A generator of high-order embedded P-stable methods for the numerical solution of the Schrödinger equation

AbstractA generator of new embedded P-stable methods of order 2n+2, where n is the number of layers used by the embedded methods, for the approximate numerical integration of the one-dimensional Schrödinger equation is developed in this paper. These new methods are called embedded methods because of a simple natural error control mechanism. Numerical results obtained for one-dimensional differential equations of the Schrödinger type show the validity of the developed theory

The time evaluation of resistance probability of a closed community against to occupation in a Sznajd like model with synchronous updating: A numerical study

In the present paper, we have briefly reviewed Sznajd's sociophysics model and its variants, and also we have proposed a simple Sznajd like sociophysics model based on Ising spin system in order to explain the time evaluation of resistance probability of a closed community against to occupation. Using a numerical method, we have shown that time evaluation of resistance probability of community has a non-exponential character which decays as stretched exponential independent the number of soldiers in one dimensional model. Furthermore, it has been astonishingly found that our simple sociophysics model is belong to the same universality class with random walk process on the trapping space.Comment: 12 pages, 5 figures. Added a paragraph and 1 figure. To be published in International Journal of Modern Physics

Robust estimators of ar-models : a comparison

Many regression-estimation techniques have been extended to cover the case of dependent observations. The majority of such techniques are developed from the classical least squares, M and GM approaches and their properties have been investigated both on theoretical and empirical grounds. However, the behavior of some alternative methods- with satisfactory performance in the regression case- has not received equal attention in the context of time series. A simulation study of four robust estimators for autoregressive models containing innovation or additive outliers is presented. The robustness and efficiency properties of the methods are exhibited, some finite-sample results are discussed in combination with theoretical properties and the relative merits of the estimators are viewed in connection with the outlier-generating scheme.peer-reviewe

Quantitative identification of functional connectivity disturbances in neuropsychiatric lupus based on resting-state fMRI: a robust machine learning approach

Neuropsychiatric systemic lupus erythematosus (NPSLE) is an autoimmune entity comprised of heterogenous syndromes affecting both the peripheral and central nervous system. Research on the pathophysiological substrate of NPSLE manifestations, including functional neuroimaging studies, is extremely limited. The present study examined person-specific patterns of whole-brain functional connectivity in NPSLE patients (n = 44) and age-matched healthy control participants (n = 39). Static functional connectivity graphs were calculated comprised of connection strengths between 90 brain regions. These connections were subsequently filtered through rigorous surrogate analysis, a technique borrowed from physics, novel to neuroimaging. Next, global as well as nodal network metrics were estimated for each individual functional brain network and were input to a robust machine learning algorithm consisting of a random forest feature selection and nested cross-validation strategy. The proposed pipeline is data-driven in its entirety, and several tests were performed in order to ensure model robustness. The best-fitting model utilizing nodal graph metrics for 11 brain regions was associated with 73.5% accuracy (74.5% sensitivity and 73% specificity) in discriminating NPSLE from healthy individuals with adequate statistical power. Closer inspection of graph metric values suggested an increased role within the functional brain network in NSPLE (indicated by higher nodal degree, local efficiency, betweenness centrality, or eigenvalue efficiency) as compared to healthy controls for seven brain regions and a reduced role for four areas. These findings corroborate earlier work regarding hemodynamic disturbances in these brain regions in NPSLE. The validity of the results is further supported by significant associations of certain selected graph metrics with accumulated organ damage incurred by lupus, with visuomotor performance and mental flexibility scores obtained independently from NPSLE patients. View Full-Text Keywords: neuropsychiatric systemic lupus erythematosus; rs-fMRI; graph theory; functional connectivity; surrogate data; machine learning; visuomotor ability; mental flexibilit

Fourier-type monitoring procedures for strict stationarity

We consider model-free monitoring procedures for strict stationarity of a given time series. The new criteria are formulated as L2-type statistics incorporating the empirical characteristic function. Asymptotic as well as Monte Carlo results are presented. The new methods are also employed in order to test for possible stationarity breaks in time-series data from the financial sector

Characterizations of multinormality and corresponding tests of fit, including for Garch models

We provide novel characterizations of multivariate normality that incorporate both the characteristic function and the moment generating function, and we employ these results to construct a class of affine invariant, consistent and easy-to-use goodness-of-fit tests for normality. The test statistics are suitably weighted L2-statistics, and we provide their asymptotic behavior both for i.i.d. observations as well as in the context of testing that the innovation distribution of a multivariate GARCH model is Gaussian. We also study the finite-sample behavior of the new tests and compare the new criteria with alternative existing tests

Fourier methods for analysing piecewise constant volatilities

We develop procedures for testing the hypothesis that a parameter of a distribution is constant throughout a sequence of independent random variables. Our proposals are illustrated considering the variance and the kurtosis. Under the null hypothesis of constant variance, the modulus of a Fourier type transformation of the volatility process is identically equal to one. The approach proposed utilizes this property considering a canonical estimator for this modulus under the assumption of indepen- dent and piecewise identically distributed observations with zero mean. Using blockwise estimators we introduce several test statistics resulting from different weight functions which are all given by simple explicit for- mulae. The methods are compared to other tests for constant volatility in extensive Monte Carlo experiments. Our proposals offer comparatively good power particularly in the case of multiple structural breaks and allow adequate estimation of the positions of the structural breaks. An appli- cation to process control data is given, and it is shown how the methods can be adapted to test for constancy of other quantities like the kurtosis