low firing rates in a compartmental model neuron a nonlinear relationship is obtained between the membrane potential of a compartmental model neuron as a function of input stimulation this is used to show how shunting effects can lead to low output firing rates in associative memory networks

numerical solution of scattering from a hard surface in a medium with a linear profile the paper is concerned with the scattering of waves incident at grazing angles upon a rough surface on which neumann boundary conditions apply when the medium has a linearly varying refractive index the scattering is governed by an integral equation which uses a parabolic form of the green s function the numerical solution of this system requires careful analytical treatment of the green s function and the purpose of this paper is to describe the details both of the analysis and the numerical scheme some computational results are shown and the accuracy of the inversion of the integral equation is tested by comparison with an analytical approximation

efficient tau p hyperbolic velocity filtering time and offset varying velocity filtering can be achieved by limiting the data input to forward tau p transforms this limiting procedure called hyperbolic velocity filtering hvf suppresses transform related artifacts as well as coherent and noncoherent noise while retaining elliptical reflection events we show that hvf can be viewed as a muting process in the slant stack domain based on this simple but physical interpretation of hvf a more efficient computer implementation is proposed we further examine possible applications of hvf for processing seismic reflection data and illustrate the results using both synthetic and real data examples

the general uq sl 2 invariant xxz integrable quantum spin chain the boundary conditions are constructed for the general xxz quantum integrable spin chain such that the resulting system is invariant under the quantum algebra uq sl 2 action the result generalizes that due to pasquier and saleur 1990 obtained for spin 1 2 and spin 1

coherent field and specular reflection at grazing incidence on a rough surface the coherent component of the field scattered at grazing angles from a slightly rough pressure release surface is found this is valid for multiple scattering and is based upon the parabolic integral equation method also examined are the scattering of planes waves under the method and in particular the effect of truncating the boundary integral it is shown that the coherent field remains invariant when the source and receiver are displaced vertically by equal and opposite distances as was found numerically in a previous paper in general this can be shown to hold because the coherent field due to any plane wave is specular however under the parabolic equation method reflection is not specular and thus the result is of particular interest reflection coefficients are given in closed form for several surface statistics valid asymptotically at large distances

sound propagation with a linear sound speed profile over a rough surface the distribution of an acoustic field propagating at grazing angles over a hard rough surface is described by an integral equation that results from the helmholz integral in the parabolic approximation the green s function corresponding to the case when the sound speed varies linearly with distance from the surface is found the integral equation is solved analytically for the case of a flat surface the field distribution in the space above the surface obtained by numerical methods is presented for a flat surface and for a rough surface in both cases the sound speed varies linearly with distance from the surface

zn n 1 generalization of the chiral potts model we show that ther matrix which intertwines twon by nn 1 state cyclicl operators related with a generalization ofuq sl n algebra can be considered as a boltzmann weight of four spin box for a lattice model with two spin interaction just as ther matrix of the checkerboard chiral potts model the rapidity variables lie on the algebraic curve of the genusg n2 n 1 n 1 n n 1 defined by 2n 3 independent moduli this curve is a natural generalization of the curve which appeared in the chiral potts model factorization properties of thel operator and its connection to the sos models are also discussed

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

on the fusion of face and vertex models some new solutions of the yang baxter or star triangle relations are found using the fusion procedure for belavin s 1981 zn zn symmetric model the relation between the fusion procedure of the vertex and face models is also constructed

l operator for belavin s r matrix acting on the space of theta functions for the z nz symmetric elliptic r matrix l operators which act on the space of a 1 n 1 integrable characters or the affine weyl group invariants of the fixed level l are constructed for l 1 the matrix elements of the l operator and those of the r matrix are shown to be the same

ruijsenaars macdonald type difference operators from belavin model with open boundary conditions antisymmetric fusions of the belavin model with integrable open boundary conditions are studied the centre of the corresponding operator algebra the sklyanin determinant is constructed we prove that the transfer matrices of the fusion hierarchies mutually commute utilizing the factorized l operators this commuting family is expressed as mutually commuting difference operators acting on a function space this gives ruijsenaars macdonald type commuting difference operators which describe the conservation laws of an integrable system

solvable quantum version of an integrable hamiltonian system solvable quantum versions of the classical dynamical system characterized by the hamiltonian h nj k 1 pjpk cos qj qk are presented the eigenvalues of the quantum hamiltonians are exhibited as well as the corresponding eigenfunctions

lateral prediction for noise attenuation by t x and f x techniques attenuating random noise with a prediction filter in the time space domain generally produces results similar to those of predictions done in the frequency space domain however in the presence of moderate to high amplitude noise time space or t x prediction passes less random noise than does frequency space or f x prediction the f x prediction may also produce false events in the presence of parallel events where t x prediction does not these advantages of t x prediction are the result of its ability to control the length of the prediction filter in time an f x prediction produces an effective t x domain filter that is as long in time as the input data gulunay s f x domain prediction tends to bias the predictions toward the traces nearest the output trace allowing somewhat more noise to be passed but this bias may be overcome by modifying the system of equations used to calculate the filter the 3 d extension to the 2 d t x and f x prediction techniques allows improved noise attenuation because more samples are used in the predictions and the requirement that events be strictly linear is relaxed

localized 2 d filter based linear coherent noise attenuation a novel localized two dimensional 2 d filter is proposed the proposed filter derived from the frequency wavenumber filter and radon transform filter with the filtering operation applied at the stage of fourier projection has good local property and less filtering distortion an example of the proposed method to attenuate linear coherent noise in a seismic image is given comparisons of the results between our method and the conventional 2 d filters including frequency wavenumber filter and radon transform filter show that the new method outperforms both frequency wavenumber method and radon transform method

complete integrability of relativistic calogero moser systems and elliptic function identities poincare invariant generalizations of the galilei invariant calogero moser a particle systems are studied a quantization of the classical integrals s1 sn is presented such that the operators si9 sn mutually commute as a corollary it follows that si9 9sn poisson commute these results hinge on functional equations satisfied by the weierstrass and 0 functions a generalized cauchy identity involving the function leads to an n x n matrix l whose symmetric functions are proportional to sl5 9sn

elliptic quantum groups and ruijsenaars models we construct symmetric and exterior powers of the vector representation of the elliptic quantum groupse sln the corresponding transfer matrices give rise to various integrable difference equations which could be solved in principle by the nested bethe ansatz method in special cases we recover the ruijsenaars systems of commuting difference operators

rough surface scattering via the smoothing method the smoothing method is used to find the first two moments i e the mean and the two point two time correlation function of the field scattered by a rough surface the results are expressed in terms of a reflection coefficient and a differential scattering coefficient they are compared with those found by several other methods

a completely integrable hamiltonian system the dynamical system characterized by the hamiltonian h q p j k 1 n p jp kf q dj q k with f x cos x sin x is completely integrable here n is an arbitrary positive integer and are 4 arbitrary constants and real and both real or both imaginary

elliptic ruijsenaars schneider model via the poisson reduction of the affine heisenberg double it is shown that the elliptic ruijsenaars schneider model can be obtained from the affine heisenberg double by means of the poisson reduction procedure the dynamical r matrix naturally appears in the construction

boundary k matrices for the six vertex and the n 2n 1 an 1 vertex models boundary conditions compatible with integrability are obtained for two dimensional models by solving the factorizability equations for the reflection matrices k or theta for the six vertex model the general solution depending on four arbitrary parameters is found for the an 1 models all diagonal solutions are found the associated integrable magnetic hamiltonians are explicitly derived

the gervais neveu felder equation and the quantum calogero moser systems we quantize the spin calogero moser model in ther matrix formalism the quantumr matrix of the model is dynamical thisr matrix has already appeared in gervais neveu s quantization of toda field theory and in felder s quantization of the knizhnik zamolodchikov bernard equation

waveform inversion using a back propagation algorithm and a huber function norm waveforminversionfacesdifficultieswhenappliedtoreal seismic data including the existence of many kinds of noise the 1 norm is more robust to noise with outliers than the least squares method nevertheless the least squares method is preferred as an objective function in many algorithms because the gradient of the 1 norm has a singularity when the residual becomes zero we propose a complex valued huber function for frequency domain waveform inversion that combines the 2 norm for small residuals with the 1 norm for large residuals we also derive a discretized formula for the gradient of the huber function through numericaltestsonsimplesyntheticmodelsandmarmousidata we find the huber function is more robust to outliers and coherent noise we apply our waveform inversion algorithm to field data taken from the continental shelf under the east sea in korea in this setting we obtain a velocity model whose syntheticshotprofilesaresimilartotherealseismicdata

fusion procedure for open chains the authors have generalized sklyanin s approach of constructing open integrable quantum spin chains to the case of pt invariant r matrices they formulate a fusion procedure for such chains in particular they show that the fused transfer matrix can be expressed in terms of products of the original transfer matrix and products of certain quantum determinants which can be explicitly evaluated applications of these results include constructing open integrable higher spin chains as well as obtaining functional equations for transfer matrix eigenvalues which may be solved by an analytical bethe ansatz

local linear coherent noise attenuation based on local polynomial approximation we propose a new technique for the attenuation of locally coherent noise we assume that the moveout of the noise is locally linear and approximate its amplitude variations with offset using piecewise local polynomial models thus our method consists of three steps detection of the noise locally linear coherent noise llcn amplitude estimation by a local polynomial approximation lpa and subtraction of the estimated coherent noise from the original data applying the proposed method to synthetic data and to a field data set shows that the lpa filter has good ability to model llcn and is insensitive to the filter parameters comparisons of the results obtained by our method with those from the traditional frequency wavenumber filter and the localized 2d filter in the fourier projection domain fpf show that the new method outperforms both traditional methods in situations with complex coherent noise

ruijsenaars commuting difference operators as commuting transfer matrices for belavin s elliptic quantum r matrix we construct an l operator as a set of difference operators acting on functions on the type a weight space according to the fundamental relation rll llr taking the trace of the l operator gives a set of commuting difference operators we show that for the above mentioned l operator this approach gives macdonald type operators with elliptic theta function coefficient actually equivalent to ruijsenaars operators the relationship between the difference l operator and krichever s lax matrix is given and an explicit formula for elliptic commuting differential operators is derived we also study the invariant subspace for the system which is spanned by symmetric theta functions on the weight space

time domain helmholtz kirchhoff integral for surface scattering in a refractive medium time domain helmholtz kirchhoff integral h k integral for forward surface scattering is extended to a refractive medium ray theory is applied to obtain the green s function while the normal derivative in the integral is evaluated analytically using a ray geometry along with the ray based green s function this approach allows for stationary phase approximation which reduces the surface integration to a line integration for high frequency signals with a narrow bandwidth an asymptotic form of the time domain h k integral then can be derived using the fourier transform the pressure field scattered from a sinusoidal surface wave in a constant gradient sound speed profile is evaluated and compared to the result based on a conventional ray model

boundary k matrix elliptic dunkl operator and quantum many body systems the infinite dimensional representation of the boundary k operator the solution of the reflection equation is considered the trigonometric k matrix is studied as a degenerate case of the elliptic operator a method to construct the elliptic dunkl operator is proposed and the relationship with the quantum many body problem is also discussed

edge preserving polynomial fitting method to suppress random seismic noise this paper focuses on suppressing random seismic noise while preserving signals and edges we propose an edge preserving polynomial fitting eppf method leading to good signal and edge preservation the eppf method assumes that a 1d signal can be modeled by a polynomial a series of shifted windows are used to estimate any sample in a 1d signal after that the window with the minimum fitting error is selected and its output is assigned as the final estimate for this sample for a point in 2d seismic data several 1d signals are extracted along different directions first and then are processed by the eppf method after that we select the direction with a minimum fitting error and assign its output as the final estimate for this point applications with synthetic and real data sets show that the eppf method suppresses the random seismic noise effectively while preserving the signals and edges comparisons of results obtained by the eppf method the edge preserving smoothing eps method and the polynomi