cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

congruence lattices of finite diagram monoids abstract we give a complete description of the congruence lattices of the following finite diagram monoids the partition monoid the planar partition monoid the brauer monoid the jones monoid also known as the temperley lieb monoid the motzkin monoid and the partial brauer monoid all the congruences under discussion arise as special instances of a new construction involving an ideal i a retraction i m onto the minimal ideal a congruence on m and a normal subgroup of a maximal subgroup outside i

enumeration of idempotents in planar diagram monoids we classify and enumerate the idempotents in several planar diagram monoids namely the motzkin jones a k a temperley lieb and kauffman monoids the classification is in terms of certain vertex and edge coloured graphs associated to motzkin diagrams the enumeration is necessarily algorithmic in nature and is based on parameters associated to cycle components of these graphs we compare our algorithms to existing algorithms for enumerating idempotents in arbitrary regular semigroups and give several tables of calculated values

cellularity of diagram algebras as twisted semigroup algebras abstract the temperley lieb and brauer algebras and their cyclotomic analogues as well as the partition algebra are all examples of twisted semigroup algebras we prove a general theorem about the cellularity of twisted semigroup algebras of regular semigroups which allows us to easily reproduce the cellularity of these algebras this theorem generalizes a result of east about the cellularity of semigroup algebras of inverse semigroups

the congruences on the semigroup of balanced transformations of an infinite set abstract in 1966 j m howie j london math soc 41 707 716 showed that the semigroup generated by all non identity idempotent transformations of an infinite set x is the disjoint union of two semigroups one of which is denoted by h and consists of all balanced transformations of x that is all transformations whose defect shift and collapse are equal and infinite subsequently j m howie 1981 proc roy soc edinburgh sect a88 159 167 169 184 and marques 1983 proc roy soc edinburgh sect a93 245 257 showed that certain rees quotient semigroups associated with h are congruence free here we describe all congruences on h

on the sphere decoding algorithm i expected complexity the problem of finding the least squares solution to a system of linear equations where the unknown vector is comprised of integers but the matrix coefficient and given vector are comprised of real numbers arises in many applications communications cryptography gps to name a few the problem is equivalent to finding the closest lattice point to a given point and is known to be np hard in communications applications however the given vector is not arbitrary but rather is an unknown lattice point that has been perturbed by an additive noise vector whose statistical properties are known therefore in this paper rather than dwell on the worst case complexity of the integer least squares problem we study its expected complexity averaged over the noise and over the lattice for the sphere decoding algorithm of fincke and pohst we find a closed form expression for the expected complexity both for the infinite and finite lattice it is demonstrated in the second part of this paper that for a wide range of signal to noise ratios snrs and numbers of antennas the expected complexity is polynomial in fact often roughly cubic since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial this suggests that maximum likelihood decoding which was hitherto thought to be computationally intractable can in fact be implemented in real time a result with many practical implications

cdma multiuser detection a nonlinear programming approach the optimum receiver to detect the bits of multiple code division multiple access cdma users has an exponential complexity in the number of active users in the system consequently many suboptimum receivers have been developed to achieve good performance with less complexity we take the approach of approximating the solution of the optimum multiuser detection problem omud using nonlinear programming relaxations first we observe that some popular suboptimum receivers indeed correspond to relaxations of the optimal detection problem in particular one proposed approximation method yields to iterative solutions which correspond to previously proposed heuristic nonlinear detectors using a nonlinear programming approach we identify the convergence properties of these iterative detectors secondly we propose a relaxation that yields a receiver which we call the generalized minimum mean squared error detector we give a simple iterative implementation of the detector its performance is evaluated and comparisons to other suboptimum detection schemes are given

the semigroup generated by the idempotents of a partition monoid we study the idempotent generated subsemigroup of the partition monoid in the finite case this subsemigroup consists of the identity and all the singular partitions in the infinite case the subsemigroup is described in terms of certain parameters that measure how far a partition is from being a permutation as one of several corollaries we deduce howie s description from 1966 of the semigroup generated by the idempotents of a full transformation semigroup

on the degrees of freedom of the lasso we study the effective degrees of freedom of the lasso in the framework of stein s unbiased risk estimation sure we show that the number of nonzero coefficients is an unbiased estimate forthe degrees of freedom of the lasso a conclusion that requires no special assumption on the predictors in addition the unbiased estimator is shown to be asymptotically consistent with these results on hand various model selection criteria cp aic and bic are available which along with the lars algorithm provide a principled and efficient approach to obtaining the optimal lasso fit with the computational effort of a single ordinary least squares fit

randomly spread cdma asymptotics via statistical physics this paper studies randomly spread code division multiple access cdma and multiuser detection in the large system limit using the replica method developed in statistical physics arbitrary input distributions and flat fading are considered a generic multiuser detector in the form of the posterior mean estimator is applied before single user decoding the generic detector can be particularized to the matched filter decorrelator linear minimum mean square error mmse detector the jointly or the individually optimal detector and others it is found that the detection output for each user although in general asymptotically non gaussian conditioned on the transmitted symbol converges as the number of users go to infinity to a deterministic function of a hidden gaussian statistic independent of the interferers thus the multiuser channel can be decoupled each user experiences an equivalent single user gaussian channel whose signal to noise ratio snr suffers a degradation due to the multiple access interference mai the uncoded error performance e g symbol error rate and the mutual information can then be fully characterized using the degradation factor also known as the multiuser efficiency which can be obtained by solving a pair of coupled fixed point equations identified in this paper based on a general linear vector channel model the results are also applicable to multiple input multiple output mimo channels such as in multiantenna systems

quasi maximum likelihood multiuser detection using semi definite relaxation with application to synchronous cdma the maximum likelihood ml multiuser detector is well known to exhibit better bit error rate ber performance than many other multiuser detectors unfortunately ml detection mld is a nondeterministic polynomial time hard np hard problem for which there is no known algorithm that can find the optimal solution with polynomial time complexity in the number of users in this paper a polynomial time approximation method called semi definite sd relaxation is applied to the mld problem with antipodal data transmission sd relaxation is an accurate approximation method for certain np hard problems the sd relaxation ml sdr ml detector is efficient in that its complexity is of the order of k3 5 where k is the number of users we illustrate the potential of the sdr ml detector by showing that some existing detectors such as the decorrelator and the linear minimum mean square error detector can be interpreted as degenerate forms of the sdr ml detector simulation results indicate that the ber performance of the sdr ml detector is better than that of these existing detectors and is close to that of the true ml detector even when the cross correlations between users are strong or the near far effect is significant

generators and relations for partition monoids and algebras abstract we investigate the manner in which the partition monoid p n and algebra p n may be presented by generators and relations making use of structural properties of p n as well as presentations for several key submonoids we obtain a number of presentations for p n including that given without a complete proof by halverson and ram in 2005 we then conclude by showing how each of these presentations gives rise to an algebra presentation for p n

boosting for high dimensional linear models we prove that boosting with the squared error loss l 2 boosting is consistent for very high dimensional linear models where the number of predictor variables is allowed to grow essentially as fast as o exp sample size assuming that the true underlying regression function is sparse in terms of the 11 norm of the regression coefficients in the language of signal processing this means consistency for de noising using a strongly overcomplete dictionary if the underlying signal is sparse in terms of the l 1 norm we also propose here an aic based method for tuning namely for choosing the number of boosting iterations this makes l 2 boosting computationally attractive since it is not required to run the algorithm multiple times for cross validation as commonly used so far we demonstrate l 2 boosting for simulated data in particular where the predictor dimension is large in comparison to sample size and for a difficult tumor classification problem with gene expression microarray data

constrained maximum likelihood detection in cdma the detection strategy usually denoted optimal multiuser detection is equivalent to the solution of a 0 1 constrained maximum likelihood ml problem a problem which is known to be np hard in contrast the unconstrained ml problem can be solved quite easily and is known as the decorrelating detector in this paper we consider the constrained ml problem where the solution vector is restricted to lie within a closed convex set ccs such a design criterion leads to detector structures which are ml under the constraint assumption a close relationship between a sphere constrained ml detector and the well known minimum mean square error detector is found and verified an iterative algorithm for solving a ccs constraint problem is derived based on results in linear variational inequality theory special cases of this algorithm subject to a box constraint are found to correspond to known nonlinear successive and parallel interference cancellation structures using a clipped soft decision for making tentative decisions while a weighted linear parallel interference canceler with signal dependent weights arises from the sphere constraint convergence issues are investigated and an efficient implementation is suggested the bit error rate performance is studied via computer simulations and the expected performance improvements over unconstrained ml are verified

a statistical mechanics approach to large system analysis of cdma multiuser detectors we present a theory based on statistical mechanics to evaluate analytically the performance of uncoded fully synchronous randomly spread code division multiple access cdma multiuser detectors with additive white gaussian noise awgn channel under perfect power control and in the large system limit application of the replica method a tool developed in the literature of statistical mechanics allows us to derive analytical expressions for the bit error rate as well as the multiuser efficiency of the individually optimum io and jointly optimum jo multiuser detectors over the whole range of noise levels the information theoretic capacity of the randomly spread cdma channel and the performance of decorrelating and linear minimum mean square error mmse detectors are also derived in the same replica formulation thereby demonstrating validity of the statistical mechanical approach

partial correlation estimation by joint sparse regression models this article features online supplementary material in this article we propose a computationally efficient approach space sparse partial correlation estimation for selecting nonzero partial correlations under the high dimension low sample size setting this method assumes the overall sparsity of the partial correlation matrix and employs sparse regression techniques for model fitting we illustrate the performance of space by extensive simulation studies it is shown that space performs well in both nonzero partial correlation selection and the identification of hub variables and also outperforms two existing methods we then apply space to a microarray breast cancer dataset and identify a set of hub genes that may provide important insights on genetic regulatory networks finally we prove that under a set of suitable assumptions the proposed procedure is asymptotically consistent in terms of model selection and parameter estimation

idempotents and one sided units in infinite partial brauer monoids abstract we study monoids generated by various combinations of idempotents and one or two sided units of an infinite partial brauer monoid this yields a total of eight such monoids each with a natural characterisation in terms of relationships between parameters associated to brauer graphs we calculate the relative ranks of each monoid modulo any other such monoid it may contain and then apply these results to determine the sierpinski rank of each monoid and ascertain which ones have the semigroup bergman property we also make some fundamental observations about idempotents and units in arbitrary monoids and prove some general results about relative ranks for submonoids generated by these sets

probabilistic analysis of semidefinite relaxation for binary quadratic minimization we consider semidefinite programming relaxation sdr of a binary quadratic minimization problem this np hard problem arises naturally in the maximum likelihood detection of discrete signals for digital communications we analyze the average performance of the sdr algorithm for a class of randomly generated binary quadratic minimization problems although the sdr worst case approximation ratio is unbounded for this np hard problem our analysis shows that sdr can provide in polynomial time a provably near optimal solution achieving a constant factor approximation of the optimal objective value in probability moreover this constant factor remains bounded with increasing problem size our proof is based on an asymptotic analysis of karush kuhn tucker optimality conditions using random matrix theory

symbol error rate performance of box relaxation decoders in massive mimo the maximum likelihood ml decoder for symbol detection in large multiple input multiple output wireless communication systems is typically computationally prohibitive in this paper we study a popular and practical alternative namely the box relaxation optimization bro decoder which is a natural convex relaxation of the ml for independent identically distributed real gaussian channels with additive gaussian noise we obtain exact asymptotic expressions for the symbol error rate ser of the bro the formulas are particularly simple they yield useful insights and they allow accurate comparisons to the matched filter bound mfb and to linear decoders such as zero forcing and linear minimum mean square error for binary phase shift keying signals the ser performance of the bro is within 3 db of the mfb for square systems and it approaches the mfb as the number of receive antennas grows large compared to the number of transmit antennas our analysis further characterizes the empirical density function of the solution of the bro and shows that error events for any fixed number of symbols are asymptotically independent the fundamental tool behind the analysis is the convex gaussian min max theorem

asymptotic performance of discrete valued vector reconstruction via box constrained optimization with sum of ell _ 1 regularizers in this paper we analyze the asymptotic performance of convex optimization based discrete valued vector reconstruction from linear measurements we firstly propose a box constrained version of the conventional sum of absolute values soav optimization which uses a weighted sum of ell 1 regularizers as a regularizer for the discrete valued vector we then derive the asymptotic symbol error rate ser performance of the box constrained soav box soav optimization theoretically by using the convex gaussian min max theorem cgmt we also derive the asymptotic distribution of the estimate obtained by the box soav optimization on the basis of the asymptotic results we can obtain the optimal parameters of the box soav optimization in terms of the asymptotic ser moreover we can also optimize the quantizer to obtain the final estimate of the unknown discrete valued vector simulation results show that the empirical ser performance of box soav and the conventional soav is very close to the theoretical result for box soav when the problem size is sufficiently large we also show that we can obtain better ser performance by using the proposed asymptotically optimal parameters and quantizers compared to the case with some fixed parameter and a naive quantizer

the diversity order of the semidefinite relaxation detector in this paper we consider the detection of binary antipodal signals transmitted in a spatially multiplexed fashion over a fading multiple input multiple output mimo channel and where the detection is done by means of semidefinite relaxation sdr the sdr detector is an attractive alternative to maximum likelihood ml detection since the complexity is polynomial rather than exponential assuming that the channel matrix is drawn with independent identically distributed i i d real valued gaussian entries we study the receiver diversity and prove that the sdr detector achieves the maximum possible diversity thus the error probability of the receiver tends to zero at the same rate as the optimal ml receiver in the high signal to noise ratio snr limit this significantly strengthens previous performance guarantees available for the semidefinite relaxation detector additionally it proves that full diversity detection is also possible in certain scenarios when using a noncombinatorial receiver structure

motzkin monoids and partial brauer monoids we study the partial brauer monoid and its planar submonoid the motzkin monoid we conduct a thorough investigation of the structure of both monoids providing information on normal forms green s relations regularity ideals idempotent generation minimal idempotent generating sets and so on we obtain necessary and sufficient conditions under which the ideals of these monoids are idempotent generated we find formulae for the rank smallest size of a generating set of each ideal and for the idempotent rank smallest size of an idempotent generating set of the idempotent generated subsemigroup of each ideal in particular when an ideal is idempotent generated the rank and idempotent rank are equal along the way we obtain a number of results of independent interest and we demonstrate the utility of the semigroup theoretic approach by applying our results to obtain new proofs of some important representation theoretic results concerning the corresponding diagram algebras the partial or rook brauer algebra and motzkin algebra