role of the admittance operator in rough surface scattering the linear operator that relates the normal gradient of a wave field to its values on an irregular surface is the basis for a new formulation of the rough surface scattering problem this formulation has led to a class of approximations that surpass traditional methods in accuracy and efficiency the connection between this approach and the standard formulation by means of a boundary integral equation is the subject of this paper while equivalent in all respects the admittance operator formulation provides helpful new perspectives on the physics of surface scattering and lends itself naturally to more elaborate problems for example at a rough boundary between dissimilar media the operators compose themselves into generalized reflection and transmission operators while at a random surface the operator terms lead to analytic forms for the scattered field moments

on involutions in symmetric groups and a conjecture of lusztig abstract let w s be a coxeter system equipped with a fixed automorphism of order 2 which preserves s lusztig and with vogan in some special cases have shown that the space spanned by set of twisted involutions i e elements w w with w w 1 was naturally endowed with a module structure of the hecke algebra of w s with two distinguished bases which can be viewed as twisted analogues of the well known standard basis and kazhdan lusztig basis the transition matrix between these bases defines a family of polynomials p y w which can be viewed as twisted analogues of the well known kazhdan lusztig polynomials of w s lusztig has conjectured that this module is isomorphic to the right ideal of the hecke algebra with hecke parameter u 2 associated to w s generated by the element x w w u l w t w in this paper we prove this conjecture in the case when id and w s n the symmetric group on n letters our methods are expected to be generalised to all the other finite crystallographic coxeter groups

a new approach to analyticity of dirichlet neumann operators this paper outlines the theoretical background of a new approach towards an accurate and well conditioned perturbative calculation of dirichlet neumann operators dnos on domains that are perturbations of simple geometries previous work on the analyticity of dnos has produced formulae that as we have found are very ill conditioned we show how a simple change of variables can lead to recursions that satisfy analyticity estimates without relying on subtle cancellation properties at the heart of previous formulae

application of the operator expansion method to scattering from one dimensional moderately rough dirichlet random surfaces a new method for computing wave scattering from rough surfaces called the operator expansion oe method has been proposed by d m milder j acoust soc am 89 2 529 541 1991 in this paper the oe method is examined in its application to acoustic scattering from one dimensional randomly rough surfaces with gaussian and pierson moskowitz roughness spectra satisfying the pressure release dirichlet boundary condition the operator expansion solution which is expressed in a systematic series is found to converge rapidly and monotonically for moderately rough surfaces that is for surfaces whose slope height roughness parameter khs given by the product of acoustic wave number k rms surface height h and rms surface slope s is less than about 0 25 through comparison with a numerically exact integral equation solution the oe method is found to be accurate over a wide range of incident and scattering angles the method is currently used in a monte carlo computation of the scattering cross sec

the combinatorics of twisted involutions in coxeter groups the open intervals in the bruhat order on twisted involutions in a coxeter group are shown to be pl spheres this implies results conjectured by f incitti and sharpens the known fact that these posets are gorenstein over z 2 we also introduce a boolean cell complex which is an analogue for twisted involutions of the coxeter complex several classical coxeter complex properties are shared by our complex when the group is finite it is a shellable sphere shelling orders being given by the linear extensions of the weak order on twisted involutions furthermore the h polynomial of the complex coincides with the polynomial counting twisted involutions by descents in particular this gives a type independent proof that the latter is symmetric

quantization based filtering method using first order approximation the quantization based filtering method see g pages and h pham bernoulli 11 2005 pp 893 932 g pages h pham and j printems optimal quantization methods and applications to numerical problems in finance in handbook of computational and numerical methods in finance s t rachev ed birkhauser boston 2004 pp 253 297 is a grid based approximation method to solve nonlinear filtering problems with discrete time observations it relies on off line preprocessing of some signal grids in order to construct fast recursive schemes for filter approximation we give here an improvement of this method by taking advantage of the stationary quantizer property the key ingredient is the use of vanishing correction terms to describe schemes based on piecewise linear approximations convergence results are given and numerical results are presented for the particular cases of linear gaussian model and stochastic volatility models

non gaussian state space modeling of nonstationary time series abstract a non gaussian state space approach to the modeling of nonstationary time series is shown the model is expressed in state space form where the system noise and the observational noise are not necessarily gaussian recursive formulas of prediction filtering and smoothing for the state estimation and identification of the non gaussian state space model are given also given is a numerical method based on piecewise linear approximation to the density functions for realizing these formulas significant merits of non gaussian modeling and the wide range of applicability of the method are illustrated by some numerical examples a typical application of this non gaussian modeling is the smoothing of a time series that has mean value function with both abrupt and gradual changes simple gaussian state space modeling is not adequate for this situation here the model with small system noise variance cannot detect jump whereas the one with large system noise variance yields unfavorable wiggle to work

stability of high order perturbative methods for the computation of dirichlet neumann operators abstract in this paper we present results on the stability of perturbation methods for the evaluation of dirichlet neumann operators dno defined on domains that are viewed as complex deformations of a basic simple geometry in such cases geometric perturbation methods based on variations of the spatial domains of definition have long been recognized to constitute efficient and accurate means for the approximation of dno and in fact several numerical implementations have been previously proposed inspired by our recent analytical work here we demonstrate that the convergence of these algorithms is quite generally limited by numerical instability indeed we show that these standard perturbative methods for the calculation of dno suffer from significant ill conditioning which is manifest even for very smooth boundaries and whose severity increases with boundary roughness moreover and again motivated by our previous work we introduce an alternative perturbative approach that we show to be numerically stable this approach can be interpreted as a reformulation of classical perturbative algorithms in suitable independent variables and thus it allows for both direct comparison and the possibility of analytic continuation of the perturbation series it can also be related to classical preconditioned spectral approaches and as such it retains in finite arithmetic the spectral convergence properties of classical perturbative methods albeit at a higher computational cost as it does not take advantage of possible dimensional reductions still as we show an alternative approach such as the one we propose may be mandated in cases where substantial information is contained in high order harmonics and or perturbation coefficients of the solution

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

intrinsic stationarity for vector quantization foundation of dual quantization we develop a new approach to vector quantization which guarantees an intrinsic stationarity property that also holds in contrast to regular quantization for nonoptimal quantization grids this goal is achieved by replacing the usual nearest neighbor projection operator for voronoi quantization by a random splitting operator which maps the random source to the vertices of a triangle of d simplex in the quadratic euclidean case it is shown that these triangles or d simplices make up a delaunay triangulation of the underlying grid furthermore we prove the existence of an optimal grid for this delaunay or dual quantization procedure we also provide a stochastic optimization method to compute such optimal grids here for higher dimensional uniform and normal distributions a crucial feature of this new approach is the fact that it automatically leads to a second order quadrature formula for computing expectations regardless of the optimality of the underlying grid

observations preprocessing and quantization for nonlinear filters methods of preprocessing the observations for nonlinear filters are investigated the aim being to reduce the computational labor involved in their implementation an example of preprocessing is quantization which involves the replacement of real valued observation samples by discrete values because the resulting likelihood functions have finite support they can be held in look up tables kept in some type of rapid access memory which renders their real time evaluation trivial preprocessed observations of this sort carry less information than raw observations this loss of information is characterized here for filters with substantially noisy observation samples by means of a functional central limit theorem among other things this supplies an asymptotic effective signal to noise ratio for preprocessed filters methods of optimizing preprocessing operations with respect to this quantified information loss are developed in particular optimal quantization thresholds are found for observations that are contaminated by gaussian noise and it is shown that the loss of information for quite coarse quantization schemes is small for example the asymptotic effective signal to noise ratio for a filter with one bit quantized observations is 2 pi times that for the same filter with raw observations simulations on two examples demonstrate the validity of the asymptotic characterization even when the observation samples are only modestly contaminated by noise

an improved formalism for wave scattering from rough surfaces the scattered field and its normal gradient obey a mutual linear relation at the scattering surface that is distinct from the physical boundary condition connecting either quantity to the incident radiation on a moderately rough surface this relation can be represented by an operator whose series expansion in surface slope converges nicely even for large values of the rayleigh parameter this allows the helmholtz integral for scattering amplitude to be written as a series of readily computable terms one or two of which provide good approximations for surfaces too irregular for the usual bragg expansion this formulation reproduces the bragg series for small surface elevations and in the limit of low roughness wavenumber gives the kirchhoff approximation with an explicit correction term in surface curvature the usual results for a composite surface also emerge naturally on several test profiles the method produces better overall accuracy than other multiscale approximations at comparable efficiency

solution of a boundary value problem for the helmholtz equation via variation of the boundary into the complex domain in this paper we deal with the problem of diffraction of electromagnetic waves by a periodic interface between two materials this corresponds to a two dimensional quasi periodic boundary value problem for the helmholtz equation we prove that solutions behave analytically with respect to variations of the interface the interest of this result is both theoretical the legitimacy of power series expansions in the parameters of the problem has indeed been questioned and perhaps more importantly practical we have found that the solution can be computed on the basis of this observation the simple algorithm that results from such boundary variations is described to establish the property of analyticity of the solution for the grating with respect to the height we present a holomorphic formulation of the problem using surface potentials we show that the densities entering into the potential theoretic formulation are analytic with respect to variations of the boundary or in other words that the integral operator that results from the transmission conditions at the interface is invertible in a space of holomorphic functions of the variables x y this permits us to conclude in particular that the partial derivatives of u with respect to at 0 satisfy certain boundary value problems for the helmholtz equation in regions with plane boundaries which can be solved in a closed form

fixed points of involutive automorphisms of the bruhat order abstract applying a classical theorem of smith we show that the poset property of being gorenstein over z 2 is inherited by the subposet of fixed points under an involutive poset automorphism as an application we prove that every interval in the bruhat order on twisted involutions in an arbitrary coxeter group has this property and we find the rank function this implies results conjectured by f incitti we also show that the bruhat order on the fixed points of an involutive automorphism induced by a coxeter graph automorphism is isomorphic to the bruhat order on the fixed subgroup viewed as a coxeter group in its own right

approximation of analytic functions a method of enhanced convergence we deal with a method of enhanced convergence for the approximation of analytic functions this method introduces conformal transformations in the approximation problems in order to help extract the values of a given analytic function from its taylor expansion around a point an instance of this method based on the euler transform has long been known recently we introduced more general versions of it in connection with certain problems in wave scattering in 2 we present a general discussion of this approach as is known in the case of the euler transform conformal transformations can enlarge the region of convergence of power series and can enhance substantially the convergence rates inside the circles of convergence we show that conformal maps can also produce a rather dramatic improvement in the conditioning of pade approximation this improvement which we discuss theoretically for stieltjes type functions is most notorious in cases of very poorly conditioned pade problems in many instances an application of enhanced convergence in conjunction with pade approximation leads to results which are many orders of magnitude more accurate than those obtained by either classical pade approximants or the summation of a truncated enhanced series

integral u deformed involution modules abstract let w s be a coxeter system and an automorphism of w with order 2 and s s lusztig and vogan 20 23 have introduced a u deformed version m u of kottwitz s involution module over the iwahori hecke algebra h u w with hecke parameter u 2 where u is an indeterminate lusztig has proved that m u is isomorphic to the left h u w submodule of h u generated by x w w w u l w t w where h u is the vector space consisting of all formal possibly infinite sums x w c x t x c x q u for each x he speculated that one can extend this by replacing u with any c 0 1 1 in this paper we give a positive answer to his speculation for any k 0 1 1 and any w where k is an arbitrary ground field

a stable high order method for two dimensional bounded obstacle scattering a stable and high order method for solving the helmholtz equation on a two dimensional domain exterior to a bounded obstacle is developed in this paper the method is based on a boundary perturbation technique transformed field expansions coupled with a well conditioned high order spectral galerkin solver the method is further enhanced with numerical analytic continuation implemented via pade approximation ample numerical results are presented to show the accuracy stability and versatility of the proposed method

numerical simulation of gravity waves abstract we present a new spectral method to simulate numerically the waterwave problem in a channel for a fluid of finite or infinite depth it is formulated in terms of the free surface elevation and the velocity potential the numerical method is based on the reduction of this problem to a lower dimensional computation involving surface variables alone to accomplish this we describe the taylor expansion of the dirichlet neumann operator in homogeneous powers of the surface elevation each term is a concatenation of fourier multipliers with powers of and its derivatives and is valid uniformly in wavenumber these are easily calculated using the fast fourier transform the method is illustrated by computing the long time evolution of modulated wave packets and of approximations to the stokes steady wave train by imposing a surface pressure we observe surface steepening in large amplitude evolution and wake and bow wave development for flows with a close to critical froude number finally we give an example of nonlinear evolution of the distribution of energy among normal modes

matrix units and generic degrees for the ariki koike algebras this paper uses the murphy basis of the ariki koike algebras to explicitly construct a complete set of primitive idempotents when these algebras are semisimple and q 1 as a consequence we obtain an explicit wedderburn basis for the ariki koike algebras finally we use these idempotents to compute the generic degrees of the ariki koike algebras