a superconvergent point interpolation method sc pim with piecewise linear strain field using triangular mesh a superconvergent point interpolation method sc pim is developed for mechanics problems by combining techniques of finite element method fem and linearly conforming point interpolation method lc pim using triangular mesh in the sc pim point interpolation methods pim are used for shape functions construction and a strain field with a parameter is assumed to be a linear combination of compatible stains and smoothed strains from lc pim we prove theoretically that sc pim has a very nice bound property the strain energy obtained from the sc pim solution lies in between those from the compatible fem solution and the lc pim solution when the same mesh is used we further provide a criterion for sc pim to obtain upper and lower bound solutions intensive numerical studies are conducted to verify these theoretical results and show that 1 the upper and lower bound solutions can always be obtained using the present sc pim 2 there exists an exact 0 1 at which the sc pim can produce the exact solution in the energy norm 3 for any 0 1 the sc pim solution is of superconvergence and 0 is an easy way to obtain a very accurate and superconvergent solution in both energy and displacement norms 4 a procedure is devised to find a prefer 0 1 that produces a solution very close to the exact solution copyright 2008 john wiley sons ltd

expanded gdof optimality regime of treating interference as noise in the m times 2 x channel treating interference as noise tin as the most appropriate approach in dealing with interference and the conditions on its optimality has attracted the interest of researchers recently however our knowledge on necessary and sufficient conditions of tin is restricted to a few setups with limited number of users in this paper we study the optimality of tin in terms of the generalized degrees of freedom gdof for a fundamental network namely the m times 2 x channel to this end the achievable gdof of tin with power allocations at the transmitters is studied it turns out that the transmit power allocation maximizing the achievable gdof is given by on off signaling as long as the receivers use tin this leads to two variants of tin namely p2p tin and 2 ic tin while in the first variant the m times 2 x channel is reduced to a point to point p2p channel in the second variant the setup is reduced to a two user interference channel in which the receivers use tin the optimality of these two variants is studied separately to this end novel genie aided upper bounds on the capacity of the x channel are established the conditions on the optimality of p2p tin can be summarized as follows p2p tin is gdof optimal if there exists a dominant multiple access channel or a dominant broadcast channel embedded in the x channel furthermore the necessary and sufficient conditions on the gdof optimality of 2 ic tin are presented interestingly it turns out that operating the m times 2 x channel in the 2 ic tin mode might be still gdof optimal although the conditions given by geng et al are violated however 2 ic tin is sub optimal if there exists a single interferer which causes sufficiently strong interference at both receivers the comparison of the results with the state of the art shows that the gdof optimality of tin is expanded significantldy

a compute and forward scheme for gaussian bi directional relaying with inter symbol interference we provide inner and outer bounds on the capacity region for the gaussian bi directional relaying over inter symbol interference channels the outer bound is obtained by the conventional cut set argument for the inner bound we propose a compute and forward coding scheme based on lattice partition chains and study its achievable rate the coding scheme is a time domain coding scheme which uses a novel precoding scheme at the transmitter in combination with lattice precoding and a minimum mean squared error receiver to recover linear combinations of lattice codewords the proposed compute and forward coding scheme substantially outperforms decode and forward schemes while it is well known that for the point to point communication case both independent coding along sub channels and time domain coding can approach the capacity limit as a byproduct of the proposed scheme we show that for the bi directional relay case independent coding along sub channels is not optimal in general and joint coding across sub channels can improve the capacity for some channel realizations

lattice codes for the gaussian relay channel decode and forward and compress and forward lattice codes are known to achieve capacity in the gaussian point to point channel achieving the same rates as i i d random gaussian codebooks lattice codes are also known to outperform random codes for certain channel models that are able to exploit their linearity in this paper we show that lattice codes may be used to achieve the same performance as known i i d gaussian random coding techniques for the gaussian relay channel and show several examples of how this may be combined with the linearity of lattices codes in multisource relay networks in particular we present a nested lattice list decoding technique in which lattice codes are shown to achieve the decode and forward df rate of single source single destination gaussian relay channels with one or more relays we next present two examples of how this df scheme may be combined with the linearity of lattice codes to achieve new rate regions which for some channel conditions outperform analogous known gaussian random coding techniques in multisource relay channels that is we derive a new achievable rate region for the two way relay channel with direct links and compare it to existing schemes and derive a new achievable rate region for the multiple access relay channel we furthermore present a lattice compress and forward cf scheme for the gaussian relay channel which exploits a lattice wyner ziv binning scheme and achieves the same rate as the cover el gamal cf rate evaluated for gaussian random codes these results suggest that structured lattice codes may be used to mimic and sometimes outperform random gaussian codes in general gaussian networks

non matching mesh gluing by meshless interpolation an alternative to lagrange multipliers rewards of using non matching meshes are great in many aspects sub meshing a complex structure in a sub structure wise manner separately and or in parallel selective local refinement unlimited scalability guarantee for generating meshes in increasingly large scale finite element simulation etc however when meshes do not match a gluing algorithm is required to enforce inter domain continuity non matching terminologically originates from mesh discretization in nature and the non matching mesh issue is therefore avoidable or does not exist in a node based or meshless discretization in meshless methods motivated by this a gluing algorithm is developed based on meshless interpolation the gluing is accomplished by continuous trial and test functions across non matching meshes constructed using nodes only the developed gluing algorithm is tested in static and wave propagation problems in two and three dimensions it is demonstrated that the gluing algorithm does not deteriorate convergence and accuracy compared with the one piece conforming mesh compared with lagrange multiplier gluing one of the most common approaches the current algorithm has two significant benefits 1 easier implementation in any dimension and 2 positive definite banded system matrices not acting against equation solvers and hence better suited for large scale finite element analysis

coding for parallel gaussian bidirectional relay channels a deterministic approach we study the capacity region of the parallel gaussian bidirectional relay channel with l independent sub channels and propose efficient coding schemes for approaching the capacity limit within a constant gap a two step approach is considered first the corresponding finite field linear deterministic model is studied for which linear network coding across sub channels is shown to achieve the capacity region of the channel next based on the insight obtained a lattice based compute and forward scheme together with simple linear network coding across sub channels is proposed and is shown to achieve the capacity region of the gaussian model to within l bits per user regardless of the channel parameters even though coding across different sub channels is necessary for approaching the capacity region it is shown that this can be realized through a simple linear network coding scheme across different sub channels at the relay

variational multiscale element free galerkin vmefg and local discontinuous galerkin ldg methods for solving two dimensional brusselator reaction diffusion system with and without cross diffusion abstract the finite element method fem is one of the basic methods for solving deterministic and stochastic partial differential equations this method is proposed in the 19 decade and after years several modifications for this well known technique such as mortal fem discontinuous galerkin fem extended fem least squares fem spectral fem mixed fem immersed fem adaptive fem etc have been proposed also for improving the accuracy and for considering complex domain shape functions of the moving least squares approximation have been replaced with the traditional shape function of the finite element technique the name of this improved method is element free galerkin efg method which is classified in the category of meshless methods the efg method has been applied for solving many problems in engineering in the current paper we select two numerical procedures that are extracted from fem the discontinuous galerkin approach is a useful technique for solving problems that their exact solutions have discontinuity it should be noted that many enriched ideas have been explained for improving accuracy of efg method in the current paper the local discontinuous galerkin and variational multiscale efg methods are applied for obtaining numerical solution of two dimensional brusselator system with and without cross diffusion the brusselator system is a theoretical model for a type of autocatalytic reaction up to best of authors knowledge the accuracy of the obtained numerical solutions using local discontinuous galerkin method is very related to the used time discrete scheme therefore fourth order exponential time differencing method has been employed for discretizing the time variable also to achieve a full discretization scheme the local discontinuous galerkin finite element method is used moreover several test problems are given that show the acceptable accuracy and efficiency of the proposed schemes

nested lattice codes for gaussian relay networks with interference in this paper we consider a class of single source multicast relay networks we assume that all outgoing channels of a node in the network to its neighbors are orthogonal while the incoming signals from its neighbors can interfere with each other we first focus on gaussian relay networks with interference and find an achievable rate using a lattice coding scheme we show that the achievable rate of our scheme is within a constant bit gap from the information theoretic cut set bound where the constant depends only on the network topology but not on the transmit power noise variance and channel gains this is similar to a recent result by avestimehr diggavi and tse who showed an approximate capacity characterization for general gaussian relay networks however our achievability uses a structured code instead of a random one using the idea used in the gaussian case we also consider a linear finite field symmetric network with interference and characterize its capacity using a linear coding scheme

a moving kriging interpolation based element free galerkin method for structural dynamic analysis in this paper a meshfree method based on the moving kriging interpolation is further developed for free and forced vibration analyses of two dimensional solids the shape function and its derivatives are essentially established through the moving kriging interpolation technique following this technique by possessing the kronecker delta property the method evidently makes it in a simple form and efficient in imposing the essential boundary conditions the governing elastodynamic equations are transformed into a standard weak formulation it is then discretized into a meshfree system of time dependent equations which are solved by the standard implicit newmark time integration scheme numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in details as a consequence it is found that the method is very efficient and accurate for dynamic analysis compared with those of other conventional methods

a meshless numerical procedure for solving fractional reaction subdiffusion model via a new combination of alternating direction implicit adi approach and interpolating element free galerkin efg method a new numerical algorithm has been investigated for solving time fractional reaction subdiffusion equation the fractional derivative of the considered equation is described in the riemann liouville sense firstly we discrete the temporal dimension of the considered model using a finite difference scheme a central difference scheme has been applied to discrete the first time derivative and then for discretizing the fractional integral term a difference scheme has been employed with convergence order o 1 moreover to achieve a full discretization scheme a type of meshless method has been improved that is known as element free galerkin efg method the efg method for integration uses a background mesh this method is based on the galerkin weak form in which the test and trial functions are shape functions of moving least squares mls approximation since the shape functions of traditional mls lack the kronecker property essential boundary conditions of a boundary value problem can not be directly computed and other methods must be employed for this issue to this end a new class of mls shape functions has been applied that is called shape functions of interpolating mls the new shape function has the mentioned property in the efg method calculating the appeared two dimensional integrals is a basic issue in this research work the alternating direction implicit approach is combined with the element free galerkin method then using the new proposed method the two dimensional integrals on rectangular domain will be changed to simple one dimensional integrals we prove that the new numerical algorithm is unconditionally stable and also we obtain an error bound for the new procedure using the energy method numerical examples are reported which demonstrate the theoretical results and the efficiency of proposed scheme

lattice codes for many to one interference channels with and without cognitive messages a new achievable rate region is given for the gaussian cognitive many to one interference channel the proposed novel coding scheme is based on the compute and forward approach with lattice codes using the idea of decoding sums of codewords our scheme improves considerably upon the conventional coding schemes which treat interference as noise or decode messages simultaneously our strategy also extends directly to the usual many to one interference channels without cognitive messages comparing to the usual compute and forward scheme where a fixed lattice is used for the code construction the novel scheme employs scaled lattices and also encompasses key ingredients of the existing schemes for the cognitive interference channel with this new component our scheme achieves a larger rate region in general for some symmetric channel settings new constant gap or capacity results are established which are independent of the number of users in the system

on the capacity region of asymmetric gaussian two way line channel lattice codes are known to outperform random codes for certain networks especially in the gaussian two way relay channels gtwrcs where lattice codes are able to exploit their linearity as an extension of the gtwrc in this paper we consider the asymmetric gaussian two way line network where two nodes exchange their messages through multiple relays we first investigate the capacity region of the full duplex two way two relay line network the results can be extended to an arbitrary number of relays and to half duplex scenarios this channel consists of four nodes 1 leftrightarrow 2 leftrightarrow 3 leftrightarrow 4 where nodes 1 and 4 with the help of two full duplex relays i e nodes 2 and 3 exchange their messages with each other using lattice codes we design a novel scheme that allows the relay nodes to send the data in both directions simultaneously under an asymmetric rate region in the proposed scheme each relay decodes the sum of lattice points and then re encodes it into another lattice codeword which satisfies the transmit power constraint at the relay it is shown that the proposed scheme achieves the capacity region of asymmetric two way line network within 0 5 bit independent of the number of relays

joint physical layer coding and network coding for bidirectional relaying we consider a communication system where two transmitters wish to exchange information through a central relay the transmitter and relay nodes exchange data over synchronized average power constrained additive white gaussian noise channels with a real input with signal to noise ratio snr of snr an upper bound on the capacity is 1 2 log 1 snr bits per transmitter per use of the multiple access phase and broadcast phase of the bidirectional relay channel we show that using lattice codes and lattice decoding we can obtain a rate of 1 2 log 1 2 snr bits per transmitter which is essentially optimal at high snr the main idea is to decode the sum of the codewords modulo a lattice at the relay followed by a broadcast phase which performs slepian wolf coding we also show that if the two transmitters use identical lattices with minimum angle decoding we can achieve the same rate of 1 2 log 1 2 snr the proposed scheme can be thought of as a joint physical layer network layer code which outperforms other recently proposed analog network coding schemes

lattices which are good for almost everything we define an ensemble of lattices and show that for asymptotically high dimension most of its members are simultaneously good as sphere packings sphere coverings additive white gaussian noise awgn channel codes and mean squared error mse quantization codes these lattices are generated by applying construction a to a random linear code over a prime field of growing size i e by lifting the code to spl ropf sup n

corrected proof of de buda s theorem lattice channel codes an error in de buda s see ieee j select areas commun vol 7 no 6 p 893 1989 proof on the asymptotic optimality of lattice channel codes is pointed out and corrected using a modification of de buda s approach comments are given on the correct interpretation and the limitations of this result

nested linear lattice codes for structured multiterminal binning network information theory promises high gains over simple point to point communication techniques at the cost of higher complexity however lack of structured coding schemes limited the practical application of these concepts so far one of the basic elements of a network code is the binning scheme wyner 1974 1978 and other researchers proposed various forms of coset codes for efficient binning yet these schemes were applicable only for lossless source or noiseless channel network coding to extend the algebraic binning approach to lossy source or noisy channel network coding previous work proposed the idea of nested codes or more specifically nested parity check codes for the binary case and nested lattices in the continuous case these ideas connect network information theory with the rich areas of linear codes and lattice codes and have strong potential for practical applications we review these developments and explore their tight relation to concepts such as combined shaping and precoding coding for memories with defects and digital watermarking we also propose a few novel applications adhering to a unified approach

enforcement of essential boundary conditions in meshless approximations using finite elements abstract a technique for easily treating essential boundary conditions for approximations which are not interpolants such as moving least square approximations in the element free galerkin method is presented the technique employs a string of elements along the essential boundaries and combines the finite element shape functions with the approximation in the resulting approximation essential boundary conditions can be treated exactly as in finite elements it is shown that the resulting approximation can exactly reproduce linear polynomials so that it satisfies the patch test numerical studies show that the method retains the high rate of convergence associated with moving least square approximations

numerical solution of transient heat conduction problems using improved meshless local petrov galerkin method an improved meshless local petrov galerkin mlpg method is presented and applied to calculate the two dimensional unsteady state heat conduction problems in this method the moving kriging interpolation is employed instead of the traditional mls approximation to construct the mlpg shape functions which possess kronecker delta function property and thus make it easy to implement essential boundary conditions and then the heaviside step function is used as the test function over a local sub domain since no mesh is needed either for integration of the local weak form or for construction of the shape functions the presently developed mlpg method is a truly meshless method several examples are performed to illustrate the accuracy and efficiency of the present method a good agreement can be found among the proposed analytical and finite element methods

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

multiple input multiple output two way relaying a space division approach we propose a novel space division based network coding scheme for multiple input multiple output mimo two way relay channels twrcs in which two multiantenna users exchange information via a multiantenna relay in the proposed scheme the overall signal space at the relay is divided into two subspaces in one subspace the spatial streams of the two users have nearly orthogonal directions and are completely decoded at the relay in the other subspace the signal directions of the two users are nearly parallel and linear functions of the spatial streams are computed at the relay following the principle of physical layer network coding based on the recovered messages and message functions the relay generates and forwards network coded messages to the two users we show that at high signal to noise ratio the proposed scheme achieves the asymptotic sum rate capacity of the mimo twrc within 1 2 log 5 4 0 161 bits per user antenna for any antenna configuration and any channel realization we perform large system analysis to derive the average sum rate of the proposed scheme over rayleigh fading mimo twrcs we show that the average asymptotic sum rate gap to the capacity is at most 0 053 bits per relay antenna it is demonstrated that the proposed scheme significantly outperforms the existing schemes

novel adaptive meshfree integration techniques in meshless methods summary we propose two strategies of novel adaptive numerical integration based on mapping techniques for solving the complicated problems of domain integration encountered in meshfree methods several mapping methods are presented in detail that map a complex integration domain to much simpler ones for example squares triangles or circles the techniques described in the paper can be applied to both global and local weak forms and the highly nonlinear meshfree integrands are evaluated with controlled accuracy the necessity of the clumsy procedure of background mesh or cell structures used for integration purpose in existing meshfree methods is avoided and many meshfree methods that require the domain integration can now become truly meshfree various numerical examples in two dimensions are considered to demonstrate the applicability and the effectiveness of the proposed methods and it shows that the accuracy is improved significantly their obtained results are compared with analytical solutions and other approaches and very good agreements are found additionally some three dimensional cases applied by the present methods are also examined copyright 2012 john wiley sons ltd

the degrees of freedom of compute and forward we analyze the asymptotic behavior of compute and forward relay networks in the regime of high signal to noise ratios we consider a section of such a network consisting of k transmitters and k relays the aim of the relays is to reliably decode an invertible function of the messages sent by the transmitters an upper bound on the capacity of this system can be obtained by allowing full cooperation among the transmitters and among the relays transforming the network into a k k multiple input multiple output mimo channel the number of degrees of freedom of compute and forward is hence at most k in this paper we analyze the degrees of freedom achieved by the lattice coding implementation of compute and forward proposed recently by nazer and gastpar we show that this lattice implementation achieves at most 2 1 1 k 2 degrees of freedom thus exhibiting a very different asymptotic behavior than the mimo upper bound this raises the question if this gap of the lattice implementation to the mimo upper bound is inherent to compute and forward in general we answer this question in the negative by proposing a novel compute and forward implementation achieving k degrees of freedom

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

a meshless local moving kriging method for two dimensional solids abstract an improved meshless local petrov galerkin method mlpg for stress analysis of two dimensional solids is presented in this paper the mlpg method based on the moving least squares approximation is one of the recent meshless approaches however accurate imposition of essential boundary conditions in the mlpg method often presents difficulties because the mlpg shape functions does not possess the kronecker delta property in order to eliminate this shortcoming this approach uses the moving kriging interpolation instead of the traditional moving least square approximation to construct the mlpg shape functions and then the heaviside step function is used as the test function over a local sub domain in this method the essential boundary conditions can be enforced as the fem no domain integration is needed and only regular boundary integration is involved in addition the sensitivity of several important parameters of the present method is mainly studied and discussed comparing with the original meshless local petrov galerkin method the present method has simpler numerical procedures and lower computation cost the effectiveness of the present method for two dimensional solids problem is investigated by numerical examples in this paper

the dirty mimo multiple access channel in the scalar dirty multiple access channel in addition to gaussian noise two additive interference signals are present each known non causally to a single transmitter it was shown by philosof et al that for strong interferences an independent identically distributed ensemble of codes does not achieve the capacity region rather a structured codes approach was presented that was shown to be optimal in the limit of high signal to noise ratios where the sum capacity is dictated by the minimal bottleneck channel gain in this paper we consider the multiple input multiple output mimo variant of this setting in order to incorporate structured codes in this case one can utilize matrix decompositions that transform the channel into effective parallel scalar dirty multiple access channels this approach however suffers from a bottleneck effect for each effective scalar channel and therefore the achievable rates strongly depend on the chosen decomposition it is shown that a recently proposed decomposition where the diagonals of the effective channel matrices are equal up to a scaling factor is optimal at high signal to noise ratios under an equal rank assumption this approach is then extended to any number of transmitters finally an application to physical layer network coding for the mimo two way relay channel is presented

proper orthogonal decomposition variational multiscale element free galerkin pod vmefg meshless method for solving incompressible navier stokes equation abstract recently because of simplicity of meshless methods they have been employed for solving many partial differential equations one of the meshless methods is element free galerkin technique the element free galerkin is very similar to the finite element method with this difference that the test and trial spaces of efg procedure are shape functions of moving least squares approximation using the mentioned shape functions solving a problem on a complex domain is very simple some researchers proposed several modifications and enriched approaches for improving the element free galerkin method that one of them is variational multiscale element free galerkin procedure up to the best of authors knowledge the element free galerkin method based on the shape functions of moving least squares approximation needs more cpu time than the element free galerkin method based on the shape functions of moving kriging interpolation thus in the current paper we employ the variational multiscale element free galerkin based on the shape functions of moving kriging interpolation also for reducing the cpu time of the presented numerical scheme we use the proper orthogonal decomposition pod approach therefore in the current paper we propose the proper orthogonal decomposition variational multiscale element free galerkin pod vmefg method for solving time dependent incompressible navier stokes equation moreover several test problems are given that show the acceptable accuracy and efficiency of the proposed scheme

pairwise check decoding for ldpc coded two way relay block fading channels partial decoding has the potential to achieve a larger capacity region than full decoding in two way relay twr channels existing partial decoding realizations are however designed for gaussian channels and with a static physical layer network coding plnc in this paper we propose a new solution for joint network coding and channel decoding at the relay called pairwise check decoding pcd for low density parity check ldpc coded twr system over block fading channels the main idea is to form a check relationship table check relation tab for the superimposed ldpc coded packet pair in the multiple access ma phase in conjunction with an adaptive plnc mapping in the broadcast bc phase using pcd we then present a partial decoding method two stage closest neighbor clustering with pcd ts cnc pcd with the aim of minimizing the worst pairwise error probability moreover we propose the minimum correlation optimization mco for selecting the better check relation tabs simulation results confirm that the proposed ts cnc pcd offers a sizable gain over the conventional xor with belief propagation bp in fading channels

deterministic coding capacity of networks in the low power regime the deterministic coding capacity of a network is the capacity of a network when nodes are restricted to transmitting reliable information that is asymptotically deterministic functions of the source messages this is a generalization of network coding to wireless networks the main contribution of this paper is to develop new outer bounds on the deterministic coding capacity in the low power regime mathrm snr to 0 this is accomplished by developing a technique for finding the limits of single letter bounds for mathrm snr to 0 even when these cannot be evaluated for finite snr it is shown that these outer bounds are tight in a number of cases including the butterfly network of ahlswede et al in a wireless setting

numerical study of three dimensional turing patterns using a meshless method based on moving kriging element free galerkin efg approach in this paper a numerical procedure is presented for solving a class of three dimensional turing system first we discrete the spatial direction using element free galerkin efg method based on the shape functions of moving kriging interpolation then to achieve a high order accuracy we use the fourth order exponential time differencing runge kutta etdrk4 method using this discretization for the temporal dimension we obtain an explicit scheme and do not need to solve nonlinear system of equations the efg method uses a weak form of the considered equation that is similar to the finite element method with the difference that in the efg method test and trial functions are moving least squares approximation mls shape functions since the shape functions of moving least squares mls approximation do not have kronecker delta property we cannot implement the essential boundary condition directly also building shape functions of mls approximation is a time consuming procedure because of the mentioned reasons we employ the shape functions of moving kriging interpolation technique which have the mentioned property and less cpu time is required for building them for testing this method on three dimensional pdes we select some equations and system of pdes such as allen cahn gray scott ginzburg landau brusselator models predator prey model with additional food supply to predator several test problems are solved and numerical simulations are reported which confirm the efficiency of the proposed scheme

development of a novel meshless local kriging lokriging method for structural dynamic analysis this paper presents a novel meshless approach to study the dynamic responses of structures it is called local kriging lokriging method where the kriging interpolation is employed to construct the field approximation function and meshless shape functions and the local weak form of partial differential governing equations is derived by the weighted residual technique since the shape functions constructed by this interpolation possess the delta function property even for a set of randomly distributed points the essential boundary condition can be easily imposed in implementation of local weak form the spline function with high continuity is used as the weight function no mesh is required either for integration of the local weak form or for construction of the shape functions thus the present lokriging method is a truly meshless method several numerical examinations for the free forced vibrational analysis of structures and the dynamic performance of microelectromechanical systems mems device are carried out to demonstrate the accuracy and efficiency of the lokriging method the numerical results show that the presently developed method is quite easy to implement very accurate and highly efficient for the problems considered

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

on the robustness of lattice interference alignment a static constant channel gains real k user interference channel is considered where all interference cross channel gains are integers for such channels previous results demonstrate that the number of degrees of freedom is very sensitive to slight variations in the direct channel gains in this paper we derive an achievable rate region for such channels that is valid for finite snr at moderate values of snr the derived rate region is robust to slight variations in the direct channel gains at asymptotic high snr conditions known results on the degrees of freedom are recovered the new rate region is based on lattice interference alignment the result is established via a new coding theorem for the two user gaussian multiple access channel where both users use a single linear code

a moving kriging interpolation based meshless method for numerical simulation of kirchhoff plate problems this paper mainly proposes an alternative way for numerical implementation of thin plates bending based on a new improvement of meshless method which is combined between the standard element free galerkin method and one different shape functions building technique the moving kriging mk interpolation is applied instead of the traditional moving least square approximation in order to overcome kronecker s delta property where the standard method does not satisfy obviously the deflection of the thin plates is approximated via the mk interpolation to illustrate this approach numerical analysis is examined in both regular and irregular systems three examples with different geometric shapes of thin plates undergoing a simply supported boundary are performed in addition two important parameters of the present method are also analyzed a good agreement can be found among the proposed analytical and finite element methods copyright 2008 john wiley sons ltd

approximate sum capacity of the y channel a network where three users want to establish multiple unicasts between each other via a relay is considered this network is called the y channel and resembles an elemental ingredient of future wireless networks the sum capacity of this network is studied a characterization of the sum capacity within an additive gap of 2 bits and a multiplicative gap of 4 for all values of channel gains and transmit powers is obtained contrary to similar setups where the cut set bounds can be achieved within a constant gap they cannot be achieved in our case where they are dominated by our new genie aided bounds furthermore it is shown that a time sharing strategy in which at each time two users exchange information using coding strategies of the bidirectional relay channel achieves the upper bounds to within a constant gap this result is further extended to the k user case where it is shown that the same scheme achieves the sum capacity within 2log k 1 bits

the use of proper orthogonal decomposition pod meshless rbf fd technique to simulate the shallow water equations abstract the main aim of this paper is to develop a fast and efficient local meshless method for solving shallow water equations in one and two dimensional cases the mentioned equation has been classified in category of advection equations the solutions of advection equations have some shock thus especial numerical methods should be employed for example discontinuous galerkin and finite volume methods here based on the proper orthogonal decomposition approach we want to construct a fast meshless method to this end we consider shallow water models and obtain a suitable time discrete scheme based on the predictor corrector technique then by applying the proper orthogonal decomposition technique a new set of basis functions can be built for the solution space in which the size of new solution space is less than the original problem thus by employing the new bases the cpu time will be reduced some examples have been studied to show the efficiency of the present numerical technique

compute and forward harnessing interference through structured codes interference is usually viewed as an obstacle to communication in wireless networks this paper proposes a new strategy compute and forward that exploits interference to obtain significantly higher rates between users in a network the key idea is that relays should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise after decoding these linear equations the relays simply send them towards the destinations which given enough equations can recover their desired messages the underlying codes are based on nested lattices whose algebraic structure ensures that integer combinations of codewords can be decoded reliably encoders map messages from a finite field to a lattice and decoders recover equations of lattice points which are then mapped back to equations over the finite field this scheme is applicable even if the transmitters lack channel state information

bayesian analysis of nonlinear structural equation models with nonignorable missing data a bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data the nonignorable missingness mechanism is specified by a logistic regression model a hybrid algorithm that combines the gibbs sampler and the metropolis hastings algorithm is used to produce the joint bayesian estimates of structural parameters latent variables parameters in the nonignorable missing model as well as their standard errors estimates a goodness of fit statistic for assessing the plausibility of the posited nonlinear structural equation model is introduced and a procedure for computing the bayes factor for model comparison is developed via path sampling results obtained with respect to different missing data models and different prior inputs are compared via simulation studies in particular it is shown that in the presence of nonignorable missing data results obtained by the proposed method with a nonignorable missing data model are significantly better than those that are obtained under the missing at random assumption a real example is presented to illustrate the newly developed bayesian methodologies

joint unitary triangularization for mimo networks this paper considers communication networks where individual links can be described as those based on multiple input multiple output channels unlike orthogonal modulation methods such as the singular value decomposition we allow interference between subchannels which can be removed by the receivers via successive cancellation the degrees of freedom earned by this relaxation are used for obtaining a basis and corresponding decomposition which are simultaneously good for more than one link specifically we derive necessary and sufficient conditions for shaping the ratio vector of subchannel gains of two broadcast channel receivers we then apply this decomposition to two scenarios first in digital multicasting we present a practical capacity achieving scheme which uses only scalar codes and linear processing then we consider the joint source channel problem of transmitting a gaussian source over a two user multiple input multiple output channel where we show the existence of nontrivial cases where the optimal distortion pair which for high signal to noise ratios snrs equals the optimal point to point distortions of the individual users may be achieved by employing a hybrid digital analog scheme over the induced equivalent channel these scenarios demonstrate the advantage of choosing a modulation basis based upon multiple links in the network thus we coin the approach network modulation

distance spectrum and performance of channel coded physical layer network coding for binary input gaussian two way relay channels we investigate a channel coded physical layer network coding cpnc scheme for binary input gaussian two way relay channels in this scheme the codewords of the two users are transmitted simultaneously the relay computes and forwards a network coded nc codeword without complete decoding of the two users individual messages we propose a new punctured codebook method to explicitly find the distance spectrum of the cpnc scheme based on that we derive an asymptotically tight performance bound for the error probability our analysis shows that compared to the single user scenario the cpnc scheme exhibits the same minimum euclidean distance but an increased multiplicity of error events with minimum distance at a high snr this leads to an snr penalty of at most ln2 in linear scale for long channel codes of various rates our analytical results match well with the simulated performance

polynomially solvable instances of the shortest and closest vector problems with applications to compute and forward a particular instance of the shortest vector problem svp appears in the context of compute and forward despite the np hardness of the svp we will show that this certain instance can be solved in complexity order o n psi log n psi where psi sqrt p text h 2 1 depends on the transmission power and the norm of the channel vector we will then extend our results to integer forcing and finally introduce a more general class of lattices for which the svp and the closest vector problem can be approximated within a constant factor

moving kriging interpolation and element free galerkin method a new formulation of the element free galerkin efg method is presented in this paper efg has been extensively popularized in the literature in recent years due to its flexibility and high convergence rate in solving boundary value problems however accurate imposition of essential boundary conditions in the efg method often presents difficulties because the kronecker delta property which is satisfied by finite element shape functions does not necessarily hold for the efg shape function the proposed new formulation of efg eliminates this shortcoming through the moving kriging mk interpolation two major properties of the mk interpolation the kronecker delta property i s j i j and the consistency property n i i x i and n i i x x l i x i are proved some preliminary numerical results arc given

the complex variable meshless local petrovgalerkin method for elastodynamic analysis of functionally graded materials as an improvement of the meshless local petrovgalerkin mlpg the complex variable meshless local petrovgalerkin cvmlpg method is extended here to dynamic analysis of functionally graded materials fgms in this method the complex variable moving least squares cvmls approximation is used instead of the traditional moving least squares mls to construct the shape functions the main advantage of the cvmls approximation over mls approximation is that the number of the unknown coefficients in the trial function of the cvmls approximation is less than that of the mls approximation thus higher efficiency and accuracy can be achieved under the same node distributions in implementation of the present method the variations of the fgms properties are computed by using material parameters at gauss points so it totally avoids the issue of the assumption of homogeneous in each element in the finite element method fem for the fgms several numerical examinations for dynamic analysis of fgms are carried out to demonstrate the accuracy and efficiency of the cvmlpg

a sub domain smoothed galerkin method for solid mechanics problems summary a sub domain smoothed galerkin method is proposed to integrate the advantages of mesh free galerkin method and fem arbitrarily shaped sub domains are predefined in problems domain with mesh free nodes in each sub domain based on mesh free galerkin weak formulation the local discrete equation can be obtained by using the moving kriging interpolation which is similar to the discretization of the high order finite elements strain smoothing technique is subsequently applied to the nodal integration of sub domain by dividing the sub domain into several smoothing cells moreover condensation of dof can also be introduced into the local discrete equations to improve the computational efficiency the global governing equations of present method are obtained on the basis of the scheme of fem by assembling all local discrete equations of the sub domains the mesh free properties of galerkin method are retained in each sub domain several 2d elastic problems have been solved on the basis of this newly proposed method to validate its computational performance these numerical examples proved that the newly proposed sub domain smoothed galerkin method is a robust technique to solve solid mechanics problems based on its characteristics of high computational efficiency good accuracy and convergence copyright 2014 john wiley sons ltd

pricing european and american options by radial basis point interpolation a rbpi method for pricing european and american options is proposed rbpi has not yet been used for option pricing the overall efficiency is improved by coupling rbpi with other approaches three different algorithms for american options are tested and compared numerical results demonstrate the effectiveness of the techniques employed we propose the use of the meshfree radial basis point interpolation rbpi to solve the black scholes model for european and american options the rbpi meshfree method offers several advantages over the more conventional radial basis function approximation nevertheless it has never been applied to option pricing at least to the very best of our knowledge in this paper the rbpi is combined with several numerical techniques namely an exponential change of variables which allows us to approximate the option prices on their whole spatial domain a mesh refinement algorithm which turns out to be very suitable for dealing with the non smooth options payoff and an implicit euler richardson extrapolated scheme which provides a satisfactory level of time accuracy finally in order to solve the free boundary problem that arises in the case of american options three different approaches are used and compared the projected successive overrelaxation method psor the bermudan approximation and the penalty approach numerical experiments are presented which demonstrate the computational efficiency of the rbpi and the effectiveness of the various techniques employed

achieving 1 2 log 1 snr on the awgn channel with lattice encoding and decoding we address an open question regarding whether a lattice code with lattice decoding as opposed to maximum likelihood ml decoding can achieve the additive white gaussian noise awgn channel capacity we first demonstrate how minimum mean square error mmse scaling along with dithering lattice randomization techniques can transform the power constrained awgn channel into a modulo lattice additive noise channel whose effective noise is reduced by a factor of spl radic 1 snr snr for the resulting channel a uniform input maximizes mutual information which in the limit of large lattice dimension becomes 1 2 log 1 snr i e the full capacity of the original power constrained awgn channel we then show that capacity may also be achieved using nested lattice codes the coarse lattice serving for shaping via the modulo lattice transformation the fine lattice for channel coding we show that such pairs exist for any desired nesting ratio i e for any signal to noise ratio snr furthermore for the modulo lattice additive noise channel lattice decoding is optimal finally we show that the error exponent of the proposed scheme is lower bounded by the poltyrev exponent

efficient decoding algorithms for the compute and forward strategy we address in this paper decoding aspects of the compute and forward cf physical layer network coding strategy under the cf framework encoders use a special class of nested lattice codes and decoders are based on suboptimal minimum distance decoding of unknown performance gap with respect to optimal decoders in this work we develop and assess the performance of novel decoding algorithms for cf operating in the multiple access channel starting with the gaussian channel we investigate the maximum a posteriori map decoder we derive a novel map decoding metric and develop practical decoding algorithms shown numerically to outperform the original one for the fading channel we analyze the ml decoder for integer valued lattices and develop a novel diophantine approximation based near ml decoding algorithm shown numerically to outperform the original cf decoder in the 1 d case using mathbb z lattices

on modulo sum computation over an erasure multiple access channel we study modulo sum computation of two binary source sequences over a two user erasure multiple access channel the channel is modeled as a binary input erasure multiple access channel which can be in one of three states either the channel output is a modulo sum of the two input symbols or the channel output equals the input symbol on the first link and an erasure on the second link or vice versa the associated state sequence is independent and identically distributed unlike previously studied multiple access channels the proposed channel is not matched to the modulo sum function and therefore we expect simple cut set upper bounds to be far from capacity in this paper we establish a new upper bound on the modulo sum capacity that is tighter than the cut set bound the key step in establishing this new bound is to provide suitable side information to the encoders to reduce the setup to a compound multiple access channel and then capture the tension across multiple receivers required to compute the modulo sum function in our lower bound it suffices to use identical linear codebooks at the two encoders when a strictly causal feedback of the channel state is available to the encoders we present a simple coding scheme that can achieve a rate larger than our upper bound for the case without feedback this shows that the modulo sum capacity is increased with feedback an extension to the case of lossy reconstruction is also treated briefly

soft decoding based strategies for relay and interference channels analysis and achievable rates using ldpc codes we provide a rigorous mathematical analysis of two communication strategies soft decode and forward soft df for relay channels and soft partial interference cancelation soft ic for interference channels both strategies involve soft estimation which assists the decoding process we consider ldpc codes not because of their practical benefits but because of their analytic tractability which enables an asymptotic analysis similar to random coding methods of information theory unlike some works on the closely related demodulate and forward we assume non memoryless code structure aware estimation with soft df we develop simultaneous density evolution to bound the decoding error probability at the destination this result applies to erasure relay channels in one variant of soft df the relay applies wyner ziv coding to enhance its communication with the destination borrowing from compress and forward to analyze soft ic we adapt existing techniques for iterative multiuser detection and focus on binary input additive white gaussian noise interference channels we prove that optimal point to point codes are unsuitable for soft ic as well as for all strategies that apply partial decoding to improve upon single user detection and multiuser detection including han kobayashi

asymptotic capacity of the separated mimo two way relay channel a multiple input multiple output two way relay channel consisting of two communication nodes and a full duplex relay node in which no direct link exists between the two communication nodes is considered we propose an achievable scheme that employs horizontally encoded lattice codes combined with generalized singular value decomposition based precoding for the first phase the second phase of the proposed scheme follows the fundamentals of the previous scheme which uses vertically encoded structural bining with the only difference that the added codeword of the two codewords from the communication nodes instead of those two individual codewords is decoded and retransmitted in the proposed scheme we show that the proposed scheme achieves the cut set bound asymptotically as the signal to noise ratios of the channels tend to infinity

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

a generalized approximation for the meshfree analysis of solids this paper presents a new approach in the construction of meshfree approximations as well as the weak kronecker delta property at the boundary referred to as a generalized meshfree gmf approximation the gmf approximation introduces an enriched basis function in the original shepard s method this enriched basis function is introduced to meet the linear or higher order reproducing conditions and at the same time to offer great flexibility on the control of the smoothness and convexity of the approximation the construction of the gmf approximation can be viewed as a special root finding scheme of constraint equations that enforces that the basis functions are corrected and the reproducing conditions with certain orders are satisfied within a set of nodes by choosing different basis functions various convex and non convex approximations including moving least squares mls reproducing kernel rk and maximum entropy me approximations can be obtained furthermore the basis function can also be translated or blended with other functions to generate a particular approximation for a special purpose one application in this paper is to incorporate a blending function at the boundary based on the concept of local convexity for the non convex approximation such as mls to acquire the weak kronecker delta property to achieve the higher order gmf approximation two possible methods are also introduced several examples are presented to examine the effectiveness of various gmf approximations copyright 2010 john wiley sons ltd

the approximate capacity region of the gaussian y channel via the deterministic approach a full duplex wireless network with three users that want to establish full message exchange via a relay is considered thus this network which is known as the y channel has a total of six messages two outgoing and two incoming at each user the users are not physically connected and thus the relay is essential for their communication the deterministic y channel is considered first its capacity region is characterized and shown not to be given by the cut set bounds the capacity achieving scheme has three different components strategies 1 a bidirectional 2 a cyclic and 3 a unidirectional strategy network coding is used to realize the bidirectional and the cyclic strategies and thus to prove the achievability of the capacity region the result is then extended to the gaussian y channel where the capacity region is characterized within a constant gap independent of the channel parameters

a point interpolation method with least square strain field pim lss for solution bounds and ultra accurate solutions using triangular mesh abstract a point interpolation method with least square strain field pim lss is developed for solid mechanics problems using triangular background mesh in the pim lss pim shape functions are used for displacement field construction that may or may not be compatible and a least square fitting technique is adopted to construct the strain field a strain constructed galerkin sc galerkin weak formulation is then proposed for establishing discretized pim lss models that have a number of special properties we proved theoretically 1 the pim lss provides a softening effect to the fem model and a stiffing effect to the node based smoothed point interpolation method ns pim model 2 the exact solution is bounded from both by pim lss solutions with strain field of zero order fitting and that with higher order fitting 3 there exists a preferred order of fitting for the strain field such that ultra accurate one order higher accuracy solution can be obtained using the pim lss these theorems and properties have been confirmed in numerical examples

the approximate sum capacity of the symmetric gaussian k user interference channel interference alignment has emerged as a powerful tool in the analysis of multiuser networks despite considerable recent progress the capacity region of the gaussian k user interference channel is still unknown in general in part due to the challenges associated with alignment on the signal scale using lattice codes this paper develops a new framework for lattice interference alignment based on the compute and forward approach within this framework each receiver decodes by first recovering two or more linear combinations of the transmitted codewords with integer valued coefficients and then solving these linear combinations for its desired codeword for the special case of symmetric channel gains this framework is used to derive the approximate sum capacity of the gaussian interference channel up to an explicitly defined outage set of the channel gains the key contributions are the capacity lower bounds for the weak through strong interference regimes where each receiver should jointly decode its own codeword along with part of the interfering codewords as part of the analysis it is shown that decoding k linear combinations of the codewords can approach the sum capacity of the k user gaussian multiple access channel up to a gap of no more than k 2 log k bits

cooperation for interference management a gdof perspective the impact of cooperation on interference management is investigated by studying an elemental wireless network the so called symmetric interference relay channel irc from a generalized degrees of freedom gdof perspective this is motivated by the fact that the deployment of relays is considered as a remedy to overcome the bottleneck of current systems in terms of achievable rates the focus of this paper is on the regime in which the interference link is weaker than the source relay link in the irc our approach toward studying the gdof goes through the capacity analysis of the linear deterministic irc ld irc new upper bounds on the sum capacity of the ld irc based on genie aided approaches are established these upper bounds together with some existing upper bounds are achieved by using four novel transmission schemes extending the upper bounds and the transmission schemes to the gaussian case the gdof of the gaussian irc is characterized for the aforementioned regime this completes the gdof results available in the literature for the symmetric gdof it turns out that even if the incoming and outgoing links of the relay are both weaker than the desired channel involving a relay can increase the gdof interestingly utilizing the relay in this case can increase the slope of the gdof from 2 in the interference channel ic to 1 or 0 this shrinks the regime where ignoring the interference by treating it as noise is optimal furthermore the analysis shows that if the relay ingoing and outgoing links are sufficiently strong the relay is able to neutralize the interference completely in this case the bottleneck of the transmission will be the interference links and hence the gdof increases if the interference link gets stronger it is shown that in the strong interference regime in contrast to the ic the gdof can be a monotonically decreasing function of the interference level

lattices over eisenstein integers for compute and forward in this paper we consider the use of lattice codes over eisenstein integers for implementing a compute and forward protocol in wireless networks when channel state information is not available at the transmitter we extend the compute and forward paradigm of nazer and gastpar to decoding eisenstein integer combinations of transmitted messages at relays by proving the existence of a sequence of pairs of nested lattices over eisenstein integers in which the coarse lattice is good for covering and the fine lattice can achieve the poltyrev limit using this result we show that both the outage performance and error correcting performance of the nested lattice codebooks over eisenstein integers surpass those of lattice codebooks over integers considered by nazer and gastpar with no additional computational complexity

bidirectional broadcast channel with random states noncausally known at the encoder in this work coding for a discrete memoryless broadcast channel with random states and two receivers is studied each receiver knows one of the two information messages at the sender and wants to know the other one assuming the channel state sequence is noncausally known at the sender an achievable rate region based on the gel fand pinsker coding strategy is derived and an outer bound to the capacity region is presented further the capacity region for the special case where in addition one receiver knows the channel state is established an equivalent characterization of an achievable rate region characterizing convex set is derived using shannon s concept of transmit strategies this characterization is used to derive an arimoto blahut like algorithm including a stopping criterion to compute the weighted rate sum maxima which can be used to characterize the whole achievable rate region the tradeoff between the input distribution and the impact of the channel state the necessity of the time sharing operation and the additive gaussian channel case assuming costa s choice of auxiliary random variables are discussed by examples

low density lattice coded relaying with joint iterative decoding low density lattice codes ldlcs are known for their high decoding efficiency and near capacity performance on point to point gaussian channels in this paper we present a distributed ldlc based cooperative relaying scheme for the multiple access relay channel marc the relay node decodes ldlc coded packets from two sources and forwards a network coded combination to the destination at the destination a joint iterative decoding structure is designed to exploit the diversity gain as well as coding gain for the ldlc based network coding operation at the relay we consider two alternative methods which offer a tradeoff between implementation complexity and performance called superposition ldlc s ldlc and modulo addition ldlc ma ldlc soft symbol relaying is considered as an alternative to hard decision relaying which is capable of reducing the effect of error propagation at the relay simulation results show that the proposed scheme can provide greater diversity gain and up to 6 2 db coding gain when compared with noncooperative ldlc coding and uncoded network coded transmission the proposed scheme also achieves 2 5 db gain over network turbo coded cooperation for the same code rate and overall transmitted power also soft symbol relaying is shown to provide approximately 2 db gain over hard decision relaying when the source relay link suffers from deep fading

moving kriging shape function modeling of vector tarma models for modal identification of linear time varying structural systems abstract this work proposes a moving kriging mk shape function modeling method for modal identification of linear time varying ltv structural systems based on vector time dependent autoregressive moving average vtarma models it aims to avoid the functional subspaces selection of the conventional functional series vtarma fs vtarma models instead of the common basis functions it constructs the time varying coefficients on the time nodes with the mk shape functions in a compact support domain the merit of the mk shape function is to determine its shape parameters upon vector random vibration signals adaptively model identification is effectively dealt with through an optimization scheme that decomposes the identification problem into two subproblems estimating model parameters via two stage least squares 2sls method and estimating shape function parameters via a discrete continuous variable hybrid optimization in addition the model order selection is achieved by the optimization scheme this method has been validated by a monte carlo study of simulation case and further by an experimental test case and the performance and potential advantages are illustrated