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

diffusive logistic equations with indefinite weights population models in disrupted environments the dynamics of a population inhabiting a strongly heterogeneous environment are modelledby diffusive logistic equations of the form u t d u m x cu u in 0 where u represents the population density c d 0 are constants describing the limiting effects of crowding and the diffusion rate of the population respectively and m x describes the local growth rate of the population if the environment is bounded and is surrounded by uninhabitable regions then u 0 on 0 the growth rate m x is positive on favourablehabitats and negative on unfavourable ones the object of the analysis is to determine how the spatial arrangement of favourable and unfavourable habitats affects the population being modelled the models are shown to possess a unique stable positive steady state implying persistence for the population provided l d where is the principle positive eigenvalue for the problem m x in 0 on analysis of how depends on m indicates that environments with favourable and unfavourable habitats closely intermingled are worse for the population than those containing large regions of uniformly favourable habitat in the limit as the diffusion rate d 0 the solutions tend toward the positive part of m x c and if m is discontinuous develop interior transition layers the analysis uses bifurcation and continuation methods the variational characterisation of eigenvalues upper and lower solution techniques and singular perturbation theory

on twistors and conformal field theories from six dimensions we discuss chiral zero rest mass field equations on six dimensional space time from a twistorial point of view specifically we present a detailed cohomological analysis develop both penrose and penrose ward transforms and analyse the corresponding contour integral formulae we also give twistor space action principles we then dimensionally reduce the twistor space of six dimensional space time to obtain twistor formulations of various theories in lower dimensions besides well known twistor spaces we also find a novel twistor space amongst these reductions which turns out to be suitable for a twistorial description of self dual strings for these reduced twistor spaces we explain the penrose and penrose ward transforms as well as contour integral formulae

canonical description of the d 10 superstring formulated in supertwistor space canonical description of the d 10 superstring action involving supertwistor variables generalizing penrose ferber supertwistors is developed primary and secondary constraints are identified and arranged into the first and second class sets dirac brackets are introduced and the deformation of the poisson bracket algebra of the first class constraints is studied the role of the deformation parameter is played by

composite operators in the twistor formulation of n 4 supersymmetric yang mills theory we incorporate gauge invariant local composite operators into the twistor space formulation of n 4 super yang mills theory in this formulation the interactions of the elementary fields are reorganized into infinitely many interaction vertices and we argue that the same applies to composite operators to test our definition of the local composite operators in twistor space we compute several corresponding form factors thereby also initiating the study of form factors using the position twistor space framework throughout this letter we use the composite operator built from two identical complex scalars as a pedagogical example we treat the general case in a follow up paper

pre hilbert spaces in twistor quantization in twistor theory the canonical quantization procedure called twistor quantization is performed with the twistor operators represented as za za c and za za however it has not been clarified what kind of function spaces this representation is valid in in the present paper we intend to find appropriate pre hilbert spaces in which the above representation is realized as an adjoint pair of operators to this end we define an inner product for the helicity eigenfunctions by an integral over the product space of the circular space s1 and the upper half of projective twistor space using this inner product we define a hilbert space in some particular case and indefinite metric pre hilbert spaces in other particular cases showing that the above mentioned representation is valid in these spaces it is also shown that only the penrose transform in the first particular case yields positive frequency massless fields without singularities while the penrose transforms in the other particular cases

limit of the smallest eigenvalue of a large dimensional sample covariance matrix in this paper the authors show that the smallest if p leq n or the p n 1 th smallest if p n eigenvalue of a sample covariance matrix of the form 1 n xx tends almost surely to the limit 1 sqrt y 2 as n rightarrow infty and p n rightarrow y in 0 infty where x is a p times n matrix with iid entries with mean zero variance 1 and fourth moment finite also as a by product it is shown that the almost sure limit of the largest eigenvalue is 1 sqrt y 2 a known result obtained by yin bai and krishnaiah the present approach gives a unified treatment for both the extreme eigenvalues of large sample covariance matrices

kodaira spencer theory of gravity and exact results for quantum string amplitudes we develop techniques to compute higher loop string amplitudes for twistedn 2 theories with 3 i e the critical case an important ingredient is the discovery of an anomaly at every genus in decoupling of brst trivial states captured to all orders by a master anomaly equation in a particular realization of then 2 theories the resulting string field theory is equivalent to a topological theory in six dimensions the kodaira spencer theory which may be viewed as the closed string analog of the chern simons theory using the mirror map this leads to computation of the number of holomorphic curves of higher genus curves in calabi yau manifolds it is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the correspondingn 2 theory relations withc 1 strings are also pointed out

demystifying the twistor construction of composite operators in n 4 super yang mills theory we explain some details of the construction of composite operators in n 4 sym that we have elaborated earlier in the context of lorentz harmonic chiral lhc superspace we give a step by step elementary derivation and show that the result coincides with the recent hypothesis put forward in arxiv 1603 04471 within the twistor approach we provide the appropriate lhc to twistors dictionary

random matrix theory of multi antenna communications the ricean channel the use of multi antenna arrays in wireless communications through disordered media promises huge increases in the information transmission rate it is therefore important to analyse the information capacity of such systems in realistic situations of microwave transmission where the statistics of the transmission amplitudes channel may be coloured here we present an approach that provides analytic expressions for the statistics i e the moments of the distribution of the mutual information for general gaussian channel statistics the mathematical method applies tools developed originally in the context of coherent wave propagation in disordered media such as random matrix theory and replicas although it is valid formally for large antenna numbers this approach produces extremely accurate results even for arrays with as few as two antennas we also develop a method to analytically optimize over the input signal distribution which enables us to calculate analytic capacities when the transmitter has knowledge of the statistics of the channel the emphasis of this paper is on elucidating the novel mathematical methods used we do this by analysing a specific case when the channel matrix is a complex gaussian with arbitrary mean and unit covariance which is usually called the ricean channel

random sequence multisets for synchronous code division multiple access channels the effect of using randomly selected sequence multisets for the uplink of a synchronous code division multiple access channel is considered a tight lower bound on the expected value of the sum capacity over the ensemble of randomly selected sequence multisets is given for large systems the sum rate penalty for using randomly selected multisets is shown to be at most 1 nat and to vanish as the number of users becomes large compared to the sequence length

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

generic multiloop methods and application to cal n 4 super yang mills we review some recent additions to the tool chest of techniques for finding compact integrand representations of multiloop gauge theory amplitudes including non planar contributions applicable for super yang mills in four and higher dimensions as well as for theories with less supersymmetry we discuss a general organization of amplitudes in terms of purely cubic graphs review the method of maximal cuts as well as some special d dimensional recursive cuts and conclude by describing the efficient organization of amplitudes resulting from the conjectured duality between color and kinematic structures on constituent graphs

optimization of ldpc codes for modulation and detection in layered multi antenna architectures in this paper we first perform the density evolution of ldpc codes in layered multi antenna architectures using bit interleaved coded modulation and detection based on successive decoding and interference cancellation the noise thresholds of ldpc codes are shown to be achieved within 1 2 db of the capacity for these architectures we then present a rate allocation method which optimizes the performance of a layered architecture and find good degree distributions for ldpc codes with the rates allocated by our method simulation results show that the performance for an optimized layered architecture is better by 4 db than that for the layered architecture using ldpc codes with the same rate in all layers

current algebra on the torus we derive the n point one loop correlation functions for the currents of an arbitrary affine kac moody algebra the one loop amplitudes which are elliptic functions defined on the torus riemann surface are specified by group invariant tensors and certain constant tau dependent functions we compute the elliptic functions via a generating function and explicitly construct the invariant tensor functions recursively in terms of young tableaux the lowest tensors are related to the character formula of the representation of the affine algebra these general current algebra loop amplitudes provide a building block for open twistor string theory among other applications

proper complex random processes with applications to information theory the covariance of complex random variables and processes when defined consistently with the corresponding notion for real random variables is shown to be determined by the usual complex covariance together with a quantity called the pseudo covariance a characterization of uncorrelatedness and wide sense stationarity in terms of covariance and pseudo covariance is given complex random variables and processes with a vanishing pseudo covariance are called proper it is shown that properness is preserved under affine transformations and that the complex multivariate gaussian density assumes a natural form only for proper random variables the maximum entropy theorem is generalized to the complex multivariate case the differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum if and only if the random vector is proper gaussian and zero mean the notion of circular stationarity is introduced for the class of proper complex random processes a discrete fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain an application of the theory is presented

asymptotic performance analysis of coded blast architectures with statistical rate and power allocations in this paper we first analyze some mathematical properties of ergodic capacity and outage capacity functions of the layers in bell labs layered space time blast architectures employing successive decoding and interference cancellation we then present statistical rate allocation and power allocation methods that optimize the asymptotic performance of blast architectures since the methods are developed by using ergodic capacity and outage capacity functions of the layers the allocated rates and powers depend only on a given channel statistic finally we prove that the rate allocation yields a better asymptotic performance than the power allocation numerical results show that blast architectures with the rate and power allocation perform better by 4 db and 3 db respectively than a blast architecture with the same rate and power in all layers

rearrangements of functions saddle points and uncountable families of steady configurations for a vortex on donne deux resultats sur l existence d une infinite de configurations stationnaires pour un tourbillon bases sur le principe de kelvin de l energie cinetique stationnaire on s interesse a des ecoulements permanents dans lesquels la vorticite est un rearrangement d une fonction donnee et on decrit les circulations de la vitesse autour des composantes convexes de la frontiere

minitwistors and 3d yang mills higgs theory we construct a minitwistor action for yang mills higgs ymh theory in three dimensions the feynman diagrams of this action will construct perturbation theory around solutions of the bogomolny equations in much the same way that mhv maximally helicity violating diagrams describe perturbation theory around the self dual yang mills equations in four dimensions we also provide a new formula for all tree amplitudes in ymh theory and its maximally supersymmetric extension in terms of degree d maps to minitwistor space we demonstrate its relationship to the roiban spradlin volovich witten rsvw formula in four dimensions and show that it generates the correct mhv amplitudes at d 1 and factorizes correctly in all channels for all degrees we construct a minitwistor action for yang mills higgs ymh theory in three dimensions the feynman diagrams of this action will construct perturbation theory around solutions of the bogomolny equations in much the same way that mhv maximally helicity violating diagrams describe perturbation theory around the self dual yang mills equations in four dimensions we also provide a new formula for all tree amplitudes in ymh theory and its maximally supersymmetric extension in terms of degree d maps to minitwistor space we demonstrate its relationship to the roiban spradlin volovich witten rsvw formula in four dimensions and show that it generates the correct mhv amplitudes at d 1 and factorizes correctly in all channels for all degrees

weak convergence and rate of convergence of mimo capacity random variable recent works on the distribution function of the capacity of independent and identically distributed i i d and semicorrelated narrowband channels show that the outage capacity computed using a gaussian approximation is close to the true outage capacity even for few antennas motivated by physical scattering considerations we study a multi antenna channel model with independent entries that are not necessarily identically distributed and show the weak convergence of capacity to a gaussian random variable the channel model considered in this paper subsumes well studied cases like the i i d and separable correlation models and thus we generalize previous results on weak convergence of multi antenna capacity using recent results from random matrix theory we also study the rate of convergence of ergodic capacity of i i d channels to its limit value employing a well known conjecture from random matrix theory we establish tight results for the rate of convergence and show a dependence of this rate on signal to noise ratio

information capacity of a random signature multiple input multiple output channel a closed form expression for information capacity of the random signature multiple input multiple output channel is given a direct calculation of the capacity is provided additional to the proof involving the capacity of minimum mean square error systems provided by verdu and shamai see ieee trans inform theory vol 45 p 622 40 1999

statistical rate allocation for layered space time structure we propose a modified layered structure for multiple input multiple output systems where the layer detection order is fixed and the data rate for each layer is allocated based on the detection order and channel statistics using a gaussian approximation of the layer capacities we derive an asymptotic optimum data rate allocation approach for optimum data rate allocation the amount of backoff from the mean layer capacity is proportional to the standard deviation of the layer capacity with statistical data rate allocation only limited channel feedback is needed to update channel statistics at the transmitter simulation results show significant performance improvement with the proposed algorithm we also find that the performance gap between the layered structure and the channel capacity diminishes with increasing ergodicity within each codeword numerical results show a singal to noise ratio improvement of 6 3 and 3 6 db for tgn channels b and d respectively for 1 outage probability and 9 b s hz spectral efficiency

an approximate capacity distribution for mimo systems in this letter we derive the exact variance of the capacity of a multiple input multiple output mimo system this enables an investigation of the accuracy of a gaussian approximation to the capacity foreshadowed by various central limit theorems we confirm recent results which state that the capacity variance appears to converge to a limit independent of absolute antenna numbers but dependent on the ratio of the numbers of receive to transmit antennas the gaussian approximation itself is surprisingly good even in the worst cases giving satisfactory results

diffusive logistic equation with constant yield harvesting i steady states we consider a reaction diffusion equation which models the constant yield harvesting to a spatially heterogeneous population which satisfies a logistic growth we prove the existence uniqueness and stability of the maximal steady state solutions under certain conditions and we also classify all steady state solutions under more restricted conditions exact global bifurcation diagrams are obtained in the latter case our method is a combination of comparison arguments and bifurcation theory

rearrangements and minimization of the principal eigenvalue of a nonlinear steklov problem this paper motivated by del pezzo et al 2006 1 discusses the minimization of the principal eigenvalue of a nonlinear boundary value problem in the literature this type of problem is called steklov eigenvalue problem the minimization is implemented with respect to a weight function the admissible set is a class of rearrangements generated by a bounded function we merely assume the generator is non negative in contrast to 1 where the authors consider weights which are positively away from zero in addition to being two valued under this generality more physical situations can be modeled finally using rearrangement theory developed by geoffrey burton we are able to prove uniqueness of the optimal solution when the domain of interest is a ball

cluster polylogarithms for scattering amplitudes motivated by the cluster structure of two loop scattering amplitudes in yang mills theory we define cluster polylogarithm functions we find that all such functions of weight four are made up of a single simple building block associated with the a2 cluster algebra adding the requirement of locality on generalized stasheff polytopes we find that these a2 building blocks arrange themselves to form a unique function associated with the a3 cluster algebra this a3 function manifests all of the cluster algebraic structure of the two loop n particle mhv amplitudes for all n and we use it to provide an explicit representation for the most complicated part of the n 7 amplitude as an example this article is part of a special issue of journal of physics a mathematical and theoretical devoted to cluster algebras in mathematical physics

perturbative gauge theory as a string theory in twistor space perturbative scattering amplitudes in yang mills theory have many unexpected properties such as holomorphy of the maximally helicity violating amplitudes to interpret these results we fourier transform the scattering amplitudes from momentum space to twistor space and argue that the transformed amplitudes are supported on certain holomorphic curves this in turn is apparently a consequence of an equivalence between the perturbative expansion of open image in new window 4 super yang mills theory and the d instanton expansion of a certain string theory namely the topological b model whose target space is the calabi yau supermanifold open image in new window

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

the asymptotic capacity of multiple antenna rayleigh fading channels we consider the asymptotic behavior of the capacity of multiple antenna rayleigh fading channels in the limit as the transmit and receive arrays become large we show that the capacity converges in distribution to a gaussian random variable and give closed form formulas for its mean and variance these results enable us to derive the first asymptotic formula for outage rates as well as a sharper estimate of the error in previously reported asymptotic formulas for ergodic capacity although these formulas are asymptotic we show by simulation that they are often quite accurate even for relatively small arrays

linear multiuser detectors for synchronous code division multiple access channels under the assumptions of symbol synchronous transmissions and white gaussian noise the authors analyze the detection mechanism at the receiver comparing different detectors by their bit error rates in the low background noise region and by their worst case behavior in a near far environment where the received energies of the users are not necessarily similar optimum multiuser detection achieves important performance gains over conventional single user detection at the expense of computational complexity that grows exponentially with the number of users it is shown that in the synchronous case the performance achieved by linear multiuser detectors is similar to that of optimum multiuser detection attention is focused on detectors whose linear memoryless transformation is a generalized inverse of the matrix of signature waveform crosscorrelations and on the optimum linear detector it is shown that the generalized inverse detectors exhibit the same degree of near far resistance as the optimum multiuser detectors the optimum linear detector is obtained

on local calabi yau supermanifolds and their mirrors we use local mirror symmetry to study a class of local calabi yau supermanifolds with bosonic sub variety vb having a vanishing first chern class solving the usual super cy condition requiring the equality of the total u 1 gauge charges of bosons b and the ghost like fields f one bqb fqf as bqb 0 and fqf 0 several examples are studied and explicit results are given for local ar supergeometries a comment on purely fermionic super cy manifolds corresponding to the special case where qb 0 b and fqf 0 is also made

optimal harvesting strategy based on rearrangements of functions abstract we study the problem of optimal harvesting of a marine species in a bounded domain with the aim of minimizing harm to the species under the general assumption that the fishing boats have different capacities this is a generalization of a result of kurata and shi in which the boats were assumed to have the same maximum harvesting capacity for this generalization we need a completely different approach as such we use the theory of rearrangements of functions we prove existence of solutions and obtain an optimality condition which indicates that the more aggressive harvesting must be pushed toward the boundary of the domain furthermore we prove that radial and steiner symmetries of the domain are preserved by the solutions we will also devise an algorithm for numerical solution of the problem and present the results of some numerical experiments

spectral efficiency of cdma with random spreading the cdma channel with randomly and independently chosen spreading sequences accurately models the situation where pseudonoise sequences span many symbol periods furthermore its analysis provides a comparison baseline for cdma channels with deterministic signature waveforms spanning one symbol period we analyze the spectral efficiency total capacity per chip as a function of the number of users spreading gain and signal to noise ratio and we quantify the loss in efficiency relative to an optimally chosen set of signature sequences and relative to multiaccess with no spreading white gaussian background noise and equal power synchronous users are assumed the following receivers are analyzed a optimal joint processing b single user matched filtering c decorrelation and d mmse linear processing

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

on the information rate of mimo systems with finite rate channel state feedback using beamforming and power on off strategy it is well known that multiple input multiple output mimo systems have high spectral efficiency especially when channel state information at the transmitter csit is available in many practical systems it is reasonable to assume that the csit is obtained by a limited i e finite rate feedback and is therefore imperfect we consider the design problem of how to use the limited feedback resource to maximize the achievable information rate in particular we develop a low complexity power on off strategy with beamforming or grassmann precoding and analytically characterize its performance given the eigenvalue decomposition of the covariance matrix of the transmitted signal refer to the eigenvectors as beams and to the corresponding eigenvalues as the beam s power a power on off strategy means that a beam is either turned on with a constant power or turned off we will first assume that the beams match the channel perfectly and show that the ratio between the optimal number of beams turned on and the number of antennas converges to a constant when the numbers of transmit and receive antennas approach infinity proportionally this motivates our power on off strategy where the number of beams turned on is independent of channel realizations but is a function of the signal to noise ratio snr when the feedback rate is finite beamforming cannot be perfect and we characterize the effect of imperfect beamforming by quantization bounds on the grassmann manifold by combining the results for power on off and beamforming a good approximation to the achievable information rate is derived simulations show that the proposed strategy is near optimal and the performance approximation is accurate for all experimented snrs

signature quantization in fading cdma with limited feedback in this work we analyze the performance of a signature quantization scheme for reverse link direct sequence ds code division multiple access cdma assuming perfect estimates of the channel and interference covariance the receiver selects the signature that minimizes interference power or maximizes signal to interference plus noise ratio sinr for a desired user from a signature codebook the codebook index corresponding to the optimal signature is then relayed to the user with a finite number of bits via a feedback channel here we are interested in the performance of a random vector quantization rvq codebook which contains independent isotropically distributed vectors assuming arbitrary transmit power allocation we consider additive white gaussian noise awgn channel first with no fading and subsequently with multipath fading we derive the corresponding sinr in a large system limit at the output of matched filter and linear minimum mean squared error mmse receiver numerical examples show that the derived large system results give a good approximation to the performance of finite size system and that the mmse receiver achieves close to a single user performance with only one feedback bit per signature element

low complexity per antenna rate and power control approach for closed loop v blast previous studies have shown that per antenna rate and power control can greatly increase the data throughput of vertical bell labs layered space time v blast while an extra transmit antenna selection can provide additional diversity advantage we combine the transmit antenna selection with power and rate control for each antenna we derive a simple criterion for minimum bit error rate ber or minimum total transmit power when the data throughput is constant over time zero forcing and zero forcing successive interference cancellation detections are considered for practical implementation we also present a fast algorithm that gives near optimal performance with very low complexity simulation results show that the proposed closed loop blast outperforms the open loop v blast significantly in terms of ber performance especially when the antennas exhibit strong fading correlations

capacity of a multiple antenna fading channel with a quantized precoding matrix given a multiple input multiple output mimo channel feedback from the receiver can be used to specify a transmit precoding matrix which selectively activates the strongest channel modes here we analyze the performance of random vector quantization rvq in which the precoding matrix is selected from a random codebook containing independent isotropically distributed entries we assume that channel elements are independent and identically distributed i i d and known to the receiver which relays the optimal rate maximizing precoder codebook index to the transmitter using b bits we first derive the large system capacity of beamforming rank one precoding matrix as a function of b where large system refers to the limit as b and the number of transmit and receive antennas all go to infinity with fixed ratios rvq for beamforming is asymptotically optimal i e no other quantization scheme can achieve a larger asymptotic rate we subsequently consider a precoding matrix with arbitrary rank and approximate the asymptotic rvq performance with optimal and linear receivers matched filter and minimum mean squared error mmse numerical examples show that these approximations accurately predict the performance of finite size systems of interest given a target spectral efficiency numerical examples show that the amount of feedback required by the linear mmse receiver is only slightly more than that required by the optimal receiver whereas the matched filter can require significantly more feedback

an iterative multiuser decoder for near capacity communications the combination of forward error correction fec coding and random interleaving is shown to overcome the limitations of multiuser detectors decoders when the user cross correlations are high in particular one can asymptotically achieve single user performance in a highly correlated multiuser system in addition an optimal iterative multiuser detector is derived from iterative techniques for cross entropy minimization a practical suboptimal implementation of this algorithm is presented and simulations demonstrate that even with highly correlated users it achieves optimal asymptotic efficiency the effects of the theoretical limits on channel capacity are evident in many of the simulation results the complexity of the suboptimal algorithm is approximately o 2 sup k o 2 sup spl kappa per bit per iteration where k is the number of users and spl kappa is the code constraint length

rearrangement minimization problems with indefinite external forces abstract this paper discusses a rearrangement minimization problem related to a boundary value problem where the differential operator is the p laplacian and the external force is indefinite by applying the rearrangement theory established by g r burton we show that the minimization problem has a unique solution in the weak closure of the admissible set in an appropriate function space what makes this paper different from many others in the literature is that the admissible set here is allowed to be indefinite takes on both positive and negative values we show that in this case the optimal solution will be a weak limit point of the admissible set and cannot be a rearrangement element itself optimality conditions are derived based on the mean value of the generator in case the generator is a three valued function we shall show that the optimality conditions lead to free boundary value problems that are of interest independently we also discuss a minimization problem where the admissible set is not seemingly related to rearrangement classes but we shall prove otherwise and apply the earlier results of the current paper to draw interesting conclusions regarding the optimal solution we have also discussed the case where the domain of interest is radial and shown that the optimal solutions are radial as well

mimo channel modeling and the principle of maximum entropy we devise theoretical grounds for constructing channel models for multiple input multiple output mimo systems based on information theoretic tools the paper provides a general method to derive a channel model which is consistent with one s state of knowledge the framework we give here has already been fruitfully explored with success in the context of bayesian spectrum analysis and parameter estimation for each channel model we conduct an asymptotic analysis in the number of antennas of the achievable transmission rate using tools from random matrix theory a central limit theorem is provided on the asymptotic behavior of the mutual information and validated in the finite case by simulations the results are useful both in terms of designing a system based on criteria such as quality of service and in optimizing transmissions in multiuser networks

one loop derivation of the wilson polygon mhv amplitude duality we discuss the origin of the wilson polygon mhv amplitude duality at a perturbative level it is shown that the duality for the mhv amplitudes at the one loop level can be proven upon a particular change of variables in feynman parametrization and with the use of the relation between feynman integrals at different space time dimensions some generalization of the duality which implies the insertion of a particular vertex operator at the wilson triangle is found for the 3 point function we discuss the analytical structure of wilson loop diagrams and present the corresponding landau equations the geometrical interpretation of the loop diagram in terms of the hyperbolic geometry is discussed

a computational method of solving free boundary problems in vortex dynamics abstract a general method for computing two dimensional and axisymmetric three dimensional solutions of the steady euler equations is developed the method is based upon variational principles which are formulated entirely in terms of the natural conserved quantities for the unsteady euler equations the vorticity fields considered have a free boundary and may be defined either in a domain with boundary or in free space moreover the common restriction to the case of constant vorticity regions is not imposed the global convergence of the resulting iterative solver is established the numerical implementation of the method is discussed and several computational examples are given

global anti self dual yang mills fields in split signature and their scattering this article concerns solutions to the anti self dual yang mills asdym equations in split signature that are global on the double cover of the appropriate conformally compactified minkowski space e m s 2 s 2 ward s asdym twistor construction is adapted to this geometry using a correspondence between points of e m and holomorphic discs in cp 3 twistor space with boundary on the real slice rp 3 smooth global u n solutions to the asdym equations on e m are shown to be in 1 1 correspondence with pairs consisting of an arbitrary holomorphic vector bundle e over cp 3 together with a positive definite hermitian metric h on e rp 3 there are no topological or other restrictions on the bundle e in ultrahyperbolic signature solutions are generically non analytic or only finitely differentiable and such solutions arise from a corresponding choice of regularity for h when e is trivial the twistor data consists of the hermitian matrix function h on rp 3 up to constants and the correspondence provides a nonlinear generalisation of the x ray transform in general it provides a higher dimensional analogue of the inverse scattering transform in which h plays the role of the reflection coefficient ande the algebraic data explicit examples are constructed for different choices of the topology of e a scattering problem for asdym fields on affine minkowski spacein split signature is set up and it is shown that sufficiently small data at past null infinity uniquely determines data at future null infinity by taking a family of holonomies associated to the initial data followed by a sequence of two birkhoff factorizations the scattering map is simple at the level of the holonomies but non trivial at the level of the connection in the non abelian case

hidden symmetries and integrable hierarchy of the mathcal n 4 supersymmetric yang mills equations we describe an infinite dimensional algebra of hidden symmetries of mathcal n 4 supersymmetric yang mills sym theory our derivation is based on a generalization of the supertwistor correspondence using the latter we construct an infinite sequence of flows on the solution space of the mathcal n 4 sym equations the dependence of the sym fields on the parameters along the flows can be recovered by solving the equations of the hierarchy we embed the mathcal n 4 sym equations in the infinite system of the hierarchy equations and show that this sym hierarchy is associated with an infinite set of graded symmetries recursively generated from supertranslations presumably the existence of such nonlocal symmetries underlies the observed integrable structures in quantum mathcal n 4 sym theory

on yangian invariant regularization of deformed on shell diagrams in mathcal n 4 super yang mills theory we investigate yangian invariance of deformed on shell diagrams with d 4 superconformal symmetry we find that invariance implies a direct relationship between the deformation parameters and the permutation associated with the on shell graph we analyse the connection with deformations of scattering amplitudes in super yang mills theory and the possibility of using the deformation parameters as a regulator preserving yangian invariance a study of higher point tree and loop graphs suggests that manifest yangian invariance of the amplitude requires trivial deformation parameters

achievable information rates and the coding spreading tradeoff in finite sized synchronous cdma systems in this letter we compute achievable information rates for finite sized synchronous code division multiple access cdma systems and low density parity check ldpc codes are adopted to approach the achievable rates the associated coding spreading tradeoff problem is also considered using these results we assume binary random spreading sequences and the computed achievable rates are averaged over ensembles of spreading sequences unlike most prior papers which analyze the spectral efficiency of large cdma systems under gaussianity assumptions channel inputs and or multiple access interference we make no such assumptions in order to display the coding spreading tradeoff we plot the minimum required signal to noise ratio for reliable transmission as a function of information rate it is shown that the coding spreading tradeoff favors all coding i e no spreading when the optimal joint multiuser detector decoder is employed whereas for systems with a suboptimal multiuser detector and single user decoders there generally exists an optimal balance between coding and spreading we also provide simulation results on the performance of ldpc coded synchronous cdma systems which approach the information theoretic limits we have computed

twistor theory at fifty from contour integrals to twistor strings we review aspects of twistor theory its aims and achievements spanning the last five decades in the twistor approach space time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold the twistor space after giving an elementary construction of this space we demonstrate how solutions to linear and nonlinear equations of mathematical physics anti self duality equations on yang mills or conformal curvature can be encoded into twistor cohomology these twistor correspondences yield explicit examples of yang mills and gravitational instantons which we review they also underlie the twistor approach to integrability the solitonic systems arise as symmetry reductions of anti self dual asd yang mills equations and einstein weyl dispersionless systems are reductions of asd conformal equations we then review the holomorphic string theories in twistor and ambitwistor spaces and explain how these theories give rise to remarkable new formulae for the computation of quantum scattering amplitudes finally we discuss the newtonian limit of twistor theory and its possible role in penrose s proposal for a role of gravity in quantum collapse of a wave function

topological strings and integrable hierarchies we consider the topological b model on local calabi yau geometries we show how one can solve for the amplitudes by using w algebra symmetries which encodes the symmetries of holomorphic diffeomorphisms of the calabi yau in the highly effective fermionic brane formulation this leads to a free fermion description of the amplitudes furthermore we argue that topological strings on calabi yau geometries provide a unifying picture connecting non critical super strings integrable hierarchies and various matrix models in particular we show how the ordinary matrix model the double scaling limit of matrix models and kontsevich like matrix model are all related and arise from studying branes in specific local calabi yau three folds we also show how a model topological string on p 1 and local toric threefolds and in particular the topological vertex can be realized and solved as b model topological string amplitudes on a calabi yau manifold

sublinear capacity scaling laws for sparse mimo channels recent attention on performance analysis of single user multiple input multiple output mimo systems has been on understanding the impact of the spatial correlation model on ergodic capacity in most of these works it is assumed that the statistical degrees of freedom dof in the channel can be captured by decomposing it along a suitable eigenbasis and that the transmitter has perfect knowledge of the statistical dof with an increased interest in large antenna systems in state of the art technologies these implicit channel modeling assumptions in the literature have to be revisited in particular multiantenna measurements have showed that large antenna systems are sparse where only a few dof are dominant enough to contribute towards capacity thus in this work it is assumed that the transmitter can only afford to learn the dominant statistical dof in the channel the focus is on understanding ergodic capacity scaling laws in sparse channels unlike classical results where linear capacity scaling is implicit sparsity of mimo channels coupled with a knowledge of only the dominant dof is shown to result in a new paradigm of sublinear capacity scaling that is consistent with experimental results and physical arguments it is also shown that uniform power signaling over all the antenna dimensions is wasteful and could result in a significant penalty over optimally adapting the antenna spacings in response to the sparsity level of the channel and transmit snr

shannon theoretic approach to a gaussian cellular multiple access channel we obtain shannon theoretic limits for a very simple cellular multiple access system in our model the received signal at a given cell site is the sum of the signals transmitted from within that cell plus a factor spl alpha 0 spl les spl alpha spl les 1 times the sum of the signals transmitted from the adjacent cells plus ambient gaussian noise although this simple model is scarcely realistic it nevertheless has enough meat so that the results yield considerable insight into the workings of real systems we consider both a one dimensional linear cellular array and the familiar two dimensional hexagonal cellular pattern the discrete time channel is memoryless we assume that n contiguous cells have active transmitters in the one dimensional case and that n sup 2 contiguous cells have active transmitters in the two dimensional case there are k transmitters per cell most of our results are obtained for the limiting case as n spl rarr spl infin the results include the following 1 we define c sub n c spl circ sub n as the largest achievable rate per transmitter in the usual shannon theoretic sense in the one and two dimensional cases respectively assuming that all signals are jointly decoded we find expressions for limn spl rarr spl infin c sub n and limn spl rarr spl infin c spl circ sub n 2 as the interference parameter spl alpha increases from 0 c sub n and c spl circ sub n increase or decrease according to whether the signal to noise ratio is less than or greater than unity 3 optimal performance is attainable using tdma within the cell but using tdma for adjacent cells is distinctly suboptimal 4 we suggest a scheme which does not require joint decoding of all the users and is in many cases close to optimal

impact of antenna correlation on the capacity of multiantenna channels this paper applies random matrix theory to obtain analytical characterizations of the capacity of correlated multiantenna channels the analysis is not restricted to the popular separable correlation model but rather it embraces a more general representation that subsumes most of the channel models that have been treated in the literature for arbitrary signal to noise ratios snr the characterization is conducted in the regime of large numbers of antennas for the low and high snr regions in turn we uncover compact capacity expansions that are valid for arbitrary numbers of antennas and that shed insight on how antenna correlation impacts the tradeoffs among power bandwidth and rate

alternative string theory in twistor space for n 4 super yang mills theory in this letter an alternative string theory in twistor space is proposed for describing perturbative n 4 super yang mills theory like the recent proposal of witten this string theory uses twistor worldsheet variables and has manifest spacetime superconformal invariance however in this proposal tree level super yang mills amplitudes come from open string tree amplitudes as opposed to coming from d instanton contributions

from scattering amplitudes to the dilatation generator in n 4 sym the complete spin chain representation of the planar n 4 sym dilatation generator has long been known at one loop where it involves leading nearestneighbor 2 2 interactions in this work we use superconformal symmetry to derive the unique solution for the leading l 2 interactions of the planar dilatation generator for arbitrarily large l we then propose that these interactions are given by a scattering operator that has n 4 sym tree level scattering amplitudes as matrix elements we provide compelling evidence for this proposal including explicit checks for l 2 3 and a proof of consistency with superconformal symmetry