physical and geometrical optics for 2 d rough surfaces with power law height spectra random rough surfaces with slowly decaying power spectral density can have infinite slope variance such surfaces do not satisfy the classical curvature criterion for validity of the physical optics po approximation and the infinite frequency geometrical optics limit or specular point scattering model breaks down we show for two dimensional surfaces with infinite slope variance that the gaussian form of the classical geometrical limit generalizes to a stable distribution function we also show that the po integral is insensitive to surface components with spatial frequency above a cutoff wavenumber which explains past observations that po can be accurate for surfaces with power law spectra this result leads to a general validity condition for the po approximation in the backscattering direction for power law surfaces which in the case of a k sup 4 spectrum requires that the significant slope of the surface be less than 0 03

rigorous formulation of scattering at a randomly varying impedance plane general case of oblique incidence the problem of scattering of electromagnetic plane waves at one dimensional surfaces random gratings is solved in the general case in which the incident wave vector does not lie on the main section of the cylindrical surface oblique incidence the scatterer is simulated by a plane boundary characterized by a coordinate dependent impedance that varies along one of the two coordinates on the surface this representation could be regarded as a canonical model of one dimensional surfaces with height corrugations a rigorous electromagnetic formalism for calculating the fields scattered at the impedance plane is presented the fields above the scatterer are represented by spectral domain expansions it is shown that the wave vectors of the scattered waves lie on the surface of a cone containing the direction of specular reflection and whose axis coincides with the direction of the grooves of the random grating the theory is exemplified by calculating the angular distribution of the mean intensity scattered from an ensemble of surfaces with similar statistical parameters

a direct search method for unconstrained quantile based simulation optimization abstract simulation optimization has gained popularity over the decades because of its ability to solve many practical problems that involve profound randomness the methodology development of simulation optimization however is largely concerned with problems whose objective function is mean based performance metric in this paper we propose a direct search method to solve the unconstrained simulation optimization problems with quantile based objective functions because the proposed method does not require gradient estimation in the search process it can be applied to solve many practical problems where the gradient of objective function does not exist or is difficult to estimate we prove that the proposed method possesses desirable convergence guarantee i e the algorithm can converge to the true global optima with probability one an extensive numerical study shows that the performance of the proposed method is promising two illustrative examples are provided in the end to demonstrate the viability of the proposed method in real settings

a smooth nonparametric estimator of a quantile function abstract a smooth alternative to the conventional sample quantile function as a nonparametric estimator of a population quantile function is proposed the proposed estimator is essentially a kernel type of estimator and has the same asymptotic distribution as the conventional sample quantile the mean squared convergence rate of the proposed estimator is also estimated monte carlo studies are conducted to compare the proposed estimator with the sample quantile and the estimator proposed by kaigh and lachenbruch the feasibility of using bootstrap techniques to estimate the optimal window width for the proposed estimator is also considered

comparison of quantile estimators in normal sampling ten nonparametric quantile estimators are compared with respect to small sample performance characteristics including bias and mean squared error the estimators considered are all linear functions of order statistics with properties that depend on sample size graphical presentations are given for the case of a normal parent distribution and comparisons are made with the minimum variance unbiased estimator for normal sampling

monte carlo simulations of wave scattering from lossy dielectric random rough surfaces using the physics based two grid method and the canonical grid method in using the method of moments to solve scattering by lossy dielectric surfaces usually a single dense grid sdg with 30 points per wavelength is required for accurate results a single coarse grid scg of ten points per wavelength does not give accurate results however the central processing unit cpu and memory requirements of sdg are much larger than that of scg in a physics based two grid method pbtg two grids are used a dense grid and a coarse grid the method is based on the two observations 1 green s function of the lossy dielectric is attenuative and 2 the free space green s function is slowly varying on the dense grid in this paper the pbtg method is combined with the banded matrix iterative approach canonical grid method to solve rough surface scattering problem for both te and tm cases and also for near grazing incidence we studied cases of dielectric permittivities as high as 25 i spl epsiv sub 0 and incidence angle up to 85 spl deg salient features of the numerical results are 1 an scg has poorer accuracy for tm case than te case 2 pbtg banded matrix iterative approach canonical grid bmia cag method speeds up cpu and preserves the accuracy it has an accuracy comparable to single dense grid and yet has cpu comparable to single coarse grid 3 pbtg bmia cag gives accurate results for emissivity calculations and also for low grazing backscattering problems lgba and 4 the computational complexity and the memory requirements of the present algorithm are o n log n and o n respectively where n is the number of surface unknowns on the coarse grid

on the cohen macaulay type of s lines in an 1 abstract let a be the coordinate ring of s lines through the origin in a n 1 k we discuss what it means for these lines to be in sufficiently general position and then with this restriction on the lines we attempt to verify our belief that the cohen macaulay type of a depends only on s and n we characterize those s and n for which a is a gorenstein ring i e of c m type 1 and explicitly calculate the cohen macaulay type in several other cases we then extend some of our results to the case of an arbitrary reduced curve whose tangent cone consists of lines in sufficiently general position finally we calculate the hubert samuel polynomials of the curves we have been considering

on determining the radar threshold for non gaussian processes from experimental data the problem of detecting radar signals embedded in clutter is an area of great interest in many radar applications it is important to set thresholds to achieve a false alarm probability p sub f of 10 sup 5 or lower using conventional monte carlo techniques where thresholds are set based on raw percentiles an extremely large number of samples is required we use the generalized pareto distribution to approximate the extreme tail of the distributions and propose the ordered sample least squares osls method for estimating its parameters

comparing one step m estimators of location corresponding to two independent groups experience with real data indicates that psychometric measures often have heavy tailed distributions this is known to be a serious problem when comparing the means of two independent groups because heavy tailed distributions can have a serious effect on power another problem that is common in some areas is outliers this paper suggests an approach to these problems based on the one step m estimator of location simulations indicate that the new procedure provides very good control over the probability of a type i error even when distributions are skewed have different shapes and the variances are unequal moreover the new procedure has considerably more power than welch s method when distributions have heavy tails and it compares well to yuen s method for comparing trimmed means wilcox s median procedure has about the same power as the proposed procedure but wilcox s method is based on a statistic that has a finite sample breakdown point of only 1 n wheren is the sample size comments on other methods for comparing groups are also included

stochastic dominance based comparison for system selection abstract we present two complementing selection procedures for comparing simulated systems based on the stochastic dominance relationship of a performance metric of interest the decision maker specifies an output quantile set representing a section of the distribution of the metric e g downside or upside risks or central tendencies as the basis for comparison the first procedure compares systems over the quantile set of interest by a first order stochastic dominance criterion the systems that are deemed nondominant in the first procedure could be compared by a weaker almost first order stochastic dominance criterion in the second procedure numerical examples illustrate the capabilities of the proposed procedures

simulation of near ground long distance radiowave propagation over terrain using nystrom method with phase extraction technique and fmm acceleration a 2d surface integral equation based nystroumlm solver in which a phase extraction technique is utilized to reduce the number of surface unknowns is described as forward scattering is the dominant mechanism for the near ground wave propagation scenario the associated rapidly varying phase components of the integral equation kernel and solution unknowns are deduced and isolated in advance and subsequently built into the solver it is shown that by applying this method when combining with an adaptive surface segmentation routine as few as one to two average unknowns per wavelength is adequate in obtaining accurate solutions this significantly reduces the memory storage and computational expense for the simulation of long distance propagation effects the efficiency of this method is further improved by incorporating it into the framework of the fast multipole scheme the full details of the algorithm are discussed along with performance comparisons of the new solver to a regular nystroumlm solver for terrain surfaces in terms of solution convergence

gaussian rough surfaces and kirchhoff approximation electromagnetic scattering is often solved by applying the kirchhoff approximation to the stratton chu scattering integral in the case of rough surfaces it is usually assumed that this is possible if the incident electromagnetic wavelength is small compared to the mean radius of curvature of the surface accordingly evaluation of the latter is an important issue this paper generalizes the groundwork of papa and lemon see ibid vol 36 p 647 50 may 1988 by computing the mean radius of curvature for gaussian rough surfaces with no restriction on its correlation function this is an interesting extension relevant to a variety of natural surfaces relations between the surface parameters and the mean radius of curvature are determined and particular attention is paid to the relevant small slope regime

coifman wavelets in 3 d scattering from very rough random surfaces the coifman wavelets are employed to perform galerkin s procedure in the method of moments mom the coiflets are continuous smooth overlapping yet orthogonal which permit significant reduction of the sampling rate and dramatic compression of the matrix size with respect to the pulse based mom in addition the wavelet based impedance matrix is sparse more importantly the vanishing moments of the coiflets of order l 4 provide us with high precision o h sup 5 one point quadrature which knocks down the computational effort in filling the matrix entries from o n sup 2 to o n our approach is different from the conventional wavelet technique which employs wavelets to sparsify an existing impedance matrix under similarity transformation with computational cost in o n sup 2 excellent agreement between this coifman wavelet method and the previous publications is observed

electromagnetic scattering from a rough layer propagation inside layer expansion method combined to an updated bmia cag approach an efficient method is developed to calculate the bistatic scattering coefficient bsc from a stack of two one dimensional rough interfaces separating homogeneous media the propagation inside layer expansion pile method recently published by dechamps was efficient with a complexity o n2 n being the number of samples per interface to reduce this complexity a fast method valid for a single rough surface the banded matrix iterative approach canonical grid bmia cag is combined to the pile method furthermore the calculation of the coupling interactions between both interfaces are also accelerated using a new method similar to the bmia cag the pile method reaches then a complexity of only o nlogn a study of the convergence of the pile is done and compared to another efficient method the forward backward

simulation of first and second order scattering by rough surfaces with a sound ray formalism the sound ray technique is developed to simulate rough surfaces scattering processes which are consistent with the kirchhoff approximation ka theory it is first proved that both approaches ka and sound rays lead to the same theoretical expression of the first order scattered intensity an algorithm based on the random generation of surfaces slopes is proposed together with some results computed for gaussian rough surfaces this algorithm could be used in room acoustics more as a physical substitute for the cosine lambert law of diffusion the method is then extended to the analysis of second order scattering effects which are not taken into account by ka this new approach does not require the generation of several profiles of rough surface however some assumptions must be made in order to derive a useful mathematical expression of the second order scattered intensity the first results obtained are fairly consistent with the present knowledge of multiple scattering effects e g enhanced backscattering for very rough surfaces but further work is needed to test the assumptions and to improve the method

kernel quantile estimators abstract for an estimator of quantiles the efficiency of the sample quantile can be improved by considering linear combinations of order statistics that is l estimators a variety of such methods have appeared in the literature an important aspect of this article is that asymptotically several of these are shown to be kernel estimators with a guassian kernel and the bandwidths are identified it is seen that some implicit choices of the smoothing parameter are asymptotically suboptimal in addition the theory of this article suggests a method for choosing the smoothing parameter how much reliance should be placed on the theoretical results is investigated through a simulation study over a variety of distributions little consistent difference is found between various estimators an important conclusion made during the theoretical analysis is that all of these estimators usually provide only modest improvement over the sample quantile the results indicate that even if one knew the best estimator

the validity of the perturbation approximation for rough surface scattering using a gaussian roughness spectrum the validity of the perturbation approximation for rough surface scattering is examined 1 by comparison with exact results obtained by solving an integral equation and 2 through comparison of low order perturbation predictions with higher order predictions the pressure release boundary condition is assumed and the field quantity calculated is the bistatic scattering cross section a gaussian roughness spectrum is used and the surfaces have height variations in only one direction it is found in general that the condition kh 1 k is the acoustic wavenumber h is the rms surface height is insufficient to guarantee the accuracy of first order or higher order perturbation theory when the surface correlation length l becomes too large or too small with h held fixed higher order perturbation terms can make larger contributions to the scattering cross section than lower order terms an explanation for this result is given the regions of validity for low order perturbation theory are also given th

control variates for quantile estimation new point and interval estimators for quantiles that employ a control variate are introduced the properties of these estimators do not depend on the usual assumption of joint normality between the random variable of interest and the control illustrative examples for queueing and stochastic activity network models are given in those examples the new estimators are superior to the standard estimator in terms of the mean squared error of the point estimator and the length of the confidence interval

testing whether independent treatment groups have equal medians the paper suggests new methods for comparing the medians corresponding to independent treatment groups the procedures are based on the harrell davis estimator in conjunction with a slight modification and extension of the bootstrap calibration technique suggested by loh alternatives to the harrell davis estimator are briefly discussed for the special case of two treatment groups the proposed procedure always had more power than the fligner rust solution as well as the procedure examined by wilcox and charlin included is an illustration using real data that comparing medians rather than means can yield a substantially different conclusion as to whether two distributions differ in terms of some measure of central location

a simplified approach to solving finite rough surface scattering problems in this paper a simplified approach is described for the computation of scattering from finite length rough surfaces in an earlier paper fawcett j acoust soc 118 1348 1357 2005 it was described how to solve such problems by considering a scattering chamber and using the method of wavefield superposition to satisfy the various boundary and continuity conditions in this paper a form of the field in the interior of the scattering chamber is assumed and the solution to the scattering problem is reduced to solving a system of equations just along the rough surface the solution to this system of equations can then be used to compute the scattered or total fields anywhere in the half space the results of this approach are compared to those obtained by other methods

a matrix computation for the cohen macaulay type of s lines in affine n 1 space let l1 ls denote s distinct lines in akn 1 passing through the origin o in this paper we compute a matrix formula for the cohen macaulay type t l1 ls of the local ring of i 1s li at o our formula is as follows t l1 ls j rs 1y j fk g s 1 n s 22 here we assume s 2 and the coordinates in akn 1 have been so chosen that the leading entries in the direction numbers p1 ps pkn of l1 ls are all ones g s 1 is a matrix and the j s are constants which depend only on the direction numbers p1 ps of the lines the number r is the minimal degree of a nonzero form passing through p1 ps when l1 ls are in generic s position our formula simplifies to t l1 ls y r s r n 11 we give examples which show that for a fixed n and s the cohen macaulay type of s lines in generic s position in akn 1 is not constant

recovery of a quantile function from moments the problem of recovering a quantile function of a positive random variable via the values of moments or given the values of its laplace transform is studied two new approximations as well as two new estimates of a quantile function given the sample from underlying distribution are proposed the uniform and l 1 upper bounds of proposed estimates are derived the plots illustrate the behavior of the recovered approximants for the moderate and large sample sizes

statistical tests for identification of the genotype at a major locus of progeny tested sires summary the use of major genes is a component of livestock improvement this requires identification of the genotypes of reproducers in particular progeny tested sires after mating with homozygous females two test statistics derived from the nonnested test of cox 1961 proceedings of the fouirth berkeley svmposium on mathematical statistics and probability 1 105 123 1962 journal of the royal statistical society series b 24 406 424 are proposed for both tests asymptotic normality is proved algebraically and the speed of convergence is studied through simulations in the cases where a uniformly most powerful ump test exists the power of one of the tests is close to the power of that ump test finally the tests are applied to a population of poultry carrying the dwarf gene

a domain decomposition finite difference time domain fdtd method for scattering problem from very large rough surfaces a domain decomposition finite difference time domain dd fdtd method is proposed to solve the problem of electromagnetic scattering from very large rough surfaces the entire computational domain is decomposed into multiple subdomains each subdomain is simulated by using the conventional fdtd method to obtain the scattered fields on a huygens surface and the total fields on the rough surface the latter is used to compute the scattered field on the huygens surface in adjacent subdomains by invoking the reciprocity theorem simulation results are compared with those in the literatures to validate this method the normalized radar cross sections nrcss from very large surfaces of 66 lambda times 66 lambda are also presented to demonstrate the efficacy of this method

boundary integral equation methods for the scattering problem by an unbounded sound soft rough surface with tapered wave incidence in this paper we consider the scattering problem of tapered acoustic wave by an unbounded sound soft surface the scattering problem is modeled as a boundary value problem governed by the helmholtz equation with dirichlet boundary condition although the tapered wave is often introduced to realize asymptotic truncation for unbounded rough surface the standard helmholtz integral equations which derive for the scattering of plane waves by an arbitrary bounded obstacle are often used to generate benchmark numerical solutions different from the scattering of plane waves by an arbitrary bounded obstacle we use the angular spectrum representation radiation condition to replace the sommerfeld radiation condition and derive a boundary integral equation for studying the scattering problem then we study the integral equation by the truncation method whereby the integral equation posed on an unbounded region is approximated by an integral equation on a bounded region some properties of the integral equation in an energy space with weights are proved then the collocation method is used to solve the integral equation on a bounded region and its convergence is also obtained a rigorous derivation of bie is presented for studying the scattering problem some properties of the integral equation in an energy space with weights are proved the convergence of the numerical method is also obtained

a quantile based approach to system selection abstract we propose a quantile based ranking and selection r s procedure for comparing a finite set of stochastic systems via simulation our r s procedure uses a quantile set of the simulated probability distribution of a performance characteristic of interest that best represents the most appropriate selection criterion as the basis for comparison since this quantile set may represent either the downside risk upside risk or central tendency of the performance characteristic the proposed approach is more flexible than the traditional mean based approach to r s we first present a procedure that selects the best system from among k systems and then we modified that procedure for the case where k 1 systems are compared against a standard system we present a set of experiments to highlight the flexibility of the proposed procedures

oblique scattering from lossy strip structures with one dimensional periodicity the intentional addition of loss to a periodic structure can be used as a technique to alter its scattering characteristics the problem of an oblique plane wave incident on an array with one dimensional periodicity is examined the unit cell of the array is composed of a number of thin resistive strips the obliqueness of the incident plane wave combined with the lossy nature of the structure causes the transverse electric te to z and the transverse magnetic tm to z fields to couple to analyze the described problem two coupled electric field integral equations that have as unknowns the equivalent surface currents on the strips in the unit cell are derived the integral equations are discretized and solved approximately using the method of moments with subdomain basis and testing functions the periodic green s function is efficiently calculated using the poisson summation formula the interaction of the structure with the surrounding environment is described in terms of a generalized scattering matrix results are presented showing the te tm coupling behavior as strip resistance is increased for representative structures