potts models with period doubling cascades chaos etc various q state potts models on bethe lattices are investigated when q is non integer models with 0 q 1 have been shown to be related to spin glasses as well as polymer models we find that such systems exhibit period doubling cascades chaos etc even in the case of a one dimensional system a bethe lattice with branching ratio equal to one the system has interesting behaviour when 0 q 1 as shown by glumac and uzelac through looking at lee yang zeros we study these systems from a completely different approach to that of dynamical systems

nonparametric quantile estimations for dynamic smooth coefficient models in this article quantile regression methods are suggested for a class of smooth coefficient time series models we use both local polynomial and local constant fitting schemes to estimate the smooth coefficients in a quantile framework we establish the asymptotic properties of both the local polynomial and local constant estimators for mixing time series also a bandwidth selector based on the nonparametric version of the akaike information criterion is suggested together with a consistent estimate of the asymptotic covariance matrix furthermore the asymptotic behaviors of the estimators at boundaries are examined a comparison of the local polynomial quantile estimator with the local constant estimator is presented a simulation study is carried out to illustrate the performance of estimates an empirical application of the model to real data further demonstrates the potential of the proposed modeling procedures

partition function zeros of the one dimensional potts model the recursive method the yang lee fisher and potts zeros of the one dimensional q state potts model are studied using the theory of dynamical systems an exact recurrence relation for the partition function is derived it is shown that zeros of the partition function may be associated with neutral fixed points of the recurrence relation further a general equation for zeros of the partition function is found and a classification of the yang lee fisher and potts zeros is given it is shown that the fisher zeros in a nonzero magnetic field are located on several lines in the complex temperature plane and that the number of these lines depends on the value of the magnetic field analytical expressions for the densities of the yang lee fisher and potts zeros are derived it is shown that densities of all types of zeros of the partition function are singular at the edge singularity points with the same critical exponent

wild bootstrap for quantile regression the existing theory of the wild bootstrap has focused on linear estimators in this note we broaden its validity by providing a class of weight distributions that is asymptotically valid for quantile regression estimators as most weight distributions in the literature lead to biased variance estimates for nonlinear estimators of linear regression we propose a modification of the wild bootstrap that admits a broader class of weight distributions for quantile regression a simulation study on median regression is carried out to compare various bootstrap methods with a simple finite sample correction the wild bootstrap is shown to account for general forms of heteroscedasticity in a regression model with fixed design points

block transmission over dispersive channels transmit filter optimization and realization and mmse dfe receiver performance optimal transmit filters for packet based data transmission on dispersive gaussian noise linear time invariant channels are derived by maximizing the mutual information subject to a fixed input power budget a quasi stationary approximation to the optimal nonstationary input covariance process is derived and shown to exhibit negligible mutual information loss from the optimal case for situations of most practical interest moreover this quasi stationary approximation results in efficiently computed lattice or pole zero implementations of the transmit filter by considering the popular finite impulse response minimum mean square error decision feedback equalizer fir mmse dfe as a receiver structure we show that transmitter optimization results in an appreciable improvement in the decision point signal to noise ratio finally we show that as the output blocklength becomes infinite the optimum finite dimensional nonstationary input covariance process converges to a stationary process whose power spectrum obeys the well known water pouring distribution

block based eigensystem of the 1 spl plusmn d and 1 d sup 2 partial response channels we find analytical expressions for the block based input and output eigenvectors and eigenvalues of the systems with responses 1 spl plusmn d and 1 d sup 2 the input eigenvectors form an orthonormal basis which is the optimum modulator for a channel with that transfer function the output eigenvectors form an orthonormal basis with the same spectral nulls as the corresponding system this basis can be used to produce line codes with spectral nulls the eigenvectors are sinusoids this reduces the computational complexity by allowing for fast transform algorithms to perform the modulation for a block of data

the partition function zeros in the one dimensional q state potts model the zeros of the partition function in the one dimensional q state potts model with arbitrary and continuous q or 0 have been studied using a transfer matrix the location of zeros and the yang lee edge singularity have been analysed and two different regimes corresponding to q 1 and q 1 have been observed a duality relation has also been derived which relates the zeros in the complex field plane to those in the complex temperature plane

metastability in the potts model on the cayley tree metastability in the ferromagneticp state potts model defined on the cayley tree is discussed it is shown that the sign of the boundary fieldhs determines the order of the transition as well as the stability of the low temperature phase lowering the temperature withhs 0 a system withp 2 will display a second first order transition to a metastable stable phase forhs 0 a second first order transition to a metastable stable phase occurs ifp 2 p 2 in this case the system also has a residual entropy which is negative forp 2

a new look at digital orthogonal transmultiplexers for cdma communications orthogonal transmultiplexers have been successfully utilized for multiuser communications they are of the fdma type in their most common version the transmultiplexers using frequency selective pr qmfs as their user codes were reported in the literature this approach conflicts with the requirements of a cdma communications system we introduce novel spread spectrum pr qmf codes wherein the orthogonality is distributed over both time and frequency domains it is shown that the proposed multivalued spread spectrum pr qmf codes with minimized auto and cross correlation properties outperform the conventional binary gold codes in cdma communication scenarios considered in the article

julia sets associated with the potts model on the bethe lattice and other recursively solved systems the q state potts model on the bethe lattice has been investigated by a number of individuals over the last several decades with some of the preceding studies taking a dynamical systems perspective however other than for the special case of the q 2 potts model i e the ising model the julia sets of the discrete dynamical systems associated with the potts model on the bethe lattice have been largely ignored we look at these sets and find an interesting connection between the phase transition temperature and the dimension of the julia set in particular we find the dimension of the julia set to be a minimum at a phase transition furthermore we show this property is not restricted to potts models on bethe lattices this adds to a number of other special properties present at temperatures where a phase transition occurs

varying coefficient models we explore a class of regression and generalized regression models in which the coefficients are allowed to vary as smooth functions of other variables general algorithms are presented for estimating the models flexibly and some examples are given this class of models ties together generalized additive models and dynamic generalized linear models into one common framework when applied to the proportional hazards model for survival data this approach provides a new way of modelling departures from the proportional hazards assumption

on the asymptotic properties of ldu based tests of the rank of a matrix abstract gill and lewbel recently introduced a test for the rank of a matrix based on the ldu decomposition unfortunately the asymptotic distribution suggested by them is incorrect except in a very limited problem in general the asymptotic distribution is that of a highly complicated nonlinear function of a normally distributed random vector that appears to defy useful characterization the ldu decomposition can be used to produce a valid test asymptotically equivalent to the minimum x 2 test

five turbulent problems abstract five questions which involve strange attractors in one way or another are discussed these are the choice of probability measures to describe turbulence the hausdorff dimension of julia sets for rational maps of the riemann sphere the existence of nonperiodic turbulent crystal structure the mechanism generating intermittency in developed hydrodynamic turbulence the distribution of characteristic exponents in a turbulent fluid

new precoding for intersymbol interference cancellation using nonmaximally decimated multirate filterbanks with ideal fir equalizers in this paper we propose a new precoding method for intersymbol interference isi cancellation by using non maximally decimated multirate filterbanks unlike the existing preceding methods such as the th and trellis precodings the new preceding i may be independent of the isi channel ii is linear and does not have to implement any modulo operation iii gives the ideal fir equalization at the receiver for any fir isi channel including spectral null channels iv expands the transmission bandwidth in a minimum amount the precoding is built on non maximally decimated multirate filterbanks based on multirate filterbank theory we present a necessary and sufficient condition on an fir isi transfer function in terms of its zero set such that there is a linear fir n spl times m precoder so that an ideal fir equalizer exists where the integers k and n are arbitrarily fixed the condition is easy to check as a consequence of the condition for any given fir isi transfer function not identically 0 there always exist such linear fir precoders moreover for almost all given fir isi transfer functions there exist linear fir precoders with size n spl times n 1 i e the bandwidth is expanded by 1 n in addition to the conditions on the isi transfer functions a method for the design of the linear fir precoders and the ideal fir equalizers is also given numerical examples are presented to illustrate the theory

recursive cyclotomic factorization a new algorithm for calculating the discrete fourier transform in this paper a new recursive algorithm for calculating the discrete fourier transformation is presented this new so called recursive cyclotomic factorization algorithm rcfa is more efficient than the fast fourier transformation fft algorithm moreover due to its recursive nature the rcfa can also be easily implemented using only a limited number of different computation cells

optimization of signal sets for partial response channels i numerical techniques given a linear time invariant discrete time channel the problem of constructing n input signals of finite length k that maximize minimum l sub 2 distance between pairs of outputs is considered two constraints on the input signals are considered a power constraint on each of the n inputs hard constraint and an average power constraint over the entire set of inputs soft constraint the hard constraint problem is equivalent to packing n points in an ellipsoid in min k n 1 dimensions to maximize the minimum euclidean distance between pairs of points gradient based numerical algorithms and a constructive technique based on dense lattices are used to find locally optimal solutions to the preceding signal design problems two numerical examples are shown for which the average spectrum of an optimized signal set resembles the water pouring spectrum that achieves shannon capacity assuming additive white gaussian noise

on the number of points on shells for shifted z sup 4 sup n lattices a conjecture is proven on the number of points on shells for the shifted z sup 4 and the shifted z sup 8 lattices furthermore the results are extended to any shifted z sup 4 sup n lattice n 0 1 these results provide an easy way to compute the number of points on shells for the type of lattices used in the design of multidimensional signal sets or in vector coding

coset codes for partial response channels or coset codes with spectral nulls known coset codes are adapted for use on partial response channels or to generate signals with spectral nulls by using coset precoding and running digital sum feedback any desired tradeoff can be achieved between the power and spectra of the relevant sequences up to the optimum tradeoff possible a fundamental theorem specifying this optimum tradeoff is given a maximum likelihood sequence estimation mlse decoder for the original code may be used for the adapted code and such a decoder then attains the minimum squared distance of the original code these methods sometimes generate codes with greater minimum squared distance than that of the original code this distance can be attained by augmented decoders although such decoders inherently require long decoding delays and may be subjected to quasi catastrophic error propagation the authors conclude that at least for sequences supporting large numbers of bits per symbol coset codes can be adapted to achieve effectively the same performance and complexity on partial response channels or for sequences with spectral nulls as they do in the ordinary memoryless case

inference of time varying regression models we consider parameter estimation hypothesis testing and variable selection for partially time varying coefficient models our asymptotic theory has the useful feature that it can allow dependent nonstationary error and covariate processes with a two stage method the parametric component can be estimated with a n 1 2 convergence rate a simulation assisted hypothesis testing procedure is proposed for testing significance and parameter constancy we further propose an information criterion that can consistently select the true set of significant predictors our method is applied to autoregressive models with time varying coefficients simulation results and a real data application are provided

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

coset codes i introduction and geometrical classification practically all known good constructive coding techniques for bandlimited channels including lattice codes and various trellis coded modulation schemes can be characterized as coset codes a coset code is defined by a lattice partition lambda lambda and by a binary encoder c that selects a sequence of cosets of the lattice lambda the fundamental coding gain of a coset code as well as other important parameters such as the error coefficient the decoding complexity and the constellation expansion factor are purely geometric parameters determined by c lambda lambda the known types of coset codes as well as a number of new classes that systematize and generalize known codes are classified and compared in terms of these parameters

generalized reduced rank tests using the singular value decomposition we propose a novel statistic to test the rank of a matrix the rank statistic overcomes deficiencies of existing rank statistics like a kronecker covariance matrix for the canonical correlation rank statistic of anderson annals of mathematical statistics 1951 22 327 351 sensitivity to the ordering of the variables for the ldu rank statistic of cragg and donald journal of the american statistical association 1996 91 1301 1309 and gill and lewbel journal of the american statistical association 1992 87 766 776 a limiting distribution that is not a standard chi squared distribution for the rank statistic of robin and smith econometric theory 2000 16 151 175 usage of numerical optimization for the objective function statistic of cragg and donald journal of econometrics 1997 76 223 250 and ignoring the non negativity restriction on the singular values in ratsimalahelo 2002 rank test based on matrix perturbation theory unpublished working paper u f r science economique university de franche comte in the non stationary cointegration case the limiting distribution of the new rank statistic is identical to that of the johansen trace statistic

spatial modulation over partially coherent multiple input multiple output channels communication over multiple input multiple output mimo channels of arbitrary coherence is considered in light of a mean square estimation error msee criterion earlier work in the field has focused on fully coherent channels and determined that use of a singular value decomposition svd of the channel transfer function matrix can realize the capacity of the mimo channel more recently research has shown that the use of arbitrary orthonormal channel excitation vectors can maximize expected capacity over fully incoherent rayleigh fading mimo channels partially coherent channels have generally been examined only in terms of their degrading influence on capacity in this discussion channel excitation techniques are proposed that minimize an msee criterion over an ensemble of mimo channels of arbitrary coherence the algorithms rely on only the second and fourth order moments of the channel transfer function two experiments were conducted to examine the new strategies using measured mimo channel transfer function ensembles one from an underwater acoustic channel and others from rf wireless channels the performance of the strategies are compared the new techniques outperform orthonormal signaling based on sinr or capacity metrics while requiring substantially less channel feedback than needed by a channel decomposition approach

the optimum combination of block codes and receivers for arbitrary channels a determination is made of the combinations of transmitted block codewords and matching receiver filters that maximize the signal to noise ratio at the detector with arbitrary channel impulse response and arbitrary noise spectrum this permits representing the channel as a set of parallel uncoupled subchannels with uncorrelated noise the representation is used to calculate the capacity of an arbitrary block coded time discrete channel it is shown that substantial coding gains compared to symbol by symbol processing can be achieved the block code used can be concatenated with trellis coded modulation so that the two coding gains are additive

a modified trellis coding technique for partial response channels the problem of trellis coding for multilevel baseband transmission over partial response channels with transfer polynomials of the form 1 or d sup n is addressed the novel method presented here accounts for the channel memory by using multidimensional signal sets and partitioning the signal set present at the noiseless channel output it is shown that this coding technique can be viewed as a generalization of a well known procedure for binary signaling the concatenation of convolutional codes and inner block codes that are tuned to the channel polynomial it results in high coding gains with moderate complexity if some bandwidth expansion is accepted

the multitone channel the maximum bit rate of multitone qam quadrature amplitude modulation over a general linear channel is found first the overall bit rate for an awgn channel with a two level transfer function is maximized using a multitone qam system the power distribution between the tones and the number of bits symbol per tone is optimized for a given symbol error rate extending these results to the general channel it is shown that the optimum power division for multitone signals is similar to the water pouring solution of information theory furthermore multitone qam performance is about 9 db worse than the channel capacity independent of the channel characteristics the multitone results throughout are compared to those of an equivalent single tone linearly equalized system the comparison shows that the multitone system is useful for some channels e g those with deep nulls in the transfer function the maximum bit error rate over a twisted pair channel which is performance dominated by near end crosstalk next is also found

local properties of an ising model on a cayley tree the ising model on a cayley tree displays a peculiar continuous order phase transition with zero long range order at all finite temperatures when one studies expection values of spins far removed from the surface which contains a finite fraction of the total number of spins in the thermodynamic limit however one obtains the so called bethe approximation here we study such a local description by setting up a simple recurrence relation for successive shell magnetizations far removed from the surface in the ferromagnetic case the local magnetization is a fixed point of the iterative transformation while in the antiferromagnetic case the fixed point bifurcates to a two cycle of the transformation for low temperatures and fields giving rise to local sublattice magnetizations in both cases local thermodynamical properties are obtained by integration

residue division multiplexing for discrete time signals multiplexing is a technique for dividing a single transmission channel into a number of virtual subchannels the present paper introduces a new multiplexing system for discrete time signals based on a polynomial factorization in this multiplexing system a linear filter additive noise channel is decomposed into independent subchannels that are also modeled as linear filter additive noise channels a configuration and an analysis of the multiplexing system as applied to mobile communications are described in detail based on a specific selection of polynomial factorization multicarrier code division multiple access mc cdma is receiving much attention in the field of mobile communications because of its time and frequency diversity property as is the case with mc cdma in the proposed multiplexing system the subchannel information is dispersed uniformly in both frequency and time so that degradation localized in frequency or time average out over the subchannels the averaging has the effect of decreasing the total error probability of transmission unlike mc cdma however the multiplexing system creates multiple carriers simply by up sampling a single complex sinusoidal carrier for each subchannel user because of the simple mechanism the implementation cost is less than that of mc cdma

trellis coding for partial response channels we consider trellis coding techniques for improving the reliability of digital transmission over noisy partial response channels such channels are commonly encountered in digital communication systems and also play a role in devices for data recording concentrating on the channels with characteristics 1 mp d we study methods to obtain codes which increase free euclidean distance between permitted sequences of channel outputs and avoid the occurrence of unlimited runs of identical outputs at the expense of some loss in data rate one technique employs the concept of set partitioning the other is based on using convolutional codes designed for maximum free hamming distance in conjunction with a precoder both methods lead to essentially equivalent codes

coset codes ii binary lattices and related codes for pt i see ibid vol 34 no 5 p 1123 51 1988 the family of barnes wall lattices including d sub 4 and e sub 8 of lengths n 2 sup n and their principal sublattices which are useful in constructing coset codes are generated by iteration of a simple construction called the squaring construction the closely related reed muller codes are generated by the same construction the principal properties of these codes and lattices are consequences of the general properties of iterated squaring constructions which also exhibit the interrelationships between codes and lattices of different lengths an extension called the cubing construction generates good codes and lattices of lengths n 3 2 sup n including the golay code and leech lattice with the use of special bases for 8 space another related construction generates the nordstrom robinson code and an analogous 16 dimensional nonlattice packing these constructions are represented by trellis diagrams that display their structure and interrelationships and that lead to efficient maximum likelihood decoding algorithms

optimization of signal sets for partial response channels ii asymptotic coding gain for pt i see ibid vol 37 no 5 p 1327 141 1991 for a linear time invariant discrete time channel with a given transfer function h f and information rate r bits t where t is the symbol interval an optimal signal set of length k is defined to be a set of 2 sup rk inputs of length k that maximizes the minimum l sub 2 distance between pairs of outputs the author studies the minimum distance between outputs or equivalently the coding gain of optimal signal sets as k to infinity he shows how to estimate the coding gain relative to single step detection of an optimal signal set length k when k is large

quantile regression inference with adaptive control of size abstractregression quantiles have asymptotic variances that depend on the conditional densities of the response variable given regressors this article develops a new estimate of the asymptotic var

trellis coded modulation with multidimensional constellations trellis coded modulation schemes using four eight or 16 dimensional constellations have a number of potential advantages over the usual two dimensional schemes a smaller constituent two dimensional constellation easier tolerance to phase ambiguities and a better trade off between complexity and coding gain a number of such schemes are presented and evaluated starting with a variety of multidimensional lattices we show how to select multidimensional constellations how to partition them into subsets how to construct trellis codes using those subsets and how to map hits to constellation points simplifications of the viterbi decoding algorithm are presented we conclude that there are multidimensional trellis coded modulation schemes that perform better for the same complexity than do two dimensional schemes

generalized likelihood ratio statistics and wilks phenomenon likelihood ratio theory has had tremendous success in parametric inference due to the fundamental theory of wilks yet there is no general applicable approach for nonparametric inferences based on function estimation maximum likelihood ratio test statistics in general may not exist in nonparametric function estimation setting even if they exist they are hard to find and can not be optimal as shown in this paper we introduce the generalized likelihood statistics to overcome the drawbacks of nonparametric maximum likelihood ratio statistics a new s wilks phenomenon is unveiled we demonstrate that a class of the generalized likelihood statistics based on some appropriate nonparametric estimators are asymptotically distribution free and follow chi 2 distributions under null hypotheses for a number of useful hypotheses and a variety of useful models including gaussian white noise models nonparametric regression models varying coefficient models and generalized varying coefficient models we further demonstrate that generalized likelihood ratio statistics are asymptotically optimal in the sense that they achieve optimal rates of convergence given by ingster they can even be adaptively optimal in the sense of spokoiny by using a simple choice of adaptive smoothing parameter our work indicates that the generalized likelihood ratio statistics are indeed general and powerful for nonparametric testing problems based on function estimation

potts model on a cayley tree and logistic equation the q state potts model on a cayley tree can be solved by a recursion formula depending on the properties at the surface the model on a bethe lattice is obtained by extrapolating the interior of a cayley tree sufficiently far from the surface in order to have a stable fixed point of the recursion for q 2 we find a second order transition of percolation type at the bethe peierls temperature and a first order transition at a higher temperature for coordination number z 3 the recursion extrapolated to q 1 is identical to the logistic equation the feigenbaum route to chaos appears for antiferromagnetic coupling of the potts model the first period doubling corresponds to a multicritical point in the phase diagram of the potts model

quantile regression with varying coefficients quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean the regression methodology is well developed for linear models but less so for nonparametric models we consider conditional quantiles with varying coefficients and propose a methodology for their estimation and assessment using polynomial splines the proposed estimators are easy to compute via standard quantile regression algorithms and a stepwise knot selection algorithm the proposed rao score type test that assesses the model against a linear model is also easy to implement we provide asymptotic results on the convergence of the estimators and the null distribution of the test statistic empirical results are also provided including an application of the methodology to forced expiratory volume fev data

optimization of a lattice based constellation for signaling over a partial response channel this article discusses the problem of optimizing a lattice based signal constellation for signaling over a partial response channel the objective is to minimize the probability of error which is determined by the combined effects of the additive gaussian noise and channel memory

estimation and testing of varying coefficients in quantile regression in this article we establish a novel connection between the null hypothesis h0 on the coefficients and a rank reducible form of the varying coefficient model in quantile regression we use b splines to approximate the varying coefficients in the rank reducible model and make use of the fact that the null hypothesis h0 implies a unidimensional structure of a transformed coefficient matrix for the b spline basis functions by evaluating the unidimensional structure we alleviate the difficulty of testing such hypotheses commonly considered in varying coefficient quantile models we demonstrate through numerical studies that the proposed method can be much more powerful than the rank score test which is widely used in the quantile regression literature supplementary materials for this article are available online

lower bound on the ber of a pre and postequalized vector communication system this paper is concerned with communication over a multiple input multiple output channel in the first reference a lower bound on the bit error rate of a pre and postequalized communication system was derived for uniform bit loading here we extend the lower bound to nonuniform bit loading the lower bound applies to communication systems for which 1 the cascade of the pre equalizer noise free channel and postequalizer is a diagonal matrix a generalized zero forcing condition satisfied by many designs in the literature and 2 the encoding modulation decoding demodulation is done independently over the dimensions of the pre equalizer input postequalizer output the lower bound is stated as a function of the bit loading channel and transmitter power only and applies to uncoded as well as coset coded systems toward deriving the lower bound we minimize a weighted average of the noise variances at the postequalizer output

new trellis codes based on lattices and cosets a new technique is proposed for constructing trellis codes which provides an alternative to ungerboeck s method of set partitioning the new codes use a signal constellation consisting of points from an n dimensional lattice lambda with an equal number of points from each coset of a sublattice lambda one part of the input stream drives a generalized convolutional code whose outputs are cosets of lambda while the other part selects points from these cosets several of the new codes are better than those previously known

vector coding for partial response channels a linear technique for combining equalization and coset codes on partial response channels with additive white gaussian noise is developed the technique vector coding uses a set of transmit filters or vectors to partition the channel into an independent set of parallel intersymbol interference isi free channels for any given finite or infinite block length the optimal transmit vectors for such channel partitioning are shown to be the eigenvectors of the channel covariance matrix for the specified block length and the gains of the individual channels are the eigenvalues an optimal bit allocation and energy distribution are derived for the set of parallel channels under an accurate extension of the continuous approximation for power in optimal multidimensional signal sets for constellations with unequal signal spacing in different dimensions examples are presented that demonstrate performance advantages with respect to zero forcing decision feedback methods that use the same coset code on the same partial response channel only resampling the channel at an optimal rate and assuming no errors in the feedback path will bring the performance of the decision feedback methods up to the level of the vector coded system

testing the rank and definiteness of estimated matrices with applications to factor state space and arma models abstract consider any consistent asymptotically normal estimate of an arbitrary rectangular or square matrix a this article derives an explicit test for the rank of a and a related test of semi definiteness of a potential applications include testing for identification of structural models testing for the number of state variables in state space models including tests for the order of autoregressive moving average arma processes consumer demand analysis applications and testing for the number of factors in factor analysis and related procedures the test is based on the gaussian elimination lower diagonal upper triangular ldu decomposition the test is illustrated with an empirical application to testing the order of arma processes

b splines and optimal stability it is proved that among all nonnegative bases of its space the b spline basis is optimally stable for evaluating spline functions

sampling rate conversion systems using a new generalized form of the discrete fourier transform a recursive factorization of the polynomial 1 z sup n leads to an efficient algorithm for the computation of the discrete fourier transform dft and the cyclic convolution the paper introduces a new recursive polynomial factorization of the polynomial when n is highly composite the factorization is used to define a generalized form of the dft and to derive an efficient algorithm for the computation the generalized form of the dft is shown to be closely related to the polyphase decomposition of a sequence and is applied for the design of sampling rate conversion systems it gives not only alternative derivations for the polyphase interpolation and the polyphase decimation by an integer factor but also a new sampling rate conversion system by a rational factor which is more efficient than the known rational polyphase implementation when the filter length is large

discrete multiple tone modulation with coset coding for the spectrally shaped channel a discrete approach to multiple tone modulation is developed for digital communication channels with arbitrary intersymbol interference isi and additive gaussian noise multiple tone modulation is achieved through the concatenation of a finite block length modulator based on discrete fourier transform dft code vectors and high gain coset or trellis codes symbol blocks from an inverse dft idft are cyclically extended to generate isi free channel output symbols that decompose the channel into a group of orthogonal and independent parallel subchannels asymptotic performance of this system is derived and examples of asymptotic and finite block length coding gain performance for several channels are evaluated at different values of bits per sample this discrete multiple tone technique is linear in both the modulation and the demodulation and is free from the effects of error propagation that often afflict systems employing bandwidth optimized decision feedback plus coset codes

optimized power allocation for packet retransmissions of non gaussian inputs through sequential awgn channels this work investigates the optimization of power allocation for hybrid arq h arq retransmissions of non gaussian inputs over a bank of independent parallel gaussian channels we establish a general solution for maximizing generic transceiver objective utility functions that are monotonically non decreasing and concave function with respect to the accumulated signal to noise ratio snr specifically we investigate optimized solutions under two performance metrics namely the mutual information mi and the union bound of symbol error rate ubser under maximal ratio combining mrc reception we establish that efficient utilization of parallel channels in h arq retransmissions requires sequential updating of signal channel pairing as well as optimizing power allocation applying geometric analysis of power loading for h arq retransmission we show that for i i d inputs that are not necessarily gaussian the optimum pairing policy should match signals of the lowest cumulative signal to noise ratio with channels of the best quality in each transmission which is consistent with a similar result of for gaussian input signals we further propose a generalized mercury waterfilling algorithm for the optimal power assignment problem in h arq simulation results illustrate substantial improvements over designs based on gaussian input assumptions

hierarchical spline models for conditional quantiles and the demand for electricity abstract methods for estimating nonparametric models for conditional quantiles are suggested based on the regression quantile methods of koenker and bassett spline parameterizations of the conditional quantile functions are used the methods are illustrated by estimating hierarchical models for household electricity demand using data from the chicago metropolitan area the empirical results show that lower quantiles of demand base load vary only slightly across residential households this variability is difficult to explain using household characteristics however upper quantiles of the demand distribution vary considerably and are systematically related to household characteristics and appliance ownership the implications of analyzing mean demand behavior rather than various quantiles of the distribution of demand are also discussed

yang lee zeros of the q state potts model on recursive lattices the yang lee zeros of the q state potts model on recursive lattices are studied for noninteger values of q considering one dimensional 1d lattice as a bethe lattice with coordination number equal to 2 the location of yang lee zeros of 1d ferromagnetic and antiferromagnetic potts models is completely analyzed in terms of neutral periodical points three different regimes for yang lee zeros are found for qg1 and 0lql1 an exact analytical formula for the equation of phase transition points is derived for the 1d case it is shown that yang lee zeros of the q state potts model on a bethe lattice are located on arcs of circles with the radius depending on q and temperature for qg1 complex magnetic field metastability regions are studied for the qg1 and 0lql1 cases the yang lee edge singularity exponents are calculated for both 1d and bethe lattice potts models the dynamics of metastability regions for different values of q is studied numerically

conditional growth charts growth charts are often more informative when they are customized per subject taking into account prior measurements and possibly other covariates of the subject we study a global semiparametric quantile regression model that has the ability to estimate conditional quantiles without the usual distributional assumptions the model can be estimated from longitudinal reference data with irregular measurement times and with some level of robustness against outliers and it is also flexible for including covariate information we propose a rank score test for large sample inference on covariates and develop a new model assessment tool for longitudinal growth data our research indicates that the global model has the potential to be a very useful tool in conditional growth chart analysis

perfect discrete multitone modulation with optimal transceivers previously discrete fourier transform dft based discrete multitone modulation dmt systems have been widely applied to various applications in this paper we study a broader class of dmt systems using more general unitary matrices instead of dft matrices for this class we show how to design optimal dmt systems over frequency selective channels with colored noise in addition asymptotical performance of dft based and optimal dmt systems are studied and shown to be equivalent however for a moderate number of bands the optimal dmt system offers significant gain over the dft based dmt system as is demonstrated by examples

practically realizable digital transmission significantly below the nyquist bandwidth proposes a practically realizable digital signaling scheme that requires a bandwidth significantly below the nyquist limit and at the same time achieves the same asymptotic performance as memoryless pam a five step iterative procedure for constructing such schemes is presented and examples that occupy down to about 60 percent of the nyquist bandwidth are demonstrated using this simple procedure practical receiver structures are also briefly discussed

quantile regression in partially linear varying coefficient models semiparametric models are often considered for analyzing longitudinal data for a good balance between flexibility and parsimony in this paper we study a class of marginal partially linear quantile models with possibly varying coefficients the functional coefficients are estimated by basis function approximations the estimation procedure is easy to implement and it requires no specification of the error distributions the asymptotic properties of the proposed estimators are established for the varying coefficients as well as for the constant coefficients we develop rank score tests for hypotheses on the coefficients including the hypotheses on the constancy of a subset of the varying coefficients hypothesis testing of this type is theoretically challenging as the dimensions of the parameter spaces under both the null and the alternative hypotheses are growing with the sample size we assess the finite sample performance of the proposed method by monte carlo simulation studies and demonstrate its value by the analysis of an aids data set where the modeling of quantiles provides more comprehensive information than the usual least squares approach

filterbank transceivers optimizing information rate in block transmissions over dispersive channels optimal finite impulse response fir transmit and receive filterbanks are derived for block based data transmissions over frequency selective additive gaussian noise agn channels by maximizing mutual information subject to a fixed transmit power constraint both fir and pole zero channels are considered the inherent flexibility of the proposed transceivers is exploited to derive as special cases zero forcing zf and minimum mean square error receive filterbanks the transmit filterbank converts transmission over a frequency selective fading channel affected by additive colored noise into a set of independent flat fading subchannels with uncorrelated noise samples two loading algorithms are also developed to distribute transmit power and number of bits across the usable subchannels while adhering to an upper bound on the bit error rate ber reduction of the signal to noise ratio snr margin required to satisfy the prescribed ber is achieved by coding each subchannel s bit stream the potential of the proposed transceivers is illustrated and compared to discrete multitone dmt with simulated examples

reduced state sequence estimation with set partitioning and decision feedback a reduced state sequence estimator for linear intersymbol interference channels is described the estimator uses a conventional viterbi algorithm with decision feedback to search a reduced state subset trellis that is constructed using set partitioning principles the complexity of maximum likelihood sequence estimation mlse due to the length of the channel memory and the size of the signal set is systematically reduced an error probability analysis shows that a good performance complexity tradeoff can be obtained in particular the results indicate that the required complexity to achieve the performance of mlse is independent of the size of the signal set for large enough signal sets simulation results are provided for two partial response systems a simple technique for quadrature partial response signaling qprs is described that eliminates the quasicatastrophic nature of the ml trellis

multirate zero forcing tx rx design for mimo channel under ber constraints this paper is concerned with communicating parallel independent streams of data possibly of different rates through a multiple input multiple output channel each data stream is required to satisfy a bit error rate ber constraint this scenario arises in multimedia communications we find the linear zero forcing transmitter receiver tx rx matrix pair that requires the minimum transmitter power to achieve the ber constraints it is well known that the tx rx pair can be chosen to partition the matrix channel into scalar subchannels corresponding to singular values and different data streams can be transmitted through different subchannels this design is suboptimum in general the optimum design has the following structure the set of input data streams is partitioned into groups called signal groups the set of subchannels is conformably partitioned into subchannel groups each signal group is collectively transmitted through its assigned subchannel group with each signal subchannel group pair is associated a unitary matrix that mixes the signals at the transmitter and unmixes them at the receiver we derive a simple algorithm to determine the optimum signal and subchannel groups we then use a known algorithm from majorization theory to determine the unitary matrices using these we completely specify the optimum tx rx pair

design of block transceivers with decision feedback detection this paper presents a method for jointly designing the transmitter receiver pair in a block by block communication system that employs intrablock decision feedback detection we provide closed form expressions for transmitter receiver pairs that simultaneously minimize the arithmetic mean squared error mse at the decision point assuming perfect feedback the geometric mse and the bit error rate of a uniformly bit loaded system at moderate to high signal to noise ratios separate expressions apply for the zero forcing and minimum mse mmse decision feedback structures in the mmse case the proposed design also maximizes the gaussian mutual information and suggests that one can approach the capacity of the block transmission system using independent instances of the same gaussian code for each element of the block our simulation studies indicate that the proposed transceivers perform significantly better than standard transceivers and that they retain their performance advantages in the presence of error propagation