single variable term semi latticized fuzzy relation geometric programming with max product operator considering the practical application background in peer to peer network system we investigate the single variable term semi latticized fuzzy relation geometric programming with max product operator in this paper based on the characteristics of the objective function and feasible domain we develop a matrix approach to deal with the proposed problem a step by step algorithm is proposed to find an optimal solution without solving all the minimal solutions of the constraint two examples are given to illustrate the feasibility and efficiency of the algorithm

a three dimensional parabolic equation model that includes the effects of rough boundaries a three dimensional parabolic equation 3dpe model that handles wide propagation angles in depth narrow propagation angles in azimuth and rough boundaries is derived and solved numerically with the method of alternating directions a homogeneous boundary condition which is easily incorporated into the numerical solution of the 3dpe is applied at the ocean surface to approximate the effects of rough boundaries in terms of a reflection coefficient that depends on grazing angle calculations are presented to demonstrate the accuracy of the 3dpe and to demonstrate that horizontal coupling the effects due to the term involving azimuth derivatives can be important in shallow water previous work has focused on deep water applications the model is applied to problems involving rough boundaries and range dependence

an energy conserving parabolic equation for elastic media the accuracy of the parabolic equation pe method is improved for range dependent elastic media the energy conserving elastic pe is a generalization of the energy conserving acoustic pe a range dependent waveguide is approximated by a sequence of range independent regions a linear approximation is derived for the nonlinear condition corresponding to conservation of compressional energy flux at the vertical interfaces between range independent regions the rotated elastic pe is applied to generate reference solutions for demonstrating accuracy the energy conserving elastic pe is applied to solve problems involving the propagation of an interface wave along a sloping ocean bottom and a problem involving mode cutoff and coupling into shear wave beams in the ocean bottom the latter problem is analogous to a cutoff problem that was first solved with the acoustic pe f b jensen and w a kuperman j acoust soc am 67 1564 1566 1980

tropical linear algebra with the łukasiewicz t norm the max ukasiewicz semiring is defined as the unit interval 0 1 equipped with the arithmetics a b max a b and a b max 0 a b 1 linear algebra over this semiring can be developed in the usual way we observe that any problem of the max ukasiewicz linear algebra can be equivalently formulated as a problem of the tropical max plus linear algebra based on this equivalence we develop a theory of the matrix powers and the eigenproblem over the max ukasiewicz semiring

on the minimal solutions of max min fuzzy relational equations in this paper the minimal solutions of max min fuzzy relational equations are investigated a sufficient and necessary condition for discriminating whether a given solution is minimal or not is shown furthermore we propose a new algorithm for computing all minimal solutions less than or equal to a given one

resolution of a system of the max product fuzzy relation equations using lou factorization in this paper the lu factorization is extended to the fuzzy square matrix with respect to the max product composition operator called l u factorization equivalently we will find two fuzzy lower and upper triangular matrices l and u for a fuzzy square matrix a such that a l u where is the max product composition an algorithm is presented to find the matrices l and u furthermore some necessary and sufficient conditions are proposed for the existence and uniqueness of the l u factorization for a given fuzzy square matrix a an algorithm is also proposed to find the solution set of a square system of fuzzy relation equations fre using the l u factorization the algorithm finds the solution set without finding its minimal solutions and maximum solution it is shown that the two algorithms have a polynomial time complexity as o n 3 since the determination of the minimal solutions is an np hard problem the algorithm can be very important from the practical point of view

linear optimization with an arbitrary fuzzy relational inequality in this paper optimization of a linear objective function with fuzzy relational inequality constraints is investigated whereby an arbitrary function is considered as fuzzy composition the feasible solution set is determined and compared with some common results in the literature a necessary and sufficient condition and three other necessary conditions are presented to conceptualize the feasibility of the problem it is shown that in general a lower bound is always attainable for the optimal objective value moreover we prove that the optimal solution of the problem is obtained if the problem is defined by a non decreasing or non increasing function an algorithm is presented to summarize the process and an example is described to illustrate the algorithm

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

fuzzy linear optimization in the presence of the fuzzy relation inequality constraints with max min composition in this paper we study the new linear objective function optimization with respect to the fuzzy relational inequalities defined by max min composition in which fuzzy inequality replaces ordinary inequality in the constraints fuzzy inequalities enable us to attain the optimal points that are better solutions than those resulting from the resolution of the similar problems with ordinary inequality constraints denoted by x o i in this paper we have presented an algorithm to generate such optimal solutions also two examples are given to illustrate the algorithm presented and some real application of this work

steady states in the scheduling of discrete time systems abstract steady solutions to a two sided max min linear system of equations with real coefficients are considered the problem is motivated by the demand to schedule cyclically repeated activities with deterministic processing times the maximum steady solutions are characterized as min eigenvectors of a special matrix q this condition is a necessary but not a sufficient one it has also been proven that the general problem of the recognition of solvability of this two sided system is np complete

a mapping approach for handling sloping interfaces a mapping approach for handling sloping interfaces in parabolic equation solutions is developed and tested at each range the medium is rigidly translated vertically so that a sloping interface becomes horizontal to simplify the approach the slope is assumed to be small and the extra terms that arise in the wave equation under the mapping are neglected the effects of these terms can be approximately accounted for by applying a leading order correction to the phase the mapping introduces variations in topography which are relatively easy to handle for the case of a pressure release boundary condition the accuracy of the approach is demonstrated for problems involving fluid sediments the approach should also be accurate for problems involving elastic sediments and should be useful for solving three dimensional problems involving variable topography

fast solving method of fuzzy relational equation and its application to lossy image compression reconstruction a fast solving method of the solution for max continuous t norm composite fuzzy relational equation of the type g i j r sup t spl square a sub i sup t spl square b sub j i 1 2 i j 1 2 j where a sub i spl isin f x x x sub 1 x sub 2 x sub m bj spl isin f y y y sub 1 y sub 2 y sub n r spl isin f x spl times y and spl square max continuous t norm composition is proposed it decreases the computation time ijmn l t p to jm i n l p where l t and p denote the computation time of min t norm and relative pseudocomplement operations respectively by simplifying the conventional reconstruction equation based on the properties of t norm and relative pseudocomplement the method is applied to a lossy image compression and reconstruction problem where it is confirmed that the computation time of the reconstructed image is decreased to 1 335 6 the compression rate being 0 0351 and it achieves almost equivalent performance for the conventional lossy image compression methods based on discrete cosine transform and vector quantization

on injectivity of semimodules over additively idempotent division semirings and chain mv semirings abstract in this paper we give a characterization of injective semimodules over additively idempotent semirings consequently we provide a complete description of injective semimodules over the semifield of tropical integers and give an explicit construction of the injective hulls of semimodules over chain division semirings we also give a criterion for self injective mv semirings with an atomic boolean center and describe the structure of finitely generated injective semimodules over finite mv semirings as well as we show that every complete mv semiring with an atomic boolean center is an exact semiring which is defined by a hahn banach type separation property on semimodules arising in the tropical case from the phenomenon of tropical matrix duality moreover we show that complete boolean algebras are precisely the mv semirings in which every principal ideal is injective

stereo effect of image converted from planar research on planar to stereo image conversion has significant theoretical and practical implications for image processing in this paper we use a method which segments an image into sub blocks to perform this kind of conversion parameters such as random variables are used for conversion control we use two quantitative criteria cross entropy and root mean square error to evaluate the stereo effect furthermore the stereo effect that the random variables create is discussed the results of the experiment show that i when all random variables have the same distribution different values of these random variables only slightly affect the stereo effect and ii when different distributions are applied to the random variables the cross entropies or root mean square errors are slightly different which indicates different distributions have a small influence on the stereo effect generally we recommend normal distribution for better stereo effect in most cases

applications and time domain solution of higher order parabolic equations in underwater acoustics a higher order parabolic equation and the corresponding higher order time domain parabolic equation are derived from a pade series and solved numerically these models provide accurate solutions for problems involving very wide angle propagation e g propagation in the nearfield or over a hard ocean bottom propagation in domains in which sound speed variations are large e g propagation in deep water deep within the ocean bottom in high speed ocean bottoms and possibly of different wave types and propagation out to very long ranges the possibility of modeling elastic wave propagation with a similar approach is considered

a higher order parabolic equation for wave propagation in an ocean overlying an elastic bottom a higher order elastic parabolic equation hepe is derived for wave propagation in depth dependent and weakly range dependent fluid solid media galerkin s method is used to discretize the depth operators in the hepe within layers in which depth variations in the lame constants and density are continuous discontinuities in material properties are handled with centered differences for the interface conditions between layers the numerical solution of the hepe also involves the method of alternating directions and crank nicolson integration the hepe is applied to underwater wave propagation problems involving a water column over an elastic bottom including a weakly range dependent problem the accuracy of the hepe is demonstrated with benchmark calculations

coupling scattering from the sea surface to a one way marching propagation model via conformal mapping validation propagation models in underwater acoustics usually incorporate sea surface scattering effects in an ad hoc manner which in most cases requires making severe approximations in particular to include in a coherent manner in a marching acoustic propagation model the scattering that occurs at a rough sea surface poses a serious problem dozier j acoust soc am 75 1415 1432 1984 introduced a rigorous approach in the framework of the split step parabolic equation model which used a sequence of conformal mappings to flatten segments of the sea surface locally each conformal mapping preserved the elliptic form of the wave equation in each transformed space the parabolic approximation is made and the solution advanced one range step the method has the attractive feature of handling surface roughness within a propagation model in a mathematically consistent manner including refraction and multiple surface interactions when and where they occur in this work the technique developed by dozier is impleme

an algorithm for solving fuzzy relation equations with max t composition operator this paper studies the problem of solving a max t composite finite fuzzy relation equation where t is a special class of pseudo t norms if the equation is solvable then its set of feasible solutions is determined by the greatest solution and a finite number of minimal solutions some necessary conditions are presented for the minimal solutions in terms of the maximum solution and zero value under these conditions some minimal solutions of the system can be obtained easily some procedures are also proposed in order to simplify the original system the simplified system is then decomposed if possible into several subsystems with smaller dimensions which are very easy to solve furthermore a method is presented to solve each subsystem by combining the method and those procedures an efficient algorithm is proposed to obtain the set of feasible solutions of the original system two examples are also given to illustrate the algorithm

latticized linear programming subject to max product fuzzy relation inequalities with application in wireless communication in this paper we introduce the latticized linear programming problem subject to max product fuzzy relation inequalities with application in the optimization management model of wireless communication emission base stations resolution of max product fuzzy relation inequalities is studied by comparing with that of the corresponding max product fuzzy relation equations a solution matrix approach is developed for solving the proposed problem without finding all the quasi minimal solutions of the constraint for carrying out the solution matrix approach we provide a step by step algorithm illustrated by a numerical example

two parabolic equations for propagation in layered poro elastic media parabolic equation methods for fluid and elastic media are extended to layered poro elastic media including some shallow water sediments a previous parabolic equation solution for one model of range independent poro elastic media collins et al j acoust soc am 98 1645 1656 1995 does not produce accurate solutions for environments with multiple poro elastic layers first a dependent variable formulation for parabolic equations used with elastic media is generalized to layered poro elastic media an improvement in accuracy is obtained using a second dependent variable formulation that conserves dependent variables across interfaces between horizontally stratified layers furthermore this formulation expresses conditions at interfaces using no depth derivatives higher than first order this feature should aid in treating range dependence because convenient matching across interfaces is possible with discretized derivatives of first order in contrast to second order

reachability of eigenspaces for interval matrices in max min algebra abstract in max min algebra the standard pair of operations plus and times is substituted by pair of operations and where a b max a b a b min a b a square matrix a is x robust if its eigenspace is reached starting at each vector of a given interval vector x x x x x various versions of the reachability for an interval vector x and an interval matrix a a a a a depending on the used quantifiers and their order are studied the universal possible tolerance and weak tolerance a robustness of x and x robustness of a over max min algebra are defined and polynomial algorithms for its checking in the case of circulant matrices are described

bayesian nonparametric estimation for incomplete data via successive substitution sampling in the problem of estimating an unknown distribution function f in the presence of censoring one can use a nonparametric estimator such as the kaplan meier estimator or one can consider parametric modeling there are many situations where physical reasons indicate that a certain parametric model holds approximately in these cases a nonparametric estimator may be very inefficient relative to a parametric estimator on the other hand if the parametric model is only a crude approximation to the actual model then the parametric estimator may perform poorly relative to the nonparametric estimator and may even be inconsistent the bayesian paradigm provides a reasonable framework for this problem in a bayesian approach one would try to put a prior distribution on f that gives most of its mass to small neighborhoods of the entire parametric family we show that certain priors based on the dirichlet process prior can be used to accomplish this for these priors the posterior distribution of f given the censored data appears to be analytically intractable we provide a method for approximating this posterior distribution through the use of a successive substitution sampling algorithm we also show convergence of the algorithm

higher order pade approximations for accurate and stable elastic parabolic equations with application to interface wave propagation higher order pade approximations are applied to derive accurate and stable parabolic equations for sound propagation in oceans bounded below by an elastic bottom or bounded above by ice cover accuracy is achieved by placing constraints on the derivatives of the pade approximations at the point corresponding to the reference wave number stability is achieved by requiring that the pade approximations map part of the lower left quadrant of the complex plane into the upper half of the complex plane elastic parabolic equations based on these pade series can handle problems involving compressional shear and interface waves very wide propagation angles and large depth variations and weak range variations in the seismoacoustic parameters a finite difference spectral solution is developed for generating reference solutions and starting fields the rotated elastic parabolic equation is used to investigate the accuracy of the elastic parabolic equation for range dependent problems

fuzzy transforms for compression and decompression of color videos we use fuzzy transforms for coding decoding color frames of videos and we compare the results with the same frames reconstructed with the standard jpeg method we classify all the frames in intra frames and predictive frames by adopting a similarity measure based on the lukasiewicz t norm and a pre processing phase which determines the best similarity threshold value the compression is made on particular frames called d frames obtained from a suitable difference defined on the values of the pixels of an intra frame and a predictive frame under high compression rates we see that the peak signal to noise ratio of the frames obtained with the fuzzy transforms is averagely close to the psnr obtained with the jpeg method we use the videos at url sampl eng ohiostate edu sampl database htm

a single scattering correction for large contrasts in elastic layers the single scattering solution is implemented in a formulation that makes it possible to accurately handle solid solid interfaces with the parabolic equation method problems involving large contrasts across sloping stratigraphy can be handled by subdividing a vertical interface into a series of two or more scattering problems the approach can handle complex layering and is applicable to a large class of seismic problems the solution of the scattering problem is based on an iteration formula which has improved convergence in the new formulation and the transverse operator of the parabolic wave equation which is implemented efficiently in terms of banded matrices accurate solutions can often be obtained by using only one iteration

a scaled mapping parabolic equation for sloping range dependent environments parabolic equation solutions use various techniques for approximating range dependent interfaces one is a mapping approach m d collins et al j acoust soc am 107 1937 1942 2000 where at each range the domain is vertically translated so that sloping bathymetry becomes horizontal and range dependence is transferred to the upper surface in this paper a scaled mapping is suggested where the domain is vertically distorted so that both the bathymetry and upper surface are horizontal accuracy is demonstrated for problems involving fluid sediments generalizations of the approach should be useful for environments with layer thicknesses that vary with range

the flattened surface parabolic equation a simple surface flattening transformation is applied to the problem of underwater acoustic scattering from an irregular sea surface the flattened surface elliptic wave equation is factored to obtain a parabolic equation that has the same high angle capability as recent parabolic equation models the flattened surface parabolic equation contains an additional surface slope term but includes forward scattering from the irregular sea surface the transformation creates additional volume irregularities and irregularities in the water sediment interface that the range and depth mesh need to resolve the surface flattening transformation is easy to implement in a parabolic equation model it compares very well with results obtained using boundary integral equations an example is given of scattering at 400 hz from a sea surface with wave heights of 3 m or nearly a wavelength

the stabilized self starter a stability problem is eliminated from the self starter which is a parabolic equation technique for generating initial conditions the stability problem is associated with evanescent modes that correspond to nearly vertical propagation it causes the solution to break down at certain frequencies for problems involving relatively low attenuation the error is restricted to relatively short ranges unless the medium is strongly range dependent near the source the stability problem is eliminated by placing the pole of the smoothing operator in the self starter away from the eigenvalues of the depth operator

markov chain monte carlo in approximate dirichlet and beta two parameter process hierarchical models summary we present some easy to construct random probability measures which approximate the dirichlet process and an extension which we will call the beta two parameter process the nature of these constructions makes it simple to implement markov chain monte carlo algorithms for fitting nonparametric hierarchical models and mixtures of nonparametric hierarchical models for the dirichlet process we consider a truncation approximation as well as a weak limit approximation based on a mixture of dirichlet processes the same type of truncation approximation can also be applied to the beta two parameter process both methods lead to posteriors which can be fitted using markov chain monte carlo algorithms that take advantage of blocked coordinate updates these algorithms promote rapid mixing of the markov chain and can be readily applied to normal mean mixture models and to density estimation problems we prefer the truncation approximations since a simple device for monitoring the adequacy of the approximation can be easily computed from the output of the gibbs sampler furthermore for the dirichlet process the truncation approximation offers an exponentially higher degree of accuracy over the weak limit approximation for the same computational effort we also find that a certain beta two parameter process may be suitable for finite mixture modelling because the distinct number of sampled values from this process tends to match closely the number of components of the underlying mixture distribution

generalization of the rotated parabolic equation to variable slopes the rotated parabolic equation j acoust soc am 87 1035 1037 1990 is generalized to problems involving ocean sediment interfaces of variable slope the approach is based on approximating a variable slope in terms of a series of constant slope regions the original rotated parabolic equation algorithm is used to march the field through each region an interpolation extrapolation approach is used to generate a starting field at the beginning of each region beyond the one containing the source for the elastic case a series of operators is applied to rotate the dependent variable vector along with the coordinate system the variable rotated parabolic equation should provide accurate solutions to a large class of range dependent seismo acoustics problems for the fluid case the accuracy of the approach is confirmed through comparisons with reference solutions for the elastic case variable rotated parabolic equation solutions are compared with energy conserving and mapping solutions

nonuniform depth grids in parabolic equation solutions the parabolic wave equation is solved using a finite difference solution in depth that involves a nonuniform grid the depth operator is discretized using galerkin s method with asymmetric hat functions examples are presented to illustrate that this approach can be used to improve efficiency for problems in ocean acoustics and seismo acoustics for shallow water problems accuracy is sensitive to the precise placement of the ocean bottom interface this issue is often addressed with the inefficient approach of using a fine grid spacing over all depth efficiency may be improved by using a relatively coarse grid with nonuniform sampling to precisely position the interface efficiency may also be improved by reducing the sampling in the sediment and in an absorbing layer that is used to truncate the computational domain nonuniform sampling may also be used to improve the implementation of a single scattering approximation for sloping fluid solid interfaces

fast algorithms for the discrete cosine transform several fast algorithms for computing discrete cosine transforms dcts and their inverses on multidimensional inputs of sizes which are powers of 2 are introduced because the 1 d 8 point dct and the 2 d 8 8 point dct are so widely used they are discussed in detail algorithms for computing scaled dcts and their inverses are also presented these have applications in compression of continuous tone image data where the dct is generally followed by scaling and quantization

the collapsed gibbs sampler in bayesian computations with applications to a gene regulation problem abstract this article describes a method of grouping and collapsing in using the gibbs sampler and proves from an operator theory viewpoint that the method is in general beneficial the norms of the forward operators associated with the corresponding nonreversible markov chains are used to discriminate among different simulation schemes when applied to bayesian missing data problems the idea of collapsing suggests skipping the steps of sampling parameter s values in standard data augmentation by doing this we obtain a predictive update version of the gibbs sampler a procedure of calculating the posterior odds ratio via the collapsed gibbs sampler when incomplete observations are involved is presented as an illustration of possible applications three examples along with a bayesian treatment for identifying common protein binding sites in unaligned dna sequences are provided

a bayesian semiparametric model for random effects meta analysis in meta analysis there is an increasing trend to explicitly acknowledge the presence of study variability through random effects models that is one assumes that for each study there is a study specific effect and one is observing an estimate of this latent variable in a random effects model one assumes that these study specific effects come from some distribution and one can estimate the parameters of this distribution as well as the study specific effects themselves this distribution is most often modeled through a parametric family usually a family of normal distributions the advantage of using a normal distribution is that the mean parameter plays an important role and much of the focus is on determining whether or not this mean is 0 for example it may be easier to justify funding further studies if it is determined that this mean is not 0 typically this normality assumption is made for the sake of convenience rather than from some theoretical justification and may not actually hold w

subeigenvectors and supereigenvectors of fuzzy matrices abstract a fuzzy algebra is a triple b where b is a nonempty bounded linearly ordered set and a b max a b a b min a b for a b b a vector x is said to be a eigenvector of a square matrix a if a x x for some b the aim of the paper is to solve subeigenproblem and supereigenproblem for some b that is to find a solution x of a x x and a x x x is called subeigenvector and supereigenvector respectively the problems are related to and motivated by the similar problems of tropical linear algebra in this paper the properties of subeigenvectors and supereigenvectors are described and the values associated with subeigenvectors and supereigenvectors are characterized as a consequence efficient algorithms for checking all equivalent conditions are introduced

rates of convergence of the hastings and metropolis algorithms we apply recent results in markov chain theory to hastings and metropolis algorithms with either independent or symmetric candidate distributions and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution pi in the independence case in mathbb r k these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of pi in the symmetric case in mathbb r only we show geometric convergence essentially occurs if and only if pi has geometric tails we also evaluate recently developed computable bounds on the rates of convergence in this context examples show that these theoretical bounds can be inherently extremely conservative although when the chain is stochastically monotone the bounds may well be effective

single scattering parabolic equation solutions for elastic media propagation including rayleigh waves the parabolic equation method with a single scattering correction allows for accurate modeling of range dependent environments in elastic layered media for problems with large contrasts accuracy and efficiency are gained by subdividing vertical interfaces into a series of two or more single scattering problems this approach generates several computational parameters such as the number of interface slices an iteration convergence parameter and the number of iterations n for convergence using a narrow angle approximation the choices of n 1 and 2 give accurate solutions analogous results from the narrow angle approximation extend to environments with larger variations when slices are used as needed at vertical interfaces the approach is applied to a generic ocean waveguide that includes the generation of a rayleigh interface wave results are presented in both frequency and time domains

a single scattering correction for the seismo acoustic parabolic equation an efficient single scattering correction that does not require iterations is derived and tested for the seismo acoustic parabolic equation the approach is applicable to problems involving gradual range dependence in a waveguide with fluid and solid layers including the key case of a sloping fluid solid interface the single scattering correction is asymptotically equivalent to a special case of a single scattering correction for problems that only have solid layers kusel et al j acoust soc am 121 808 813 2007 the single scattering correction has a simple interpretation conservation of interface conditions in an average sense that facilitated its generalization to problems involving fluid layers promising results are obtained for problems in which the ocean bottom interface has a small slope

distribution functions of means of a dirichlet process let be a random probability measure chosen by a dirichlet process on r b with parameter and such that x dx turns out to be a finite random variable the main concern of this paper is the statement of a suitable expression for the distribution function of that random variable such an expression is deduced through an extension of a procedure based on the use of generalized stieltjes transforms

łukasiewicz transform and its application to compression and reconstruction of digital images we define the lukasiewicz transform as a residuated map and a homomorphism between semimodules over the semiring reducts of an mv algebra then we describe the lukasiewicz transform based ltb algorithm for image processing demonstrating its applicability

the problem of energy conservation in one way models it is shown that the standard stair step representation of a sloping bottom may result in significant prediction errors in fact current parabolic equation implementations are not energy conserving the problem is shown to derive from the approximate treatment of the interface conditions at vertical boundaries along the stair steps several improved interface conditions are proposed

peruse a numerical treatment of rough surface scattering for the parabolic wave equation scattering of underwater acoustic signals from real ocean surfaces often does not fit into any of the classical theoretical approaches to the problem thus the need for a numerical approach is clear a novel method is presented that uses a sequence of conformal mappings to locally flatten successive segments of the surface which is assumed piecewise linear and frozen in time each conformal mapping preserves the elliptic form of the reduced wave equation so that in each transformed space the parabolic approximation can be made and the solution advanced one range step using the split step fourier algorithm this peruse pe rough surface numerical method is validated by exhibiting classically predicted bragg angle peaks for single scatter of a plane wave from a sinusoidal surface for multiple rough surface scattering in surface ducts peruse results are analyzed by resolution in depth into the virtual modes of labianca j acoust soc am 53 1137 1147 1973 the resulting modal intensities are then

fuzzy relation equations for coding decoding processes of images and videos we adopt fuzzy relation equations with continuous triangular norms for compression decompression processes of grey images colour images in the rgb space and frames of videos by comparing the results of the reconstructed images with standard methods like jpeg and mpeg 4 any image is subdivided in blocks and each block is coded decoded using arbitrary fuzzy sets as coders in the fuzzy equations we evaluate the peak signal to noise ratio psnr on the decompressed images for several values of the compression rates as measure of the quality of images and frames reconstructed the original frames of a video are classified in intra frames and predictive frames by using a similarity measure based on the well known lukasiewicz t norm

a split step pade solution for the parabolic equation method a split step pade solution is derived for the parabolic equation pe method higher order pade approximations are used to reduce both numerical errors and asymptotic errors e g phase errors due to wide angle propagation this approach is approximately two orders of magnitude faster than solutions based on pade approximations that account for asymptotic errors but not numerical errors in contrast to the split step fourier solution which achieves similar efficiency for some problems the split step pade solution is valid for problems involving very wide propagation angles large depth variations in the properties of the waveguide and elastic ocean bottoms the split step pade solution is practical for global scale problems

higher order paraxial wave equation approximations in heterogenous media a new family of paraxial wave equation approximations is derived these approximations are of higher order accuracy than the parabolic approximation and they can be applied to the same computationa

modeling rayleigh and stoneley waves and other interface and boundary effects with the parabolic equation an improved approach for handling boundaries interfaces and continuous depth dependence with the elastic parabolic equation is derived and benchmarked the approach is applied to model the propagation of rayleigh and stoneley waves depending on the choice of dependent variables the operator in the elastic wave equation may not factor or the treatment of interfaces may be difficult these problems are resolved by using a formulation in terms of the vertical displacement and the range derivative of the horizontal displacement these quantities are continuous across horizontal interfaces which permits the use of galerkin s method to discretize in depth this implementation extends the capability of the elastic parabolic equation to handle arbitrary depth dependence and should lead to improvements for range dependent problems

an approximation to the three dimensional parabolic equation method for acoustic propagation we have reported previously ralph n baer j acoust soc am 69 70 75 1981 on an algorithm based on the parabolic approximation to the reduced wave equation for the propagation of sound in three dimensions in the ocean we present here a simpler algorithm solve n two dimensional problems and combine the results to form an approximate three dimensional solution analytic and numerical results show that this n 2d approach is an excellent approximation to the original algorithm for realistic ocean environments even those where fronts and eddies are present provided redirection of energy in azimuth due to boundary interaction is not important we compare the two computer models based on these algorithms for several test cases by considering how they distribute energy spatially and by simulating the performance of a hypothetical horizontal array of hydrophones placed in the calculated complex valued acoustic fields in an example of propagation through a large and strong ocean eddy the n 2d metho

on bayesian analysis of mixtures with an unknown number of components with discussion new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

fuzzy transforms theory and applications the technique of direct and inverse fuzzy f transforms of three different types is introduced and approximating properties of the inverse f transforms are described all three types of the direct f transform are transformations from a function space to a finite dimensional vector space the first ordinary f transform is constructed on the basis of the ordinary algebra of reals while the other two types of the f transform are constructed on the basis of residuated lattice the core idea of the technique of f transforms is a fuzzy partition of a universe into fuzzy subsets factors clusters granules etc we claim that for a sufficient representation of a function defined on this universe we may consider its average values over fuzzy subsets from the partition thus a function can be associated with a mapping from a set of fuzzy subsets to the set of its thus obtained average values a number of theorems establishing best approximation properties of the inverse f transforms are proved in fact three types of the inverse f transform are the best approximations in average from below and from above respectively as one of many possible applications we present a method of image compression and reconstruction on the basis of the f transform

a self starter for the parabolic equation method an efficient method is developed for generating accurate starting fields for the parabolic equation pe method for both fluid and solid media the self starter which is constructed by solving a one dimensional boundary value problem bvp involving the pe operator is more efficient than the normal mode starter which requires the solution of a large number of similar bvps the self starter depends on the depth dependent properties of the medium and satisfies all interface and boundary conditions since the self starter is based on higher order parabolic approximations it is accurate for problems involving wide propagation angles large depth variations in the properties of the medium low frequencies interface waves and the continuous spectrum

retrospective markov chain monte carlo methods for dirichlet process hierarchical models inference for dirichlet process hierarchical models is typically performed using markov chain monte carlo methods which can be roughly categorized into marginal and conditional methods the former integrate out analytically the infinite dimensional component of the hierarchical model and sample from the marginal distribution of the remaining variables using the gibbs sampler conditional methods impute the dirichlet process and update it as a component of the gibbs sampler since this requires imputation of an infinite dimensional process implementation of the conditional method has relied on finite approximations in this paper we show how to avoid such approximations by designing two novel markov chain monte carlo algorithms which sample from the exact posterior distribution of quantities of interest the approximations are avoided by the new technique of retrospective sampling we also show how the algorithms can obtain samples from functionals of the dirichlet process the marginal and the conditional methods are compared and a careful simulation study is included which involves a non conjugate model different datasets and prior specifications

compression and decompression of images with discrete fuzzy transforms in foregoing papers we have used the compression decompression method of images based on the concept of discrete fuzzy transform and its inverse of a function f defined on a real interval with respect to the fuzzy sets a 1 a n forming a fuzzy partition of such interval here we make a detailed experimental comparison with the similar method based on the fuzzy transforms f 6 and f 7 of f defined via a continuous triangular norm and its corresponding residuum respectively we consider some images of sizes 256x256 pixels extracted from the well known database corel galery arizona directory by using the same compression rate in both methods we have that the psnr peak signal to noise ratio obtained with the discrete fuzzy transform and its inverse of f is more higher than the psnr determined with the operators f 6 and f 7 defined via the usual lukasiewicz product and minimum triangular norms moreover we compare our results with the classical jpeg method for values of compression rate approximately equal to those used in the previous methods

bayesian clustering and product partition models summary we present a decision theoretic formulation of product partition models ppms that allows a formal treatment of different decision problems such as estimation or hypothesis testing and clustering methods simultaneously a key observation in our construction is the fact that ppms can be formulated in the context of model selection the underlying partition structure in these models is closely related to that arising in connection with dirichlet processes this allows a straightforward adaptation of some computational strategies originally devised for nonparametric bayesian problems to our framework the resulting algorithms are more flexible than other competing alternatives that are used for problems involving ppms we propose an algorithm that yields bayes estimates of the quantities of interest and the groups of experimental units we explore the application of our methods to the detection of outliers in normal and student t regression models with clustering structure equivalent to that induced by a dirichlet process prior we also discuss the sensitivity of the results considering different prior distributions for the partitions

a higher order energy conserving parabolic equqation for range dependent ocean depth sound speed and density outgoing solutions of the wave equation including parabolic equation pe and normal mode solutions are usually formulated so that pressure is continuous with range for range dependent problems the accuracy of normal mode solutions has been improved by conserving energy rather than maintaining continuity of pressure porter et al the problem of energy conservation in one way equations j acoust soc am 89 1058 1067 1991 this approach is applied to derive a higher order energy conserving pe that provides improved accuracy for problems involving large ocean bottom slopes and large range and depth variations in sound speed and density a special numerical approach and complex pade coefficients are applied to suppress gibbs oscillations the back propagated half space field an improved pe starter is applied to handle wide propagation angles reference solutions generated with a complex ray model and with the rotated pe are used for comparison

bayesian curve fitting using multivariate normal mixtures summary problems of regression smoothing and curve fitting are addressed via predictive inference in a flexible class of mixture models multidimensional density estimation using dirichlet mixture models provides the theoretical basis for semi parametric regression methods in which fitted regression functions may be deduced as means of conditional predictive distributions these bayesian regression functions have features similar to generalised kernel regression estimates but the formal analysis addresses problems of multivariate smoothing parameter estimation and the assessment of uncertainties about regression functions naturally computations are based on multidimensional versions of existing markov chain simulation analysis of univariate dirichlet mixture models

nonparametric hierarchical bayes via sequential imputations we consider the empirical bayes estimation of a distribution using binary data via the dirichlet process let d denote a dirichlet process with being a finite measure on 0 1 instead of having direct samples from an unknown random distribution f from d we assume that only indirect binomial data are observable this paper presents a new interpretation of lo s formula and thereby relates the predictive density of the observations based on a dirichlet process model to likelihoods of much simpler models as a consequence the log likelihood surface as well as the maximum likelihood estimate of c 0 1 is found when the shape of is assumed known together with a formula for the fisher information evaluated at the estimate the sequential imputation method of kong liu and wong is recommended for overcoming computational difficulties commonly encountered in this area the related approximation formulas are provided an analysis of the tack data of beckett and diaconis which motivated this study is supplemented to illustrate our methods

the coupled mode parabolic equation the coupled mode parabolic equation pe is a generalization of the adiabatic mode pe that includes mode coupling terms it is practical to apply this approach to large scale problems involving coupling of energy between both modes and azimuths the solution is expressed in terms of the normal modes and mode coefficients which satisfy coupled horizontal wave equations the coupled mode pe may be solved efficiently with the splitting method the first step is equivalent to solving the adiabatic mode pe over one range step the second step involves the integration of the coupling term the coupling mode pe solution conserves energy which is an important aspect of a range dependent propagation model the derivation of the coupled mode pe which involves completing the square of an operator is related to the derivation of an adiabatic mode pe that accounts for ambient flow examples are presented to illustrate the accuracy of the coupled mode pe