quasi steady state reduction for compartmental systems abstract we present a method to determine an asymptotic reduction in the sense of tikhonov and fenichel for singularly perturbed compartmental systems in the presence of slow transport it turns out that the reduction can be derived from the individual interaction terms alone we apply the result to spatially discretized reaction diffusion systems and obtain based on the reduced discretized systems a heuristic to reduce reaction diffusion systems in presence of slow diffusion

parameterization of suboptimal solutions of the nehari problem for infinite dimensional systems the nehari problem plays an important role in hinfin control theory it is well known that hinfin control problem can be reduced to solving this problem this note gives a parameterization of all suboptimal solutions of the nehari problem for a class of infinite dimensional systems many earlier solutions of this problem are seen to be special cases of this new parameterization it is also shown that for finite impulse response systems this parameterization takes a particularly simple form

runge kutta methods for hyperbolic conservation laws with stiff relaxation terms underresolved numerical schemes for hyperbolic conservation laws with stiff relaxation terms may generate unphysical spurious numerical results or reduce to lower order if the small relaxation time is not temporally well resolved we design a second order runge kutta type splitting method that possesses the discrete analogue of the continuous asymptotic limit which thus is able to capture the correct physical behaviors with high order accuracy even if the initial layer and the small relaxation time are not numerically resolved

numerical approximation of the euler maxwell model in the quasineutral limit we derive and analyze an asymptotic preserving scheme for the euler maxwell system in the quasi neutral limit we prove that the linear stability condition on the time step is independent of the scaled debye length l when l 0 numerical validation performed on riemann initial data and for a model plasma opening switch device show that the ap scheme is convergent to the euler maxwell solution when dx l 0 where dx is the spatial discretization but when l dx 0 the ap scheme is consistent with the quasi neutral euler maxwell system the scheme is also perfectly consistent with the gauss equation the possibility of using large time and space steps leads to several orders of magnitude reductions in computer time and storage

efficient asymptotic preserving ap schemes for some multiscale kinetic equations many kinetic models of the boltzmann equation have a diffusive scaling that leads to the navier stokes type parabolic equations as the small scaling parameter approaches zero in practical applications it is desirable to develop a class of numerical schemes that can work uniformly with respect to this relaxation parameter from the rarefied kinetic regimes to the hydrodynamic diffusive regimes an earlier approach in s jin l pareschi and g toscani siam j numer anal 35 1998 pp 2405 2439 reformulates such systems into the common hyperbolic relaxation system by jin and xin for hyperbolic conservation laws used to construct the relaxation schemes and then uses a multistep time splitting method to solve the relaxation system here we observe that the combination of the two time split steps may yield hyperbolic parabolic systems that are more advantageous in both stability and efficiency for numerical computations we show that such an approach yields a class of asymptotic preserving ap schemes which are suitable for the computation of multiscale kinetic problems we use the goldstein taylor and carleman models to illustrate this approach

on the asymptotic preserving property of the unified gas kinetic scheme for the diffusion limit of linear kinetic models the unified gas kinetic scheme ugks of k xu et al 2010 37 originally developed for multiscale gas dynamics problems is applied in this paper to a linear kinetic model of radiative transfer theory while such problems exhibit purely diffusive behavior in the optically thick or small knudsen regime we prove that ugks is still asymptotic preserving ap in this regime but for the free transport regime as well moreover this scheme is modified to include a time implicit discretization of the limit diffusion equation and to correctly capture the solution in case of boundary layers contrary to many ap schemes this method is based on a standard finite volume approach it does neither use any decomposition of the solution nor staggered grids several numerical tests demonstrate the properties of the scheme

a realizability preserving discontinuous galerkin method for the m1 model of radiative transfer the m 1 model for radiative transfer coupled to a material energy equation in planar geometry is studied in this paper for this model to be well posed its moment variables must fulfill certain realizability conditions our main focus is the design and implementation of an explicit runge kutta discontinuous galerkin method which under a more restrictive cfl condition guarantees the realizability of the moment variables and the positivity of the material temperature an analytical proof for our realizability preserving scheme which also includes a slope limiting technique is provided and confirmed by various numerical examples among other things we present accuracy tests showing convergence up to fourth order compare our results with an analytical solution in a riemann problem and consider a marshak wave problem

optimal classification in sparse gaussian graphic model consider a two class classification problem where the number of features is much larger than the sample size the features are masked by gaussian noise with mean zero and covariance matrix sigma where the precision matrix omega sigma 1 is unknown but is presumably sparse the useful features also unknown are sparse and each contributes weakly i e rare and weak to the classification decision by obtaining a reasonably good estimate of omega we formulate the setting as a linear regression model we propose a two stage classification method where we first select features by the method of innovated thresholding it and then use the retained features and fisher s lda for classification in this approach a crucial problem is how to set the threshold of it we approach this problem by adapting the recent innovation of higher criticism thresholding hct we find that when useful features are rare and weak the limiting behavior of hct is essentially just as good as the limiting behavior of ideal threshold the threshold one would choose if the underlying distribution of the signals is known if only somewhat surprisingly when omega is sufficiently sparse its off diagonal coordinates usually do not have a major influence over the classification decision compared to recent work in the case where omega is the identity matrix proc natl acad sci usa 105 2008 14790 14795 philos trans r soc lond ser a math phys eng sci 367 2009 4449 4470 the current setting is much more general which needs a new approach and much more sophisticated analysis one key component of the analysis is the intimate relationship between hct and fisher s separation another key component is the tight large deviation bounds for empirical processes for data with unconventional correlation structures where graph theory on vertex coloring plays an important role

cal h _ infty control and estimation problems with delayed measurements state space solutions most physical processes exhibit transport delay in the measured output and it is well known that this can have disastrous effects on system stability and performance if it is not accounted for in this paper we give necessary and sufficient conditions for existence of estimators and controllers that achieve the desired cal h infty performance criterion when such a measurement delay is present we also give the complete characterization of all controllers and estimators that achieve the desired performance criterion the necessary and sufficient conditions are easy to check and are given in terms of the familiar pair of algebraic riccati equations that appear in the nondelay versions of the corresponding cal h infty problems along with an additional riccati differential equation explicit state space formulas for the controllers and estimators are also obtained they have a linear periodic structure and are easily implementable to obtain these results we first obtain state space results for a modified nehari problem which may be of independent interest see problem 5 in section 2

numerical schemes for hyperbolic conservation laws with stiff relaxation terms hyperbolic systems often have relaxation terms that give them a partially conservative form and that lead to a long time behavior governed by reduced systems that are parabolic in nature in this article it is shown by asymptotic analysis and numerical examples that semidiscrete high resolution methods for hyperbolic conservation laws fail to capture this asymptotic behavior unless the small relaxation rate is resolved by a fine spatial grid we introduce a modification of higher order godunov methods that possesses the correct asymptotic behavior allowing the use of coarse grids large cell peclet numbers the idea is to build into the numerical scheme the asymptotic balances that lead to this behavior numerical experiments on 2 2 systems verify our analysis

asymptotic high order mass preserving schemes for a hyperbolic model of chemotaxis we introduce a new class of finite difference schemes for approximating the solutions to an initial boundary value problem on a bounded interval for a one dimensional dissipative hyperbolic system with an external source term which arises as a simple model of chemotaxis since the solutions to this problem may converge to nonconstant asymptotic states for large times standard schemes usually fail to yield a good approximation therefore we propose a new class of schemes which use an asymptotic higher order correction second and third order in our examples to balance the effects of the source term and the influence of the asymptotic solutions special care is needed to deal with boundary conditions to avoid harmful loss of mass convergence results are proved for these new schemes and several numerical tests are presented and discussed to verify the effectiveness of their behavior

a constrained l1 minimization approach to sparse precision matrix estimation this article proposes a constrained l1 minimization method for estimating a sparse inverse covariance matrix based on a sample of n iid p variate random variables the resulting estimator is shown to have a number of desirable properties in particular the rate of convergence between the estimator and the true s sparse precision matrix under the spectral norm is when the population distribution has either exponential type tails or polynomial type tails we present convergence rates under the elementwise l norm and frobenius norm in addition we consider graphical model selection the procedure is easily implemented by linear programming numerical performance of the estimator is investigated using both simulated and real data in particular the procedure is applied to analyze a breast cancer dataset and is found to perform favorably compared with existing methods

sparsistency and rates of convergence in large covariance matrix estimation this paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions here sparsistency refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one depending on the case of applications sparsity priori may occur on the covariance matrix its inverse or its cholesky decomposition we study these three sparsity exploration problems under a unified framework with a general penalty function we show that the rates of convergence for these problems under the frobenius norm are of order s n log p n n 1 2 where s n is the number of nonzero elements p n is the size of the covariance matrix and n is the sample size this explicitly spells out the contribution of high dimensionality is merely of a logarithmic factor the conditions on the rate with which the tuning parameter n goes to 0 have been made explicit and compared under different penalties as a result for the l 1 penalty to guarantee the sparsistency and optimal rate of convergence the number of nonzero elements should be small sn o pn at most among o pn2 parameters for estimating sparse covariance or correlation matrix sparse precision or inverse correlation matrix or sparse cholesky factor where sn is the number of the nonzero elements on the off diagonal entries on the other hand using the scad or hard thresholding penalty functions there is no such a restriction

a linear discontinuous spatial differencing scheme forsnradiative transfer calculations various types of linear discontinuous spatial differencing schemes have been developed for thesn discrete ordinates equations approximating the linear boltzmann transport equation it has been shown through an asymptotic analysis that the 1d slab geometry lumped linear discontinuous scheme not only goes over to a convergent and robust differencing of the diffusion equation in the monoenergetic thick diffusion limit but it also yields the correct interior solution even when boundary layers are left unresolved by the spatial mesh in the present work we generalize this scheme to obtain a 1d slab geometry lumped linear discontinuous scheme for the nonlinear radiative transfer equation and the associated material temperature equation we present a full nonlinear energy dependent asymptotic analysis of the behavior of this scheme in the thick equilibrium diffusion limit we find that this scheme goes over to a convergent and robust differencing of the equilibrium diffusion equation on the interior of the mesh but it does not yield the exact interior solution when boundary layers are left unresolved by the spatial mesh nevertheless the interior solution obtained with spatially unresolved boundary layers is always well behaved and fairly accurate computational results are presented which test the predictions of our asymptotic analysis and demonstrate the efficiency of our solution technique

numerical passage from kinetic to fluid equations a numerical way to pass from the bhatnagar gross krook model of the boltzmann equation to compressible euler equations is presented in order to do so a stable discretization of the kinetic equati

asymptotic equilibrium diffusion analysis of time dependent monte carlo methods for grey radiative transfer the equations of nonlinear time dependent radiative transfer are known to yield the equilibrium diffusion equation as the leading order solution of an asymptotic analysis when the mean free path and mean free time of a photon become small we apply this same analysis to the fleck cummings carter forest and n kaoua monte carlo approximations for grey frequency independent radiative transfer although monte carlo simulation usually does not require the discretizations found in deterministic transport techniques monte carlo methods for radiative transfer require a time discretization due to the nonlinearities of the problem if an asymptotic analysis of the equations used by a particular monte carlo method yields an accurate time discretized version of the equilibrium diffusion equation the method should generate accurate solutions if a time discretization is chosen that resolves temperature changes even if the time steps are much larger than the mean free time of a photon this analysis is of interest because in many radiative transfer problems it is a practical necessity to use time steps that are large compared to a mean free time our asymptotic analysis shows that i the n kaoua method has the equilibrium diffusion limit ii the carter forest method has the equilibrium diffusion limit if the material temperature change during a time step is small and iii the fleck cummings method does not have the equilibrium diffusion limit we include numerical results that verify our theoretical predictions

on solutions to the pn equations for thermal radiative transfer we present results for the spherical harmonics p n method for solving problems of time dependent thermal radiative transport we prove a theorem that demonstrates that in the streaming limit the spatially and temporally continuous p n equations will allow negative energy densities for any finite order of n we also develop an implicit numerical method for solving the p n equations to explore the impact of the theorem the numerical method uses a high resolution riemann solver to produce an upwinded discretization we employ a quasi linear approach to integrate the nonlinearites added to make the scheme non oscillatory we use the backward euler method for time integration and treat the material interaction terms fully nonlinearly reflecting boundary conditions for the p n equations are presented and we show how to implement this boundary condition using ghost cells the implicit method was able to produce robust results to thermal transport problems in one and two dimensions the numerical method is used to analyze the accuracy of various p n expansion orders on several problems in two dimensional problems the numerical p n solutions contained negative radiation energy densities as predicted by our theorem the numerical results showed that the material temperature also became negative a result outside the scope of the theorem our numerical method can handle these negative values but they would cause problems in a radiation hydrodynamics calculation

uniformly accurate schemes for hyperbolic systems with relaxation we develop high resolution shock capturing numerical schemes for hyperbolic systems with relaxation in such systems the relaxation time may vary from order 1 to much less than unity when the relaxation time is small the relaxation term becomes very strong and highly stiff and underresolved numerical schemes may produce spurious results usually one cannot decouple the problem into separate regimes and handle different regimes with different methods thus it is important to have a scheme that works uniformly with respect to the relaxation time using the broadwell model of the nonlinear boltzmann equation we develop a second order scheme that works effectively with a fixed spatial and temporal discretization for all ranges of the mean free path formal uniform consistency proof for a first order scheme and numerical convergence proof for the second order scheme are also presented we also make numerical comparisons of the new scheme with some other schemes this study is motivated by the reentry problem in hypersonic computations

exponential stabilization of linear systems with time varying delayed state feedback via partial spectrum assignment abstract we consider the problem of controlling a linear system when the state is available with a known time varying delay delayed state feedback control or the actuator is affected by a delay the solution proposed in this paper consists in partially assigning the spectrum of the closed loop system to guarantee the exponential zero state stability with a prescribed decay rate by means of a finite dimensional control law a non conservative bound on the maximum allowed delay for the prescribed decay rate is presented which holds for both cases of constant and time varying delays an advantage over recent and similar approaches is that differentiability or continuity of the delay function is not required we compare the performance of our approach in terms of delay bound and input signal with another recent approach

covariance regularization by thresholding this paper considers regularizing a covariance matrix of p variables estimated from n observations by hard thresholding we show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is sparse in a suitable sense the variables are gaussian or sub gaussian and log p n 0 and obtain explicit rates the results are uniform over families of covariance matrices which satisfy a fairly natural notion of sparsity we discuss an intuitive resampling scheme for threshold selection and prove a general cross validation result that justifies this approach we also compare thresholding to other covariance estimators in simulations and on an example from climate data 1 introduction estimation of covariance matrices is important in a number of areas of statistical analysis including dimension reduction by principal component analysis pca classification by linear or quadratic discriminant analysis lda and qda establishing independence and conditional independence relations in the context of graphical models and setting confidence intervals on linear functions of the means of the components in recent years many application areas where these tools are used have been dealing with very high dimensional datasets and sample sizes can be very small relative to dimension examples include genetic data brain imaging spectroscopic imaging climate data and many others it is well known by now that the empirical covariance matrix for samples of size n from a p variate gaussian distribution np p is not a good estimator of the population covariance if p is large many results in random matrix theory illustrate this from the classical mary law 29 to the more recent work of johnstone and his students on the theory of the largest eigenvalues 12 23 30 and associated eigenvectors 24 however with the exception of a method for estimating the covariance spectrum 11 these probabilistic results do not offer alternatives to the sample covariance matrix alternative estimators for large covariance matrices have therefore attracted a lot of attention recently two broad classes of covariance estimators have emerged those that rely on a natural ordering among variables and assume that variables

an asymptotic induced scheme for nonstationary transport equations in the diffusive limit an asymptotic induced scheme for nonstationary transport equations with the diffusion scaling is developed the scheme works uniformly for all ranges of mean free paths it is based on the asymptotic analysis of the diffusion limit of the transport equation a theoretical investigation of the behavior of the scheme in the diffusion limit is given and an approximation property is proven moreover numerical results for different physical situations are shown and the uniform convergence of the scheme is established numerically

high dimensional covariance matrix estimation using a factor model abstract high dimensionality comparable to sample size is common in many statistical problems we examine covariance matrix estimation in the asymptotic framework that the dimensionality p tends to as the sample size n increases motivated by the arbitrage pricing theory in finance a multi factor model is employed to reduce dimensionality and to estimate the covariance matrix the factors are observable and the number of factors k is allowed to grow with p we investigate the impact of p and k on the performance of the model based covariance matrix estimator under mild assumptions we have established convergence rates and asymptotic normality of the model based estimator its performance is compared with that of the sample covariance matrix we identify situations under which the factor approach increases performance substantially or marginally the impacts of covariance matrix estimation on optimal portfolio allocation and portfolio risk assessment are studied the asymptotic results are supported by a thorough simulation study

innovated higher criticism for detecting sparse signals in correlated noise higher criticism is a method for detecting signals that are both sparse and weak although first proposed in cases where the noise variables are independent higher criticism also has reasonable performance in settings where those variables are correlated in this paper we show that by exploiting the nature of the correlation performance can be improved by using a modified approach which exploits the potential advantages that correlation has to offer indeed it turns out that the case of independent noise is the most difficult of all from a statistical viewpoint and that more accurate signal detection for a given level of signal sparsity and strength can be obtained when correlation is present we characterize the advantages of correlation by showing how to incorporate them into the definition of an optimal detection boundary the boundary has particularly attractive properties when correlation decays at a polynomial rate or the correlation matrix is toeplitz

an asymptotic preserving automatic domain decomposition method for the vlasov poisson bgk system with applications to plasmas in this work we present an efficient strategy to deal with plasma physics simulations in which localized departures from thermodynamical equilibrium are present the method is based on the introduction of intermediate regions which allows smooth transitions between kinetic and fluid zones in this paper we extend domain decomposition techniques obtained through dynamic coupling and buffer zones to the study of plasmas and moreover we combine them with asymptotic preserving and asymptotically accurate strategies for the time integration we use a hybrid scheme in which both kinetic and fluid descriptions are considered and coupled together while the kinetic model is solved by asymptotic preserving and accurate methods in order to guarantee high efficiency and accuracy in all regimes the numerical scheme is validated and its performances are analyzed by numerical simulations

spatial discretizations for self adjoint forms of the radiative transfer equations there are three commonly recognized second order self adjoint forms of the neutron transport equation the even parity equations the odd parity equations and the self adjoint angular flux equations because all of these equations contain second order spatial derivatives and are self adjoint for the mono energetic case standard continuous finite element discretization techniques have proved quite effective when applied to the spatial variables we first derive analogs of these equations for the case of time dependent radiative transfer the primary unknowns for these equations are functions of the angular intensity rather than the angular flux hence the analog of the self adjoint angular flux equation is referred to as the self adjoint angular intensity equation then we describe a general arbitrary order continuous spatial finite element approach that is applied to each of the three equations in conjunction with backward euler differencing in time we refer to it as the standard technique we also introduce an alternative spatial discretization scheme for the self adjoint angular intensity equation that requires far fewer unknowns than the standard method but appears to give comparable accuracy computational results are given that demonstrate the validity of both of these discretization schemes

on standard h sub spl infin control of processes with a single delay this note presents a frequency domain method to solve the standard h sub spl infin control problem for processes with a single delay for a given bound on the closed loop h sub spl infin norm there exist proper stabilizing controllers that achieve this bound if and only if both the corresponding delay free h sub spl infin problem and an extended nehari problem with a delay or a one block problem are all solvable the solvability of the extended nehari problem or the one block problem is equivalent to the nonsingularity of a delay dependent matrix the solvability conditions of the standard h sub spl infin control problem with a delay are formulated in terms of the existence of solutions to two delay independent algebraic riccati equations and a delay dependent nonsingularity property all suboptimal controllers solving the three problems are respectively parameterized as a structure incorporating a modified smith predictor

symbolic implicit monte carlo radiation transport in the difference formulation a piecewise constant discretization the equations of radiation transport for thermal photons are notoriously difficult to solve in thick media without resorting to asymptotic approximations such as the diffusion limit one source of this difficulty is that in thick absorbing media thermal emission and absorption are almost completely balanced a new formulation for thermal radiation transport called the difference formulation was recently introduced in order to remove the stiff balance between emission and absorption in the new formulation thermal emission is replaced by derivative terms that become small in thick media it was proposed that the difficulties of solving the transport equation in thick media would be ameliorated by the difference formulation while preserving full rigor and accuracy of the transport solution in the streaming limit in this paper the transport equation is solved by the symbolic implicit monte carlo method and comparisons are made between the standard formulation and the difference formulation the method is easily adapted to the derivative source terms of the difference formulation and a remarkable reduction in noise is obtained when the difference formulation is applied to problems involving thick media

adaptive covariance matrix estimation through block thresholding estimation of large covariance matrices has drawn considerable recent attention and the theoretical focus so far has mainly been on developing a minimax theory over a fixed parameter space in this paper we consider adaptive covariance matrix estimation where the goal is to construct a single procedure which is minimax rate optimal simultaneously over each parameter space in a large collection a fully data driven block thresholding estimator is proposed the estimator is constructed by carefully dividing the sample covariance matrix into blocks and then simultaneously estimating the entries in a block by thresholding the estimator is shown to be optimally rate adaptive over a wide range of bandable covariance matrices a simulation study is carried out and shows that the block thresholding estimator performs well numerically some of the technical tools developed in this paper can also be of independent interest

blessing of massive scale spatial graphical model estimation with a total cardinality constraint approach we consider the problem of estimating high dimensional spatial graphical models with a total cardinality constraint i e the ell 0 constraint though this problem is highly nonconvex we show that its primal dual gap diminishes linearly with the dimensionality and provide a convex geometry justification of this blessing of massive scale phenomenon motivated by this result we propose an efficient algorithm to solve the dual problem which is concave and prove that the solution achieves optimal statistical properties extensive numerical results are also provided

asymptotically stable particle in cell methods for the vlasov poisson system with a strong external magnetic field this paper deals with the numerical resolution of the vlasov poisson system with a strong external magnetic field by particle in cell pic methods in this regime classical pic methods are subject to stability constraints on the time and space steps related to the small larmor radius and plasma frequency here we propose an asymptotic preserving pic scheme which is not subjected to these limitations our approach is based on first and higher order semi implicit numerical schemes already validated on dissipative systems s boscarino f filbet and g russo j sci comput 2016 doi 10 1007 s10915 016 0168 y additionally when the magnitude of the external magnetic field becomes large this method provides a consistent pic discretization of the guiding center equation that is an incompressible euler equation in vorticity form we propose several numerical experiments which provide a solid validation of the method and its underlying concepts

frequency domain solution to delay type nehari problem this paper generalizes the frequency domain results on the delay type nehari problem in the stable case to the unstable case the solvability condition of the delay type nehari problem is formulated in terms of the nonsingularity of three matrices the optimal value c o p t is the maximal c 0 such that one of the three matrices becomes singular all sub optimal compensators are parameterized in a transparent structure incorporating a modified smith predictor

adaptive thresholding for sparse covariance matrix estimation in this article we consider estimation of sparse covariance matrices and propose a thresholding procedure that is adaptive to the variability of individual entries the estimators are fully data driven and demonstrate excellent performance both theoretically and numerically it is shown that the estimators adaptively achieve the optimal rate of convergence over a large class of sparse covariance matrices under the spectral norm in contrast the commonly used universal thresholding estimators are shown to be suboptimal over the same parameter spaces support recovery is discussed as well the adaptive thresholding estimators are easy to implement the numerical performance of the estimators is studied using both simulated and real data simulation results demonstrate that the adaptive thresholding estimators uniformly outperform the universal thresholding estimators the method is also illustrated in an analysis on a dataset from a small round blue cell tumor microarray experiment a supplement to this ar

model selection and estimation in the gaussian graphical model summary we propose penalized likelihood methods for estimating the concentration matrix in the gaussian graphical model the methods lead to a sparse and shrinkage estimator of the concentration matrix that is positive definite and thus conduct model selection and estimation simultaneously the implementation of the methods is nontrivial because of the positive definite constraint on the concentration matrix but we show that the computation can be done effectively by taking advantage of the efficient maxdet algorithm developed in convex optimization we propose a bic type criterion for the selection of the tuning parameter in the penalized likelihood methods the connection between our methods and existing methods is illustrated simulations and real examples demonstrate the competitive performance of the new methods

central schemes for balance laws of relaxation type several models in mathematical physics are described by quasi linear hyperbolic systems with source term and in several cases the production term can become stiff here suitable central numerical schemes for such problems are developed and applications to the broadwell model and extended thermodynamics are presented the numerical methods are a generalization of the nessyahu tadmor scheme to the nonhomogeneous case by including the cell averages of the production terms in the discrete balance equations a second order scheme uniformly accurate in the relaxation parameter is derived and its properties analyzed numerical tests confirm the accuracy and robustness of the scheme

a numerical method for kinetic semiconductor equations in the drift diffusion limit an asymptotic induced scheme for kinetic semiconductor equations with the diffusion scaling is developed the scheme is based on the asymptotic analysis of the kinetic semiconductor equation it works uniformly for all ranges of mean free paths the velocity discretization is done using quadrature points equivalent to a moment expansion method numerical results for different physical situations are presented

robust and accurate filtered spherical harmonics expansions for radiative transfer we present a novel application of filters to the spherical harmonics p n expansion for radiative transfer problems in the high energy density regime the filter we use is based on non oscillatory spherical splines and a filter strength chosen to i preserve the equilibrium diffusion limit and ii vanish as the expansion order tends to infinity our implementation is based on modified equations that are derived by applying the filter after every time step in a simple first order time integration scheme the method is readily applied to existing codes that solve the p n equations numerical results demonstrate that the solution to the filtered p n equations are i more robust and less oscillatory than standard p n solutions and ii more accurate than discrete ordinates solutions of comparable order in particular the filtered p 7 solution demonstrates comparable accuracy to an implicit monte carlo solution for a benchmark hohlraum problem in 2d cartesian geometry

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

numerical analysis of time integration errors for nonequilibrium radiation diffusion numerical analysis of time integration errors for nonequilibrium radiation diffusion is considered two first order implicit time integration methods are studied asymptotic analysis and modified equation analysis are applied to both time integration methods numerical experiments are used to highlight the results of the analysis asymptotic analysis is used to highlight the source of temperature spiking when a hot radiation wave propagates into a cold material modified equation analysis is used to provide insight into the thermal wave speed coming from the two different first order methods

piecewise linear discretization of symbolic implicit monte carlo radiation transport in the difference formulation we describe a monte carlo solution for time dependent photon transport in the difference formulation with the material in local thermodynamic equilibrium that is piecewise linear in its treatment of the material state variable our method employs a galerkin solution for the material energy equation while using symbolic implicit monte carlo to solve the transport equation in constructing the scheme one has the freedom to choose between expanding the material temperature or the equivalent black body radiation energy density at the material temperature in terms of finite element basis functions the former provides a linear treatment of the material energy while the latter provides a linear treatment of the radiative coupling between zones subject to the conditional use of a lumped material energy in the vicinity of strong gradients possible with a linear treatment of the material energy our approach provides a robust solution for time dependent transport of thermally emitted radiation that can address a wide range of problems it produces accurate results in thick media

robust controller design for delay systems in the gap metric a robust stabilization problem in the gap metric is discussed for a system with delays in control the authors derive a design procedure of robust controllers based on finite dimensional ricatti equations and it is shown that the resulting controller has a structure of observer based predictive action by employing completing the square argument a game theoretic interpretation is also provided on the trade off between the initial uncertainties and attenuating the disturbance caused by plant uncertainties

a comparison of implicit time integration methods for nonlinear relaxation and diffusion several time integration methods for nonlinear systems are compared all of the time discretizations are based on the method but differ in their treatment of the implicit nonlinear terms one method converges the implicit nonlinear terms to a small tolerance and is often referred to as nonlinearly consistent nc newton s method or its approximation newton krylov is used to converge the nonlinearities the other methods considered are linearized and comparisons are made for a relaxation problem and a radiation diffusion problem the linearized one step method that uses the full jacobian is shown to have similar accuracy as nc methods the lagged linearization method and an extension that is second order accurate are also studied a trunction error analysis complements the numerical results for the relaxation problem it is shown that each of the second order accurate linearized methods may be more accurate than an nc method depending on the degree of nonlinearity in the problem for the radiation diffusion problem in general the nc method is most accurate and allows a larger time step however the linearized methods perfom surprisingly well

radiation transport modeling using extended quadrature method of moments abstract the radiative transfer equation describes the propagation of radiation through a material medium while it provides a highly accurate description of the radiation field the large phase space on which the equation is defined makes it numerically challenging as a consequence significant effort has gone into the development of accurate approximation methods recently an extended quadrature method of moments eqmom has been developed to solve univariate population balance equations which also have a large phase space and thus face similar computational challenges the distinct advantage of the eqmom approach over other moment methods is that it generates moment equations that are consistent with a positive phase space density and has a moment inversion algorithm that is fast and efficient the goal of the current paper is to present the eqmom method in the context of radiation transport to discuss advantages and disadvantages and to demonstrate its performance on a set of standard one dimensional benchmark problems that encompass optically thin thick and transition regimes special attention is given in the implementation to the issue of realizability that is consistency with a positive phase space density numerical results in one dimension are promising and lay the foundation for extending the same framework to multiple dimensions

uniformly accurate diffusive relaxation schemes for multiscale transport equations many transport equations such as the neutron transport radiative transfer and transport equations for waves in random media have a diffusive scaling that leads to the diffusion equations in many physical applications the scaling parameter mean free path may differ in several orders of magnitude from the rarefied regimes to the hydrodynamic diffusive regimes within one problem and it is desirable to develop a class of robust numerical schemes that can work uniformly with respect to this relaxation parameter in an earlier work jin pareschi and toscani siam j numer anal 35 1998 pp 2405 2439 we handled this numerical problem for discrete velocity kinetic models by reformulating the system into a form commonly used for a relaxation scheme for conservation laws jin and xin comm pure appl math 48 1995 pp 235 277 such a reformulation allows us to use the splitting technique for relaxation schemes to design a class of implicit yet explicitly implementable schemes that work with high resolution uniformly with respect to the relaxation parameter in this paper we show that such a numerical technique can be applied to a large class of transport equations with continuous velocities when one uses the even and odd parities of the transport equation

a linear stability analysis for nonlinear grey thermal radiative transfer problems we present a new linear stability analysis of three time discretizations and monte carlo interpretations of the nonlinear grey thermal radiative transfer trt equations the widely used implicit monte carlo imc equations the carter forest cf equations and the ahrens larsen or semi analog monte carlo smc equations using a spatial fourier analysis of the 1 d implicit monte carlo imc equations that are linearized about an equilibrium solution we show that the imc equations are unconditionally stable undamped perturbations do not exist if the imc time discretization parameter satisfies 0 5 1 this is consistent with conventional wisdom however we also show that for sufficiently large time steps unphysical damped oscillations can exist that correspond to the lowest frequency fourier modes after numerically confirming this result we develop a method to assess the stability of any time discretization of the 0 d nonlinear grey thermal radiative transfer problem subsequent analyses of the cf and smc methods then demonstrate that the cf method is unconditionally stable and monotonic but the smc method is conditionally stable and permits unphysical oscillatory solutions that can prevent it from reaching equilibrium this stability theory provides new conditions on the time step to guarantee monotonicity of the imc solution although they are likely too conservative to be used in practice theoretical predictions are tested and confirmed with numerical experiments

estimating sparse precision matrix optimal rates of convergence and adaptive estimation precision matrix is of significant importance in a wide range of applications in multivariate analysis this paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting optimal rates of convergence are established for a range of matrix norm losses a fully data driven estimator based on adaptive constrained l1 minimization is proposed and its rate of convergence is obtained over a collection of parameter spaces the estimator called aclime is easy to implement and performs well numerically a major step in establishing the minimax rate of convergence is the derivation of a rate sharp lower bound a two directional lower bound technique is applied to obtain the minimax lower bound the upper and lower bounds together yield the optimal rates of convergence for sparse precision matrix estimation and show that the aclime estimator is adaptively minimax rate optimal for a collection of parameter spaces and a range of matrix norm losses simultaneously

control of systems with i o delay via reduction to a one block problem in this paper the standard four block h sup spl infin control problem for systems with a single delay in the feedback loop is studied a simple procedure of the reduction of the problem to an equivalent one block problem having particularly simple structure is proposed the one block problem is then solved by the j spectral factorization approach resulting in the so called dead time compensator dtc form of the controller the advantages of the proposed procedure are its simplicity intuitively clear derivation of the dtc form of the h sup spl infin controller and extensibility to the multiple delay case

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

gaussian graphical model estimation with false discovery rate control this paper studies the estimation of a high dimensional gaussian graphical model ggm typically the existing methods depend on regularization techniques as a result it is necessary to choose the regularized parameter however the precise relationship between the regularized parameter and the number of false edges in ggm estimation is unclear in this paper we propose an alternative method by a multiple testing procedure based on our new test statistics for conditional dependence we propose a simultaneous testing procedure for conditional dependence in ggm our method can control the false discovery rate fdr asymptotically the numerical performance of the proposed method shows that our method works quite well

nonconcave penalized likelihood with a diverging number of parameters a class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by fan and li to simultaneously estimate parameters and select important variables they demonstrated that this class of procedures has an oracle property when the number of parameters is finite however in most model selection problems the number of parameters should be large and grow with the sample size in this paper some asymptotic properties of the nonconcave penalized likelihood are established for situations in which the number of parameters tends to as the sample size increases under regularity conditions we have established an oracle property and the asymptotic normality of the penalized likelihood estimators furthermore the consistency of the sandwich formula of the covariance matrix is demonstrated nonconcave penalized likelihood ratio statistics are discussed and their asymptotic distributions under the null hypothesis are obtained by imposing some mild conditions on the penalty functions the asymptotic results are augmented by a simulation study and the newly developed methodology is illustrated by an analysis of a court case on the sexual discrimination of salary

asymptotic diffusion limit of cell temperature discretisation schemes for thermal radiation transport abstract this paper attempts to unify the asymptotic diffusion limit analysis of thermal radiation transport schemes for a linear discontinuous representation of the material temperature reconstructed from cell centred temperature unknowns in a process known as source tilting the asymptotic limits of both monte carlo continuous in space and deterministic approaches based on linear discontinuous finite elements for solving the transport equation are investigated in slab geometry the resulting discrete diffusion equations are found to have nonphysical terms that are proportional to any cell edge discontinuity in the temperature representation based on this analysis it is possible to design accurate schemes for representing the material temperature for coupling thermal radiation transport codes to a cell centred representation of internal energy favoured by ale arbitrary lagrange eulerian hydrodynamics schemes

moment closures based on minimizing the residual of the pn angular expansion in radiation transport in this work we present two new closures for the spherical harmonics p n method in slab geometry transport problems our approach begins with an analysis of the squared residual of the transport equation where we show that the standard truncation and diffusive closures do not minimize the residual of the p n expansion based on this analysis we derive two models a moment limited diffusive ml d n closure and a transient p n tp n closure that attempt to address shortcomings of common closures the form of these closures is similar to flux limiters for diffusion with the addition of a time derivative in the definition of the closure numerical results on a pulsed plane source problem the gordian knot of slab geometry transport problems indicate that our new closure outperforms existing linear closures additionally on a deep penetration problem we demonstrate that the tp n closure does not suffer from the artificial shocks that can arise in the m n entropy based closure finally results for reed s problem demonstrate that the tp n solution is as accurate as the p n 3 solution we further extend the t p n closure to 2d cartesian geometry the line source test problem demonstrates the model effectively damps oscillations and negative densities

asymptotic normality and optimalities in estimation of large gaussian graphical models the gaussian graphical model a popular paradigm for studying relationship among variables in a wide range of applications has attracted great attention in recent years this paper considers a fundamental question when is it possible to estimate low dimensional parameters at parametric square root rate in a large gaussian graphical model a novel regression approach is proposed to obtain asymptotically efficient estimation of each entry of a precision matrix under a sparseness condition relative to the sample size when the precision matrix is not sufficiently sparse or equivalently the sample size is not sufficiently large a lower bound is established to show that it is no longer possible to achieve the parametric rate in the estimation of each entry this lower bound result which provides an answer to the delicate sample size question is established with a novel construction of a subset of sparse precision matrices in an application of le cam s lemma moreover the proposed estimator is proven to have optimal convergence rate when the parametric rate cannot be achieved under a minimal sample requirement the proposed estimator is applied to test the presence of an edge in the gaussian graphical model or to recover the support of the entire model to obtain adaptive rate optimal estimation of the entire precision matrix as measured by the matrix ell q operator norm and to make inference in latent variables in the graphical model all of this is achieved under a sparsity condition on the precision matrix and a side condition on the range of its spectrum this significantly relaxes the commonly imposed uniform signal strength condition on the precision matrix irrepresentability condition on the hessian tensor operator of the covariance matrix or the ell 1 constraint on the precision matrix numerical results confirm our theoretical findings the roc curve of the proposed algorithm asymptotic normal thresholding ant for support recovery significantly outperforms that of the popular glasso algorithm

a high order asymptotic preserving scheme for kinetic equations using projective integration we investigate a high order fully explicit asymptotic preserving scheme for a kinetic equation with linear relaxation both in the hydrodynamic and diffusive scalings in which a hyperbolic resp parabolic limiting equation exists the scheme first takes a few small inner steps with a simple explicit method such as direct forward euler to damp out the stiff components of the solution and estimate the time derivative of the slow components these estimated time derivatives are then used in an outer runge kutta method of arbitrary order we show that with an appropriate choice of inner step size the time step restriction on the outer time step is similar to the stability condition for the limiting macroscopic equation moreover the number of inner time steps is also independent of the scaling parameter we analyze stability and consistency and illustrate with numerical results

uniform stability of a finite difference scheme for transport equations in diffusive regimes an asymptotic preserving numerical scheme with respect to diffusion scalings for a linear transport equation is investigated the scheme is adopted from a class of schemes developed in s jin l pareschi and g toscani siam j numer anal 38 2000 pp 913 936 and a klar siam j numer anal 35 1998 pp 1073 1094 stability is proven uniformly in the mean free path under a cfl type condition turning into a parabolic cfl condition in the diffusion limit

technical communique j spectral factorization of regular para hermitian transfer matrices this paper characterizes a class of regular para hermitian transfer matrices and then reveals the elementary characteristics of j spectral factorization for this class a transfer matrix l in this class admits a j spectral factorization if and only if there exists a common nonsingular matrix to similarly transform the a matrices of l and l 1 resp into 2x2 lower upper resp triangular block matrices with the 1 1 block including all the stable modes of l l 1 resp for a transfer matrix in a smaller subset this nonsingular matrix is formulated in terms of the stabilizing solutions of two algebraic riccati equations the j spectral factor is formulated in terms of the original realization of the transfer matrix

explicit formulas for optimally robust controllers for delay systems this paper considers single input single output systems whose transfer functions take the form of a strictly proper rational function times a delay a closed form expression is presented for the controller which is optimally robust with respect to perturbations measured in the gap metric the formula allows the h sub spl infin loop shaping procedure of glover mcfarlane to be carried out explicitly for this class of systems without the need to first find a rational approximation of the plant the form of the controller involves a certain algebra of pseudo derivation operators these operators and their matrix generalizations play a central role in the derivation of the controller a discussion of the main properties of these operators is given an example is presented of a controller design to achieve disturbance attenuation and robust set point following for a plant with two lightly damped poles and a nontrivial time delay the performance is compared and shown to be superior to that of a smith predictor

partial correlation estimation by joint sparse regression models this article features online supplementary material in this article we propose a computationally efficient approach space sparse partial correlation estimation for selecting nonzero partial correlations under the high dimension low sample size setting this method assumes the overall sparsity of the partial correlation matrix and employs sparse regression techniques for model fitting we illustrate the performance of space by extensive simulation studies it is shown that space performs well in both nonzero partial correlation selection and the identification of hub variables and also outperforms two existing methods we then apply space to a microarray breast cancer dataset and identify a set of hub genes that may provide important insights on genetic regulatory networks finally we prove that under a set of suitable assumptions the proposed procedure is asymptotically consistent in terms of model selection and parameter estimation

the standard h sub spl infin problem in systems with a single input delay the standard h sub spl infin problem is solved for lti systems with a single pure input lag the solution is based on state space analysis mixing a finite dimensional and an abstract evolution model utilizing the relatively simple structure of these distributed systems the associated operator riccati equations are reduced to a combination of two algebraic riccati equations and one differential riccati equation over the delay interval the results easily extend to finite time and time varying problems where the algebraic riccati equations are substituted by differential riccati equations over the process time duration

robust control in the gap a state space solution in the presence of a single input delay a solution is provided to the problem of sub optimal robust design in the gap for a system with a single input lag the problem is shown to reduce to two matrix algebraic riccati equations that solve an allied linear quadratic gaussian h sub 2 problem and a parameterized differential matrix riccati equation the analysis intertwines finite dimensional delay equations and distributed abstract evolution models the parameterized family of suboptimal compensators is presented in terms of a neutral equation model

on spl hscr sub spl infin control for dead time systems a mixed sensitivity spl hscr sub spl infin problem is solved for dead time systems it is shown that for a given bound on the spl hscr sub spl infin norm causal stabilizing controllers exist that achieve this bound if and only if a related finite dimensional riccati equation has a solution with a certain nonsingularity property in the case of zero time delay the riccati equation is a standard riccati equation and the nonsingularity condition is that the solution be nonnegative definite for nonzero time delay the nonsingularity condition is more involved but still allows us to obtain controllers all suboptimal controllers are parameterized and the central controller is shown to be a feedback interconnection of a finite dimensional system and a finite memory system both of which can be implemented some spl hscr sub spl infin problems are rewritten as pure rational spl hscr sub spl infin problems using a smith predictor parameterization of the controller

h controller synthesis by j lossless coprime factorization this paper develops a coprime factorization approach to the synthesis of internally stabilizing controllers for a given system such that the mathcal h infty norm of the closed loop is strictly less than a given bound by the use of coprime factorizations it is shown that the mathcal h infty control problem is fundamentally related to the so called analytic systems considered by helton et al regional conference series in mathematics 68 1987 such problems admit a solution if and only if a certain j lossless factorization exists interpreted in the mathcal h infty control context this means that for a controller of the requisite type to exist the plant must admit a certain j lossless coprime factorization the full mathcal h infty synthesis problem requires that two nested j lossless factorizations exist the results are independent of whether discrete time or continuous time systems are being considered it is then shown that j lossless factorization is equivalent to the existen

analysis of a monte carlo method for nonlinear radiative transfer it has recently been proved that solutions of nonlinear radiative transfer problems satisfy a maximum principle andreev kozmanov and rachilov u s s r comput math math phys 23 104 1983 mercier siam j math anal in press in this article it is shown that monte carlo solutions of such problems obtained using the method of fleck and cummings j comput phys 8 313 1971 must satisfy this maximum principle for sufficiently small time steps but can violate it for sufficiently large time steps analyses of the frequency dependent and grey cases are given and a numerical solution violating the maximum principle is discussed

h2 optimal control of systems with multiple i o delays time domain approach in this paper the h 2 optimal control problem of systems with multiple i o delays is presented the problem is first converted to an equivalent h 2 regulator problem with multiple delays the idea is to view the regulator problem in time domain as a linear quadratic regulator problem with multiple input delays it is shown that the rational part of the optimal controller has the same dimension as the plant and the non rational part may be chosen to have finite impulse response furthermore the regulator problem solution is also used to solve the h 2 filtering problem with multiple measurement delays

second order discretization in space and time for radiation hydrodynamics second order accurate discretizations for radiation hydrodynamics are currently an area of interest in the high energy density laboratory physics and astrophysics communities second order methods used to solve the hydrodynamics equations and second order methods used to solve the radiation transport equation often differ fundamentally making it difficult to combine them in a second order manner here we present an implicitexplicit imex method for solving the 1d equations of radiation hydrodynamics that is second order accurate in space and time our radiation hydrodynamics model consists of the 1d euler equations coupled with a gray radiation s2 approximation our rh method combines the muscl hancock method for solving the euler equations with the tr bdf2 time integration scheme and the linear discontinuous galerkin finite element spatial discretization scheme for the s2 radiation equations the muscl hancock method is commonly used for hydrodynamic calculations and the linear discontinuous galerkin scheme is the standard for the sn equations of radiative transfer while somewhat similar these schemes vary fundamentally with respect to the treatment of spatial slopes we address the challenges inherent to coupling these different numerical methods and demonstrate how these challenges can be overcome using the method of manufactured solutions we show that the method is second order accurate in space and time for both the equilibrium diffusion and streaming limit and we show that the method is capable of computing radiative shock solutions accurately by comparing our results with semi analytic solutions

regularized estimation of large covariance matrices this paper considers estimating a covariance matrix of p variables from n observations by either banding the sample covariance matrix or estimating a banded version of the inverse of the covariance we show that these estimates are consistent in the operator norm as long as logp 2 n 0 and obtain explicit rates the results are uniform over some fairly natural well conditioned families of covariance matrices we also introduce an analogue of the gaussian white noise model and show that if the population covariance is embeddable in that model and well conditioned then the banded approximations produce consistent estimates of the eigenvalues and associated eigenvectors of the covariance matrix the results can be extended to smooth versions of banding and to non gaussian distributions with su ciently short tails a resampling approach is proposed for choosing the banding parameter in practice this approach is illustrated numerically on both simulated and real data

nonoscillatory high order accurate self similar maximum principle satisfying shock capturing schemes i this is the first paper in a series in which a class of nonoscillatory high order accurate self similar local maximum principle satisfying in scalar conservation law shock capturing schemes for solving multidimensional systems of conservation laws are constructed and analyzed in this paper a scheme which is of third order of accuracy in the sense of flux approximation is presented using scalar one dimensional initial value problems as a model for this model the schemes are made to satisfy a local maximum principle and a nonoscillatory property the method uses a simple centered stencil with quadratic reconstruction followed by two modifications imposed as needed the first enforces a local maximum principle the second guarantees that no new extrema develop the schemes are self similar in the sense that the numerical flux does not depend explicitly on the grid size i e there are no grid size dependent limits involving free parameters as in e g math comp 49 1987 pp 105 121 math comp

asymptotic analysis of a computational method for time and frequency dependent radiative transfer we consider a time dependent energy dependent nonlinear radiative transfer problem in which opacities are large o 1 and interior sources are small o an asymptotic analysis of this problem as 0 leads to the equilibrium diffusion equation in the interior of the system along with boundary conditions and initial conditions for this equation we apply the same asymptotic analysis to a discrete version of the problem in which the frequency variable is discretized by the multigroup method the direction variable by the discrete ordinates method the time variable by the fully implicit method and the spatial variable by a subcell balance method we find that as 0 the discrete solution satisfies a robust discretized version of the correct equilibrium diffusion equation with boundary conditions and initial conditions that are remarkably accurate the analysis thus predicts that if a spatial grid is chosen that resolves interior temperature gradients then the numerical method obtains an accurate solution in the interior of the system even though the optical thickness of the spatial cells tends to and boundary layers in the transport solution are not resolved we go a step further to analyze problems that are optically thin at some photon frequencies but thick at others and show that once again the discrete solution is remarkably accurate we present numerical results that verify these and other predictions of the analyses

innovated scalable efficient estimation in ultra large gaussian graphical models large scale precision matrix estimation is of fundamental importance yet challenging in many contemporary applications for recovering gaussian graphical models in this paper we suggest a new approach of innovated scalable efficient estimation isee for estimating large precision matrix motivated by the innovated transformation we convert the original problem into that of large covariance matrix estimation the suggested method combines the strengths of recent advances in high dimensional sparse modeling and large covariance matrix estimation compared to existing approaches our method is scalable and can deal with much larger precision matrices with simple tuning under mild regularity conditions we establish that this procedure can recover the underlying graphical structure with significant probability and provide efficient estimation of link strengths both computational and theoretical advantages of the procedure are evidenced through simulation and real data examples

semi implicit time integration for pn thermal radiative transfer implicit time integration involving the solution of large systems of equations is the current paradigm for time dependent radiative transfer in this paper we present a semi implicit linear discontinuous galerkin method for the spherical harmonics p n equations for thermal radiative transfer in planar geometry our method is novel in that the material coupling terms are treated implicitly via linearizing the emission source and the streaming operator is treated explicitly using a second order accurate runge kutta method the benefit of this approach is that each time step only involves the solution of equations that are local to each cell this benefit comes at the cost of having the time step limited by a cfl condition based on the speed of light to guarantee positivity and avoid artificial oscillations we use a slope limiting technique we present analysis and numerical results that show the method is robust in the diffusion limit when the photon mean free path is not resolved by the spatial mesh also in the diffusion limit the time step restriction relaxes to a less restrictive explicit diffusion cfl condition we demonstrate with numerical results that away from the diffusion limit our method demonstrates second order error convergence as the spatial mesh is refined with a fixed cfl number

asymptotic analysis of the spatial discretization of radiation absorption and re emission in implicit monte carlo we perform an asymptotic analysis of the spatial discretization of radiation absorption and re emission in implicit monte carlo imc a monte carlo technique for simulating nonlinear radiative transfer specifically we examine the approximation of absorption and re emission by a spatially continuous artificial scattering process and either a piecewise constant or piecewise linear emission source within each spatial cell we consider three asymptotic scalings representing i a time step that resolves the mean free time ii a courant limit on the time step size and iii a fixed time step that does not depend on any asymptotic scaling for the piecewise constant approximation we show that only the third scaling results in a valid discretization of the proper diffusion equation which implies that imc may generate inaccurate solutions with optically large spatial cells if time steps are refined however we also demonstrate that for a certain class of problems the piecewise linear approximation yields an appropriate discretized diffusion equation under all three scalings we therefore expect imc to produce accurate solutions for a wider range of time step sizes when the piecewise linear instead of piecewise constant discretization is employed we demonstrate the validity of our analysis with a set of numerical examples

high dimensional classification using features annealed independence rules classification using high dimensional features arises frequently in many contemporary statistical studies such as tumor classification using microarray or other high throughput data the impact of dimensionality on classifications is largely poorly understood in a seminal paper bickel and levina 2004 show that the fisher discriminant performs poorly due to diverging spectra and they propose to use the independence rule to overcome the problem we first demonstrate that even for the independence classification rule classification using all the features can be as bad as the random guessing due to noise accumulation in estimating population centroids in high dimensional feature space in fact we demonstrate further that almost all linear discriminants can perform as bad as the random guessing thus it is paramountly important to select a subset of important features for high dimensional classification resulting in features annealed independence rules fair the conditions under which all the important features can be selected by the two sample t statistic are established the choice of the optimal number of features or equivalently the threshold value of the test statistics are proposed based on an upper bound of the classification error simulation studies and real data analysis support our theoretical results and demonstrate convincingly the advantage of our new classification procedure

sparse precision matrix estimation via lasso penalized d trace loss we introduce a constrained empirical loss minimization framework for estimating high dimensional sparse precision matrices and propose a new loss function called the d trace loss for that purpose a novel sparse precision matrix estimator is defined as the minimizer of the lasso penalized d trace loss under a positive definiteness constraint under a new irrepresentability condition the lasso penalized d trace estimator is shown to have the sparse recovery property examples demonstrate that the new condition can hold in situations where the irrepresentability condition for the lasso penalized gaussian likelihood estimator fails we establish rates of convergence for the new estimator in the elementwise maximum frobenius and operator norms we develop a very efficient algorithm based on alternating direction methods for computing the proposed estimator simulated and real data are used to demonstrate the computational efficiency of our algorithm and the finite sample performance of the new estimator the lasso penalized d trace estimator is found to compare favourably with the lasso penalized gaussian likelihood estimator

relaxation schemes for nonlinear kinetic equations a class of numerical schemes for nonlinear kinetic equations of boltzmann type is described following wild s approach the solution is represented as a power series with parameter depending exponentially on the knudsen number this permits us to derive accurate and stable time discretizations for all ranges of the mean free path these schemes preserve the main physical properties positivity conservation of mass momentum and energy moreover for some particular models the entropy property is also shown to hold

stability analysis of a multilevel quasidiffusion method for thermal radiative transfer problems abstract in this paper we analyze a multilevel quasidiffusion qd method for solving time dependent multigroup nonlinear radiative transfer problems which describe interaction of photons with matter the multilevel method is formulated by means of the high order radiative transfer equation and a set of low order moment equations the fully implicit scheme is used to discretize equations in time the stability analysis is applied to the method in semi continuous and discretized forms to perform fourier analysis the system of equations of the multilevel method is linearized about an equilibrium solution the effects of discretization with respect to different independent variables are studied the multilevel method is shown to be stable and fast converging we also consider a version of the method in which time evolution in the radiative transfer equation is treated by means of the approximation the fleck cummings test problem is used to demonstrate performance of the multilevel qd method and study its iterative stability

asymptotic preserving implicit explicit runge kutta methods for nonlinear kinetic equations we discuss implicit explicit imex runge kutta methods which are particularly adapted to stiff kinetic equations of boltzmann type we consider both the case of easy invertible collision operators and the challenging case of boltzmann collision operators we give sufficient conditions in order that such methods are asymptotic preserving and asymptotically accurate their monotonicity properties are also studied in the case of the boltzmann operator the methods are based on the introduction of a penalization technique for the collision integral this reformulation of the collision operator permits us to construct penalized imex schemes which work uniformly for a wide range of relaxation times avoiding the expensive implicit resolution of the collision operator finally we show some numerical results which confirm the theoretical analysis

the effects of slope limiting on asymptotic preserving numerical methods for hyperbolic conservation laws many hyperbolic systems of equations with stiff relaxation terms reduce to a parabolic description when relaxation dominates an asymptotic preserving numerical method is a discretization of the hyperbolic system that becomes a valid discretization of the parabolic system in the asymptotic limit we explore the consequences of applying a slope limiter to the discontinuous galerkin dg method with linear elements for hyperbolic systems with stiff relaxation terms without a limiter the dg method gives an accurate discretization of the chapman enskog approximation of the system when the relaxation length scale is not resolved it is well known that the first order upwind or step method fails to obtain the proper asymptotic limit we show that using the minmod slope limiter also fails but that using double minmod gives the proper asymptotic limit despite its effectiveness in the asymptotic limit the double minmod limiter allows artificial extrema at cell interfaces referred to as sawteeth we present a limiter that eliminates the sawteeth but maintains the proper asymptotic limit the systems that we analyze are the hyperbolic heat equation and the p n thermal radiation equations numerical examples are used to verify our analysis

finite rank criteria for h infty control of infinite dimensional systems this paper studies the hinfin control of infinite dimensional systems whose transfer matrices are expressible as a series connection of a rational transfer matrix and a scalar possibly irrational inner function this class of systems is adequate for describing many control problems in practice when weighting functions are rational and plants have at most finitely many unstable modes we show that this problem can be reduced to solving two matrix valued riccati equations and an additional rank condition furthermore the obtained controller structure is characterized by the inner function and controllers for the finite dimensional part this result provides us with a solution that is easily implementable without much prior knowledge on infinite dimensional control theory a numerical example is given to illustrate the result

positive p_n closures we introduce a modification to the standard spherical harmonic closure used with linear kinetic equations of particle transport while the standard closure is known to produce negative particle concentrations the modification corrects this defect by requiring that the ansatz used to close the equations itself be a nonnegative function we impose this requirement via explicit constraints in a quadratic optimization problem