General Moment Research Articles

Multivariate moment closure techniques for stochastic kinetic models

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.

Effects of wind shear on wind turbine rotor loads and planetary bearing reliability

AbstractRecent studies suggest that wind shear and the resulting pitch moments increase bearing loads and thereby contribute to premature wind turbine gearbox failure. In this paper, we use momentum‐based modeling approaches to predict the pitch moments from wind shear. The non‐dimensionalized results, which have been validated against accepted aeroelastic results, can be used to determine thrust force, pitch moment and power of a general rotor as a function of the wind shear exponent. Even in extreme wind shear (m = 1), the actual thrust force and power for a typical turbine (R* < 0.5) were within 8% and 20% of the nominal values (those without wind shear), respectively. The mean pitch moment increased monotonically with turbine thrust, rotor radius and wind shear exponent. For extreme wind shear (m = 1) on a typical turbine (R* = 0.5), the mean pitch moment is ~25% the product of thrust force and rotor radius. Analysis of wind shear for a typical 750 kW turbine revealed that wind shear does not significantly affect bearing loads because it counteracts the effects of rotor weight. Furthermore, even though general pitch moments did significantly increase bearing loads, they were found to be unlikely to cause bearing fatigue. Analyses of more common low wind‐speed cases suggest that bearing under‐loading and wear are more likely to contribute to premature bearing failure than overloading and classical surface contact fatigue. Copyright © 2015 John Wiley & Sons, Ltd.

Asymptotic Mutual Information Statistics of MIMO Channels and CLT of Sample Covariance Matrices

In this paper, we consider the fluctuation of mutual information statistics of a multiple input multiple output channel communication systems without assuming that the entries of the channel matrix have zero pseudovariance. To this end, we also establish a central limit theorem of the linear spectral statistics for sample covariance matrices under general moment conditions by removing the restrictions imposed on the second moment and fourth moment on the matrix entries in Bai and Silverstein (2004).

Load Height and Moment Factors for Doubly Symmetric Wide Flange Beams

AbstractAn analytical procedure is used to study the effects of moment gradient and load height on the elastic stability of wide flange steel beams. Lateral torsional buckling is the limit state considered. Solutions are developed for a series of general moment functions which are produced by continuous load types with possible end moments. For each load type, an equivalent uniform moment factor is developed. Additionally, a load height factor is developed to modify the equivalent uniform moment factor for these load types where loading is applied above the shear center. Solutions are processed numerically using a Taylor series polynomial approximation. Results are presented in terms of an equivalent uniform moment factor and a load height factor. Comparison with national code procedures for moment factor show discrepancies that are conservative in some circumstances by up to 51% and unconservative in others by up to 8%. The largest discrepancies occur under the effect of reverse curvature bending and loa...

Formula omitted]- and [formula omitted]-violating Lagrangians in chiral effective field theory and nuclear electric dipole moments

A scheme to derive hadronic interactions induced by effective multi-quark terms is presented within the framework of chiral effective field theory. It is employed to work out the list of parity- and time-reversal-symmetry-violating hadronic interactions that are relevant for the computation of nuclear contributions to the electric dipole moments of the hydrogen-2, helium-3 and hydrogen-3 nuclei. We also derive the scattering and Faddeev equations required to compute electromagnetic form factors in general and electric dipole moments in particular.

Viscosity cross sections for the heavy noble gases

We have calculated viscosity cross sections for argon, krypton and xenon from zero to 1 keV using the phase shifts from our previous publication [R.P. McEachran, A.D. Stauffer, Eur. Phys. J. D 68, 153 (2014)] which presented total elastic and momentum transfer cross sections for these gases. As previously, we present simple analytic fits to our results to aid in modelling plasmas containing these atoms. By using the current results and those in reference [R.P. McEachran, A.D. Stauffer, Eur. Phys. J. D 68, 153 (2014)] the first two ‘partial cross sections’ used in the general moment method of solving the Boltzmann equation can be obtained. The agreement of our viscosity cross sections with experimentally derived results indicates the overall reliability of our calculations.

Score function of distribution and revival of the moment method

The article deals with the scalar-valued score function SF defined for a regular unimodal and continuous probability distribution F with arbitrary interval support , recently introduced by the author. The concept of the central characteristic that describes a relative influence of is described in a much more general way in order to improve its usefulness in parametric estimation by means of the general moment method. In particular, the whole approach is elucidated by describing it in a more suitable framework than before. Further, we show that the inference function to be used in the moment estimating equations is either the score function of distribution (bounded for heavy-tailed parametric distribution models) or its modification based on the Huber’s approach.

Linear spin wave theory for single-Q incommensurate magnetic structures

Linear spin wave theory provides the leading term in the calculation of the excitation spectra of long-range ordered magnetic systems as a function of . This term is acquired using the Holstein–Primakoff approximation of the spin operator and valid for small δS fluctuations of the ordered moment. We propose an algorithm that allows magnetic ground states with general moment directions and single-Q incommensurate ordering wave vector using a local coordinate transformation for every spin and a rotating coordinate transformation for the incommensurability. Finally we show, how our model can determine the spin wave spectrum of the magnetic C-site langasites with incommensurate order.

On the determinacy problem for measures

We study the general moment problem for measures on the real line, with polynomials replaced by more general spaces of entire functions. As a particular case, we describe measures that are uniquely determined by a restriction of their Fourier transform to a finite interval. We apply our results to prove an extension of a theorem by Eremenko and Novikov on the frequency of oscillations of measures with a spectral gap (high-pass signals) near infinity.

The Spatial Chemical Langevin Equation and Reaction Diffusion Master Equations: moments and qualitative solutions.

BackgroundIt has been established that stochastic effects play an important role in spatio-temporal biochemical networks. A popular method of representing such stochastic systems is the Reaction Diffusion Master Equation (RDME). However, simulating sample paths from the RDME can be computationally expensive, particularly at large populations. Here we investigate an uncommon, but much faster alternative: the Spatial Chemical Langevin Equation (SCLE).MethodsWe investigate moment equations and correlation functions analytically, then we compare sample paths and moments of the SCLE to the RDME and associated deterministic solutions. Sample paths are generated computationally by the Next Subvolume method (RDME) and the Euler-Maruyama method (SCLE), while a deterministic solution is obtained with an Euler method. We consider the Gray-Scott model, a well-known pattern generating system, and a predator–prey system with spatially inhomogeneous parameters as sample applications.ResultsFor linear reaction networks, it is well known that the first order moments of all three approaches match, that the RDME and SCLE match to the second moment, and that all approaches diverge at third order moments. For non-linear reaction networks, differential equations governing moments do not form a closed system, but a general moment equation can be compared term wise. All approaches match at the leading order, and the RDME and SCLE match at the second leading order. As expected, the SCLE captures many dynamics of the RDME where deterministic methods fail to represent them. However, areas of the parameter space in the Gray-Scott model exist where either the SCLE and RDME give qualitatively different predictions, or the RDME predicts patterns, while the SCLE does not.ConclusionsThe SCLE provides a fast alternative to existing methods for simulation of spatial stochastic biochemical networks, capturing many aspects of dynamics represented by the RDME. This becomes very useful in search of quantitative parameters yielding desired qualitative solutions. However, there exist parameter sets where both the qualitative and quantitative behaviour of the SCLE can differ when compared to the RDME, so care should be taken in its use for applications demanding greater accuracy.Electronic supplementary materialThe online version of this article (doi:10.1186/s12976-015-0001-6) contains supplementary material, which is available to authorized users.

Loop equation analysis of the circular β ensembles

We construct a hierarchy of loop equations for invariant circular ensembles. These are valid for general classes of potentials and for arbitrary inverse temperatures $ {\rm Re}\,\beta>0 $ and number of eigenvalues $ N $. Using matching arguments for the resolvent functions of linear statistics $ f(\zeta)=(\zeta+z)/(\zeta-z) $ in a particular asymptotic regime, the global regime, we systematically develop the corresponding large $ N $ expansion and apply this solution scheme to the Dyson circular ensemble. Currently we can compute the second resolvent function to ten orders in this expansion and also its general Fourier coefficient or moment $ m_{k} $ to an equivalent length. The leading large $ N $, large $ k $, $ k/N $ fixed form of the moments can be related to the small wave-number expansion of the structure function in the bulk, scaled Dyson circular ensemble, known from earlier work. From the moment expansion we conjecture some exact partial fraction forms for the low $ k $ moments. For all of the forgoing results we have made a comparison with the exactly soluble cases of $ \beta = 1,2,4 $, general $ N $ and even, positive $ \beta $, $ N=2,3 $.

General Magnetic Transition Dipole Moments for Electron Paramagnetic Resonance

We present general expressions for the magnetic transition rates in electron paramagnetic resonance (EPR) experiments of anisotropic spin systems in the solid state. The expressions apply to general spin centers and arbitrary excitation geometry (Voigt, Faraday, and intermediate). They work for linear and circular polarized as well as unpolarized excitation, and for crystals and powders. The expressions are based on the concept of the (complex) magnetic transition dipole moment vector. Using the new theory, we determine the parities of ground and excited spin states of high-spin (S=5/2) Fe(III) in hemin from the polarization dependence of experimental EPR line intensities.

El impacto emocional del incivismo laboral y el abuso verbal en el trabajo: influencia de la recuperación diaria

The aim was to study daily fluctuations from workplace incivility and verbal abuse in the emotional well-being of employees and examine the daily role of recovery. It was recruited 1575 evaluations in a sample of 105 workers of service sector. It is a multilevel study with a diary design and two levels: level 1 (i), day-level; and level 2 (j), person-level. It was evaluated on two different times, general and diary moments. Diary measure was completed in a work week, three times per day. Data were analyzed with MLwiN software. The multilevel analysis showed significant results for workplace incivility and verbal abuse as predictors of emotional exhaustion, as well as an impact of all these variables on negative affect at night. However, non-significant relationships were found for positive affect at night. Recovery from daily work was a key factor predicting affect at night. Relaxation showed main effects on negative affect at night and mastery on positive affect at night. Both psychological detachment and relaxation showed a moderating role. The present diary study of occupational health psychology helps us achieve greater knowledge in this area and contribute on the prevention of aggression in the organizational context.

El impacto emocional del incivismo laboral y el abuso verbal en el trabajo: El papel protector de la recuperación diaria

Title: Emotional impact of workplace incivility and verbal abuse at work: Daily recovery protective role. Abstract: The aim was to study daily fluctuations from workplace incivility and verbal abuse in the emotional well-being of employees and examine the daily role of recovery. It was conducted a diary study over five consecu- tive working days (total of 525 days) with 105 employees. It was evaluated on two different times, general and diary moments. Diary measure was completed in a work week, three times per day, morning, afternoon and night. Multilevel modeling showed significant results for workplace incivili- ty and verbal abuse as predictors of emotional exhaustion, as well as an im- pact of all these variables on negative affect at night. However, non- significant relationships were found for positive affect at night. Recovery from daily work was a key factor predicting affect at night. Relaxation showed main effects on negative affect at night and mastery on positive af- fect at night. Both psychological detachment and relaxation showed a moderating role. The present diary study of occupational health psychology helps us achieve greater knowledge in this area and contribute on the pre- vention of aggression in the organizational context.

CLT for linear spectral statistics of Hermitian Wigner matrices with general moment conditions

Изучается эрмитова матрица Вигнера $W_n=(x_{ij})_{1\leq i,j\leq n}$ с независимыми (с точностью до симметрии) внедиагональными элементами, имеющими нулевое среднее и единичную дисперсию. При некотором условии типа Линдеберга на четвертые моменты элементов матрицы доказана центральная предельная теорема для линейных статистик собственных значений матрицы $W_n$. Наш результат распространяет предыдущие результаты подобного рода на более общий случай, когда отсутствует ограничение $\bf E x^2_{ij}=0$ для $1\leq i < j \leq n$. Вместо этого мы предполагаем только, что вещественная и мнимая части наддиагональных элементов некоррелированы. Более точно, мы требуем, чтобы математические ожидания $\bf E x^2_{ij}$ были вещественными и однородными для всех $1\leq i < j \leq n$. Показано, что предельное нормальное распределение в центральной предельной теореме зависит от параметра $\bf E x^2_{ij}\in [-1,1]$.

General moment system for plasma physics based on minimum entropy principle

In plasma physics domain, the electrons transport can be described from kinetic and hydrodynamical models. Both methods present disadvantages and thus cannot be considered in practical computations for Inertial Confinement Fusion (ICF). That is why we propose in this paper a new model which is intermediate between these two descriptions. More precisely, the derivation of such models is based on an angular closure in the phase space and retains only the energy of particles as a kinetic variable. The closure of the moment system is obtained from a minimum entropy principle. The resulting continuous model is proved to satisfy fundamental properties. Moreover the model is discretized w.r.t the energy variable and the semi-discretized scheme is shown to satisfy conservation properties and entropy decay.

Characterization of the Skew-Normal Distribution Via Order Statistics and Record Values

Characterization of a probability distribution is the investigation of those unique properties enjoyed by that distribution. In this article the general condition moments technique is used to obtain some new characterization results for the skew-normal distribution based on the order statistics as well as the record values of a random sample drawn from this distribution. The achieved results can be used to improve fitting and modeling skew data using the skew-normal distribution. Further, the new results are specialized to the standard normal distribution.

Covariance matrices associated to general moments of a random vector

It turns out that there exist general covariance matrices associated not only to a random vector itself but also to its general moments. In this paper we introduce and characterize general covariance matrices of a random vector that are associated to some important general moments, which are determined by a specific class of convex functions. As special cases, the original covariance matrices of a random vector, as well as the p th covariance matrices characterized recently, are included. The covariance matrices associated to the p -power function distribution and the logistic distribution are characterized as by-products.

First time to exit of a continuous Itô process: General moment estimates and ${\mathrm{L}}_{1}$-convergence rate for discrete time approximations

We establish general moment estimates for the discrete and continuous exit times of a general It\^{o} process in terms of the distance to the boundary. These estimates serve as intermediate steps to obtain strong convergence results for the approximation of a continuous exit time by a discrete counterpart, computed on a grid. In particular, we prove that the discrete exit time of the Euler scheme of a diffusion converges in the $L_1$ norm with an order $1/2$ with respect to the mesh size.

A generalised failure envelope for undrained capacity of circular shallow foundations under general loading

This paper presents a generalised failure envelope for the prediction of the undrained capacity of circular shallow foundations under general vertical, horizontal and moment (VHM) loading. Uniaxial capacities and failure envelopes under combined loading are presented for shallow circular foundations over a practical range of embedment ratio and soil strength heterogeneity. An approximating expression is proposed to describe the shape of the normalised VHM failure envelope as a function of foundation embedment ratio, normalised soil strength heterogeneity index and vertical load mobilisation.