commuting difference operators with elliptic coefficients from baxter s vacuum vectors for quantum integrable models with elliptic r matrix we construct the baxter q operator in infinite dimensional representations of the algebra of observables

multi hamiltonian structure for the finite defocusing ablowitz ladik equation we study the poisson structure associated to the defocusing ablowitz ladik equation from a functional analytical point of view by reexpressing the poisson bracket in terms of the associated caratheodory function using this expression we are able to introduce a family of compatible poisson brackets that form a multi hamiltonian structure for the ablowitz ladik equation furthermore we show using some of these new poisson brackets that the geronimus relations between orthogonal polynomials on the unit circle and those on the interval define an algebraic and symplectic mapping between the ablowitz ladik and toda hierarchies 2008 wiley periodicals inc

nonparametric association analysis of bivariate competing risks data although nonparametric analyses of bivariate failure times under independent censoring have been widely studied nonparametric analyses of bivariate competing risks data have not yet been investigated such analyses are important in familial association studies where multiple interacting failure types may violate the independent censoring assumption we develop nonparametric estimators for the bivariate cause specific hazards function and the bivariate cumulative incidence function that are natural analogs of their univariate counterparts and make no assumptions about the dependence of the risks the estimators are shown to be uniformly consistent and to converge weakly to gaussian processes they provide the basis for novel time dependent association measures with the associated inferences yielding tests of cause specific independence in pairs the methodology performs well in simulations with realistic sample sizes its practical utility is illustrated in an analysis of dementia in the cache county st

adaptive linear filtering using interior point optimization techniques we propose a novel approach for the linear adaptive filtering problem using techniques from interior point optimization the main idea is to formulate a feasibility problem at each iteration and obtain as an estimate a filter near the center of the feasible region it is shown under some mild conditions that this algorithm generates a sequence of filters converging to the optimum linear filter at the rate o 1 n where n is the number of data samples furthermore we show that the algorithm can be made recursive with a per sample complexity of o m sup 2 3 where m is the filter length the potential of the algorithm for practical applications is demonstrated via numerical simulations where the new algorithm is shown to have superior transient behavior and improved robustness to the source signal statistics when compared to the recursive least squares rls method

baxter t q equation for shape invariant potentials the finite gap potentials case the darboux transformation applied recurrently on a schrodinger operator generates what is called a dressing chain or from a different point of view a set of supersymmetric shape invariant potentials the finite gap potential theory is a special case of the chain for the finite gap case the equations of the chain can be expressed as a time evolution of a hamiltonian system we apply sklyanin s method of separation of variables to the chain we show that the classical equation of the separation of variables is the baxter t q relation after quantization

adaptive blind channel estimation by least squares smoothing a least squares smoothing lss approach is presented for the blind estimation of single input multiple output simo finite impulse response systems by exploiting the isomorphic relation between the input and output subspaces this geometrical approach identifies the channel from a specially formed least squares smoothing error of the channel output lss has the finite sample convergence property i e in the absence of noise the channel is estimated perfectly with only a finite number of data samples referred to as the adaptive least squares smoothing a lss algorithm the adaptive implementation has a high convergence rate and low computation cost with no matrix operations a lss is order recursive and is implemented in part using a lattice filter it has the advantage that when the channel order varies channel estimates can be obtained without structural change of the implementation for uncorrelated input sequence the proposed algorithm performs direct deconvolution as a by product

discrete skew selfadjoint canonical systems and the isotropic heisenberg magnet model abstract a discrete analog of a skew self adjoint canonical zakharov shabat or akns system with a pseudo exponential potential is introduced for the corresponding weyl function the direct and inverse problem are solved explicitly in terms of three parameter matrices as an application explicit solutions are obtained for the discrete integrable nonlinear equation corresponding to the isotropic heisenberg magnet model state space techniques from mathematical system theory play an important role in the proofs

the periodic toda chain and a matrix generalization of the bessel function recursion relations the authors obtain the quantization conditions of the periodic toda lattice in the baxter form lambda u q u inq u i i nq u i lambda is the transfer matrix containing the information about the spectrum and q is an integral operator commuting with lambda the logarithms of the matrix elements of q are the generating functions of the canonical backlund transformation the requirement that q is analytic and vanishes when u goes to infinity completely determines the spectrum of lambda

baxter s q operator for the homogeneous xxx spin chain applying the pasquier gaudin procedure we construct baxter s q operator for the homogeneous xxx model as an integral operator in the standard representation of sl 2 the connection between the q operator and the local hamiltonians is discussed we show that lipatov s duality symmetry operator arises naturally as the leading term of the asymptotic expansion of the q operator for large values of the spectral parameter

a q difference baxter operator for the ablowitz ladik chain we construct the baxter operator and the corresponding baxter equation for a quantum version of the ablowitz ladik model the result is achieved in two different ways by using the well known bethe ansatz technique and by looking at the quantum analogue of the classical backlund transformations general results about integrable models governed by the same r matrix algebra will be given baxter s equation comes out to be a q difference equation involving both the trace and the quantum determinant of the monodromy matrix the spectrality property of the classical backlund transformations gives a trace formula representing the classical analogue of baxter s equation a q integral representation of the baxter operator is discussed

interior point least squares estimation transient convergence analysis and application to mmse decision feedback equalization in many communication systems training sequences are used to help the receiver identify and or equalize the channel the amount of training data required depends on the convergence properties of the adaptive filtering algorithms used for equalization in this paper we propose the use of a new adaptive filtering method called interior point least squares ipls for adaptive equalization first we show that ipls converges exponentially fast in the transient phase then we use the ipls algorithm to update the weight vector for a minimum mean square error decision feedback equalizer mmse dfe in a cdma downlink scenario numerical simulations show that when training sequences are short ipls consistently outperforms rls in terms of system bit error rate and packet error rate as the training sequence gets longer ipls matches the performance of the rls algorithm

estimation of bivariate and marginal distributions with censored data consider a pair of random variables both subject to random right censoring new estimators for the bivariate and marginal distributions of these variables are proposed the estimators of the marginal distributions are not the marginals of the corresponding estimator of the bivariate distribution both estimators require estimation of the conditional distribution when the conditioning variable is subject to censoring such a method of estimation is proposed the weak convergence of the estimators proposed is obtained a small simulation study suggests that the estimators of the marginal and bivariate distributions perform well relatively to respectively the kaplan meier estimator for the marginal distribution and the estimators of pruitt and van der laan for the bivariate distribution the use of the estimators in practice is illustrated by the analysis of a data set

separation of variables for the ruijsenaars model and a new integral representation for the macdonald polynomials using the baker akhiezer function technique we construct a separation of variables for the classical trigonometric three particle ruijsenaars model a relativistic generalization of the calogero moser sutherland model in the quantum case an integral operator m is constructed from the askey wilson contour integral the operator m transforms the eigenfunctions of the commuting hamiltonians the macdonald polynomials for the root sytem into the factorized form where s y is a laurent polynomial of one variable expressed in terms of the basic hypergeometric series the inversion of m produces a new integral representation for the macdonald polynomials we also present some results and conjectures for the general n particle case

structure of matrix elements in the quantum toda chain we consider the quantum toda chain using the method of separation of variables we show that the matrix elements of operators in the model are written in terms of a finite number of deformed abelian integrals the properties of these integrals are discussed we explain that these properties are necessary in order to provide the correct number of independent operators a comparison with the classical theory is made

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

nonparametric estimators of the bivariate survival function under simplified censoring conditions summary new bivariate survival function estimators are proposed in the case where the dependence relationship between the censoring variables are modelled specific examples include the cases when censoring variables are univariate mutually independent or specified by a marginal model large sample properties of the proposed estimators are discussed the finite sample performance of the proposed estimators compared with other fully nonparametric estimators is studied via simulations a real data example is given

remarks on kowalevski s top we present a review of some results on kowalevski s top kt in classical and quantum mechanics the following items are considered i the generalized kt gkt on the lie algebras so 4 e 3 and so 3 1 ii kowalevski s gyrostat on these algebras iii action of the gkt iv quantum counterparts of the kt v semiclassical quantization of the gkt vi generalization of the kt by chaplygin and goryachev at l 0 and its lax representation unsolved questions are also discussed

analysis of a randomized trial to prevent vertical transmission of hiv 1 abstract we analyze data from a randomized trial of breastfeeding versus formula feeding in hiv 1 infected mothers and their infants estimates of infant hiv 1 free survival and the timing of vertical transmission of hiv 1 are complicated by the fact that the infants hiv 1 status at death may be unknown the time of hiv 1 infection may be interval censored and the tests used to detect hiv 1 infection in the infants may be less than 100 sensitive or specific to address these problems we develop nonparametric and semiparametric approaches to estimating the joint distribution of hiv 1 infection time and death time the nonparametric estimator is based on a self consistency algorithm and in the current application provides a unique estimate of the hiv 1 free survival at 24 months old however the estimate of the cumulative probability of hiv 1 infection over time is nonunique to resolve the nonuniqueness of the nonparametric estimator a semiparametric approach is proposed in which the joint distributi

there s more than one way to skin schro dinger s cat abstract two methods for studying quantum discrete dynamical systes i e with a finite or countably infinite number of degrees of freedom are described and compared for i the discrete self trapping dst equation ii the ablowitz ladik al equation and iii a fermionic polaron fp model the first method called the quantum inverse scattering method qism emphasizes the relationship between the quantum theory and classical integrability the second method which we call the number state method nsm cam be extended to systems that are not classically integrable thus the two methods are not equivalent

baxterization of glq 2 and its application to the liouville model and some other models on a lattice we develop the baxterization approach to an extension of the quantum group gl q 2 we introduce two matrices which play the role of spectral parameter dependent l matrices and observe that they are naturally related to two different comultiplications using these comultiplication structures we find the related fundamental r operators in terms of powers of coproducts and also give their equivalent forms in terms of quantum dilogarithms the corresponding quantum local hamiltonians are given in terms of logarithms of positive operators an analogous construction is developed for the q oscillator and weyl algebras using the fact that their algebraic and coalgebraic structures can be obtained as reductions of those for the quantum group as an application the lattice liouville model the q dst model the volterra model a lattice regularization of the free field and the relativistic toda model are considered

a special case of neumann s system and the kowalewski chaplygin goryachev top the authors present l operators both for the special case of neumann s system and the kowalewski chaplygin goryachev top these are quantum systems integrable by the quantum inverse scattering r matrix method l operators being 2 2 matrices satisfy an algebra generated by an r matrix of the xxx type the close connection between the two models is demonstrated they carry out a non obvious separation of variables and also give a dynamical group scheme for the eigenstate problem of neumann s system this separation differs from those in euler angles and allows them to find eigenenergies in an effective way

factorization of the transfer matrices for the quantum sl 2 spin chains and baxter equation it is shown that the transfer matrices of homogeneous sl 2 invariant spin chains with generic spin both closed and open are factorized into the product of two operators the latter satisfy the baxter equation that follows from the structure of the reducible representations of the sl 2 algebra

on baxter q operators for the toda chain we suggest a procedure for the construction of baxter q operators for the toda chain apart from the one parametric family of q operators considered in our recent paper pronko 2000 commun math phys to appear we also give the method of construction of two basic q operators and the derivation of the functional relations for these operators also we have found the relation of the basic q operators with bloch solutions of the quantum linear problem

additive deformations of the r matrix algebras we show how to construct new representations of the various r matrix algebras starting from known representations for linear r matrix algebras we investigate a dynamical r matrix which depends on the spectral parameter and half of the dynamical variables particle coordinates only the toda lattices and the henon heiles systems illustrate the scheme

separation of variables and backlund transformations for the symmetric lagrange top we construct the one and two point integrable maps backlund transformations for the symmetric lagrange top we show that the lagrange top has the same algebraic poisson structure that belongs to the sl 2 gaudin magnet the two point map leads to a real time discretization of the continuous flow therefore it provides an integrable numerical scheme for integrating the physical flow we illustrate the construction by a few pictures of the discrete flow calculated in matlab

identifiability of bivariate survival curves from censored data abstract we show that the survival curve is identifiable in bivariate censored data problems under weaker independence assumptions than have commonly been made the common assumption has been mutual independence of t 1 t 2 and z 1 z 2 where t 1 t 2 is the true survival vector z 1 z 2 is a nuisance censoring vector and bivariate right censored data is observed we show that the distribution of t 1 t 2 is identifiable under weaker conditional independence assumptions for distributions with full support bivariate survival analysis is a more powerful analysis tool than univariate analysis if multiple possibly related times are of interest the mutual independence model has become popular as a nonparametric way of analyzing such data analysis of the bivariate problem and analogy with univariate models are used to show that the conditional independence model is more widely applicable as a general nonparametric model for bivariate survival data

the kowalewski top a new lax representation the 2 2 monodromy matrices for the kowalewski top on the lie algebras e 3 so 4 and so 3 1 are presented the corresponding quadratic r matrix structure is the dynamical deformation of the standard r matrix algebras some tops and toda lattices related to the kowalewski top are discussed

nearest neighbor estimation of a bivariate distribution under random censoring we consider the problem of estimating the bivariate distribution of the random vector x y when y may be subject to random censoring the censoring variable c is allowed to depend on x but it is assumed that y and c are conditionally independent given x x the estimate of the bivariate distribution is obtained by averaging estimates of the conditional distribution of y given x x over a range of values of x the weak convergence of the centered estimator multiplied by n 1 2 is obtained and a closed form expression for the covariance function of the limiting process is given it is shown that the proposed estimator is optimal in the beran sense this is similar to an optimality property the product limit estimator enjoys using the proposed estimator of the bivariate distribution an extension of the least squares estimator to censored data polynomial regression is obtained and its asymptotic normality established

mmse interference suppression for direct sequence spread spectrum cdma we consider interference suppression for direct sequence spread spectrum code division multiple access cdma systems using the minimum mean squared error mmse performance criterion the conventional matched filter receiver suffers from the near far problem and requires strict power control typically involving feedback from receiver to transmitter for acceptable performance multiuser detection schemes previously proposed mitigate the near far problem but are complex and require explicit knowledge or estimates of the interference parameters in this paper we present and analyze several new mmse interference suppression schemes which have the advantage of being near far resistant to varying degrees depending on their complexity and can be implemented adaptively when interference parameters are unknown and or time varying numerical results are provided that show that these schemes offer significant performance gains relative to the matched filter receiver we conclude that mmse detectors can alleviate the need for stringent power control in cdma systems and may be a practical alternative to the matched filter receiver

backlund transformations for the sl 2 gaudin magnet elementary one and two point backlund transformations are constructed for the generic case of the sl 2 gaudin magnet the spectrality property is used to construct these explicitly given poisson integrable maps which are time discretizations of the continuous flows with any hamiltonian from the spectral curve of the 2 2 lax matrix

covariance and survivor function estimation using censored multivariate failure time data summary the covariance between counting process martingales is used to characterize the dependence between two failure time variates a representation of the bivariate survivor function is obtained in terms of the marginal survivor functions and this covariance function a closely related representation expresses the bivariate survivor function in terms of marginal survivor functions and a conditional covariance function leading to a new nonparametric survivor function estimator generalizations to higher dimensional failure time variates are also given simulation evaluations of the survivor function estimator are presented and generalizations to regression problems are outlined

orthogonal confluent hypergeometric lattice polynomials here is a method of solving the difference differential equations of the confluent hypergeometric differential equation using a generalized pochhammer matrix product this method provides a convenient analytical way to relate various solutions of the confluent hypergeometric function to each other when their parameters fall on the same point lattice these solutions also are of interest to the general classification of orthogonal polynomials and the metrics used to generate them this method generates laurent polynomials over the complex domain that are an orthogonal system utilizing a 2 2 matrix weight function where the weight matrix has elements that are products of a kummer solution and its derivative the index incremented pochhammer matrix polynomials obey a 4 4 system of differential equations with a frobenius solution involving non commuting matrices that also extends these results to non integer values but with infinite laurent series the termination condition for a polynomial series in the midst of infinite series sheds light on solving general systems of regular linear differential equations the differential equations generalize heun s double confluent equation with matrix coefficients for a radiative transfer flux integral there is a distinct advantage of using these lattice polynomials compared to an asymptotic series power series combination we conjecture similar convergence properties for evaluations of confluent hypergeometric functions of either kind and that these matrix methods can be extended to gauss hypergeometric functions and generalized hypergeometric functions

kaplan meier estimate on the plane estimation of the bivariate survival function from censored data is considered the product integral representation of univariate survival functions is generalized to the bivariate case and used to determine identifiability of the survival function of the partially observed data a bivariate analogue of the kaplan meier estimate is introduced and its almost sure consistency is studied extensions to the general multivariate case are sketched

study of the transient phase of the forgetting factor rls we investigate the convergence properties of the forgetting factor rls algorithm in a stationary data environment using the settling time as our performance measure we show that the algorithm exhibits a variable performance that depends on the particular combination of the initialization and noise level specifically when the observation noise level is low high snr rls when initialized with a matrix of small norm it has an exceptionally fast convergence convergence speed decreases as we increase the norm of the initialization matrix in a medium snr environment the optimum convergence speed of the algorithm is reduced as compared with the previous case however rls becomes more insensitive to initialization finally in a low snr environment we show that it is preferable to initialize the algorithm with a matrix of large norm

a τ function on the inhomogeneous lattice and the classical isotropic heisenberg spin chain a function on the inhomogeneous lattice is introduced by a deformation of that of the toda lattice hierarchy an associated discrete time integrable system is constructed in sato and lax formalisms it is shown that a one dimensional reduction of the system gives a backlund transformation of the classical isotropic heisenberg spin chain which is equivalent to the rii chain proposed by spiridonov and zhedanov

cumulative incidence association models for bivariate competing risks data association models like frailty and copula models are frequently used to analyze clustered survival data and evaluate within cluster associations the assumption of noninformative censoring is commonly applied to these models though it may not be true in many situations in this paper we consider bivariate competing risk data and focus on association models specified for the bivariate cumulative incidence function cif a nonparametrically identifiable quantity copula models are proposed which relate the bivariate cif to its corresponding univariate cifs similarly to independently right censored data and accommodate frailty models for the bivariate cif two estimating equations are developed to estimate the association parameter permitting the univariate cifs to be estimated either parametrically or nonparametrically goodness of fit tests are presented for formally evaluating the parametric models both estimators perform well with moderate sample sizes in simulation studies the practical use of the methodology is illustrated in an analysis of dementia associations

generalized polyspheroidal periodic functions and the quantum inverse scattering method bounded and periodic eigenfunctions of the operator d2 dv2 2 1 cos 2v sin 2v d dv 8 cos 2v 4 2 sin2 2v are studied these solutions are new special functions particular cases of which will be the spheroidal the coulomb spheroidal and the hyperspheroidal harmonics the algebraic technique due to the quantum inverse scattering method is applied to obtain the three term recursion relations for the coefficients of eigenfunctions expansion at the jacobi polynomials series and hence the suitable equation the continued fraction is equal to zero for eigenvalues the special functions considered generalize the truskova polyspheroidal periodic functions 0

mmse decision feedback equalizers and coding i equalization results the minimum mean squared error decision feedback equalizer mmse dfe has properties that suggest that it is a canonical equalization structure for systems that combine equalization with coded modulation the structure and performance of the mmse dfe are succinctly derived using linear estimation theoretic principles in this first part of this two part paper the front end of the mmse dfe called the mean square whitened matched filter ms wmf is preferable in some ways to a matched filter or a whitened matched filter as a canonical receiver front end in a coded system the feedback filter of the mmse dfe may be implemented in the transmitter using precoding the mmse dfe can perform significantly better than a zero forcing decision feedback equalizer particularly at moderate to low snr s and on severe isi channels the mmse dfe is biased the optimum unbiased mmse dfe is the mmse dfe with the bias removed removing bias improves error probability but reduces the snr to snr sub mmse dfe u snr sub mmse dfe 1 it is shown that this snr relationship is a particular case of a very general result and that snr sub mmse dfe u gives a more realistic estimate of snr the results are extended to partial response equalization and to equalization with correlated inputs in an appendix

integrable structure of conformal field theory ii q operator and ddv equation this paper is a direct continuation of 1 where we began the study of the integrable structures in conformal field theory we show here how to construct the operators bf q pm lambda which act in the highest weight virasoro module and commute for different values of the parameter these operators appear to be the cft analogs of the q matrix of baxter 2 in particular they satisfy baxter s famous t q equation we also show that under natural assumptions about analytic properties of the operators as the functions of the baxter s relation allows one to derive the nonlinear integral equations of destri de vega ddv 3 for the eigenvalues of the q operators we then use the ddv equation to obtain the asymptotic expansions of the q operators at large it is remarkable that unlike the expansions of the t operators of 1 the asymptotic series for q contains the dual nonlocal integrals of motion along with the local ones we also discuss an intriguing relation between the vacuum eigenvalues of the q operators and the stationary transport properties in the boundary sine gordon model on this basis we propose a number of new exact results about finite voltage charge transport through the point contact in the quantum hall system

mmse decision feedback equalizers finite length results this paper extends a number of results on the infinite length minimum mean square error decision feedback equalizer mmse dfe reported by cioffi dudevoir eyuboglu and forney see ieee trans commun 1995 to the finite length case cholesky factorization and displacement structure theory are demonstrated to be two powerful analytical tools for analyzing the finite length mmse dfe our objective throughout the paper is to establish finite length analogs of the well known infinite length mmse dfe results similarities and differences between the two cases are examined and delineated finally convergence of our derived finite length results to their well established infinite length counterparts is shown

on the quantum inverse scattering method for the dst dimer abstract the quantum inverse scattering method is used to solve the spectral problem of the discrete self trapping dimer in the case of both a quadratic and a linear r matrix algebra representation the first case is solved by the algebraic bethe ansatz while in the case of the linear r matrix algebra we use the method of separation of variables in this last case it is shown that the wave functions of the quantum discrete self trapping dimer are related to the solutions of a heun s type equation and that the system is equivalent to the two site hyperbolic gaudin magnet separable in elliptic coordinates

quantum backlund transformation for the integrable dst model for the integrable case of the discrete self trapping dst model we construct a backlund transformation the dual lax matrix and the corresponding dual backlund transformation are also found and studied the quantum analogue of the backlund transformation q operator is constructed as the trace of a monodromy matrix with an infinite dimensional auxiliary space we present the q operator as an explicit integral operator as well as describing its action on the monomial basis as a result we obtain a family of integral equations for multivariable polynomial eigenfunctions of the quantum integrable dst model these eigenfunctions are special functions of the heun class which is beyond the hypergeometric class the integral equations found are new and they shall provide a basis for efficient analytical and numerical studies of such complicated functions

on backlund transformations for many body systems using the n particle periodic toda lattice and the relativistic generalization due to ruijsenaars of the elliptic calogero moser system as examples we revise the basic properties of the backlund transformations bts from the hamiltonian point of view the analogy between the bt and baxter s quantum q operator pointed out by pasquier and gaudin is exploited to produce a conjugated variable for the parameter of the bt such that belongs to the spectrum of the lax operator as a consequence the generating function of the composition of n bts gives rise to another canonical transformation separating variables for the model for the toda lattice the dual bt parametrized by is introduced

a family of the poisson brackets compatible with the sklyanin bracket we introduce a family of compatible poisson brackets on the space of 2 2 polynomial matrices which contains the sklyanin bracket and use it to derive a multi hamiltonian structure for a set of integrable systems that includes the xxx heisenberg magnet the open and periodic toda lattices the discrete self trapping model and the goryachev chaplygin gyrostat

let s baxterise we recall the concept of baxterisation of an r matrix or of a monodromy matrix which corresponds to build from one point in the r matrix parameter space the algebraic variety where the spectral parameter s live we show that the baxterisation which amounts to studying the iteration of a birational transformation is a win win strategy it enables to discard efficiently the non integrable situations focusing directly on the two interesting cases where the algebraic varieties are of the so called general type finite order iteration or are abelian varieties infinite order iteration we emphasize the heuristic example of the sixteen vertex model and provide a complete description of the finite order iterations situations for the baxter model we show that the baxterisation procedure can be introduced in much larger frameworks where the existence of some underlying yang baxter structure is not used we baxterise l operators local quantum lax matrices and quantum hamiltonians

nonparametric estimation of a bivariate survival function in the presence of censoring a new family of estimators of a bivariate survival function based on censored vectors is obtained from a decomposition of the bivariate survival function these estimators are uniformly consistent under bivariate censoring and are self consistent under univariate censoring

estimation of survival curves from dependent censorship models via a generalized self consistent property with nonparametric bayesian estimation application on presente une famille d estimateurs obtenue par generalisation de la propriete autoconsistante efron 1967 de l estimateur de kaplan meier 1958

applications of convex optimization in signal processing and digital communication in the last two decades the mathematical programming community has witnessed some spectacular advances in interior point methods and robust optimization these advances have recently started to significantly impact various fields of applied sciences and engineering where computational efficiency is essential this paper focuses on two such fields digital signal processing and communication in the past the widely used optimization methods in both fields had been the gradient descent or least squares methods both of which are known to suffer from the usual headaches of stepsize selection algorithm initialization and local minima with the recent advances in conic and robust optimization the opportunity is ripe to use the newly developed interior point optimization techniques and highly efficient software tools to help advance the fields of signal processing and digital communication this paper surveys recent successes of applying interior point and robust optimization to solve some core problems in these two fields the successful applications considered in this paper include adaptive filtering robust beamforming design and analysis of multi user communication system channel equalization decoding and detection throughout our emphasis is on how to exploit the hidden convexity convex reformulation of semi infinite constraints analysis of convergence complexity and performance as well as efficient practical implementation

kowalewski s top on the lie algebras o 4 e 3 and o 3 1 the authors extend the lax pair for kowalewski s top kt obtained by haine and horozov 1987 to the lie algebras o 4 and o 3 1 the results are expressed in terms of a solution of the neumann system they derive formulae for the action variables by analogy with the e 3 kt case and obtain a useful representation for the equations of motion that demonstrate explicitly the separation of variables