gaussian interference channel capacity to within one bit the capacity of the two user gaussian interference channel has been open for 30 years the understanding on this problem has been limited the best known achievable region is due to han and kobayashi but its characterization is very complicated it is also not known how tight the existing outer bounds are in this work we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges and by deriving new outer bounds we show that a very simple and explicit han kobayashi type scheme can achieve to within a single bit per second per hertz bit s hz of the capacity for all values of the channel parameters we also show that the scheme is asymptotically optimal at certain high signal to noise ratio snr regimes using our results we provide a natural generalization of the point to point classical notion of degrees of freedom to interference limited scenarios

hierarchical cooperation in ad hoc networks optimal clustering and achievable throughput for a wireless network with n nodes distributed in an area a and with n source destination pairs communicating with each other at some common rate the hierarchical cooperation scheme proposed in ozgur leveque and tse 2007 is analyzed and optimized by choosing the number of hierarchical stages and the corresponding cluster sizes that maximize the total throughput it turns out that increasing the number of stages does not necessarily improve the throughput and the closed form solutions for the optimization problem can be explicitly obtained based on the expression of the maximum achievable throughput it is found that the hierarchical scheme achieves a scaling with the exponent depending on n in addition to apply the hierarchical cooperation scheme to random networks a clustering algorithm is developed which divides the whole network into quadrilateral clusters each with exactly the number of nodes required

n k user interference channels degrees of freedom this paper analyzes the gains of opportunistic communication in multiuser interference channels consider a fully connected n user gaussian interference channel at each time instance only k n transmitters are allowed to be communicating with their respective receivers and the remaining n k transmitter receiver pairs remain inactive for finite n if the transmitters can acquire the instantaneous channel realizations and if all channel gains are bounded away from zero and infinity the seminal results on interference alignment establish that for any k arbitrary active pairs the total number of spatial degrees of freedom per orthogonal time and frequency domain is k 2 in dense networks n however as the size of the network increases it becomes less likely to sustain the bounding conditions on the channel gains by exploiting this fact we show that when n obeys certain scaling laws by opportunistically and dynamically selecting the k active pairs at each time instance the number of degrees of freedom can exceed k 2 and in fact can be made arbitrarily close to k more specifically for single antenna transmitters and receivers the network size scaling as n snrd d 1 when power allocation is allowed and scaling as n snrd k 1 without power allocation are sufficient conditions for achieving d 1 k degrees of freedom moreover for achieving these degrees of freedom the transmitters do not require the knowledge of the instantaneous channel realizations hence invoking opportunistic communication in the context of interference channels leads to achieving higher degrees of freedom that are not achievable otherwise we extend the results for multi antenna gaussian interference channels

cut set bound is loose for gaussian relay networks the cut set bound developed by cover and el gamal in 1979 has since remained the best known upper bound on the capacity of the gaussian relay channel we develop a new upper bound on the capacity of the gaussian primitive relay channel which is tighter than the cut set bound our proof uses gaussian measure concentration to establish geometric relations satisfied with high probability between the n letter random variables associated with a reliable code for communicating over this channel we then translate these geometric relations into new information inequalities that cannot be obtained with classical methods combined with a tensorization argument proposed by courtade and ozgur in 2015 our result also implies that the current capacity approximations for gaussian relay networks which have linear gap to the cut set bound in the number of nodes are order optimal and lead to a lower bound on the pre constant

degrees of freedom of two hop wireless networks everyone gets the entire cake we show that fully connected two hop wireless networks with k sources k relays and k destinations have k degrees of freedom both in the case of time varying channel coefficients and constant channel coefficients in which case the result holds for almost all values of constant channel coefficients our main contribution is a new achievability scheme which we call aligned network diagonalization this scheme allows the data streams transmitted by the sources to undergo a diagonal linear transformation from the sources to the destinations thus being received free of interference by their intended destination in addition we extend our scheme to multihop networks with fully connected hops and multihop networks with mimo nodes for which the degrees of freedom are also fully characterized

capacity regions and sum rate capacities of vector gaussian interference channels the capacity regions of vector or multiple input multiple output gaussian interference channels are established for very strong interference and aligned strong interference furthermore the sum rate capacities are established for z interference noisy interference and mixed aligned weak intermediate and aligned strong interference these results generalize known results for scalar gaussian interference channels

multivariate locally weighted least squares regression nonparametric regression using locally weighted least squares was first discussed by stone and by cleveland recently it was shown by fan and by fan and gijbels that the local linear kernel weighted least squares regression estimator has asymptotic properties making it superior in certain senses to the nadaraya watson and gasser muller kernel estimators in this paper we extend their results on asymptotic bias and variance to the case of multivariate predictor variables we are able to derive the leading bias and variance terms for general multivariate kernel weights using weighted least squares matrix theory this approach is especially convenient when analysing the asymptotic conditional bias and variance of the estimator at points near the boundary of the support of the predictors we also investigate the asymptotic properties of the multivariate local quadratic least squares regression estimator discussed by cleveland and devlin and in the univariate case higher order polynomial fits and derivative estimation

on the product determinant sum of central wishart matrices and its application to wireless networks abstract inspired by multiaccess in dense cellular systems the paper first considers minimizing the determinant of the sum of a subset of n i i d central wishart matrices for any given size when n goes to infinity the exact scaling for more general case selecting a subset to minimize the product determinant sum of n i i d central wishart matrix vectors is provided specifically suppose each vector has k wishart matrices of format gg with g of dimension nr nt then for any subset of size n the k determinants each being the sum over one of the vector elements will have a product no less than exp k nr 1 1 k nrnt log n for all a between 1 1 k nrnt and 1 the paper then applies the results to study multiaccess with cross cell collaborations in dense environment when each cell allows multi users to be on and decodes by treating signals from neighboring cells as noise the maximum throughput is characterized and achieved by selecting users based on their channels specifically if every cell allows same number of nodes to be on and decodes by successive interference cancellation for in cell nodes the maximum throughput is nr 1 k nrnt log n bit s hz cell when n goes to infinity where n k nr nt are numbers of nodes per cell neighbors per cell receive antennas per user and transmit antennas per base station respectively it is also shown that time sharing across cells achieves higher throughput determined by the chromatic number of the interference graph

robust lattice alignment for k user mimo interference channels with imperfect channel knowledge in this paper we consider a robust lattice alignment design for k user quasi static multiple input multiple output mimo interference channels with imperfect channel knowledge with random gaussian inputs the conventional interference alignment ia method has the feasibility problem when the channel is quasi static on the other hand structured lattices can create structured interference as opposed to the random interference caused by random gaussian symbols the structured interference space can be exploited to transmit the desired signals over the gaps however the existing alignment methods on the lattice codes for quasi static channels either require infinite signal to noise ratio snr or symmetric interference channel coefficients furthermore perfect channel state information csi is required for these alignment methods which is difficult to achieve in practice in this paper we propose a robust lattice alignment method for quasi static mimo interference channels with imperfect csi at all snr regimes and a two stage decoding algorithm to decode the desired signal from the structured interference space we derive the achievable data rate based on the proposed robust lattice alignment method where the design of the precoders decorrelators scaling coefficients and interference quantization coefficients is jointly formulated as a mixed integer and continuous optimization problem the effect of imperfect csi is also accommodated in the optimization formulation and hence the derived solution is robust to imperfect csi we also design a low complex iterative optimization algorithm for our robust lattice alignment method by using the existing iterative ia algorithm that was designed for the conventional ia method numerical results verify the advantages of the proposed robust lattice alignment method compared with the time division multiple access tdma two stage maximum likelihood ml decoding generalized han kobayashi hk distributive ia and conventional ia methods in the literature

superposition signaling in broadcast interference networks it is known that superposition signaling in gaussian interference networks is capable of improving the achievable rate region however the problem of maximizing the rate gain offered by superposition signaling is computationally prohibitive even in the simplest case of two user single input single output interference networks this paper examines superposition signaling for the general multiple input multiple output broadcast gaussian interference networks the problem of maximizing either the sum rate or the minimal user s rate under superposition signaling and dirty paper coding is solved by a computationally efficient path following procedure which requires only a convex quadratic program for each iteration but ensures convergence at least to a locally optimal solution numerical results demonstrate the substantial performance advantage of the proposed approach

a network information theory for wireless communication scaling laws and optimal operation how much information can be carried over a wireless network with a multiplicity of nodes and how should the nodes cooperate to transfer information to study these questions we formulate a model of wireless networks that particularly takes into account the distances between nodes and the resulting attenuation of radio signals and study a performance measure that weights information by the distance over which it is transported consider a network with the following features i n nodes located on a plane with minimum separation distance spl rho sub min 0 ii a simplistic model of signal attenuation e sup spl gamma spl rho spl rho sup spl delta over a distance spl rho where spl gamma spl ges 0 is the absorption constant usually positive unless over a vacuum and spl delta 0 is the path loss exponent iii all receptions subject to additive gaussian noise of variance spl sigma sup 2 the performance measure we mainly but not exclusively study is the transport capacity c sub t sup spl sigma on sub spl lscr 1 sup m r sub spl lscr spl middot spl rho sub spl lscr where the supremum is taken over m and vectors r sub 1 r sub 2 r sub m of feasible rates for m source destination pairs and spl rho sub spl lscr is the distance between the spl lscr th source and its destination it is the supremum distance weighted sum of rates that the wireless network can deliver we show that there is a dichotomy between the cases of relatively high and relatively low attenuation when spl gamma 0 or spl delta 3 the relatively high attenuation case the transport capacity is bounded by a constant multiple of the sum of the transmit powers of the nodes in the network however when spl gamma 0 and spl delta 3 2 the low attenuation case we show that there exist networks that can provide unbounded transport capacity for fixed total power yielding zero energy priced communication examples show that nodes can profitably cooperate over large distances using coherence and multiuser estimation when the attenuation is low these results are established by developing a coding scheme and an achievable rate for gaussian multiple relay channels a result that may be of interest in its own right

mmse of bad codes we examine codes over the additive gaussian noise channel designed for reliable communication at some specific signal to noise ratio snr and constrained by the permitted minimum mean square error mmse at lower snrs the maximum possible rate is below point to point capacity and hence these are nonoptimal codes alternatively referred to as bad codes we show that the maximum possible rate is the one attained by superposition codebooks moreover the mmse and mutual information behavior as a function of snr for any code attaining the maximum rate under the mmse constraint is known for all snr we also provide a lower bound on the mmse for finite length codes as a function of the error probability of the code

the degrees of freedom of wireless networksvia cut set integrals the problem of determining the number of spatial degrees of freedom d o f of the signals carrying information in a wireless network is reduced to the computation of the geometric variation of the environment with respect to the cut through which the information must flow physically this has an appealing interpretation in terms of the diversity induced on the cut by the possible richness of the scattering environment mathematically this variation is expressed as an integral along the cut which we call cut set integral and whose scaling order is evaluated exactly in the case of planar networks embedded in arbitrary three dimensional 3 d environments presented results shed some new light on the problem of computing the capacity of wireless networks showing a fundamental limitation imposed by the size of the cut through which the information must flow in an attempt to remove what may appear as apparent inconsistencies with previous literature we also discuss how our upper bounds relate to corresponding lower bounds obtained using the techniques of multihop hierarchical cooperation and interference alignment

on the capacity of the k user cyclic gaussian interference channel this paper studies the capacity region of a k user cyclic gaussian interference channel where the kth user interferes with only the k 1 th user mod k in the network inspired by the work of etkin tse and wang who derived a capacity region outer bound for the two user gaussian interference channel and proved that a simple han kobayashi power splitting scheme can achieve to within one bit of the capacity region for all values of channel parameters this paper shows that a similar strategy also achieves the capacity region of the k user cyclic interference channel to within a constant gap in the weak interference regime specifically for the k user cyclic gaussian interference channel a compact representation of the han kobayashi achievable rate region using fourier motzkin elimination is first derived a capacity region outer bound is then established it is shown that the etkin tse wang power splitting strategy gives a constant gap of at most 2 bits in the weak interference regime for the special three user case this gap can be sharpened to 1 bits by time sharing of several different strategies the capacity result of the k user cyclic gaussian interference channel in the strong interference regime is also given further based on the capacity results this paper studies the generalized degrees of freedom gdof of the symmetric cyclic interference channel it is shown that the gdof of the symmetric capacity is the same as that of the classic two user interference channel no matter how many users are in the network

the worst additive noise under a covariance constraint the maximum entropy noise under a lag p autocorrelation constraint is known by burg s theorem to be the pth order gauss markov process satisfying these constraints the question is what is the worst additive noise for a communication channel given these constraints is it the maximum entropy noise the problem becomes one of extremizing the mutual information over all noise processes with covariances satisfying the correlation constraints r sub 0 r sub p for high signal powers the worst additive noise is gauss markov of order p as expected but for low powers the worst additive noise is gaussian with a covariance matrix in a convex set which depends on the signal power

information theoretic upper bounds on the capacity of large extended ad hoc wireless networks we derive an information theoretic upper bound on the rate per communication pair in a large ad hoc wireless network we show that under minimal conditions on the attenuation due to the environment and for networks with a constant density of users this rate tends to zero as the number of users gets large

system utility maximization with interference processing for cognitive radio networks in spectrum underlay cognitive radio networks secondary users sus are allowed to reuse the spectrum allocated to a primary system the interference between sus actually carries information and can potentially be exploited to improve the network performance through information theoretic interference processing in this paper we design an optimal joint power and rate control algorithm that maximizes the secondary system utility subject to the interference temperature constraints of primary users based on the capacity approaching interference processing scheme called as the han kobayashi scheme the optimal solution is difficult to achieve because the optimization problem is in general non convex to make the optimization problem tractable this paper first transforms the problem into a monotonic optimization problem through exploiting its hidden monotonicity we then devise an effective algorithm to obtain the global optimal solution to the joint power and rate control problem in the han kobayashi scheme the key idea behind the proposed algorithm is to construct a sequence of shrinking polyblocks that approximate the upper boundary of the feasible region with increasing precision numerical results further show that the achieved utility of our scheme significantly outperforms the utility of conventional schemes which treat the interference between sus as the noise

on the capacity of symmetric m user gaussian interference channels with feedback a general time varying feedback coding scheme is proposed for m user fully connected symmetric gaussian interference channels based on the analysis of the general coding scheme we prove a theorem which gives a criterion for designing good time varying feedback codes for gaussian interference channels the proposed scheme improves the suh tse and kramer inner bounds of the channel capacity for the cases of weak and not very strong interference when m 2 this capacity improvement is more significant when the signal to noise ratio snr is not very high in addition our coding scheme can be proved mathematically and numerically to outperform the kramer code for m geq 2 when the snr is equal to the interference to noise ratio inr besides the generalized degrees of freedom gdof of our proposed coding scheme can be proved to be optimal in the all network situations very weak weak strong very strong for any m the numerical results show that our coding scheme can attain better performance than the suh tse coding scheme for m 2 or the mohajer tandon poor lattice coding scheme for m 2 furthermore the simplicity of the encoding decoding algorithms is another strong point of our proposed coding scheme compared with the suh tse coding scheme when m 2 and the mohajer tandon poor lattice coding scheme when m 2 more importantly our results show that an optimal coding scheme for the symmetric gaussian interference channels with feedback can be achieved by only using marginal posterior distributions under a better cooperation strategy between transmitters

on secrecy capacity scaling in wireless networks this paper studies the achievable secure rate per source destination pair in wireless networks first a path loss model is considered where the legitimate and eavesdropper nodes are assumed to be placed according to poisson point processes with intensities and e respectively it is shown that as long as e o logn 2 almost all of the nodes achieve a perfectly secure rate of 1 n for the extended and dense network models therefore under these assumptions securing the network does not entail a loss in the per node throughput the achievability argument is based on a novel multihop forwarding scheme where randomization is added in every hop to ensure maximal ambiguity at the eavesdropper s second an ergodic fading model with n source destination pairs and ne eavesdroppers is considered employing the ergodic interference alignment scheme with an appropriate secrecy precoding each user is shown to achieve a constant positive secret rate for sufficiently large n remarkably the scheme does not require eavesdropper csi only the statistical knowledge is assumed and the secure throughput per node increases as we add more legitimate users to the network in this setting finally the effect of eavesdropper collusion on the performance of the proposed schemes is characterized

improper signaling for symbol error rate minimization in k user interference channel the rate maximization for the k user interference channels ics has been investigated extensively in the literature however the practical problem of minimizing the error probability with given signal modulations and or data rates of the users is less studied in this paper by utilizing additional degrees of freedom from the improper signaling versus the conventional proper signaling we seek to optimize the precoding matrices for the k user single input single output siso ics to minimize pair wise error probability pep and symbol error rate ser with two proposed algorithms respectively compared with conventional proper signaling and other state of the art improper signaling designs our proposed improper signaling schemes achieve notable error rate improvement in siso ics under both the additive white gaussian noise awgn and cellular system setups with or without channel coding our study provides another viewpoint for optimizing transmissions in ics and further justifies the practical benefit of improper signaling in interference limited communication systems

generalized degrees freedom of noncoherent mimo channels with asymmetric link strengths we study the generalized degrees of freedom gdof of block fading noncoherent multiple input multiple output mimo channels with asymmetric distributions of link strengths and a coherence time of t symbol durations we derive the optimal signaling structure for communication for the asymmetric mimo channel which is distinct from that for the mimo channel with independent and identically distributed i i d links we extend the existing results for the single input multiple output simo channel with i i d links to the asymmetric case proving that selecting the statistically best antenna is gdof optimal using the gdof result for the simo channel we prove that for t 1 the gdof is zero for mimo channels with arbitrary link strengths we show that selecting the statistically best antenna is gdof optimal for the multiple input single output miso channel we also derive the gdof for the 2 times 2 mimo channel with different exponents in the direct and cross links in this setting we show that it is always necessary to use both the antennas to achieve the gdof in contrast to the results for the 2 times 2 mimo channel with i i d links we show that having weaker crosslinks gives gdof gain compared to the case with i i d links for the noncoherent mimo channel with i i d links the traditional method of training each transmit antenna independently is degrees of freedom dof optimal whereas we observe that for the asymmetric 2 times 2 mimo channel the traditional training is not gdof optimal we extend this observation to a larger m times m mimo channel by demonstrating a strategy that can achieve larger gdof than a traditional training based method

on the generalized degrees of freedom of the gaussian interference relay channel the symmetric two user gaussian interference relay channel irc is studied from a generalized degrees of freedom gdof perspective while it is known that the relay does not in crease the dof of the irc such a characterization has not been reported for the gdof yet the focus of this paper is on all cases where the interference link is stronger than the link from the source to the relay this regime basically covers half the space of all possible parameters of the irc by using genie aided approaches new sum capacity upper bounds are derived these bounds are then compared with rates achieved with a novel transmission scheme which is based on a functional decode and forward fdf strategy it is shown that the gdof of the irc is achieved by fdf in the given regime and that a relay can indeed increase the gdof of irc finally the fdf scheme is compared with other schemes like decode and forward as well as compress and forward at low moderate and high signal to noise ratios

design of frames against buckling using a rayleigh quotient approximation a rayleigh quotient approximation is applied to the design of structures while guarding against elastic instability it approximates buckling eigenvalues by separately estimating the modal strain energy due to the linear and geometric stiffness of the structure previously used during structural optimization for the fundamental natural eigenvalue the rayleigh quotient approximation is derived for the buckling design problem for the first time the critical buckling load is found by solving the eigenvalue problem that arises by considering the geometric nonlinearity of the deforming structure rayleigh s principle is used to justify the choice of intermediate design variables for approximating terms in the rayleigh quotient a truss model illustrates the importance of the design space chosen for approximating the modal strain energy a beamtcolumn two plane frames and a space frame are used to verify the formulation special attention is paid to difficult bimodal optima

integer forcing linear receivers linear receivers are often used to reduce the implementation complexity of multiple antenna systems in a traditional linear receiver architecture the receive antennas are used to separate out the codewords sent by each transmit antenna which can then be decoded individually although easy to implement this approach can be highly suboptimal when the channel matrix is near singular this paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer valued entries rather than attempting to recover transmitted codewords directly the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix the codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords provided that the effective channel is full rank these integer combinations can then be digitally solved for the original codewords this paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter s which corresponds either to a multiuser uplink scenario or to single user v blast encoding in this setting the proposed integer forcing linear receiver significantly outperforms conventional linear architectures such as the zero forcing and linear minimum mean squared error receiver in the high signal to noise ratio regime the proposed receiver attains the optimal diversity multiplexing tradeoff for the standard multiple input multiple output mimo channel with no coding across transmit antennas it is further shown that in an extended mimo model with interference the integer forcing linear receiver achieves the optimal generalized degrees of freedom

interference alignment based sum capacity bounds for random dense gaussian interference networks we consider a dense k user gaussian interference network formed by paired transmitters and receivers placed independently at random in a fixed spatial region under natural conditions on the node position distributions and signal attenuation we prove convergence in probability of the average per user capacity c k to 1 2e log 1 2snr the achievability result follows directly from results based on an interference alignment scheme presented in recent work of nazer et al our main contribution comes through an upper bound motivated by ideas of bottleneck capacity developed in recent work of jafar by controlling the physical location of transmitter receiver pairs we can match a large proportion of these pairs to form so called e bottleneck links with consequent control of the sum capacity

structural optimization with frequency constraints this paper presents a design optimization algorithm for structural weight minimization with multiple frequency constraints an optimality criterion method based on uniform lagrangian density for resizing and a scaling procedure to locate the constraint boundary were used in optimization multiple frequency constraints of equality and inequality types were addressed the effectiveness of the algorithm was demonstrated by designing a number of truss structures with as many as 489 design variables no attempt was made to reduce the number of design variables by such procedures as linking and or invoking symmetry conditions the design examples include a 10 bar truss 200 bar truss a modified acoss ii and cofs control of flexible structures mast truss all the structures contain nonstructural mass besides their own mass the algorithm is extremely stable and in all cases the optimum designs were obtained in less than 20 iterations regardless of the size of the structure and the number of design variables

interference as noise friend or foe this paper shows that for the two user gaussian interference channel g ic treating interference as noise without time sharing tinnots achieves the closure of the capacity region to within either a constant gap or to within a gap of the order o log ln min mathsf s mathsf i gamma up to a set of lebesgue measure gamma in 0 1 where mathsf s is the largest signal to noise ratio on the direct links and mathsf i is the largest interference to noise ratio on the cross links as a consequence tinnots is optimal from a generalized degrees of freedom gdof perspective for all channel gains except for a subset of zero measure tinnots with gaussian inputs is known to be optimal within 1 2 bit for a subset of the weak interference regime rather surprisingly this paper shows that tinnots is gdof optimal in all parameter regimes even in the strong and very strong interference regimes where joint decoding of gaussian inputs is optimal for approximate optimality of tinnots in all parameter regimes it is critical to use non gaussian inputs this paper thus proposes to use mixed inputs as channel inputs for the g ic where a mixed input is the sum of a discrete and a gaussian random variable interestingly with reference to the han kobayashi achievable scheme the discrete part of a mixed input is shown to effectively behave as a common message in the sense that although treated as noise its effect on the achievable rate region is as if it were jointly decoded together with the desired messages at a non intended receiver the practical implication is that a discrete interfering input is a friend while an gaussian interfering input is in general a foe this paper also discusses other practical implications of the proposed tinnots scheme with mixed inputs since tinnots requires neither explicit joint decoding nor time sharing the results of this paper are applicable to a variety of oblivious or asynchronous channels such as the block asynchronous g ic which is not an information stable channel and the g ic with partial codebook knowledge at one or more receivers

learnability and the vapnik chervonenkis dimension valiant s learnability model is extended to learning classes of concepts defined by regions in euclidean space e n the methods in this paper lead to a unified treatment of some of valiant s results along with previous results on distribution free convergence of certain pattern recognition algorithms it is shown that the essential condition for distribution free learnability is finiteness of the vapnik chervonenkis dimension a simple combinatorial parameter of the class of concepts to be learned using this parameter the complexity and closure properties of learnable classes are analyzed and the necessary and sufficient conditions are provided for feasible learnability

the approximate capacity of the gaussian n relay diamond network we consider the gaussian diamond or parallel relay network in which a source node transmits a message to a destination node with the help of n relays even for the symmetric setting in which the channel gains to the relays are identical and the channel gains from the relays are identical the capacity of this channel is unknown in general the best known capacity approximation is up to an additive gap of order n bits and up to a multiplicative gap of order n2 with both gaps independent of the channel gains in this paper we approximate the capacity of the symmetric gaussian n relay diamond network up to an additive gap of 1 8 bits and up to a multiplicative gap of a factor 14 both gaps are independent of the channel gains and unlike the best previously known result are also independent of the number of relays n in the network achievability is based on bursty amplify and forward showing that this simple scheme is uniformly approximately optimal both in the low rate as well as in the high rate regimes the upper bound on capacity is based on a careful evaluation of the cut set bound we also present approximation results for the asymmetric gaussian n relay diamond network in particular we show that bursty amplify and forward combined with optimal relay selection achieves a rate within a factor o log4 n of capacity with preconstant in the order notation independent of the channel gains

minimum weight design of truss structures with geometric nonlinear behavior the paper presents an optimization method based on optimality criterion for minimum weight design of structures with geometric nonlinear behavior the nonlinear critical load is determined by finding the load level at which the hessian of the potential energy ceases to be positive definite a recurrence relation based on the criterion that at optimum the nonlinear strain energy density be equal in all the members is used to develop an algorithm sample problems are given to illustrate the application of the method to truss type structures with a large number of design variables number of algorithms based on the optimality criterion approach have been developed to design a minimum weight structure with specified constraints on nodal displacements element stresses system stability etc 1 2 the optimization algorithm consisted of analyzing the structure by the finite element method and using a recurrence relation derived from the appropriate optimality criterion to modify the design variables the optimality criterion was derived by differentiating the lagrangian with respect to the design variables the displacements were assumed to be small and in the finite element analysis linear equilibrium equations were solved to determine the response of the structure to the ap plied loads in the case of system stability the constraints were defined see refs 3 6 by the associated linear eigenvalue problem this definition of system stability for some structures may not be valid because of the nonlinear behavior of the structure which may be due to the geometry of the structure or the presence of geometric imperfections the correct procedure for these structures would be to analyze the structure by using nonlinear equilibrium equations this will be particularly true for large space structures lss in this paper an optimization method based on the optimality criterion approach is presented for structures with geometric nonlinear behavior in the case of a structure optimized with constraints on linear stability the optimum structure can have more than one critical buckling mode this design tends to become im perfection sensitive and a small deviation in the geometry of the structure can reduce its load carrying capacity sub stantially the imperfection sensitivity of the optimized structure can be reduced by designing the structure so that buckling loads associated with the critical buckling modes are not equal see ref 7 a real structure has geometric im perfections and these structures tend to have nonlinear

quantile regression methods for reference growth charts estimation of reference growth curves for children s height and weight has traditionally relied on normal theory to construct families of quantile curves based on samples from the reference population age specific parametric transformation has been used to significantly broaden the applicability of these normal theory methods non parametric quantile regression methods offer a complementary strategy for estimating conditional quantile functions we compare estimated reference curves for height using the penalized likelihood approach of cole and green statistics in medicine 1992 11 1305 1319 with quantile regression curves based on data used for modern finnish reference charts an advantage of the quantile regression approach is that it is relatively easy to incorporate prior growth and other covariates into the analysis of longitudinal growth data quantile specific autoregressive models for unequally spaced measurements are introduced and their application to diagnostic screening is illustrated copyright 2005 john wiley sons ltd

a new achievable rate region for the interference channel a new achievable rate region for the general interference channel which extends previous results is presented and evaluated the technique used is a generalization of superposition coding to the multivariable case a detailed computation for the gaussian channel case clarifies to what extent the new region improves previous ones the capacity of a class of gaussian interference channels is also established

outer bounds on the capacity of gaussian interference channels two outer bounds on the capacity region of the two user gaussian interference channel ifc are derived the idea of the first bound is to let a genie give each receiver just enough information to decode both messages this bound unifies and improves the best known outer bounds of sato and carleial furthermore the bound extends to discrete memoryless ifcs and is shown to be equivalent to another bound of carleial the second bound follows directly from existing results of costa and sato and possesses certain optimality properties for weak interference

computation alignment capacity approximation without noise accumulation consider several source nodes communicating across a wireless network to a destination node with the help of several layers of relay nodes recent work by avestimehr has approximated the capacity of this network up to an additive gap the communication scheme achieving this capacity approximation is based on compress and forward resulting in noise accumulation as the messages traverse the network as a consequence the approximation gap increases linearly with the network depth this paper develops a computation alignment strategy that can approach the capacity of a class of layered time varying wireless relay networks up to an approximation gap that is independent of the network depth this strategy is based on the compute and forward framework which enables relays to decode deterministic functions of the transmitted messages alone compute and forward is insufficient to approach the capacity as it incurs a penalty for approximating the wireless channel with complex valued coefficients by a channel with integer coefficients here this penalty is circumvented by carefully matching channel realizations across time slots to create integer valued effective channels that are well suited to compute and forward unlike prior constant gap results the approximation gap obtained in this paper also depends closely on the fading statistics which are assumed to be i i d rayleigh

application of nonparametric quantile regression to body mass index percentile curves from survey data increasing rates of overweight among children in the u s stimulated interest in obtaining national percentile curves of body size to serve as a benchmark in assessing growth development in clinical and population settings in 2000 the u s centers for disease control and prevention cdc developed conditional percentile curves for body mass index bmi for ages 2 20 years the 2000 cdc bmi for age curves are partially parametric and only partially incorporated the survey sample weights in the curve estimation as a result they may not fully reflect the underlying pattern of bmi for age in the population this motivated us to develop a nonparametric double kernel based method and automatic bandwidth selection procedure we include sample weights in the bandwidth selection conduct median correction to reduce small sample smoothing bias and rescale the bandwidth to make it scale invariant using this procedure we re estimate the national percentile bmi for age curves and the prevalence of high bmi children in the u s

reference curves based on non parametric quantile regression reference curves which take time into account such as those for age are often required in medicine but simple systematic and efficient statistical methods for constructing them are lacking classical methods are based on parametric fitting polynomial curves semi parametric methods are also widely used especially in europe here we propose a new methodology for the estimation of reference intervals for data sets based on non parametric estimation of conditional quantiles the derived methods should be applicable to all clinical or more generally biological variables that are measured on a continuous quantitative scale as an example we analyse a data set collected to establish reference curves for biophysical properties of the skin of healthy french women the results are compared to those obtained with royston s polynomial parametric method and the semi parametric lms approach

on the optimality of treating interference as noise it is shown that in the k user interference channel if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user all values in decibel scale then the simple scheme of using point to point gaussian codebooks with appropriate power levels at each transmitter and treating interference as noise tin at every receiver in short tin scheme achieves all points in the capacity region to within a constant gap the generalized degrees of freedom gdof region under this condition is a polyhedron which is shown to be fully achieved by the same scheme without the need for time sharing the results are proved by first deriving a polyhedral relaxation of the gdof region achieved by tin and then providing a dual characterization of this polyhedral region via the use of potential functions and finally proving the optimality of this region in the desired regime

the ergodic capacity of phase fading interference networks we identify the role of equal strength interference links as bottlenecks on the ergodic sum capacity of a k user phase fading interference network i e an interference network where the fading process is restricted primarily to independent and uniform phase variations while the channel magnitudes are held fixed across time it is shown that even though there are k k 1 cross links only about k 2 disjoint and equal strength interference links suffice to determine the capacity of the network regardless of the strengths of the rest of the cross channels this scenario is called a minimal bottleneck state it is shown that ergodic interference alignment is capacity optimal for a network in a minimal bottleneck state the results are applied to large networks it is shown that large networks are close to bottleneck states with a high probability so that ergodic interference alignment is close to optimal for large networks limitations of the notion of bottleneck states are also highlighted for channels where both the phase and the magnitudes vary with time it is shown through an example that for these channels joint coding across different bottleneck states makes it possible to circumvent the capacity bottlenecks

the gaussian multiple access diamond channel in this paper we study the capacity of the diamond channel we focus on the special case where the channel between the source node and the two relay nodes are two separate links with finite capacities and the link from the two relay nodes to the destination node is a gaussian multiple access channel we call this model the gaussian multiple access diamond channel we first propose an upper bound on the capacity this upper bound is a single letterization of an n letter upper bound proposed by traskov and kramer and is tighter than the cut set bound as for the lower bound we propose an achievability scheme based on sending correlated codes through the multiple access channel with superposition structure we then specialize this achievable rate to the gaussian multiple access diamond channel noting the similarity between the upper and lower bounds we provide sufficient and necessary conditions that a gaussian multiple access diamond channel has to satisfy such that the proposed upper and lower bounds meet thus for a gaussian multiple access diamond channel that satisfies these conditions we have found its capacity

on the han kobayashi region for theinterference channel in this correspondence we derive a simplified description of the han kobayashi rate region for the general interference channel using this result we establish that the recently discovered chong motani garg rate region is a new representation of the han kobayashi region moreover a tighter bound for the cardinality of the time sharing auxiliary random variable emerges from our simplified description

local linear quantile regression abstract in this article we study nonparametric regression quantile estimation by kernel weighted local linear fitting two such estimators are considered one is based on localizing the characterization of a regression quantile as the minimizer of e pp y a x x where p is the appropriate check function the other follows by inverting a local linear conditional distribution estimator and involves two smoothing parameters rather than one our aim is to present fully operational versions of both approaches and to show that each works quite well although either might be used in practice we have a particular preference for the second our automatic smoothing parameter selection method is novel the main regression quantile smoothing parameters are chosen by rule of thumb adaptations of state of the art methods for smoothing parameter selection for regression mean estimation the techniques are illustrated by application to two datasets and compared in simulations

the degrees of freedom of isotropic mimo interference channels without state information at the transmitters this paper fully determines the degree of freedom dof region of two user interference channels with arbitrary number of transmit and receive antennas in the case of isotropic and independent or block wise independent fading where the channel state information is available to the receivers but not to the transmitters thus the dof gap between previous upper and lower bounds due to the authors vaze and varanasi and huang jafar shamai and vishwanath is closed the dof result characterizes the capacity region to the first order of the logarithm of the signal to noise ratio snr in the high snr regime the dof region is achievable by using random gaussian codebooks independent of the channel states which implies that it is impossible to increase the dof using beamforming and interference alignment in the absence of channel state information at the transmitters

regularized transceiver designs for multi user mimo interference channels for multi user interference channels ic an altruistic approach based on the zero forcing zf criterion shows the near optimal performance at high signal to noise ratio snr whereas its performance at low snr becomes poor compared to a simple egoistic algorithm selfish beamforming thus balancing between the egoism and the altruism has been an important issue to achieve good sum rate performance at overall snr regime in this paper we propose a new approach for enhancing the performance by regularizing the zf based transceivers to this end we start with investigating efficient zf transceivers for 2 user and 3 user ics first coordinated spatial multiplexing csm is proposed for 2 user ic for the 3 user case it is shown that the enhanced interference alignment e ia introduced in our previous work is the optimal zf transceivers in terms of the sum rate performance next to improve the performance of the csm and e ia schemes at low snr we propose a non iterative regularization method under the high snr approximation the distributed implementation of the proposed regularization method is also presented where each node is able to compute its own precoding or decoding matrix using local channel state information from simulations it is observed that the proposed regularized design outperforms the conventional schemes in overall snr regime also we confirm that our distributed approach provides a substantial performance gain over the conventional distributed scheme with reduced computational complexity

optimality criterion techniques applied to frames having general cross sectional relationships an optimality criterion based method developed in this research is capable of locating the optimal design of wf steel frames with members having general cross sectional relationships among the area moment of inertia and section modulus the method uses the idea of one most critical constraint to avoid the calculation of large sets of lagrange multipliers and also avoids the scaling procedure normally used in other optimality criterion techniques several example structures designed under stress displacement and minimum area constraints demonstrate the efficiency reliability and simplicity of the method although the method of this research uses the idea of one most critical constraint the optimal designs presented in this paper have several active constraints

transmit optimization with improper gaussian signaling for interference channels this paper studies the achievable rates of gaussian interference channels with additive white gaussian noise awgn when improper or circularly asymmetric complex gaussian signaling is applied for the gaussian multiple input multiple output interference channel mimo ic with the interference treated as gaussian noise we show that the user s achievable rate can be expressed as a summation of the rate achievable by the conventional proper or circularly symmetric complex gaussian signaling in terms of the users transmit covariance matrices and an additional term which is a function of both the users transmit covariance and pseudo covariance matrices the additional degrees of freedom in the pseudo covariance matrix which is conventionally set to be zero for the case of proper gaussian signaling provide an opportunity to further improve the achievable rates of gaussian mimo ics by employing improper gaussian signaling to this end this paper proposes widely linear precoding which efficiently maps proper information bearing signals to improper transmitted signals at each transmitter for any given pair of transmit covariance and pseudo covariance matrices in particular for the case of two user gaussian single input single output interference channel siso ic we propose a joint covariance and pseudo covariance optimization algorithm with improper gaussian signaling to achieve the pareto optimal rates by utilizing the separable structure of the achievable rate expression an alternative algorithm with separate covariance and pseudo covariance optimization is also proposed which guarantees the rate improvement over conventional proper gaussian signaling

the capacity of the gaussian interference channel under strong interference corresp the capacity region of a gaussian interference channel with two separate messages is obtained for the case of moderately strong interference it is shown that the region coincides with the one where both messages are required in both receiving terminals

diversity multiplexing tradeoff for the interference channel with a relay we study the diversity multiplexing tradeoff dmt for the slow fading interference channel with a relay icr we derive four inner bounds on the dmt region the first is based on the compress and forward cf relaying scheme the second is based on the decode and forward df relaying scheme and the last two bounds are based on the half duplex hd and full duplex fd amplify and forward af schemes for the cf and df schemes we find conditions on the channel parameters and the multiplexing gains under which the corresponding inner bound achieves the optimal dmt region we also identify the cases in which the dmt region of the icr corresponds to that of two parallel slow fading relay channels implying that interference does not decrease the dmt for each pair and that a single relay can be dmt optimal for two pairs simultaneously for the hd af scheme we derive conditions on the channel coefficients under which the proposed scheme achieves the optimal dmt for the af based relay channel finally we identify the conditions under which adding a relay strictly enlarges the dmt region relative to the interference channel without a relay

optimization of geometrically nonlinear thin shells subject to displacement and stability constraints a methodology is developed for shape optimization of thin plate and shell structures undergoing large deflections subject to displacement and system stability constraints the optimization method considers shape parameters and overall thickness of the structure as the design variables and aims to minimize the total mass of the structure subject to stability or displacement constraint two optimality criteria based on karush kuhn tucker conditions are developed for mass minimization problems optimality criteria are combined with nonlinear corotational analysis to optimize structures with geometric nonlinearity the method is applied to plate and shallow shell structures the efficiency of the developed design optimization methodology is compared with that of the gradient based method of optimization sequential quadratic programming

nonlinear analysis of optimized structure with constraints on systemstability an optimization algorithm based on an optimality criterion was used to design a minimum weight space truss with different constraint requirements on system stability the constraints were specified so that the eigenvalues associated with all the critical buckling modes are either equal or separated by a specified factor for the second case the critical buckling mode was preselected from all the possible critical modes the designs obtained for the various constraint conditions were analyzed with and without specified geometric imperfections using a nonlinear finite element program which accounts for geometric nonlinearity the results obtained for various designs were compared for their imperfection sensitivity

outage analysis of block fading gaussian interference channels this paper considers the asymptotic behavior of the outage probability of a two source block fading single antenna gaussian interference channel in the high snr regime by means of the diversity multiplexing tradeoff a general setting where the user rates and the average channel gains are not restricted to be symmetric is investigated this asymmetric scenario allows to analyze networks with mixed interference i e when different sources are at different distance from their intended destination that are not possible under the commonly used symmetric assumption inner and outer bounds for the diversity are derived the outer bound is based on the recent to within one bit capacity result of etkin for the unfaded gaussian channel and is a re derivation of a known bound for which an error is pointed out the inner bound is based on the han and kobayashi achievable region both without rate splitting and with a rate spitting inspired by the to within one bit capacity result an analytical comparison of the diversity upper and lower bounds for a general channel seems difficult by numerical evaluations the two bounds are shown to coincide for a fairly large set of channel parameters

partial interference alignment for k user mimo interference channels in this paper we consider a partial interference alignment and interference detection piaid design for k user quasi static mimo interference channels with discrete constellation inputs each transmitter has m antennas and transmits l independent data streams to the desired receiver with n receive antennas we focus on the case where not all k 1 interfering transmitters can be aligned at every receiver as a result there will be residual interference at each receiver that cannot be aligned each receiver detects and cancels the residual interference based on the constellation map however there is a window of unfavorable interference profile at the receiver for interference detection id in this paper we propose a low complexity partial interference alignment scheme in which we dynamically select the user set for ia so as to create a favorable interference profile for id at each receiver we first derive the average symbol error rate ser by taking into account of the non guassian residual interference due to discrete constellation using graph theory we then devise a low complexity user set selection algorithm for the piaid scheme which minimizes the asymptotically tight bound for the average end to end ser performance moreover we substantially simplify interference detection at the receiver using semi definite relaxation sdr techniques it is shown that the ser performance of the proposed piaid scheme has significant gain compared with various conventional baseline solutions

a two part model for reference curve estimation subject to a limit of detection reference curves are commonly used to identify individuals with extreme values of clinically relevant variables or stages of progression which depend naturally on age or maturation estimation of reference curves can be complicated by a technical limit of detection lod that censors the measurement from the left as is the case in our study of reproductive hormone levels in boys around the time of the onset of puberty we discuss issues with common approaches to the lod problem in the context of our pubertal hormone study and propose a two part model that addresses those issues one part of the proposed model specifies the probability of a measurement exceeding the lod as a function of age the other part of the model specifies the conditional distribution of a measurement given that it exceeds the lod again as a function of age information from the two parts can be combined to estimate the identifiable portion i e above the lod of a reference curve and to calculate the relative standing of a given measurement above the lod unlike some common approaches to lod problems the two part model is free of untestable assumptions involving unobservable quantities flexible for modeling the observable data and easy to implement with existing software the method is illustrated with hormone data from the third national health and nutrition examination survey

a study of optimal membrane triangles with drilling freedoms abstract this article compares derivation methods for constructing optimal membrane triangles with corner drilling freedoms the term optimal is used in the sense of exact inplane pure bending response of rectangular mesh units of arbitrary aspect ratio following a comparative summary of element formulation approaches the construction of an optimal three node triangle using the andes formulation is presented the construction is based upon techniques developed by 1991 in student term projects but taking advantage of the more general framework of templates developed since the optimal element that fits the andes template is shown to be unique if energy orthogonality constraints are enforced two other formulations are examined and compared with the optimal model retrofitting the conventional linear strain triangle element by midpoint migrating and congruential transformations is shown unable to produce an optimal element while rank deficiency is inevitable use of the quadratic strain field of the 1988 allman triangle or linear filtered versions thereof is also unable to reproduce the optimal element moreover these elements exhibit serious aspect ratio lock these predictions are verified on benchmark examples

precoded integer forcing universally achieves the mimo capacity to within a constant gap an open loop single user multiple input multiple output mimo communication scheme is considered where a transmitter equipped with multiple antennas encodes the data into independent streams all taken from the same linear code the coded streams are then linearly precoded using the encoding matrix of a perfect linear dispersion space time code at the receiver side integer forcing equalization is applied followed by standard single stream decoding it is shown that this communication architecture achieves the capacity of any gaussian mimo channel up to a gap that depends only on the number of transmit antennas

shape optimal design using fictitious loads implementation aspects of the natural velocity field approach for shape optimal design are discussed the problem of concern is to find the optimum shape of an elastic body that requires minimizing an objective function subject to stress displacement frequency and manufacturing constraints in this paper fictitious loads are applied at certain control nodes on an auxiliary structure and the deformation produced by these loads is used to update the shape the use of beam stiffeners in the auxiliary structure leads to smoother shapes furthermore softer material properties in the auxiliary structure result in faster convergence when iterating through the feasibile region the method is applied in conjunction with both discrete and continuum methods of design sensitivity analysis

capacity of 3d erasure networks in this paper we introduce a large scale 3d erasure network where n wireless nodes are randomly distributed in a cuboid of n lambda times n mu times n nu with lambda mu nu 1 for lambda mu nu 0 and completely characterize its capacity scaling laws two fundamental path loss attenuation models i e exponential and polynomial power law models are used to suitably model an erasure probability for packet transmission then under the two erasure models we introduce a routing protocol using percolation highway in 3d space and then analyze its achievable throughput scaling laws it is shown that under the two erasure models the aggregate throughput scaling n mathop mathrm min limits 1 lambda 1 mu 1 nu can be achieved in the 3d erasure network this implies that the aggregate throughput scaling n 2 3 can be achieved in 3d cubic erasure networks while sqrt n can be achieved in 2d square erasure networks the gain comes from the fact that compared with 2d space more geographic diversity can be exploited via 3d space which means that generating more simultaneous percolation highways is possible in addition cut set upper bounds on the capacity scaling are derived to verify that the achievable scheme based on the 3d percolation highway is order optimal within a polylogarithmic factor under certain practical operating regimes on the decay parameters

gaussian half duplex relay networks improved constant gap and connections with the assignment problem this paper considers a gaussian relay network where a source transmits a message to a destination with the help of n half duplex relays the information theoretic cut set upper bound to the capacity is shown to be achieved to within 1 96 n 2 bits by noisy network coding thereby reducing the previously known gap this gap is obtained as a special case of a more general constant gap result for gaussian half duplex multicast networks it is then shown that the generalized degrees of freedom of this network is the solution of a linear program where the coefficients of the linear inequality constraints are proved to be the solution of several linear programs referred as the assignment problem in graph theory for which efficient numerical algorithms exist the optimal schedule that is the optimal value of the 2 n possible transmit receive configuration states for the relays is investigated and known results for diamond networks are extended to general relay networks it is shown for the case of n 2 relays that only n 1 3 out of the 2 n 4 possible states have a strictly positive probability and suffice to characterize the capacity to within a constant gap extensive experimental results show that for a general n relay network with n leq 8 the optimal schedule has at most n 1 states with a strictly positive probability as an extension of a conjecture presented for diamond networks it is conjectured that this result holds for any half duplex relay network and any number of relays finally a network with n 2 relays is studied in detail to illustrate the channel conditions under which selecting the best relay is not optimal and to highlight the nature of the rate gain due to multiple relays

an effective bandwidth selector for local least squares regression abstract local least squares kernel regression provides an appealing solution to the nonparametric regression or scatterplot smoothing problem as demonstrated by fan for example the practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter in this article we apply the ideas of plug in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators our results are applicable to odd degree local polynomial fits and can be extended to other settings such as derivative estimation and multiple nonparametric regression an implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice a by product of our work is the development of a class of nonparametric variance estimators based on local least squares ideas and plug in rules for their implementation