some omnibus exponentially weighted moving average statistical process monitoring schemes exponentially weighted moving average ewma quality monitoring schemes capahlc of detecting changes in both location and spread referred to as omnibus ewma s are proposed omnibus ewma s are based on the exponentiation of the absolute value of the standardized sample mean of the observations the process target mean and standard deviation are used for standardizing design procedures and considerations including a fast initial response feature are discussed average run lengths for exponents of 5 and 2 and various values of the weighting constant are presented the proposed schemes are compared with each other and with a number of selected well known omnibus schemes and a proposed omnibus cumulative sum scheme schemes with different sample sizes are used and off target models include both static and dynamic alternatives comparisons are based on average number of observations to detection and expected loss due to poor quality one of the omnibus ewma schemes is shown to be best with regard to exp

a computational dna solution approach for the quadratic diophantine equation abstract we present a fast parallel algorithm based on stickers for the dna computing model to solve the classical mathematical quadratic diophantine equation ax 2 by c with a b c x y z this problem also in a decision form is np complete and has no known polynomial time solving within the deterministic turing machine model

a dna based solution to the graph isomorphism problem using adleman lipton model with stickers since the experimental demonstration of its feasibility dna based computing has been applied to a number of decision or combinatorial optimization problems the graph isomorphism problem belongs to the class of np problems and has been conjectured intractable although probably not np complete in this paper we demonstrate the power of dna based computing by showing the graph isomorphism problem can be efficiently solved under this computation model by generating the solution space using stickers we present dna based algorithms to solve the problem using polynomial number of basic biological operations

multivariate quality control based on regression adjusted variables when performing quality control in a situation in which measures are made of several possibly related variables it is desirable to use methods that capitalize on the relationship between the variables to provide controls more sensitive than those that may be made on the variables individually the most common methods of multivariate quality control that assess the vector of variables as a whole are those based on the hotelling t 2 between the variables and the specification vector although t 2 is the optimal single test statistic for a general multivariate shift in the mean vector it is not optimal for more structured mean shifts for example shifts in only some of the variables measures based on quadratic forms like t 2 also confound mean shifts with variance shifts and require quite extensive analysis following a signal to determine the nature of the shift this article proposes shewhart and cumulative sum cusum controls based on the vector z of scaled residuals from the regression of each varia

a note on multivariate cusum procedures cumulative sum cusum procedures are among the most powerful tools for detecting a shift from a good quality distribution to a bad quality distribution this article discusses the natural application of cusum procedures to the multivariate normal distribution it discusses two cases detecting a shift in the mean vector and detecting a shift in the covariance matrix as an example the procedure is applied to measurements taken on optical fibers

high order hamiltonian splitting for the vlasov poisson equations we consider the vlasov poisson equation in a hamiltonian framework and derive new time splitting methods based on the decomposition of the hamiltonian functional between the kinetic and electric energy assuming smoothness of the solutions we study the order conditions of such methods it appears that these conditions are of runge kutta nystrom type in the one dimensional case the order conditions can be further simplified and efficient methods of order 6 with a reduced number of stages can be constructed in the general case high order methods can also be constructed using explicit computations of commutators numerical results are performed and show the benefit of using high order splitting schemes in that context complete and self contained proofs of convergence results and rigorous error estimates are also given

multivariate cusum quality control procedures it is a common practice to use simultaneously several one sided or two sided cusum procedures of the type proposed by page 1954 in this article this method of control is considered to be a single multivariate cusum mcusum procedure methods are given for approximating parameters of the distribution of the minimum of the run lengths of the univariate cusum charts using a new method of comparing multivariate control charts it is shown that an mcusum procedure is often preferable to hotelling s tz procedure for the case in which the quality characteristics are bivariate normal random variables

partitioned runge kutta methods for separable hamiltonian problems separable hamiltonian systems of differential equations have the form dp dt dh dq dq dt dh dp with a hamiltonian function h that satisfies h t p k q t and v are respectively the kinetic and potential energies we study the integration of these systems by means of partitioned runge kutta methods i e by means of methods where different runge kutta tableaux are used for the p and q equations we derive a suffi cient and almost necessary condition for a partitioned runge kutta method to be canonical i e to conserve the symplectic structure of phase space thereby reproducing the qualitative properties of the hamiltonian dynamics we show that the requirement of canonicity operates as a simplifying assumption for the study of the order conditions of the method

semi lagrangian schemes for the vlasov equation on an unstructured mesh of phase space a new scheme for solving the vlasov equation using an unstructured mesh for the phase space is proposed the algorithm is based on the semi lagrangian method which exploits the fact that the distribution function is constant along the characteristic curves we use different local interpolation operators to reconstruct the distribution function f some of which need the knowledge of the gradient of f we can use limiter coefficients to maintain the positivity and the l bound of f and optimize these coefficients to ensure the conservation of the l1 norm that is to say the mass by solving a linear programming problem several numerical results are presented in two and three axisymmetric case dimensional phase space the local interpolation technique is well suited for parallel computation

a simple method for studying run length distribution of exponentially weighted moving average charts a numerical procedure using integral equations is presented for the tabulation of moments of run lengths of exponentially weighted moving average ewma charts both average run lengths arl s and standard deviations of run lengths sdrl s are presented for the twosided ewma chart assuming normal observations along with an example illustrating how to design such a chart the procedure given extends easily to many nonnormal cases and to one sided versions of the ewma chart

hierarchical poisson regression modeling abstract the poisson model and analyses here feature nonexchangeable gamma distributions although exchangeable following a scale transformation for individual parameters with standard deviations proportional to means a relatively uninformative prior distribution for the shrinkage values eliminates the ill behavior of maximum likelihood estimators of the variance components when tested in simulation studies the resulting procedure provides better coverage probabilities and smaller risk than several other published rules and thus works well from bayesian and frequentist perspectives alike the computations provide fast accurate density approximations to individual parameters and to structural regression coefficients the computer program is publicly available through statlib

a symplectic integration algorithm for separable hamiltonian functions abstract we derive an algorithm to numerically integrate differential equations derivable from a separable hamiltonian function this symplectic algorithm is accurate to fourth order in the time step and preserves exactly the poincare cartan integral invariants associated with the topology of the phase flow we compare the efficiency and accuracy of this method to that of existing integrators both symplectic and non symplectic by integrating the equations of motion corresponding to a nonlinear pendulum a particle in the field of a standing wave and a harmonic oscillator perturbed by a plane wave

conservative numerical schemes for the vlasov equation abstract a new scheme for solving the vlasov equation using a phase space grid is proposed the algorithm is based on the conservation of the flux of particles and the distribution function is reconstructed using various techniques that allow control of spurious oscillations or preservation of the positivity several numerical results are presented in two and four dimensional phase space and the scheme is compared with the semilagrangian method this method is almost as accurate as the semilagrangian one and the local reconstruction technique is well suited for parallel computation

coldice a parallel vlasov poisson solver using moving adaptive simplicial tessellation abstract resolving numerically vlasov poisson equations for initially cold systems can be reduced to following the evolution of a three dimensional sheet evolving in six dimensional phase space we describe a public parallel numerical algorithm consisting in representing the phase space sheet with a conforming self adaptive simplicial tessellation of which the vertices follow the lagrangian equations of motion the algorithm is implemented both in six and four dimensional phase space refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase space sheet at second order relying on additional tracers created when needed at runtime in order to preserve in the best way the hamiltonian nature of the system refinement is anisotropic and constrained by measurements of local poincare invariants resolution of poisson equation is performed using the fast fourier method on a regular rectangular grid similarly to particle in cells codes to compute the density projected onto this grid the intersection of the tessellation and the grid is calculated using the method of franklin and kankanhalli 65 66 67 generalised to linear order as preliminary tests of the code we study in four dimensional phase space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves we also perform a warm dark matter simulation in six dimensional phase space that we use to check the parallel scaling of the code

hotelling s t2 charts with variable sample size and control limit abstract the ideas of variable sampling interval vsi variable sample size vss variable sample size and sampling interval vssi and variable parameters vp in the univariate case have been successfully applied to the multivariate case to improve the efficiency of hotelling s t 2 chart with fixed sampling rate fsr in detecting small process shifts however the main disadvantage in using most of these control schemes is an increasing in the complexity due to the adaptive changes in sampling intervals in this paper retaining the lengths of sampling intervals constant a variable sample size and control limit vssc t 2 chart is proposed and described the statistical efficiency of the vssc t 2 chart in terms of the average time to signal a shift in process mean vector is compared with that of the vp vssi vss vsi and fsr t 2 charts from the results of comparison it shows that the vssc t 2 chart for a very small shift in the process mean vector gives a better performance than the vssi vss vsi and fsr t 2 charts meanwhile it presents a similar performance to the vp t 2 chart furthermore from the viewpoint of practicability it is more convenient for administrating the control chart than the vsi vssi and vp t 2 chart thus it may provide a good option for quick response to small shifts in a multivariate process

block structured adaptive mesh refinement algorithms for vlasov simulation direct discretization of continuum kinetic equations like the vlasov equation are under utilized because the distribution function generally exists in a high dimensional 3d space and computational cost increases geometrically with dimension we propose to use high order finite volume techniques with block structured adaptive mesh refinement amr to reduce the computational cost the primary complication comes from a solution state comprised of variables of different dimensions we develop the algorithms required to extend standard single dimension block structured amr to the multi dimension case specifically algorithms for reduction and injection operations that transfer data between mesh hierarchies of different dimensions are explained in detail in addition modifications to the basic amr algorithm that enable the use of high order spatial and temporal discretizations are discussed preliminary results for a standard 1d 1v vlasov poisson test problem are presented results indicate that there is potential for significant savings for some classes of vlasov problems

multivariate bayesian process control for a finite production run abstract most industrial products and processes are characterized by several typically correlated measurable variables which jointly describe the product or process quality various control charts such as hotelling s t2 ewma and cusum charts have been developed for multivariate quality control where the values of the chart parameters namely the sample size sampling interval and the control limits are determined to satisfy given economic and or statistical requirements it is well known that this traditional non bayesian approach to a control chart design is not optimal but very few results regarding the form of the optimal bayesian control policy have appeared in the literature all limited to a univariate chart design in this paper we consider a multivariate bayesian process mean control problem for a finite production run under the assumption that the observations are values of independent normally distributed vectors of random variables the problem is formulated in the pomdp partially observable markov decision process framework and the objective is to determine a control policy minimizing the total expected cost it is proved that under standard operating and cost assumptions the control limit policy is optimal cost comparisons with the benchmark chi squared chart and the mewma chart show that the bayesian chart is highly cost effective the savings are larger for smaller values of the critical mahalanobis distance between the in control and out of control process mean

monitoring processes that wander using integrated moving average models often the least appropriate assumption in traditional control charting technology is that process data constitute a random sample in reality most process data are correlated either temporally spatially or due to nested sources of variation one approach to monitoring temporally correlated data uses a control chart on the forecast errors from a time series model of the process with possibly a transfer function term to model compensatory adjustments if the time series term is an integrated moving average then a sudden level shift in the process results in a patterned shift in the mean of forecast errors initially the mean shifts by the same amount as the process level but then it decays geometrically back to 0 corresponding to the ability of the forecast to recover from the upset we study four monitoring schemes umulative sums cusum s exponentially weighted moving averages shewhart individuals charts and a likelihood ratio scheme comparisons of signaling probabilities and average run lengt

design and performance analysis of the exponentially weighted moving average mean estimate for processes subject to random step changes the exponentially weighted moving average ewma is a well known and popular statistic used for smoothing and forecasting time series and as a process mean estimator due to its simplicity and ability to capture nonstationarity the ewma statistic has been shown to be an optimal mean estimator for a certain disturbance process and an effective estimator for various other processes in this article we focus on a practical disturbance process relatively small random step changes that are difficult to distinguish from white noise and usually overlooked by practitioners we propose an optimal ewma parameter for step change disturbance processes as well as methodologies to identify and estimate the process models the ewma estimator s performance is then evaluated analytically we demonstrate that a well designed ewma control scheme can effectively reduce the process variation even for processes subject to infrequent small step changes a semiconductor process example illustrates the design and analysis

multivariate generalizations of cumulative sum quality control schemes this article presents the design procedures and average run lengths for two mulativariater cumulative sum cusum quality control procedures the first cusum procedure reduces each multivariate observation to a scalar and then forms a cusum of the scalars the second cusum procedure forms a cusum vector directly from the observations these two procedures are compared with each other and with the multivariate shewhart chart other multivariate quality control procedures are mentioned robustness the fast initial response feature for cusum schemes and combined shewhart cusum schemes are discussed

convergence analysis for a class of high order semi lagrangian advection schemes the convergence properties of a class of high order semi lagrangian schemes for pure advection equations are studied here in the framework of the theory of viscosity solutions we review the general convergence results for discrete time approximation schemes belonging to that class and we prove some a priori estimates in l infty and l2 for the rate of convergence of fully discrete schemes we prove then that a careful coupling of time and space discretizations can allow large time steps in the numerical integration still preserving the accuracy of the solutions several examples of schemes and numerical tests are presented

arbitrarily high order convected scheme solution of the vlasov poisson system abstract the convected scheme cs is a forward trajectory semi lagrangian method for solution of transport equations which has been most often applied to the kinetic description of plasmas and rarefied neutral gases in its simplest form the cs propagates the solution forward in time by advecting the so called moving cells along their characteristic trajectories and by remapping them on the mesh at the end of the time step the cs is conservative positivity preserving simple to implement and it is not subject to time step restriction to maintain stability recently guclu and hitchon 2012 1 a new methodology was introduced for reducing numerical diffusion based on a modified equation analysis the remapping error was compensated by applying small corrections to the final position of the moving cells prior to remapping while the spatial accuracy was increased from 2nd to 4th order the new scheme retained the important properties of the original method and was shown to be extremely simple and efficient for constant advection problems here the cs is applied to the solution of the vlasov poisson system which describes the evolution of the velocity distribution function of a collection of charged particles subject to reciprocal coulomb interactions the vlasov equation is split into two constant advection equations one in configuration space and one in velocity space and high order time accuracy is achieved by proper composition of the operators the splitting procedure enables us to use the constant advection solver which we extend to arbitrarily high order of accuracy in time and space a new improved procedure is given which makes the calculation of the corrections straightforward focusing on periodic domains we describe a spectrally accurate scheme based on the fast fourier transform the proposed implementation is strictly conservative and positivity preserving the ability to correctly reproduce the system dynamics as well as resolving small scale features in the solution is shown in classical 1d 1v test cases both in the linear and the non linear regimes

analysis of a new class of forward semi lagrangian schemes for the 1d vlasov poisson equations the vlasov equation is a kinetic model describing the evolution of a plasma which is a globally neutral gas of charged particles it is self consistently coupled with poisson s equation which rules the evolution of the electric field in this paper we introduce a new class of forward semi lagrangian schemes for the vlasov poisson system based on a cauchy kovalevsky ck procedure for the numerical solution of the characteristic curves exact conservation properties of the first moments of the distribution function for the schemes are derived and a convergence study is performed that applies as well for the ck scheme as for a more classical verlet scheme a l 1 convergence of the schemes will be proved error estimates in o left delta t 2 h 2 frac h 2 delta t right for verlet are obtained where t and h max x v are the discretization parameters

multivariate statistical process control using lasso this article develops a new multivariate statistical process control spc methodology based on adapting the lasso variable selection method to the spc problem the lasso method has the sparsity property of being able to select exactly the set of nonzero regression coefficients in multivariate regression modeling which is especially useful in cases where the number of nonzero coefficients is small in multivariate spc applications process mean vectors often shift in a small number of components our primary goals are to detect such a shift as soon as it occurs and to identify the shifted mean components using this connection between the two problems we propose a lasso based multivariate test statistic and then integrate this statistic into the multivariate ewma charting scheme for phase ii multivariate process monitoring we show that this approach balances protection against various shift levels and shift directions and thus provides an effective tool for multivariate spc applications this article

on the markov chain approach to the two sided cusum procedure a markov chain representation is given for the two sided possibly asymmetric cumulative sum cusum procedure of ewan and kemp 1960 for integer valued random variables the approach taken by brook and evans 1972 for the one sided cusum procedure to determine exact and approximate expressions for the run length distribution its moments and its percentage points is extended to the two sided cusum procedure the number of states included in the markov chain is minimized in order to make the methods as efftcient as possible

monitoring profiles based on nonparametric regression methods the use statistical process control spc in monitoring and diagnosis of process and product quality profiles remains an important problem in various manufacturing industries the spc problem with a nonlinear profile is particularly challenging this article proposes a novel scheme to monitor changes in both the regression relationship and the variation of the profile online it integrates the multivariate exponentially weighted moving average procedure with the generalized likelihood ratio test based on nonparametric regression the proposed scheme not only provides an effective spc solution to handle nonlinear profiles which are common in industrial practice but it also resolves the latent problem in popular parametric monitoring methods of being unable to detect certain types of changes due to a misspecified out of control model our simulation results demonstrate the effectiveness and efficiency of the proposed monitoring scheme in addition a systematic diagnostic approach is provided to locate t

the inertial properties of quality control charts many types of control charts have an ability to detect process changes that can weaken over time depending on the past data observed this is often referred to as the inertia problem we propose a new measure of inertia the signal resistance to be the largest standardized deviation from target not leading to an immediate out of control signal we calculate the signal resistance values for several types of univariate and multivariate charts our conclusions support the recommendation that shewhart limits should be used with exponentially weighted moving average charts especially when the smoothing parameter is small

higher order time splitting for the linear vlasov equation many semi lagrangian schemes for solving the vlasov equation use a second order time splitting method proposed by cheng and knorr in this paper a fourth order time splitting method is proposed this is combined with cubic spline interpolation in x and v and a rigorous ell 2 error bound is obtained for the linear vlasov equation in arbitrary space dimension also this method and that of cheng and knorr are implemented and compared for a test case in one space dimension

practical symplectic partitioned runge kutta and runge kutta nystrom methods we present new symmetric fourth and sixth order symplectic partitioned runge kutta and runge kutta nystrom methods we studied compositions using several extra stages optimising the efficiency an effective error ef is defined and an extensive search is carried out using the extra parameters the new methods have smaller values of ef than other methods found in the literature when applied to several examples they perform up to two orders of magnitude better than previously known method which is in very good agreement with the values of ef

on landau damping going beyond the linearized study has been a longstanding problem in the theory of landau damping in this paper we establish exponential landau damping in analytic regularity the damping phenomenon is reinterpreted in terms of transfer of regularity between kinetic and spatial variables rather than exchanges of energy phase mixing is the driving mechanism the analysis involves new families of analytic norms measuring regularity by comparison with solutions of the free transport equation new functional inequalities a control of non linear echoes sharp deflection estimates and a newton approximation scheme our results hold for any potential no more singular than coulomb or newton interaction the limit cases are included with specific technical effort as a side result the stability of homogeneous equilibria of the non linear vlasov equation is established under sharp assumptions we point out the strong analogy with the kam theory and discuss physical implications finally we extend these results to some gevrey non analytic distribution functions

bounds for the distribution of the run length of one sided and two sided cusum quality control schemes upper and lower bounds are derived for the distribution of the run length n of both the one sided and two sided cusum schemes based upon a sequence of iterates pr n 0 pr n 1 bounds are constructed such that m n i pr n n pr n n i m n i pr n n holds for all n i 1 2 with constants 0 m n m n 1 suitably chosen the bounds converge monotonically in the sense that m n i 1pr n n m n 1 i pr n n 1 m n i 1pr n n m n 1 i pr n n 1 and under some mild and natural conditions as a by product bounds are presented for the percentage points of the distribution function of n for the average run length of the inspection scheme for the standard deviation of n and finally for the probability mass function of n some numerical results are displayed to demonstrate the effkiency of the method

on the numerical integration of ordinary differential equations by processed methods we provide a theoretical analysis of the processing technique for the numerical integration of odes we get the effective order conditions for processed methods in a general setting so that the results obtained can be applied to different types of numerical integrators we also propose a procedure to approximate the postprocessor such that its evaluation is virtually cost free the analysis is illustrated for a particular class of composition methods

fourth order symplectic integration abstract in this paper we present an explicit fourth order method for the integration of hamilton s equations this method preserves the property that the time evolution of such a system yields a canonical transformation from the initial conditions to the final state that is the integration step is an explicit symplectic map although the result is first derived for a specific type of hamiltonian it is shown to be quite general in particular the results can be applied to any lie group

a high order semi lagrangian discontinuous galerkin method for vlasov poisson simulations without operator splitting abstract in this paper we develop a high order semi lagrangian sl discontinuous galerkin dg method for nonlinear vlasov poisson vp simulations without operator splitting in particular we combine two recently developed novel techniques one is the high order non splitting sldg transport method cai et al 2017 4 and the other is the high order characteristics tracing technique proposed in qiu and russo 2017 29 the proposed method with up to third order accuracy in both space and time is locally mass conservative free of splitting error positivity preserving stable and robust for large time stepping size the sldg vp solver is applied to classic benchmark test problems such as landau damping and two stream instabilities for vp simulations efficiency and effectiveness of the proposed scheme is extensively tested tremendous cpu savings are shown by comparisons between the proposed sl dg scheme and the classical runge kutta dg method

using an autoregressive model to detect departures from steady states in unequally spaced tumour biomarker data a new method based on a continuous time autoregressive car 1 model of time series data is provided for detecting departures of tumour markers from steady states in breast cancer patients following surgery a kalman filter recursive algorithm is used to calculate the likelihood function arising from the car 1 model and to calculate recursive residuals which are monitored by a shewhart cusum scheme this approach can be used to monitor the serial marker data of large numbers of patients even when the series are short and the data are serially correlated and unequally spaced further the methodology can be used to recommend appropriate testing intervals

multivariate bayesian control chart a multivariate bayesian control chart for monitoring process mean under the assumption that the vector of process observations follows a multivariate normal distribution is considered traditional control charts such as hotelling s t2 ewma and cusum charts have been applied to control industrial processes characterized by several measurable variables it is well known that these traditional non bayesian process control techniques are not optimal but very few results regarding the structure of the bayesian control policy have been reported in the literature all dealing with the univariate finite horizon case in this paper we formulate the multivariate bayesian process control problem in the optimal stopping framework the objective is to find a stopping rule under partial observations minimizing the long run expected average cost per unit time for a given sample size and sampling interval under standard operating and cost assumptions it is proved that a control limit policy is optimal and an algorithm is presented to find the optimal control limit and the minimum average cost

sequential changepoint detection in quality control and dynamical systems after a brief survey of a large variety of sequential detection procedures that are widely scattered in statistical references on quality control and engineering references on fault detection and signal processing we study some open problems concerning these procedures and introduce a unified theory of sequential changepoint detection this theory leads to a class of sequential detection rules which are not too demanding in computational and memory requirements for on line implementation and yet are nearly optimal under several performance criteria

a rank based multivariate cusum procedure we consider statistical process control when measurements are multivariate a cumulative sum cusum procedure is suggested in detecting a shift in the mean vector of the measurements which is based on the cross sectional antiranks of the measurements at each time point the measurements are ordered and their antiranks which are the indices of the order statistics are recorded when the process is in control and the joint distribution of the multivariate measurements satisfies some regularity conditions the antirank vector at each time point has a given distribution this distribution changes to some other distribution when the process is out of control and the components of the shift in the mean vector of the process are not all the same this cusum can therefore detect shifts in all directions except the one in which the components of the shift in the mean vector are all the same but not 0 the shift with equal components however can be easily detected by another univariate cusum the former cusu

a multivariate exponentially weighted moving average control chart a multivariate extension of the exponentially weighted moving average ewma control chart is presented and guidelines given for designing this easy to implement multivariate procedure a comparison shows that the average run length arl performance of this chart is similar to that of multivariate cumulative sum cusum control charts in detecting a shift in the mean vector of a multivariate normal distribution as with the hotelling s 2 and multivariate cusum charts the arl performance of the multivariate ewma chart depends on the underlying mean vector and covariance matrix only through the value of the noncentrality parameter worst case scenarios show that hotelling s 2 charts should always be used in conjunction with multivariate cusum and ewma charts to avoid potential inertia problems examples are given to illustrate the use of the proposed procedure

control chart tests based on geometric moving averages a geometrical moving average gives the most recent observation the greatest weight and all previous observations weights decreasing in geometric progression from the most recent back to the first a graphical procedure for generating geometric moving averages is described in which the most recent observation is assigned a weight r the properties of control chart tests based on geometric moving averages are compared to tests based on ordinary moving averages

a performance comparison of semi lagrangian discontinuous galerkin and spline based vlasov solvers in four dimensions abstract the purpose of the present paper is to compare two semi lagrangian methods in the context of the four dimensional vlasov poisson equation more specifically our goal is to compare the performance of the more recently developed semi lagrangian discontinuous galerkin scheme to cubic spline interpolation which is widely used in eulerian vlasov simulation to that end we perform simulations for nonlinear landau damping and a two stream instability and provide benchmarks for the selalib and sldg codes both on a workstation and using mpi on a cluster in addition we will present results for the graphic processing unit gpu implementation contained in sldg we find that the semi lagrangian discontinuous galerkin scheme shows a moderate improvement in run time for nonlinear landau damping and a substantial improvement for the two stream instability it should be emphasized that these results are markedly different from results obtained in the asymptotic regime which favor spline interpolation thus we conclude that the traditional approach of evaluating numerical methods is misleading even for short time simulations in addition the absence of any global communication in the semi lagrangian discontinuous galerkin method gives it a decisive advantage for scaling to more than 256 cores

optimal design of second order linear filters for control charting in many common control charting situations the statistic to be charted can be viewed as the output of a linear filter applied to the sequence of process measurement data in recent work that has generalized this concept the charted statistic is the output of a general linear filter in impulse response form and the filter is designed by selecting its impulse response coefficients to optimize its average run length performance in this work we restrict attention to the class of all second order linear filters applied to the residuals of a time series model of the process data we present an algorithm for optimizing the design of the second order filter that is more computationally efficient and robust than the algorithm for optimizing the general linear filter we demonstrate that the optimal second order filter performs almost as well as the optimal general linear filter in many situations both methods share a number of interesting characteristics and are tuned to detect any distinct features of the p

conservative semi lagrangian schemes for vlasov equations conservative methods for the numerical solution of the vlasov equation are developed in the context of the one dimensional splitting in the case of constant advection these methods and the traditional semi lagrangian ones are proven to be equivalent but the conservative methods offer the possibility to add adequate filters in order to ensure the positivity in the non constant advection case they present an alternative to the traditional semi lagrangian schemes which can suffer from bad mass conservation in this time splitting setting

properties of the t2 control chart when parameters are estimated moments of the run length distribution are often used to design and study the performance of quality control charts in this article the run length distribution of the t2 chart for monitoring a multivariate process mean is analyzed it is assumed that the in control process observations are iid random samples from a multivariate normal distribution with unknown mean vector and covariance matrix it is shown that the in control run length distribution of the chart does not depend on the unknown process parameters furthermore it is shown that the out of control run length distribution of the chart depends only on the statistical distance between the in control and out of control mean vectors it follows that a performance analysis can be given without knowledge of the in control values of the parameters or their estimates the performance of charts constructed using traditional f distribution based control limits is studied recommendations are given for sample size requirements necessary to achieve desir

numerical study of the two species vlasov ampere system in this paper we propose energy conserving eulerian solvers for the two species vlasov ampere va system and apply the methods to simulate current driven ion acoustic instability the two species va systems are of practical importance in applications and they conserve many physical quantities including the particle number of each species and the total energy that is comprised of kinetic energy for both species and the electric energy the main goal of this paper is to generalize our previous work for the single species va system 9 and vlasov maxwell vm system 8 to the two species case the methodologies proposed involve careful design of temporal discretization and the use of the discontinuous galerkin dg spatial discretizations we show that the energy conserving time discretizations for single species equations 9 8 can also work for the two species case if extended properly compared to other high order schemes we emphasize that our schemes can preserve the total particle number and total energy on the fully discrete level regardless of mesh size making them very attractive for long time simulations we benchmark our algorithms on a test example to check the one species limit and the current driven ion acoustic instability to simulate the current driven ion acoustic instability a slight modification for the implicit method is necessary to fully decouple the split equations this is achieved by a gauss seidel type iteration technique numerical results verified the conservation and performance of our methods finally we remark that the schemes in this paper can be readily extended to applications when the models take more general form such as the multi species vm equations

short note a charge and energy conserving implicit electrostatic particle in cell algorithm on mapped computational meshes we describe the extension of the recent charge and energy conserving one dimensional electrostatic particle in cell algorithm in ref g chen l chacon d c barnes an energy and charge conserving implicit electrostatic particle in cell algorithm journal of computational physics 230 2011 7018 7036 to mapped body fitted computational meshes the approach maintains exact charge and energy conservation properties key to the algorithm is a hybrid push where particle positions are updated in logical space while velocities are updated in physical space the effectiveness of the approach is demonstrated with a challenging numerical test case the ion acoustic shock wave the generalization of the approach to multiple dimensions is outlined

joint economic design of ewma control charts for mean and variance abstract control charts with exponentially weighted moving average ewma statistics mean and variance are used to jointly monitor the mean and variance of a process an ewma cost minimization model is presented to design the joint control scheme based on pure economic or both economic and statistical performance criteria the pure economic model is extended to the economic statistical design by adding constraints associated with in control and out of control average run lengths the quality related production costs are calculated using taguchi s quadratic loss function the optimal values of smoothing constants sampling interval sample size and control chart limits are determined by using a numerical search method the average run length of the control scheme is computed by using the markov chain approach computational study indicates that optimal sample sizes decrease as the magnitudes of shifts in mean and or variance increase and higher values of quality loss coefficient lead to shorter sampling intervals the sensitivity analysis results regarding the effects of various inputs on the chart parameters provide useful guidelines for designing an ewma based process control scheme when there exists an assignable cause generating concurrent changes in process mean and variance

a markov chain model for the multivariate exponentially weighted moving averages control chart abstract a markov chain approximation is used to determine the run length performance of a multivariate statistical process control chart the markov chain approach is widely used in the analysis of univariate control charts we extend the advantages of this type of analysis to a multivariate exponentially weighted moving averages control chart the analysis can be applied whenever the multivariate control statistic can be modeled as a markov chain and the run length performance depends on the off target mean only through the noncentrality parameter

frequentist bayesian monte carlo test for mean vectors in high dimension abstract conventional methods for testing the mean vector of a p variate gaussian distribution require a sample size n greater than or equal to p but in high dimensional situations that is when n is smaller than p special and new adjustments are needed although bayesian empirical methods are well succeeded for testing in high dimension their performances are strongly dependent on the actual unknown covariance matrix of the gaussian random vector in this paper we introduce a hybrid frequentist bayesian monte carlo test and prove that i under the null hypothesis the performance of the proposed test is invariant with respect to the real unknown covariance matrix and ii the decision rule is valid which means that in terms of expected loss the performance of the proposed procedure can always be made as good as the exact bayesian test and in terms of type i error probability the method is always of level for arbitrary 0 1

a least angle regression control chart for multidimensional data in multidimensional applications it is very rare that all variables shift at the same time a statistical process control procedure would have superior efficiency when limited to the subset of variables likely responsible for the out of control conditions the key idea of this article consists of combining a variable selection method with a multivariate control chart to detect changes in both the mean and variability of a multidimensional process with gaussian errors in particular we develop a control chart for phase ii monitoring which integrates the least angle regression algorithm with a multivariate exponentially weighted moving average comparisons with related multivariate control schemes demonstrate the efficiency of the proposed control chart in a wide range of practical applications including profile and multistage process monitoring further the proposed scheme may also provide valuable diagnostic information for fault isolation supplemental materials including an r package are available

towards an ultra efficient kinetic scheme part ii in a recent paper we presented a new ultra efficient numerical method for solving kinetic equations of the boltzmann type dimarco and loubere 2013 17 the key idea on which the method relies is to solve the collision part on a grid and then to solve exactly the transport part by following the characteristics backward in time on the contrary to classical semi lagrangian methods one does not need to reconstruct the distribution function at each time step this allows to tremendously reduce the computational cost and to perform efficient numerical simulations of kinetic equations up to the six dimensional case without parallelization however the main drawback of the method developed was the loss of spatial accuracy close to the fluid limit in the present work we modify the scheme in such a way that it is able to preserve the high order spatial accuracy for extremely rarefied and fluid regimes in particular in the fluid limit the method automatically degenerates into a high order method for the compressible euler equations numerical examples are presented which validate the method show the higher accuracy with respect to the previous approach and measure its efficiency with respect to well known schemes direct simulation monte carlo finite volume muscl weno

multivariate control charts based on the james stein estimator abstract in this study we focus on improving parameter estimation in phase i study to construct more accurate phase ii control limits for monitoring multivariate quality characteristics for a multivariate normal distribution with unknown mean vector the usual mean estimator is known to be inadmissible under the squared error loss function when the dimension of the variables is greater than 2 shrinkage estimators such as the james stein estimators are shown to have better performance than the conventional estimators in the literature we utilize the james stein estimators to improve the phase i parameter estimation multivariate control limits for the phase ii monitoring based on the improved estimators are proposed in this study the resulting control charts js type charts are shown to have substantial performance improvement over the existing ones

multivariate exponentially weighted moving covariance matrix multivariate exponentially weighted moving average mewma charts are among the best control charts for detecting small changes in any direction the well known mewma is directed at changes in the mean vector but changes can occur in either the location or the variability of the correlated multivariate quality characteristics calling for parallel methodologies for detecting changes in the covariance matrix this article discusses an exponentially weighted moving covariance matrix for monitoring the stability of the covariance matrix of a process used together with the location mewma this chart provides a way to satisfy shewhart s dictum that proper process control monitor both mean and variability we show that the chart is competitive generally outperforming current control charts for the covariance matrix

a new two sided cumulative sum quality control scheme a new two sided cumulative sum quality control scheme is proposed the new scheme was developed specifically to be generalized to a multivariate cumulative sum quality control scheme the multivariate version will be examined in a subsequent paper this article evaluates the univariate version a comparison of the conventional two sided cumulative sum scheme and the proposed scheme indicates that the new scheme has slightly better properties ratio of on aim to off aim average run lengths than the conventional scheme steady state average run lengths are discussed the new scheme and the conventional two sided cumulative sum scheme have equivalent steady state average run lengths methods for implementing the fast initial response feature for the new cumulative sum scheme are given a comparison of average run lengths for the conventional and proposed schemes with fast initial response features is also favorable to the new scheme a markov chain approximation is used to calculate the average run lengths

a splitting algorithm for vlasov simulation with filamentation filtration a fourier fourier transformed version of the splitting algorithm for simulating solutions of the vlasov poisson system of equations is introduced it is shown that with the inclusion of filamentation filtration in this transformed algorithm it is both faster and more stable than the standard splitting algorithm it is further shown that in a scalar computer environment this new algorithm is approximately equal in speed and far less noisy than its particle in cell counterpart it is conjectured that in a multiprocessor environment the filtered splitting algorithm would be faster while producing more precise results

higher order hybrid monte carlo algorithms we present a simple recursive iteration of the leapfrog discretization of newton s equations which leads to a removal of the finite step size error to any desired order this is done in a manner that preserves phase space areas and reversibility as required for use in the hybrid monte carlo method for simulating fermionic fields the resulting asymptotic volume dependence is exp ln ital v sup 1 2 we test the scheme on the 2 1 dimensional hubbard model

a splitting fourier pseudospectral method for vlasov poisson fokker planck system abstract in this paper we propose a splitting fourier pseudospectral method for vlasov poisson fokker planck vpfp system which describes the motion of charged particles in plasma the numerical integration for the system is performed by employing the splitting method in time fourier galerkin method in space direction and fourier collocation method in phase direction respectively the algorithm has spectral accuracy in both space and phase directions and can be implemented efficiently with the fast fourier transform and technique of diagonalization respectively extensive numerical results in one dimensional phase space or 1 x 1 v from the proposed numerical method are shown and have proven the good agreement with the theory and previous studies numerical algorithm for the vpfp system in two dimensional phase space or 2 x 2 v has been summarized in appendix

a positivity preserving high order semi lagrangian discontinuous galerkin scheme for the vlasov poisson equations the vlasov poisson equations describe the evolution of a collisionless plasma represented through a probability density function pdf that self interacts via an electrostatic force one of the main difficulties in numerically solving this system is the severe time step restriction that arises from parts of the pdf associated with moderate to large velocities the dominant approach in the plasma physics community for removing these time step restrictions is the so called particle in cell pic method which discretizes the distribution function into a set of macro particles while the electric field is represented on a mesh several alternatives to this approach exist including fully lagrangian fully eulerian and so called semi lagrangian methods the focus of this work is the semi lagrangian approach which begins with a grid based eulerian representation of both the pdf and the electric field then evolves the pdf via lagrangian dynamics and finally projects this evolved field back onto the original eulerian mesh in particular we develop in this work a method that discretizes the 1 1 vlasov poisson system via a high order discontinuous galerkin dg method in phase space and an operator split semi lagrangian method in time second order accuracy in time is relatively easy to achieve via strang operator splitting with additional work using higher order splitting and a higher order method of characteristics we also demonstrate how to push this scheme to fourth order accuracy in time we show how to resolve all of the lagrangian dynamics in such a way that mass is exactly conserved positivity is maintained and high order accuracy is achieved the poisson equation is solved to high order via the smallest stencil local discontinuous galerkin ldg approach we test the proposed scheme on several standard test cases

cusum charts with variable sampling intervals a standard cumulative sum cusum chart for controlling the process mean takes samples from the process at fixed length sampling intervals and uses a control statistic based on a cumulative sum of differences between the sample means and the target value this article proposes a modification of the standard cusum scheme that varies the time intervals between samples depending on the value of the cusum control statistic the variable sampling interval vsi cusum chart uses short sampling intervals if there is an indication that the process mean may have shifted and long sampling intervals if there is no indication of a change in the mean if the cusum statistic actually enters the signal region then the vsi cusum chart signals in the same manner as the standard cusum chart a markov chain approach is used to evaluate properties such as the average time to signal and the average number of samples to signal results show that the proposed vsi cusum chart is considerably more efficient than the standard cus

the distribution of the run length of one sided cusum procedures for continuous random variables a method is given for approximating the moments and percentage points of the run length distribution of one sided cusum procedures for continuous random variables the run length probabilities are calculated recursively using numerical quadrature until the ratio of successive probabilities stabilizes this ratio and the probabilities of low run length values are then used to approximate parameters of the run length distribution the accuracy of this method is compared with that of previous methods in examples involving normally distributed random variables

multivariate profile charts for statistical process control the multivariate profile mp chart is a new control chart for simultaneous display of univariate and multivariate statistics it is designed to analyze and display extended structures of statistical process control data for various cases of grouping reference distribution and use of nominal specifications for each group of observations the scaled deviations from reference values are portrayed together as a modified profile plot symbol the vertical location of the symbol is determined by the multivariate distance of the vector of means from the reference values the graphical display in the mp chart enjoys improved visual characteristics as compared with previously suggested methods moreover the perceptual tasks required by the use of the mp chart provide higher accuracy in retrieving the quantitative information this graphical display is used to display other combined univariate and multivariate statistics such as measures of dispersion principal components and cumulative sums

monitoring paired binary surgical outcomes using cumulative sum charts correlated binary data are encountered in many areas of medical research system reliability and quality control for monitoring failures rates in such situations simultaneous bivariate cumulative sum cusum charts with the addition of secondary control limits are proposed using an approach based on a markov chain model the run length properties of such a monitoring scheme can be determined for sudden or gradual changes in the failure rates the proposed control charts are easy to implement and are shown to be very effective at detecting small changes in the rate of undesirable outcomes especially when the changes are gradual this procedure is illustrated using bivariate outcome data arising from a series of paediatric surgeries the methodology is sufficiently general that it may be adapted for multivariate normal binomial or poisson responses

exponentially weighted moving average control schemes properties and enhancements roberts 1959 first introduced the exponentially weighted moving average ewma control scheme using simulation to evaluate its properties he showed that the ewma is useful for detecting small shifts in the mean of a process the recognition that an ewma control scheme can be represented as a markov chain allows its properties to be evaluated more easily and completely than has previously been done in this article we evaluate the properties of an ewma control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value a design procedure for ewma control schemes is given parameter values not commonly used in the literature are shown to be useful for detecting small shifts in a process in addition several enhancements to ewma control schemes are considered these include a fast initial response feature that makes the ewma control scheme more sensitive to start up problems a combined shewhart ewma that provides protection against both larg

a critical comparison of eulerian grid based vlasov solvers a common problem with direct vlasov solvers is ensuring that the distribution function remains positive a related problem is to guarantee that the numerical scheme does not introduce false oscillations in velocity space in this paper we use a variety of schemes to assess the importance of these issues and to determine an optimal strategy for eulerian split approaches to vlasov solvers from these tests we conclude that maintaining positivity is less important than correctly dissipating the fine scale structure which arises naturally in the solution to many vlasov problems furthermore we show that there are distinct advantages to using high order schemes i e third order rather than second a natural choice which satisfies all of these requirements is the piecewise parabolic method ppm which is applied here to vlasov s equation for the first time

on the numerical integration of ordinary differential equations by symmetric composition methods differential equations of the form dot x x a b are considered where the vector fields a and b can be integrated exactly enabling numerical integration of x by composition of the flows of a and b various symmetric compositions are investigated for order complexity and reversibility free lie algebra theory gives simple formulae for the number of determining equations for a method to have a particular order a new more accurate way of applying the methods thus obtained to compositions of an arbitrary first order integrator is described and tested the determining equations are explored and new methods up to 100 times more accurate at constant work than those previously known are given

solving hyperbolic elliptic problems on singular mapped disk like domains with the method of characteristics and spline finite elements abstract a common strategy in the numerical solution of partial differential equations is to define a uniform discretization of a tensor product multi dimensional logical domain which is mapped to a physical domain through a given coordinate transformation by extending this concept to a multi patch setting simple and efficient numerical algorithms can be employed on relatively complex geometries the main drawback of such an approach is the inherent difficulty in dealing with singularities of the coordinate transformation this work suggests a comprehensive numerical strategy for the common situation of disk like domains with a singularity at a unique pole where one edge of the rectangular logical domain collapses to one point of the physical domain for example a circle we present robust numerical methods for the solution of vlasov like hyperbolic equations coupled to poisson like elliptic equations in such geometries we describe a semi lagrangian advection solver that employs a novel set of coordinates named pseudo cartesian coordinates to integrate the characteristic equations in the whole domain including the pole and a finite element elliptic solver based on globally c 1 smooth splines toshniwal et al 2017 27 the two solvers are tested both independently and on a coupled model namely the 2d guiding center model for magnetized plasmas equivalent to a vorticity model for incompressible inviscid euler fluids the numerical methods presented show high order convergence in the space discretization parameters uniformly across the computational domain without effects of order reduction due to the singularity dedicated tests show that the numerical techniques described can be applied straightforwardly also in the presence of point charges equivalently point like vortices within the context of particle in cell methods

a multivariate change point model for statistical process control multivariate statistical process control spc carries out ongoing checks to ensure that a process is in control these checks on the process are traditionally done by t2 multivariate cusum and multivariate exponentially weighted moving average control charts these traditional spc charts assume that the in control true parameters are known exactly and use these assumed true values to set the control limits the reality however is that true parameter values are seldom if ever known exactly rather they are commonly estimated from a phase i sample it is increasingly recognized that this phase i study needs to involve large samples if the parameter estimates are to provide run behavior matching that of the known parameter situation but apart from the general undesirability of large and thus expensive studies preliminary to actual charting some industrial settings have a paucity of relevant data for estimating the process parameters an attractive alternative to traditional charting methods when mon

symplectic integration with processing a general study the number of conditions to be satisfied by the operators k and p in symplectic integrators with processing given by epe hke p is determined for a hamiltonian of the form h cal a cal b the conditions for k are explicitly written up to order six and used to obtain more efficient methods with fewer evaluations per step than other symplectic integrators special cases in which the number of conditions for the kernel is drastically reduced are also studied it is shown that the kernel completely determines the optimal method one can obtain by processing

a multivariate sign ewma control chart nonparametric control charts are useful in statistical process control spc when there is a lack of or limited knowledge about the underlying process distribution especially when the process measurement is multivariate this article develops a new multivariate spc methodology for monitoring location parameters it is based on adapting a powerful multivariate sign test to online sequential monitoring the weighted version of the sign test is used to formulate the charting statistic by incorporating the exponentially weighted moving average control ewma scheme which results in a nonparametric counterpart of the classical multivariate ewma mewma it is affine invariant and has a strictly distribution free property over a broad class of population models that is the in control ic run length distribution can attain or is always very close to the nominal one when using the same control limit designed for a multivariate normal distribution moreover when the process distribution comes from the elli

a multi level multi domain method for particle in cell plasma simulations a novel adaptive technique for electromagnetic particle in cell pic plasma simulations is presented here two main issues are identified as regards the development of the algorithm first the choice of the size of the particle shape function in progressively refined grids with the decision to avoid both time dependent shape functions and cumbersome particle to grid interpolation techniques and second the necessity to comply with the strict stability constraints of the explicit pic algorithm the adaptive implementation presented responds to these demands with the introduction of a multi level multi domain mlmd system where a cloud of self similar domains is fully simulated with both fields and particles and the use of an implicit moment pic method as baseline algorithm for the adaptive evolution information is exchanged between the levels with the projection of the field information from the refined to the coarser levels and the interpolation of the boundary conditions for the refined levels from the coarser level fields particles are bound to their level of origin and are prevented from transitioning to coarser levels but are repopulated at the refined grid boundaries with a splitting technique the presented algorithm is tested against a series of simulation challenges

comparison of ewma cusum and shiryayev roberts procedures for detecting a shift in the mean pollak and siegmund compared the shiryayev roberts procedure with the cusum procedure for detecting a change in the drift of a brownian motion based on the conditional average delay time in this paper the exponentially weighted moving average ewma procedure proposed by roberts is compared with the shiryayev roberts and cusum procedures the comparison is based on the stationary average delay time as advocated by shiryayev the optimal design for the ewma procedure and its asymptotic properties are studied when the average in control run length is large the results show that the ewma procedure is less efficient than the other two procedures

the domination numbers of cylindrical grid graphs abstract let p m c n denote the domination number of the cylindrical grid graph formed by the cartesian product of the graphs p m the path of length m m 2 and the graph c n the cycle of length n n 3 in this paper methods to find the domination numbers of graphs of the form p m c n with n 3 and m 2 3 and 4 are proposed moreover bounds on domination numbers of the graphs p 5 c n n 3 are found the methods that are used to prove that results readily lead to algorithms for finding minimum dominating sets of the above mentioned graphs

a polynomial time dna computing solution for the bin packing problem it is suggested here an algorithm based on stickers for the dna computing model s roweis e winfree r burgoyne n chelyapov m goodman p rothemund l adleman a sticker based model for dna computation journal of computational biology 5 1998 615 629 that solves the well known bin packing problem bpp that belongs to the class np hard in the strong sense in a time bounded by o n 2q where n is the quantity of items and q the space requirements expressed in bits to the best of the authors knowledge this is the first polynomial time algorithmic solution for the bpp in such a model

using autoregressive and random walk models to detect trends and shifts in unequally spaced tumour biomarker data continuous time autoregressive car 1 and random walk models of time series data are provided for detecting non random shifts and trends of tumour markers in breast cancer patients following resection for cure the continuous time random walk model with observation error is extended to the case of multiple patient time series these models can be used to monitor large numbers of patients with time series with few sampling events that are serially correlated and unequally spaced further the methodologies can be used to recommend appropriate testing intervals a kalman filter recursive algorithm is used to calculate the likelihood functions arising from the car 1 and random walk models and to calculate recursive residuals which are monitored by shewhart cusum schemes

an efficient scheme for convection dominated transport partial differential equations describing transport processes involving a significant effect of the flow velocity may be solved efficiently and easily using a simple algorithm the algorithm is based on the propagator s or green s functions for the equations of transport theory the numerical method employed is always at least as fast as finite differencing and it reduces to a finite difference method in the short time step limit but is especially efficient in cases where flow dominates over diffusion and is consequently widely applicable in kinetic theory and fluid dynamics using this method the ion distribution function and the potential in a plasma sheath were calculated in the presence of charge exchange collisions for a wide range of neutral densities