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This research suggests an efficient method that is better suited for speech processing applications to retrieve the accurate fundamental frequencies from speech in noisy conditions. For this objective, a fundamental frequency extraction algorithm that is tolerant to the non-stationary changes of the amplitude and frequency of the input signal is presented. Moreover, autocorrelation function is used as a pre-processor, which uses the power spectrum of the input signal to reduce the noise characteristics of the speech signals. In order to increase the accuracy of the fundamental frequency extraction, the focus has been on maintaining the speech harmonics in their original state and suppressing the noise elements involved in the noisy speech signal. The two stages that make up the suggested fundamental frequency extraction approach are producing the autocorrelation function of the speech signal as a pre-processor and applying it with the spectral subtraction method. As per the experiment results, the proposed technique appears to be better in noisy situations than other existing state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Extensive molecular dynamics simulations of liquid sodium have been carried out to evaluate correlation functions of several dynamical quantities. We report the results of a novel analysis of the longitudinal and transverse correlation functions obtained by evaluating directly their self- and distinct contributions at different wavevectors k. It is easily recognized that the self-contribution remains close to its k → 0 limit, which turns out to be exactly the autocorrelation function of the single particle velocity. The wavevector dependence of the longitudinal and transverse spectra and their selfand distinct parts is also presented. By making use of the decomposition of the velocity autocorrelation spectrum in terms of longitudinal and transverse parts, our analysis is able to recognize the effect of different dynamical processes in different frequency ranges. [ABSTRACT FROM AUTHOR]

Neutrosophic statistics are used when one is dealing with imprecise and indeterminate data or parameters. In the present paper we propose a method for performing a neutrosophic Student's t -type of statistical test that concerns the population mean when data arise from an autoregressive process of order 1 (AR (1)). In classical statistics, data obtained through this process are not independent when the autocorrelation coefficient of the process is not equal to 0, and hence the usual Student's t distribution is inadequate for inferring about the population mean; however a result obtained in earlier literature states that a Student's t -type of statistic, which is asymptotically normally distributed, can be used instead. Our method is based on the neutrosophic version of this result and it is implemented using simulated data. [ABSTRACT FROM AUTHOR]

Inventory lot-sizing and supplier selection problem has been studied in the literature considering mainly time-varying deterministic demand. However, in real life, most of the products exhibit non-stationary stochastic demand. In this context, we propose an integer linear programming model for inventory lot-sizing and supplier selection problem under non-stationary stochastic demand with all-units quantity discounts and fill rate constraints. Through detailed analysis of experimental results, we show the impacts of fill rate requirements and demand coefficient of variation on costs, inventory levels and order allocations. [ABSTRACT FROM PUBLISHER]

This letter studies the impact of auto-correlation of stochastic processes on the dynamic response of power systems. The frequency spectrum of the trajectories of the state variables of the system is utilized as a metric to evaluate this impact. Simulation results indicate that the auto-correlation have a direct impact on the amplitude of the dominant electro-mechanical modes of the system. Results also show that, for a wide range of the values of the auto-correlation, the impact of stochastic processes on system dynamics is local, affects differently each area of the system and, in some cases, can lead to instability and voltage collapse. [ABSTRACT FROM AUTHOR]

The theoretical and experimental evaluation of the cyclostationary random data transferring process corrupted by the individually and jointly cyclostationary crosstalk interference is presented. The interference and the message signals were measured by the real time digital oscilloscope. Autocorrelation functions were evaluated by synchronous cyclic averaging procedure. The analyzed periodic two-dimensional impulse response of the time-varying filter allows to obtain the output random process with the same cyclic frequency at the output of the filter by separation of orthogonal stationary waveforms constituting the input cyclostationary random process (CSRP). The filtering of the measured random process was implemented by the cyclic Wiener filter. The evaluation of the two-dimensional autocorrelation function and eye diagrams at the output of the cyclic Wiener filter showed significant reduction of the independent interference components in the estimated message signal. [ABSTRACT FROM AUTHOR]

The autocorrelation function of a stochastic process is one of the essential mathematical tools in the description of variability that is successfully applied in many scientific fields such as signal processing or financial time series analysis and forecasting. The aim of the paper is to provide an analysis of fuzzy transform of higher degree applied to stochastic processes with a focus on its autocorrelation function. We introduce a higher-degree fuzzy transform of a stochastic process and investigate its basic properties. Further, we introduce a higher-degree fuzzy transform of bivariate functions in the tensor product of polynomial spaces and demonstrate its approximation ability. In addition, we show that the bivariate higher-degree fuzzy transform of multiplicative separable functions is a product of univariate fuzzy transform of the respective functions, which is a desirable property in the processing of functions of higher dimensions. The obtained results are used to demonstrate an interesting identity between the autocorrelation function of the fuzzy transform of a stochastic process and the bivariate fuzzy transform of the autocorrelation function of the stochastic process. This identity provides two ways to determine the autocorrelation function of the fuzzy transform of a stochastic process, which can be useful, especially in a situation where its direct calculation becomes complex or even impossible, for example, the calculation of a sample autocorrelation function. [ABSTRACT FROM AUTHOR]

Due to its efficiency, convenience, non-destructive nature and strong anti-interference capability, the microtremor survey method (MSM) has found wide applications in urban geological surveys. The spatial autocorrelation method is diffusely applied to extract the dispersion curves from microtremor signals, which needs to satisfy the assumption that the energy of the fundamental Rayleigh wave is dominant. However, for layered media containing a layer with a significant low- or high-velocity contrast, this assumption is distinctly incorrect for certain frequency ranges. We present a processing methodology comprising the extraction and inversion of the apparent dispersion curves based on extended spatial autocorrelation method and fast simulated-annealing algorithm. We analyse synthetic microtremor signals for three selected geological models, and then compare the S-wave velocity structures estimated from their inversions with the actual models. Subsequently, a filed data example is given to detect the shallow stratigraphic structures in Guangzhou city, China, in which the new MSM was used. The estimated two-dimensional S-wave velocity model provided an accurate description of the thickness and depth of the strata in the study area, based on a priori information. Moreover, the S-wave velocity structures estimated from the MSM and the results from the drilling match very well, indicating that MSM is a reliable geophysical technique in urban geological surveys. Combined with available borehole information, MSM can be a very robust and effective method for detecting the shallow three-dimensional velocity structures in an urban area. [ABSTRACT FROM AUTHOR]

Stochastic electromagnetic fields caused by the data transferring signals along the printed circuit boards are potentially harmful interference sources for modern digital electronic devices. The characterization of the near-field electromagnetic emissions from the electronic device in time domain was implemented by real-time digital oscilloscope in conjunction with the sequential scanning system of the near-field probes. Excluding of the periodic sample mean function reveals the hidden cyclostationarity of the data transferring process measured by the near-field scanning system. In this article, the quantitative autocorrelation analysis of the hidden cyclostationary properties of the random nonperiodic data sequences is presented. The time-domain evolution of the autocovariance cross sections estimated at each scanning point were exploited for spatial-time localization of the transmission line. [ABSTRACT FROM AUTHOR]

We analyze how the choice of the sampling weight affects efficiency of the Monte Carlo evaluation of classical time autocorrelation functions. Assuming uncorrelated sampling or sampling with constant correlation length, we propose a sampling weight for which the number of trajectories needed for convergence is independent of the correlated quantity, dimensionality, dynamics, and phase-space density. By contrast, it is shown that the computational cost of the 'standard' algorithm sampling from the phase-space density may scale exponentially with the number of degrees of freedom. Yet, for the stationary Gaussian distribution of harmonic systems and for the autocorrelation function of a linear function of phase-space coordinates, the computational cost of this standard algorithm is also independent of dimensionality. [ABSTRACT FROM AUTHOR]

The paper proposes a new methodology for time-dependent reliability analysis of vibratory systems using a combination of a first-order, four-moment (FOFM) method and a non-Gaussian Karhunen-Loeve (NG-KL) expansion. The approach can also be used for random vibrations studies. The vibratory system is nonlinear and is excited by stationary non-Gaussian input random processes which are characterized by their first four marginal moments and autocorrelation function. The NG-KL expansion expresses each input non-Gaussian process as a linear combination of uncorrelated, non-Gaussian random variables and computes their first four moments. The FOFM method then uses the moments of the NG-KL variables to calculate the moments and autocorrelation function of the output processes based on a first-order Taylor expansion (linearization) of the system equations of motion. Using the output moments and autocorrelation function, another NG-KL expansion expresses the output processes in terms of uncorrelated non-Gaussian variables in the time domain, allowing the generation of output trajectories. The latter are used to estimate the time-dependent probability of failure using Monte Carlo simulation (MCS). The computational cost of the proposed approach is proportional to the number of NG-KL random variables and is significantly lower than that of other recently developed methodologies which are based on sampling. The accuracy and efficiency of the proposed methodology is demonstrated using a two-degree-of-freedom nonlinear vibratory system with random coefficients excited by a stationary non-Gaussian random process. [ABSTRACT FROM AUTHOR]

We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are discussed. The propagator of the Wigner function based on van Vleck’s approximation replaces the Liouville propagator by a quantum spot with an oscillatory pattern reflecting the interference between pairs of classical trajectories. Employing phase-space path integration instead, caustics in the quantum spot are resolved in terms of Airy functions. We apply both to two benchmark models of nonlinear molecular potentials, the Morse oscillator and the quartic double well, to test them in standard tasks such as computing autocorrelation functions and propagating coherent states. The performance of semiclassical Wigner propagation is very good even in the presence of marked quantum effects, e.g., in coherent tunneling and in propagating Schrödinger cat states, and of classical chaos in four-dimensional phase space. We suggest options for an effective numerical implementation of our method and for integrating it in Monte-Carlo–Metropolis algorithms suitable for high-dimensional systems. [ABSTRACT FROM AUTHOR]

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-cell variability even in clonal populations. Stochastic biochemical networks are modeled as continuous time discrete state Markov processes whose probability density functions evolve according to a chemical master equation (CME). The CME is not solvable but for the simplest cases, and one has to resort to kinetic Monte Carlo techniques to simulate the stochastic trajectories of the biochemical network under study. A commonly used such algorithm is the stochastic simulation algorithm (SSA). Because it tracks every biochemical reaction that occurs in a given system, the SSA presents computational difficulties especially when there is a vast disparity in the timescales of the reactions or in the number of molecules involved in these reactions. This is common in cellular networks, and many approximation algorithms have evolved to alleviate the computational burdens of the SSA. Here, we present a rigorously derived modified CME framework based on the partition of a biochemically reacting system into restricted and unrestricted reactions. Although this modified CME decomposition is as analytically difficult as the original CME, it can be naturally used to generate a hierarchy of approximations at different levels of accuracy. Most importantly, some previously derived algorithms are demonstrated to be limiting cases of our formulation. We apply our methods to biologically relevant test systems to demonstrate their accuracy and efficiency. [ABSTRACT FROM AUTHOR]

The geometrical error in the stereolithography process is analysed using a stochastic approach. This approach is based on a unified methodology, developed by the authors, for studying the mechanical error in different rapid prototyping processes. The tolerances and clearances have been assumed to be random variables. The coordinates of a point on the resin surface, traced by the laser beam, are expressed as a function of random variables. In a numerical example, the geometrical error has been found for a grid of points traced by the laser beam. The three-sigma error bands are plotted when tracing example curves. This is the band in which the laser beams of 99.73% of machines, produced on a mass scale, lie on the work surface for the given tolerances and clearances. Stringent values of tolerances and clearances reduce the error at the tool tip, but the cost of manufacturing and assembling the machines may become prohibitive. [ABSTRACT FROM AUTHOR]

A figure of merit (FOM) has been developed for focusing quadrupole multiplet lenses for ion micro- and nanobeam systems. The method which is based on measurement of the central peak of the two-dimensional autocorrelation function of an image provides separate FOM for the horizontal and vertical directions. The approach has been tested by comparison with the edge widths obtained by nonlinear fitting the edge widths of a Ni grid and found to be reliable. The FOM has the important advantage for ion beam imaging of biomedical samples that the fluence needed is considerably lower than for edge fitting. [ABSTRACT FROM AUTHOR]

Statistical process control procedures that use one-step-ahead forecasts, including special cause control charts, tend to have outstanding average run length properties when applied to a negatively auto-correlated data. However, nearly all industrial data, which is auto-correlated, exhibits a positive auto-correlation structure. In this paper, a simple transformation on a positively auto-correlated data is proposed which results in a data set with the same mean and nearly the same variance. The resulting auto-correlation coefficient is opposite in sign and approximately equal to that of the original data set. Two simulated examples using the special cause control chart are used to illustrate the proposed procedure. [ABSTRACT FROM AUTHOR]

We propose a model for the short-time dynamics of fluids confined in slit-shaped pores. The model has been developed from the observation that the real lobe of the instantaneous normal mode density of states (INM DOS) closely follows a γ distribution. By proposing that the density of states of the confined fluid can be represented by a γ distribution, the resulting velocity autocorrelation function (VACF) is constructed such that it is accurate upto the fourth frequency moment. The proposed model results in an analytical expression for the VACF and relaxation times. The VACFs obtained from the model have been compared with the VACFs obtained from molecular dynamic simulations and INM analysis for fluids confined in slit-shaped pores over a wide range of confinement and temperatures. The model is seen to capture the short-time behavior of the VACF extremely accurately and in this region is superior to the predictions of the VACF obtained from the real lobe of the INM DOS. Although the model predicts a zero self-diffusivity, the predicted relaxation times are in better agreement with the molecular dynamics results when compared with those obtained from the INM theory. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Highlights • We study the stochastic behavior of the LMS algorithm when the input signal is a cyclostationary colored Gaussian process. • The analysis is performed for cyclostationary input signals modeled as colored Gaussian random processes with periodically time-varying power. • A new model is proposed for the autocorrelation matrix of an input vector of samples of a second order wide sense cyclostationary signal. • The proposed model is a good approximation of the autocorrelation matrix of an autoregressive signal with periodically varying power. • Simulation results show excellent agreement with the theoretically predicted behavior. Abstract This paper studies the stochastic behavior of the LMS algorithm for a system identification framework when the input signal is a cyclostationary colored Gaussian process. The unknown system is modeled by the standard random walk model. Well-known results for the LMS algorithm are extended to the cyclostationary case and used for predicting the mean-square weight deviation (MSD) and excess mean-square error (EMSE) behavior of the algorithm. Monte Carlo simulations provide strong support for the theory. [ABSTRACT FROM AUTHOR]

This paper introduces a class of generalized linear models with a Box{ Cox link for the spectrum of a time series. The Box{Cox transformation of the spectral density is represented as a finite Fourier polynomial. Here, the coefficients of the polynomial, called generalized cepstral coefficients, provide a complete characterization of the properties of the random process. The link function depends on a power-transformation parameter, and can be expressed as an exponential model (logarithmic link), an autoregressive model (inverse link), or a moving average model (identity link). An advantage of this model class is the possibility of nesting alternative spectral estimation methods within the same likelihood-based framework. As a result, selecting a particular parametric spectrum is equivalent to estimating the transformation parameter. We also show that the generalized cepstral coefficients are a one-to-one function of the inverse partial autocorrelations of the process, which can be used to evaluate the mutual information between the past and the future of the process. [ABSTRACT FROM AUTHOR]

The objective of this study is to develop segmented polynomial taper equations using the nonlinear mixed-effects modeling approach for Caucasian fir (Abies nordmanniana (Steven) Spach. subsp. nordmanniana) - Oriental spruce (Picea orientalis (L.) Link.) mixed stands in Artvin-Ardanuç region of Turkey. For this purpose, the data obtained from 213 felled sample trees in total, which are 107 fir and 106 spruce, were used. Jiang et al.'s (2005) stem profile model produced the best prediction results for both tree species. The Radj2, RMSE, Ē , MAE, AIC and BIC values of the model were found as 98.7% and 98.3%, 1.700 and 1.814 cm, 0.143 and 0.167 cm, 1.179 and 1.269 cm, 4142.2 and 3951.7, 4148.5 and 3957.8 for fir and spruce, respectively. Based on AIC, BIC and -2LnL criteria, the model including random-effects in two parameters (b3 and b4) were the best for both tree species. This mixed-effects model with two random parameters showed homogeneous residual variance and autocorrelation was almost removed. Mixed-effects models provided much better fits than their fixed model counterparts for both species. In addition, among 12 different calibration choices, the best results were obtained with the choice involving the measurement of five diameters that divide the sample tree measurements into two equal parts for fir and of four diameters that bottom of the sample tree for spruce. [ABSTRACT FROM AUTHOR]

Highlights • Temporal variability of the clear-sky index is modeled with an N-state Markov-chain mixture. • The model output is comparable to state-of-the-art CSI generators. • It is computationally faster with lower complexity than existing models. Abstract This paper presents an N -state Markov-chain mixture distribution approach to model the clear-sky index. The model is based on dividing the clear-sky index data into bins of magnitude and determining probabilities for transitions between bins. These transition probabilities are then used to define a Markov-chain, which in turn is connected to a mixture distribution of uniform distributions. When trained on measured data, this model is used to generate synthetic data as output. The model is an N -state generalization of a previously published two-state Markov-chain mixture distribution model applied to the clear-sky index. The model is tested on clear-sky index data sets for two different climatic regions: Norrköping, Sweden, and Oahu, Hawaii, USA. The model is also compared with the two-state model and a copula model for generating synthetic clear-sky index time-series as well as other existing clear-sky index generators in the literature. Results show that the N -state model is generally on par with, or superior to, state-of-the-art synthetic clear-sky index generators in terms of Kolmogorov–Smirnov test statistic, autocorrelation and computational speed. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to develop and test a general stochastic process for common stock returns that is applicable over any arbitrary time interval for which the return is computed. During a trading day we propose that the stochastic process of stock transaction returns is an autoregressive jump process. This process consists of a calendar time diffusion process and a jump process in which the magnitudes of the jumps may be autocorrelated. Over non-trading periods, it is assumed that the same diffusion process operates, but a separate jump process is specified for overnights, holidays, weekends, and holiday-weekends. The resultant multiple component jump process is used to investigate returns over days, weeks, and months. Several statistical analyses using actual transaction data over different time intervals lend support to the proposed theory. [ABSTRACT FROM AUTHOR]

The authors discuss a special case of multiple time series models in which the autoregressive and moving average parameter matrices are diagonal. These models, called MTS-D, are appropriate if the random shocks which drive the series are only contemporaneously correlated. The flexibility and usefulness of this approach are illustrated in the context of a competitive market situation with five sales series, where individual components follow different univariate time series models. Theoretical as well as empirical justifications for expecting more precise parameter estimates are given. Forecasts from the model compare favorably with those from the univariate models. [ABSTRACT FROM AUTHOR]

Regression techniques provide the cost analyst with a valuable analytical tool. This paper describes means of expanding the utility of regression analysis applications in this area. Part I of the paper presented basic definitions and developed measures to assess the accuracy and sensitivity of a regression formula. In particular, it was shown that tho Association index, rather than tho more commonly used R, is the pertinent measure of formula sensitivity. We also described several other aspects of evaluating formula reliability--the confidence level, variability in the data, parameter stability, autocorrelation--and discussed indexes especially developed to quantify these factors.
Part II deals with the application of regression techniques to such areas as shop machining costs and long-term overhead relationships. The selection of variables and observations for a model, and the use of non-linear regressions, are discussed. Several examples from aerospace, ship construction, and other manufacturing industries illustrate the discussion of complex non-linear formulae which includes several situations characterized by cost-improvement curves. The overall reasonableness of a formula is then discussed in terms of data comparability, statistical adequacy, operational relevance, and prediction potential, and the paper concludes with further comments on intercorrelation of variables. [ABSTRACT FROM AUTHOR]

We obtain analytic expressions for normalized autocorrelation functions of frequency variations for the main types of noise in frequency fluctuations. These expressions enable one to calculate central moments of the distribution of estimates of the Allan variance and the function of this distribution. Using the χ2 distribution, we analyze the errors of the quantiles of the distribution as well as the displacements of the Allan variance estimates. [ABSTRACT FROM AUTHOR]

Abstract Quantitative assessment of cooperativity effects is essential for a better understanding of the interactions between system components that is an important step on the way from black-box to structural models of various complex dynamical systems. In this paper, we consider five widely used mutual information metrics and test their performance using simulated stochastic data series with introduced phase- or amplitude randomization as well as data series generated by chaotic maps. We show the performance of all studied methods in both stationary mode and during phase transitions, indicating specific coupling patterns they can reveal from the system dynamics, as well as certain properties they appear invariant to. Finally, we demonstrate how a combination of several metrics can be used for a more detailed analysis of dynamical systems exhibiting characteristic phase transitions, including examples of both simulated chaotic maps and observational data series from physiological and geophysical complex systems. Highlights • Cooperativity metrics in complex systems are affected by both cross- and autocorrelations. • Time delay stability is unaffected by additive while affected by multiplicative white noise. • Coherence is invariant to short-term, while cross-conditional entropy to long-term correlations. • Combination of several metrics provide a better characterization of phase transitions. • Phase transition in geomagnetic network reveals a characteristic pattern during a solar flare. [ABSTRACT FROM AUTHOR]

Hu introduced a simple method to compute the 2-adic complexity of any periodic binary sequence with ideal two-level autocorrelation. We extend this approach to some other sequences. First, we provide a substantially shorter proof of the maximality of the 2-adic complexity of the Legendre sequence of period $N\equiv 1\bmod 4$ first proved by Xiong et al. Then, we show that the 2-adic complexity of the two-prime generator of period $pq$ with two odd primes $p\ne q$ attains the maximum if $(q+1)/4\le p\le 4q-1$. This result was only known for twin primes $q=p+2$ before. For arbitrary odd primes $p\ne q$ , we can still prove that the 2-adic complexity of the two-prime generator is close to its period. [ABSTRACT FROM AUTHOR]

Although residential crowding has various impacts on household socioeconomic and health circumstances, there has been a dearth of research investigating and predicting spatial patterns of overcrowding in Arab nations. In this work, analytical modeling techniques are applied to investigate the interrelationships between residential overcrowding and other explanatory variables in Alexandria, Egypt. Global (Ordinarily Least Squared) and local (Autoregressive, Error Term and Geographically Weighted regression) models are employed to conduct the analysis. As global model, OLS assumes homogeneity among spatial predictors and it fails to account for spatial non-stationary. In contrast, the proposed local spatial econometric models can easily model spatial autocorrelation and spatial heterogeneity. Population density and one-room-dwelling were found to be positively and significantly associated with overcrowding, while higher education of residents and five rooms dwelling were negatively related to residential overcrowding across Alexandria districts. Significant implications ranging from governmental subsidy to planning public housing are discussed. [ABSTRACT FROM AUTHOR]

In recent years, driven by scientific and clinical concerns, there has been an increased interest in the analysis of functional brain networks. The goal of these analyses is to better understand how brain regions interact, how this depends upon experimental conditions and behavioral measures and how anomalies (disease) can be recognized. In this paper, we provide, first, a brief review of some of the main existing methods of functional brain network analysis. But rather than compare them, as a traditional review would do, instead, we draw attention to their significant limitations and blind spots. Then, second, relevant experts, sketch a number of emerging methods, which can break through these limitations. In particular we discuss five such methods. The first two, stochastic block models and exponential random graph models, provide an inferential basis for network analysis lacking in the exploratory graph analysis methods. The other three addresses: network comparison via persistent homology, time-varying connectivity that distinguishes sample fluctuations from neural fluctuations, and network system identification that draws inferential strength from temporal autocorrelation. [ABSTRACT FROM AUTHOR]

We give an introduction to the calculation of path integrals on a lattice, with the quantum harmonic oscillator as an example. In addition to providing an explicit computational setup and corresponding pseudocode, we pay particular attention to the existence of autocorrelations and the calculation of reliable errors. The over-relaxation technique is presented as a way to counter strong autocorrelations. The simulation methods can be extended to compute observables for path integrals in other settings. [ABSTRACT FROM AUTHOR]

The generation of non-Gaussian random processes with a given autocorrelation function (ACF) is addressed. The generation is based on a compound process with two components. Both components are solutions of appropriate stochastic differential equations (SDEs). One of the components is a Gaussian process and the other one is non-Gaussian with an exponential ACF. The analytical study shows that a compound combination of these processes may be used for the generation of a non-Gaussian random process with a required ACF. The results are verified by two numerical examples. [ABSTRACT FROM AUTHOR]

An extended version of the Continuous-Time Random Walk (CTRW) model with memory is herein developed. This memory involves the dependence between arbitrary number of successive jumps of the process while waiting times between jumps are considered as i.i.d. random variables. This dependence was established analyzing empirical histograms for the stochastic process of a single share price on a market within the high frequency time scale. Then, it was justified theoretically by considering bid-ask bounce mechanism containing some delay characteristic for any double-auction market. Our model appeared exactly analytically solvable. Therefore, it enables a direct comparison of its predictions with their empirical counterparts, for instance, with empirical velocity autocorrelation function. Thus, the present research significantly extends capabilities of the CTRW formalism. [ABSTRACT FROM AUTHOR]

This paper investigates properties of some dynamic panel data estimators including Ordinary Least Squares (OLS), the Anderson-Hsiao IV (AH), Arellano- Bond Generalized Method of Moment (GMM) first-step, Blundell- Bond System (SYS1) first-step, M and MM estimators in the presence of serial correlation. Absolute Bias and Root Mean Squares Error were used to evaluate finite properties of the estimators and revealed improving performances asymptotically under different sample sizes and varying degrees of autocorrelation. The results showed that in small and large sample situations, irrespective of time dimension, Anderson-Hsiao IV estimator (AH) outperforms all other estimators. Arellano-Bond Generalized Method of Moment (GMM) one-step proves to be relatively superior among the estimators when the time period (T) is small, though it may not be the best but performance improved drastically as the number of cross-sectional units increases. However, Ordinary Least Squares estimator has least performance among all the estimators considered in this study. [ABSTRACT FROM AUTHOR]

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A desalination plant – considered in two configurations (once-through and brine recirculation) – is modelled and controlled using a system of coupled PDEs that describe the desalination processes. The analysis is conducted in two separate parts. First, the operating point of the plant is obtained based on the deterministic process models of the plant. The steady-state distillate production is optimized with respect to a reference pressure head (operating point) that is achieved by applying relatively simple boundary controls. Both deterministic plant configurations are compared in term of characteristic numbers that evaluates the energy-efficient operation of the plant. In particular, those are the thermal ratio and the specific flow rate, where gains of roughly 5.5% and 21.5% are obtained in favour of the brine recirculation plant. The pressure head is subject to turbulence phenomena that disturb its surface so that a deterministic model is an insufficient representation of the real-case scenario. Concerning the second part of the paper, the effects of turbulence are incorporated through stochastic elements given as generalized and cylindrical Wiener processes located on the boundaries and throughout the plant (subdomain), respectively. The pressure head residual is defined as the difference between the deterministic and stochastic system. As both systems are actuated by the same type of boundary controls, the residual field is interpreted as a measure of a regulation error. It is statistical characterization is done spatially by means of the first four statistical moments (sampled) and temporarily with the autocorrelation function. It is found that the applied boundary controls are robust enough to keep the regulation error within tight bounds throughout the whole subdomain of the plant. Throughout the plant, the spatial standard deviation (std) is less than 0.3. [ABSTRACT FROM AUTHOR]

The autocorrelation method, proposed at first by [E. K. K. H. Salje, M. I. A. Carpenter, T. H. Malcherek, T. Boffa Ballaran, Eur. J. Min. 2000, 12, 503.] for the evaluation of FTIR data, is an efficient method the evaluation of data depending on external parameters like temperature, pressure, chemical composition etc. In this study a new single parameter value λ'(ω') is proposed which is computational more efficient with a higher reproducibility than the Δcorr parameter proposed earlier. The method is additionally transferred from Fourier transform infrared (FTIR) spectroscopy to X-ray diffraction data. It is shown that the autocorrelation method has some beneficial properties compared to the often used Pearson's r-value. [ABSTRACT FROM AUTHOR]

Populations can show temporal autocorrelation in the dynamics arising from different mechanisms, including fluctuations in the demographic structure. This autocorrelation is often treated as a complicating factor in the analyses of stochastic population growth and extinction risk. However, it also reflects important information about the demographic structure. Here, we consider how temporal autocorrelation is related to demographic stochasticity in structured populations. Demographic stochasticity arises from inherent randomness in the demographic processes of individuals, like survival and reproduction, and the resulting impact on population growth is measured by the demographic variance. Earlier studies have shown that population structure have positive or negative effects on the demographic variance compared to a model where the structure is ignored. Here, we derive a new expression for the demographic variance of a structured population, using the temporal autocorrelation function of the population growth rate. We show that the relative difference in demographic variance when the structure is included or ignored (the effect of structure on demographic variance) is approximately twice the sum of the autocorrelations. We demonstrate the result for a simple hypothetical example, as well as a set of empirical examples using age-structured models of 24 mammals from the demographic database COMADRE. In the empirical examples, the sum of the autocorrelation function was negative in all cases, indicating that age structure generally has a negative effect on the demographic variance (i.e. the demographic variance is lower compared to that of a model where the structure is ignored). Other kinds of structure, such as spatial heterogeneity affecting fecundity, can have positive effects on the demographic variance, and the sum of the autocorrelations will then be positive. These results yield new insights into the complex interplay between population structure, demographic variance, and temporal autocorrelation, that shapes the population dynamics and extinction risk of populations. [ABSTRACT FROM AUTHOR]

This study empirically investigates the states of Six Sigma from a stochastic point of view. By the means of an advanced survey, 97 respondents are asked to rate the effect of Six Sigma on different performance categories, the cost of implementing Six Sigma, the level of enthusiasm and expectations from Six Sigma over 20 years. The autocorrelation and cross-correlation functions of these processes are analyzed to investigate the stages of Six Sigma. Consequently, new concepts namelysteady state of Six SigmaandSix Sigma experience functionsare introduced which shed light on the life cycle of Six Sigma within the companies. [ABSTRACT FROM PUBLISHER]

Volatility is a key variable in the modeling of financial markets. The most striking feature of volatility is that it is a long-range correlated stochastic variable, i.e. its autocorrelation function decays like a power-law τ − β for large time lags. In the present work we investigate the determinants of such feature, starting from the empirical observation that the exponent β of a certain stock’s volatility is a linear function of the average correlation of such stock’s volatility with all other volatilities. We propose a simple approach consisting in diagonalizing the cross-correlation matrix of volatilities and investigating whether or not the diagonalized volatilities still keep some of the original volatility stylized facts. As a result, the diagonalized volatilities result to share with the original volatilities either the power-law decay of the probability density function and the power-law decay of the autocorrelation function. This would indicate that volatility clustering is already present in the diagonalized un-correlated volatilities. We therefore present a parsimonious univariate model based on a non-linear Langevin equation that well reproduces these two stylized facts of volatility. The model helps us in understanding that the main source of volatility clustering, once volatilities have been diagonalized, is that the economic forces driving volatility can be modeled in terms of a Smoluchowski potential with logarithmic tails. [ABSTRACT FROM AUTHOR]

Background Multiscale entropy (MSE) estimates the predictability of a signal over multiple temporal scales. It has been recently applied to study brain signal variability, notably during aging. The grounds of its application and interpretation remain unclear and subject to debate. Method We used both simulated and experimental data to provide an intuitive explanation of MSE and to explore how it relates to the frequency content of the signal, depending on the amount of (non)linearity and stochasticity in the underlying dynamics. Results The scaling and peak-structure of MSE curves relate to the scaling and peaks of the power spectrum in the presence of linear autocorrelations. MSE also captures nonlinear autocorrelations and their interactions with stochastic dynamical components. The previously reported crossing of young and old adults’ MSE curves for EEG data appears to be mainly due to linear stochastic processes, and relates to young adults’ EEG dynamics exhibiting a slower time constant. Comparison with existing methods We make the relationship between MSE curve and power spectrum as well as with a linear autocorrelation measure, namely multiscale root-mean-square-successive-difference, more explicit. MSE allows gaining insight into the time-structure of brain activity fluctuations. Its combined use with other metrics could prevent any misleading interpretations with regard to underlying stochastic processes. Conclusions Although not straightforward, when applied to brain signals, the features of MSE curves can be linked to their power content and provide information about both linear and nonlinear autocorrelations that are present therein. [ABSTRACT FROM AUTHOR]

In the recent years, there has been a growing interest in proposing covariance models for multivariate Gaussian random fields. Some of these covariance models are very flexible and can capture both the marginal and the cross-spatial dependence of the components of the associated multivariate Gaussian random field. However, effective estimation methods for these models are somehow unexplored. Maximum likelihood is certainly a useful tool, but it is impractical in all the circumstances where the number of observations is very large. In this work, we consider two possible approaches based on composite likelihood for multivariate covariance model estimation. We illustrate, through simulation experiments, that our methods offer a good balance between statistical efficiency and computational complexity. Asymptotic properties of the proposed estimators are assessed under increasing domain asymptotics. Finally, we apply the method for the analysis of a bivariate dataset on chlorophyll concentration and sea surface temperature in the Chilean coast. [ABSTRACT FROM AUTHOR]

We consider the isotropic XY quantum spin chain in a random external field in the z direction, with single site distributions given by i.i.d. random variables times the critical decaying envelope $$j^{-1/2}$$ . Our motivation is the study of many-body localization. We investigate transport properties in terms of polynomial Lieb-Robinson (PLR) bounds. We prove a zero-velocity PLR bound for large disorder strength $$\lambda $$ and for small $$\lambda $$ we show a partial converse, which suggests the existence of a transition to non-trivial transport in the model. [ABSTRACT FROM AUTHOR]

Statistical averaging theorems allow us to derive a set of equations for the averaged magnetization dynamics in the presence of colored (non-Markovian) noise. The non-Markovian character of the noise is described by a finite auto-correlation time, $\tau $ , that can be identified with the finite response time of the thermal bath to the system of interest. Hitherto, this model was only tested for the case of weakly correlated noise (when $\tau $ is equivalent or smaller than the integration timestep). In order to probe its validity for a broader range of auto-correlation times, a non-Markovian integration model, based on the stochastic Landau–Lifshitz–Gilbert equation is presented. Comparisons between the two models are discussed, and these provide evidence that both formalisms remain equivalent, even for strongly correlated noise (i.e., $\tau $ much larger than the integration timestep). [ABSTRACT FROM PUBLISHER]