an efficient method for simulation of noisy coupled multi dimensional oscillators we present an efficient computational method for the study of populations of noisy coupled oscillators by taking a population density approach in which the probability density of observing an oscillator at a point of state space is the primary variable instead of the states of all of the oscillators we are able to seamlessly account for intrinsic noise within the oscillators and global coupling within the population the population is assumed to consist of a large number of oscillators so that the noise process is well sampled over the population our numerical method is able to solve the governing equation even in the challenging case of limit cycle oscillators with a large number of state variables instead of simulating a prohibitive number of oscillators our particle method simulates relatively few particles allowing for the efficient solution of the governing equation

vortex methods and vortex motion vortex phenomena in fluid flows and the experimental theoretical and numerical methods used to characterize them are discussed in reviews by leading experts chapters are devoted to an overview of vortex methods the convergence of vortex methods graphic displays from numerical simulations physical vortex visualizations the four principles of vortex motion the visualization and computation of hovering mode vortex dynamics turbulence and vortices in superfluid he and statistical mechanics approaches to vortices and turbulence extensive photographs and sample computer graphics are provided

intertwining operators into dolbeault cohomology representations let gl be the quotient of a semisimple lie group g by the centralizer l of a torus the space of dolbeault cohomology sections of a holomorphic line bundle over gl is a natural place to realize interesting irreducible unitary representations of g and was first studied for this purpose by bott and schmid zuckerman and vogan later introduced derived functor modules to provide an algebraic analog of these representations the authors give a nonzero integral intertwining operator from derived functor modules realized in the langlands classification to the dolbeault cohomology representations under the assumption that l and g have the same real rank

the weighted particle method for convection diffusion equations ii the anisotropic case on etend la methode particulaire utilisee dans la partie i pour les equations de convection diffusion aux operateurs de diffusion anisotrope des conditions plus complexes que dans le cas isotrope sont exigees pour les fonctions de cutoff une analyse d erreur detaillee est effectuee

two geometric character formulas for reductive lie groups in this paper we prove two formulas for the characters of representations of reductive groups both express the character of a representation in terms of the same geometric data attached to when specialized to the case of a compact lie group one of them reduces to kirillov s character formula in the compact case and the other to an application of the atiyah bott fixed point formula to the borel weil realization of the representation to set the stage let us first recall the borel weil theorem for a connected compact lie group gr for simplicity we assume that gr is simply connected we let gr denote its lie algebra and g c r gr the complexified lie algebra via the adjoint action gr operates on igr the space of all r linear functions gr ir every gr orbit in igr coadjoint orbit for short carries a canonical grinvariant symplectic structure the orbit is said to be integral if some or equivalently any exponentiates to a character e of the isotropy subgroup gr in that case the one dimensional representation spaces of the characters e fit together into a gr equivariant real algebraic hermitian line bundle l the pair l carries a unique positive polarization a gr invariant complex structure on the manifold and the structure of a gr equivariant holomorphic line bundle on l positive in the sense of algebraic geometry the hypothesis of simple connectivity ensures that the square root k of the canonical bundle k exists as a gr equivariant holomorphic line bundle according to the borel weil theorem the natural action of gr on the space of holomorphic l valued half forms h0 o k l is irreducible moreover the association h0 o k l 1 1

population density approach for discrete mrna distributions in generalized switching models for stochastic gene expression we present a generalization of a population density approach for modeling and analysis of stochastic gene expression in the model the gene of interest fluctuates stochastically between an inactive state in which transcription cannot occur and an active state in which discrete transcription events occur and the individual mrna molecules are degraded stochastically in an independent manner this sort of model in simplest form with exponential dwell times has been used to explain experimental estimates of the discrete distribution of random mrna copy number in our generalization the random dwell times in the inactive and active states t 0 and t 1 respectively are independent random variables drawn from any specified distributions consequently the probability per unit time of switching out of a state depends on the time since entering that state our method exploits a connection between the fully discrete random process and a related continuous process we present numerical methods for computing steady state mrna distributions and an analytical derivation of the mrna autocovariance function we find that empirical estimates of the steady state mrna probability mass function from monte carlo simulations of laboratory data do not allow one to distinguish between underlying models with exponential and nonexponential dwell times in some relevant parameter regimes however in these parameter regimes and where the autocovariance function has negative lobes the autocovariance function disambiguates the two types of models our results strongly suggest that temporal data beyond the autocovariance function is required in general to characterize gene switching

localization and standard modules for real semisimple lie groups i the duality theorem in this paper we relate two constructions of representations of semisimple lie groups constructions that appear quite different at first glance homogeneous vector bundles are one source of representations if a real semisimple lie group go acts on a vector bundle e m over a quotient space m go ho then go acts also on the space of sections c m e and on any subspace vcc m e defined by a go invariant system of differential equations ordinary induction so called cohomological induction and the construction of representations by quantizat ion all fit into the framework of homogeneous vector bundles for any complex semisimple lie algebra g there is an equivalence of categories due to beilinson bernstein 1 between modules on the one hand and sheaves of modules over the flag variety x of g on the other in the context of real semisimple lie groups this equivalence of categories associates infinitesimal representations to orbits in the flag variety of the complexified lie algebra orbits not of the group go itself but of the complexification of maximal compact subgroup ko c go we shall show that these beilinson bernstein modules are naturally dual to modules attached to certain homogeneous vector bundles in the special case of a compact group both the beilinson bernstein construction and the construction via homogeneous vector bundles reduce to the borel weil bott theorem our duality theorem is then a particular instance of serre duality

a finite volume eulerian lagrangian localized adjoint method for solution of the contaminant transport equations in two dimensional multiphase flow systems an eulerian lagrangian localized adjoint method ellam numerical solution is developed for the multiphase contaminant transport equations in two dimensions the ellam uses finite volume test functions in the space time domain defined by the characteristics of the hyperbolic part of the governing equation the use of the characteristics results in an approximation that allows large time steps while still maintaining accurate solutions this greatly reduces the computational effort required to find solutions to the advection dispersion equation combination of the finite volume test functions with the conservative form of the governing equation results in a local conservation of mass property for problems with a constant saturation such as that of contaminant transport in the saturated zone this property is highly advantageous as the resulting numerical approximation conserves mass both globally and locally for problems with a variable saturation the requirement of local conservation of mass is too stringent particularly around first type boundaries where oscillations can occur because of errors inherent in the numerical determination of fluid velocities and in the backtracking routine a combined conservative nonconservative ellam is developed with an ellam formulation based on the nonconservative form of the governing equation being applied to subdomains intersecting first type boundaries and a conservative ellam being used for all other subdomains the combined conservative nonconservative ellam is compared to a galerkin finite element scheme and is found to have greatly superior performance requiring far fewer time steps to obtain a solution of equivalent accuracy

an ellam scheme for advection diffusion equations in two dimensions we develop an eulerian lagrangian localized adjoint method ellam to solve two dimensional advection diffusion equations with all combinations of inflow and outflow dirichlet neumann and flux boundary conditions the ellam formalism provides a systematic framework for implementation of general boundary conditions leading to mass conservative numerical schemes the computational advantages of the ellam approximation have been demonstrated for a number of one dimensional transport systems practical implementations of ellam schemes in multiple spatial dimensions that require careful algorithm development are discussed in detail in this paper extensive numerical results are presented to compare the ellam scheme with many widely used numerical methods and to demonstrate the strength of the ellam scheme

numerical analyses of operator splitting algorithms for the two dimensional advection diffusion equation abstract holly and preissmann s hp scheme has been the basis of a large number of operator splitting algorithms for the solution of the advection diffusion equation however these algorithms including hp are first order accurate in time due to splitting errors error analyses of these algorithms incorporating splitting error and errors resulting from numerical solutions of the split advection and diffusion equations are lacking in this paper error analysis of a second order accurate adaptation of the hp scheme ahp is presented for the two dimensional advection diffusion equation a modified ahp scheme mahp is suggested to remove the ad hoc nature of boundary conditions during the diffusion step of computations in both hp and ahp as boundary conditions specified for the advection diffusion equation are not applicable to the split equations second order accurate boundary conditions for the split advection and diffusion equations are derived an analysis of numerical dispersion and dissipation associated with the numerical procedure for the advection equation is presented the analysis establishes a criterion so that computational errors are small in two dimensional advection dominated transport problems several numerical examples are presented to verify the numerical analyses presented in the paper in addition a review of the current status of operator splitting algorithms for the advection diffusion equation is presented the objective of the review is to identify the issues that have not been addressed in the previous studies

intermediate boundary conditions for time split methods applied to hyperbolic partial differential equations determination des conditions aux limites intermediaires appropriees pour les methodes de decomposition appliquees aux equations aux derivees partielles hyperboliques

nonparametric neyman scott problems telescoping product methods summary in this paper we consider some generalizations of the neyman scott problem of estimating a common variance in the presence of infinitely many mean nuisance parameters for example suppose observations are independent and stratified such that they have common distribution of the form f x lk within the kth stratum if both f and the location parameters glk are unknown then estimates for f obtained by centring the samples in each stratum and constructing an estimate directly from the pooled centred samples are generally inconsistent unless the stratum sizes go to infinity similarly nuisance parameters can arise from an exponential tilt of a common unknown distribution analogous estimators for the distribution produced by tilting the data and pooling the strata will be inconsistent for similar reasons to the location parameter problem in this paper we concentrate on the case where the stratum sizes are fixed and propose a method for the estimation of f using telescoping products partially multiplicative functions are introduced as a tool for the construction of counterexamples to the consistent estimation of f

on the phase reduction and response dynamics of neural oscillator populations weundertake a probabilistic analysis of the response of repetitively firing neural populations to simple pulselike stimuli recalling and extending results from the literature we compute phase response curves prcs valid near bifurcations to periodic firing for hindmarsh rose hodgkin huxley fitzhugh nagumo and morris lecar models encompassing the four generic codimension one bifurcations phase density equations are then used to analyze the role of the bifurcation and the resulting prc in responses to stimuli in particular we explore the interplay among stimulus duration baseline firing frequency and population level response patterns we interpret the results in terms of the signal processing measure of gain and discuss further applications and experimentally testable predictions

characterization of distributions from maximal invariant statistics g w brown yu v prokhorov l bondesson and others have developed characterization results for maximal invariant statistics such results show that it is possible to construct tests to distinguish between types of distributions in this paper these results are proved for a large number of cases that arise in particular in spatial statistics and directional statistics the class of n collected distributions n 3 is introduced it is proved that if a distribution is n collected then a sample of size n has sufficient information to distinguish the type of the distribution in other words the distribution of the maximal invariant characterizes type

the stein condition for cycle spaces of open orbits on complex flag manifolds the g orbit structure of x is well understood see 13 there are only finitely many orbits in particular there are open orbits if x e x let px be the corresponding parabolic subalgebra of g that is if x gp then px ad g p let denote the complex conjugation of gc over g then px n px contains a cartan subalgebra of g of the form io or c where ho is a cartan subalgebra of go let a a g denote the root system fix

geometric quantization and derived functor modules for semisimple lie groups abstract let g be a semisimple lie group g the complexified lie algebra and x the flag variety of g the mechanism of geometric quantization suggests that the various g orbits in x should give rise to representations of g on the other hand zuckerman s derived functor construction attaches algebraic representations of g to g orbits in this paper we show that geometric quantization leads to frechet representations of finite length which are the maximal globalizations of the derived functor modules we give two alternate realizations of the representations as cohomology spaces of b complexes with hyperfunction coefficients and as local cohomology groups along g orbits in x we use the latter realization to implement the duality between the derived functor modules and the beilinson bernstein modules as cup product between local cohomology group followed by evaluation over the fundamental cycle

on the treatment of time dependent boundary conditions in splitting methods for parabolic differential equations splitting methods for time dependent partial differential equations usually exhibit a drop in accuracy if boundary conditions become time dependent this phenomenon is investigated for a class of splitting methods for two space dimensional parabolic partial differential equations a boundary value correction discussed in a paper by fairweather and mitchell for the laplace equation with dirichlet conditions is generalized for a wide class of initial boundary value problems a numerical comparison is made for the adi method of peaceman rachford and the lod method of yanenko applied to problems with dirichlet boundary conditions and non dirichlet boundary conditions

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

k statistics and dispersion effects in regression on donne deux ensembles d estimateurs sans biais pour le cas ou la reponse moyenne depend lineairement de covariables connues

a general deterministic treatment of derivatives in particle methods a unified approach to approximating spatial derivatives in particle methods using integral operators is presented the approach is an extension of particle strength exchange originally developed for treating the laplacian in advection diffusion problems kernels of high order of accuracy are constructed that can be used to approximate derivatives of any degree a new treatment for computing derivatives near the edge of particle coverage is introduced using one sided integrals that only look for information where it is available the use of these integral approximations in wave propagation applications is considered and their error is analyzed in this context using fourier methods finally simple tests are performed to demonstrate the characteristics of the treatment including an assessment of the effects of particle dispersion and their results are discussed

a fractional step ellam approach to high dimensional convection diffusion problems with forward particle tracking in this paper a fractional step method combined with an eulerian lagrangian localized adjoint method ellam is proposed to solve high dimensional convection diffusion problems the method reduces high dimensional problems to a series of uncoupled one dimensional problems in each time step interval in which one dimensional ellam is used to solve the one dimensional splitting equations the approach takes the attractive advantages of the ellam method and the fractional step technique it reduces computational complexities large memory requirements and long computation durations due to the application of the splitting technique it reduces temporal errors and generates accurate numerical solutions even if large time and coarse spatial step sizes are used in computation it effectively eliminates non physical oscillation or excessive numerical dispersion and treats boundary conditions well and in a natural way numerical experiments show the efficient performance of the approach

a high order upwind method for the convection diffusion problem abstract in this paper a high order upwind method for the convection diffusion problems is proposed the scheme satisfies the maximum principle overcomes numerical oscillation and has astonishingly high order computing accuracy at the same time the error estimateso h3 c 4 0 in discretel2 h1 andlx norms in which the constants ino h3 c 4 0 do not depend on the diffusion coefficienta the velocity b the solutionc and the domain partition are obtained by using a new analytic technique several numerical examples are given in order to demonstrate the efficiency of the method

eulerian lagrangian localized adjoint methods for a nonlinear advection diffusion equation eulerian lagrangian localized adjoint methods ellam are developed for the non linear buckley leverett equation which is characterized by degenerate diffusion and sharpening near shock solutions the ellam methodology employs space time finite elements with edges oriented along flow paths and space time test functions that satisfy a local adjoint condition this combination extends eulerian lagrangian concepts in a systematic mass conservative fashion to problems with general boundary conditions various kinds of boundary conditions are considered and a local time stepping procedure is developed for a no flow outlet condition that leads to a boundary layer numerical experiments illustrate the potential of these methods

energy conserved splitting fdtd methods for maxwell s equations in this paper two new energy conserved splitting methods ec s fdtdi and ec s fdtdii for maxwell s equations in two dimensions are proposed both algorithms are energy conserved unconditionally stable and can be computed efficiently the convergence results are analyzed based on the energy method which show that the ec s fdtdi scheme is of first order in time and of second order in space and the ec s fdtdii scheme is of second order both in time and space we also obtain two identities of the discrete divergence of electric fields for these two schemes for the ec s fdtdii scheme we prove that the discrete divergence is of first order to approximate the exact divergence condition numerical dispersion analysis shows that these two schemes are non dissipative numerical experiments confirm well the theoretical analysis results

an approximation to miscible fluid flows in porous media with point sources and sinks by an eulerian lagrangian localized adjoint method and mixed finite element methods we develop an eulerian lagrangian localized adjoint method ellam mixed finite element method mfem solution technique for accurate numerical simulation of coupled systems of partial differential equations pdes which describe complex fluid flow processes in porous media an ellam which was shown previously to outperform many widely used methods in the context of linear convection diffusion pdes is presented to solve the transport equation for concentration since accurate fluid velocities are crucial in numerical simulations an mfem is used to solve the pressure equation for the pressure and darcy velocity this minimizes the numerical difficulties occurring in standard methods for approximating velocities caused by differentiation of the pressure and then multiplication by rough coefficients the ellam mfem solution technique significantly reduces temporal errors symmetrizes the governing transport equation eliminates nonphysical oscillation and or excessive numerical dispersion in many simulators conserves mass and treats boundary conditions accurately numerical experiments show that the ellam mfem solution technique simulates miscible displacements of incompressible fluid flows in porous media accurately with fairly coarse spatial grids and very large time steps which are one or two orders of magnitude larger than the time steps used in many methods moreover the ellam mfem solution technique can treat large mobility ratios discontinuous permeabilities and porosities anisotropic dispersion in tensor form and point sources and sinks