role of the edge orbits in the semiclassical quantization of the stadium billiard in the periodic orbit quantization of the stadium billiard we show that important contributions may be due to the edge orbits i e to orbits bouncing between points where the curvature of the boundary is discontinuous we explicitly show that these edge orbits are necessary to reproduce several amplitudes of the length spectrum defined by the fourier transform of the staircase function in this way we explain some features overlooked in recent experiments on microwave cavities

an effective mom solution with nested complex source beam method for electromagnetic scattering problems a nested complex source beam ncsb method based on octree structure is proposed to accelerate the method of moments mom solution for three dimensional 3 d electromagnetic scattering analysis at the finest level the far field contribution of each basis function is expressed with that of complex source beams csbs distributed on the equivalent sphere surface for every group furthermore the far field radiated by csbs of the source group at child level can be represented by that radiated by csbs of the source group at parent level similarly the received field of csbs for each observation group at the parent level can be expressed with that of csbs belong to their child level group an equivalent relationship of csbs between every two adjacent levels is built to obtain the nested equivalent process for ncsb method and only the csbs at the finest level have the direct association with the basis functions in their group the ncsb method is shown to be o nlogn computational complexity for both matrix vector product mvp time and memory storage by numerical examples with appropriate parameters and numerical results demonstrate the better efficiency of the proposed method than the current multilevel csb method

rate of quantum ergodicity in euclidean billiards for a large class of quantized ergodic flows the quantum ergodicity theorem states that almost all eigenfunctions become equidistributed in the semiclassical limit in this work we give a short introduction to the formulation of the quantum ergodicity theorem for general observables in terms of pseudodifferential operators and show that it is equivalent to the semiclassical eigenfunction hypothesis for the wigner function in the case of ergodic systems of great importance is the rate by which the quantum mechanical expectation values of an observable tend to their mean value this is studied numerically for three euclidean billiards stadium cosine and cardioid billiard using up to 6000 eigenfunctions we find that in configuration space the rate of quantum ergodicity is strongly influenced by localized eigenfunctions such as bouncing ball modes or scarred eigenfunctions we give a detailed discussion and explanation of these effects using a simple but powerful model for the rate of quantum ergodicity in momentum space we observe a slower decay we also study the suitably normalized fluctuations of the expectation values around their mean and find good agreement with a gaussian distribution

on multivariate lagrange interpolation lagrange interpolation by polynomials in several variables is studied through a finite difference approach we establish an interpolation formula analogous to that of newton and a remainder formula both of them in terms of finite differences we prove that the finite difference admits an integral representation involving simplex spline functions in particular this provides a remainder formula for lagrange interpolation of degree n of a function f which is a sum of integrals of certain n 1 st directional derivatives of f multiplied by simplex spline functions we also provide two algorithms for the computation of lagrange interpolants which use only addition scalar multiplication and point evaluation of polynomials

fast iterative solution of integral equations with method of moments and matrix decomposition algorithm singular value decomposition the multilevel matrix decomposition algorithm mlmda was originally developed by michielsen and boag for 2d tmz scattering problems and later implemented in 3d by rius et al the 3d mlmda was particularly efficient and accurate for piece wise planar objects such as printed antennas however for arbitrary 3d problems it was not as efficient as the multilevel fast multipole algorithm mlfma and the matrix compression error was too large for practical applications this paper will introduce some improvements in 3d mlmda like new placement of equivalent functions and svd postcompression the first is crucial to have a matrix compression error that converges to zero as the compressed matrix size increases as a result the new mda svd algorithm is comparable with the mlfma and the adaptive cross approximation aca in terms of computation time and memory requirements remarkably in high accuracy computations the mda svd approach obtains a matrix compression error one order of magnitude smaller than aca or mlfma in less computation time like the aca the mda svd algorithm can be implemented on top of an existing mom code with most commonly used green s functions but the mda svd is much more efficient in the analysis of planar or piece wise planar objects like printed antennas

accelerated direct solution of electromagnetic scattering via characteristic basis function method with sherman morrison woodbury formula based algorithm the characteristic basis function method has been proposed to accelerate the direct solution of the method of moments by reducing the number of unknowns however with the increase in the target size the reduced matrix will still become too large to directly solve and store in this communication the algorithm based on the sherman morrison woodbury smw formula is employed to address this problem for the first time it compresses the reduced matrix into a product of block diagonal matrices with the aid of the smw formula and the adaptive cross approximation subsequently the inverse of the reduced matrix can be easily obtained by the inverses of these block diagonal matrices the numerical results about the electromagnetic scattering are shown to demonstrate the performance of the proposed method

bifurcations and complete chaos for the diamagnetic kepler problem we describe the structure of bifurcations in the unbounded classical diamagnetic kepler problem we conjecture that this system does not have any stable orbits and that the non wandering set is described by a complete trinary symbolic dynamics for scaled energies larger then epsilon c 0 328782 ldots

block size optimization of cbfm for scattering problems the characteristic basis function method cbfm was developed as an algorithm to accelerate the analysis based on direct matrix solver in cbfm the optimum block size greatly influences the overall analysis time in this paper we propose a guideline for setting the optimal block size that can be applied to every algorithm based on cbfm rough estimation of the optimal block size is l b rough approx 0 05 n 6 29 and the exact optimal block size can be determined through preprocessing based on rough estimation numerical results of electromagnetic scattering problems are shown to demonstrate the performance of the proposed method

symbolic dynamics and periodic orbits for the cardioid billiard the periodic orbits of the strongly chaotic cardioid billiard are studied by introducing a binary symbolic dynamics the corresponding partition is mapped to a topologically well ordered symbol plane in the symbol plane the pruning front is obtained from orbits running either into or through the cusp we show that all periodic orbits correspond to maxima of the lagrangian and give a complete list up to code length 15 the symmetry reduction is done on the level of the symbol sequences and the periodic orbits are classified using symmetry lines we show that there exists an infinite number of families of periodic orbits accumulating in length and that all other families of geometrically short periodic orbits eventually get pruned all these orbits are related to finite orbits starting and ending in the cusp we obtain an analytical estimate of the kolmogorov sinai entropy and find a good agreement with the numerically calculated value and the one obtained by averaging periodic orbits furthermore the statistical properties of periodic orbits are investigated

classical dynamics of a family of billiards with analytic boundaries the classical dynamics of a billiard which is a quadratic conformal image of the unit disc is investigated the author gives the stability analysis of major periodic orbits present the poincare maps demonstrate the mixing properties by following the evolution of a small element in phase space show the existence of homoclinic points and calculate the lyapunov exponent and the kolmogorov entropy h it turns out that the system becomes strongly chaotic positive h for sufficiently large deformations of the unit disc the system shows a generic stochastic transition the computations suggest that the system is mixing if the boundary is not convex

comments on fast direct solution of method of moments linear system in the above named work a new algorithm is presented for direct non iterative frequency domain method of moments mom calculations based on block wise compression of the impedance matrix the storage requirements and computational complexity of the algorithm are claimed to be n3 2 and n2 respectively if n is the number of unknowns for a mom surface discretization that is fixed with respect to the wavelength a more rigorous analysis explicitly using the asymptotic expression for the number of degrees of freedom dof in the interaction between groups of scatterers is presented here showing that this should be n3 2log n and n2log2 n respectively the complexity analysis applies to problems that can be formulated as a surface integral equation sie on surfaces in or between homogeneous media such as a ship or an airplane it does not apply to volume discretization mom or multilayer problems the results presented here are also relevant for block wise compression methods using iterative solvers since the compressed impedance matrix is the same consequently the above complexity analysis applies to very large problems well beyond the reach of even the largest existent computers for moderate size problems the measured complexity is lower

non generic spectral statistics in the quantized stadium billiard we consider the effect of a continuous family of neutral bouncing ball orbits on the energy spectrum of the quantized stadium billiard using a semiclassical approximation we derive analytic expressions for standard two point spectral measures the corrections due to the bouncing ball orbits account for some of the non generic features observed in the analysis of the spectrum of a stadium cavity which was recently measured once the bouncing ball contributions are subtracted the spectrum is shown to be well reproduced by the semi classical trace formula based on unstable periodic orbits we also study special patterns in the spectrum which are due to other non generic features such as edge effects and whispering gallery trajectories

coding chaotic billiards i non compact billiards on a negative curvature manifold abstract this paper presents a method for coding billiards the main device is to use a proper surface of section the bounce mapping and foliate the reduced phase space into regions associated with a given code the alphabet is merely the ensemble of the labels of the sides of the billiard the procedure is applied here to non compact polygonal billiards defined on a manifold of constant negative curvature with all vertices at infinity a simple grammar rule is necessary and sufficient to ensure existence and uniqueness of the coding

periodic orbits and semiclassical quantization of dispersing billiards periodic orbits in a dispersing billiard system consisting of three circular arcs are studied numerically by using a partial coding rule together with an efficient method for enumerating periodic orbits on the real billiard plane by examining several statistical measures it is shown that the length spectrum and the stability exponents are highly uncorrelated the validity of the semiclassical trace formula is also tested and a remarkable agreement of the semiclassical and quantum density of states is obtained at least for about the lower 15 levels

the symbolic representation of billiards without boundary condition we consider a dynamical system with elastic reflections in the whole plane and show that such a dynamical system can be represented as a symbolic flow over a mixing subshift of finite type this fact enables us to prove an analogue of the prime number theorem for the closed orbits of such a dynamical system

on the fast matrix multiplication in the boundary element method by panel clustering the boundary element method bem leads to a system of linear equations with a full matrix while fem yields sparse matrices this fact seems to require much computational work for the definition of the matrix for the solution of the system and in particular for the matrix vector multiplication which always occurs as an elementary in this paper a method for the approximate matrix vector multiplication is described which requires much less arithmetical work in addition the storage requirements are strongly reduced

uniformization and hybrid simulation analytic models of renewal processes in this paper we demonstrate the use of uniformization in the simulation of renewal processes using uniformization we represent the continuous random variable of interest as the first passage time of a continuous time stochastic process associated with a poisson process we then use this result to develop a hybrid simulation analytic method to model renewal processes the estimators obtained from the hybrid simulation analytic models have lower variance than the variance of the estimators of the traditional simulation models we also discuss the possible impact of this method on the future of simulation methodology

geometrical theory of diffraction and spectral statistics we investigate the influence of diffraction on the statistics of energy levels in quantum systems with a chaotic classical limit by applying the geometrical theory of diffraction we show that diffraction on singularities of the potential can lead to modifications in semiclassical approximations for spectral statistics that persist in the semiclassical limit 0 this result is obtained by deriving a classical sum rule for trajectories that connect two points in coordinate space

efficient scalable parallel higher order direct mom sie method with hierarchically semiseparable structures for 3 d scattering a novel fast scalable parallel algorithm is proposed for the solution of large 3 d scattering problems based on 1 the double geometrical and current approximation higher order dho method of moments mom in the surface integral equation sie formulation and 2 a direct solver for dense linear systems utilizing hierarchically semiseparable hss structures namely an hss matrix representation is used for compression factorization and solution of the system matrix in addition a rank revealing qr decomposition for memory compression is used with a stopping criterion in terms of the relative rank tolerance value a method for geometrical preprocessing of the scatterers based on the cobblestone distance sorting technique is employed in order to enhance the hss algorithm accuracy and parallelization numerical examples show how the accuracy of the dho hss mom sie method is easily controllable by using the relative tolerance for the matrix compression moreover the examples demonstrate low memory consumption as well as much faster simulation time when compared to the direct lu decomposition the method enables dramatically faster monostatic scattering computations than iterative solvers and reduced number of unknowns when compared to low order discretizations finally great scalability of the algorithm is demonstrated on more than one thousand processes

on bivariate hermite interpolation with minimal degree polynomials a newton type approach is used to deal with bivariate polynomial hermite interpolation problems when the data are distributed in the intersections of two families of straight lines as a generalization of regular grids the interpolation operator is degree reducing and the interpolation space is a minimal degree space integral remainder formulas are given for the lagrange case then extended to the hermite case and finally used to obtain error estimates

correlations of chaotic eigenfunctions a semiclassical analysis we derive a semiclassical expression for an energy smoothed autocorrelation function defined on a group of eigenstates of the schr odinger equation the system we consider is an energy conserved hamiltonian system possessing time invariant symmetry the energy smoothed autocorrelation function is expressed as a sum of three terms the first one is analogous to berry s conjecture which is a bessel function of the zeroth order the second and the third terms are trace formulae made from special trajectories the second term is found to be direction dependent in the case of spacing averaging which agrees qualitatively with previous numerical observations in high lying eigenstates of a chaotic billiard

coding chaotic billiards ii compact billiards defined on the pseudosphere abstract we study a la morse coding of compact billiards defined on the pseudosphere as for most bounded systems the coding is non exact except for the non generic case of tiling billiards however two sets of approximate grammar rules can be obtained one specifying forbidden codes and the other allowed ones in between some sequences remain in the unknown zone but their relative amount can be reduced to zero as one lets the length of the approximate grammar rules go to infinity the relationship between these approximate grammar rules and the pruning front introduced by cvitanovic et al is discussed

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

sparsified adaptive cross approximation algorithm for accelerated method of moments computations this paper presents a modification of the adaptive cross approximation aca algorithm for accelerated solution of the method of moments linear system for electrically large radiation and scattering problems as with aca subblocks of the impedance matrix that represent the interaction between well separated subdomains are substituted by compressed approximations allowing for reduced storage and accelerated iterative solution the modified algorithm approximates the original subblocks with products of sparse matrices constructed with the aid of the aca algorithm and of a sub sampling of the original basis functions belonging to either subdomain because of the sampling an additional error is introduced with respect to aca but this error is controllable just like ordinary aca sparsified aca is kernel independent and needs no problem specific information except for the topology of the basis functions as a numerical example rcs computations of the nasa almond are presented showing an important gain in efficiency furthermore the numerical experiment reveals a computational complexity close to n logn for sparsified aca for a target electrical size of up to 50 wavelengths

principles for the design of billiards with nonvanishing lyapunov exponents we introduce a large class of billiards with convex pieces of the boundary which have nonvanishing lyapunov exponents

energy level statistics in the transition region between integrability and chaos a generic one parameter family of billiards discovered and introduced by robnik 1983 is used to study the spectral properties of corresponding quantum systems when the parameter is varied a smooth transition from an integrable system over a typical kam system to an almost ergodic system can be observed the authors calculate up to 7600 lowest reliable energy levels a detailed analysis of the numerical data shows significant deviation from the semiclassical berry robnik formulae for the nearest neighbour level spacing distribution p s except for large level spacings s 1 which can only be explained by a very slow convergence towards the semiclassical regime where these formulae are predicted to be correct at small s the power law level repulsion is clearly observed and a fit by the phenomenological formula by izrailev 1988 1989 is statistically significant

symbolic dynamics and the discrete variational principle we show how to construct symbolic dynamics for the class of 2d dimensional twist mappings generated by piecewise strictly convex concave generating functions the method is constructive and gives an efficient way to find all periodic orbits of these high dimensional symplectic mappings it is illustrated with the cardioid and the stadium billiard

classical chaotic scattering periodic orbits symmetries multifractal invariant sets the infinite set of periodic orbits of a chaotic system is investigated their globally exact symbolic dynamics is related to birkhoff s method of iterated symmetry lines which produces symmetric periodic orbits of various classes a complete picture emerges as to what part of the periodic orbits can be obtained by means of the birkhoff lines in addition the thermodynamic formalism is applied to the multifractal structure created by the horseshoe arrangement of the periodic orbits

quantising a generic family of billiards with analytic boundaries a generic family of plane billiards has been discovered recently the shape of the boundary is given by the quadratic conformal image of the unit circle and is thus real analytic for small deformations of the unit disc the billiard is a typical kam system but becomes ergodic or even mixing when the curvature of the boundary vanishes at some point the kolmogorov entropy has been calculated and it increases with the deformation of the boundary the author studies aspects of the quantum chaos for this billiard he solves numerically the eigenvalue problem for the laplace operator with dirichlet s boundary condition he examines the spectrum and inspects the avoided crossings at which mixing of nearby states occurs the variation of the nodal structure and of the localisation properties of the eigenfunctions is studied in analysing the level spacing distribution he finds a continuous transition from the poisson distribution towards the wigner distribution the exponent in the level repulsion law varies continuously along with a generic perturbation for small perturbations it seems to be proportional to the square root of the perturbation parameter

mixed form nested approximation for wideband multiscale simulations we propose a mixed skeleton and equivalence nested approximation method to compress the impedance matrix of the method of moments for the wideband multiscale simulations we first introduce a nested skeleton approximation where the impedance matrix is expressed recursively by sampling the dominant basis functions e g skeletons with a fully algebraic implementation from the original basis functions the idea is to introduce the automatically constructed test surface around the interface between near and far field regions for each group the dominant rwgs are sampled recursively with the adaptive cross approximation to compress the matrix against the test surface second we introduce a mixed form algorithm of skeleton and equivalence nested approximation method at low levels the nested skeleton approximation is employed and it is smoothly transferred to standard wideband nested equivalence approximation wnesa at high levels an accurate number of skeletons can be always found with a predetermined threshold at a low level which will improve computation efficiency with respect to wnesa the computational complexity of the proposed algorithm is mathcal o n log n n is the number of unknowns numerical wideband multiscale simulations demonstrate the efficiency of the proposed algorithm

approximation of boundary element matrices this article considers the problem of approximating a general asymptotically smooth function in two variables typically arising in integral formulations of boundary value problems by a sum of products of two functions in one variable from these results an iterative algorithm for the low rank approximation of blocks of large unstructured matrices generated by asymptotically smooth functions is developed this algorithm uses only few entries from the original block and since it has a natural stopping criterion the approximative rank is not needed in advance

on the k property of some planar hyperbolic billiards thek property is demonstrated for a class of planar billiards satisfying wojtkowski s principles their boundary may consist of convex scattering concave and linear pieces earlier wojtkowski showed that these billards had non zero lyapunov exponents

minimal topological chaos coexisting with a finite set of homoclinic and periodic orbits abstract in this note we explain how to find the minimal topological chaos relative to finite set of homoclinic and periodic orbits the main tool is the pruning method which is used for finding a hyperbolic map obtained uncrossing pieces of the invariant manifolds whose basic set contains all orbits forced by the finite set under consideration then we will show applications related to transport phenomena and to the problem of determining the orbits structure coexisting with a finite number of periodic orbits arising from the bouncing ball model

nonparametric estimation of the cumulative intensity function for a nonhomogeneous poisson process a nonparametric technique for estimating the cumulative intensity function of a nonhomogeneous poisson process from one or more realizations is developed this technique does not require any arbitrary parameters from the modeler and the estimated cumulative intensity function can be used to generate a point process for monte carlo simulation by inversion three examples are given

trace formulae for three dimensional hyperbolic lattices and application to a strongly chaotic tetrahedral billiard abstract this paper is devoted to the quantum chaology of three dimensional systems a trace formula is derived for compact polyhedral billiards which tessellate the three dimensional hyperbolic space of constant negative curvature the exact trace formula is compared with gutzwiller s semiclassical periodic orbit theory in three dimensions and applied to a tetrahedral billiard being strongly chaotic geometric properties as well as the conjugacy classes of the defining group are discussed the length spectrum and the quantal level spectrum are numerically computed allowing the evaluation of the trace formula as is demonstrated in the case of the spectral staircase n e which in turn is successfully applied in a quantization condition

a free energy bound for the hopfield model the author gives a simple upper and lower bound on the free energy density of the hopfield model of size n with p stored patterns in the limit where n and p tend to infinity with p n to alpha 1 the two bounds coincide for alpha 0

distribution of resonance strengths in microwave billiards of mixed and chaotic dynamics a new measure for statistical properties of the wave function components of quantum systems the distribution of the product of two partial widths is introduced it is tested with data obtained in analog experiments with microwave billiards where the product of two partial widths equals the resonance strengths in the microwave spectra the billiards are from the family of the limacons one with chaotic and two with mixed classical dynamics for completely chaotic systems the partial widths generically obey a porter thomas distribution we show that in this case the distribution of their product equals a k0 distribution while we find deviations of the experimental strength distribution from the k0 distribution for the billiards with mixed dynamics the distributions agree perfectly for the chaotic billiard when taking into account the experimental threshold of detection in the theoretical description hence the strength distribution provides another stringent test for the connection between statistical properties of systems with classical chaotic dynamics and random matrix theory

a multilevel matrix decomposition algorithm for analyzing scattering from large structures a multilevel algorithm is presented for analyzing scattering from electrically large surfaces the algorithm accelerates the iterative solution of integral equations that arise in computational electromagnetics the algorithm permits a fast matrix vector multiplication by decomposing the traditional method of moment matrix into a large number of blocks with each describing the interaction between distant scatterers the multiplication of each block by a trial solution vector is executed using a multilevel scheme that resembles a fast fourier transform fft and that only relies on well known algebraic techniques the computational complexity and the memory requirements of the proposed algorithm are o n log sup 2 n

semiclassical trace formulas for noninteracting identical particles we extend the gutzwiller trace formula to systems of noninteracting identical particles the standard relation for isolated orbits does not apply since the energy of each particle is separately conserved causing the periodic orbits to occur in continuous families the identical nature of the particles also introduces discrete permutational symmetries we exploit the formalism of creagh and littlejohn phys rev a 44 836 1991 who have studied semiclassical dynamics in the presence of continuous symmetries to derive many body trace formulas for the full and symmetry reduced densities of states numerical studies of the three particle cardioid billiard are used to explicitly illustrate and test the results of the theory

multilevel fast adaptive cross approximation algorithm with characteristic basis functions this paper presents a multilevel fast adaptive cross approximation mlfaca algorithm for accelerated iterative solution of the method of moments mom matrix equation for electrically large targets the mlfaca compresses the impedance submatrices between well separated blocks into products of sparse matrices constructed with the aid of the fast adaptive cross sampling facs scheme and the butterfly algorithm as a result the mlfaca can reduce both the computational time and the storage of the mom to mathbf o mathbf n mathbf log mathbf 2 text n where mathbf n is the number of the rao wilton glisson rwg basis functions in the analyzed target meanwhile the mlfaca maintains the adaptive and kernel independent properties furthermore the characteristic basis function method cbfm is employed to decrease the size of the outer matrices of the mlfaca to further reduce the storage and iteration time numerical results are presented to demonstrate the advantages of the proposed method including a successful solution of a scattering problem involving 10 861 668 rwg basis functions

analysis of partial geometry modification problems using the partitioned inverse formula and sherman morrison woodbury formula based method in this paper we present an efficient method for accelerated analysis of the partial geometry modification problem involving an original structure with small modifications the conventional method of moments can be very time consuming for this type of problem because the impedance matrix equation has to be solved anew each time the original structure is modified however the proposed method only requires the solution of the impedance matrix equation of the original structure any small modification of the original object is handled into two steps first by subtracting a small part from the original structure and then by adding a small part to the rest structure both of these steps can be efficiently computed by using the partitioned inverse and sherman morrison woodbury formulas with the solution of the original structure when the structure is modified the proposed method only requires additional operations whose computational burden is o n 2 as opposed to o n 3 where n is the number of unknowns in the original structure furthermore the presented method is purely algebraic and rigorous rather than based on approximations numerical results for electromagnetic scattering are included in this paper to demonstrate the efficiency and accuracy of this method

multilevel adaptive cross approximation mlaca the multilevel adaptive cross approximation mlaca is proposed as a fast method to accelerate the matrix vector products in the iterative solution of the linear system that results from the discretization of electromagnetic integral equations ie with the method of moments mom the single level aca already described in the literature is extended with a multilevel recursive algorithm in order to improve the asymptotical complexity of both the computational cost and the memory requirements the main qualities of aca are maintained it is purely algebraic and independent of the integral equation kernel green s function as long as it produces pseudo rank deficient matrix blocks the algorithm is presented in such a way that it can be easily implemented on top of an existing mom code with most commonly used green s functions

periodic orbits and a correlation function for the semiclassical density of states through the rule that there is one quantum state per planck cell in phase space classical mechanics supplies an average semiclassical density of states for a system with bound motion can it supply more refined averages such as the correlation function for the density of states i shall argue that for the two extreme cases of integrable classical motion and ergodic classical motion information can indeed be obtained on not quite this but a closely related correlation function the results for the two types of motion are markedly different

spectral statistics in the quantized cardioid billiard the spectral statistics of the strongly chaotic cardioid billiard is studied the analysis is based on the first 11 000 quantal energy levels for both odd and even symmetry it is found that the level spacing distribution is in good agreement with the gaussian orthogonal ensemble distribution of random matrix theory in the cases of the number variance and rigidity we observe agreement with the random matrix model for short range correlations only whereas for long range correlations both statistics saturate in agreement with semiclassical expectations furthermore the conjecture that for classically chaotic systems the normalized mode fluctuations have a universal gaussian distribution with unit variance is tested and found to be in very good agreement for both symmetry classes by means of the gutzwiller trace formula the trace of the cosine modulated heat kernel is studied since the billiard boundary is focusing there are conjugate points that give rise to zeros instead of exclusively at gaussian peaks at the locations of the periodic orbits

error bound of the multilevel adaptive cross approximation mlaca an error bound of the multilevel adaptive cross approximation mlaca which is a multilevel version of the adaptive cross approximation singular value decomposition aca svd is rigorously derived for compressing an off diagonal submatrix of the method of moments mom impedance matrix with a binary tree the l level mlaca includes l 1 steps and each step includes 2 l aca svd decompositions if the relative frobenius norm error of the aca svd used in the mlaca is smaller than varepsilon the rigorous proof in this communication shows that the relative frobenius norm error of the l level mlaca is smaller than 1 varepsilon l 1 1 in practical applications the error bound of the mlaca can be approximated as varepsilon l 1 because varepsilon is always ll 1 the error upper bound can be used to control the accuracy of the mlaca to ensure an error of the l level mlaca smaller than varepsilon for different l the aca svd threshold can be set to 1 varepsilon tfrac 1 l 1 1 which approximately equals varepsilon l 1 for practical applications

new universal aspects of diffusion in strongly chaotic systems we study some new universal aspects of diffusion in chaotic systems especially those having very large lyapunov coefficients on the chaotic indecomposable topologically transitive component we do this by discretizing the chaotic component on the surface of section sos in a large number n of simplectically equally big cells in the sense of equal relative invariant ergodic measure normalized so that the total measure of the chaotic component is unity by iterating the transition of the chaotic orbit through the sos where j counts the number of iterations discrete time and assuming complete lack of correlation even between consecutive crossings which can be justified due to the very large lyapunov exponents we show the universal approach of the relative measure of the occupied cells denoted by to the asymptotic value of unity in the following way so that in the limit of big n we have for j n fixed the exponential law this analytic result is verified numerically in a variety of specific systems for a plane billiard robnik 1983 for a 3d billiard prosen 1997 for an ergodic logistic map tent map for a standard map k 400 and for the hydrogen atom in a strong magnetic field the agreement is almost perfect except in the latter two systems for some long time deviations on very small scales however for henon heiles system and for the standard map k 3 the deviations are noticeable though not very big only about 1 we have tested the random number generators press et al 1986 and confirmed that some are almost perfect ran0 and ran3 whilst two of them ran1 and ran2 exhibit big deviations

estimation of a low intensity filtered poisson process in additive white gaussian noise a poisson gauss process is defined as the sum of a filtered poisson process a poisson process passed through a linear filter and a white gaussian noise this model describes the electrical signal at the output of an optical measuring unit consisted of a photodetector and its following amplifying circuits the intensity of the poisson process in this model is proportional to the received optical power with the observations of a poisson gauss process three estimation problems are considered minimum mean squared error estimation of the poisson process at every fixed but arbitrary time minimum mean squared error estimation of the poisson intensity and the maximum likelihood estimation of the intensity the solutions to these problems are presented in terms of a complicated functional of the observed poisson gauss process which is hard to compute for an arbitrary value of the poisson intensity however under a low intensity regime nonlinear filtering schemes are developed to efficiently compute this functional this special case provides a signal processing framework for single photon detection a technology dedicated to measurement of low optical powers