to schedule retransmissions after collisions. The paper’s goal is to minimize the time transmission cycle of the information between mobiles moving in a Wi-Fi by changing the BEB algorithm. The Protocol CSMA / CA manage access to the radio channel by performing an arbitration based on time. This causes many problems in relation to time transmission between mobiles moving in a cell 802.11. what we have done show that the protocol using CSMA / CA access time believed rapidly when the number of stations and / or the network load increases or other circumstances affects the network.
Multi-exponentially Photoelectric Response of Bacteriorhodopsin
姚保利; 徐大纶; 侯洵; 胡坤生; 王敖金
2001-01-01
A thin oriented bacteriorhodopsin (bR) film is deposited on a stainless steel slide by use of the electrophoretic sedimentation method. A junction is made with electrolyte gels having a counterelectrode to construct a bRbased photoelectric detector. The photoelectric response signal to a 10ns laser pulse is measured. A theory on the photoelectric kinetics of bR is developed based on the concept of the charge displacement current and the bR photocycle rate equations. Comparison between the theoretical and experimental results proves that the bR photoelectric response to a short laser pulse is a multi-exponential process. The decay time constants and amplitudes of each exponential component are obtained by data fitting.
Matrix-exponential distributions in applied probability
Bladt, Mogens
2017-01-01
This book contains an in-depth treatment of matrix-exponential (ME) distributions and their sub-class of phase-type (PH) distributions. Loosely speaking, an ME distribution is obtained through replacing the intensity parameter in an exponential distribution by a matrix. The ME distributions can also be identified as the class of non-negative distributions with rational Laplace transforms. If the matrix has the structure of a sub-intensity matrix for a Markov jump process we obtain a PH distribution which allows for nice probabilistic interpretations facilitating the derivation of exact solutions and closed form formulas. The full potential of ME and PH unfolds in their use in stochastic modelling. Several chapters on generic applications, like renewal theory, random walks and regenerative processes, are included together with some specific examples from queueing theory and insurance risk. We emphasize our intention towards applications by including an extensive treatment on statistical methods for PH distribu...
Statistical estimation for truncated exponential families
Akahira, Masafumi
2017-01-01
This book presents new findings on nonregular statistical estimation. Unlike other books on this topic, its major emphasis is on helping readers understand the meaning and implications of both regularity and irregularity through a certain family of distributions. In particular, it focuses on a truncated exponential family of distributions with a natural parameter and truncation parameter as a typical nonregular family. This focus includes the (truncated) Pareto distribution, which is widely used in various fields such as finance, physics, hydrology, geology, astronomy, and other disciplines. The family is essential in that it links both regular and nonregular distributions, as it becomes a regular exponential family if the truncation parameter is known. The emphasis is on presenting new results on the maximum likelihood estimation of a natural parameter or truncation parameter if one of them is a nuisance parameter. In order to obtain more information on the truncation, the Bayesian approach is also considere...
Harmonic analysis on exponential solvable Lie groups
Fujiwara, Hidenori
2015-01-01
This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated alge...
Perturbing Misiurewicz Parameters in the Exponential Family
Dobbs, Neil
2015-04-01
In one-dimensional real and complex dynamics, a map whose post-singular (or post-critical) set is bounded and uniformly repelling is often called a Misiurewicz map. In results hitherto, perturbing a Misiurewicz map is likely to give a non-hyperbolic map, as per Jakobson's Theorem for unimodal interval maps. This is despite genericity of hyperbolic parameters (at least in the interval setting). We show the contrary holds in the complex exponential family Misiurewicz maps are Lebesgue density points for hyperbolic parameters. As a by-product, we also show that Lyapunov exponents almost never exist for exponential Misiurewicz maps. The lower Lyapunov exponent is -∞ almost everywhere. The upper Lyapunov exponent is non-negative and depends on the choice of metric.
Six-Parameter Exponential-Type Potential and the Identity for the Exponential-Type Potentials
JIA Chun-Sheng; ZENG Xiang-Lin; LI Shu-Chuan; SUN Liang-Tian; YANG Qiu-Bo
2002-01-01
We propose a six-parameter exponential-type potential (SPEP), which has been shown to be a shape-invariant potential with a translation of parameters. For this reducible potential, the exact energy levels are obtained byusing the supersymmetric shape invariance technique. Choosing appropriate parameters, four classes of exponential-typepotentials and their exact energy spectra are reduced from the SPEP and a general energy level formula, respectively.Each class shows the identity except for the different definitions of parameters.
Financing exponential growth at H3
2012-01-01
H3 is a fast-food chain that introduced the concept of gourmet hamburgers in the Portuguese market. This case-study illustrates its financing strategy that supported an exponential growth represented by opening 33 restaurants within approximately 3 years of its inception. H3 is now faced with the challenge of structuring its foreign ventures and change its financial approach. The main covered topics are the options an entrepreneur has for financing a new venture and how it evolves along th...
An exponential correction to Starobinsky's inflationary model
Fabris, Júlio C; Piattella, Oliver F
2016-01-01
We analyse $f(R)$ theories of gravity from a dynamical system perspective, showing how the $R^2$ correction in Starobinsky's model plays a crucial role from the viewpoint of the inflationary paradigm. Then, we propose a modification of Starobinsky's model by adding an exponential term in the $f(R)$ Lagrangian. We show how this modification could allow to test the robustness of the model by means of the predictions on the scalar spectral index $n_s$.
Exponential Stabilization of an Underactuated Surface Vessel
Kristin Y. Pettersen
1997-07-01
Full Text Available The paper shows that a large class of underactuated vehicles cannot be asymptotically stabilized by either continuous or discontinuous state feedback. Furthermore, stabilization of an underactuated surface vessel is considered. Controllability properties of the surface vessels is presented, and a continuous periodic time-varying feedback law is proposed. It is shown that this feedback law exponentially stabilizes the surface vessel to the origin, and this is illustrated by simulations.
Scalar field collapse with an exponential potential
Chakrabarti, Soumya
2017-02-01
An analogue of the Oppenheimer-Synder collapsing model is treated analytically, where the matter source is a scalar field with an exponential potential. An exact solution is derived followed by matching to a suitable exterior geometry, and an analysis of the visibility of the singularity. In some situations, the collapse indeed leads to a finite time curvature singularity, which is always hidden from the exterior by an apparent horizon.
Exponential Attractor for a Nonlinear Boussinesq Equation
Ahmed Y. Abdallah
2006-01-01
This paper is devoted to prove the existence of an exponential attractor for the semiflow generated by a nonlinear Boussinesq equation. We formulate the Boussinesq equation as an abstract equation in the Hilbert space H20(0, 1) × L2(0, 1). The main step in this research is to show that there exists an absorbing set for the solution semiflow in the Hilbert space H03(0, 1) × H10(0, 1).
On the ranges of discrete exponentials
Florin Caragiu
2004-01-01
Full Text Available Let a>1 be a fixed integer. We prove that there is no first-order formula ϕ(X in one free variable X, written in the language of rings, such that for any prime p with gcd(a,p=1 the set of all elements in the finite prime field Fp satisfying ϕ coincides with the range of the discrete exponential function t↦at(modp.
Asynchronous exponential growth of a bacterial population
Mohamed Boulanouar
2014-01-01
Full Text Available In this work, we complete a study started earlier in [1,2] wherein a model of growing bacterial population has been the matter of a mathematical analysis. We show that the full model is governed by a strongly continuous semigroup. Beside the positivity and the irreducibility of the generated semigroup, we describe its asymptotic behavior in the uniform topology which leads to the asynchronous exponential growth of the bacterial population.
Exponential Stability of Uncertain T-S Fuzzy Switched Systems with Time Delay
Fatima Ahmida; El Houssaine Tissir
2013-01-01
This paper discusses the delay-dependent exponential stability of a class of uncertain T-S fuzzy switched systems with time delay.The method is based on Lyapunov stability theorem and free weighting matrices approach.Two illustrative examples are given to demonstrate the effectiveness of the proposed method.
Unwrapped phase inversion with an exponential damping
Choi, Yun Seok
2015-07-28
Full-waveform inversion (FWI) suffers from the phase wrapping (cycle skipping) problem when the frequency of data is not low enough. Unless we obtain a good initial velocity model, the phase wrapping problem in FWI causes a result corresponding to a local minimum, usually far away from the true solution, especially at depth. Thus, we have developed an inversion algorithm based on a space-domain unwrapped phase, and we also used exponential damping to mitigate the nonlinearity associated with the reflections. We construct the 2D phase residual map, which usually contains the wrapping discontinuities, especially if the model is complex and the frequency is high. We then unwrap the phase map and remove these cycle-based jumps. However, if the phase map has several residues, the unwrapping process becomes very complicated. We apply a strong exponential damping to the wavefield to eliminate much of the residues in the phase map, thus making the unwrapping process simple. We finally invert the unwrapped phases using the back-propagation algorithm to calculate the gradient. We progressively reduce the damping factor to obtain a high-resolution image. Numerical examples determined that the unwrapped phase inversion with a strong exponential damping generated convergent long-wavelength updates without low-frequency information. This model can be used as a good starting model for a subsequent inversion with a reduced damping, eventually leading to conventional waveform inversion.
Non-exponential decay of atomic systems
Ishkhanyan, A M
2014-01-01
We discuss the possibility of non-exponential decay of various quantum quasi-stationary systems. This effect can occur at the times which are greater than the lifetime of a considered system. The mechanism for non-exponential depletion of an initial quasi-stationary state is the cutting of the energy spectrum of final continuous states at long times. We first consider the known examples of cold emission of electrons from metal, tunneling alpha-decay of atomic nuclei, and spontaneous decay in two-level systems. The new physical situations discussed are the single-photon atomic ionization by a weak electromagnetic field and tunneling ionization of atoms by a strong low-frequency electromagnetic field. In both cases the decay obeys a power-law dependence on the (long) interaction time. We find that the most promising possibility for observing non-exponential decay at long times is the single-photon ionization of negative atomic ions near the threshold.
Effects of microperfusion in hepatic diffusion weighted imaging
Dijkstra, Hildebrand; Baron, Paul; Kappert, Peter; Oudkerk, Matthijs; Sijens, Paul E.
2012-01-01
Clinical hepatic diffusion weighted imaging (DWI) generally relies on mono-exponential diffusion. The aim was to demonstrate that mono-exponential diffusion in the liver is contaminated by microperfusion and that the bi-exponential model is required. Nineteen fasting healthy volunteers were examined
Effects of microperfusion in hepatic diffusion weighted imaging
Dijkstra, Hildebrand; Baron, Paul; Kappert, Peter; Oudkerk, Matthijs; Sijens, Paul E.
Clinical hepatic diffusion weighted imaging (DWI) generally relies on mono-exponential diffusion. The aim was to demonstrate that mono-exponential diffusion in the liver is contaminated by microperfusion and that the bi-exponential model is required. Nineteen fasting healthy volunteers were examined
A Generalization of Exponential Class and Its Applications
Hongya Gao
2013-01-01
Full Text Available A function space, Lθ,∞(Ω, 0≤θ<∞, is defined. It is proved that Lθ,∞(Ω is a Banach space which is a generalization of exponential class. An alternative definition of Lθ,∞(Ω space is given. As an application, we obtain weak monotonicity property for very weak solutions of -harmonic equation with variable coefficients under some suitable conditions related to Lθ,∞(Ω, which provides a generalization of a known result due to Moscariello. A weighted space Lwθ,∞(Ω is also defined, and the boundedness for the Hardy-Littlewood maximal operator Mw and a Calderón-Zygmund operator T with respect to Lwθ,∞(Ω is obtained.
Kanit Mukdasai
2012-01-01
Full Text Available This paper investigates the problem of robust exponential stability for linear parameter-dependent (LPD systems with discrete and distributed time-varying delays and nonlinear perturbations. Parameter dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, and linear matrix inequality are proposed to analyze the stability. On the basis of the estimation and by utilizing free-weighting matrices, new delay-dependent exponential stability criteria are established in terms of linear matrix inequalities (LMIs. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.
J. Thipcha
2013-01-01
Full Text Available The global exponential stability for bidirectional associative memory neural networks with time-varying delays is studied. In our study, the lower and upper bounds of the activation functions are allowed to be either positive, negative, or zero. By constructing new and improved Lyapunov-Krasovskii functional and introducing free-weighting matrices, a new and improved delay-dependent exponential stability for BAM neural networks with time-varying delays is derived in the form of linear matrix inequality (LMI. Numerical examples are given to demonstrate that the derived condition is less conservative than some existing results given in the literature.
Exponential Stability Criteria for Nonautonomous Difference Systems
Rigoberto Medina
2014-01-01
Full Text Available The aim of this paper is to characterize the exponential stability of linear systems of difference equations with slowly varying coefficients. Our approach is based on the generalization of the freezing method for difference equations combined with new estimates for the norm of bounded linear operators. The main novelty of this work is that we use estimates for the absolute values of entries of a matrix-valued function, instead of bounds on its eigenvalues. By this method, new explicit stability criteria for linear nonautonomous systems are derived.
Exponential sums over primes in short intervals
LIU Jianya; L(U) Guangshi; ZHAN Tao
2006-01-01
In this paper we establish one new estimate on exponential sums over primes in short intervals. As an application of this result, we sharpen Hua's result by proving that each sufficiently large integer N congruent to 5 modulo 24 can be written as N = p21 +p22 +p23 +p24 +p25, with |pj - √N/5| ≤ U = N1/2-1/20+ε,where pj are primes. This result is as good as what one can obtain from the generalized Riemann hypothesis.
Finite difference computing with exponential decay models
Langtangen, Hans Petter
2016-01-01
This text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming, verification, and visualization. The pedagogical strategy is to use one case study – an ordinary differential equation describing exponential decay processes – to illustrate fundamental concepts in mathematics and computer science. The book is easy to read and only requires a command of one-variable calculus and some very basic knowledge about computer programming. Contrary to similar texts on numerical methods and programming, this text has a much stronger focus on implementation and teaches testing and software engineering in particular. .
Two Interesting Properties of the Exponential Distribution
Chen, Robert W.
2015-01-01
Let $X_1, X_2,\\ldots, X_n$ be $n$ independent and identically distributed random variables, here $n \\geq 2.$ Let $X_{(1)}, X_{(2)}, \\ldots, X_{(n)}$ be the order statistics of $X_1, X_2,..., X_n.$ In this note we proved that: (I) If $X_1, X_2,..., X_n$ are exponential random variables with parameter $c > 0,$ then the "correlation coefficient" between $X_{(k)}$ and $X_{(k+t)}$ is strictly increasing in $k$ from $1$ to $m,$ and then is strictly decreasing in $k$ from $m$ to $n - t,$ here $t$ is...
Progressive Exponential Clustering-Based Steganography
Li Yue
2010-01-01
Full Text Available Cluster indexing-based steganography is an important branch of data-hiding techniques. Such schemes normally achieve good balance between high embedding capacity and low embedding distortion. However, most cluster indexing-based steganographic schemes utilise less efficient clustering algorithms for embedding data, which causes redundancy and leaves room for increasing the embedding capacity further. In this paper, a new clustering algorithm, called progressive exponential clustering (PEC, is applied to increase the embedding capacity by avoiding redundancy. Meanwhile, a cluster expansion algorithm is also developed in order to further increase the capacity without sacrificing imperceptibility.
Exponentially Convergent Algorithms for Abstract Differential Equations
Gavrilyuk, Ivan; Vasylyk, Vitalii
2011-01-01
This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for the practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as the partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which
Information and exponential families in statistical theory
Barndorff-Nielsen, O
2014-01-01
First published by Wiley in 1978, this book is being re-issued with a new Preface by the author. The roots of the book lie in the writings of RA Fisher both as concerns results and the general stance to statistical science, and this stance was the determining factor in the author's selection of topics. His treatise brings together results on aspects of statistical information, notably concerning likelihood functions, plausibility functions, ancillarity, and sufficiency, and on exponential families of probability distributions.
Compact vs. Exponential-Size LP Relaxations
Carr, R.D.; Lancia, G.
2000-09-01
In this paper we introduce by means of examples a new technique for formulating compact (i.e. polynomial-size) LP relaxations in place of exponential-size models requiring separation algorithms. In the same vein as a celebrated theorem by Groetschel, Lovasz and Schrijver, we state the equivalence of compact separation and compact optimization. Among the examples used to illustrate our technique, we introduce a new formulation for the Traveling Salesman Problem, whose relaxation we show equivalent to the subtour elimination relaxation.
Exponential algorithmic speedup by quantum walk
Childs, A M; Deotto, E; Farhi, E; Gutmann, S; Spielman, D A; Childs, Andrew M.; Cleve, Richard; Deotto, Enrico; Farhi, Edward; Gutmann, Sam; Spielman, Daniel A.
2002-01-01
We construct an oracular problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different technique from previous quantum algorithms based on quantum Fourier transforms. We show how to implement the quantum walk efficiently in our oracular setting. We then show how this quantum walk can be used to solve our problem by rapidly traversing a graph. Finally, we prove that no classical algorithm can solve this problem with high probability in subexponential time.
An Investigation of the Properties of the Exponential Moving Average Point Process
1976-03-01
Postgraduate School Monterey, California 93940 II. CONTROLLING OFFICE KAME AND ADDRESS Naval Postgraduate School Monterey, California 93940 l«. MONITORING ...Ii Poci +2Ii Ii Ii » Assume the result is also true when k=m then, when k=m+l itt+1 j This completes the proof. 42 2. The distribution of tho intervals
Rounded stretched exponential for time relaxation functions.
Powles, J G; Heyes, D M; Rickayzen, G; Evans, W A B
2009-12-01
A rounded stretched exponential function is introduced, C(t)=exp{(tau(0)/tau(E))(beta)[1-(1+(t/tau(0))(2))(beta/2)]}, where t is time, and tau(0) and tau(E) are two relaxation times. This expression can be used to represent the relaxation function of many real dynamical processes, as at long times, t>tau(0), the function converges to a stretched exponential with normalizing relaxation time, tau(E), yet its expansion is even or symmetric in time, which is a statistical mechanical requirement. This expression fits well the shear stress relaxation function for model soft soft-sphere fluids near coexistence, with tau(E)Cole-Cole plots for dielectric and shear stress relaxation (both the modulus and viscosity forms). It is shown that both the dielectric spectra and dynamic shear modulus imaginary parts approach the real axis with a slope equal to 0 at high frequency, whereas the dynamic viscosity has an infinite slope in the same limit. This indicates that inertial effects at high frequency are best discerned in the modulus rather than the viscosity Cole-Cole plot. As a consequence of the even expansion in time of the shear stress relaxation function, the value of the storage modulus derived from it at very high frequency exceeds that in the infinite frequency limit (i.e., G(infinity)).
Reviving Quintessence with an Exponential Potential
Chang, Hui-Yiing
2016-01-01
We examine a quintessence model with a modified exponential potential given by $V(\\phi) = V_0(1+e^{-\\lambda \\phi})$. Unlike quintessence with a standard exponential potential, our model can yield an acceptable accelerated expansion at late times, while producing a distinct "early dark energy" signature at high redshift. We determine the evolution of the equation of state parameter, $w_\\phi$, and the density parameter, $\\Omega_\\phi$, as a function of the scale factor. The strongest constraints on the model come from cosmic microwave background observations rather than supernova data. The former give the limit $\\lambda > 13$. This model predicts a value of the effective neutrino number during Big Bang nucleosynthesis larger than the standard model value. It also provides a partial solution to the coincidence problem, in that the ratio of the quintessence energy density is always within a few orders of magnitude of the background radiation or matter density from the early universe up to the present, but it does ...
On the single-exponential closed form of the product of two exponential operators
Tudor, Tiberiu [Faculty of Physics, University of Bucharest, PO Box MG-11, 0771253 Bucharest-Magurele (Romania)
2007-12-07
In the frame of a vectorial Pauli algebraic approach it is shown that the product of two exponentials of any two-by-two linear operators can be put in a single-exponential closed form. As a first application, a compact vectorial expression for the characteristics (angle and axis) of the product of two R{sup 3} rotations is established. The same mathematics can be used in a large diversity of problems of the whole class of two-states physical systems. An exemplification in the field of polarization optics is given.
Exponential and double exponential tails for maximum of two-dimensional discrete Gaussian free field
Ding, Jian
2011-01-01
We study the tail behavior for the maximum of discrete Gaussian free field on a 2D box with Dirichlet boundary condition after centering by its expectation. We show that it exhibits an exponential decay for the right tail and a double exponential decay for the left tail. In particular, our result implies that the variance of the maximum is of order 1, improving an $o(\\log n)$ bound by Chatterjee (2008) and confirming a folklore conjecture. An important ingredient for our proof is a result of Bramson and Zeitouni (2010), who proved the tightness of the centered maximum together with an evaluation of the expectation up to an additive constant.
Exponential Disks from Stellar Scattering: III. Stochastic Models
Elmegreen, Bruce G
2016-01-01
Stellar scattering off irregularities in a galaxy disk has been shown to make an exponential radial profile, but no fundamental reason for this has been suggested. Here we show that exponentials are mathematically expected from random scattering in a disk when there is a slight inward bias in the scattering probability. Such a bias was present in our previous scattering experiments that formed exponential profiles. Double exponentials can arise when the bias varies with radius. This is a fundamental property of scattering and may explain why piece-wise exponential profiles are ubiquitous in galaxies, even after minor mergers and other disruptive events.
Vortex structures in exponentially shaped Josephson junctions
Shukrinov, Yu. M.; Semerdjieva, E. G.; Boyadjiev, T. L.
2005-04-01
We report the numerical calculations of the static vortex structure and critical curves in exponentially shaped long Josephson junctions for in-line and overlap geometries. Stability of the static solutions is investigated by checking the sign of the smallest eigenvalue of the associated Sturm-Liouville problem. The change in the junction width leads to the renormalization of the magnetic flux in comparison with the case of a linear one-dimensional model. We study the influence of the model's parameters, and particularly, the shape parameter on the stability of the states of the magnetic flux. We compare the vortex structure and critical curves for the in-line and overlap geometries. Our numerically constructed critical curve of the Josephson junction matches well with the experimental one.
On exponential stabilizability of linear neutral systems
Dusser Xavier
2001-01-01
Full Text Available In this paper, we deal with linear neutral functional differential systems. Using an extended state space and an extended control operator, we transform the initial neutral system in an infinite dimensional linear system. We give a sufficient condition for admissibility of the control operator B , conditions under which operator B can be acceptable in order to work with controllability and stabilizability. Necessary and sufficient conditions for exact controllability are provided; in terms of a gramian of controllability N ( μ . Assuming admissibility and exact controllability, a feedback control law is defined from the inverse of the operator N ( μ in order to stabilize exponentially the closed loop system. In this case, the semigroup generated by the closed loop system has an arbitrary decay rate.
Controlling chaos using an exponential control
Gadre, S D; Gadre, Sangeeta D; Varma, V S
1995-01-01
We demonstrate that chaos can be controlled using a multiplicative exponential feedback control. All three types of unstable orbits - unstable fixed points, limit cycles and chaotic trajectories can be stabilized using this control. The control is effective both for maps and flows. The control is significant, particularly for systems with several degrees of freedom, as knowledge of only one variable on the desired unstable orbit is sufficient to settle the system on to that orbit. We find, that in all the cases studied, the transient time is a decreasing function of the stiffness of control. But increasing the stiffness beyond an optimum value can increase the transient time. The control can also be used to create suitable new stable attractors in a map, which did not exist in the original system.
Poissonian renormalizations, exponentials, and power laws
Eliazar, Iddo
2013-05-01
This paper presents a comprehensive “renormalization study” of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to “white noise” and to “1/f noise.” Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.
Generalized exponential function and discrete growth models
Souto Martinez, Alexandre; Silva González, Rodrigo; Lauri Espíndola, Aquino
2009-07-01
Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamic models into a simple formula. A physical interpretation is given to this new introduced parameter in the context of the continuous Richards model, which remains valid for the discrete case. From the discretization of the continuous Richards’ model (generalization of the Gompertz and Verhulst models), one obtains a generalized logistic map and we briefly study its properties. Notice, however that the physical interpretation for the introduced parameter persists valid for the discrete case. Next, we generalize the (scramble competition) θ-Ricker discrete model and analytically calculate the fixed points as well as their stabilities. In contrast to previous generalizations, from the generalized θ-Ricker model one is able to retrieve either scramble or contest models.
Nonlinear elliptic systems with exponential nonlinearities
Said El Manouni
2002-12-01
Full Text Available In this paper we investigate the existence of solutions for {gather*} -mathop{m div}( a(| abla u | ^N| abla u |^{N-2}u = f(x,u,v quad mbox{in } Omega -mathop{m div}(a(| abla v| ^N| abla v |^{N-2}v = g(x,u,v quad mbox{in } Omega u(x = v(x = 0 quad mbox{on }partial Omega. end{gather*} Where $Omega$ is a bounded domain in ${mathbb{R}}^N$, $Ngeq 2$, $f$ and $g$ are nonlinearities having an exponential growth on $Omega$ and $a$ is a continuous function satisfying some conditions which ensure the existence of solutions.
Exponential Networks and Representations of Quivers
Eager, Richard; Walcher, Johannes
2016-01-01
We study the geometric description of BPS states in supersymmetric theories with eight supercharges in terms of geodesic networks on suitable spectral curves. We lift and extend several constructions of Gaiotto-Moore-Neitzke from gauge theory to local Calabi-Yau threefolds and related models. The differential is multi-valued on the covering curve and features a new type of logarithmic singularity in order to account for D0-branes and non-compact D4-branes, respectively. We describe local rules for the three-way junctions of BPS trajectories relative to a particular framing of the curve. We reproduce BPS quivers of local geometries and illustrate the wall-crossing of finite-mass bound states in several new examples. We describe first steps toward understanding the spectrum of framed BPS states in terms of such "exponential networks."
Transient accelerating scalar models with exponential potentials
Wen-Ping Cui; Yang Zhang; Zheng-Wen Fu
2013-01-01
We study a known class of scalar dark energy models in which the potential has an exponential term and the current accelerating era is transient.We find that,although a decelerating era will return in the future,when extrapolating the model back to earlier stages (z(≥) 4),scalar dark energy becomes dominant over matter.So these models do not have the desired tracking behavior,and the predicted transient period of acceleration cannot be adopted into the standard scenario of the Big Bang cosmology.When couplings between the scalar field and matter are introduced,the models still have the same problem; only the time when deceleration returns will be varied.To achieve re-deceleration,one has to turn to alternative models that are consistent with the standard Big Bang scenario.
An Economic Model of Coupled Exponential Maps
López-Ruiz, R; Cosenza, M G; Sánchez, J R
2007-01-01
In this work, an ensemble of economic interacting agents is considered. The agents are arranged in a linear array where only local couplings are allowed. The deterministic dynamics of each agent is given by a map. This map is expressed by two factors. The first one is a linear term that models the expansion of the agent's economy and that is controlled by the {\\it growth capacity parameter}. The second one is an inhibition exponential term that is regulated by the {\\it local environmental pressure}. Depending on the parameter setting, the system can display Pareto or Boltzmann-Gibbs behavior in the asymptotic dynamical regime. The regions of parameter space where the system exhibits one of these two statistical behaviors are delimited. Other properties of the system, such as the mean wealth, the standard deviation and the Gini coefficient, are also calculated.
Modeling Aftershocks as a Stretched Exponential Relaxation
Mignan, Arnaud
2015-01-01
The decay rate of aftershocks has been modeled as a power law since the pioneering work of Omori in the late nineteenth century. Considered the second most fundamental empirical law after the Gutenberg-Richter relationship, the power law paradigm has rarely been challenged by the seismological community. By taking a view of aftershock research not biased by prior conceptions of Omori power law decay and by applying statistical methods recommended in applied mathematics, I show that all aftershock sequences tested in three regional earthquake catalogs (Southern and Northern California, Taiwan) and with three declustering techniques (nearest-neighbor, second-order moment, window methods) follow a stretched exponential instead of a power law. These results infer that aftershocks are due to a simpler relaxation process than originally thought, in accordance with most other relaxation processes observed in Nature.
Poissonian renormalizations, exponentials, and power laws.
Eliazar, Iddo
2013-05-01
This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.
Exponential Approximations Using Fourier Series Partial Sums
Banerjee, Nana S.; Geer, James F.
1997-01-01
The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.
Exponential Reliability Coefficient based Reputation Mechanism for isolating selfish nodes in MANETs
J. Sengathir
2015-07-01
Full Text Available In mobile ad hoc networks, cooperation among active mobile nodes is considered to play a vital role in reliable transmission of data. But, the selfish mobile nodes present in an ad hoc environment refuse to forward neighbouring nodes’ packet for conserving its own energy. This intentional selfish behaviour drastically reduces the degree of cooperation maintained between the mobile nodes. Hence, a need arises for devising an effective mechanism which incorporates both energy efficiency and reputation into account for mitigating selfish behaviour in MANETs. In this paper, we propose an Exponential Reliability Coefficient based reputation Mechanism (ERCRM which isolates the selfish nodes from the routing path based on Exponential Reliability Coefficient (ExRC. This reliability coefficient manipulated through exponential failure rate based on moving average method highlights the most recent past behaviour of the mobile nodes for quantifying its genuineness. From the simulation results, it is evident that, the proposed ERCRM approach outperforms the existing Packet Conservation Monitoring Algorithm (PCMA and Spilt Half Reliability Coefficient based Mathematical Model (SHRCM in terms of performance evaluation metrics such as packet delivery ratio, throughput, total overhead and control overhead. Further, this ERCRM mechanism has a successful rate of 28% in isolating the selfish nodes from the routing path. Furthermore, it also aids in framing the exponential threshold point of detection as 0.4, where a maximum number of selfish nodes are identified when compared to the existing models available in the literature.
Deformed Algebras and Generalizations of Independence on Deformed Exponential Families
Hiroshi Matsuzoe
2015-08-01
Full Text Available A deformed exponential family is a generalization of exponential families. Since the useful classes of power law tailed distributions are described by the deformed exponential families, they are important objects in the theory of complex systems. Though the deformed exponential families are defined by deformed exponential functions, these functions do not satisfy the law of exponents in general. The deformed algebras have been introduced based on the deformed exponential functions. In this paper, after summarizing such deformed algebraic structures, it is clarified how deformed algebras work on deformed exponential families. In fact, deformed algebras cause generalization of expectations. The three kinds of expectations for random variables are introduced in this paper, and it is discussed why these generalized expectations are natural from the viewpoint of information geometry. In addition, deformed algebras cause generalization of independences. Whereas it is difficult to check the well-definedness of deformed independence in general, the κ-independence is always well-defined on κ-exponential families. This is one of advantages of κ-exponential families in complex systems. Consequently, we can well generalize the maximum likelihood method for the κ-exponential family from the viewpoint of information geometry.
... Happens in the Operating Room? Are Your Bowels Moving? KidsHealth > For Kids > Are Your Bowels Moving? A A A What's in this article? What's ... to Know? en español ¿Se mueven tus intestinos? Moving your bowels means to poop. If you said " ...
An exponential decay model for mediation.
Fritz, Matthew S
2014-10-01
Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, address many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed.
Black Hole Instabilities and Exponential Growth
Prabhu, Kartik
2015-01-01
Recently, a general analysis has been given of the stability with respect to axisymmetric perturbations of stationary-axisymmetric black holes and black branes in vacuum general relativity in arbitrary dimensions. It was shown that positivity of canonical energy on an appropriate space of perturbations is necessary and sufficient for stability. However, the notions of both "stability" and "instability" in this result are significantly weaker than one would like to obtain. In this paper, we prove that if a perturbation of the form $\\pounds_t \\delta g$---with $\\delta g$ a solution to the linearized Einstein equation---has negative canonical energy, then that perturbation must, in fact, grow exponentially in time. The key idea is to make use of the $t$- or ($t$-$\\phi$)-reflection isometry, $i$, of the background spacetime and decompose the initial data for perturbations into their odd and even parts under $i$. We then write the canonical energy as $\\mathscr E\\ = \\mathscr K + \\mathscr U$, where $\\mathscr K$ and $...
On Simple Graphs Arising from Exponential Congruences
M. Aslam Malik
2012-01-01
Full Text Available We introduce and investigate a new class of graphs arrived from exponential congruences. For each pair of positive integers a and b, let G(n denote the graph for which V={0,1,…,n−1} is the set of vertices and there is an edge between a and b if the congruence ax≡b (mod n is solvable. Let n=p1k1p2k2⋯prkr be the prime power factorization of an integer n, where p1
Evidence for super-exponentially accelerating atmospheric carbon dioxide growth
Hüsler, Andreas D
2011-01-01
We analyze the growth rates of atmospheric carbon dioxide and human population, by comparing the relative merits of two benchmark models, the exponential law and the finite-time-singular (FTS) power law. The later results from positive feedbacks, either direct or mediated by other dynamical variables, as shown in our presentation of a simple endogenous macroeconomic dynamical growth model. Our empirical calibrations confirm that human population has decelerated from its previous super-exponential growth until 1960 to ``just' an exponential growth, but with no sign of more deceleration. As for atmospheric CO2 content, we find that it is at least exponentially increasing and most likely characterized by an accelerating growth rate as off 2009, consistent with an unsustainable FTS power law regime announcing a drastic change of regime. The coexistence of a quasi-exponential growth of human population with a super-exponential growth of carbon dioxide content in the atmosphere is a diagnostic of insignificant impr...
Twisted exponential sums of polynomials in one variable
无
2010-01-01
The twisted T-adic exponential sums associated to a polynomial in one variable are studied.An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the C-function of the twisted T-adic exponential sums.This bound gives lower bounds for the Newton polygon of the L-function of twisted p-power order exponential sums.
An Exponential Lower Bound on OBDD Refutations for Pigeonhole Formulas
Tveretina, Olga; Zantema, Hans
2009-01-01
Haken proved that every resolution refutation of the pigeonhole formula has at least exponential size. Groote and Zantema proved that a particular OBDD computation of the pigeonhole formula has an exponential size. Here we show that any arbitrary OBDD refutation of the pigeonhole formula has an exponential size, too: we prove that the size of one of the intermediate OBDDs is at least $\\Omega(1.025^n)$.
... Anger Weight Management Weight Management Smoking and Weight Healthy Weight Loss Being Comfortable in Your Own Skin Your Weight Loss Expectations & Goals Healthier Lifestyle Healthier Lifestyle Physical Fitness Food & Nutrition Sleep, Stress & Relaxation Emotions & Relationships HealthyYouTXT ...
The exponential-logarithmic equivalence classes of surreal numbers
Kuhlmann, Salma
2012-01-01
In his monograph, H. Gonshor showed that Conway's real closed field of surreal numbers carries an exponential and logarithmic map. Subsequently, L. van den Dries and P. Ehrlich showed that it is a model of the elementary theory of the field of real numbers with the exponential function. In this paper, we give a complete description of the exponential equivalence classes in the spirit of the classical Archimedean and multiplicative equivalence classes. This description is made in terms of a recursive formula as well as a sign sequence formula for the family of representatives of minimal length of these exponential classes.
Using Differentials to Differentiate Trigonometric and Exponential Functions
Dray, Tevian
2013-01-01
Starting from geometric definitions, we show how differentials can be used to differentiate trigonometric and exponential functions without limits, numerical estimates, solutions of differential equations, or integration.
Using Differentials to Differentiate Trigonometric and Exponential Functions
Dray, Tevian
2013-01-01
Starting from geometric definitions, we show how differentials can be used to differentiate trigonometric and exponential functions without limits, numerical estimates, solutions of differential equations, or integration.
Exponential sums over primes in short intervals
LIU; Jianya
2006-01-01
[1]Vinogradov,I.M.,Estimation of certain trigonometric sums with prime variables,Izv.Acad.Nauk.SSSR,1939,3:371-398.[2]Zhan,T.,On the representation of large odd integer as a sum of three almost equal primes,Acta Math.Sin.,1991,7:259-272.[3]Ren,X.M.,On exponential sums over primes and application in the Waring-Goldbach problem,Sci.China,Ser.A-Math.,2005,48(6):785-797.[4]Liu,J.Y.,Wooley,T.D.,Yu,G.,The quadratic Waring-Goldbach problem,J.Number Theory,2004,107:298-321.[5]Hua,L.K.,Some results in the additive prime number theory,Quart.J.Math.(Oxford),1938,9:68-80.[6]Liu,J.Y.,Zhan,T.,On sums of five almost equal prime squares,Acta Arith.,1996,77:369-383.[7]Bauer,C.,A note on sums of five almost equal prime squares,Arch.Math,1997,69:20-30.[8]Liu,J.Y.,Zhan,T.,Sums of five almost equal prime squares,Science in China,Ser.A,1998,41:710-722.[9]Liu,J.Y.,Zhan,T.,Hua's theorem on prime squares in short intervals,Acta Math.Sin.,2000,16:1-22.[10]Bauer,C.,Sums of five almost equal prime squares,Acta Math.Sin.,2005,21(4):833-840.[11]Lü,G.S.,Hua's Theorem with five almost equal prime variables,Chin.Ann.Math.,Ser.B,2005,26(2):291-304.[12]Vinogradov,I.M.,Elements of Number Theory,Dover Publications,1954.[13]Titchmarsh,E.C.,The Theory of the Riemann Zeta-function,2nd ed.,Oxford:Oxford University Press,1986.
A. Zerga; B. Benyoucef; J.-P. Charles
1998-01-01
Single and double exponential models are confronted to determine the most adapted model for optimization of solar cells efficiency. It is shown that the single exponential model (SEM) presents some insufficiencies for efficiency optimization. The interest of the double exponential model to optimize the efficiency and to achieve an adequate simulation of the operation of solar cells is demonstrated by means of I-V characteristics plotting.
Sharp interface limit of the Fisher-KPP equation when initial data have slow exponential decay
Alfaro, Matthieu
2010-01-01
We investigate the singular limit, as $\\ep \\to 0$, of the Fisher equation $\\partial_t u=\\ep \\Delta u + \\ep ^{-1}u(1-u)$ in the whole space. We consider initial data with compact support plus perturbations with {\\it slow exponential decay}. We prove that the sharp interface limit moves by a constant speed, which dramatically depends on the tails of the initial data. By performing a fine analysis of both the generation and motion of interface, we provide a new estimate of the thickness of the transition layers.
Minimizing Mobiles Communication Time Using Modified Binary Exponential Backoff Algorithm
Ibrahim Sayed Ahmad
2013-11-01
Full Text Available The domain of wireless Local Area Networks (WLANsis growing speedily as a consequence ofdevelopments in digital communications technology.The early adopters of this technology have mainlybeen vertical applicationthat places a premium on the mobility offered by such systems. Examples of thesetypes of applications consist of stocking control in depot environments,point of sale terminals, and rentalcar check-in. Furthermore to the mobility thatbecomes possible with wireless LANs; these systemshavealso been used in environments where cable installation is expensive or impractical. Such environmentsincludemanufacturingfloors, tradingfloors on stock exchanges, conventions and trade shows,and historicbuildings. With the increasing propagation of wireless LANs comes theneed for standardization so as toallow interoperability for an increasingly mobileworkforce. Despite all the advantages and facilities thatWi-FI offers, there is still the delay problem thatis due to many reasons that are introduced in details inour case study which also presents the solutions and simulation that can reduce this delay for betterperformance of the wireless networks.Binary Exponential Backoff (BEB refers to a collision resolution mechanism used in random access MACprotocols. This algorithm is used in Ethernet (IEEE802.3 wired LANs. In Ethernet networks, thisalgorithm is commonly used to schedule retransmissions after collisions.The paper’s goal is to minimize the time transmission cycle of the information between mobiles movingin aWi-Fi by changing the BEB algorithm. The Protocol CSMA / CA manage access to the radio channel byperforming an arbitration based on time. This causes many problems in relation to time transmissionbetween mobiles moving in a cell 802.11. what we have done show that the protocol using CSMA / CAaccess time believed rapidly when the number of stations and / or the network load increases or othercircumstances affects the network.
Exponential Correlation of IQ and the Wealth of Nations
Dickerson, Richard E.
2006-01-01
Plots of mean IQ and per capita real Gross Domestic Product for groups of 81 and 185 nations, as collected by Lynn and Vanhanen, are best fitted by an exponential function of the form: GDP = "a" * 10["b"*(IQ)], where "a" and "b" are empirical constants. Exponential fitting yields markedly higher correlation coefficients than either linear or…
A Learning Cycle on Exponential Growth and the Energy Crises.
Dykstra, D. I., Jr.
1982-01-01
Describes nature and logistics of a learning cycle approach to teaching exponential growth and the energy crisis. Used with both science and nonscience majors, the cycle uses no algebra, never mentions the terms exponential or logarithmic, and requires a calculator. Instructions for obtaining student and instructor materials are provided.…
Exponential Shear Flow of Linear, Entangled Polymeric Liquids
Neergaard, Jesper; Park, Kyungho; Venerus, David C.
2000-01-01
A previously proposed reptation model is used to interpret exponential shear flow data taken on an entangled polystyrenesolution. Both shear and normal stress measurements are made during exponential shear using mechanical means. The model iscapable of explaining all trends seen in the data, and ...
Molecular integrals for exponential-type orbitals using hyperspherical harmonics
Avery, James Emil; Avery, John Scales
2015-01-01
Exponential-type orbitals are better suited to calculations of molecular electronic structure than are Gaussians, since ETO's can accurately represent the behavior of molecular orbitals near to atomic nuclei, as well as their long-distance exponential decay. Orbitals based on Gaussians fail in bo...
A nomogram for deconvolution of single exponential fluorescence decays.
Rockley, M.G.
1980-01-01
An extremely rapid technique for deconvolving single exponential luminescence decay data is described that involves essentially no mathematical manipulation of the experimental data. The method permits "real time" measurement of deconvolved luminescence lifetimes with conventional pulsed, lifetime-fluorometers and phosphorimeters. The method assumes that the true luminescence decay of the chromophore is accurately represented by a single exponential decay function.
Residual, restarting and Richardson iteration for the matrix exponential
Botchev, M.A.
2010-01-01
A well-known problem in computing some matrix functions iteratively is a lack of a clear, commonly accepted residual notion. An important matrix function for which this is the case is the matrix exponential. Assume, the matrix exponential of a given matrix times a given vector has to be computed.
Residual, restarting and Richardson iteration for the matrix exponential
Botchev, Mike A.; Grimm, Volker; Hochbruck, Marlis
2013-01-01
A well-known problem in computing some matrix functions iteratively is the lack of a clear, commonly accepted residual notion. An important matrix function for which this is the case is the matrix exponential. Suppose the matrix exponential of a given matrix times a given vector has to be computed.
Exponential Decay of Correlations for the Strongly Coupled Toom Model
de Maere, Augustin
2011-01-01
We prove that, for the two-dimensional probabilistic cellular automaton of Toom in the low-noise regime, there are two classes of initial measures, each of which converges exponentially fast toward one of the two natural invariant measures. We also show that these two invariant measures have exponential decay of correlations in space and in time and are strongly mixing.
Exponential B-splines and the partition of unity property
Christensen, Ole; Massopust, Peter
2012-01-01
We provide an explicit formula for a large class of exponential B-splines. Also, we characterize the cases where the integer-translates of an exponential B-spline form a partition of unity up to a multiplicative constant. As an application of this result we construct explicitly given pairs of dual...
Review of "Going Exponential: Growing the Charter School Sector's Best"
Garcia, David
2011-01-01
This Progressive Policy Institute report argues that charter schools should be expanded rapidly and exponentially. Citing exponential growth organizations, such as Starbucks and Apple, as well as the rapid growth of molds, viruses and cancers, the report advocates for similar growth models for charter schools. However, there is no explanation of…
Jajodia, Sushil; Swarup, Vipin; Wang, Cliff; Wang, X Sean
2011-01-01
Moving Target Defense: Creating Asymmetric Uncertainty for Cyber Threats was developed by a group of leading researchers. It describes the fundamental challenges facing the research community and identifies new promising solution paths. Moving Target Defense which is motivated by the asymmetric costs borne by cyber defenders takes an advantage afforded to attackers and reverses it to advantage defenders. Moving Target Defense is enabled by technical trends in recent years, including virtualization and workload migration on commodity systems, widespread and redundant network connectivity, instr
Pravin K Gupta; Sri Niwas; Neeta Chaudhary
2006-06-01
The computation of electromagnetic (EM)ﬁelds,for 1-D layered earth model,requires evaluation of Hankel Transform (HT)of the EM kernel function.The digital ﬁltering is the most widely used technique to evaluate HT integrals.However,it has some obvious shortcomings.We present an alternative scheme,based on an orthonormal exponential approximation of the kernel function, for evaluating HT integrals.This approximation of the kernel function was chosen because the analytical solution of HT of an exponential function is readily available in literature.This expansion reduces the integral to a simple algebraic sum.The implementation of such a scheme requires that the weights and the exponents of the exponential function be estimated.The exponents were estimated through a guided search algorithm while the weights were obtained using Marquardt matrix inversion method.The algorithm was tested on analytical HT pairs available in literature. The results are compared with those obtained using the digital ﬁltering technique with Anderson ﬁlters.The ﬁeld curves for four types (A-,K-,H-and Q-type)of 3-layer earth models are generated using the present scheme and compared with the corresponding curves obtained using the Anderson scheme.It is concluded that the present scheme is more accurate than the Anderson scheme.
Exponentially slow traveling waves on a finite interval for Burgers' type equation
Pieter De Groen
1998-11-01
Full Text Available In this paper we study for small positive $epsilon$ the slow motion of the solution for evolution equations of Burgers' type with small diffusion, $$ u_t=epsilon u_{xx}+f(u,u_x,, quad u(x,0=u_0(x, quad u(pm 1,t=pm 1, $$ on the bounded spatial domain $[-1,1]$; $f$ is a smooth function satisfying $f(1>0, f(-1<0$ and $int_{-1}^{1}f(tdt=0$. The initial and boundary value problem~($star$ has a unique asymptotically stable equilibrium solution that attracts all solutions starting with continuous initial data $u_0$. On the infinite spatial domain ${mathbb R}$ the differential equation has slow speed traveling wave solutions generated by profiles that satisfy the boundary conditions of~($star$. As long as its zero stays inside the interval $[-1,1]$, such a traveling wave suitably describes the slow long term behaviour of the solution of ($star$ and its speed characterizes the local velocity of the slow motion with exponential precision. A solution that starts near a traveling wave moves in a small neighborhood of the traveling wave with exponentially slow velocity (measured as the speed of the unique zero during an exponentially long time interval $(0,T$. In this paper we give a unified treatment of the problem, using both Hilbert space and maximum principle methods, and we give rigorous proofs of convergence of the solution and of the asymptotic estimate of the velocity.
Moving a House by Moved Participants
Axel, Erik
? The participant observer believed it was a matter of changing coordinates, but the engineers immediately saw it was an issue of pipes in the ground, could they be moved and still function as planned? To decide the possibility of this suggestion the engineer was given the task of investigating the consequences......The author performed an investigation of how a house was designed. He participated mainly in meetings, in which the house was engineered. The meetings proceeded in an agreeable atmosphere. While the architect was mostly concerned with integrating the functionality of the house, the engineer engaged...... of moving the house with respect to its servicing pipes. It was immediately underlined that this task was a surplus task and would therefore trigger an extra payment. When I interviewed the participants and asked them how they understood the function of the engineer, they revealed some irritation, since...
Exponential Decay of Loop Lengths in the Loop O( n) Model with Large n
Duminil-Copin, Hugo; Peled, Ron; Samotij, Wojciech; Spinka, Yinon
2017-02-01
The loop O( n) model is a model for a random collection of non-intersecting loops on the hexagonal lattice, which is believed to be in the same universality class as the spin O( n) model. It has been conjectured that both the spin and the loop O( n) models exhibit exponential decay of correlations when n > 2. We verify this for the loop O( n) model with large parameter n, showing that long loops are exponentially unlikely to occur, uniformly in the edge weight x. Our proof provides further detail on the structure of typical configurations in this regime. Putting appropriate boundary conditions, when nx 6 is sufficiently small, the model is in a dilute, disordered phase in which each vertex is unlikely to be surrounded by any loops, whereas when nx 6 is sufficiently large, the model is in a dense, ordered phase which is a small perturbation of one of the three ground states.
Embodied affectivity: On moving and being moved
Thomas eFuchs
2014-06-01
Full Text Available There is a growing body of research indicating that bodily sensation and behaviour strongly influences one’s emotional reaction towards certain situations or objects. On this background, a framework model of embodied affectivity is suggested: we regard emotions as resulting from the circular interaction between affective qualities or affordances in the environment and the subject’s bodily resonance, be it in the form of sensations, postures, expressive movements or movement tendencies. Motion and emotion are thus intrinsically connected: one is moved by movement (perception; impression; affection and moved to move (action; expression; e-motion. Through its resonance, the body functions as a medium of emotional perception: it colours or charges self-experience and the environment with affective valences while it remains itself in the background of one’s own awareness. This model is then applied to emotional social understanding or interaffectivity which is regarded as an intertwinement of two cycles of embodied affectivity, thus continuously modifying each partner’s affective affordances and bodily resonance. We conclude with considerations of how embodied affectivity is altered in psychopathology and can be addressed in psychotherapy of the embodied self.
T. Venkata Rama Krishna
2008-01-01
Full Text Available This paper presented a theoretical and numerical assessment for nonidentical segmented exponential- (NISE- convex and NISE-concave serrated plane CATRs by changing number of serrations. The investigation was based on diffraction theory and, more specifically, on the diffraction formulation of Fresnel. The compact antenna test range (CATR provides uniform illumination within the Fresnel region to the test antenna. Application of serrated edges has been shown to be a good method to control diffraction at the edges of the reflectors. In this paper, the Fresnel fields of NISE-convex and NISE-concave serrated CATRs are analyzed using physical optics (PO technique. The PO analysis is applied in this paper for plane reflector serrated CATR only. The same analysis is applied to any type of reflector. In this paper, lens-based reflector is not considered. It is observed that NISE-concave serrated CATR gives less ripple and enhanced quiet zone width than NISE-convex.
Laminar phase flow for an exponentially tapered Josephson oscillator
Benabdallah, A.; Caputo, J. G.; Scott, Alwyn C.
2000-01-01
Exponential tapering and inhomogeneous current feed were recently proposed as means to improve the performance of a Josephson flux flow oscillator. Extensive numerical results backed up by analysis are presented here that support this claim and demonstrate that exponential tapering reduces...... the small current instability region and leads to a laminar flow regime where the voltage wave form is periodic giving the oscillator minimal spectral width. Tapering also leads to an increased output power. Since exponential tapering is not expected to increase the difficulty of fabricating a flux flow...
A modified exponential model for reported death toll during earthquakes
Xinyan Wu; Jianhua Gu
2009-01-01
Reliable earthquake death toll estimate can provide valuable references for disaster relief headquarters and civil administration departments to make arrangement and deployment plan during post-earthquake relief work, thus increasing the efficiency of the relief work to a certain extent. In this study, we acquired the death toll data of Wenchuan earthquake, fitted the data using modified exponential curve and compared the result with that of the exponential function. Experimental verification with Chi-Chi earthquake and Kobe earthquake data shows that the fitted result by modified exponential curve is more satisfactory. The final death toll resulting from future destructive earthquakes can be estimated by the acquired fitting function.
Exponential decay estimates for Singular Integral operators
Ortiz-Caraballo, Carmen; Rela, Ezequiel
2012-01-01
The following subexponential estimate for commutators is proved |[|\\{x\\in Q: |[b,T]f(x)|>tM^2f(x)\\}|\\leq c\\,e^{-\\sqrt{\\alpha\\, t\\|b\\|_{BMO}}}\\, |Q|, \\qquad t>0.\\] where $c$ and $\\alpha$ are absolute constants, $T$ is a Calder\\'on--Zygmund operator, $M$ is the Hardy Littlewood maximal function and $f$ is any function supported on the cube $Q$. It is also obtained \\[|\\{x\\in Q: |f(x)-m_f(Q)|>tM_{1/4;Q}^#(f)(x) \\}|\\le c\\, e^{-\\alpha\\,t}|Q|,\\qquad t>0,\\] where $m_f(Q)$ is the median value of $f$ on the cube $Q$ and $M_{1/4;Q}^#$ is Str\\"omberg's local sharp maximal function. As a consequence it is derived Karagulyan's estimate \\[|\\{x\\in Q: |Tf(x)|> tMf(x)\\}|\\le c\\, e^{-c\\, t}\\,|Q|\\qquad t>0,\\] improving Buckley's theorem. A completely different approach is used based on a combination of "Lerner's formula" with some special weighted estimates of Coifman-Fefferman obtained via Rubio de Francia's algorithm. The method is flexible enough to derive similar estimates for other operators such as multilinear Calder\\'on--Z...
Weihua Mao
2012-01-01
Full Text Available This paper discusses the mean-square exponential stability of uncertain neutral linear stochastic systems with interval time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF has been constructed to derive improved delay-dependent robust mean-square exponential stability criteria, which are forms of linear matrix inequalities (LMIs. By free-weight matrices method, the usual restriction that the stability conditions only bear slow-varying derivative of the delay is removed. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.
Effects of Exponential Trends on Correlations of Stock Markets
Ai-Jing Lin
2014-01-01
Full Text Available Detrended fluctuation analysis (DFA is a scaling analysis method used to estimate long-range power-law correlation exponents in time series. In this paper, DFA is employed to discuss the long-range correlations of stock market. The effects of exponential trends on correlations of Hang Seng Index (HSI are investigated with emphasis. We find that the long-range correlations and the positions of the crossovers of lower order DFA appear to have no immunity to the additive exponential trends. Further, our analysis suggests that an increase in the DFA order increases the efficiency of eliminating on exponential trends. In addition, the empirical study shows that the correlations and crossovers are associated with DFA order and magnitude of exponential trends.
Asymptotic expansions of Feynman integrals of exponentials with polynomial exponent
Kravtseva, A. K.; Smolyanov, O. G.; Shavgulidze, E. T.
2016-10-01
In the paper, an asymptotic expansion of path integrals of functionals having exponential form with polynomials in the exponent is constructed. The definition of the path integral in the sense of analytic continuation is considered.
Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay
Wenli Zhu
2013-01-01
Full Text Available Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to an n-dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our results.
Super-Exponential Solution for a Retrial Supermarket Model
Li, Quan-Lin; Wang, Yang
2011-01-01
In this paper, we provide a new and effective approach for studying super-exponential solution of a retrial supermarket model with Poisson arrivals, exponential service times and exponential retrial times and with two different probing-server numbers. We describe the retrial supermarket model as a system of differential equations by means of density-dependent jump Markov processes, and obtain an iterative algorithm for computing the fixed point of the system of differential equations. Based on the fixed point, we analyze the expected sojourn time that a tagged arriving customer spends in this system, and use numerical examples to indicate different influence of the two probing-server numbers on system performance including the fixed point and the expected sojourn time. Furthermore, we analyze exponential convergence of the current location of the retrial supermarket model to the fixed point, and apply the Kurtz Theorem to study density-dependent jump Markov process given in the retrial supermarket model, whic...
Construction of extended exponential general linear methods 524 ...
Construction of extended exponential general linear methods 524 for solving semi-linear problems. ... Journal Home > Vol 13, No 2 (2014) > ... This paper introduces a new approach for constructing higher order of EEGLM which have become ...
Combinatorial polynomials as moments, Hankel transforms and exponential Riordan arrays
Barry, Paul
2011-01-01
In the case of two combinatorial polynomials, we show that they can exhibited as moments of paramaterized families of orthogonal polynomials, and hence derive their Hankel transforms. Exponential Riordan arrays are the main vehicles used for this.
The true quantum face of the "exponential" decay law
Urbanowski, K
2016-01-01
Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature od the quantum decay process is the presence of three time regimes of the decay process: the early time (initial) leading to the Quantum Zeno (or Anti Zeno) Effects, "exponential" (or "canonical") described by the decay law of the exponential form, and late time characterized by the decay law having inverse--power law form. Based on the fundamental principles of the quantum theory we give the proof that there is no time interval in which the survival probability (decay law) could be a decreasing function of time of the purely exponential form but even at the "exponential" regime the decay curve is oscillatory modulated with a smaller or a large amplitude of oscillations depending on parameters of the model considered.
True quantum face of the "exponential" decay law
Urbanowski, Krzysztof
2017-05-01
Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature of the quantum decay process is the presence of three time regimes of the decay process: the early time (initial) leading to the Quantum Zeno (or Anti Zeno) Effects, "exponential" (or "canonical") described by the decay law of the exponential form, and late time characterized by the decay law having inverse-power law form. Based on the fundamental principles of the quantum theory we give the proof that there is no time interval in which the survival probability (decay law) could be a decreasing function of time of the purely exponential form but even at the "exponential" regime the decay curve is oscillatory modulated with a smaller or a large amplitude of oscillations depending on parameters of the model considered.
Uniformly Exponential Growth and Mapping Class Groups of Surfaces
Anderson, J. W.; Aramayona, J.; Shackleton, K.J.
2005-01-01
We show that the mapping class group (as well as closely related groups) of an orientable surface with finitely generated fundamental group has uniformly exponential growth. We further demonstrate the uniformly non-amenability of many of these groups.
Boundary value problems for partial differential equations with exponential dichotomies
Laederich, Stephane
We are extending the notion of exponential dichotomies to partial differential evolution equations on the n-torus. This allows us to give some simple geometric criteria for the existence of solutions to certain nonlinear Dirichlet boundary value problems.
Heterogeneous Highly Parallel Implementation of Matrix Exponentiation Using GPU
Raja, Chittampally Vasanth; Raghavendra, Prakash S; 10.5121/ijdps.2012.3209
2012-01-01
The vision of super computer at every desk can be realized by powerful and highly parallel CPUs or GPUs or APUs. Graphics processors once specialized for the graphics applications only, are now used for the highly computational intensive general purpose applications. Very expensive GFLOPs and TFLOP performance has become very cheap with the GPGPUs. Current work focuses mainly on the highly parallel implementation of Matrix Exponentiation. Matrix Exponentiation is widely used in many areas of scientific community ranging from highly critical flight, CAD simulations to financial, statistical applications. Proposed solution for Matrix Exponentiation uses OpenCL for exploiting the hyper parallelism offered by the many core GPGPUs. It employs many general GPU optimizations and architectural specific optimizations. This experimentation covers the optimizations targeted specific to the Scientific Graphics cards (Tesla-C2050). Heterogeneous Highly Parallel Matrix Exponentiation method has been tested for matrices of ...
Algebraic and transcendental solutions of some exponential equations
Sondow, Jonathan
2011-01-01
We study algebraic and transcendental powers of positive real numbers, including solutions of each of the equations $x^x=y$, $x^y=y^x$, $x^x=y^y$, $x^y=y$, and $x^{x^y}=y$. Applications to values of the iterated exponential functions are given. The main tools used are classical theorems of Hermite-Lindemann and Gelfond-Schneider, together with solutions of exponential Diophantine equations.
EXPODE -- Advanced Exponential Time Integration Toolbox for MATLAB
2014-01-01
We present a MATLAB toolbox for five different classes of exponential integrators for solving (mildly) stiff ordinary differential equations or time-dependent partial differential equations. For the efficiency of such exponential integrators it is essential to approximate the products of the matrix functions arising in these integrators with vectors in a stable, reliable and efficient way. The toolbox contains options for computing the matrix functions directly by diagonalization or by Pade a...
AN ANALYTICAL SOLUTION FOR AN EXPONENTIAL TYPE DISPERSION PROCESS
王子亭
2001-01-01
The dispersion process in heterogeneous porous media is distance-dependent,which results from multi-scaling property of heterogeneous structure. An analytical model describing the dispersion with an exponential dispersion function is built, which is transformed into ODE problem with variable coefficients, and obtained analytical solution for two type boundary conditions using hypergeometric function and inversion technique.According to the analytical solution and computing results the difference between the exponential dispersion and constant dispersion process is analyzed.
Confronting quasi-exponential inflation with WMAP seven
Pal, Barun Kumar; Pal, Supratik; Basu, B., E-mail: barunp1985@rediffmail.com, E-mail: pal@th.physik.uni-bonn.de, E-mail: banasri@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700 108 (India)
2012-04-01
We confront quasi-exponential models of inflation with WMAP seven years dataset using Hamilton Jacobi formalism. With a phenomenological Hubble parameter, representing quasi exponential inflation, we develop the formalism and subject the analysis to confrontation with WMAP seven using the publicly available code CAMB. The observable parameters are found to fair extremely well with WMAP seven. We also obtain a ratio of tensor to scalar amplitudes which may be detectable in PLANCK.
Exponential order statistic models of software reliability growth
Miller, D. R.
1986-01-01
Failure times of a software reliability growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.
FTEC: a coalescent simulator for modeling faster than exponential growth
Reppell, Mark; Boehnke, Michael; Zöllner, Sebastian
2012-01-01
Summary: Recent genetic studies as well as recorded history point to massive growth in human population sizes during the recent past. To model and understand this growth accurately we introduce FTEC, an easy-to-use coalescent simulation program capable of simulating haplotype samples drawn from a population that has undergone faster than exponential growth. Samples drawn from a population that has undergone faster than exponential growth show an excess of very rare variation and more rapid LD...
Demonstration of the exponential decay law using beer froth
Leike, A. [Ludwig-Maximilians-Universitaet, Sektion Physik, Munich (Germany)]. E-mail: leike@theorie.physik.uni-muenchen.de
2002-01-01
The volume of beer froth decays exponentially with time. This property is used to demonstrate the exponential decay law in the classroom. The decay constant depends on the type of beer and can be used to differentiate between different beers. The analysis shows in a transparent way the techniques of data analysis commonly used in science - consistency checks of theoretical models with the data, parameter estimation and determination of confidence intervals. (author)
PARALLEL MOVING MECHANICAL SYSTEMS
Florian Ion Tiberius Petrescu
2014-09-01
Full Text Available Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 Moving mechanical systems parallel structures are solid, fast, and accurate. Between parallel systems it is to be noticed Stewart platforms, as the oldest systems, fast, solid and precise. The work outlines a few main elements of Stewart platforms. Begin with the geometry platform, kinematic elements of it, and presented then and a few items of dynamics. Dynamic primary element on it means the determination mechanism kinetic energy of the entire Stewart platforms. It is then in a record tail cinematic mobile by a method dot matrix of rotation. If a structural mottoelement consists of two moving elements which translates relative, drive train and especially dynamic it is more convenient to represent the mottoelement as a single moving components. We have thus seven moving parts (the six motoelements or feet to which is added mobile platform 7 and one fixed.
Ayala, R.E.; Gupta, R.P.; Chuck, T.
1995-12-01
The objective of this program is to develop mixed-metal oxide sorbent formulations that are suitable for moving-bed, high-temperature, desulfurization of coal gas. Work continues on zinc titanates formulations and Z-sorb III sorbent.
Hansen, Lennard Højbjerg
2014-01-01
Every day we are presented with bodily expressions in audiovisual media – by anchors, journalists and characters in films for instance. This article explores how body language in the moving image has been and can be approached in a scholarly manner.......Every day we are presented with bodily expressions in audiovisual media – by anchors, journalists and characters in films for instance. This article explores how body language in the moving image has been and can be approached in a scholarly manner....
Hansen, Lennard Højbjerg
2014-01-01
Every day we are presented with bodily expressions in audiovisual media – by anchors, journalists and characters in films for instance. This article explores how body language in the moving image has been and can be approached in a scholarly manner.......Every day we are presented with bodily expressions in audiovisual media – by anchors, journalists and characters in films for instance. This article explores how body language in the moving image has been and can be approached in a scholarly manner....
Upper bounds on a two-term exponential sum
Todd; Cochrane
2001-01-01
［1］Davenport, H. , Heibronn, H., On an exponential sum, Proc. Lond. Math. Soc., 1936, 41(2): 449-453.［2］Hua, L. K., On exponential sums, Sci. Record (Peking) (N.S.), 1957, 1: 1-4.［3］Vaughan, R. C. , The Hardy-Littlewood Method, 2nd ed. , Cambridge Tracts in Math. , Cambridge: Cambridge Univ. Press, 1997, 125.［4］Weil, A., On some exponential sums, Proc. Nat. Acad. Sci. USA, 1948, 34: 204-207.［5］Cochrane, T., Zheng, Z., Pure and mixed exponential sums, Acta Arith. , 1999, 91(3): 249-278.［6］Chalk, J. H. H., On Hua's estimate for exponential sums, Mathematika, 1987, 34: 115-123.［7］Loh, W. K. A. , Hua's Lemma, Bull. Australian Math. Soc., 1994, 50(3): 451-458.［8］Ding, P., An improvement to Chalk's estimation of exponential sums, Acta Arith. , 1991, 59(2): 149-155.
... Health Information Weight Management English English Español Weight Management Obesity is a chronic condition that affects more ... Liver (NASH) Heart Disease & Stroke Sleep Apnea Weight Management Topics About Food Portions Bariatric Surgery for Severe ...
Minimal sets of Reidemeister moves
Polyak, Michael
2009-01-01
It is well known that any two diagrams representing the same oriented link are related by a finite sequence of Reidemeister moves O1, O2 and O3. Depending on orientations of fragments involved in the moves, one may distinguish 4 different versions of each of the O1 and O2 moves, and 8 versions of the O3 move. We introduce a minimal generating set of oriented Reidemeister moves, which includes two moves of types O1 and O2, and only one move of type O3. We then consider other sets of moves and show that only few of them generate all Reidemeister moves.
Elmegreen, Bruce G.
2016-10-01
Exponential radial profiles are ubiquitous in spiral and dwarf Irregular galaxies, but the origin of this structural form is not understood. This talk will review the observations of exponential and double exponential disks, considering both the light and the mass profiles, and the contributions from stars and gas. Several theories for this structure will also be reviewed, including primordial collapse, bar and spiral torques, clump torques, galaxy interactions, disk viscosity and other internal processes of angular momentum exchange, and stellar scattering off of clumpy structure. The only process currently known that can account for this structure in the most theoretically difficult case is stellar scattering off disks clumps. Stellar orbit models suggest that such scattering can produce exponentials even in isolated dwarf irregulars that have no bars or spirals, little shear or viscosity, and profiles that go out too far for the classical Mestel case of primordial collapse with specific angular momentum conservation.
Yang Fang
2016-01-01
Full Text Available The robust exponential stability problem for a class of uncertain impulsive stochastic neural networks of neutral-type with Markovian parameters and mixed time-varying delays is investigated. By constructing a proper exponential-type Lyapunov-Krasovskii functional and employing Jensen integral inequality, free-weight matrix method, some novel delay-dependent stability criteria that ensure the robust exponential stability in mean square of the trivial solution of the considered networks are established in the form of linear matrix inequalities (LMIs. The proposed results do not require the derivatives of discrete and distributed time-varying delays to be 0 or smaller than 1. Moreover, the main contribution of the proposed approach compared with related methods lies in the use of three types of impulses. Finally, two numerical examples are worked out to verify the effectiveness and less conservativeness of our theoretical results over existing literature.
The discrete Laplace exponential family and estimation of Y-STR haplotype frequencies
Andersen, Mikkel Meyer; Eriksen, Poul Svante; Morling, Niels
2013-01-01
Estimating haplotype frequencies is important in e.g. forensic genetics, where the frequencies are needed to calculate the likelihood ratio for the evidential weight of a DNA profile found at a crime scene. Estimation is naturally based on a population model, motivating the investigation...... of the Fisher-Wright model of evolution for haploid lineage DNA markers. An exponential family (a class of probability distributions that is well understood in probability theory such that inference is easily made by using existing software) called the 'discrete Laplace distribution' is described. We illustrate...
Ackerman, Margareta; Branzei, Simina; Loker, David
2011-01-01
In this paper we investigate clustering in the weighted setting, in which every data point is assigned a real valued weight. We conduct a theoretical analysis on the influence of weighted data on standard clustering algorithms in each of the partitional and hierarchical settings, characterising the precise conditions under which such algorithms react to weights, and classifying clustering methods into three broad categories: weight-responsive, weight-considering, and weight-robust. Our analysis raises several interesting questions and can be directly mapped to the classical unweighted setting.
Bayesian estimation of generalized exponential distribution under noninformative priors
Moala, Fernando Antonio; Achcar, Jorge Alberto; Tomazella, Vera Lúcia Damasceno
2012-10-01
The generalized exponential distribution, proposed by Gupta and Kundu (1999), is a good alternative to standard lifetime distributions as exponential, Weibull or gamma. Several authors have considered the problem of Bayesian estimation of the parameters of generalized exponential distribution, assuming independent gamma priors and other informative priors. In this paper, we consider a Bayesian analysis of the generalized exponential distribution by assuming the conventional noninformative prior distributions, as Jeffreys and reference prior, to estimate the parameters. These priors are compared with independent gamma priors for both parameters. The comparison is carried out by examining the frequentist coverage probabilities of Bayesian credible intervals. We shown that maximal data information prior implies in an improper posterior distribution for the parameters of a generalized exponential distribution. It is also shown that the choice of a parameter of interest is very important for the reference prior. The different choices lead to different reference priors in this case. Numerical inference is illustrated for the parameters by considering data set of different sizes and using MCMC (Markov Chain Monte Carlo) methods.
Non-exponential and oscillatory decays in quantum mechanics
Peshkin, Murray [Argonne National Lab. (ANL), Argonne, IL (United States); Volya, Alexander [Florida State Univ., Tallahassee, FL (United States); Zelevinsky, Vladimir [Michigan State Univ., East Lansing, MI (United States)
2014-08-07
The quantum-mechanical theory of the decay of unstable states is revisited. We show that the decay is non-exponential both in the short-time and long-time limits using a more physical definition of the decay rate than the one usually used. We report results of numerical studies based on Winter's model that may elucidate qualitative features of exponential and non-exponential decay more generally. The main exponential stage is related to the formation of a radiating state that maintains the shape of its wave function with exponentially diminishing normalization. We discuss situations where the radioactive decay displays several exponents. The transient stages between different regimes are typically accompanied by interference of various contributions and resulting oscillations in the decay curve. The decay curve can be fully oscillatory in a two-flavor generalization of Winter's model with some values of the parameters. We consider the implications of that result for models of the oscillations reported by GSI.
Enhancing Trust in the Smart Grid by Applying a Modified Exponentially Weighted Averages Algorithm
2012-06-01
11 HVDC High Voltage Direct Current . . . . . . . . . . . . . . . . . . . . . . . . 19 etc. et cetera...System Separation 6.3 Turbine Valve Control 6.3 Load & Generator Rejection 4.5 Stabilizers 4.5 HVDC Controls 3.6 Out-of-Step Relaying 2.7 Discrete
Joung, Haewon
2002-01-01
Let $\\beta>0$ and $W_\\beta (x) = \\exp (-|x|^\\beta )$, $x \\in \\mathbb{R}$. For $c>0$, define $W_{\\beta, cn} (x) = W_\\beta (x)$ if $|x| \\leq c^{1/\\beta}\\,a_{2n}$ and $W_{\\beta, cn} (x) = 0$ if $|x| > c^{1/\\beta}\\,a_{2n}$, where $a_{2n}$ denotes Mhaskar-Rahmanov-Saff number for $W_\\beta$. Let $\\gamma_n (W_{\\beta, cn})$ be the leading coefficient of the $n$th orthonormal polynomial corresponding to $W_{\\beta, cn}$ and write $\\alpha_n(W_{\\beta, cn}) = \\gamma_{n-1}(W_{\\beta, cn})/...
Pac-bayesian bounds for sparse regression estimation with exponential weights
Alquier, Pierre
2010-01-01
We consider the sparse regression model where the number of parameters $p$ is larger than the sample size $n$. The difficulty when considering high-dimensional problems is to propose estimators achieving a good compromise between statistical and computational performances. The BIC estimator for instance performs well from the statistical point of view \\cite{BTW07} but can only be computed for values of $p$ of at most a few tens. The Lasso estimator is solution of a convex minimization problem, hence computable for large value of $p$. However stringent conditions on the design are required to establish fast rates of convergence for this estimator. Dalalyan and Tsybakov \\cite{arnak} propose a method achieving a good compromise between the statistical and computational aspects of the problem. Their estimator can be computed for reasonably large $p$ and satisfies nice statistical properties under weak assumptions on the design. However, \\cite{arnak} proposes sparsity oracle inequalities in expectation for the emp...
Moving Spatial Keyword Queries
Wu, Dingming; Yiu, Man Lung; Jensen, Christian S.
2013-01-01
Web users and content are increasingly being geo-positioned. This development gives prominence to spatial keyword queries, which involve both the locations and textual descriptions of content. We study the efficient processing of continuously moving top-k spatial keyword (MkSK) queries over spatial...... text data. State-of-the-art solutions for moving queries employ safe zones that guarantee the validity of reported results as long as the user remains within the safe zone associated with a result. However, existing safe-zone methods focus solely on spatial locations and ignore text relevancy. We...
BOYLE, PAUL J.; KULU, HILL; COOKE, THOMAS; GAYLE, VERNON; MULDER, CLARAH.
2008-01-01
This paper examines the effect of migration and residential mobility on union dissolution among married and cohabiting couples. Moving is a stressful life event, and a large, multidisciplinary literature has shown that family migration often benefits one partner (usually the man) more than the other. Even so, no study to date has examined the possible impact of within-nation geographical mobility on union dissolution. We base our longitudinal analysis on retrospective event-history data from Austria. Our results show that couples who move frequently have a significantly higher risk of union dissolution, and we suggest a variety of mechanisms that may explain this. PMID:18390300
David-Tabibi, Omid
2008-01-01
In this article we review standard null-move pruning and introduce our extended version of it, which we call verified null-move pruning. In verified null-move pruning, whenever the shallow null-move search indicates a fail-high, instead of cutting off the search from the current node, the search is continued with reduced depth. Our experiments with verified null-move pruning show that on average, it constructs a smaller search tree with greater tactical strength in comparison to standard null-move pruning. Moreover, unlike standard null-move pruning, which fails badly in zugzwang positions, verified null-move pruning manages to detect most zugzwangs and in such cases conducts a re-search to obtain the correct result. In addition, verified null-move pruning is very easy to implement, and any standard null-move pruning program can use verified null-move pruning by modifying only a few lines of code.
Moving Mesh Cosmology: Properties of Gas Disks
Torrey, Paul; Sijacki, Debora; Springel, Volker; Hernquist, Lars
2011-01-01
We compare the structural properties of galaxies formed in cosmological simulations using the smoothed particle hydrodynamics (SPH) code GADGET with those using the moving-mesh code AREPO. Both codes employ identical gravity solvers and the same sub-resolution physics but use very different methods to track the hydrodynamic evolution of gas. This permits us to isolate the effects of the hydro solver on the formation and evolution of galactic disks. In a matching sample of GADGET and AREPO haloes we fit simulated gas disks with exponential profiles. We find that the cold gas disks formed using AREPO have systematically larger disk scale lengths and higher specific angular momenta than their GADGET counterparts. The reason for these differences is rooted in the inaccuracies of the SPH solver and calls for a reassessment of commonly adopted feedback prescriptions in cosmological simulations.
Exponential Sensitivity and its Cost in Quantum Physics.
Gilyén, András; Kiss, Tamás; Jex, Igor
2016-02-10
State selective protocols, like entanglement purification, lead to an essentially non-linear quantum evolution, unusual in naturally occurring quantum processes. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. Here we demonstrate that chaotic behaviour is a rather generic feature in state selective protocols: exponential sensitivity can exist for all initial states in an experimentally realisable optical scheme. Moreover, any complex rational polynomial map, including the example of the Mandelbrot set, can be directly realised. In state selective protocols, one needs an ensemble of initial states, the size of which decreases with each iteration. We prove that exponential sensitivity to initial states in any quantum system has to be related to downsizing the initial ensemble also exponentially. Our results show that magnifying initial differences of quantum states (a Schrödinger microscope) is possible; however, there is a strict bound on the number of copies needed.
On the Exponential Probability Bounds for the Bernoulli Random Variables
Nikulin, Vladimir
2010-01-01
We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha, beta}. In order to optimize the bound we are interested to minimize linear coefficient alpha and to maximize exponential coefficient beta. Generally, the value of linear coefficient alpha may not be smaller than one. The following 2 settings were proved: 1) {1, 2} in the case of classical discreet problem as it was formulated by Bernoulli in the 17th century, and 2) {1, 2/(1+epsilon^2)} in the general discreet case with arbitrary rational p and epsilon. The second setting represents a new structure of the exponential bound which may be extended to continuous case.
Exponential rise of dynamical complexity in quantum computing through projections.
Burgarth, Daniel Klaus; Facchi, Paolo; Giovannetti, Vittorio; Nakazato, Hiromichi; Pascazio, Saverio; Yuasa, Kazuya
2014-10-10
The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once 'observed' as outlined above. Conversely, we show that any complex quantum dynamics can be 'purified' into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics.
Kullback-Leibler divergence and the Pareto-Exponential approximation.
Weinberg, G V
2016-01-01
Recent radar research interests in the Pareto distribution as a model for X-band maritime surveillance radar clutter returns have resulted in analysis of the asymptotic behaviour of this clutter model. In particular, it is of interest to understand when the Pareto distribution is well approximated by an Exponential distribution. The justification for this is that under the latter clutter model assumption, simpler radar detection schemes can be applied. An information theory approach is introduced to investigate the Pareto-Exponential approximation. By analysing the Kullback-Leibler divergence between the two distributions it is possible to not only assess when the approximation is valid, but to determine, for a given Pareto model, the optimal Exponential approximation.
On the performance of exponential integrators for problems in magnetohydrodynamics
Einkemmer, Lukas; Loffeld, John
2016-01-01
Exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations. Over the past decades these methods have been studied theoretically and their performance was evaluated using a range of test problems. While the results of these investigations showed that exponential integrators can provide significant computational savings, the research on validating this hypothesis for large scale systems and understanding what classes of problems can particularly benefit from the use of the new techniques is in its initial stages. Resistive magnetohydrodynamic (MHD) modeling is widely used in studying large scale behavior of laboratory and astrophysical plasmas. In many problems numerical solution of MHD equations is a challenging task due to the temporal stiffness of this system in the parameter regimes of interest. In this paper we evaluate the performance of exponential integrators on large MHD problems and compare the...
Exponential stretch-rotation (ESR) formulation of general relativity
Khokhlov, A M
2003-01-01
We study a tensorial exponential transformation of a three-dimensional metric of space-like hypersurfaces embedded in a four-dimensional space-time, $\\gamma_{ij} = e^{\\epsilon_{ikm}\\theta_m} e^{\\phi_k} e^{-\\epsilon_{jkn}\\theta_n}$, where $\\phi_k$ are logarithms of the eigenvalues of $\\gamma_{ij}$, $\\theta_k$ are rotation angles, and $\\epsilon_{ijk}$ is a fully anti-symmetric symbol. Evolution part of Einstein's equations, formulated in terms of $\\phi_k$ and $\\theta_k$, describes time evolution of the metric at every point of a hyper-surface as a continuous stretch and rotation of a local coordinate system in a tangential space. The exponential stretch-rotation (ESR) transformation generalizes particular exponential transformations used previously in cases of spatial symmetry. The ESR 3+1 formulation of Einstein's equations may have certain advantages for long-term stable integration of these equations.
Design of a 9-loop quasi-exponential waveform generator.
Banerjee, Partha; Shukla, Rohit; Shyam, Anurag
2015-12-01
We know in an under-damped L-C-R series circuit, current follows a damped sinusoidal waveform. But if a number of sinusoidal waveforms of decreasing time period, generated in an L-C-R circuit, be combined in first quarter cycle of time period, then a quasi-exponential nature of output current waveform can be achieved. In an L-C-R series circuit, quasi-exponential current waveform shows a rising current derivative and thereby finds many applications in pulsed power. Here, we have described design and experiment details of a 9-loop quasi-exponential waveform generator. In that, design details of magnetic switches have also been described. In the experiment, output current of 26 kA has been achieved. It has been shown that how well the experimentally obtained output current profile matches with the numerically computed output.
On the performance of exponential integrators for problems in magnetohydrodynamics
Einkemmer, Lukas; Tokman, Mayya; Loffeld, John
2017-02-01
Exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations. Over the past decades these methods have been studied theoretically and their performance was evaluated using a range of test problems. While the results of these investigations showed that exponential integrators can provide significant computational savings, the research on validating this hypothesis for large scale systems and understanding what classes of problems can particularly benefit from the use of the new techniques is in its initial stages. Resistive magnetohydrodynamic (MHD) modeling is widely used in studying large scale behavior of laboratory and astrophysical plasmas. In many problems numerical solution of MHD equations is a challenging task due to the temporal stiffness of this system in the parameter regimes of interest. In this paper we evaluate the performance of exponential integrators on large MHD problems and compare them to a state-of-the-art implicit time integrator. Both the variable and constant time step exponential methods of EPIRK-type are used to simulate magnetic reconnection and the Kevin-Helmholtz instability in plasma. Performance of these methods, which are part of the EPIC software package, is compared to the variable time step variable order BDF scheme included in the CVODE (part of SUNDIALS) library. We study performance of the methods on parallel architectures and with respect to magnitudes of important parameters such as Reynolds, Lundquist, and Prandtl numbers. We find that the exponential integrators provide superior or equal performance in most circumstances and conclude that further development of exponential methods for MHD problems is warranted and can lead to significant computational advantages for large scale stiff systems of differential equations such as MHD.
Chowell, Gerardo; Viboud, Cécile
2016-10-01
The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing models that capture the baseline transmission characteristics in order to generate reliable epidemic forecasts. Improved models for epidemic forecasting could be achieved by identifying signature features of epidemic growth, which could inform the design of models of disease spread and reveal important characteristics of the transmission process. In particular, it is often taken for granted that the early growth phase of different growth processes in nature follow early exponential growth dynamics. In the context of infectious disease spread, this assumption is often convenient to describe a transmission process with mass action kinetics using differential equations and generate analytic expressions and estimates of the reproduction number. In this article, we carry out a simulation study to illustrate the impact of incorrectly assuming an exponential-growth model to characterize the early phase (e.g., 3-5 disease generation intervals) of an infectious disease outbreak that follows near-exponential growth dynamics. Specifically, we assess the impact on: 1) goodness of fit, 2) bias on the growth parameter, and 3) the impact on short-term epidemic forecasts. Designing transmission models and statistical approaches that more flexibly capture the profile of epidemic growth could lead to enhanced model fit, improved estimates of key transmission parameters, and more realistic epidemic forecasts.
Rennie, Richard
2015-01-01
The history of the moving image (the cinema) is well documented in books and on the Internet. This article offers a number of activities that can easily be carried out in a science class. They make use of the phenomenon of "Persistence of Vision." The activities presented herein demonstrate the functionality of the phenakistoscope, the…
Maximilien Brice
2002-01-01
DELPHI (DEtector for Lepton, Photon and Hadron Identification) was one of four experiments at CERN's Large Electron-Positron collider (LEP). Following LEP's decommissioning, the DELPHI detector has been moved within the cavern at Point 8, and now awaits permanent display.
Leitheiser, Erin
two, fell short of increased expectations. This is significant because it demonstrates how external factors alone can change notions and attributions of responsibility (move the goalpost) as well as the effort needed to meet these new expectations. Overall, this shift illustrates the further...
Mortensen, Kristian; Hazel, Spencer
2014-01-01
Opening an interaction is a crucial step in establishing and maintaining social relationships. In this paper we describe how participants in an institutional setting, a help desk counter for exchange students at an international university, literally move into interaction. This is accomplished...
Christensen, Mark Schram; Grünbaum, Thor
2017-01-01
In this chapter, we assume the existence of a sense of “movement activity” that arises when a person actively moves a body part. This sense is usually supposed to be part of sense of agency (SoA). The purpose of the chapter is to determine whether the already existing experimental paradigms can...
Geertzen, Jan H. B.
2008-01-01
Moving beyond Disability was the theme of the 12th World Congress of the International Society for Prosthetics and Orthotics. This paper is a reflection of one of the keynote lectures discussing the International Classification of Functioning, Disability and Health (ICF). Multicultural aspects in di
Simonsen, Gunvor
2008-01-01
as characterized by cultural diversity and variation. Moreover, the field has been haunted by a tendency of moving to easily from descriptive evidence to conclusions about African identity in the Americas. A promising way to overcome these problems, it is suggested, is to develop research that focuses on single...
Ainscow, Mel; Hopkins, David
1992-01-01
In many countries, education legislation embodies contradictory pressures for centralization and decentralization. In the United Kingdom, there is growing government control over policy and direction of schools; schools are also being given more responsibility for resource management. "Moving" schools within Improving the Quality of Education for…
New results on robust exponential stability of integral delay systems
Melchor-Aguilar, Daniel
2016-06-01
The robust exponential stability of integral delay systems with exponential kernels is investigated. Sufficient delay-dependent robust conditions expressed in terms of linear matrix inequalities and matrix norms are derived by using the Lyapunov-Krasovskii functional approach. The results are combined with a new result on quadratic stabilisability of the state-feedback synthesis problem in order to derive a new linear matrix inequality methodology of designing a robust non-fragile controller for the finite spectrum assignment of input delay systems that guarantees simultaneously a numerically safe implementation and also the robustness to uncertainty in the system matrices and to perturbation in the feedback gain.
Exponential sensitivity of noise-driven switching in genetic networks
Mehta, Pankaj; Mukhopadhyay, Ranjan; Wingreen, Ned S.
2008-06-01
There is increasing experimental evidence that cells can utilize biochemical noise to switch probabilistically between distinct gene-expression states. In this paper, we demonstrate that such noise-driven switching is dominated by tails of probability distributions and is therefore exponentially sensitive to changes in physiological parameters such as transcription and translation rates. Exponential sensitivity limits the robustness of noise-driven switching, suggesting cells may use other mechanisms in order to switch reliably. We discuss our results in the context of competence in the bacterium Bacillus subtilis.
Exponential Lower Bounds and Separation for Query Rewriting
Kikot, Stanislav; Podolskii, Vladimir; Zakharyaschev, Michael
2012-01-01
We establish connections between the size of circuits and formulas computing monotone Boolean functions and the size of first-order and nonrecursive Datalog rewritings for conjunctive queries over OWL 2 QL ontologies. We use known lower bounds and separation results from circuit complexity to prove similar results for the size of rewritings that do not use non-signature constants. For example, we show that, in the worst case, positive existential and nonrecursive Datalog rewritings are exponentially longer than the original queries; nonrecursive Datalog rewritings are in general exponentially more succinct than positive existential rewritings; while first-order rewritings can be superpolynomially more succinct than positive existential rewritings.
Real-Time Exponential Curve Fits Using Discrete Calculus
Rowe, Geoffrey
2010-01-01
An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.
AN EXPONENTIAL INEQUALITY FOR AUTOREGRESSIVE PROCESSES IN ADAPTIVE TRACKING
Bernard BERCU
2007-01-01
A wide range of literature concerning classical asymptotic properties for linear models with adaptive control is available, such as strong laws of large numbers or central limit theorems.Unfortunately, in contrast with the situation without control, it appears to be impossible to find sharp asymptotic or nonasymptotic properties such as large deviation principles or exponential inequalities.Our purpose is to provide a first step towards that direction by proving a very simple exponential inequality for the standard least squares estimator of the unknown parameter of Gaussian autoregressive process in adaptive tracking.
Exponential stability for uncertain neutral systems with Markov jumps
Shuping HE; Fei LIU
2009-01-01
This paper deals with the global exponential stability problems for stochastic neutral Markov jump sys-tems(MJSs) with uncertain parameters and multiple time-delays,The delays are respectively considered as constant and time varying cases,and the uncertainties are assumed to be norm bounded.By selecting appropriate Lyapunov-Krasovskii functions,it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties.The stability criteria are formulated in the form of linear matrix inequalities(LMIs),which can be easily checked in practice.Finally,two numerical examples are exploited to illustrate the effectiveness of the developed techniques.
THE ROC CURVE MODEL FROM GENERALIZED-EXPONENTIAL DISTRIBUTION
Ehtesham Hussain
2011-04-01
Full Text Available Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 In biomedical studies often yield continuously positively skewed (non- normal distributed data. In this regard Generalized-Exponential Distribution is suggested for analyzing such data. In this paper the parametric equation of the Receiving Operating Characteristic (ROC curve model is established under the assumptions of bi-distributional population based on pair of Generalized-Exponential Distributions. Also its maximum likelihood estimator MLE, sampling distribution , equivalence test statistic and exact confidence interval are derived.
On an Asymptotic Behavior of Exponential Functional Equation
Soon Mo JUNG
2006-01-01
The stability problems of the exponential (functional) equation on a restricted domain will be investigated, and the results will be applied to the study of an asymptotic property of that equation. More precisely, the following asymptotic property is proved: Let X be a real (or complex)normed space. A mapping f : X → C is exponential if and only if f(x + y) - f(x)f(y) → 0 as ‖x‖ + ‖y‖→∞ under some suitable conditions.
Stability of the Exponential Functional Equation in Riesz Algebras
Bogdan Batko
2014-01-01
Full Text Available We deal with the stability of the exponential Cauchy functional equation F(x+y=F(xF(y in the class of functions F:G→L mapping a group (G, + into a Riesz algebra L. The main aim of this paper is to prove that the exponential Cauchy functional equation is stable in the sense of Hyers-Ulam and is not superstable in the sense of Baker. To prove the stability we use the Yosida Spectral Representation Theorem.
On unit root formulas for toric exponential sums
Adolphson, Alan
2010-01-01
Starting from a classical generating series for Bessel functions due to Schlomilch, we use Dwork's relative dual theory to broadly generalize unit-root results of Dwork on Kloosterman sums and Sperber on hyperkloosterman sums. In particular, we express the (unique) p-adic unit root of an arbitrary exponential sum on the torus in terms of special values of the p-adic analytic continuation of a ratio of A-hypergeometric functions. In contrast with the earlier works, we use noncohomological methods and obtain results that are valid for arbitrary exponential sums without any hypothesis of nondegeneracy.
TESTING FOR VARYING DISPERSION IN DISCRETE EXPONENTIAL FAMILY NONLINEAR MODELS
LinJinguan; WeiBocheng; ZhangNansong
2003-01-01
It is necessary to test for varying dispersion in generalized nonlinear models. Wei ,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models. This type of problem in the framework of general discrete exponential family nonlinear models is discussed. Two types of varying dispersion, which are random coefficients model and random effects model, are proposed,and corresponding score test statistics are constructed and expressed in simple ,easy to use ,matrix formulas.
Exponential model for option prices: Application to the Brazilian market
Ramos, Antônio M. T.; Carvalho, J. A.; Vasconcelos, G. L.
2016-03-01
In this paper we report an empirical analysis of the Ibovespa index of the São Paulo Stock Exchange and its respective option contracts. We compare the empirical data on the Ibovespa options with two option pricing models, namely the standard Black-Scholes model and an empirical model that assumes that the returns are exponentially distributed. It is found that at times near the option expiration date the exponential model performs better than the Black-Scholes model, in the sense that it fits the empirical data better than does the latter model.
Generic super-exponential stability of elliptic equilibrium positions for symplectic vector fields
Niederman, Laurent
2013-11-01
In this article, we consider linearly stable elliptic fixed points (equilibrium) for a symplectic vector field and prove generic results of super-exponential stability for nearby solutions. We will focus on the neighborhood of elliptic fixed points but the case of linearly stable isotropic reducible invariant tori in a Hamiltonian system should be similar. More specifically, Morbidelli and Giorgilli have proved a result of stability over superexponentially long times if one considers an analytic Lagrangian torus, invariant for an analytic Hamiltonian system, with a diophantine translation vector which admits a sign-definite torsion. Then, the solutions of the system move very little over times which are super-exponentially long with respect to the inverse of the distance to the invariant torus. The proof proceeds in two steps: first one constructs a high-order Birkhoff normal form, then one applies the Nekhoroshev theory. Bounemoura has shown that the second step of this construction remains valid if the Birkhoff normal form linked to the invariant torus or the elliptic fixed point belongs to a generic set among the formal series. This is not sufficient to prove this kind of super-exponential stability results in a general setting. We should also establish that the most strongly non resonant elliptic fixed point or invariant torus in a Hamiltonian system admits Birkhoff normal forms fitted for the application of the Nekhoroshev theory. Actually, the set introduced by Bounemoura is already very large but not big enough to ensure that a typical Birkhoff normal form falls into this class. We show here that this property is satisfied generically in the sense of the measure (prevalence) through infinite-dimensional probe spaces (that is, an infinite number of parameters chosen at random) with methods similar to those developed in a paper of Gorodetski, Kaloshin and Hunt in another setting.
Propagation of exponential shock wave in an axisymmetric rotating non-ideal dusty gas
Nath, G.
2016-09-01
One-dimensional unsteady isothermal and adiabatic flow behind a strong exponential shock wave propagating in a rotational axisymmetric mixture of non-ideal gas and small solid particles, which has variable azimuthal and axial fluid velocities, is analyzed. The shock wave is driven out by a piston moving with time according to exponential law. The azimuthal and axial components of the fluid velocity in the ambient medium are assumed to be varying and obeying exponential laws. In the present work, small solid particles are considered as pseudo-fluid with the assumption that the equilibrium flow-conditions are maintained in the flow-field, and the viscous-stress and heat conduction of the mixture are negligible. Solutions are obtained in both the cases, when the flow between the shock and the piston is isothermal or adiabatic by taking into account the components of vorticity vector and compressibility. It is found that the assumption of zero temperature gradient brings a profound change in the density, axial component of vorticity vector and compressibility distributions as compared to that of the adiabatic case. To investigate the behavior of the flow variables and the influence on the shock wave propagation by the parameter of non-idealness of the gas overline{b} in the mixture as well as by the mass concentration of solid particles in the mixture Kp and by the ratio of the density of solid particles to the initial density of the gas G1 are worked out in detail. It is interesting to note that the shock strength increases with an increase in G1 ; whereas it decreases with an increase in overline{b} . Also, a comparison between the solutions in the cases of isothermal and adiabatic flows is made.
Hong-Ling Ye; Wei-Wei Wang; Ning Chen; Yun-Kang Sui
2016-01-01
In this paper, a model of topology optimization with linear buckling constraints is established based on an independent and continuous mapping method to minimize the plate/shell structure weight. A composite exponential function (CEF) is selected as filtering functions for element weight, the element stiffness matrix and the element geomet-ric stiffness matrix, which recognize the design variables, and to implement the changing process of design variables from“discrete”to“continuous”and back to“discrete”. The buck-ling constraints are approximated as explicit formulations based on the Taylor expansion and the filtering function. The optimization model is transformed to dual programming and solved by the dual sequence quadratic programming algo-rithm. Finally, three numerical examples with power function and CEF as filter function are analyzed and discussed to demonstrate the feasibility and efficiency of the proposed method.
Berti, E; González, J A; Sperhake, U; Berti, Emanuele; Cardoso, Vitor; Gonzalez, Jose A.; Sperhake, Ulrich
2007-01-01
The ringdown phase following a binary black hole merger is usually assumed to be well described by a linear superposition of complex exponentials (quasinormal modes). In the strong-field conditions typical of a binary black hole merger, non-linear effects may produce mode coupling. Mode coupling can also be induced by the black hole's rotation, or by expanding the radiation field in terms of spin-weighted spherical harmonics (rather than spin-weighted spheroidal harmonics). Observing deviations from the predictions of linear black hole perturbation theory requires optimal fitting techniques to extract ringdown parameters from numerical waveforms, which are inevitably affected by numerical error. So far, non-linear least-squares fitting methods have been used as the standard workhorse to extract frequencies from ringdown waveforms. These methods are known not to be optimal for estimating parameters of complex exponentials. Furthermore, different fitting methods have different performance in the presence of noi...
Tijani A. Apalara
2014-12-01
Full Text Available In this article we consider one-dimensional linear thermoelastic system of Timoshenko type with linear frictional damping and a distributed delay acting on the displacement equation. The heat flux of the system is governed by Cattaneo's law. Under suitable assumption on the weight of the delay and that of frictional damping, we establish the well-posedness result and prove that the system is exponentially stable regardless of the speeds of wave propagation.
... obese. Achieving a healthy weight can help you control your cholesterol, blood pressure and blood sugar. It ... use more calories than you eat. A weight-control strategy might include Choosing low-fat, low-calorie ...
Ackerman, Margareta; Ben-David, Shai; Branzei, Simina
2012-01-01
We investigate a natural generalization of the classical clustering problem, considering clustering tasks in which different instances may have different weights.We conduct the first extensive theoretical analysis on the influence of weighted data on standard clustering algorithms in both...... the partitional and hierarchical settings, characterizing the conditions under which algorithms react to weights. Extending a recent framework for clustering algorithm selection, we propose intuitive properties that would allow users to choose between clustering algorithms in the weighted setting and classify...
Wuttke, Joachim
2009-01-01
An algorithm is described for computing the Laplace transform (one-sided Fourier sine and cosine transform) of the stretched (or compressed) exponential function exp(-t^beta) (also known as Kohlrausch-Williams-Watts function, as characteristic function of a Levy stable distribution, or as complementary cumulative Weibull distribution) for exponents beta between 0.1 and 2. For low and high frequencies, the well-known series expansions are used; for intermediate frequencies, the explicit integration is strongly accelerated by the Ooura-Mori double exponential transformation. The algorithm is implemented in C as library libkww. The source code is available at http://www.messen-und-deuten.de/kww
... baby, taken just after he or she is born. A low birth weight is less than 5.5 pounds. A high ... weight is more than 8.8 pounds. A low birth weight baby can be born too small, too early (premature), or both. This ...
Towards multi-exponential analysis in optically stimulated luminescence
Ankjærgaard, Christina; Jain, Mayank; Hansen, Per Christian
2010-01-01
Optically stimulated luminescence (OSL) data from quartz can follow different mathematical forms depending on the stimulation mode. These data can be described in terms of different multi-exponential models and can be numerically fitted using several well-known methods. Here we make a comparative...
Geometry of exponential family nonlinear models and some asymptotic inference
韦博成
1995-01-01
A differential geometric framework in Euclidean space for exponential family nonlinear models is presented. Based on this framework, some asymptotic inference related to statistical curvatures and Fisher information are studied. This geometric framework can also be extended to more genera) dass of models and used to study some other problems.
Exponentially Localized Wannier Functions in Periodic Zero Flux Magnetic Fields
De Nittis, Giuseppe
2011-01-01
n this work, we investigate conditions which ensure the existence of an exponentially localized Wannier basis for a given periodic hamiltonian. We extend previous results [Pan07, Kuc09] to include periodic zero flux magnetic fields. The new notion of magnetic symmetry plays a crucial r\\^ole; to a large class of symmetries for a non-magnetic system, one can associate "magnetic" symmetries of the related magnetic system. Observing that the existence of an exponentially localized Wannier basis is equivalent to the triviality of the so-called Bloch bundle, a rank m hermitian vector bundle over the Brillouin zone, we prove that magnetic time-reversal symmetry is sufficient to ensure the triviality of the Bloch bundle in spatial dimension d = 1, 2, 3. For d = 4, an exponentially localized Wannier basis exists provided that the trace per unit volume of a suitable function of the Fermi projection vanishes. For d > 4 and d \\leq 2m (stable rank regime) only the exponential localization of a subset of Wannier functions ...
Fine Tuning in Quintessence Models with Exponential Potentials
Rosenfeld, R; Jr., Urbano Lopes Franca; Rosenfeld, Rogerio
2002-01-01
We show that there still are reasonable regions of the parameter space of the simple exponential potential model for quintessence that are allowed by observational constraints. We find that the level of fine tuning that is required in this model is not too stringent.
Exponentially Fitted Variants of Euler's Method for ODEs
Kanwar, V.; Tomar, S. K.
2008-01-01
A new class of Euler's method for the numerical solution of ordinary differential equations is presented in this article. The methods are iterative in nature and admit their geometric derivation from an exponentially fitted osculating straight line. They are single-step methods and do not require evaluation of any derivatives. The accuracy and…
Meet and Join Matrices in the Poset of Exponential Divisors
Ismo Korkee; Pentti Haukkanen
2009-06-01
It is well-known that $(\\mathbb{Z}_+,|)=(\\mathbb{Z}_+,GCD,LCM)$ is a lattice, where $|$ is the usual divisibility relation and $GCD$ and $LCM$ stand for the greatest common divisor and the least common multiple of positive integers. The number $d=\\prod^r_{k=1}p^{d^{(k)}}_k$ is said to be an exponential divisor or an -divisor of $n=\\prod^r_{k=1}p^{n^{(k)}}_k(n >1)$, written as $d|_e n$, if $d^{(k)}|n^{(k)}$ for all prime divisors $p_k$ of . It is easy to see that $(\\mathbb{Z}_+\\backslash\\{1\\},|_e)$ is a poset under the exponential divisibility relation but not a lattice, since the greatest common exponential divisor $(GCED)$ and the least common exponential multiple $(LCEM)$ do not always exist. In this paper we embed this poset in a lattice. As an application we study the $GCED$ and $LCEM$ matrices, analogues of $GCD$ and $LCM$ matrices, which are both special cases of meet and join matrices on lattices.
Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation
Gordon, Sheldon P.; Yang, Yajun
2017-01-01
This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…
Einstein Static Universe in Exponential $f(T)$ Gravity
Li, Jung-Tsung; Geng, Chao-Qiang
2013-01-01
We analyze the stability of the Einstein static closed and open universe in two types of exponential $f(T)$ gravity theories. We show that the stable solutions exist in these two models. In particular, we find that large regions of parameter space in equation of state $w=p/\\rho$ for the stable universe are allowed in the $f(T)$ theories.
Einstein static universe in exponential f(T) gravity
Li, Jung-Tsung; Lee, Chung-Chi; Geng, Chao-Qiang [National Tsing Hua University, Department of Physics, Hsinchu (China); National Center for Theoretical Sciences, Physics Division, Hsinchu (China)
2013-02-15
We analyze the stability of the Einstein static closed and open universe in two types of exponential f(T) gravity theory. We show that stable solutions exist in these two models. In particular, we find that large regions of parameter space in equation of state w=p/{rho} for the stable universe are allowed in the f(T) theories. (orig.)
The universe evolution in exponential $F(R)$-gravity
Bamba, K; Myrzakulov, R; Odintsov, S D; Sebastiani, L
2013-01-01
A generic feature of viable exponential $F(R)$-gravity is investigated. An additional modification to stabilize the effective dark energy oscillations during matter era is proposed and applied to two viable models. An analysis on the future evolution of the universe is performed. Furthermore, a unified model for early and late-time acceleration is proposed and studied.
Exact Exponential-Time Algorithms for Domination Problems in Graphs
van Rooij, J.M.M.
2011-01-01
This PhD thesis studies exact exponential-time algorithms for domination problems in graphs. Domination problems in graphs are a special kind of subset problems in graphs. A subset problem in a graph is a problem where one is given a graph G=(V,E), and one is asked whether there exist some subset S
Electron traps in semiconducting polymers: exponential versus Gaussian trap distribution
Nicolai, H.T.; Mandoc, M.M.; Blom, P.W.M.
2011-01-01
The low electron currents in poly(dialkoxy-p-phenylene vinylene) (PPV) derivatives and their steep voltage dependence are generally explained by trap-limited conduction in the presence of an exponential trap distribution. Here we demonstrate that the electron transport of several PPV derivatives can
Electron traps in semiconducting polymers : Exponential versus Gaussian trap distribution
Nicolai, H. T.; Mandoc, M. M.; Blom, P. W. M.
2011-01-01
The low electron currents in poly(dialkoxy-p-phenylene vinylene) (PPV) derivatives and their steep voltage dependence are generally explained by trap-limited conduction in the presence of an exponential trap distribution. Here we demonstrate that the electron transport of several PPV derivatives can
Using Logarithms to Explore Power and Exponential Functions.
Rahn, James R.; Berndes, Barry A.
1994-01-01
Discusses activities to help students make visual generalizations about power and exponential functions, methods to determine an approximate function represented by data using logarithms, hands-on activities, and student activity sheets. Includes a Pascal Turbo computer program which generates random numbers. (MKR)
Long-lasting Exponential Spreading in Periodically Driven Quantum Systems
Wang, Jiao; Casati, Giulio; Gong, Jiangbin; 10.1103/PhysRevLett.107.234104
2012-01-01
Using a dynamical model relevant to cold-atom experiments, we show that long-lasting exponential spreading of wave packets in momentum space is possible. Numerical results are explained via a pseudo-classical map, both qualitatively and quantitatively. Possible applications of our findings are also briefly discussed.
Cycles in Repeated Exponentiation Modulo $p^n$
Glebsky, Lev
2010-01-01
Given a number $r$, we consider the dynamical system generated by repeated exponentiations modulo $r$, that is, by the map $u \\mapsto f_g(u)$, where $f_g(u) \\equiv g^u \\pmod r$ and $0 \\le f_g(u) \\le r-1$. The number of cycles of the defined above dynamical system is considered for $r=p^n$.
Loss of exponential stability for a thermoelastic system with memory
Bruno Ferreira Alves
2010-09-01
Full Text Available In this article we study a thermoelastic system considering the linearized model proposed by Gurtin and Pipkin [8] instead of the Fourier's law for the heat flux. We use theory of semigroups [9, 11] combining Pruss' Theorem [10] and the idea developed in [5] to show that the system is not exponentially stable.
A simple proof of Renner's exponential de Finetti theorem
Vidick, Thomas; Yuen, Henry
2016-01-01
We give a simple proof of the exponential de Finetti theorem due to Renner. Like Renner's proof, ours combines the post-selection de Finetti theorem, the Gentle Measurement lemma, and the Chernoff bound, but avoids virtually all calculations, including any use of the theory of types.
Quadratic Lyapunov Function and Exponential Dichotomy on Time Scales
ZHANG JI; LIU ZHEN-XIN
2011-01-01
In this paper, we study the relationship between exponential dichotomy and quadratic Lyapunov function for the linear equation x△ ＝ A(t)x on time scales.Moreover, for the nonlinear perturbed equation x△ ＝ A(t)x + f(t,x) we give the instability of the zero solution when f is sufficiently small.
An Exponentially Small $\\mu$--term in String Theory
Halyo, Edi
2009-01-01
We describe a mechanism that produces an exponentially small $\\mu$--term on the world--volumes of D5 branes wrapping a deformed and fibered $A_3$ singularity. The small $\\mu$ arises due to brane instanton effects which can be calculated after a geometric transition at one of the nodes of the singularity.
EXPONENTIAL STABILITY OF INTERVAL DYNAMICAL SYSTEM WITH MULTIDELAY
孙继涛; 张银萍; 刘永清; 邓飞其
2002-01-01
Using the matrix measure and delay differential inequality, the sufficient conditions were obtained for exponential stability of interval dynamical system with multidelay. These conditions are an improvement and extension of the results achieved in earlier papers presented by LIAO, LIU, ZHANG, SUN, et al.
The Harmonic Decomposition Reconstruction for the Exponential Radon Transform
无
2002-01-01
The exponential Radon transform, a generalization of the Radon transform, is defined andstudied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain andrange, and this leads to the harmonic decomposition reconstruction. The results are similar results of Tre-tiak and Metz.
Exponential Stabilization for C0 -Semigroups Under Compact Perturbation
LILT Li-xin
2008-01-01
It is proved that a system under compact perturbation cannot be uniformly exponentially stable for an isometric C0-semigroup or a C0-group with polynomial growth for negative time in a Banach space. The results extend and improve the corresponding results of previous literature.
Minimal requirements for exponential growth of Lactococcus lactis
Jensen, Peter Ruhdal; Hammer, Karin
1993-01-01
A minimal growth medium containing glucose, acetate, vitamins, and eight amino acids allowed for growth of Lactococcus lactis subsp. lactis, with a specific growth rate in batch culture of mu = 0.3 h-1. With 19 amino acids added, the growth rate increased to mu = 0.7 h-1 and the exponential growth...
Weinstein-Sobolev Spaces of Exponential Type and Applications
Hassen BEN MOHAMED; Belgacem GHRIBI
2013-01-01
In this paper,we introduce and study the Sobolev spaces of exponential type associated with the Weinstein operator,via some elements of harmonic analysis related to this operator.In particular,some properties,including completeness and imbedding theorem,are proved.Finally,using the theory of reproducing kernels,some applications are given for these spaces.
Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation
Gordon, Sheldon P.; Yang, Yajun
2017-01-01
This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…
On some Vongruence with Application to Exponential Sums
Soon-Mo Jung
2004-02-01
We will study the solution of a congruence, $x≡ g^{(1/2)_g(2^n)}\\mathrm{mod} 2^n$, depending on the integers and , where $_g(2^n)$ denotes the order of modulo $2^n$. Moreover, we introduce an application of the above result to the study of an estimation of exponential sums.
Exponential stability of dynamic equations on time scales
Raffoul Youssef N
2005-01-01
Full Text Available We investigate the exponential stability of the zero solution to a system of dynamic equations on time scales. We do this by defining appropriate Lyapunov-type functions and then formulate certain inequalities on these functions. Several examples are given.
Exponential decay for solutions to semilinear damped wave equation
Gerbi, Stéphane
2011-10-01
This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Intro- ducing an appropriate Lyapunov function, we prove that when the damping is linear, we can find initial data, for which the solution decays exponentially. This result improves an early one in [4].
The generalized exponential function and fractional trigonometric identities
Radwan, Ahmed G.
2011-08-01
In this work, we recall the generalized exponential function in the fractional-order domain which enables defining generalized cosine and sine functions. We then re-visit some important trigonometric identities and generalize them from the narrow integer-order subset to the more general fractional-order domain. Generalized hyperbolic function relations are also given. © 2011 IEEE.
The exponential age distribution and the Pareto firm size distribution
Coad, Alex
2008-01-01
Recent work drawing on data for large and small firms has shown a Pareto distribution of firm size. We mix a Gibrat-type growth process among incumbents with an exponential distribution of firm’s age, to obtain the empirical Pareto distribution.
Modelling income data using two extensions of the exponential distribution
Calderín-Ojeda, Enrique; Azpitarte, Francisco; Gómez-Déniz, Emilio
2016-11-01
In this paper we propose two extensions of the Exponential model to describe income distributions. The Exponential ArcTan (EAT) and the composite EAT-Lognormal models discussed in this paper preserve key properties of the Exponential model including its capacity to model distributions with zero incomes. This is an important feature as the presence of zeros conditions the modelling of income distributions as it rules out the possibility of using many parametric models commonly used in the literature. Many researchers opt for excluding the zeros from the analysis, however, this may not be a sensible approach especially when the number of zeros is large or if one is interested in accurately describing the lower part of the distribution. We apply the EAT and the EAT-Lognormal models to study the distribution of incomes in Australia for the period 2001-2012. We find that these models in general outperform the Gamma and Exponential models while preserving the capacity of the latter to model zeros.
RMS slope of exponentially correlated surface roughness for radar applications
Dierking, Wolfgang
2000-01-01
In radar signature analysis, the root mean square (RMS) surface slope is utilized to assess the relative contribution of multiple scattering effects. For an exponentially correlated surface, an effective RMS slope can be determined by truncating the high frequency tail of the roughness spectrum...
Boyle, P.J.; Kulu, H.; Cooke, T.; Gayle, V.; Mulder, C.H.
2008-01-01
This paper examines the effect of migration and residential mobility on union dissolution among married and cohabiting couples. Moving is a stressful life event, and a large, multidisciplinary literature has shown that family migration often benefits one partner (usually the man) more than the other. Even so, no study to date has examined the possible impact of within-nation geographical mobility on union dissolution. We base our longitudinal analysis on retrospective event-history data from ...
Ana M. González Ramos
2013-07-01
Full Text Available The special issue Women on the Move that the reader holds in their hands is the result of the hard work of very creative specialists in gender and mobility. Research on mobility and gender has progressively advanced from traditional, non-gender-specific literature on migration or mobility of highly skilled people. And, as these authors prove, the topic is already quantitatively and qualitatively relevant.
2012-01-01
As part of the "Move! Eat better" campaign, Novae’s nutrition adviser, Irène Rolfo, will give a talk on the subject of everyday good nutrition. This will be held in the main building auditorium at 12:30 on Thursday, 20 September 2012. Don’t miss this informative event. For more information, go to http://cern.ch/bpmm
2005-01-01
The Transport Service pulled out all the stops and, more specifically, its fleet of moving and lifting equipment for the Discovery Monday on 6 June - a truly moving experience for all the visitors who took part ! Visitors could play at being machine operator, twiddling the controls of a lift truck fitted with a jib to lift a dummy magnet into a wooden mock-up of a beam-line.They had to show even greater dexterity for this game of lucky dip...CERN-style.Those with a head for heights took to the skies 20 m above ground in a telescopic boom lift.Children were allowed to climb up into the operator's cabin - this is one of the cranes used to move the LHC magnets around. Warm thanks to all members of the Transport Service for their participation, especially B. Goicoechea, T. Ilkei, R. Bihery, S. Prodon, S. Pelletier, Y. Bernard, A. Sallot, B. Pigeard, S. Guinchard, B. Bulot, J. Berrez, Y. Grandjean, A. Bouakkaz, M. Bois, F. Stach, T. Mazzarino and S. Fumey.
Telegraph equations for the case of a waveguide with moving boundary
Baryshevsky, V G
2016-01-01
Telegraph equation describing the compression of electromagnetic waves in a waveguide (resonator) with moving boundary are derived. It is shown that the character of oscillations of the compressed electromagnetic field depends on the parameters of the resonator, and under certain conditions, the oscillations of voltage (current) yield the exponential growth, leading to a noticeable change in the radiation losses.
Bounds of Spectral Radii of Weighted Trees
杨华中; 胡冠章; 洪渊
2003-01-01
Graphs for the design of networks or electronic circuits are usually weighted and the spectrum of weighted graphs are often analyzed to solve problems. This paper discusses the spectrum and the spectral radii of trees with edge weights. We derive expressions for the spectrum and the spectral radius of a weighted star, together with the boundary limits of the spectral radii for weighted paths and weighted trees. The analysis uses the theory of nonnegative matrices and applies the "moving edge" technique. Some simple examples of weighted paths and trees are presented to explain the results. Then, we propose some open problems in this area.
Moving related to separation : who moves and to what distance
Mulder, Clara H.; Malmberg, Gunnar
2011-01-01
We address the issue of moving from the joint home on the occasion of separation. Our research question is: To what extent can the occurrence of moves related to separation, and the distance moved, be explained by ties to the location, resources, and other factors influencing the likelihood of movin
1999-01-01
Many people live away from their homes and communities. Worldwide, about 125 million people are migrant workers, immigrants, or refugees in search of education, employment, or safety, making them vulnerable to sexually transmitted infections (STIs), including HIV. Some practical approaches to HIV prevention with people on the move are delineated. These include: 1) the project in Niger describing its work with migrant peer educators; 2) a national program improving health services; 3) a program in India providing STI treatment and health information for truck drivers; 4) a South African HIV program, which includes activities within communities; and 5) HIV prevention programs for refugees in Tanzania and Mozambique.
The scaling of human mobility by taxis is exponential
Liang, Xiao; Lv, Weifeng; Zhu, Tongyu; Xu, Ke
2011-01-01
As a significant factor in urban planning, traffic forecasting and prediction of epidemics, modeling patterns of human mobility draws intensive attention from researchers for decades. Power-law distribution and its variations are observed from quite a few real-world human mobility datasets such as the movements of banking notes, trackings of cell phone users' locations and trajectories of vehicles. In this paper, we build models for 20 million trajectories with fine granularity collected from more than 10 thousand taxis in Beijing. In contrast to most models observed in human mobility data, the taxis' traveling displacements in urban areas tend to follow an exponential distribution instead of a power-law. Similarly, the elapsed time can also be well approximated by an exponential distribution. Worth mentioning, analysis of the interevent time indicates the bursty nature of human mobility, similar to many other human activities.
A stochastic evolutionary model generating a mixture of exponential distributions
Fenner, Trevor; Loizou, George
2015-01-01
Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic urn-based model proposed in \\cite{FENN15} so that it can generate mixture models,in particular, a mixture of exponential distributions. The model is designed to capture the dynamics of survival analysis, traditionally employed in clinical trials, reliability analysis in engineering, and more recently in the analysis of large data sets recording human dynamics. The mixture modelling approach, which is relatively simple and well understood, is very effective in capturing heterogeneity in data. We provide empirical evidence for the validity of the model, using a data set of popular search engine queries collected over a period of 114 months. We show that the survival function of these queries is closely matched by the exponential mixture solution for our model.
THE JOINT DISTRIBUTION OF BIVARIATE EXPONENTIAL UNDER LINEARLY RELATED MODEL
Norou Diawara
2010-09-01
Full Text Available In this paper, fundamental results of the joint distribution of the bivariate exponential distributions are established. The positive support multivariate distribution theory is important in reliability and survival analysis, and we applied it to the case where more than one failure or survival is observed in a given study. Usually, the multivariate distribution is restricted to those with marginal distributions of a specified and familiar lifetime family. The family of exponential distribution contains the absolutely continuous and discrete case models with a nonzero probability on a set of measure zero. Examples are given, and estimators are developed and applied to simulated data. Our findings generalize substantially known results in the literature, provide flexible and novel approach for modeling related events that can occur simultaneously from one based event.
Handbook of exponential and related distributions for engineers and scientists
Pal, Nabendu; Lim, Wooi K
2005-01-01
The normal distribution is widely known and used by scientists and engineers. However, there are many cases when the normal distribution is not appropriate, due to the data being skewed. Rather than leaving you to search through journal articles, advanced theoretical monographs, or introductory texts for alternative distributions, the Handbook of Exponential and Related Distributions for Engineers and Scientists provides a concise, carefully selected presentation of the properties and principles of selected distributions that are most useful for application in the sciences and engineering.The book begins with all the basic mathematical and statistical background necessary to select the correct distribution to model real-world data sets. This includes inference, decision theory, and computational aspects including the popular Bootstrap method. The authors then examine four skewed distributions in detail: exponential, gamma, Weibull, and extreme value. For each one, they discuss general properties and applicabi...
Exponentially fitted explicit Runge-Kutta-Nystrom methods
Franco, J. M.
2004-05-01
Exponentially fitted Runge-Kutta-Nystrom (EFRKN) methods for the numerical integration of second-order IVPs with oscillatory solutions are derived. These methods integrate exactly differential systems whose solutions can be expressed as linear combinations of the set of functions {exp(λt),exp(-λt)}, , or equivalently {sin(ωt),cos(ωt)} when λ=iω, . Explicit EFRKN methods with two and three stages and algebraic orders 3 and 4 are constructed. In addition, a 4(3) embedded pair of explicit EFRKN methods based on the FSAL technique is obtained, which permits to introduce an error and step length control with a small cost added. Some numerical experiments show the efficiency of our explicit EFRKN methods when they are compared with other exponential fitting type codes proposed in the scientific literature.
Exponentials and Laplace transforms on nonuniform time scales
Ortigueira, Manuel D.; Torres, Delfim F. M.; Trujillo, Juan J.
2016-10-01
We formulate a coherent approach to signals and systems theory on time scales. The two derivatives from the time-scale calculus are used, i.e., nabla (forward) and delta (backward), and the corresponding eigenfunctions, the so-called nabla and delta exponentials, computed. With these exponentials, two generalised discrete-time Laplace transforms are deduced and their properties studied. These transforms are compatible with the standard Laplace and Z transforms. They are used to study discrete-time linear systems defined by difference equations. These equations mimic the usual continuous-time equations that are uniformly approximated when the sampling interval becomes small. Impulse response and transfer function notions are introduced. This implies a unified mathematical framework that allows us to approximate the classic continuous-time case when the sampling rate is high or to obtain the standard discrete-time case, based on difference equations, when the time grid becomes uniform.
Statistical region-based active contours with exponential family observations
Lecellier, François; Fadili, Jalal; Aubert, Gilles; Revenu, Marinette
2008-01-01
In this paper, we focus on statistical region-based active contour models where image features (e.g. intensity) are random variables whose distribution belongs to some parametric family (e.g. exponential) rather than confining ourselves to the special Gaussian case. Using shape derivation tools, our effort focuses on constructing a general expression for the derivative of the energy (with respect to a domain) and derive the corresponding evolution speed. A general result is stated within the framework of multi-parameter exponential family. More particularly, when using Maximum Likelihood estimators, the evolution speed has a closed-form expression that depends simply on the probability density function, while complicating additive terms appear when using other estimators, e.g. moments method. Experimental results on both synthesized and real images demonstrate the applicability of our approach.
A recursion identity for formal iterated logarithms and iterated exponentials
Robinson, Thomas J
2010-01-01
We prove a recursive identity involving formal iterated logarithms and formal iterated exponentials. These iterated logarithms and exponentials appear in a natural extension of the logarithmic formal calculus used in the study of logarithmic intertwining operators and logarithmic tensor category theory for modules for a vertex operator algebra. This extension has a variety of interesting arithmetic properties. We develop one such result here, the aforementioned recursive identity. We have applied this identity elsewhere to certain formal series expansions related to a general formal Taylor theorem and these series expansions in turn yield a sequence of combinatorial identities which have as special cases certain classical combinatorial identities involving (separately) the Stirling numbers of the first and second kinds.
THE SENSITIVITY OF THE EXPONENTIAL OF AN ESSENTIALLY NONNEGATIVE MATRIX
Weifang Zhu; Jungong Xue; Weiguo Gao
2008-01-01
This paper performs perturbation analysis for the exponential of an essentially nonnegative matrix which is perturbed in the way that each entry has a small relative perturbation.For a general essentially nonnegative matrix,we obtain an upper bound for the relative error in 2-norm,which is sharper than the existing perturbation results.For a triangular essentially nonnegative matrix,we obtain an upper bound for the relative error in entrywise sense.This bound indicates that,if the spectral radius of an essentially nonnegative matrix is not large,then small entrywise relative perturbations cause small relative error in each entry of its exponential.Finally,we apply our perturbation results to the sensitivity analysis of RC networks and complementary distribution functions of phase-type distributions.
Interval Estimations of the Two-Parameter Exponential Distribution
Lai Jiang
2012-01-01
Full Text Available In applied work, the two-parameter exponential distribution gives useful representations of many physical situations. Confidence interval for the scale parameter and predictive interval for a future independent observation have been studied by many, including Petropoulos (2011 and Lawless (1977, respectively. However, interval estimates for the threshold parameter have not been widely examined in statistical literature. The aim of this paper is to, first, obtain the exact significance function of the scale parameter by renormalizing the p∗-formula. Then the approximate Studentization method is applied to obtain the significance function of the threshold parameter. Finally, a predictive density function of the two-parameter exponential distribution is derived. A real-life data set is used to show the implementation of the method. Simulation studies are then carried out to illustrate the accuracy of the proposed methods.
Historical remarks on exponential product and quantum analysis
Suzuki, Masuo [Computational Astrophysics Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan)
2015-03-10
The exponential product formula [1, 2] was substantially introduced in physics by the present author [2]. Its systematic applications to quantum Monte Carlo Methods [3] were preformed [4, 5] first in 1977. Many interesting applications [6] of the quantum-classical correspondence (namely S-T transformation) have been reported. Systematic higher-order decomposition formulae were also discovered by the present author [7-11], using the recursion scheme [7, 9]. Physically speaking, these exponential product formulae play a conceptual role of separation of procedures [3,14]. Mathematical aspects of these formulae have been integrated in quantum analysis [15], in which non-commutative differential calculus is formulated and a general quantum Taylor expansion formula is given. This yields many useful operator expansion formulae such as the Feynman expansion formula and the resolvent expansion. Irreversibility and entropy production are also studied using quantum analysis [15].
Exponential time-dependent perturbation theory in rotationally inelastic scattering
Cross, R. J.
1983-08-01
An exponential form of time-dependent perturbation theory (the Magnus approximation) is developed for rotationally inelastic scattering. A phase-shift matrix is calculated as an integral in time over the anisotropic part of the potential. The trajectory used for this integral is specified by the diagonal part of the potential matrix and the arithmetic average of the initial and final velocities and the average orbital angular momentum. The exponential of the phase-shift matrix gives the scattering matrix and the various cross sections. A special representation is used where the orbital angular momentum is either treated classically or may be frozen out to yield the orbital sudden approximation. Calculations on Ar+N2 and Ar+TIF show that the theory generally gives very good agreement with accurate calculations, even where the orbital sudden approximation (coupled-states) results are seriously in error.
Truncated $\\gamma$-exponential models for tidal stellar systems
Gomez-Leyton, Y J
2016-01-01
We introduce a parametric family of models to characterize the properties of astrophysical systems in a quasi-stationary evolution under the incidence evaporation. We start from an one-particle distribution $f_{\\gamma}\\left(\\mathbf{q},\\mathbf{p}|\\beta,\\varepsilon_{s}\\right)$ that considers an appropriate deformation of Maxwell-Boltzmann form with inverse temperature $\\beta$, in particular, a power-law truncation at the scape energy $\\varepsilon_{s}$ with exponent $\\gamma>0$. This deformation is implemented using a generalized $\\gamma$-exponential function obtained from the \\emph{fractional integration} of ordinary exponential. As shown in this work, this proposal generalizes models of tidal stellar systems that predict particles distributions with \\emph{isothermal cores and polytropic haloes}, e.g.: Michie-King models. We perform the analysis of thermodynamic features of these models and their associated distribution profiles. A nontrivial consequence of this study is that profiles with isothermal cores and p...
The scaling of human mobility by taxis is exponential
Liang, Xiao; Zheng, Xudong; Lv, Weifeng; Zhu, Tongyu; Xu, Ke
2012-03-01
As a significant factor in urban planning, traffic forecasting and prediction of epidemics, modeling patterns of human mobility draws intensive attention from researchers for decades. Power-law distribution and its variations are observed from quite a few real-world human mobility datasets such as the movements of banking notes, trackings of cell phone users' locations and trajectories of vehicles. In this paper, we build models for 20 million trajectories with fine granularity collected from more than 10 thousand taxis in Beijing. In contrast to most models observed in human mobility data, the taxis' traveling displacements in urban areas tend to follow an exponential distribution instead of a power-law. Similarly, the elapsed time can also be well approximated by an exponential distribution. Worth mentioning, analysis of the interevent time indicates the bursty nature of human mobility, similar to many other human activities.
Excitation of a single atom with exponentially rising light pulses
Aljunid, Syed Abdullah
2013-01-01
We investigate the interaction between a single atom and optical pulses in a coherent state with a controlled temporal envelope. In a comparison between a rising exponential and a square envelope, we show that the rising exponential envelope leads to a higher excitation probability for fixed low average photon numbers, in accordance to a time-reversed Weisskopf-Wigner model. We characterize the atomic transition dynamics for a wide range of the average photon numbers, and are able to saturate the optical transition of a single atom with ~50 photons in a pulse by a strong focusing technique. For photon numbers of ~1000 in a 15ns long pulse, we clearly observe Rabi oscillations.
On the exponential of matrices in su(4)
Ramakrishna, Viswanath; Zhou, Hong [Department of Mathematical Sciences and Center for Signals, Systems and Communications, University of Texas at Dallas, PO Box 830688, Richardson, TX 75083 (United States)
2006-03-24
This paper provides explicit techniques to compute the exponentials of a variety of anti-Hermitian matrices in dimension 4. Many of these formulae can be written down directly from the entries of the matrix. Whenever any spectral calculations are required, these can be done in closed form. In many instances only 2 x 2 spectral calculations are required. These formulae cover a wide variety of applications. Conditions on the matrix which render it to admit one of three minimal polynomials are also given. Matrices with these minimal polynomials admit simple and tractable representations for their exponentials. One of these is the Euler-Rodrigues formula. The key technique is the relation between real 4 x 4 matrices and the quaternions.
Sherman, Karen; Collins, Brian; Donnelly, Kay
2007-01-01
Today's generation of American children may be the first to have a lower life expectancy than their parents. Childhood obesity has increased 35% in the past 10 years. Carrying excess weight for years can lead to high cholesterol, high blood pressure, Type 2 diabetes, heart disease, stroke and premature death. For the first time, there are…
Robust exponential control of a class of systems with uncertainties
无
2002-01-01
The robust exponential stabilization problem for uncertain systems is studied. Based on the solution for a nominal linear quadratic regulator problem with a prescribed degree of stability, the methods of constructing state feedback controllers are developed to ensure the robust stability of the closed loop system under the conditions weaker than the matching condition. Also, the cases where the matching condition is satisfied are considered in detail. Some examples are included to show the solution methods.
Exponential Stability of Complex-Valued Memristive Recurrent Neural Networks.
Wang, Huamin; Duan, Shukai; Huang, Tingwen; Wang, Lidan; Li, Chuandong
2017-03-01
In this brief, we establish a novel complex-valued memristive recurrent neural network (CVMRNN) to study its stability. As a generalization of real-valued memristive neural networks, CVMRNN can be separated into real and imaginary parts. By means of M -matrix and Lyapunov function, the existence, uniqueness, and exponential stability of the equilibrium point for CVMRNNs are investigated, and sufficient conditions are presented. Finally, the effectiveness of obtained results is illustrated by two numerical examples.
Modified Binary Exponential Backoff Algorithm to Minimize Mobiles Communication Time
Ibrahim Sayed Ahmad; Ali Kalakech; Seifedine Kadry
2014-01-01
the field of Wireless Local Area Networks (LANs) is expanding rapidly as a result of advances in digital communications, portable computers, and semiconductor technology. The early adopters of this technology have primarily been vertical application that places a premium on the mobility offered by such systems. Binary Exponential Backoff (BEB) refers to a collision resolution mechanism used in random access MAC protocols. This algorithm is used in Ethernet (IEEE 802.3) wired LANs. In Ethe...
Fractal structures in a generalized square map with exponential terms
Li Xian-Feng; Chu Yan-Dong; Zhang Hui
2012-01-01
Fractal structures in a generalized squared map with exponential terms are expanded in this paper.We describe how complex behaviors can arise as the parameters change.The appearances of different kinds of fractal structures,in both the attractive and the divergent regions,and most interestingly,on small regular islands embedded in the chaotic region,are manifested to have a variety of extraordinary geometries in the parameter plane.
Inverse Problems for Matrix Exponential in System Identification: System Aliasing
Yue, Zuogong; Thunberg, Johan; Goncalves, Jorge
2016-01-01
This note addresses identification of the $A$-matrix in continuous time linear dynamical systems on state-space form. If this matrix is partially known or known to have a sparse structure, such knowledge can be used to simplify the identification. We begin by introducing some general conditions for solvability of the inverse problems for matrix exponential. Next, we introduce "system aliasing" as an issue in the identification of slow sampled systems. Such aliasing give rise to non-unique mat...
Exponential Inequalities for Positively Associated Random Variables and Applications
Yang Shanchao
2008-01-01
Full Text Available Abstract We establish some exponential inequalities for positively associated random variables without the boundedness assumption. These inequalities improve the corresponding results obtained by Oliveira (2005. By one of the inequalities, we obtain the convergence rate for the case of geometrically decreasing covariances, which closes to the optimal achievable convergence rate for independent random variables under the Hartman-Wintner law of the iterated logarithm and improves the convergence rate derived by Oliveira (2005 for the above case.
Short Cycles in Repeated Exponentiation Modulo a Prime
Glebsky, Lev
2009-01-01
Given a prime $p$, we consider the dynamical system generated by repeated exponentiations modulo $p$, that is, by the map $u \\mapsto f_g(u)$, where $f_g(u) \\equiv g^u \\pmod p$ and $0 \\le f_g(u) \\le p-1$. This map is in particular used in a number of constructions of cryptographically secure pseudorandom generators. We obtain nontrivial upper bounds on the number of fixed points and short cycles in the above dynamical system.
EXPONENTIAL ESTIMATES FOR STOCHASTIC DELAY HYBRID SYSTEMS WITH MARKOVIAN SWITCHING
无
2007-01-01
This paper deals with the problem of norm bounds for the solutions of stochastic hybrid systems with Markovian switching and time delay. Based on Lyapunov-Krasovskii theory for functional differential equations and the linear matrix inequality (LMI) approach, mean square exponential estimates for the solutions of this class of linear stochastic hybrid systems are derived. Finally, An example is illustrated to show the applicability and effectiveness of our method.
Tachyonic matter cosmology with exponential and hyperbolic potentials
Pourhassan, B.; Naji, J.
In this paper, we consider tachyonic matter in spatially flat Friedmann-Robertson-Walker (FRW) universe, and obtain behavior of some important cosmological parameters for two special cases of potentials. First, we assume the exponential potential and then consider hyperbolic cosine type potential. In both cases, we obtain behavior of the Hubble, deceleration and EoS parameters. Comparison with observational data suggest the model with hyperbolic cosine type scalar field potentials has good model to describe universe.
An exponential polynomial observer for synchronization of chaotic systems
Mata-Machuca, J. L.; Martínez-Guerra, R.; Aguilar-López, R.
2010-12-01
In this paper, we consider the synchronization problem via nonlinear observer design. A new exponential polynomial observer for a class of nonlinear oscillators is proposed, which is robust against output noises. A sufficient condition for synchronization is derived analytically with the help of Lyapunov stability theory. The proposed technique has been applied to synchronize chaotic systems (Rikitake and Rössler systems) by means of numerical simulation.
INFLUENCE ANALYSIS ON EXPONENTIAL NONLINEAR MODELS WITH RANDOM EFFECTS
宗序平; 赵俊; 王海斌; 韦博成
2003-01-01
This paper presents a unified diagnostic method for exponential nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991.The authors show that the case deletion model is equivalent to mean shift outlier model.From this point of view,several diagnostic measures,such as Cook distance,score statistics are derived.The local influence measure of Cook is also presented.Numerical example illustrates that our method is available.
Chaos and Exponentially Localized Eigenstates in Smooth Hamiltonian Systems
Santhanam, M S; Lakshminarayan, A
1998-01-01
We present numerical evidence to show that the wavefunctions of smooth classically chaotic Hamiltonian systems scarred by certain simple periodic orbits are exponentially localized in the space of unperturbed basis states. The degree of localization, as measured by the information entropy, is shown to be correlated with the local phase space structure around the scarring orbit; indicating sharp localization when the orbit undergoes a pitchfork bifurcation and loses stability.
Discrete power law with exponential cutoff and Lotka's Law
Smolinsky, Lawrence
2015-01-01
The first bibliometric law appeared in Alfred J. Lotka's 1926 examination of author productivity in chemistry and physics. The result is that the productivity distribution is thought to be described by a power law. In this paper, Lotka's original data on author productivity in chemistry is reconsidered by comparing the fit of the data to both a discrete power law and a discrete power law with exponential cutoff.
A Spectral Lyapunov Function for Exponentially Stable LTV Systems
Zhu, J. Jim; Liu, Yong; Hang, Rui
2010-01-01
This paper presents the formulation of a Lyapunov function for an exponentially stable linear timevarying (LTV) system using a well-defined PD-spectrum and the associated PD-eigenvectors. It provides a bridge between the first and second methods of Lyapunov for stability assessment, and will find significant applications in the analysis and control law design for LTV systems and linearizable nonlinear time-varying systems.
Epidemic Dynamics with Feedback Mechanism in Exponential Networks
LIU Zi-Ran; YAN Jia-Ren; ZHANG Jian-Guo; WANG Li
2006-01-01
@@ We introduce a feedback mechanism to study the spreading of an epidemic by analytical methods and large scale simulations in exponential networks. It is found that introducing the feedback mechanism can reduce the density of infected individuals. Furthermore, it does not change the epidemic threshold (critical point) λc. These results can help us to understand epidemic spreading phenomena on social networks more practically and design appropriate strategies to control social infections.
Exponential wealth distribution : a new approach from functional iteration theory*
López José-Luis
2012-08-01
Full Text Available Different approaches are possible in order to derive the exponential regime in statistical systems. Here, a new functional equation is proposed in an economic context to explain the wealth exponential distribution. Concretely, the new iteration [1] given by egin{equation} f_{n+1}(x = int!!int_{u+v>x},{f_n(uf_n(vover u+v} ; {mathrm d}u{mathrm d}v ,. onumber label{syst1} end{equation} f n + 1 ( x = ∫ ∫ u + v > x f n ( u f n ( v u + v d u d v . It is found that the exponential distribution is a stable fixed point of this functional iteration equation. From this point of view, it is easily understood why the exponential wealth distribution (or by extension, other kind of distributions is asymptotically obtained in different multi-agent economic models. Différentes approches pour dériver le régime asymptotique exponentiel dans les systèmes statistiques sont possibles. Ici une nouvelle équation fonctionnelle est proposée, dans le cadre des systèmes économiques, pour expliquer la distribution exponentielle. Nous montrons que cette distribution est le seul point fixe vers lequel la dynamique de cette équation fonctionnelle évolue quand l’itération va vers l’infini. De ce point de vue, il est facile de comprendre l’ubiquité de cette distribution (ou d’autres en différents problèmes statistiques réels.
Extracting the exponential behaviors in the market data
Watanabe, K; Takayasu, M; Watanabe, Kota; Takayasu, Hideki; Takayasu, Misako
2006-01-01
We introduce a mathematical criterion defining the bubbles or the crashes in financial market price fluctuations by considering exponential fitting of the given data. By applying this criterion we can automatically extract the periods in which bubbles and crashes are identified. From stock market data of so-called the Internet bubbles it is found that the characteristic length of bubble period is about 100 days.
Agarwal, Pankaj K.; Arge, Lars Allan; Erickson, Jeff
2003-01-01
also describe an indexing scheme in which the number of I/Os required to answer a query depends monotonically on the difference between the query time stamp t and the current time. Finally, we develop an efficient indexing scheme to answer approximate nearest-neighbor queries among moving points.......We propose three indexing schemes for storing a set S of N points in the plane, each moving along a linear trajectory, so that any query of the following form can be answered quickly: Given a rectangle R and a real value t, report all K points of S that lie inside R at time t. We first present...... an indexing structure that, for any given constant >0, uses O(N/B) disk blocks and answers a query in O((N/B)1/2+ +K/B) I/Os, where B is the block size. It can also report all the points of S that lie inside R during a given time interval. A point can be inserted or deleted, or the trajectory of a point can...
Anaïs Schaeffer
2012-01-01
This year, the CERN Medical Service is launching a new public health campaign. Advertised by the catchphrase “Move! & Eat Better”, the particular aim of the campaign is to encourage people at CERN to take more regular exercise, of whatever kind. The CERN annual relay race is scheduled on 24 May this year. The CERN Medical Service will officially launch its “Move! & Eat Better” campaign at this popular sporting event. “We shall be on hand on the day of the race to strongly advocate regular physical activity,” explains Rachid Belkheir, one of the Medical Service doctors. "We really want to pitch our campaign and answer any questions people may have. Above all we want to set an example. So we are going to walk the same circuit as the runners to underline to people that they can easily incorporate movement into their daily routine.” An underlying concern has prompted this campaign: during their first few year...
复指数函数系在Lpα空间中的完备性%Completeness of Complex Exponential System in Space
闫峰; 邓冠铁
2008-01-01
A necessary and sufficient condition is obtained for the complex exponential system to be dense in the weighted Banach space Lpα = {f : f∞-∞ |f(t)e-α(t)|pdt ∞}, where 1 ≤ p + ∞and α(t) is a nonnegative continuous function on R.
A kernel representation for exponential splines with global tension
Barendt, Sven; Fischer, Bernd; Modersitzki, Jan
2009-02-01
Interpolation is a key ingredient in many imaging routines. In this note, we present a thorough evaluation of an interpolation method based on exponential splines in tension. They are based on so-called tension parameters, which allow for a tuning of their properties. As it turns out, these interpolants have very many nice features, which are, however, not born out in the literature. We intend to close this gap. We present for the first time an analytic representation of their kernel which enables one to come up with a space and frequency domain analysis. It is shown that the exponential splines in tension, as a function of the tension parameter, bridging the gap between linear and cubic B-Spline interpolation. For example, with a certain tension parameter, one is able to suppress ringing artefacts in the interpolant. On the other hand, the analysis in the frequency domain shows that one derives a superior signal reconstruction quality as known from the cubic B-Spline interpolation, which, however, suffers from ringing artifacts. With the ability to offer a trade-off between opposing features of interpolation methods we advocate the use of the exponential spline in tension from a practical point of view and use the new kernel representation to qualify the trade-off.
Evidence for Truncated Exponential Probability Distribution of Earthquake Slip
Thingbaijam, Kiran K. S.
2016-07-13
Earthquake ruptures comprise spatially varying slip on the fault surface, where slip represents the displacement discontinuity between the two sides of the rupture plane. In this study, we analyze the probability distribution of coseismic slip, which provides important information to better understand earthquake source physics. Although the probability distribution of slip is crucial for generating realistic rupture scenarios for simulation-based seismic and tsunami-hazard analysis, the statistical properties of earthquake slip have received limited attention so far. Here, we use the online database of earthquake source models (SRCMOD) to show that the probability distribution of slip follows the truncated exponential law. This law agrees with rupture-specific physical constraints limiting the maximum possible slip on the fault, similar to physical constraints on maximum earthquake magnitudes.We show the parameters of the best-fitting truncated exponential distribution scale with average coseismic slip. This scaling property reflects the control of the underlying stress distribution and fault strength on the rupture dimensions, which determines the average slip. Thus, the scale-dependent behavior of slip heterogeneity is captured by the probability distribution of slip. We conclude that the truncated exponential law accurately quantifies coseismic slip distribution and therefore allows for more realistic modeling of rupture scenarios. © 2016, Seismological Society of America. All rights reserverd.
Move Ordering using Neural Networks
Kocsis, L.; Uiterwijk, J.; Van Den Herik, J.
2001-01-01
© Springer-Verlag Berlin Heidelberg 2001. The efficiency of alpha-beta search algorithms heavily depends on the order in which the moves are examined. This paper focuses on using neural networks to estimate the likelihood of a move being the best in a certain position. The moves considered more like
An exponential-related function for decision-making in engineering and management
Aikhuele, Daniel O.; Turan, Faiz Mohd
2017-06-01
An intuitionistic fuzzy TOPSIS model, which is based on an exponential-related function (IF-TOPSIS) and a fuzzy entropy method, has been proposed in this study. The exponential-related function, which represents the aggregated effect of positive and negative evaluations in the performance ratings of the alternatives, based on the intuitionistic fuzzy set (IFS) data. Serves, as a computational tool for measuring the separation distance of decision alternatives from the intuitionistic fuzzy positive and negative ideal solution to determine the relative closeness coefficient. The main advantage of this new approach is that (1) it uses a subjective and objective based approach for the computation of the criteria weight and (2) its simplicity both in its concept and computational procedures. The proposed method has successfully been implemented for the evaluation of some engineering designs related problems including the selection of a preferred floppy disk from a group of design alternatives, the selection of the best concept design for a new air-conditions system and finally, the selection of a preferred mouse from a group of alternatives as a reference for a new design. Also, for each of the three case studies, the method has been compared with some similar computational approaches.
Exponential processes in human auditory excitation and adaptation.
Formby, C; Rutledge, J C; Sherlock, L P
2002-02-01
Peripheral auditory adaptation has been studied extensively in animal models, and multiple exponential components have been identified. This study explores the feasibility of estimating these component processes for human listeners with a peripheral model of adaptation. The processes were estimated from off-frequency masked detection data that probed temporal masking responses to a gated narrowband masker. The resulting response patterns reflected step-like onset and offset features with characteristically little evidence of confounding backward and forward masking. The model was implemented with linear combinations of exponential functions to represent the unadapted excitation response to gating the masker on and then off and the opposing effects of adaptation in each instance. The onset and offset of the temporal masking response were assumed to be approximately inverse operations and were modeled independently in this scheme. The unadapted excitation response at masker onset and the reversed excitation response at masker offset were each represented in the model by a single exponential function. The adaptation processes were modeled by three independent exponential functions, which were reversed at masker offset. Each adaptation component was subtractive and partially negated the unadapted excitation response to the dynamic masker. This scheme allowed for quantification of the response amplitude, action latency, and time constant for the unadapted excitation component and for each adaptation component. The results reveal that (1) the amplitudes of the unadapted excitation and reversed excitation components grow nonlinearly with masker level and mirror the 'compressive' input-output velocity response of the basilar membrane; (2) the time constants for the unadapted excitation and reversed excitation components are related inversely to masker intensity, which is compatible with neural synchrony increasing at masker onset (or offset) with increasing masker strength
Weight Distributions of Multi-Edge type LDPC Codes
KASAI, Kenta; DECLERCQ, David; POULLIAT, Charly; SAKANIWA, Kohichi
2010-01-01
The multi-edge type LDPC codes, introduced by Richardson and Urbanke, present the general class of structured LDPC codes. In this paper, we derive the average weight distributions of the multi-edge type LDPC code ensembles. Furthermore, we investigate the asymptotic exponential growth rate of the average weight distributions and investigate the connection to the stability condition of the density evolution.
Long Strange Segments, Ruin Probabilities and the Effect of Memory on Moving Average Processes
Ghosh, Souvik
2010-01-01
We obtain the rate of growth of long strange segments and the rate of decay of infinite horizon ruin probabilities for a class of infinite moving average processes with exponentially light tails. The rates are computed explicitly. We show that the rates are very similar to those of an i.i.d. process as long as moving average coefficients decay fast enough. If they do not, then the rates are significantly different. This demonstrates the change in the length of memory in a moving average process associated with certain changes in the rate of decay of the coefficients.
Morris, Tim; Manley, David; Northstone, Kate;
2016-01-01
A large literature exists suggesting that residential mobility leads to increased participation in risky health behaviours such as cannabis use amongst youth. However, much of this work fails to account for the impact that underlying differences between mobile and non-mobile youth have on this re......A large literature exists suggesting that residential mobility leads to increased participation in risky health behaviours such as cannabis use amongst youth. However, much of this work fails to account for the impact that underlying differences between mobile and non-mobile youth have...... regression models (log odds: 0.94, standard error: 0.42), indicating that children who move houses are more likely to use cannabis than those who remain residentially stable. However, decomposing this relationship into within- and between-child components reveals that the conventional model is underspecified...
Banichuk, Nikolay; Neittaanmäki, Pekka; Saksa, Tytti; Tuovinen, Tero
2014-01-01
This book deals with theoretical aspects of modelling the mechanical behaviour of manufacturing, processing, transportation or other systems in which the processed or supporting material is travelling through the system. Examples of such applications include paper making, transmission cables, band saws, printing presses, manufacturing of plastic films and sheets, and extrusion of aluminium foil, textiles and other materials. The work focuses on out-of-plane dynamics and stability analysis for isotropic and orthotropic travelling elastic and viscoelastic materials, with and without fluid-structure interaction, using analytical and semi-analytical approaches. Also topics such as fracturing and fatigue are discussed in the context of moving materials. The last part of the book deals with optimization problems involving physical constraints arising from the stability and fatigue analyses, including uncertainties in the parameters. The book is intended for researchers and specialists in the field, providin...
CHRIS; DEVONSHIRE-ELLIS
2008-01-01
Central China, initially overlooked by many foreign investors as being too far from the ports in Tianjin, Shanghai and Shenzhen, is emerging as an essential destination for multinationals in China.The Future of Central China: A Provincial Roadmap There is a huge manufacturing drive in central China. Businesses are moving inland to set up projects, investments and operations here, primarily due to lower labor and land costs as well as preferential policies for manufacturers. Multinational companies also are starting to view the region as the next step toward an integrated China strategy, and the consumer population in the second-and third-tier cities in central China represents a growing, largely untapped domestic market for foreign products and services.
2013-01-01
Are you curious to know whether you’re doing enough daily exercise…? Test yourself with a pedometer! Through the Move! Eat better campaign, launched in May 2012, the CERN medical service is aiming to improve the health of members of the personnel by encouraging them to prioritise physical activity in conjunction with a balanced diet. Various successful activities have already taken place: relay race/Nordic walk, Bike2work, Zumba and fitness workshops, two conferences (“Physical activity for health” and “Good nutrition every day”), events in the restaurants, as well as posters and a website. Although everyone has got the message from our various communications that physical activity is good for your health, there is still a relevant question being asked: “What is the minimum amount of exercise recommended?” 10,000 steps per day is the ideal figure, which has been demonstrated as beneficial by scientific studies ...
Rai, Sudhanshu
In this article I discuss the Indian outsourcing phenomena and ask the question now what? Using data from the Euro-India project I demonstrate that a small but significant part of the Indian IT entities are moving beyond outsourcing, to co-creation where Innovation and the desire to create new...... markets is the key driver. This does not imply that outsourcing will disappear but it does mean that firms will engage in globalization using innovative mix of business models and technical platforms. We discuss the implication of this slow transformation to co-creation of innovation for the global...... outsourcing industry. The key thesis of this paper is to discuss co-creation as a form of innovation and how such a form of innovation is likely to bring Indian companies rich dividends....
Web-based application on employee performance assessment using exponential comparison method
Maryana, S.; Kurnia, E.; Ruyani, A.
2017-02-01
Employee performance assessment is also called a performance review, performance evaluation, or assessment of employees, is an effort to assess the achievements of staffing performance with the aim to increase productivity of employees and companies. This application helps in the assessment of employee performance using five criteria: Presence, Quality of Work, Quantity of Work, Discipline, and Teamwork. The system uses the Exponential Comparative Method and Weighting Eckenrode. Calculation results using graphs were provided to see the assessment of each employee. Programming language used in this system is written in Notepad++ and MySQL database. The testing result on the system can be concluded that this application is correspond with the design and running properly. The test conducted is structural test, functional test, and validation, sensitivity analysis, and SUMI testing.
A dynamic CMOS multiplier for analog VLSI based on exponential pulse-decay modulation
Massengill, Lloyd W.
1991-03-01
A clocked, charge-based, CMOS modulator circuit is presented. The circuit, which performs a semilinear multiplication function, has applications in arrayed analog VLSI architectures such as parallel filters and neural network systems. The design presented is simple in structure, uses no operational amplifiers for the actual multiplication function, and uses no power in the static mode. Two-quadrant weighting of an input signal is accomplished by control of the magnitude and decay time of an exponential current pulse, resulting in the delivery of charge packets to a shared capacitive summing bus. The cell is modular in structure and can be fabricated in a standard CMOS process. An analytical derivation of the operation of the circuit, SPICE simulations, and MOSIS fabrication results are presented. The simulation studies indicate that the circuit is inherently tolerant to temperature effects, absolute device sizing errors, and clock-feedthrough transients.
T. Botmart
2013-01-01
Full Text Available The problem of guaranteed cost control for exponential synchronization of cellular neural networks with interval nondifferentiable and distributed time-varying delays via hybrid feedback control is considered. The interval time-varying delay function is not necessary to be differentiable. Based on the construction of improved Lyapunov-Krasovskii functionals is combined with Leibniz-Newton's formula and the technique of dealing with some integral terms. New delay-dependent sufficient conditions for the exponential synchronization of the error systems with memoryless hybrid feedback control are first established in terms of LMIs without introducing any free-weighting matrices. The optimal guaranteed cost control with linear error hybrid feedback is turned into the solvable problem of a set of LMIs. A numerical example is also given to illustrate the effectiveness of the proposed method.
Role of moving planes and moving spheres following Dupin cyclides
Jia, Xiaohong
2014-03-01
We provide explicit representations of three moving planes that form a μ-basis for a standard Dupin cyclide. We also show how to compute μ-bases for Dupin cyclides in general position and orientation from their implicit equations. In addition, we describe the role of moving planes and moving spheres in bridging between the implicit and rational parametric representations of these cyclides. © 2014 Elsevier B.V.
Sirada Pinjai
2013-01-01
Full Text Available This paper is concerned with the problem of robust exponential stability for linear parameter-dependent (LPD neutral systems with mixed time-varying delays and nonlinear perturbations. Based on a new parameter-dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, decomposition technique of coefficient matrix, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria are established in terms of linear matrix inequalities (LMIs. Numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.
On exponential stability for systems with state delays
无
2007-01-01
This paper considers the issue of delay-dependent exponential stability for time-delay systems. Both nominal and uncertain systems are investigated. New sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained. These criteria are simple owing to the use of an integral inequality. The model transformation approaches, bounding techniques for cross terms and slack matrices are all avoided in the derivation. Rigorous proof and numerical examples showed that the proposed criteria and those based on introducing slack matrices are equivalent.
Exponential integrators for the incompressible Navier-Stokes equations.
Newman, Christopher K.
2004-07-01
We provide an algorithm and analysis of a high order projection scheme for time integration of the incompressible Navier-Stokes equations (NSE). The method is based on a projection onto the subspace of divergence-free (incompressible) functions interleaved with a Krylov-based exponential time integration (KBEI). These time integration methods provide a high order accurate, stable approach with many of the advantages of explicit methods, and can reduce the computational resources over conventional methods. The method is scalable in the sense that the computational costs grow linearly with problem size. Exponential integrators, used typically to solve systems of ODEs, utilize matrix vector products of the exponential of the Jacobian on a vector. For large systems, this product can be approximated efficiently by Krylov subspace methods. However, in contrast to explicit methods, KBEIs are not restricted by the time step. While implicit methods require a solution of a linear system with the Jacobian, KBEIs only require matrix vector products of the Jacobian. Furthermore, these methods are based on linearization, so there is no non-linear system solve at each time step. Differential-algebraic equations (DAEs) are ordinary differential equations (ODEs) subject to algebraic constraints. The discretized NSE constitute a system of DAEs, where the incompressibility condition is the algebraic constraint. Exponential integrators can be extended to DAEs with linear constraints imposed via a projection onto the constraint manifold. This results in a projected ODE that is integrated by a KBEI. In this approach, the Krylov subspace satisfies the constraint, hence the solution at the advanced time step automatically satisfies the constraint as well. For the NSE, the projection onto the constraint is typically achieved by a projection induced by the L{sup 2} inner product. We examine this L{sup 2} projection and an H{sup 1} projection induced by the H{sup 1} semi-inner product. The H
DISRUPTION MANAGEMENT FOR SUPPLY CHAIN COORDINATION WITH EXPONENTIAL DEMAND FUNCTION
无
2006-01-01
The coordination problem of a supply chain comprising one supplier and one retailer under market demand disruption is studied in this article. A novel exponential demand function is adopted, and the penalty cost is introduced explicitly to capture the deviation production cost caused by the market demand disruption. The optimal strategies are obtained for different disruption scale under the centralized mode. For the decentralized mode, it is proved that the supply chain can be fully coordinated by adjusting the price discount policy appropriately when disruption occurs. Furthermore, the authors point out that similar results can be established for more general demand functions that represent different market circumstances if certain assumptions are satisfied.
New robust chaotic system with exponential quadratic term
Bao Bo-Cheng; Li Chun-Biao; Xu Jian-Peing; Liu Zhong
2008-01-01
This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term.This system can display a double-scroll chaotic attractor with only two equilibria,and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent.Some basic dynamical properties and chaotic behaviour of novel attractor are studied.By numerical simulation,this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviottrs by a constant controller.
Problems on Finite Automata and the Exponential Time Hypothesis
Henning Fernau
2017-02-01
Full Text Available We study several classical decision problems on finite automata under the (Strong Exponential Time Hypothesis. We focus on three types of problems: universality, equivalence, and emptiness of intersection. All these problems are known to be CoNP-hard for nondeterministic finite automata, even when restricted to unary input alphabets. A different type of problems on finite automata relates to aperiodicity and to synchronizing words. We also consider finite automata that work on commutative alphabets and those working on two-dimensional words.
Power exponential velocity distributions in disordered porous media
Matyka, Maciej; Koza, Zbigniew
2016-01-01
Velocity distribution functions link the micro- and macro-level theories of fluid flow through porous media. Here we study them for the fluid absolute velocity and its longitudinal and lateral components relative to the macroscopic flow direction in a model of a random porous medium. We claim that all distributions follow the power exponential law controlled by an exponent $\\gamma$ and a shift parameter $u_0$ and examine how these parameters depend on the porosity. We find that $\\gamma$ has a universal value $1/2$ at the percolation threshold and grows with the porosity, but never exceeds 2.
Exponential quadruplex priming amplification for DNA-based isothermal diagnostics.
Partskhaladze, Tamar; Taylor, Adam; Lomidze, Levan; Gvarjaladze, David; Kankia, Besik
2015-02-01
Polymerase chain reaction (PCR) is a method of choice for molecular diagnostics. However, PCR relies on thermal cycling, which is not compatible with the goals of point-of-care diagnostics. A simple strategy to turn PCR into an isothermal method would be to use specific primers, which upon polymerase elongation can self-dissociate from the primer-binding sites. We recently demonstrated that a monomolecular DNA quadruplex, GGGTGGGTGGGTGGG, meets these requirements, which led to the development of the linear versions of quadruplex priming amplification (QPA). Here we demonstrate exponential version of isothermal QPA, which allows an unprecedented 10(10)-fold amplification of DNA signal in less than 40 min.
Exponential speed of mixing for skew-products with singularities
Markarian, R; Vieitez, J
2012-01-01
Let $f: [0,1]\\times [0,1] \\setminus {1/2} \\to [0,1]\\times [0,1]$ be the $C^\\infty$ endomorphism given by $$f(x,y)=(2x- [2x], y+ c/|x-1/2|- [y+ c/|x-1/2|]),$$ where $c$ is a positive real number. We prove that $f$ is topologically mixing and if $c>1/4$ then $f$ is mixing with respect to Lebesgue measure. Furthermore we prove that the speed of mixing is exponential.
Exponential Family Techniques for the Lognormal Left Tail
Asmussen, Søren; Jensen, Jens Ledet; Rojas-Nandayapa, Leonardo
[Xe−θX]/L(θ)=x. The asymptotic formulas involve the Lambert W function. The established relations are used to provide two different numerical methods for evaluating the left tail probability of lognormal sum Sn=X1+⋯+Xn: a saddlepoint approximation and an exponential twisting importance sampling estimator. For the latter we...... demonstrate logarithmic efficiency. Numerical examples for the cdf Fn(x) and the pdf fn(x) of Sn are given in a range of values of σ2,n,x motivated from portfolio Value-at-Risk calculations....
Exponential reduction of finite volume effects with twisted boundary conditions
Cherman, Aleksey; Wagman, Michael L; Yaffe, Laurence G
2016-01-01
Flavor-twisted boundary conditions can be used for exponential reduction of finite volume artifacts in flavor-averaged observables in lattice QCD calculations with $SU(N_f)$ light quark flavor symmetry. Finite volume artifact reduction arises from destructive interference effects in a manner closely related to the phase averaging which leads to large $N_c$ volume independence. With a particular choice of flavor-twisted boundary conditions, finite volume artifacts for flavor-singlet observables in a hypercubic spacetime volume are reduced to the size of finite volume artifacts in a spacetime volume with periodic boundary conditions that is four times larger.
Exponential Martingales and Changes of Measure for Counting Processes
Sokol, Alexander; Hansen, Niels Richard
2015-01-01
We give sufficient criteria for the Doléans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are adapted particularly to the case of counting processes and are sufficiently weak to be useful and verifiable, as we i...... illustrate by several examples. In particular, the criteria allow for the construction of for example nonexplosive Hawkes processes, counting processes with stochastic intensities depending on diffusion processes as well as inhomogeneous finite-state Markov processes....
On the Linear Combination of Exponential and Gamma Random Variables
Samuel Kotz
2005-06-01
Full Text Available Abstract: The exact distribution of the linear combination ÃŽÂ± X + ÃŽÂ² Y is derived when X and Y are exponential and gamma random variables distributed independently of each other. A measure of entropy of the linear combination is investigated. We also provide computer programs for generating tabulations of the percentage points associated with the linear combination. The work is motivated by examples in automation, control, fuzzy sets, neurocomputing and other areas of computer science.
Della Mussia, S
2004-01-01
The first large active detector component was lowered into the ATLAS cavern on 1st March. It consisted of the 8 modules forming the lower part of the central barrel of the tile hadronic calorimeter. The work of assembling the barrel, which comprises 64 modules, started the following day. Two road trailers each with 64 wheels, positioned side by side. This was the solution chosen to transport the lower part of the central barrel of ATLAS' tile hadronic calorimeter from Building 185 to the PX16 shaft at Point 1 (see Figure 1). The transportation, and then the installation of the component in the experimental cavern, which took place over three days were, to say the least, rather spectacular. On 25 February, the component, consisting of eight 6-metre modules, was loaded on to the trailers. The segment of the barrel was transported on a steel support so that it wouldn't move an inch during the journey. On 26 February, once all the necessary safety checks had been carried out, the convoy was able to leave Buildi...
撒哈拉
2005-01-01
还怀念当年跳舞毯风靡的时光吗？左脚、右脚向前．向后，在不经意间展示你炫目的舞步。而最近PS2平台上的《EyeToy》让我们又接触到了一种需要游戏者舞动身体来参与的摄像头游戏．既玩了游戏又锻炼了身体．而昂达Eyebob摄像头让PC用户也能参与其中。想要玩玩摄像头游戏．现在不用转投Ps2的阵营．也不用改造你的硬件．只要你拥有一款摄像头．你就可以和家人与朋友轻松享受游戏的乐趣。来吧！Come on! Move your body now!
2012-01-01
CERN has many traditions, but in a week that’s seen the launch of the Medical Service’s ‘Move & eat better’ campaign, it’s refreshing to note that among the oldest is a sporting one. The CERN relay race dates back to 15 October 1971 when 21 pioneering teams set off to pound the pavements of CERN. Back then, the Focus users group came in first with a time of 12 minutes and 42 seconds. Today’s route is slightly different, and the number of teams has risen to over 100, with a new category of Nordic Walking introduced, as part of the campaign, for the first time. The relay has provided some memorable events, and perhaps one of the longest-standing records in the history of sport, with the UA1 strollers’ 10 minutes and 13 seconds unbeaten for thirty years. In the women’s category, the UN Gazelles set the fastest time of 13 minutes and 16 seconds in 1996, while in the veterans category, you wi...
A stochastic evolutionary model generating a mixture of exponential distributions
Fenner, Trevor; Levene, Mark; Loizou, George
2016-02-01
Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic urn-based model proposed in [T. Fenner, M. Levene, G. Loizou, J. Stat. Mech. 2015, P08015 (2015)] so that it can generate mixture models, in particular, a mixture of exponential distributions. The model is designed to capture the dynamics of survival analysis, traditionally employed in clinical trials, reliability analysis in engineering, and more recently in the analysis of large data sets recording human dynamics. The mixture modelling approach, which is relatively simple and well understood, is very effective in capturing heterogeneity in data. We provide empirical evidence for the validity of the model, using a data set of popular search engine queries collected over a period of 114 months. We show that the survival function of these queries is closely matched by the exponential mixture solution for our model.
Exponential Fuzzy C-Means for Collaborative Filtering
Kiatichai Treerattanapitak; Chuleerat Jaruskulchai
2012-01-01
Collaborative filtering (CF) is one of the most popular techniques behind the success of recommendation system. It predicts the interest of users by collecting information from past users who have the same opinions. The most popular approaches used in CF research area are Matrix factorization methods such as SVD.However,many wellknown recommendation systems do not use this method but still stick with Neighborhood models because of simplicity and explainability.There are some concerns that limit neighborhood models to achieve higher prediction accuracy.To address these concerns,we propose a new exponential fuzzy clustering (XFCM) algorithm by reformulating the clustering's objective function with an exponential equation in order to improve the method for membership assignment.The proposed method assigns data to the clusters by aggressively excluding irrelevant data,which is better than other fuzzy C-means (FCM) variants.The experiments show that XFCM-based CF improved 6.9％ over item-based method and 3.0％ over SVD in terms of mean absolute error for 100 K and 1 M MovieLens dataset.
Online System Identification Method Using Modified Regularized Exponential Forgetting
Ján VACHÁLEK
2013-12-01
Full Text Available The paper deals with the use of regularized exponential forgetting (REF in the process of online system identification. The deployment of this type of forgetting strategy is advantageous for very long runs with small changes in the identified input parameters (in the range of 100 000 steps. In these cases, the classical methods of forgetting, such as an exponential (EF or directional forgetting (DF lack the required quality and reach the limit of numerical stability of the calculations of system parameters, which may lead to the early termination of system identification procedure. To avoid this undesirable effect and maintain sufficient primary information about the identified system, a modified REF method is used that employs alternative covariance matrix (ACM formulation to store the primary information of the identified system (REFACM and prevents the numerical destabilization of the identification process. The quality of the modified REFACM forgetting method —along with its validation and comparison with REZ to verify its properties—is performed using standard tests.
Stretched exponential relaxation and ac universality in disordered dielectrics
Milovanov, Alexander V.; Rypdal, Kristoffer; Juul Rasmussen, Jens
2007-01-01
This paper is concerned with the connection between the properties of dielectric relaxation and alternating-current (ac) conduction in disordered dielectrics. The discussion is divided between the classical linear-response theory and a self-consistent dynamical modeling. The key issues are stretc......This paper is concerned with the connection between the properties of dielectric relaxation and alternating-current (ac) conduction in disordered dielectrics. The discussion is divided between the classical linear-response theory and a self-consistent dynamical modeling. The key issues...... are stretched exponential character of dielectric relaxation, power-law power spectral density, and anomalous dependence of ac conduction coefficient on frequency. We propose a self-consistent model of dielectric relaxation in which the relaxations are described by a stretched exponential decay function....... Mathematically, our study refers to the expanding area of fractional calculus and we propose a systematic derivation of the fractional relaxation and fractional diffusion equations from the property of ac universality....
The Non-Abelian Exponentiation theorem for multiple Wilson lines
Gardi, Einan; White, Chris D
2013-01-01
We study the structure of soft gluon corrections to multi-leg scattering amplitudes in a non-Abelian gauge theory by analysing the corresponding product of semi-infinite Wilson lines. We prove that diagrams exponentiate such that the colour factors in the exponent are fully connected. This completes the generalisation of the non-Abelian exponentiation theorem, previously proven in the case of a Wilson loop, to the case of multiple Wilson lines in arbitrary representations of the colour group. Our proof is based on the replica trick in conjunction with a new formalism where multiple emissions from a Wilson line are described by effective vertices, each having a connected colour factor. The exponent consists of connected graphs made out of these vertices. We show that this readily provides a general colour basis for webs. We further discuss the kinematic combinations that accompany each connected colour factor, and explicitly catalogue all three-loop examples, as necessary for a direct computation of the soft a...
The non-Abelian exponentiation theorem for multiple Wilson lines
Gardi, Einan; Smillie, Jennifer M.; White, Chris D.
2013-06-01
We study the structure of soft gluon corrections to multi-leg scattering amplitudes in a non-Abelian gauge theory by analysing the corresponding product of semi-infinite Wilson lines. We prove that diagrams exponentiate such that the colour factors in the exponent are fully connected. This completes the generalisation of the non-Abelian exponentiation theorem, previously proven in the case of a Wilson loop, to the case of multiple Wilson lines in arbitrary representations of the colour group. Our proof is based on the replica trick in conjunction with a new formalism where multiple emissions from a Wilson line are described by effective vertices, each having a connected colour factor. The exponent consists of connected graphs made out of these vertices. We show that this readily provides a general colour basis for webs. We further discuss the kinematic combinations that accompany each connected colour factor, and explicitly catalogue all three-loop examples, as necessary for a direct computation of the soft anomalous dimension at this order.
Bayesian inference and life testing plans for generalized exponential distribution
KUNDU; Debasis; PRADHAN; Biswabrata
2009-01-01
Recently generalized exponential distribution has received considerable attentions.In this paper,we deal with the Bayesian inference of the unknown parameters of the progressively censored generalized exponential distribution.It is assumed that the scale and the shape parameters have independent gamma priors.The Bayes estimates of the unknown parameters cannot be obtained in the closed form.Lindley’s approximation and importance sampling technique have been suggested to compute the approximate Bayes estimates.Markov Chain Monte Carlo method has been used to compute the approximate Bayes estimates and also to construct the highest posterior density credible intervals.We also provide different criteria to compare two different sampling schemes and hence to ?nd the optimal sampling schemes.It is observed that ?nding the optimum censoring procedure is a computationally expensive process.And we have recommended to use the sub-optimal censoring procedure,which can be obtained very easily.Monte Carlo simulations are performed to compare the performances of the different methods and one data analysis has been performed for illustrative purposes.
Exponential decay and scaling laws in noisy chaotic scattering
Seoane, Jesus M. [Nonlinear Dynamics and Chaos Group, Departamento de Fisica, Universidad Rey Juan Carlos, Tulipan s/n, 28933 Mostoles, Madrid (Spain)], E-mail: jesus.seoane@urjc.es; Sanjuan, Miguel A.F. [Nonlinear Dynamics and Chaos Group, Departamento de Fisica, Universidad Rey Juan Carlos, Tulipan s/n, 28933 Mostoles, Madrid (Spain)], E-mail: miguel.sanjuan@urjc.es
2008-01-07
In this Letter we present a numerical study of the effect of noise on a chaotic scattering problem in open Hamiltonian systems. We use the second order Heun method for stochastic differential equations in order to integrate the equations of motion of a two-dimensional flow with additive white Gaussian noise. We use as a prototype model the paradigmatic Henon-Heiles Hamiltonian with weak dissipation which is a well-known example of a system with escapes. We study the behavior of the scattering particles in the scattering region, finding an abrupt change of the decay law from algebraic to exponential due to the effects of noise. Moreover, we find a linear scaling law between the coefficient of the exponential law and the intensity of noise. These results are of a general nature in the sense that the same behavior appears when we choose as a model a two-dimensional discrete map with uniform noise (bounded in a particular interval and zero otherwise), showing the validity of the algorithm used. We believe the results of this work be useful for a better understanding of chaotic scattering in more realistic situations, where noise is presented.
Data assimilation on the exponentially accurate slow manifold.
Cotter, Colin
2013-05-28
I describe an approach to data assimilation making use of an explicit map that defines a coordinate system on the slow manifold in the semi-geostrophic scaling in Lagrangian coordinates, and apply the approach to a simple toy system that has previously been proposed as a low-dimensional model for the semi-geostrophic scaling. The method can be extended to Lagrangian particle methods such as Hamiltonian particle-mesh and smooth-particle hydrodynamics applied to the rotating shallow-water equations, and many of the properties will remain for more general Eulerian methods. Making use of Hamiltonian normal-form theory, it has previously been shown that, if initial conditions for the system are chosen as image points of the map, then the fast components of the system have exponentially small magnitude for exponentially long times as ε→0, and this property is preserved if one uses a symplectic integrator for the numerical time stepping. The map may then be used to parametrize initial conditions near the slow manifold, allowing data assimilation to be performed without introducing any fast degrees of motion (more generally, the precise amount of fast motion can be selected).
Five Exponential Diophantine Equations and Mayhem Problem M429
Zelator, Konstantine
2011-01-01
Crux Mathematicorum with Mathematical Mayhem, is a problem solving journal published by the Canadian Mathematical Society. In the March 2010 issue(see reference[1]) ,the following problem was proposed:Determine all positive integers a,b, and c such that a^(b^c)=(a^b)^c; or equivalently, a^(b^c)=a^(b^c). A solution by this author was published in the December2010 issue of Crux(see reference[2]). Accordingly, all such positive integer triples are the following:The triples of the form (1,b,c); with b, c any positive integers; the triples (a,b,1); a, b positive integers, with a being at least 2; and the triples of the form (a,2,2); a being a positive integer not equal to 1.These are then the positive integer solutions to the 3-variable exponential diophantine equation, x^(y^z)=x^(yz) (1) Motivated by mayhem problem M429, in this work we investigate for more 3-variable exponential diophantine equations: x^(y^z)=x^(z^y) (2), x^(y^z)=y^(xz) (3) x^(yz)=y^(xz) (4), x^(y^z)=z^(xy) (5) We completely determine the positi...
77 FR 74452 - Bus Testing: Calculation of Average Passenger Weight and Test Vehicle Weight
2012-12-14
... passenger weight estimations then underway by the Federal Aviation Administration and the United States... Moving Ahead for Progress in the 21st Century Act (MAP-21) (Pub. L. 112-141). Section 20014 of...
Ghosh, Pranoy
2017-01-01
``A problem with defining force as rate of change of linear momentum'': Let us consider a body of mass m, moving with velocity u initially, in the next time interval it is acted by a force in the direction of motion, and at instant t + its mass is M and velocity v. F .t =Mv-mu or,v = m/M.u +F/M.t or,v =B.u +A.t where A =F/M,B =m/M. So other eqn of motion are: dS =vdt or dS =(B.u +A.t)dt or S =B.u.t +A/2.t2 Andv2 =B2 u2 +2A .B .u .t +A2 t2 or,v2 =B2 u2 +2A.S However, defining acceleration as rate of change of velocity, we have established an identity v =u +a.t which is independent of choice of v, u. M>>m, B is very small, product B.u or its higher power always tend to be negligible, even in cases when u is finitely large.In cases v ->c,F,M -> ∞ , thus A becomes indeterminate.There is inconvenience as A, B are not predetermined and are functions of u, v and thus the definition goes in circle. Hence we conclude, our hypothesis that force =rate of change of linear momentum is not sufficient; we would now find trial solutions to define force in most convenient way.
On the construction of bivariate exponential distributions with an arbitrary correlation coefficient
Bladt, Mogens; Nielsen, Bo Friis
In this paper we use a concept of multivariate phase-type distributions to define a class of bivariate exponential distributions. This class has the following three appealing properties. Firstly, we may construct a pair of exponentially distributed random variables with any feasible correlation...... the exponential random vectors....
On the Construction of Bivariate Exponential Distributions with an Arbitrary Correlation Coefficient
Bladt, Mogens; Nielsen, Bo Friis
2010-01-01
In this article we use the concept of multivariate phase-type distributions to define a class of bivariate exponential distributions. This class has the following three appealing properties. Firstly, we may construct a pair of exponentially distributed random variables with any feasible correlation...... the exponential random vectors....
Global Exponential Stability Analysis of a Class of Dynamical Neural Networks
Jin-Liang Shao; Ting-Zhu Huang
2009-01-01
The problem of the global exponential stability of a class of Hopfield neural networks is considered. Based on nonnegative matrix theory, a sufficient condition for the existence, uniqueness and global exponential stability of the equilibrium point is presented. And the upper bound for the degree of exponential stability is given. Moreover, a simulation is given to show the effectiveness of the result.
Complete Convergence for Weighted Sums of WOD Random Variables
ZHANG Ying; ZHANG Yu; SHEN Ai-ting
2016-01-01
In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weighted sums of widely orthant dependent ran-dom variables under mild conditions of weights and moments. The result obtained in the paper generalizes the corresponding ones for independent random variables and negatively dependent random variables.
Haroldo V Ribeiro
Full Text Available The complexity of chess matches has attracted broad interest since its invention. This complexity and the availability of large number of recorded matches make chess an ideal model systems for the study of population-level learning of a complex system. We systematically investigate the move-by-move dynamics of the white player's advantage from over seventy thousand high level chess matches spanning over 150 years. We find that the average advantage of the white player is positive and that it has been increasing over time. Currently, the average advantage of the white player is 0.17 pawns but it is exponentially approaching a value of 0.23 pawns with a characteristic time scale of 67 years. We also study the diffusion of the move dependence of the white player's advantage and find that it is non-Gaussian, has long-ranged anti-correlations and that after an initial period with no diffusion it becomes super-diffusive. We find that the duration of the non-diffusive period, corresponding to the opening stage of a match, is increasing in length and exponentially approaching a value of 15.6 moves with a characteristic time scale of 130 years. We interpret these two trends as a resulting from learning of the features of the game. Additionally, we find that the exponent [Formula: see text] characterizing the super-diffusive regime is increasing toward a value of 1.9, close to the ballistic regime. We suggest that this trend is due to the increased broadening of the range of abilities of chess players participating in major tournaments.
Ribeiro, Haroldo V; Mendes, Renio S; Lenzi, Ervin K; del Castillo-Mussot, Marcelo; Amaral, Luís A N
2013-01-01
The complexity of chess matches has attracted broad interest since its invention. This complexity and the availability of large number of recorded matches make chess an ideal model systems for the study of population-level learning of a complex system. We systematically investigate the move-by-move dynamics of the white player's advantage from over seventy thousand high level chess matches spanning over 150 years. We find that the average advantage of the white player is positive and that it has been increasing over time. Currently, the average advantage of the white player is 0.17 pawns but it is exponentially approaching a value of 0.23 pawns with a characteristic time scale of 67 years. We also study the diffusion of the move dependence of the white player's advantage and find that it is non-Gaussian, has long-ranged anti-correlations and that after an initial period with no diffusion it becomes super-diffusive. We find that the duration of the non-diffusive period, corresponding to the opening stage of a match, is increasing in length and exponentially approaching a value of 15.6 moves with a characteristic time scale of 130 years. We interpret these two trends as a resulting from learning of the features of the game. Additionally, we find that the exponent [Formula: see text] characterizing the super-diffusive regime is increasing toward a value of 1.9, close to the ballistic regime. We suggest that this trend is due to the increased broadening of the range of abilities of chess players participating in major tournaments.
Repetition priming from moving faces.
Lander, Karen; Bruce, Vicki
2004-06-01
Recent experiments have suggested that seeing a familiar face move provides additional dynamic information to the viewer, useful in the recognition of identity. In four experiments, repetition priming was used to investigate whether dynamic information is intrinsic to the underlying face representations. The results suggest that a moving image primes more effectively than a static image, even when the same static image is shown in the prime and the test phases (Experiment 1). Furthermore, when moving images are presented in the test phase (Experiment 2), there is an advantage for moving prime images. The most priming advantage is found with naturally moving faces, rather than with those shown in slow motion (Experiment 3). Finally, showing the same moving sequence at prime and test produced more priming than that found when different moving sequences were shown (Experiment 4). The results suggest that dynamic information is intrinsic to the face representations and that there is an advantage to viewing the same moving sequence at prime and test.
Congestion and residential moving behaviour
Larsen, Morten Marott; Pilegaard, Ninette; Van Ommeren, Jos
2008-01-01
we study how congestion and residential moving behaviour are interrelated, using a two-region job search model. Workers choose between interregional commuting and residential moving, in order to live closer to their place of work. This choice affects the external costs of commuting, due...
Lopes, Sílvia R. C.; Prass, Taiane S.
2014-05-01
Here we present a theoretical study on the main properties of Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroskedastic (FIEGARCH) processes. We analyze the conditions for the existence, the invertibility, the stationarity and the ergodicity of these processes. We prove that, if { is a FIEGARCH(p,d,q) process then, under mild conditions, { is an ARFIMA(q,d,0) with correlated innovations, that is, an autoregressive fractionally integrated moving average process. The convergence order for the polynomial coefficients that describes the volatility is presented and results related to the spectral representation and to the covariance structure of both processes { and { are discussed. Expressions for the kurtosis and the asymmetry measures for any stationary FIEGARCH(p,d,q) process are also derived. The h-step ahead forecast for the processes {, { and { are given with their respective mean square error of forecast. The work also presents a Monte Carlo simulation study showing how to generate, estimate and forecast based on six different FIEGARCH models. The forecasting performance of six models belonging to the class of autoregressive conditional heteroskedastic models (namely, ARCH-type models) and radial basis models is compared through an empirical application to Brazilian stock market exchange index.
Average weighted receiving time in recursive weighted Koch networks
DAI MEIFENG; YE DANDAN; LI XINGYI; HOU JIE
2016-06-01
Motivated by the empirical observation in airport networks and metabolic networks, we introduce the model of the recursive weighted Koch networks created by the recursive division method. As a fundamental dynamical process, random walks have received considerable interest in the scientific community. Then, we study the recursive weighted Koch networks on random walk i.e., the walker, at each step, starting from its current node, moves uniformly to any of itsneighbours. In order to study the model more conveniently, we use recursive division method again to calculate the sum of the mean weighted first-passing times for all nodes to absorption at the trap located in the merging node. It is showed that in a large network, the average weighted receiving time grows sublinearly with the network order.
Thermal dynamics on the lattice with exponentially improved accuracy
Pawlowski, Jan
2016-01-01
We present a novel simulation prescription for thermal quantum fields on a lattice that operates directly in imaginary frequency space. By distinguishing initial conditions from quantum dynamics it provides access to correlation functions also outside of the conventional Matsubara frequencies $\\omega_n=2\\pi n T$. In particular it resolves their frequency dependence between $\\omega=0$ and $\\omega_1=2\\pi T$, where the thermal physics $\\omega\\sim T$ of e.g.~transport phenomena is dominantly encoded. Real-time spectral functions are related to these correlators via an integral transform with rational kernel, so their unfolding is exponentially improved compared to Euclidean simulations. We demonstrate this improvement within a $0+1$-dimensional scalar field theory and show that spectral features inaccessible in standard Euclidean simulations are quantitatively captured.
Noise facilitation in associative memories of exponential capacity.
Karbasi, Amin; Salavati, Amir Hesam; Shokrollahi, Amin; Varshney, Lav R
2014-11-01
Recent advances in associative memory design through structured pattern sets and graph-based inference algorithms have allowed reliable learning and recall of an exponential number of patterns that satisfy certain subspace constraints. Although these designs correct external errors in recall, they assume neurons that compute noiselessly, in contrast to the highly variable neurons in brain regions thought to operate associatively, such as hippocampus and olfactory cortex. Here we consider associative memories with boundedly noisy internal computations and analytically characterize performance. As long as the internal noise level is below a specified threshold, the error probability in the recall phase can be made exceedingly small. More surprising, we show that internal noise improves the performance of the recall phase while the pattern retrieval capacity remains intact: the number of stored patterns does not reduce with noise (up to a threshold). Computational experiments lend additional support to our theoretical analysis. This work suggests a functional benefit to noisy neurons in biological neuronal networks.
Static vortices in long Josephson junctions of exponentially varying width
Semerdjieva, E. G.; Boyadjiev, T. L.; Shukrinov, Yu. M.
2004-06-01
A numerical simulation is carried out for static vortices in a long Josephson junction with an exponentially varying width. At specified values of the parameters the corresponding boundary-value problem admits more than one solution. Each solution (distribution of the magnetic flux in the junction) is associated to a Sturm-Liouville problem, the smallest eigenvalue of which can be used, in a first approximation, to assess the stability of the vortex against relatively small spatiotemporal perturbations. The change in width of the junction leads to a renormalization of the magnetic flux in comparison with the case of a linear one-dimensional model. The influence of the model parameters on the stability of the states of the magnetic flux is investigated in detail, particularly that of the shape parameter. The critical curve of the junction is constructed from pieces of the critical curves for the different magnetic flux distributions having the highest critical currents for the given magnetic field.
Income inequality in Romania: The exponential-Pareto distribution
Oancea, Bogdan; Andrei, Tudorel; Pirjol, Dan
2017-03-01
We present a study of the distribution of the gross personal income and income inequality in Romania, using individual tax income data, and both non-parametric and parametric methods. Comparing with official results based on household budget surveys (the Family Budgets Survey and the EU-SILC data), we find that the latter underestimate the income share of the high income region, and the overall income inequality. A parametric study shows that the income distribution is well described by an exponential distribution in the low and middle incomes region, and by a Pareto distribution in the high income region with Pareto coefficient α = 2.53. We note an anomaly in the distribution in the low incomes region (∼9,250 RON), and present a model which explains it in terms of partial income reporting.
Auxiliary Parameter MCMC for Exponential Random Graph Models
Byshkin, Maksym; Stivala, Alex; Mira, Antonietta; Krause, Rolf; Robins, Garry; Lomi, Alessandro
2016-11-01
Exponential random graph models (ERGMs) are a well-established family of statistical models for analyzing social networks. Computational complexity has so far limited the appeal of ERGMs for the analysis of large social networks. Efficient computational methods are highly desirable in order to extend the empirical scope of ERGMs. In this paper we report results of a research project on the development of snowball sampling methods for ERGMs. We propose an auxiliary parameter Markov chain Monte Carlo (MCMC) algorithm for sampling from the relevant probability distributions. The method is designed to decrease the number of allowed network states without worsening the mixing of the Markov chains, and suggests a new approach for the developments of MCMC samplers for ERGMs. We demonstrate the method on both simulated and actual (empirical) network data and show that it reduces CPU time for parameter estimation by an order of magnitude compared to current MCMC methods.
Fitting and Analyzing Randomly Censored Geometric Extreme Exponential Distribution
Muhammad Yameen Danish
2016-06-01
Full Text Available The paper presents the Bayesian analysis of two-parameter geometric extreme exponential distribution with randomly censored data. The continuous conjugate prior of the scale and shape parameters of the model does not exist while computing the Bayes estimates, it is assumed that the scale and shape parameters have independent gamma priors. It is seen that the closed-form expressions for the Bayes estimators are not possible; we suggest the Lindley’s approximation to obtain the Bayes estimates. However, the Bayesian credible intervals cannot be constructed while using this method, we propose Gibbs sampling to obtain the Bayes estimates and also to construct the Bayesian credible intervals. Monte Carlo simulation study is carried out to observe the behavior of the Bayes estimators and also to compare with the maximum likelihood estimators. One real data analysis is performed for illustration.
Coexistence of exponentially many chaotic spin-glass attractors.
Peleg, Y; Zigzag, M; Kinzel, W; Kanter, I
2011-12-01
A chaotic network of size N with delayed interactions which resembles a pseudoinverse associative memory neural network is investigated. For a load α = P/N chaotic network functions as an associative memory of 2P attractors with macroscopic basin of attractions which decrease with α. At finite α, a chaotic spin-glass phase exists, where the number of distinct chaotic attractors scales exponentially with N. Each attractor is characterized by a coexistence of chaotic behavior and freezing of each one of the N chaotic units or freezing with respect to the P patterns. Results are supported by large scale simulations of networks composed of Bernoulli map units and Mackey-Glass time delay differential equations.
Predicting jet radius in electrospinning by superpositioning exponential functions
Widartiningsih, P. M.; Iskandar, F.; Munir, M. M.; Viridi, S.
2016-08-01
This paper presents an analytical study of the correlation between viscosity and fiber diameter in electrospinning. Control over fiber diameter in electrospinning process was important since it will determine the performance of resulting nanofiber. Theoretically, fiber diameter was determined by surface tension, solution concentration, flow rate, and electric current. But experimentally it had been proven that significantly viscosity had an influence to fiber diameter. Jet radius equation in electrospinning process was divided into three areas: near the nozzle, far from the nozzle, and at jet terminal. There was no correlation between these equations. Superposition of exponential series model provides the equations combined into one, thus the entire of working parameters on electrospinning take a contribution to fiber diameter. This method yields the value of solution viscosity has a linear relation to jet radius. However, this method works only for low viscosity.
Increasing hazard rate of mixtures for natural exponential families
Bar-Lev, Shaul K
2010-01-01
Hazard rates play an important role in various areas, e.g., reliability theory, survival analysis, biostatistics, queueing theory and actuarial studies. Mixtures of distributions are also of a great preeminence in such areas as most populations of components are indeed heterogeneous. In this study we present a sufficient condition for mixtures of two elements\\ of the same natural exponential family (NEF) to have an increasing hazard rate. We then apply this condition to some classical NEF's having either quadratic, or cubic variance functions (VF) and others as well. A particular attention is devoted to the hyperbolic cosine NEF having a quadratic VF, the Ressel NEF having a cubic VF and to the Kummer distributions of type 2 NEF. The application of such a sufficient condition is quite intricate and cumbersome, in particular when applied to the latter three NEF's. Various lemmas and propositions are needed then to verify this condition for these NEF's.
Exact inference for two exponential populations with competing risks data
Song Mao; Yimin Shi; Liang Wang
2014-01-01
In a reliability comparative test, the joint censoring model is usual y adopted to evaluate the performances of units with the same facility. However, most researchers ignore the pos-sibility that there is more than one factor for the failure when a test unit fails. To solve this problem, we consider a joint Type-II hybrid censoring model for the analysis of exponential competing failure data. Based on the maximum likelihood theory, we compute the maximum likelihood estimators (MLEs) of parameters and then obtain the condition ensuring MLEs existence for every unknown parameter. Then we derive the conditional exact distributions and corresponding moment properties for parameters by the moment generating function (MGF). A Monte-Carlo simulation is conducted to compare the performances of different ways. And final y, we conduct a numerical example to il ustrate the proposed method.
Control of Spacecraft Formation with Disturbance Rejection and Exponential Gains
R. Schlanbusch
2013-01-01
Full Text Available We address the problem of state feedback translational motion control of a spacecraft formation through a modified sliding surface controller using variable gains and I^2 action for disturbance rejection. The exponential varying gains ensure faster convergence of the state trajectories during attitude maneuver while keeping the gains small (and the system less stiff for station keeping. Integral action is introduced for rejection of disturbances with a constant nonzero mean such as aerodynamic drag. A direct consequence is a drop in energy consumption when affected by sensor noise and a decrease in size of the error states residual when operating close to the equilibrium point. A large number of simulation results are presented to show the control performance.
Application of Multi-Exponential Inversion Method to NMR Measurements
XiaoLizhi; WangZhongdong; LiuTangyan
2004-01-01
A new multi-exponential inversion method for NMR relaxation signals is presented and tested, which is based on a solid iteration rebuild technique (SIRT). The T2 spectra inversed by the new method are compared with MAP-Ⅱ results. The T1 and T2 inversion results with different pre-assigned relaxation times and different SNR show that 16 to 64 logarithm equal spaced time constants is better obviously than MAP-Ⅱ. And in particular, it can ensure the relaxation time distribution when the SNR of the measured signal is very low. The new algorithm has been applied in rock core NMR analysis and NMR logging data process and interpretation.
A generalized exponential time series regression model for electricity prices
Haldrup, Niels; Knapik, Oskar; Proietti, Tomasso
We consider the issue of modeling and forecasting daily electricity spot prices on the Nord Pool Elspot power market. We propose a method that can handle seasonal and non-seasonal persistence by modelling the price series as a generalized exponential process. As the presence of spikes can distort...... the estimation of the dynamic structure of the series we consider an iterative estimation strategy which, conditional on a set of parameter estimates, clears the spikes using a data cleaning algorithm, and reestimates the parameters using the cleaned data so as to robustify the estimates. Conditional...... on the estimated model, the best linear predictor is constructed. Our modeling approach provides good fit within sample and outperforms competing benchmark predictors in terms of forecasting accuracy. We also find that building separate models for each hour of the day and averaging the forecasts is a better...
Hyponormal quantization of planar domains exponential transform in dimension two
Gustafsson, Björn
2017-01-01
This book exploits the classification of a class of linear bounded operators with rank-one self-commutators in terms of their spectral parameter, known as the principal function. The resulting dictionary between two dimensional planar shapes with a degree of shade and Hilbert space operators turns out to be illuminating and beneficial for both sides. An exponential transform, essentially a Riesz potential at critical exponent, is at the heart of this novel framework; its best rational approximants unveil a new class of complex orthogonal polynomials whose asymptotic distribution of zeros is thoroughly studied in the text. Connections with areas of potential theory, approximation theory in the complex domain and fluid mechanics are established. The text is addressed, with specific aims, at experts and beginners in a wide range of areas of current interest: potential theory, numerical linear algebra, operator theory, inverse problems, image and signal processing, approximation theory, mathematical physics.
Exponential fading to white of black holes in quantum gravity
Barceló, Carlos; Garay, Luis J
2016-01-01
Quantization of the gravitational field could allow the existence of a hypothetical decay channel of black holes into white holes with an explicit time-reversal symmetry. The definition of a meaningful decay probability for this channel is studied in spherically symmetric situations. As a first nontrivial calculation, we present the functional integration over a set of geometries using a single-variable function to interpolate between black-hole and white-hole geometries in a bounded region of spacetime. This computation gives a finite result which depends only on the Schwarzschild mass and a parameter measuring the width of the interpolating region. The associated probability distribution displays an exponential decay law on the latter parameter, with the Planck time as its mean lifetime (up to subdominant terms). In physical terms this would imply that matter collapsing to a black hole from a finite radius bounces back elastically and instantaneously, with negligible time delay as measured by external obser...
Exponential Family Techniques for the Lognormal Left Tail
Asmussen, Søren; Jensen, Jens Ledet; Rojas-Nandayapa, Leonardo
Let X be lognormal(μ,σ2) with density f(x), let θ>0 and define L(θ)=Ee−θX. We study properties of the exponentially tilted density (Esscher transform) fθ(x)=e−θxf(x)/L(θ), in particular its moments, its asymptotic form as θ→∞ and asymptotics for the saddlepoint θ(x) determined by E[Xe−θX]/L(θ)=x....... demonstrate logarithmic efficiency. Numerical examples for the cdf Fn(x) and the pdf fn(x) of Sn are given in a range of values of σ2,n,x motivated from portfolio Value-at-Risk calculations....
Iterative exponential growth of stereo- and sequence-controlled polymers.
Barnes, Jonathan C; Ehrlich, Deborah J C; Gao, Angela X; Leibfarth, Frank A; Jiang, Yivan; Zhou, Erica; Jamison, Timothy F; Johnson, Jeremiah A
2015-10-01
Chemists have long sought sequence-controlled synthetic polymers that mimic nature's biopolymers, but a practical synthetic route that enables absolute control over polymer sequence and structure remains a key challenge. Here, we report an iterative exponential growth plus side-chain functionalization (IEG+) strategy that begins with enantiopure epoxides and facilitates the efficient synthesis of a family of uniform >3 kDa macromolecules of varying sequence and stereoconfiguration that are coupled to produce unimolecular polymers (>6 kDa) with sequences and structures that cannot be obtained using traditional polymerization techniques. Selective side-chain deprotection of three hexadecamers is also demonstrated, which imbues each compound with the ability to dissolve in water. We anticipate that these new macromolecules and the general IEG+ strategy will find broad application as a versatile platform for the scalable synthesis of sequence-controlled polymers.
Statistical modelling of agrometeorological time series by exponential smoothing
Murat, Małgorzata; Malinowska, Iwona; Hoffmann, Holger; Baranowski, Piotr
2016-01-01
Meteorological time series are used in modelling agrophysical processes of the soil-plant-atmosphere system which determine plant growth and yield. Additionally, long-term meteorological series are used in climate change scenarios. Such studies often require forecasting or projection of meteorological variables, eg the projection of occurrence of the extreme events. The aim of the article was to determine the most suitable exponential smoothing models to generate forecast using data on air temperature, wind speed, and precipitation time series in Jokioinen (Finland), Dikopshof (Germany), Lleida (Spain), and Lublin (Poland). These series exhibit regular additive seasonality or non-seasonality without any trend, which is confirmed by their autocorrelation functions and partial autocorrelation functions. The most suitable models were indicated by the smallest mean absolute error and the smallest root mean squared error.
Iterative Exponential Growth Synthesis and Assembly of Uniform Diblock Copolymers.
Jiang, Yivan; Golder, Matthew R; Nguyen, Hung V-T; Wang, Yufeng; Zhong, Mingjiang; Barnes, Jonathan C; Ehrlich, Deborah J C; Johnson, Jeremiah A
2016-08-03
Studies on the phase segregation of unimolecular block copolymers (BCPs) are limited by a lack of reliable, versatile methods for the synthesis of such polymers on the preparative scale. Herein, we describe an advancement of Iterative Exponential Growth (IEG) wherein chiral allyl-based IEG oligomers are subjected to thiol-ene reactions and converted into unimolecular BCPs. With this strategy we have synthesized uniform BCPs with molar masses up to 12.1 kDa on ∼1 g scale. BCPs composed of decane-based side chains and either triethyleneglycol- or thioglycerol-based side chains phase-segregate into hexagonal cylinder morphologies. The assembly is not driven by side-chain crystallization, but is instead the result of amorphous BCP assembly.
Academia-industry collaboration feeds exponential growth curve
Jones Bey Hassaun, A
2004-01-01
The use of silicon strip detectors in high-energy particle tracking is discussed. The functional strength of silicon for high-energy particle physics as well as astrophysics lies in the ability to detect passage of charged particles with micron-scale spatial resolution. In addition to vertex detection, silicon strip detectors also provide full tracking detection to include momentum determination of particles in the magnetic field. Even if silicon detectors for basic science applications do not continue to grow larger, exponential growth of the technology for terrestrial commercial applications is likely to follow a healthy growth curve, as researchers continue to adapt silicon detector technology for low- dose medical x-ray imaging. (Edited abstract)
Rotating Dilaton Black Strings Coupled to Exponential Nonlinear Electrodynamics
Ahmad Sheykhi
2014-01-01
Full Text Available We construct a new class of charged rotating black string solutions coupled to dilaton and exponential nonlinear electrodynamic fields with cylindrical or toroidal horizons in the presence of a Liouville-type potential for the dilaton field. Due to the presence of the dilaton field, the asymptotic behaviors of these solutions are neither flat nor (AdS. We analyze the physical properties of the solutions in detail. We compute the conserved and thermodynamic quantities of the solutions and verify the first law of thermodynamics on the black string horizon. When the nonlinear parameter β2 goes to infinity, our results reduce to those of black string solutions in Einstein-Maxwell-dilaton gravity.
Control of a heterogeneous two-server exponential queueing system
Larsen, R. L.; Agrawala, A. K.
1983-01-01
A dynamic control policy known as 'threshold queueing' is defined for scheduling customers from a Poisson source on a set of two exponential servers with dissimilar service rates. The slower server is invoked in response to instantaneous system loading as measured by the length of the queue of waiting customers. In a threshold queueing policy, a specific queue length is identified as a 'threshold,' beyond which the slower server is invoked. The slower server remains busy until it completes service on a customer and the queue length is less than its invocation threshold. Markov chain analysis is employed to analyze the performance of the threshold queueing policy and to develop optimality criteria. It is shown that probabilistic control is suboptimal to minimize the mean number of customers in the system. An approximation to the optimum policy is analyzed which is computationally simple and suffices for most operational applications.
Galilean invariance in the exponential model of atomic collisions
del Pozo, A.; Riera, A.; Yaez, M.
1986-11-01
Using the X/sup n//sup +/(1s/sup 2/)+He/sup 2+/ colliding systems as specific examples, we study the origin dependence of results in the application of the two-state exponential model, and we show the relevance of polarization effects in that study. Our analysis shows that polarization effects of the He/sup +/(1s) orbital due to interaction with X/sup (//sup n//sup +1)+/ ion in the exit channel yield a very small contribution to the energy difference and render the dynamical coupling so strongly origin dependent that it invalidates the basic premises of the model. Further study, incorporating translation factors in the formalism, is needed.
The group exponential lasso for bi-level variable selection.
Breheny, Patrick
2015-09-01
In many applications, covariates possess a grouping structure that can be incorporated into the analysis to select important groups as well as important members of those groups. One important example arises in genetic association studies, where genes may have several variants capable of contributing to disease. An ideal penalized regression approach would select variables by balancing both the direct evidence of a feature's importance as well as the indirect evidence offered by the grouping structure. This work proposes a new approach we call the group exponential lasso (GEL) which features a decay parameter controlling the degree to which feature selection is coupled together within groups. We demonstrate that the GEL has a number of statistical and computational advantages over previously proposed group penalties such as the group lasso, group bridge, and composite MCP. Finally, we apply these methods to the problem of detecting rare variants in a genetic association study.
On Quantified Propositional Logics and the Exponential Time Hierarchy
Miika Hannula
2016-09-01
Full Text Available We study quantified propositional logics from the complexity theoretic point of view. First we introduce alternating dependency quantified boolean formulae (ADQBF which generalize both quantified and dependency quantified boolean formulae. We show that the truth evaluation for ADQBF is AEXPTIME(poly-complete. We also identify fragments for which the problem is complete for the levels of the exponential hierarchy. Second we study propositional team-based logics. We show that DQBF formulae correspond naturally to quantified propositional dependence logic and present a general NEXPTIME upper bound for quantified propositional logic with a large class of generalized dependence atoms. Moreover we show AEXPTIME(poly-completeness for extensions of propositional team logic with generalized dependence atoms.
Exponential protection of zero modes in Majorana islands.
Albrecht, S M; Higginbotham, A P; Madsen, M; Kuemmeth, F; Jespersen, T S; Nygård, J; Krogstrup, P; Marcus, C M
2016-03-10
Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of fault-tolerant quantum computers. They are expected to exhibit non-Abelian particle statistics, in contrast to the usual statistics of fermions and bosons, enabling quantum operations to be performed by braiding isolated modes around one another. Quantum braiding operations are topologically protected insofar as these modes are pinned near zero energy, with the departure from zero expected to be exponentially small as the modes become spatially separated. Following theoretical proposals, several experiments have identified signatures of Majorana modes in nanowires with proximity-induced superconductivity and atomic chains, with small amounts of mode splitting potentially explained by hybridization of Majorana modes. Here, we use Coulomb-blockade spectroscopy in an InAs nanowire segment with epitaxial aluminium, which forms a proximity-induced superconducting Coulomb island (a 'Majorana island') that is isolated from normal-metal leads by tunnel barriers, to measure the splitting of near-zero-energy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometres, sub-gap state energies oscillate as the magnetic field is varied, as is expected for hybridized Majorana modes. Splitting decreases by a factor of about ten for each half a micrometre of increased wire length. For devices longer than about one micrometre, transport in strong magnetic fields occurs through a zero-energy state that is energetically isolated from a continuum, yielding uniformly spaced Coulomb-blockade conductance peaks, consistent with teleportation via Majorana modes. Our results help to explain the trivial-to-topological transition in finite systems and to quantify the scaling of topological protection with end-mode separation.
Exponentiation for products of Wilson lines within the generating function approach
Vladimirov, Alexey A
2015-01-01
We present the generating function approach to the perturbative exponentiation of correlators of a product of Wilson lines and loops. The exponentiated expression is presented in the closed form as an algebraic function of correlators of known operators, which can be seen as a generating function for web diagrams. The expression is naturally split onto two parts: the exponentiation kernel, which accumulates all non-trivial information about web diagrams, and the defect of exponentiation, which reconstructs the matrix exponent and is a function of the exponentiation kernel. The detailed comparison of the presented approach with existing approaches to exponentiation is presented as well. We also give examples of calculations within the generating function exponentiation, namely, we consider different configurations of light-like Wilson lines in the multi-gluon-exchange-webs (MGEW) approximation. Within this approximation the corresponding correlators can be calculated exactly at any order of perturbative expans...
Geloni, Gianluca [European XFEL GmbH, Hamburg (Germany); Kocharyan, Vitali; Saldin, Evgeni [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2017-04-15
It is generally accepted that in order to describe the dynamics of relativistic particles in the laboratory (lab) frame it is sufficient to take into account the relativistic dependence of the particle momenta on the velocity. This solution of the dynamics problem in the lab frame makes no reference to Lorentz transformations. For this reason they are not discussed in particle tracking calculations in accelerator and plasma physics. It is generally believed that the electrodynamics problem can be treated within the same ''single inertial frame'' description without reference to Lorentz transformations. In particular, in order to evaluate radiation fields arising from charged particles in motion we need to know their velocities and positions as a function of the lab frame time t. The relativistic motion of a particle in the lab frame is described by Newton's second law ''corrected'' for the relativistic dependence of momentum on velocity. It is assumed in all standard derivations that one can perform identification of the trajectories in the source part of the usual Maxwell's equations with the trajectories vector x(t) measured (or calculated by using the corrected Newton's second law) in the lab frame. This way of coupling fields and particles is considered since more than a century as the relativistically correct procedure.We argue that this procedure needs to be changed, and we demonstrate the following, completely counterintuitive statement: the results of conventional theory of radiation by relativistically moving charges are not consistent with the principle of relativity. In order to find the trajectory of a particle in the lab frame consistent with the usual Maxwell's equations, one needs to solve the dynamic equation inmanifestly covariant form by using the coordinate-independent proper time τ to parameterize the particle world-line in space-time. We show that there is a difference between &apos
Robust moving mesh algorithms for hybrid stretched meshes: Application to moving boundaries problems
Landry, Jonathan; Soulaïmani, Azzeddine; Luke, Edward; Ben Haj Ali, Amine
2016-12-01
A robust Mesh-Mover Algorithm (MMA) approach is designed to adapt meshes of moving boundaries problems. A new methodology is developed from the best combination of well-known algorithms in order to preserve the quality of initial meshes. In most situations, MMAs distribute mesh deformation while preserving a good mesh quality. However, invalid meshes are generated when the motion is complex and/or involves multiple bodies. After studying a few MMA limitations, we propose the following approach: use the Inverse Distance Weighting (IDW) function to produce the displacement field, then apply the Geometric Element Transformation Method (GETMe) smoothing algorithms to improve the resulting mesh quality, and use an untangler to revert negative elements. The proposed approach has been proven efficient to adapt meshes for various realistic aerodynamic motions: a symmetric wing that has suffered large tip bending and twisting and the high-lift components of a swept wing that has moved to different flight stages. Finally, the fluid flow problem has been solved on meshes that have moved and they have produced results close to experimental ones. However, for situations where moving boundaries are too close to each other, more improvements need to be made or other approaches should be taken, such as an overset grid method.
Gaussian moving averages and semimartingales
Basse-O'Connor, Andreas
2008-01-01
In the present paper we study moving averages (also known as stochastic convolutions) driven by a Wiener process and with a deterministic kernel. Necessary and sufficient conditions on the kernel are provided for the moving average to be a semimartingale in its natural filtration. Our results...... are constructive - meaning that they provide a simple method to obtain kernels for which the moving average is a semimartingale or a Wiener process. Several examples are considered. In the last part of the paper we study general Gaussian processes with stationary increments. We provide necessary and sufficient...
Rehabilitation Counselor Certification: Moving Forward
Saunders, Jodi L.; Barros-Bailey, Mary; Chapman, Cindy; Nunez, Patricia
2009-01-01
This article provides a brief history of the Commission on Rehabilitation Counselor Certification and presents recent changes and strategic goals for moving forward. Challenges and opportunities for the profession in relation to certification are also discussed. (Contains 3 tables.)
Minimum Delay Moving Object Detection
Lao, Dong
2017-01-08
We present a general framework and method for detection of an object in a video based on apparent motion. The object moves relative to background motion at some unknown time in the video, and the goal is to detect and segment the object as soon it moves in an online manner. Due to unreliability of motion between frames, more than two frames are needed to reliably detect the object. Our method is designed to detect the object(s) with minimum delay, i.e., frames after the object moves, constraining the false alarms. Experiments on a new extensive dataset for moving object detection show that our method achieves less delay for all false alarm constraints than existing state-of-the-art.
Transient heating of moving objects
E.I. Baida
2014-06-01
Full Text Available A mathematical model of transient and quasistatic heating of moving objects by various heat sources is considered. The mathematical formulation of the problem is described, examples of thermal calculation given.
Astrophysical Weighted Particle Magnetohydrodynamics
Gaburov, Evghenii
2010-01-01
This paper presents applications of weighted meshless scheme for conservation laws to the Euler equations and the equations of ideal magnetohydrodynamics. The divergence constraint of the latter is maintained to the truncation error by a new meshless divergence cleaning procedure. The physics of the interaction between the particles is described by an one-dimensional Riemann problem in a moving frame. As a result, necessary diffusion which is required to treat dissipative processes is added automatically. As a result, our scheme has no free parameters that controls the physics of inter-particle interaction, with the exception of the number of the interacting neighbours which control the resolution and accuracy. The resulting equations have the form similar to SPH equations, and therefore existing SPH codes can be used to implement the weighed particle scheme. The scheme is validated in several hydrodynamic and MHD test cases. In particular, we demonstrate for the first time the ability of a meshless MHD schem...
Autowaves in moving excitable media
V.A.Davydov
2004-01-01
Full Text Available Within the framework of kinematic theory of autowaves we suggest a method for analytic description of stationary autowave structures appearing at the boundary between the moving and fixed excitable media. The front breakdown phenomenon is predicted for such structures. Autowave refraction and, particulary, one-side "total reflection" at the boundary is considered. The obtained analytical results are confirmed by computer simulations. Prospects of the proposed method for further studies of autowave dynamics in the moving excitable media are discussed.
Soeryana, Endang; Halim, Nurfadhlina Bt Abdul; Sukono, Rusyaman, Endang; Supian, Sudradjat
2017-03-01
Investments in stocks investors are also faced with the issue of risk, due to daily price of stock also fluctuate. For minimize the level of risk, investors usually forming an investment portfolio. Establishment of a portfolio consisting of several stocks are intended to get the optimal composition of the investment portfolio. This paper discussed about optimizing investment portfolio of Mean-Variance to stocks by using mean and volatility is not constant based on the Negative Exponential Utility Function. Non constant mean analyzed using models Autoregressive Moving Average (ARMA), while non constant volatility models are analyzed using the Generalized Autoregressive Conditional heteroscedastic (GARCH). Optimization process is performed by using the Lagrangian multiplier technique. As a numerical illustration, the method is used to analyze some stocks in Indonesia. The expected result is to get the proportion of investment in each stock analyzed
Gorakh Nath
2010-01-01
Non-similarity solutions are obtained for one-dimensional isothermal and adiabatic flow behind strong cylindrical shock wave propagation in a rotational axisymmetric dusty gas,which has a variable azimuthal and axial fluid velocity.The dusty gas is assumed to be a mixture of small solid particles and perfect gas.The equilibrium flow conditions are assumed to be maintained,and the density of the mixture is assumed to be varying and obeying an exponential law.The fluid velocities in the ambient medium are assumed to obey exponential laws.The shock wave moves with variable velocity.The effects of variation of the mass concentration of solid particles in the mixture,and the ratio of the density of solid particles to the initial density of the gas on the flow variables in the region behind the shock are investigated at given times.Also,a comparison between the solutions in the cases of isothermal and adiabatic flows is made.
Predictors of the peak width for networks with exponential links
Troutman, B.M.; Karlinger, M.R.
1989-01-01
We investigate optimal predictors of the peak (S) and distance to peak (T) of the width function of drainage networks under the assumption that the networks are topologically random with independent and exponentially distributed link lengths. Analytical results are derived using the fact that, under these assumptions, the width function is a homogeneous Markov birth-death process. In particular, exact expressions are derived for the asymptotic conditional expectations of S and T given network magnitude N and given mainstream length H. In addition, a simulation study is performed to examine various predictors of S and T, including N, H, and basin morphometric properties; non-asymptotic conditional expectations and variances are estimated. The best single predictor of S is N, of T is H, and of the scaled peak (S divided by the area under the width function) is H. Finally, expressions tested on a set of drainage basins from the state of Wyoming perform reasonably well in predicting S and T despite probable violations of the original assumptions. ?? 1989 Springer-Verlag.
Exponential 6 parameterization for the JCZ3-EOS
McGee, B.C.; Hobbs, M.L.; Baer, M.R.
1998-07-01
A database has been created for use with the Jacobs-Cowperthwaite-Zwisler-3 equation-of-state (JCZ3-EOS) to determine thermochemical equilibrium for detonation and expansion states of energetic materials. The JCZ3-EOS uses the exponential 6 intermolecular potential function to describe interactions between molecules. All product species are characterized by r*, the radius of the minimum pair potential energy, and {var_epsilon}/k, the well depth energy normalized by Boltzmann`s constant. These parameters constitute the JCZS (S for Sandia) EOS database describing 750 gases (including all the gases in the JANNAF tables), and have been obtained by using Lennard-Jones potential parameters, a corresponding states theory, pure liquid shock Hugoniot data, and fit values using an empirical EOS. This database can be used with the CHEETAH 1.40 or CHEETAH 2.0 interface to the TIGER computer program that predicts the equilibrium state of gas- and condensed-phase product species. The large JCZS-EOS database permits intermolecular potential based equilibrium calculations of energetic materials with complex elemental composition.
Characterizing quantum correlations. Entanglement, uncertainty relations and exponential families
Niekamp, Soenke
2012-04-20
This thesis is concerned with different characterizations of multi-particle quantum correlations and with entropic uncertainty relations. The effect of statistical errors on the detection of entanglement is investigated. First, general results on the statistical significance of entanglement witnesses are obtained. Then, using an error model for experiments with polarization-entangled photons, it is demonstrated that Bell inequalities with lower violation can have higher significance. The question for the best observables to discriminate between a state and the equivalence class of another state is addressed. Two measures for the discrimination strength of an observable are defined, and optimal families of observables are constructed for several examples. A property of stabilizer bases is shown which is a natural generalization of mutual unbiasedness. For sets of several dichotomic, pairwise anticommuting observables, uncertainty relations using different entropies are constructed in a systematic way. Exponential families provide a classification of states according to their correlations. In this classification scheme, a state is considered as k-correlated if it can be written as thermal state of a k-body Hamiltonian. Witness operators for the detection of higher-order interactions are constructed, and an algorithm for the computation of the nearest k-correlated state is developed.
Kinetically Modified Non-Minimal Inflation With Exponential Frame Function
Pallis, C
2016-01-01
We consider Supersymmetric (SUSY) and non-SUSY models of chaotic inflation based on the phi^n potential with n=2 or 4. We show that the coexistence of an exponential nonminimal coupling to gravity, fR=Exp(cR phi^p), with a kinetic mixing of the form fK=cK fR^m can accommodate inflationary observables favored by the Planck and Bicep2/Keck Array results for p=1 and 2, 1<=m<=15 and 2.6x10^(-3)<=rRK=cR/cK^(p/2)<=1, where the upper limit is not imposed for p=1. Inflation is of hilltop type and it can be attained for subplanckian inflaton values with the corresponding effective theories retaining the perturbative unitarity up to the Planck scale. The supergravity embedding of these models is achieved employing two chiral gauge singlet supefields, a monomial superpotential and several (semi)logarithmic or semipolynomial Kaehler potentials.
Absence of exponential clustering in quantum Coulomb fluids
Alastuey, A.; Martin, Ph. A.
1989-12-01
We show that the quantum corrections to the classical correlations of a Coulomb fluid do not decay exponentially fast for all values of the thermodynamical parameters. Specifically, the ħ4 term in the Wigner-Kirkwood expansion of the equilibrium charge-charge correlations of the quantum one-component plasma is found to decay like ||r||-10. More generally, using functional integration, we present a diagrammatic representation of the ħ expansion of the correlations in a multicomponent fluid with a locally regularized Coulomb potential and Maxwell-Boltzmann statistics. The ħ2n terms are found to decay algebraically for all n>=2. Furthermore, an analysis of the hierarchy equations for the correlations provides upper bounds that are compatible with the findings of the perturbative expansion. Except for the monopole, all higher-order multipole sum rules do not hold, in general, in the quantum system. This violation of the multipole sum rules as well as the related algebraic tails are due to the intrinsic quantum fluctuations that prevent a perfect organization of the screening clouds. This phenomenon is illustrated in a simpler model where the large-distance correlations between two quantum particles embedded in a classical plasma can be exactly computed.
A Study on The Mixture of Exponentiated-Weibull Distribution
Adel Tawfik Elshahat
2016-12-01
Full Text Available Mixtures of measures or distributions occur frequently in the theory and applications of probability and statistics. In the simplest case it may, for example, be reasonable to assume that one is dealing with the mixture in given proportions of a finite number of normal populations with different means or variances. The mixture parameter may also be denumerable infinite, as in the theory of sums of a random number of random variables, or continuous, as in the compound Poisson distribution. The use of finite mixture distributions, to control for unobserved heterogeneity, has become increasingly popular among those estimating dynamic discrete choice models. One of the barriers to using mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive reparability of the log likelihood function. In this thesis, the maximum likelihood estimators have been obtained for the parameters of the mixture of exponentiated Weibull distribution when sample is available from censoring scheme. The maximum likelihood estimators of the parameters and the asymptotic variance covariance matrix have been also obtained. A numerical illustration for these new results is given.
Optimal ambiguity functions and Weil's exponential sum bound
Benedetto, John J; Woodworth, Joseph T
2011-01-01
Complex-valued periodic sequences, u, constructed by Goran Bjorck, are analyzed with regard to the behavior of their discrete periodic narrow-band ambiguity functions A_p(u). The Bjorck sequences, which are defined on Z/pZ for p>2 prime, are unimodular and have zero autocorrelation on (Z/pZ)\\{0}. These two properties give rise to the acronym, CAZAC, to refer to constant amplitude zero autocorrelation sequences. The bound proven is |A_p(u)| \\leq 2/\\sqrt{p} + 4/p outside of (0,0), and this is of optimal magnitude given the constraint that u is a CAZAC sequence. The proof requires the full power of Weil's exponential sum bound, which, in turn, is a consequence of his proof of the Riemann hypothesis for finite fields. Such bounds are not only of mathematical interest, but they have direct applications as sequences in communications and radar, as well as when the sequences are used as coefficients of phase-coded waveforms.
Mutant number distribution in an exponentially growing population
Keller, Peter; Antal, Tibor
2015-01-01
We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrück (1943 Genetics 28 491-511) 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to grow exponentially in a deterministic fashion. Proportional to the wild-type population size, mutants arrive randomly and initiate new sub-populations of mutants that grow stochastically according to a supercritical birth and death process. We give an exact expression for the generating function of the total number of mutants at a given wild-type population size. We present a simple expression for the probability of finding no mutants, and a recursion formula for the probability of finding a given number of mutants. In the ‘large population-small mutation’ limit we recover recent results of Kessler and Levine (2014 J. Stat. Phys. doi:10.1007/s10955-014-1143-3) for a fully stochastic version of the process.
Exponential flux-controlled memristor model and its floating emulator
Liu, Wei; Wang, Fa-Qiang; Ma, Xi-Kui
2015-11-01
As commercial memristors are still unavailable in the market, mathematic models and emulators which can imitate the features of the memristor are meaningful for further research. In this paper, based on the analyses of characteristics of the q-φ curve, an exponential flux-controlled model, which has the quality that its memductance (memristance) will keep monotonically increasing or decreasing unless the voltage’s polarity reverses (if not approach the boundaries), is constructed. A new approach to designing the floating emulator of the memristor is also proposed. This floating structure can flexibly meet various demands for the current through the memristor (especially the demand for a larger current). The simulations and experiments are presented to confirm the effectiveness of this model and its floating emulator. Project supported by the National Natural Science Foundation of China (Grant Nos. 51377124 and 51221005), the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 201337), the Program for New Century Excellent Talents in University of China (Grant No. NCET-13-0457), and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2012JQ7026).
Fermat quotients: Exponential sums, value set and primitive roots
Shparlinski, Igor E
2011-01-01
For a prime $p$ and an integer $u$ with $\\gcd(u,p)=1$, we define Fermat quotients by the conditions $$ q_p(u) \\equiv \\frac{u^{p-1} -1}{p} \\pmod p, \\qquad 0 \\le q_p(u) \\le p-1. $$ D. R. Heath-Brown has given a bound of exponential sums with $N$ consecutive Fermat quotients that is nontrivial for $N\\ge p^{1/2+\\epsilon}$ for any fixed $\\epsilon>0$. We use a recent idea of M. Z. Garaev together with a form of the large sieve inequality due to S. Baier and L. Zhao, to show that on average over $p$ one can obtain a nontrivial estimate for much shorter sums starting with $N\\ge p^{\\epsilon}$. We also obtain lower bounds on the image size of the first $N$ consecutive Fermat quotients and use it to prove that there is a positive integer $n\\le p^{3/4 + o(1)}$ such that $q_p(n)$ is a primitive root modulo $p$.