representation type for block algebras of hecke algebras of classical type abstract we find representation type of the cyclotomic quiver hecke algebras r of level two in affine type a in particular we have determined representation type for all the block algebras of hecke algebras of classical type except for characteristic two in type d which has not been known for a long time as an application of this result we prove that block algebras of finite representation type are brauer tree algebras whose brauer trees are straight lines without exceptional vertex if the hecke algebras are of classical type in good characteristic we conjecture that this statement should hold for hecke algebras of exceptional type

knowledge diffusion in complex networks by considering time varying information channels abstract in this article based on a model of epidemic spreading we explore the knowledge diffusion process with an innovative mechanism for complex networks by considering time varying information channels to cover the knowledge diffusion process in homogeneous and heterogeneous networks two types of networks the ba network and the er network are investigated the mean field theory is used to theoretically draw the knowledge diffusion threshold numerical simulation demonstrates that the knowledge diffusion threshold is almost linearly correlated with the mean of the activity rate in addition under the influence of the activity rate and distinct from the classic susceptible infected susceptible sis model the density of knowers almost linearly grows with the spreading rate finally in consideration of the ubiquitous mechanism of innovation we further study the evolution of knowledge in our proposed model the results suggest that compared with the effect of the spreading rate the average knowledge version of the population is affected more by the innovation parameter and the mean of the activity rate furthermore in the ba network the average knowledge version of individuals with higher degree is always newer than those with lower degree

designing structured tight frames via an alternating projection method tight frames also known as general welch bound equality sequences generalize orthonormal systems numerous applications including communications coding and sparse approximation require finite dimensional tight frames that possess additional structural properties this paper proposes an alternating projection method that is versatile enough to solve a huge class of inverse eigenvalue problems ieps which includes the frame design problem to apply this method one needs only to solve a matrix nearness problem that arises naturally from the design specifications therefore it is the fast and easy to develop versions of the algorithm that target new design problems alternating projection will often succeed even if algebraic constructions are unavailable to demonstrate that alternating projection is an effective tool for frame design the paper studies some important structural properties in detail first it addresses the most basic design problem constructing tight frames with prescribed vector norms then it discusses equiangular tight frames which are natural dictionaries for sparse approximation finally it examines tight frames whose individual vectors have low peak to average power ratio par which is a valuable property for code division multiple access cdma applications numerical experiments show that the proposed algorithm succeeds in each of these three cases the appendices investigate the convergence properties of the algorithm

z4 kerdock codes orthogonal spreads and extremal euclidean line sets when m is odd spreads in an orthogonal vector space of type omega 2m 2 2 are related to binary kerdock codes and extremal line sets in rr 2 m 1 with prescribed angles spreads in a 2m dimensional binary symplectic vector space are related to kerdock codes over zz 4 and extremal line sets in cc 2 m with prescribed angles these connections involve binary real and complex geometry associated with extraspecial 2 groups a geometric map from symplectic to orthogonal spreads is shown to induce the gray map from a corresponding zz 4 kerdock code to its binary image these geometric considerations lead to the construction for any odd composite m of large numbers of zz 4 kerdock codes they also produce new zz 4 linear kerdock and preparata codes 1991 mathematics subject classification primary 94b60 secondary 51m15 20c99

representation type of hecke algebras of type a in this paper we provide a complete classification of the representation type for the blocks for the hecke algebra of type a stated in terms of combinatorical data the computation of the complexity of young modules is a key component in the proof of this classification result

optimum sequence multisets for synchronous code division multiple access channels it is shown that the sum capacity of the symbol synchronous code division multiple access channel with equal average input energy constraints is maximized precisely by those spreading sequence multisets that meet welch s lower bound on total squared correlation it is further shown that the symmetric capacity of the channel determined by these same sequence multisets is equal to the sum capacity

iterative construction of optimum signature sequence sets in synchronous cdma systems optimum signature sequence sets that maximize the capacity of single cell synchronous code division multiple access cdma systems have been identified optimum signature sequences minimize the total squared correlation tsc they form a set of orthogonal sequences if the number of users is less than or equal to the processing gain and a set of welch 1994 bound equality wbe sequences otherwise we present an algorithm where users update their transmitter signature sequences sequentially in a distributed fashion by using available receiver measurements we show that each update decreases the tsc of the set and produces better signature sequence sets progressively we prove that the algorithm converges to a set of orthogonal signature sequences when the number of users is less than or equal to the processing gain we observe and conjecture that the algorithm converges to a wbe set when the number of users is greater than the processing gain at each step the algorithm replaces one signature sequence from the set with the normalized minimum mean squared error mmse receiver corresponding to that signature sequence since the mmse filter can be obtained by a distributed algorithm for each user the proposed algorithm is amenable to distributed implementation

on projection algorithms for solving convex feasibility problems due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences most notably computerized tomography algorithms for solving convex feasibility problems continue to receive great attention to unify generalize and review some of these algorithms a very broad and flexible framework is investigated several crucial new concepts which allow a systematic discussion of questions on behaviour in general hilbert spaces and on the quality of convergence are brought out numerous examples are given

on the existence of a w graph for an irreducible representation of a coxeter group on montre que toute representation irreductible d un groupe de coxeter fini peut etre fournie par un graphe w

fourier based transmit beampattern design using mimo radar in multiple input multiple output mimo radar settings it is often desirable to transmit power only to a given location or set of locations defined by a beampattern transmit waveform design is a topic that has received much attention recently involving synthesis of both the signal covariance matrix r as well as the actual waveforms current methods involve a two step process of designing r via iterative solutions and then using r to generate waveforms that fulfill practical constraints such as having a constant envelope or drawing from a finite alphabet in this paper a closed form method to design r for a uniform linear array is proposed that utilizes the discrete fourier transform dft coefficients and toeplitz matrices the resulting covariance matrix fulfills the practical constraints such as positive semidefiniteness and the uniform elemental power constraint and provides performance similar to that of iterative methods which require a much greater computation time next a transmit architecture is presented that exploits the orthogonality of frequencies at discrete dft values to transmit a sum of orthogonal signals from each antenna the resulting waveforms provide a lower mean square error than current methods at a much lower computational cost and a simulated detection scenario demonstrates the performance advantages achieved

nonuniform sampling and reconstruction in shift invariant spaces this article discusses modern techniques for nonuniform sampling and reconstruction of functions in shift invariant spaces it is a survey as well as a research paper and provides a unified framework for uniform and nonuniform sampling and reconstruction in shift invariant subspaces by bringing together wavelet theory frame theory reproducing kernel hilbert spaces approximation theory amalgam spaces and sampling inspired by applications taken from communication astronomy and medicine the following aspects will be emphasized a the sampling problem is well defined within the setting of shift invariant spaces b the general theory works in arbitrary dimension and for a broad class of generators c the reconstruction of a function from any sufficiently dense nonuniform sampling set is obtained by efficient iterative algorithms these algorithms converge geometrically and are robust in the presence of noise d to model the natural decay conditions of real signals and images the sampling theory is developed in weighted l p spaces

irreducible projective modules of the hecke algebras of a finite coxeter group in this paper we classify the irreducible projective modules or equivalently see e g 6 the irreducible principal indecomposable modules of a non semisimple hecke algebra h w e of a finite coxeter group w let w 3 be a finite coxeter system 2 and t an indeterminate q t we denote by h w q the generic hecke iwaho algebra 9 2 lo this means that h w q is the c t algebra with the basis t w we w and the multiplication defined by

on the design of constant modulus probing signals for mimo radar probing signal waveforms play a central role in the signal processing performance of a multiple input multiple output mimo radar in practice for a given desired beam pattern we need to design a probing signal waveform whose beam pattern closely matches the desired one and whose autocorrelation and cross correlation sidelobes are kept low the latter properties are important to mitigate undesirable interference caused by multiple targets or scatterers in this correspondence we present an efficient optimization method to design a constant modulus probing signal which can synthesize a desired beam pattern while maximally suppressing both the autocorrelation and cross correlation sidelobes at between given spacial angles we formulate this problem as an unconstrained minimization of a fourth order trigonometric polynomial and propose an efficient quasi newton iterative algorithm to solve it besides we provide an analysis of the local minima of the fourth order trigonometric polynomial and prove that any local minima is a 1 2 approximation of its global optimal solution numerical examples show that the proposed approach compares favorably with the existing approach

existence and construction of noncoherent unitary space time codes we consider transmission using n transmit and reception using m receive antennas in a wireless environment assuming that neither the transmitter nor the receiver knows the channel coefficients for the scenario that the transmission employs noncoherent t spl times n unitary space time codes and for a block fading channel model where the channel is static during t channel uses and varies from t channel uses to the other we establish the bound r spl les min t n n on the diversity advantage rm provided by the code in order to show that the requirement r spl les min t n n cannot be relaxed for any given r n t and r spl les min t n n we then construct unitary t spl times n space time codes of rate r that guarantee diversity advantage rm two constructions are given that are also amenable to simple encoding and noncoherent maximum likelihood ml decoding algorithms

unconstrained synthesis of covariance matrix for mimo radar transmit beampattern multiple input multiple output mimo radars have many advantages over their phased array counterparts improved spatial resolution better parametric identifiably and greater flexibility to design the transmit beampattern the design of the transmit beampatterns generally requires the waveforms to have arbitrary auto and cross correlation properties the correlation covariance matrix r of the waveforms must be positive semidefinite therefore synthesis of a desired beampattern is usually a constrained optimization problem in this paper to simplify the constrained optimization problem two algorithms are proposed to synthesize the waveform covariance matrix for the desired beampattern in the first proposed algorithm the elements of a square root matrix of the covariance matrix r are parameterized using the coordinates of a hypersphere that implicitly fulfil the constraints this yields an iterative algorithm whose convergence speed can be increased significantly by providing good initial values in the second algorithm the constraints and redundant information in the covariance matrix r are exploited to find a closed form solution the drawback of the second algorithm is that it may yield a pseudocovariance matrix pseudo cm that is not guaranteed to be positive semidefinite however the pseudo cm can be easily converted into a covariance matrix using eigenvalue decomposition and or shrinkage methods moreover a pseudo cm can also be used to provide good initial values for the first algorithm to enable faster convergence

mimo radar transmit beampattern matching design in this paper a novel transmit beampattern matching design method is proposed for a multiple input multiple output mimo radar system whereas previous approaches first solve the correlation matrix r and then use r to design the transmit signal s the proposed one step method obtains the transmit signal s directly through solving the waveform matrix p since mimo radar transmit beampattern matching design is an inverse problem of the transmit beampattern in this paper we first discuss some important properties of the transmit beampattern and standardize the beampattern matching design problem we then theoretically explain the value of the signal waveform matrix p followed by an unconstrained optimization problem to solve p numerical examples demonstrate the advantages of the proposed one step method for the mimo radar transmit beampattern matching design problem including uniform and non uniform linear arrays

cdma codeword optimization interference avoidance and convergence via class warfare interference avoidance has been shown to reduce total square correlation tsc for given ensembles of user signature waveforms codewords in a synchronous code division multiple access cdma system in all experiments we have conducted sequential application of interference avoidance produces an optimal codeword set when starting from randomly chosen initial codewords here we provide the first formal proof of convergence to optimal codeword ensembles for greedy interference avoidance algorithms augmented by a technique called class warfare whereby users which reside in more heavily loaded areas of the signal space purposely interfere with attack the reception of users in less crowded areas coordination of deliberate interference by a complete class of aggrieved user is also sometimes necessary such attacks and subsequent codeword adjustment by attacked users are shown to strictly decrease tsc along the way we also show using linear algebra and a variant of stochastic ordering equivalence between minimization of tsc and maximization of sum capacity

mimo radar transmit beampattern design without synthesising the covariance matrix compared to phased array multiple input multiple output mimo radars provide more degrees of freedom dof that can be exploited for improved spatial resolution better parametric identifiability lower sidelobe levels at the transmitter receiver and design variety of transmit beampatterns the design of the transmit beampattern generally requires the waveforms to have arbitrary auto and cross correlation properties the generation of such waveforms is a two step complicated process in the first step a waveform covariance matrix is synthesized which is a constrained optimization problem in the second step to realize this covariance matrix actual waveforms are designed which is also a constrained optimization problem our proposed scheme converts this two step constrained optimization problem into a one step unconstrained optimization problem in the proposed scheme in contrast to synthesizing the covariance matrix for the desired beampattern nt independent finite alphabet constant envelope waveforms are generated and preprocessed with weight matrix w before transmitting from the antennas in this work two weight matrices are proposed that can be easily optimized for the desired symmetric and nonsymmetric beampatterns and guarantee equal average power transmission from each antenna simulation results validate our claims

behaviors of susceptible infected epidemics on scale free networks with identical infectivity in this paper we propose a susceptible infected model with identical infectivity in which at every time step each node can only contact a constant number of neighbors we implemented this model on scale free networks and found that the infected population grows in an exponential form with the time scale proportional to the spreading rate furthermore by numerical simulation we demonstrated that the targeted immunization of the present model is much less efficient than that of the standard susceptible infected model finally we investigate a fast spreading strategy when only local information is available different from the extensively studied path finding strategy the strategy preferring small degree nodes is more efficient than that preferring large degree nodes our results indicate the existence of an essential relationship between network traffic and network epidemic on scale free networks

hecke algebras of classical type and their representation type the purpose of this article is to determine the representation type for all of the hecke algebras of classical type to do this we combine methods from our previous work which is used to obtain information on their gabriel quivers and recent advances in the theory of finite dimensional algebras the principal computation is for hecke algebras of type b with two parameters then we show that the representation type of hecke algebras is governed by their poincare polynomials

signal enhancement a composite property mapping algorithm a signal enhancement algorithm is developed that seeks to recover a signal from noise contaminated distorted measurements made on that signal this object is achieved by utilizing a set of properties which the signal is known or is hypothesized as possessing the measured signal is modified to the smallest degree necessary to sequentially possess each of the individual properties conditions for the algorithm s convergence are established in which the primary requirement is that a composite property mapping be closed this is a relatively unrestricted condition in comparison to that required of most existing signal enhancement algorithms

optimal sequences for cdma under colored noise a schur saddle function property we consider direct sequence code division multiple access ds cdma modeling interference from users communicating with neighboring base stations by additive colored noise we consider two types of receiver structures first we consider the information theoretically optimal receiver and use the sum capacity of the channel as our performance measure second we consider the linear minimum mean square error lmmse receiver and use the signal to interference ratio sir of the estimate of the symbol transmitted as our performance measure our main result is a constructive characterization of the possible performance in both these scenarios a central contribution of this characterization is the derivation of a qualitative feature of the optimal performance measure in both the scenarios studied we show that the sum capacity is a saddle function it is convex in the additive noise covariances and concave in the user received powers in the linear receiver case we show that the mini average power required to meet a set of target performance requirements of the users is a saddle function it is convex in the additive noise covariances and concave in the set of performance requirements

relaxation properties of small world networks recently watts and strogatz introduced the so called small world networks in order to describe systems that combine simultaneously properties of regular and random lattices in this work we study diffusion processes defined on such structures by considering explicitly the probability for a random walker to be present at the origin the results are intermediate between the corresponding ones for fractals and cayley trees

optimal sequences and sum capacity of synchronous cdma systems the sum capacity of a multiuser synchronous cdma system is completely characterized in the general case of asymmetric user power constraints this solves the open problem posed by rupf and massey see ibid vol 40 p 1261 6 1994 which had solved the equal power constraint case we identify the signature sequences with real components that achieve sum capacity and indicate a simple recursive algorithm to construct them

representation type of schur algebras we give a complete classification of the classical schur algebras and the infinitesimal schur algebras which have tame representation type in combination with earlier work of some of the authors on semisimplicity and finiteness this completes the classification of representation type of all classical and infinitesimal schur algebras in all characteristics

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

dual coordinate ascent methods for non strictly convex minimization we consider a dual method for solving non strictly convex programs possessing a certain separable structure this method may be viewed as a dual version of a block coordinate ascent method studied by auslender 1 section 6 we show that the decomposition methods of han 6 7 and the method of multipliers may be viewed as special cases of this method we also prove a convergence result for this method which can be applied to sharpen the available convergence results for han s methods

tame representation type of infinitesimal q schur algebras abstract in this paper we give a classification of the infinitesimal q schur algebras which have tame representation type

mimo radar beampattern design via psl isl optimization we deal with the robust design of multiple input multiple output mimo waveform covariance matrices that optimize the worst case over steering mismatches transmit beampattern assuming either the peak sidelobe level psl or the integrated sidelobe level isl as figure of merit to this end we model the uncertainty set associated with each steering vector through two double sided potentially non convex quadratic constraints in addition we force two suitable constraints on the optimization variable the former accounts for the width of the mainbeam whereas the latter is either a uniform or a relaxed elemental power requirement allowing to control the amount of transmitted power we prove that both the mentioned waveform covariance designs lead to non convex optimization problems which remarkably share some hidden convexity properties hence we devise polynomial time procedures aimed at synthesizing the desired optimal mimo waveform covariance matrices finally at the analysis stage we assess the performance of the proposed techniques showing their capability to ensuring improved worst case performance than some counterparts available in open literature

oversampled filter banks perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in l sup 2 z these frames are the subject of this paper first the necessary and sufficient conditions of a filter bank for implementing a frame or a tight frame expansion are established as well as a necessary and sufficient condition for perfect reconstruction using fir filters after an fir analysis complete parameterizations of oversampled filter banks satisfying these conditions are given further we study the condition under which the frame dual to the frame associated with an fir filter bank is also fir and give a parameterization of a class of filter banks satisfying this property then we focus on non subsampled filter banks non subsampled filter banks implement transforms similar to continuous time transforms and allow for very flexible design we investigate the relations of these filter banks to continuous time filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two channel filter banks that yield highly regular wavelets with a given number of vanishing moments

ensuring convergence of the mmse iteration for interference avoidance to the global optimum viswanath and anantharam 1999 characterize the sum capacity of multiaccess vector channels for a given number of users received powers spreading gain and noise covariance matrix in a code division multiple access cdma system viswanath and anantharam present a combinatorial algorithm to generate a set of signature sequences that achieves the maximum sum capacity these sets also minimize a performance measure called generalized total square correlation tsc sub g ulukus and yates 2001 propose an iterative algorithm suitable for distributed implementation at each step one signature sequence is replaced by its linear minimum mean square error mmse filter this algorithm results in a decrease of tsc sub g at each step the mmse iteration has fixed points not only at the optimal configurations which attain the global minimum tsc sub g but also at other configurations which are suboptimal the authors of claim that simulations show that when starting with random sequences the algorithm converges to optimum sets of sequences but they give no formal proof we show that the tsc sub g function has no local minima in the sense that given any suboptimal set of sequences there exist arbitrarily close sets with lower tsc sub g therefore only the optimal sets are stable fixed points of the mmse iteration we define a noisy version of the mmse iteration as follows after replacing all the signature sequences one at a time by their linear mmse filter we add a bounded random noise to all the sequences using our observation about the tsc sub g function we can prove that if we choose the bound on the noise adequately making it decrease to zero the noisy mmse iteration converges to the set of optimal configurations with probability one for any initial set of sequences

numerical methods for inverse singular value problems3 two numerical methods one continuous and the other discrete are proposed for solving inverse singular value problems the first method consists of solving an ordinary differential equation obtained from an explicit calculation of the projected gradient of a certain objective function the second method generalizes an iterative process proposed originally by friedland nocedal and overton siam j numer anal 24 1987 pp 634 667 for solving inverse eigenvalue problems with the geometry understood from the first method it is shown that the second method also the method proposed by friedland nocedal and overton for inverse eigenvalue problems is a variation of the newton method while the continuous method is expected to converge globally at a slower rate in finding a stationary point of the objective function the discrete method is proved to converge locally at a quadratic rate if there is a solution some numerical examples are presented

a successive projection method it is of both theoretical and practical interest to find the projection of a point to the intersection of a finite number of closed convex sets by a sequence of projections to the individual sets successively in this paper we study such a method and analyze its convergence properties a main feature of the method is its capability to decompose the projection problem into several small ones for some structured sparse problems these small subproblems can be solved independently and the presented method has a potential use in parallel computation

computing a nearest symmetric positive semidefinite matrix the nearest symmetric positive semidefinite matrix in the frobenius norm to an arbitrary real matrix a is shown to be b h 2 where h is the symmetric polar factor of b a at 2 in the 2 norm a nearest symmetric positive semidefinite matrix and its distance 2 a from a are given by a computationally challenging formula due to halmos we show how the bisection method can be applied to this formula to compute upper and lower bounds for 2 a differing by no more than a given amount a key ingredient is a stable and efficient test for positive definiteness based on an attempted choleski decomposition for accurate computation of 2 a we formulate the problem as one of zero finding and apply a hybrid newton bisection algorithm some numerical difficulties are discussed and illustrated by example

the effect of generalized deactivation mechanism in weighted networks abstract in this paper we propose a generalized deactivation model to characterize weighted networks by introducing the special aging mechanism the model can produce power law distributions of degree strength and weight as confirmed in many real networks we also characterize the clustering and correlation properties of this class of networks a scaling behavior of clustering coefficient c 1 m is observed where m refers to the number of active nodes the generated network simultaneously exhibits hierarchical organization and disassortative degree correlation all of these structural properties are confirmed by present empirical evidence

finite step algorithms for constructing optimal cdma signature sequences a description of optimal sequences for direct spread code division multiple access ds cdma is a byproduct of recent characterizations of the sum capacity this paper restates the sequence design problem as an inverse singular value problem and shows that the problem can be solved with finite step algorithms from matrix theory it proposes a new one sided algorithm that is numerically stable and faster than previous methods

revealing the efficiency of information diffusion in online social networks of microblog abstract online social networks osns such as microblogs enable people to simultaneously share information with a large number of peers and revealing the properties of the formed network structure and the corresponding impacts on information diffusion are important in this article we empirically study 10 millions user profiles from the largest chinese mircoblog sina weibo and 41 7 millions profiles from twitter by studying followers topology we find an invariant characteristic that the followers count of users obeys a power law distribution with exponent near 2 we then investigate the reason from the theoretical view and find this network structure achieves the optimal information diffusion in terms of inducing a minimal propagation times our study thus reveals the efficiency of information diffusion in osns of microblogs which is validated by experimental examination theoretical analysis and numerical simulation

a generalization of the eckart young mirsky matrix approximation theorem abstract the eckart young mirsky theorem solves the problem of approximating a matrix by one of lower rank however the approximation generally differs from the original in all its elements in this paper it is shown how to obtain a best approximation of lower rank in which a specified set of columns of the matrix remains fixed the paper concludes with some applications of the generalization

tractable transmit mimo beampattern design under a constant modulus constraint multiple input multiple output mimo radar systems allow each antenna element to transmit a different waveform this waveform diversity can be exploited to enhance the beampattern design in particular effective management of radar radiation power in directions of interest we address the problem of designing a beampattern for mimo radar which in turn is determined by the transmit waveform while unconstrained design is straightforward a key open challenge is enforcing the constant modulus constraint on the radar waveform it is well known that the problem of minimizing deviation of the designed beampattern from an idealized one subject to the constant modulus constraint constitutes a hard nonconvex problem existing methods that address constant modulus invariably lead to a stiff tradeoff between analytical tractability achieved by relaxations and approximations and realistic design that exactly achieves constant modulus but is computationally burdensome a new approach is proposed in our paper which involves solving a sequence of convex equality constrained quadratic programs each of which has a closed form solution and such that constant modulus is achieved at convergence we further prove that the converged solution satisfies the karush kuhn tucker optimality conditions of the aforementioned hard nonconvex problem we evaluate the proposed successive closed forms scf algorithm against the state of the art mimo beampattern design techniques in both narrowband and wideband setups and show that the scf breaks the tradeoff between desirable performance and the associated computation cost

mimo radar waveform covariance matrix for high sinr and low side lobe levels multiple input multiple output mimo radar has better parametric identifiability but compared to phased array radar it shows loss in signal to noise ratio due to noncoherent processing to exploit the benefits of both mimo radar and phased array a waveform covariance matrix is proposed to generate the proposed covariance matrix the values of the cosine function between 0 and with a step size of nt are used to form a positive semi definite toeplitz matrix where nt is the number of transmit antennas the proposed covariance matrix yields gain in the signal to interference plus noise ratio sinr compared to mimo radar and have lower sidelobe levels slls compared to phased array mimo radar and the recently proposed phased mimo scheme moreover in contrast to the phased mimo scheme where each antenna transmits a different power our proposed scheme allows same power transmission from each antenna simulation results validate our analytical results

scale free network provides an optimal pattern for knowledge transfer abstract we study numerically the knowledge innovation and diffusion process on four representative network models such as regular networks small world networks random networks and scale free networks the average knowledge stock level as a function of time is measured and the corresponding growth diffusion time is defined and computed on the four types of networks the growth diffusion times all depend linearly on the network size n as n while the slope for scale free network is minimal indicating the fastest growth and diffusion of knowledge the calculated variance and spatial distribution of knowledge stock illustrate that optimal knowledge transfer performance is obtained on scale free networks we also investigate the transient pattern of knowledge diffusion on the four networks and a qualitative explanation of this finding is proposed

finite alphabet constant envelope waveform design for mimo radar the design of waveforms with specified auto and cross correlation properties has a number of applications in multiple input multiple output mimo radar beampattern design in this work two algorithms are proposed to generate finite alphabet constant envelope ce waveforms with required cross correlation properties the first algorithm proposes a closed form solution to find the finite alphabet ce waveforms to realize the given covariance matrix here gaussian random variables rv s are mapped onto binary phase shift keying bpsk and quadrature phase shift keying qpsk symbols using nonlinear functions and the cross correlation relationship between the gaussian rv s and bpsk qpsk rv s is established this cross correlation relationship is exploited to convert the problem of finding the bpsk qpsk waveforms to realize the covariance matrix corresponding to the given beampattern into finding the gaussian rv s to realize another covariance matrix that can be easily found in the second algorithm by exploiting the results of first algorithm a generalized algorithm to generate bpsk waveforms to approximate the given beampattern is proposed simulation results show that proposed finite alphabet ce waveforms outperform the existing algorithms to approximate the desired beampattern

the representation type of ariki koike algebras and cyclotomic q schur algebras abstract we give a necessary and sufficient condition on parameters for ariki koike algebras resp cyclotomic q schur algebras to be of finite representation type

constant modulus waveform design for mimo radar transmit beampattern a multiple input multiple output radar has great flexibility to design the transmit beampattern via selecting the probing waveform the idea of current transmit beampattern design is to approximate the disired transimit beampattern and minimize the cross correlation sidelobes in this paper under the constant modulus constraint two algorithms are proposed to design the probing waveform directly in the first algorithm the optimization criterion is minimizing the squared error between the designed beampattern and the given beampattern since the objective function is a nonconvex fourth order polynomial and the constant modulus constraint can be regarded as many nonconvex quadratic equality constraints an efficient alternating direction method of multipliers admm algorithm whose convergence speed is very fast is proposed to solve it in the second algorithm the criterion is minimizing the absolute error between the designed beampattern and the given beampattern this nonconvex problem can be formulated as l 1 norm problem which can be solved through a double admm algorithm finally we assess the performance of the two proposed algorithms via numerical results

structured low rank approximation this paper concerns the construction of a structured low rank matrix that is nearest to a given matrix the notion of structured low rank approximation arises in various applications ranging from signal enhancement to protein folding to computer algebra where the empirical data collected in a matrix do not maintain either the specified structure or the desirable rank as is expected in the original system the task to retrieve useful information while maintaining the underlying physical feasibility often necessitates the search for a good structured lower rank approximation of the data matrix this paper addresses some of the theoretical and numerical issues involved in the problem two procedures for constructing the nearest structured low rank matrix are proposed the procedures are flexible enough that they can be applied to any lower rank any linear structure and any matrix norm in the measurement of nearness the techniques can also be easily implemented by utilizing available optimization packages the special case of symmetric toeplitz structure using the frobenius matrix norm is used to exemplify the ideas throughout the discussion the concept rather than the implementation details is the main emphasis of the paper

the representation type of hecke algebras of type b abstract this paper determines the representation type of the iwahori hecke algebras of type b when q 1 in particular we show that a single parameter non semisimple iwahori hecke algebra of type b has finite representation type if and only if q is a simple root of the poincare polynomial confirming a conjecture of uno s j algebra 149 1992 287

the projected gradient methods for least squares matrix approximations with spectral constraints the problems of computing least squares approximations for various types of real and symmetric matrices subject to spectral constraints share a common structure this paper describes a general procedure in using the projected gradient method it is shown that the projected gradient of the objective function on the manifold of constraints usually can be formulated explicitly this gives rise to the construction of a descent flow that can be followed numerically the explicit form also facilitates the computation of the second order optimality conditions examples of applications are discussed with slight modifications the procedure can be extended to solve least squares problems for general matrices subject to singular value constraints

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

constant modulus mimo radar waveform design with minimum peak sidelobe transmit beampattern this paper addresses the problem of minimum peak sidelobe transmit beampattern design for colocated multiple input multiple output radar systems two new methods are proposed to achieve it via designing constant modulus cm waveforms directly one is to maximize the ratio of the minimum mainlobe level to the peak sidelobe level psl without specifying pattern masks and another is to minimize psl under the mainlobe ripple and unspecified waveform modulus constraints the resultant optimization problems are difficult to solve due to the coupled numerator and denominator of the quadratic fractional programming problem formulation in the former and double sided quadratic constraints and unknown waveform modulus in the latter for the former we decouple the numerator and denominator by equivalent transformation and introduction of boundary type auxiliary variables in order that feasible methods are derived to tackle them independently and efficiently for the latter we simplify the coupled double sided quadratic constraints on the same waveform vector into those on different single auxiliary variables to tackle the corresponding nonconvex optimization problem numerical examples show that the proposed algorithms can attain sufficient low peak sidelobe beampattern levels under the cm constraints

an algorithm for restricted least squares regression abstract a commonly occurring problem in statistics is that of minimizing a least squares expression subject to side constraints here a simple iterative algorithm is presented and shown to converge to the desired solution several examples are presented including finding the closest concave convex function to a set of points and other general quadratic programming problems the dual problem to the basic problem is also discussed and a solution for it is given in terms of the algorithm finally extensions to expressions other than least squares are given

accelerating the convergence of the method of alternating projections the powerful von neumann halperin method of alternating projections map is an algorithm for determining the best approximation to any given point in a hilbert space from the intersection of a finite number of subspaces it achieves this by reducing the problem to an iterative scheme which involves only computing best approximations from the it individual subspaces which make up the intersection the main practical drawback of this algorithm at least for some applications is that the method is slowly convergent in this paper we consider a general class of iterative methods which includes the map as a special case for such methods we study an accelerated version of this algorithm which was considered earlier by gubin polyak and raik 14 and by gearhart and koshy 13 we show that the accelerated algorithm converges faster than the map in the case of two subspaces but is in general it not faster than the map for more than two subspaces however for a symmetric version of the map the accelerated algorithm always converges faster for any number of subspaces our proof seems to require the use of the spectral theorem for self adjoint mappings

synthesis of linear and planar arrays with minimum element selection a new method for the synthesis of linear and planar arrays having prescribed beamwidth and sidelobe levels and a minimum number of elements is proposed in the method the number of elements in an array is minimized while constraining the amplitude response error in the mainlobe region the attenuation in the sidelobe region and the array dimensions an iterative constrained optimization method is used where the amplituderesponse error is linearly approximated at each iteration while concurrently minimizing a re weighted l1 norm of the array coefficients to ensure robustness of the array we constrain a sensitivity parameter namely the white noise gain to be above a prescribed level furthermore the method also provides the additional flexibility of controlling the array dimensions symmetry properties and element positions of the array two variants have been developed in the first variant both the array coefficients and the positions of the elements are optimized in the second variant only the array coefficients are optimized while the elements are fixed at predefined positions experimental comparisons with several state of the art competing methods show that the proposed method provides greater flexibility of controlling the robustness beampattern response error array dimensions and element positions while at the same time the number of elements is less than or equal to that of the competing methods

inverse eigenvalue problems a collection of inverse eigenvalue problems are identified and classified according to their characteristics current developments in both the theoretic and the algorithmic aspects are summarized and reviewed in this paper this exposition also reveals many open questions that deserve further study an extensive bibliography of pertinent literature is attached

low complexity moving target parameter estimation for mimo radar using 2d fft in multiple input multiple output radar to localize a target and estimate its reflection coefficient a given cost function is usually optimized over a grid of points the performance of such algorithms is directly affected by the grid resolution increasing the number of grid points enhances the resolution of the estimator but also increases its computational complexity exponentially in this paper two reduced complexity algorithms are derived based on capon and amplitude and phase estimation apes to estimate the reflection coefficient angular location and doppler shift of multiple moving targets by exploiting the structure of the terms the cost function is brought into a form that allows us to apply the two dimensional fast fourier transform 2d fft and reduce the computational complexity of estimation using low resolution 2d fft the proposed algorithm identifies suboptimal estimates and feeds them as initial points to the derived newton gradient algorithm in contrast to the grid based search algorithms the proposed algorithm can optimally estimate on and off the grid targets in very low computational complexity a new apes cost function with better estimation performance is also discussed generalized expressions of the cramer rao lower bound are derived to assess the performance of the proposed algorithm

on quasi orthogonal signatures for cdma systems sum capacity optimal signatures in synchronous code division multiple access cdma systems are functions of the codebook length as well as the number of active users a new signature set must be assigned every time the number of active users changes this correspondence considers signature sets that are less sensitive to changes in the number of active users equiangular signature sequences are proven to solve a certain max min signal to interference plus noise problem which results from their interference invariance unions of orthonormal bases have subsets that come close to satisfying the welch bound bounds on the maximum number of bases with minimum maximum correlation are derived and a new construction algorithm is provided connections are made between these signature design problems grassmannian line packing frame theory and algebraic geometry

communication on the grassmann manifold a geometric approach to the noncoherent multiple antenna channel we study the capacity of multiple antenna fading channels we focus on the scenario where the fading coefficients vary quickly thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver we use a noncoherent block fading model proposed by marzetta and hochwald see ibid vol 45 p 139 57 1999 the model does not assume any channel side information at the receiver or at the transmitter but assumes that the coefficients remain constant for a coherence interval of length t symbol periods we compute the asymptotic capacity of this channel at high signal to noise ratio snr in terms of the coherence time t the number of transmit antennas m and the number of receive antennas n while the capacity gain of the coherent multiple antenna channel is min m n bits per second per hertz for every 3 db increase in snr the corresponding gain for the noncoherent channel turns out to be m 1 m t bits per second per hertz where m min m n t 2 the capacity expression has a geometric interpretation as sphere packing in the grassmann manifold

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved