einstein maxwell solitons the application of the inverse scattering method to the einstein maxwell equations for stationary axisymmetric exterior fields leads the authors to an explicit formula for the ernst and electromagnetic potentials of new exact solutions generated from an arbitrary seed solution

optimal power allocation for n k limited access channels in this paper we consider a system that consists of n independent parallel channels where the receiver starts to decode the information being transmitted when it has access to at least k of them we refer to this system as the n k limited access channel no prior knowledge for the distribution about which transmissions will be received is assumed in addition both the channel inputs and channel disturbances can be arbitrary except that the mutual information function for each channel is assumed strictly concave with respect to the input power hence the channel capacity below which the code rate is guaranteed to be attainable by a sequence of codes with vanishing error can be determined by the minimum mutual information among any k out of n channels we then investigate the power allocation that maximizes this minimum mutual information subject to a total power constraint as a result the optimal solution can be determined via a systematic algorithmic procedure by performing at most k single power sum constrained maximizations based on this result the closed form formula of the optimal power allocation for an n k limited access channel with channel inputs and additive noises respectively scaled from two independent and identically distributed random vectors of length n is subsequently established and is shown to be well interpreted by a two phase water filling principle specifically in the first noise power redistribution phase the least n k noise powers equivalently second moments are first poured as noise water into a tank consisting of k interconnected unit width vessels with solid base heights respectively equal to the remaining k largest noise powers afterward those w vessels either with noise water inside or with solid base height equal to the new water surface level are subdivided into n k w vessels of rectangular shape with the same heights as the water surface level and widths in proportion to their noise powers in the second signal power allocation phase the heights of vessel bases will be first either lifted or lowered according to the total signal power and channel mutual information functions followed by the usual signal power water filling scheme the two phase water filling interpretation then hints that the degree of noisiness for a general possibly nonadditive and non gaussian limited access channel might be identified by composing the derivative of the mutual information function with its inverse

exact solutions to higher order nonlinear equations through gauge transformation abstract a highly nonlinear hydrodynamic equation proposed by johnson is solved exactly by gauge transforming gt it to the mixed nonlinear schrodinger equation the gt is generalized further to generate a hierarchy of integrable higher order nonlinear systems including some known equations along with their lax pairs infinite sets of conserved quantities and exact solutions

n channel symmetric multiple descriptions part ii an achievable rate distortion region in this part ii of a two part paper we present a new achievable rate distortion region for the symmetric n channel multiple descriptions coding problem n 2 where the rate of every description is the same and the reconstruction distortion depends only on the number of descriptions received using a new approach for the random coding constructions along with a generalization of the technique used in the two channel el gamal and cover region to any n the rate region presented here achieves points that have not been known in the literature previously this rate region is derived from a concatenation of source channel erasure codes developed in part i of this work by deploying the framework of source coding with side information random binning the key idea is that by using the framework of source coding with side information multiple statistically identical realizations representing the coarse version of a source can be simultaneously refined by a single encoding we point out that there is an important conceptual difference in random coding construction for the multiple descriptions coding problem between the case of n 2 and n 2 to illustrate the framework we also present the important case of the gaussian source in detail

painleve analysis of the non linear schrodinger family of equations the authors apply the painleve test to the generalised derivative non linear schrodinger equation iut uxx iauu ux ibu2ux cu3u 2 where u denotes the complex conjugate of u and a b and c are real constants to determine under what conditions the equation might be completely integrable it is shown that apart from a trivial multiplicative factor this equation possesses the painleve property for partial differential equations as formulated by weiss tabor and carnevale 1983 only if c 1 4b 2b a when then this relation holds this is equivalent under a gauge transformation to the derivative non linear schrodinger equation dnls of kaup and newell which is known to be completely integrable or else to a linear equation

optical solitons in a monomode fiber we discuss the propagation of optical solitons in a monomode fiber as a model of long distance high bit rate transmission system we give several new results which did not appear in our previous papers on this subject such as 1 a derivation of the perturbed nonlinear schrodinger equation from the maxwell equation 2 on the integrability of the perturbed nonlinear schrodinger equation 3 a discussion of the soliton as a stable fixed point of certain infinite dimensional map generated by a transmission system with periodic excitations

capacity of the class of mimo channels with incomplete cdi properties of mutual information for a class of channels this paper is concerned with multiple input multiple output mimo wireless channel capacity when the probability distribution of the channel matrix p h is not completely known to the transmitter and the receiver the partial knowledge of a true probability distribution of the channel matrix p h is modelled by a relative entropy d middot middot such that d p pnom les d d ges 0 where d is the distance from the so called nominal channel matrix distribution pnom h the capacity of this compound channel is equal to the maximin of the mutual information where the minimum is with respect to the channel matrix distribution and the maximum is with respect to the covariance matrix of a transmitted signal the existence of a minimizing probability distribution is proved and the explicit formula for the minimizing distribution is derived in terms of the nominal distribution pnom h and parameter d a number of properties of the mutual information minimized over the set of channel distributions are derived specifically upper and lower bounds are derived for the minimized mutual information while its convexity with respect to d is shown in the case of the rayleigh fading an explicit formula for the capacity and the optimal transmit covariance matrix are derived

exact solutions of the multidimensional derivative nonlinear schrodinger equation for many body systems of criticality the authors investigate the problem of strongly interacting many body systems near criticality as recently described in terms of nonlinear dynamics by dixon and tuszynski 1989 they show that in the first order of approximation the equation of motion for the order parameter can be mapped on the derivative nonlinear schrodinger equation and thus can be solved exactly they solve the equations both in the absence and presence of current densities

using factorization to solve soliton equations it was shown in our previous paper that each equation in a soliton hierarchy can be factorized into two commuting x and finite dimensional integrable hamiltonian systems fdihss the separation variables for these fdihss are constructed by using their lax representation by means of the factorization and the separability of the fdihss we obtain the jacobi inversion problem which is solvable in terms of riemann theta functions for soliton equations this provides a method analogous to the separation of variables for solving soliton equations

darboux transformation and solutions for an equation in 2 1 dimensions painleve analysis and the singular manifold method are the tools used in this paper to perform a complete study of an equation in 2 1 dimensions this procedure has allowed us to obtain the lax pair darboux transformation and functions in such a way that a plethora of different solutions with solitonic behavior can be constructed iteratively

robust minimax detection of a weak signal in noise with a bounded variance and density value at the center of symmetry in practical communication environments it is frequently observed that the underlying noise distribution is not gaussian and may vary in a wide range from short tailed to heavy tailed forms to describe partially known noise distribution densities a distribution class characterized by the upper bounds upon a noise variance and a density dispersion in the central part is used the results on the minimax variance estimation in the huber sense are applied to the problem of asymptotically minimax detection of a weak signal the least favorable density minimizing fisher information over this class is called the weber hermite density and it has the gaussian and laplace densities as limiting cases the subsequent minimax detector has the following form i with relatively small variances it is the minimum l2 norm distance rule ii with relatively large variances it is the l1 norm distance rule iii it is a compromise between these extremes with relatively moderate variances it is shown that the proposed minimax detector is robust and close to huber s for heavy tailed distributions and more efficient than huber s for short tailed ones both in asymptotics and on finite samples

landau lifshitz and higher order nonlinear systems gauge generated from nonlinear schrodinger type equations new landau lifshitz ll and higher order nonlinear systems gauge generated from nonlinear schrodinger ns type equations are presented the consequences of gauge equivalence between different dynamical systems are discussed the gauge connections among various ll and ns equations are found and depicted through a schematic representation

the trace identity a powerful tool for constructing the hamiltonian structure of integrable systems a new approach to hamiltonian structures of integrable systems is proposed by making use of a trace identity for a variety of isospectral problems that can be unified to one model x u it is shown that both the related hierarchy of evolution equations and the hamiltonian structure can be obtained from the same solution of the equation vx u v

integrable evolution systems based on gerdjikov ivanov equations bi hamiltonian structure finite dimensional integrable systems and n fold darboux transformation a spectral problem and the associated gerdjikov ivanov gi hierarchy of nonlinear evolution equations is presented as a reduction the well known gi equation of derivative nonlinear schrodinger equations is obtained it is shown that the gi hierarchy is integrable in a liouville sense and possesses bi hamiltonian structure moreover the spectral problem can be nonlinearized as a finite dimensional completely integrable system under the bargmann constraint between the potentials and the eigenfunctions in particular an explicit n fold darboux transformation for the gi equation is constructed with the help of a gauge transformation of spectral problems and a reduction technique some explicit solitonlike solutions of the gi equation are given by applying its darboux transformation

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

an algebraic method to construct the darboux matrix we present an effective procedure to construct the 1 soliton darboux matrix our approach based on the zakharov shabat mikhailov s dressing method is especially useful in the case of non canonical normalization and for non isospectral linear problems the construction is divided into two steps first we represent a given linear problem as a system of some algebraic constraints on two matrices in this context we introduce and discuss invariants of the darboux matrix second we derive the darboux matrix demanding that it preserves the algebraic constraints in particular we consider in details the restrictions imposed by various reduction groups on the form of the darboux matrix

finite band solutions of the classical boussinesq burgers equations the classical boussinesq burgers hierarchy is decomposed into two systems of solvable ordinary differential equations with the help of the lax representations of stationary evolution equations from which the finite band solutions of the higher order classical boussinesq burgers equations are obtained

robust minimum variance beamforming this paper introduces an extension of minimum variance beamforming that explicitly takes into account variation or uncertainty in the array response sources of this uncertainty include imprecise knowledge of the angle of arrival and uncertainty in the array manifold in our method uncertainty in the array manifold is explicitly modeled via an ellipsoid that gives the possible values of the array for a particular look direction we choose weights that minimize the total weighted power output of the array subject to the constraint that the gain should exceed unity for all array responses in this ellipsoid the robust weight selection process can be cast as a second order cone program that can be solved efficiently using lagrange multiplier techniques if the ellipsoid reduces to a single point the method coincides with capon s method we describe in detail several methods that can be used to derive an appropriate uncertainty ellipsoid for the array response we form separate uncertainty ellipsoids for each component in the signal path e g antenna electronics and then determine an aggregate uncertainty ellipsoid from these we give new results for modeling the element wise products of ellipsoids we demonstrate the robust beamforming and the ellipsoidal modeling methods with several numerical examples

a bargmann system and the involutive representation of solutions of the levi hierarchy the author considers a linear spectral problem associated with the levi hierarchy of equations a bargmann system under the so called bargmann constraint between the eigenfunctions and potentials is proposed and is proved to be a completely integrable hamiltonian system in the liouville sense moreover by the involutive solution of the compatible systems under the bargmann constraint he presents the involutive representation of solutions of the levi hierarchy especially he obtains the involutive representation of the solution of the well known burgers equation ut uxx 2uux

mutual information and minimum mean square error in gaussian channels this paper deals with arbitrarily distributed finite power input signals observed through an additive gaussian noise channel it shows a new formula that connects the input output mutual information and the minimum mean square error mmse achievable by optimal estimation of the input given the output that is the derivative of the mutual information nats with respect to the signal to noise ratio snr is equal to half the mmse regardless of the input statistics this relationship holds for both scalar and vector signals as well as for discrete time and continuous time noncausal mmse estimation this fundamental information theoretic result has an unexpected consequence in continuous time nonlinear estimation for any input signal with finite power the causal filtering mmse achieved at snr is equal to the average value of the noncausal smoothing mmse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr

finite dimensional discrete systems and integrable systems through nonlinearization of the discrete eigenvalue problem a method is developed that extends the nonlinearization procedure of eigenvalue problems to the discrete case from which the finite dimensional discrete systems and finite dimensional completely integrable systems associated with the toda hierarchy are obtained a new model for solving discrete soliton equations is proposed which enables one to get the solutions of the toda lattice equations by solving the compatible systems of discrete equations and nonlinear ordinary differential equations

on a new class of completely integrable nonlinear wave equations ii multi hamiltonian structure the multi hamiltonian structure of a class of nonlinear wave equations governing the propagation of finite amplitude waves is discussed infinitely many conservation laws had earlier been obtained for these equations starting from a primary hamiltonian formulation of these equations the necessary and sufficient conditions for the existence of bi hamiltonian structure are obtained and it is shown that the second hamiltonian operator can be constructed solely through a knowledge of the first hamiltonian function the recursion operator which first appears at the level of bi hamiltonian structure gives rise to an infinite sequence of conserved hamiltonians it is found that in general there exist two different infinite sequences of conserved quantities for these equations the recursion relation defining higher hamiltonian structures enables one to obtain the necessary and sufficient conditions for the existence of the k 1 st hamiltonian operator which depends on the kth hamiltonian function the infinite sequence of conserved hamiltonians are common to all the higher hamiltonian structures the equations of gas dynamics are discussed as an illustration of this formalism and it is shown that in general they admit tri hamiltonian structure with two distinct infinite sets of conserved quantities the isothermal case of 1 is an exceptional one that requires separate treatment this corresponds to a specialization of the equations governing the expansion of plasma into vacuum which will be shown to be equivalent to poisson s equation in nonlinear acoustics

lax representation r matrix method and separation of variables for the neumann type restricted flow the r matrix method and the method of separation of variables for restricted flows with neumann constraints are considered restricted jaulent miodek flows are taken as illustrative examples lax representations are obtained from the adjoint representation of the corresponding soliton hierarchy the r matrix formula based on this lax representation is derived and the separation of variables for the hamilton jacobi equation are performed

robust detection in nominally laplace noise the authors consider the robust detection of a known constant signal in additive mutually independent and identically distributed noise which is nominally laplace employing the classical saddlepoint methodology of huber 1951 they specify the form of the robust detector and obtain closed form results which allow for the analysis of the performance of the robust detector they show via examples that the robustness can entail a considerable cost in detector performance in addition they compare the performance of the robust detector to that of the neyman pearson detector for examples where the noise is laplace and also where the noise is least favorable for the given detector

c neumann and bargmann systems associated with the coupled kdv soliton hierarchy under two different constraints between the potentials and the eigenfunctions the eigenvalue problem associated with the coupled kdv hierarchy is nonlinearised to be a completely integrable c neumann system on the tangent bundle of sphere tsn 1 with the hamiltonian h 1 2 lambda q p 1 2 q q p p 1 2 q p 2 1 2 q p lambda p p and a completely integrable bargmann system r2n dpdq h with the hamiltonian h 1 2 lambda q p 1 2 p p q p 1 2 q q respectively the involutive solutions of the coupled kdv equation associated with the two systems are given

estimation of the parameters of sinusoidal signals in non gaussian noise accurate estimation of the amplitude and frequency parameters of sinusoidal signals from noisy observations is an important problem in many signal processing applications in this paper the problem is investigated under the assumption of non gaussian noise in general and laplace noise in particular it is proven mathematically that the maximum likelihood estimator derived under the condition of laplace white noise is able to attain an asymptotic cramer rao lower bound which is one half of that achieved by periodogram maximization and nonlinear least squares it is also proven that when applied to non laplace situations the laplace maximum likelihood estimator which may also be referred to as the nonlinear least absolute deviations estimator can achieve an even higher statistical efficiency especially when the noise distribution has heavy tails a computational procedure is proposed to overcome the difficulty of local extrema in the likelihood function simulation results are provided to validate the analytical findings

new factorization of the kaup newell hierarchy abstract the new factorizations of each equation in the kaup newell kn hierarchy into two commuting x and t n finite dimensional integrable hamiltonian systems fdihs via the higher order potential eigenfunction constraints are presented the integrability commutativity and lax representation for these fdihss are deduced from the adjoint representations of the auxiliary linear problems for the kn hierarchy this approach provides a natural way to study soliton hierarchies with source the zero curvature representation and darboux transformation for the kn hierarchy with source related to eigenfunctions are found

mimo gaussian channels with arbitrary inputs optimal precoding and power allocation in this paper we investigate the linear precoding and power allocation policies that maximize the mutual information for general multiple input multiple output mimo gaussian channels with arbitrary input distributions by capitalizing on the relationship between mutual information and minimum mean square error mmse the optimal linear precoder satisfies a fixed point equation as a function of the channel and the input constellation for non gaussian inputs a nondiagonal precoding matrix in general increases the information transmission rate even for parallel noninteracting channels whenever precoding is precluded the optimal power allocation policy also satisfies a fixed point equation we put forth a generalization of the mercury waterfilling algorithm previously proposed for parallel noninterfering channels in which the mercury level accounts not only for the non gaussian input distributions but also for the interference among inputs

optimum power allocation for parallel gaussian channels with arbitrary input distributions the mutual information of independent parallel gaussian noise channels is maximized under an average power constraint by independent gaussian inputs whose power is allocated according to the waterfilling policy in practice discrete signaling constellations with limited peak to average ratios m psk m qam etc are used in lieu of the ideal gaussian signals this paper gives the power allocation policy that maximizes the mutual information over parallel channels with arbitrary input distributions such policy admits a graphical interpretation referred to as mercury waterfilling which generalizes the waterfilling solution and allows retaining some of its intuition the relationship between mutual information of gaussian channels and nonlinear minimum mean square error mmse proves key to solving the power allocation problem

n channel symmetric multiple descriptions part i n k source channel erasure codes in this two part paper we present a new achievable rate region for the general n channel symmetric multiple descriptions problem in part i inspired by the concept of maximum distance separable mds erasure channel codes we consider a special case of this rate region where the source is encoded into n descriptions each with rate r these descriptions are transmitted over n bandwidth constrained and errorless channels during transmission a subset of these channels can break down thus erasing the corresponding descriptions the decoder is interested in recovering the source with the reception of at least k descriptions thus the encoder is allowed to sample only one realization of this breakdown process during the entire transmission for gaussian sources we have the following interesting result when any k descriptions arrive the achievable distortion exactly matches the optimal distortion rate performance corresponding to a source rate of kr bits with the reception of any m k descriptions the source reconstruction quality is strictly better the improvement being nearly linear in the number of descriptions received

clustering coefficient and community structure of bipartite networks abstract many real world networks display natural bipartite structure where the basic cycle is a square in this paper with the similar consideration of standard clustering coefficient in binary networks a definition of the clustering coefficient for bipartite networks based on the fraction of squares is proposed in order to detect community structures in bipartite networks two different edge clustering coefficients l c 4 and l c 3 of bipartite networks are defined which are based on squares and triples respectively with the algorithm of cutting the edge with the least clustering coefficient communities in artificial and real world networks are identified the results reveal that investigating bipartite networks based on the original structure can show the detailed properties that is helpful to get deep understanding about the networks

on liouville integrability of zero curvature equations and the yang hierarchy sufficient conditions for a zero curvature equation ut vx u v 0 being liouville integrable are investigated in the case that the equation is integrable an explicit formula of the poisson bracket h lambda h mu for hamiltonians h is proposed the yang hierarchy is derived and shown to be liouville integrable

algebro geometric solutions for the gerdjikov ivanov hierarchy this paper is dedicated to provide theta function representations of algebro geometric solutions and related crucial quantities for the gerdjikov ivanov gi hierarchy our main tools include the polynomial recursive formalism the hyperelliptic curve with finite number of genus the baker akhiezer functions the meromorphic function the dubrovin type equations for auxiliary divisors and the associated trace formulas with the help of these tools the explicit representations of the baker akhiezer functions the meromorphic function and the algebro geometric solutions are obtained for the entire gi hierarchy

a generalized fractional kn equation hierarchy and its fractional hamiltonian structure a generalized hamiltonian structure of the fractional soliton equation hierarchy is presented by using differential forms and exterior derivatives of fractional orders we construct the generalized fractional trace identity through the riemann liouville fractional derivative an example of the fractional kn soliton equation hierarchy and hamiltonian structure is presented which is a new integrable hierarchy and possesses hamiltonian structure