universal space time coding a universal framework is developed for constructing full rate and full diversity coherent space time codes for systems with arbitrary numbers of transmit and receive antennas the proposed framework combines space time layering concepts with algebraic component codes optimized for single input single output siso channels each component code is assigned to a thread in the space time matrix allowing it thus full access to the channel spatial diversity in the absence of the other threads diophantine approximation theory is then used in order to make the different threads transparent to each other within this framework a special class of signals which uses algebraic number theoretic constellations as component codes is thoroughly investigated the lattice structure of the proposed number theoretic codes along with their minimal delay allow for polynomial complexity maximum likelihood ml decoding using algorithms from lattice theory combining the design framework with the cayley transform allows to construct full diversity differential and noncoherent space time codes the proposed framework subsumes many of the existing codes in the literature extends naturally to time selective and frequency selective channels and allows for more flexibility in the tradeoff between power efficiency bandwidth efficiency and receiver complexity simulation results that demonstrate the significant gains offered by the proposed codes are presented in certain representative scenarios

observability of boolean control networks with state time delays this brief deals with the problem of the observability for the boolean control networks with time delays in states first using semi tensor product of matrices and the matrix expression of logic the boolean control networks with state delays can be converted into discrete time delay dynamics then the observability of the boolean control networks via two kinds of inputs is investigated by giving necessary and sufficient conditions finally examples are given to illustrate the efficiency of the obtained results

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

synchronization in an array of output coupled boolean networks with time delay this brief presents an analytical study of synchronization in an array of coupled deterministic boolean networks bns with time delay two kinds of models are considered in one model the outputs contain time delay while in another one the outputs do not one restriction in this brief is that the state delay and output delay are restricted to be equal by referring to the algebraic representations of logical dynamics and using the techniques of semitensor product of matrices some necessary and sufficient conditions are derived for the synchronization of delay coupled bns examples including a practical epigenetic example are given for illustration

an energy stable fourth order finite difference scheme for the cahn hilliard equation abstract in this paper we propose and analyze an energy stable numerical scheme for the cahn hilliard equation with second order accuracy in time and the fourth order finite difference approximation in space in particular the truncation error for the long stencil fourth order finite difference approximation over a uniform numerical grid with a periodic boundary condition is analyzed via the help of discrete fourier analysis instead of the standard taylor expansion this in turn results in a reduced regularity requirement for the test function in the temporal approximation we apply a second order bdf stencil combined with a second order extrapolation formula applied to the concave diffusion term as well as a second order artificial douglas dupont regularization term for the sake of energy stability as a result the unique solvability energy stability are established for the proposed numerical scheme and an optimal rate convergence analysis is derived in the l 0 t l 2 l 2 0 t h h 2 norm a few numerical experiments are presented which confirm the robustness and accuracy of the proposed scheme

an energetic variational approach for the cahn hilliard equation with dynamic boundary condition model derivation and mathematical analysis the cahn hilliard equation is a fundamental model that describes phase separation processes of binary mixtures in recent years several types of dynamic boundary conditions have been proposed in order to account for possible short range interactions of the material with the solid wall our first aim in this paper is to propose a new class of dynamic boundary conditions for the cahn hilliard equation in a rather general setting the derivation is based on an energetic variational approach that combines the least action principle and onsager s principle of maximum energy dissipation one feature of our model is that it naturally fulfills three important physical constraints conservation of mass dissipation of energy and force balance relations next we provide a comprehensive analysis of the resulting system of partial differential equations under suitable assumptions we prove the existence and uniqueness of global weak strong solutions to the initial boundary value problem with or without surface diffusion furthermore we establish the uniqueness of the asymptotic limit as t to infty and characterize the stability of local energy minimizers for the system

averaging q parxpar for a complex circularly gaussian random vector x a novel approach in this correspondence we average where is the euclidean norm of an complex circularly gaussian vector this is done by finding the characteristic function of the decision variable and subsequently applying the gil pelaez theorem to obtain a one dimensional real integral the integral is then converted to a contour integral which is evaluated using a variant of the cauchy s integral formula to obtain an expression for where is the expectation operator

number and length of attractors in a critical kauffman model with connectivity one the kauffman model describes a system of randomly connected nodes with dynamics based on boolean update functions though it is a simple model it exhibits very complex behavior for critical parameter values at the boundary between a frozen and a disordered phase and is therefore used for studies of real network problems we prove here that the mean number and mean length of attractors in critical random boolean networks with connectivity one both increase faster than any power law with network size we derive these results by generating the networks through a growth process and by calculating lower bounds

numerical methods for porous medium equation by an energetic variational approach abstract we study numerical methods for porous media equation pme there are two important characteristics the finite speed propagation of the free boundary and the potential waiting time which make the problem difficult to handle based on different dissipative energy laws we develop two numerical schemes by an energetic variational approach firstly based on f log f as the total energy form of the dissipative law we obtain the trajectory equation and then construct a fully discrete scheme it is proved that the scheme is uniquely solvable on an admissible convex set by taking the advantage of the singularity of the total energy next based on 1 2 f as the total energy form of the dissipation law we construct a linear numerical scheme for the corresponding trajectory equation both schemes preserve the corresponding discrete dissipation law meanwhile under some smoothness assumption both schemes are second order convergent in space and first order convergent in time each scheme yields a good approximation for the solution and the free boundary no oscillation is observed for the numerical solution around the free boundary furthermore the waiting time problem could be naturally treated which has been a well known difficult issue for all the existing methods due to its linear nature the second scheme is more efficient

stable and efficient finite difference nonlinear multigrid schemes for the phase field crystal equation in this paper we present and compare two unconditionally energy stable finite difference schemes for the phase field crystal equation the first is a one step scheme based on a convex splitting of a discrete energy by wise et al s m wise c wang j s lowengrub an energy stable and convergent finite difference scheme for the phase field crystal equation siam j numer anal in press in this scheme which is first order in time and second order in space the discrete energy is non increasing for any time step the second scheme we consider is a new fully second order two step algorithm in the new scheme the discrete energy is bounded by its initial value for any time step in both methods the equations at the implicit time level are nonlinear but represent the gradients of strictly convex functions and are thus uniquely solvable regardless of time step size we solve the nonlinear equations using an efficient nonlinear multigrid method numerical simulations are presented and confirm the stability efficiency and accuracy of the schemes

brief paper controllability of boolean control networks with time delays in states this paper investigates the controllability of boolean networks with time invariant delays in states after a brief introduction on converting the logic dynamics to discrete time delay systems the controllability via two kinds of controls is studied one kind of control is generated by boolean control networks another kind of control is free boolean sequences in both cases necessary and sufficient conditions of the controllability of boolean control networks are proved finally examples are given to illustrate the efficiency of the obtained results

on the periodic trajectories of boolean control networks abstract in this note we first characterize the periodic trajectories or equivalently the limit cycles of a boolean network and their global attractiveness we then investigate under which conditions all the trajectories of a boolean control network may be forced to converge to the same periodic trajectory if every trajectory can be driven to such a periodic trajectory this is possible by means of a feedback control law

exact pairwise error probability of space time codes we describe a simple technique for the numerical calculation within any desired degree of accuracy of the pairwise error probability pep of space time codes over fading channels this method applies also to the calculation of e q spl radic spl xi for any nonnegative random variable spl xi whose moment generating function spl phi sub spl xi s e exp s spl xi is known its application to the multiple antenna independent rayleigh fading channel and to the rayleigh block fading channel is discussed and illustrated by two simple examples

numerical simulation of nonlinear continuity equations by evolving diffeomorphisms abstract in this paper we present a numerical scheme for nonlinear continuity equations which is based on the gradient flow formulation of an energy functional with respect to the quadratic transportation distance it can be applied to a large class of nonlinear continuity equations whose dynamics are driven by internal energies given external potentials and or interaction energies the solver is based on its variational formulation as a gradient flow with respect to the wasserstein distance positivity of solutions as well as energy decrease of the semi discrete scheme are guaranteed by its construction we illustrate this property with various examples in spatial dimension one and two

space time code design for correlated ricean mimo channels at finite snr space time code stc designs commonly rely on the assumptions of independent and identically distributed i i d rayleigh channels being either slow or fast fading and high signal to noise ratio snr however it has been shown that poor scattering conditions can have detrimental effects on the performance of stcs and that the behavior of codes at high snr is radically different from the finite snr behavior this calls for new design criteria that correctly predict the behavior of codes in correlated channels at finite snr in this paper we investigate how spatially and temporally correlated ricean fading affects the performance of stcs at finite snr we derive a code design criterion leading to robust stcs in a wide variety of propagation conditions and do not require any channel knowledge at the transmitter codes satisfying this criterion are shown to perform sensibly better in correlated channels than codes designed only for i i d slow or fast rayleigh fading channels examples of space time trellis codes and algebraic codes are proposed in order to illustrate the developed criterion

finite snr performance analysis of space time coding in correlated ricean mimo channels the performance analysis and the subsequent design of space time codes stc in multiantenna channels commonly assume an infinite signal to noise ratio snr this assumption has been shown to be justified in uncorrelated rayleigh fading channels by contrast this correspondence investigates stc in all snr regimes and in the broad class of space time correlated ricean fading multiple input multiple output mimo channels for rank deficient codes it is proven analytically that the error probability is significantly affected by spatial correlations and coherent components irrespective of the snr range and the temporal correlation for full rank codes the performance and the code design are shown to be affected by spatial correlations and or coherent paths only at finite snr in slow fading channels whereas in time varying channels they are affected in all snr regimes hence there is no guarantee that stc designed for independent and indentically distributed i i d rayleigh fading channels perform adequately in space time correlated rayleigh ricean channels simulation examples confirm the conclusions drawn from the analytical derivations they further illustrate that the use of a high snr assumption does not allow to accurately estimate the behavior of stc in practical scenarios and should thus be used with care

remarks on space time codes including a new lower bound and an improved code this article presents a new asymptotically exact lower bound on pairwise error probability of a space time code as well as an example code that outperforms the comparable orthogonal design based space time odst code also contained in the article are an exact expression for pairwise error probability pep signal design guidelines and some observations relating to the reception of odst codes

pinning control design for the stabilization of boolean networks in this brief pinning control design for the stabilization of boolean network bn is addressed using the semitensor product of matrices transition matrix of the bn can be obtained we achieve global stability to the fixed point or the elementary cycle for the bn by changing the columns of the transition matrix then pinning nodes can be chosen and pinning control design algorithms are proposed finally an example is employed to show the proposed control design procedure

an energy stable and convergent finite difference scheme for the modified phase field crystal equation we present an unconditionally energy stable finite difference scheme for the modified phase field crystal equation a generalized damped wave equation for which the usual phase field crystal equation is a special degenerate case the method is based on a convex splitting of a discrete pseudoenergy and is semi implicit the equation at the implicit time level is nonlinear but represents the gradient of a strictly convex function and is thus uniquely solvable regardless of time step size we present a local in time error estimate that ensures the pointwise convergence of the scheme

on stabilization and set stabilization of multivalued logical systems the stabilization and set stabilization of a multivalued logical system are investigated in this paper by using pinning control first new algorithms are presented to redesign the transition matrix of the multivalued logical system such that the system is stable or set stable then by using reconstruction theory of a k valued logical system the pinning nodes are selected in addition the transition matrix of the pinning control is given by solving some logical matrix equations then a pinning control design algorithm is provided finally an example is employed to illustrate the proposed control design procedure

fast time stability of temporal boolean networks in real systems most of the biological functionalities come from the fact that the connections are not active all the time based on the fact temporal boolean networks tbns are proposed in this paper and the fast time stability is analyzed via semi tensor product stp of matrices and incidence matrices first the algebraic form of a tbn is obtained based on the stp method and one necessary and sufficient condition for global fast time stability is presented moreover incidence matrices are used to obtain several sufficient conditions which reduce the computational complexity from mathcal o n2 n exponential type to mathcal o n 4 polynomial type compared with the stp method in addition the global fast time stabilization of tbns is considered and pinning controllers are designed based on the neighbors of controlled nodes rather than all the nodes finally the local fast time stability of tbns is considered based on the incidence matrices as well several examples are provided to illustrate the effectiveness of the obtained results

an interface tracking algorithm for the porous medium equation we study the convergence of a finite difference scheme for the cauchy problem for the porous medium equation u m av m 1 the scheme exhibits the following two features the first is that it employs a discretization of the known interface condition for the propagation of the support of the solution we thus generate approximate interfaces as well as an approximate solution the second feature is that it contains a vanishing viscosity term this term permits an estimate of the form i 1 a viii r c t we prove that both the approximate solution and the approximate interfaces converge to the correct ones finally error bounds for both solution and free boundaries are proved in terms of the mesh parameters 1 introduction in this paper we derive and analyze a finite difference scheme for computing both the solution and the interfaces for the porous medium equation in one space dimension we demonstrate that the approximate solutions and the approximate interface curves converge to the correct ones and we obtain l00 bounds for the error in terms of the mesh parameter consider the laminar flow of a polytropic fluid of density x t u x t in a porous medium which is assumed to occupy the whole space and suppose that at time t 0 the fluid is contained in the slab 0 x fr 0 the phenomenon can be modeled by

exact symbol error probability analysis for orthogonal space time block codes two and higher dimensional constellations cases exact expressions are obtained for the symbol error probability of orthogonal space time block codes at the output of the coherent maximum likelihood decoder in the general case of arbitrary input signal constellation and code such expressions are derived for the cases of both deterministic fixed and random rayleigh ricean fading channels and both the two and higher dimensional constellations

analysis of the error performance of trellis coded modulations in rayleigh fading channels this work presents an exact expression for the pairwise error event probability of trellis coded modulation tcm transmitted over rayleigh fading channels it includes phase shift keying psk and multilevel quadrature amplitude modulation qam codes as well as coherent and partially coherent e g differential pilot tone etc detection due to the form of the exact pairwise error event probabilities this calculation technique cannot be used with the transfer function technique to obtain an upper union bound on the overall bit error probability for this reason the authors estimate the bit error probability by considering only a small number of short error events through simulations they found that the estimation is usually very accurate at high signal to noise ratios but not as accurate at lower signal to noise ratios they study several coded modulation schemes this way among the results are the fact that tcm provides significant improvement in the error floor when detected differentially and an asymmetry in the pairwise error event probability for 16 qam

a unified snr dependent analysis of space time codes in fading channels the pairwise error probability pep for multiple input multiple output mimo radio interfaces is investigated by means of a novel formulation based on compound matrices the proposed approach is suitable for any mimo system having average upper bounded pep written as det i gamma a zeta where a is a hermitian matrix zeta an integer number and gamma the signal to noise ratio snr that bound frequently results in mimo single and multicarrier transmissions it is shown that the minimization of the bounded pep should consider the whole set of nonzero compound matrices of a in particular the snr of interest marks the compound matrix that mainly drives the system performance both diversity advantage and coding gain are given as continuous functions of the variable gamma hence their asymptotic behaviors are taken as important case of studies the interaction effects between channel code and propagation environment are also discussed it is shown how the eigenvectors and eigenvalues of the autocorrelation channel matrix may be considered for code design it is also proved the maximization of the code rank is not always a necessary requirement for performance improvement being its optimal value fixed by the channel structure and snr of interest finally the analysis is applied to space time trellis coded transmissions over spatially correlated slow rayleigh fading channels

capacity scaling in mimo wireless systems under correlated fading previous studies have shown that single user systems employing n element antenna arrays at both the transmitter and the receiver can achieve a capacity proportional to n assuming independent rayleigh fading between antenna pairs we explore the capacity of dual antenna array systems under correlated fading via theoretical analysis and ray tracing simulations we derive and compare expressions for the asymptotic growth rate of capacity with n antennas for both independent and correlated fading cases the latter is derived under some assumptions about the scaling of the fading correlation structure in both cases the theoretic capacity growth is linear in n but the growth rate is 10 20 smaller in the presence of correlated fading we analyze our assumption of separable transmit receive correlations via simulations based on a ray tracing propagation model results show that empirical capacities converge to the limit capacity predicted from our asymptotic theory even at moderate n 16 we present results for both the cases when the transmitter does and does not know the channel realization

second order convex splitting schemes for gradient flows with ehrlich schwoebel type energy application to thin film epitaxy we construct unconditionally stable unconditionally uniquely solvable and second order accurate in time schemes for gradient flows with energy of the form int omega f nabla phi bf x frac epsilon 2 2 delta phi bf x 2 d bf x the construction of the schemes involves the appropriate combination and extension of two classical ideas i appropriate convex concave decomposition of the energy functional and ii the secant method as an application we derive schemes for epitaxial growth models with slope selection f bf y frac14 bf y 2 1 2 or without slope selection f bf y frac12 ln 1 bf y 2 two types of unconditionally stable uniquely solvable second order schemes are presented the first type inherits the variational structure of the original continuous in time gradient flow while the second type does not preserve the variational structure we present numerical simulations for the case with slope selection which verify well known physical scaling laws for the long time coarsening process

state feedback stabilization for boolean control networks state feedback stabilization for boolean control networks is investigated in this technical note based on the algebraic representation of logical dynamics in terms of the semi tensor product of matrices a necessary and sufficient condition is derived for the existence of a globally stabilizing state feedback controller and a general control design approach is proposed when global stabilization is feasible via state feedback instead of designing the logical form of a stabilizing feedback law directly we first construct its algebraic representation and then convert the algebraic representation back to the logical form an example is worked out to illustrate the proposed design procedure

controllability and observability of boolean control networks the controllability and observability of boolean control networks are investigated after a brief review on converting a logic dynamics to a discrete time linear dynamics with a transition matrix some formulas are obtained for retrieving network and its logical dynamic equations from this network transition matrix based on the discrete time dynamics the controllability via two kinds of inputs is revealed by providing the corresponding reachable sets precisely then the problem of observability is also solved by giving necessary and sufficient conditions

on lagrangian schemes for porous medium type generalized diffusion equations a discrete energetic variational approach abstract in this paper we present a systematic framework to derive a variational lagrangian scheme for porous medium type generalized diffusion equations by employing a discrete energetic variational approach such discrete energetic variational approaches are analogous to energetic variational approaches 39 25 in a semidiscrete level which provide a basis of deriving the semi discrete equations and can be applied to a large class of partial differential equations with energy dissipation laws and kinematic relations the numerical schemes derived by this framework can inherit the variational structure from the continuous energy dissipation law as an illustration we develop two variational lagrangian schemes for the multidimensional porous medium equations pme based on two different energy dissipation laws we focus on the numerical scheme based on the energy dissipation law with 1 2 u 2 d x as the dissipation functional several numerical experiments demonstrate the accuracy of this scheme as well as its ability in capturing the free boundary and estimating the waiting time for the pme in both 1d and 2d

projection method i convergence and numerical boundary layers this is the first of a series of papers on the subject of projection methods for viscous incompressible flow calculations the purpose of these papers is to provide a thorough understanding of the

disturbance decoupling of mix valued logical networks via the semi tensor product method this paper addresses the disturbance decoupling problem ddp of mix valued logical networks by using both the semi tensor product of matrices and the matrix expression of logical functions and presents a number of new results on the ddp first in order to solve the ddp a new algorithm is proposed to construct a kind of y friendly subspace for the state space of mix valued logical networks second based on the constructed y friendly subspace several necessary and sufficient conditions are obtained for the existence of decoupling controllers and a new control design procedure is established to deal with the ddp finally an illustrative example is studied by the new method proposed in this paper and two kinds of decoupling controllers are designed the study of the illustrative example shows that the new method is effective in dealing with the ddp of mix valued logical networks

on algorithms for state feedback stabilization of boolean control networks abstract this paper deals with the algorithms for state feedback stabilization of boolean control networks bcns by resorting to the semi tensor product stp technique the labelled digraph that can be used to completely characterize the dynamics of bcns is derived which leads to an equivalent graphical description for the stabilization of bcns what is more interesting is the fact that the existence of a state feedback control law stabilizing the bcn to some given equilibrium point can be characterized in terms of its spanning in tree consequently two in tree search algorithms namely the breadth first search and the depth first search are proposed to design the state feedback stabilizing law when global stabilization is feasible besides some basic properties about the tree search algorithms are addressed a biological example is employed to illustrate the applicability and usefulness of the developed algorithms

second order leader following consensus of nonlinear multi agent systems via pinning control abstract without assuming that the interaction diagraph is strongly connected or contains a directed spanning tree this paper studies the second order leader following consensus problem of nonlinear multi agent systems with general network topologies based on graph theory matrix theory and lasalle s invariance principle a pinning control algorithm is proposed to achieve leader following consensus in a network of agents with nonlinear second order dynamics furthermore a pinning consensus protocol is developed for coupled double integrators with a constant reference velocity in particular this paper addresses what kind of agents and how many agents should be pinned and establishes some sufficient conditions to guarantee that all agents asymptotically follow the virtual leader numerical simulations are given to verify the theoretical analysis

input state incidence matrix of boolean control networks and its applications the input state incidence matrix of a control boolean network is proposed it is shown that this matrix contains complete information of the input state mapping using it an easily verifiable necessary and sufficient condition for the controllability of a boolean control network is obtained the corresponding control which drives a point to a given reachable point is designed moreover certain topological properties such as the fixed points and cycles of a boolean control network are investigated then as another application a sufficient condition for the observability is presented finally the results are extended to mix valued logical control systems

a phase field model for the mixture of two incompressible fluids and its approximation by a fourier spectral method abstract a phase field model for the mixture of two incompressible fluids is presented in this paper the model is based on an energetic variational formulation it consists of a navier stokes system linear momentum equation coupled with a cahn hilliard equation phase field equation through an extra stress term and the transport term the extra stress represents the phase induced capillary effect for the mixture due to the surface tension a fourier spectral method for the numerical approximation of this system is proposed and analyzed numerical results illustrating the robustness and versatility of the model are presented

a matrix approach to graph maximum stable set and coloring problems with application to multi agent systems using the semi tensor product of matrices this paper investigates the maximum weight stable set and vertex coloring problems of graphs with application to the group consensus of multi agent systems and presents a number of new results and algorithms firstly by defining a characteristic logical vector and using the matrix expression of logical functions an algebraic description is obtained for the internally stable set problem based on which a new algorithm to find all the internally stable sets is established for any graph secondly the maximum weight stable set problem is considered and a necessary and sufficient condition is presented by which an algorithm to find all the maximum weight stable sets is obtained thirdly the vertex coloring problem is studied by using the semi tensor product method and two necessary and sufficient conditions are proposed for the colorability based on which a new algorithm to find all the k coloring schemes and minimum coloring partitions is put forward finally the obtained results are applied to multi agent systems and a new protocol design procedure is presented for the group consensus problem the study of illustrative examples shows that the results algorithms presented in this paper are very effective

error probability for orthogonal space time block code diversity system using rectangular qam transmission over rayleigh fading channels in this paper theoretical symbol error probability sep expressions are derived for orthogonal space time block code ostbc diversity systems employing arbitrary rectangular m qam transmission over flat rayleigh fading channels independent fading between diversity channels is assumed channel average powers may be distinctive identical or mixed with both the rectangular m qam results are extended to square m qam m pam and binary antipodal signaling all derived expressions are in elementary forms without complicated high order transcendental functions and unevaluated integrals and hence are strictly exact and can be readily simulated by the computer moreover it is shown that mixed rayleigh fading results can be readily extended to various nakagami m fading results a four transmit antenna system with a half rate ostbc for 16 qam signaling is used to demonstrate that the theoretical result is in excellent agreement with the monte carlo simulated result from simulation curves it is shown that under the independent channel fading condition channels with identical powers have better error rate performance than channels with distinctive powers

pinning stabilization of linearly coupled stochastic neural networks via minimum number of controllers pinning stabilization problem of linearly coupled stochastic neural networks lcsnns is studied in this paper a minimum number of controllers are used to force the lcsnns to the desired equilibrium point by fully utilizing the structure of the network in order to pinning control the lcsnns to a certain desired state only one controller is required for strongly connected network topology and m controllers which will be shown to be the minimum number are needed for lcsnns with m reducible coupling matrix the isolate node of the lcsnns can be stable periodic or even chaotic the coupling laplacian matrix of the lcsnns can be symmetric irreducible asymmetric irreducible or m reducible which means that the network topology can be strongly connected weakly connected or even unconnected there is no constraint on the network topology some criteria are derived to judge whether the lcsnns can be controlled in mean square by using designed controllers the given criteria are expressed in terms of strict linear matrix inequalities which can be easily checked by resorting to recently developed algorithm moreover numerical examples including small world and scale free networks are also given to demonstrate that our theoretical results are valid and efficient for large systems

on the performance of concatenated convolutional code and alamouti space time code with noisy channel estimates and finite depth interleaving in this paper performance of the alamouti space time code stc 1 and performance of the concatenation between the convolutional code and the alamouti stc are derived in order to describe realistic performance issues we assume that the channel estimates are calculated from linear filters using noisy pilot symbols we also assume non quasi static channels spatially correlated transmit antennas and finite depth interleaving two types of receivers are investigated for the alamouti stc namely the linear combining space time decoder lc std and the maximum likelihood space time decoder ml std two types of receivers are investigated for the concatenated system namely the lc std with the ml convolutional decoder and the joint alamouti and convolutional ml decoder the results have shown that the lc std is more sensitive to the doppler spread than the ml std however since the ml std is very sensitive to the channel estimation error the gains provided by the decoder in fast fading channels will be offset unless an optimized channel estimator is employed performance comparisons between the alamouti systems and the siso systems indicate that when the system environment is not ideal the siso systems may outperform the alamouti systems lastly analytical results are compared with simulation results to illustrate the accuracy of the analysis

controller design for disturbance decoupling of boolean control networks we investigate a type of disturbance decoupling problem ddp of boolean control networks using the semi tensor product of matrices the dynamics of a boolean control network is expressed in its algebraic form under the framework of output friendly subspace we give a necessary and sufficient condition for the solvability of ddp by analyzing the redundant variables and we present a computationally feasible method to construct all the valid feedback control matrices the logical functions of each controller can be recovered from the obtained feedback control matrix finally an example is provided to show the effectiveness of the proposed method

a matrix approach to modeling and optimization for dynamic games with random entrance this paper investigates the algebraic formulation and optimization control for a class of dynamic games with random entrance by using the semi tensor product method and presents a number of new results first the given dynamic game is considered as a kind of networked evolutionary games with switch networks based on which it is formulated as a markov processes to analyze second using receding horizon control method the given game s optimization problem is solved by a state feedback controller when the major player is considered as a control finally an illustrative example is studied to support our new results

multiple antenna signaling over fading channels with estimated channel state information performance analysis multiple antenna concepts for wireless communication systems promise high spectral efficiency and low error rates by proper exploitation of the randomness in multipath propagation in this paper we investigate the impact of channel uncertainty caused by channel estimation errors on the error rate performance we consider a training based multiple antenna system that reserves a portion of time to sound the channel training symbols are used to estimate the channel by means of an arbitrary linear filter at the receiver no channel state information csi is assumed at the transmitter we present a new framework to analyze training based multiple antenna systems by introducing an equivalent system model that specifies the channel by the estimated and hence known channel coefficients and an uncorrelated data dependent multiplicative noise we derive the maximum likelihood ml detector and highlight its behavior in the limiting cases of perfect csi and no csi and its relation to several mismatched detectors we deduce new exact expressions and chernoff bounds of the pairwise error probability pep used to assess word error and bit error rate bounds for ml and mismatched detection finally we review the code design guidelines in terms of the deleterious effect of channel uncertainty for coherent and noncoherent signaling schemes and present numerical results

error rates of the maximum likelihood detector for arbitrary constellations convex concave behavior and applications motivated by a recent surge of interest in convex optimization techniques convexity concavity properties of error rates of the maximum likelihood detector operating in the awgn channel are studied and extended to frequency flat slow fading channels generic conditions are identified under which the symbol error rate ser is convex concave for arbitrary multidimensional constellations in particular the ser is convex in snr for any one and two dimensional constellation and also in higher dimensions at high snr pairwise error probability and bit error rate are shown to be convex at high snr for arbitrary constellations and bit mapping universal bounds for the ser first and second derivatives are obtained which hold for arbitrary constellations and are tight for some of them applications of the results are discussed which include optimum power allocation in spatial multiplexing systems optimum power time sharing to decrease or increase jamming problem error rate an implication for fading channels fading is never good in low dimensions and optimization of a unitary precoded ofdm system for example the error rate bounds of a unitary precoded ofdm system with qpsk modulation which reveal the best and worst precoding are extended to arbitrary constellations which may also include coding the reported results also apply to the interference channel under gaussian approximation to the bit error rate when it can be expressed or approximated as a nonnegative linear combination of individual symbol error rates and to coded systems

asymptotic stability of differential systems with impulsive effects suffered by logic choice in this paper we investigate the asymptotic stability of differential systems with impulsive effects suffered by logic choice first we give the expression of system with logic selected impulsive effects which is a hybrid system second by using semi tensor product a criterion of asymptotic stability for the system is provided third we study the linearly coupled system with impulsive effects under logic choice and give a sufficient condition for asymptotic stability finally a numerical simulation is given to illustrate the effectiveness of our results

on the performance of space time codes over spatially correlated rayleigh fading channels we derive the exact pairwise error probability pep for space time coding over quasi static rayleigh fading channels in the presence of spatial fading correlation we show that receive correlation always degrades the pep for all signal to noise ratios snrs we quantify the effect of receive correlation by employing the notion of majorization we show that the stronger the receive correlation the worse the pep for all snrs we show that at low snr depending on the codes transmit correlation can either improve or degrade the pep performance we show that to guarantee robust performance for arbitrary transmit correlation the minimum eigenvalue of the codeword pair difference matrix should be maximized among all codeword pairs

global robust stability and stabilization of boolean network with disturbances abstract based on semi tensor product of matrices global robust stability and stabilization of boolean network bn with disturbances are investigated firstly the definition of global robust stability for bn with disturbances is presented by using the algebraic state space representation of disturbed bn some necessary and sufficient criteria are obtained to ensure the global robust stability with respect to w r t a fixed point or w r t a limit cycle in contrast if a given disturbed bn is not globally robust stable w r t a fixed point or w r t a limit cycle system can achieve stability by a matrix transformation technique however it is a difficult task to find such a suitable matrix transformation in this paper a pinning state feedback control design is proposed to find a suitable transformation the obtained results are well illustrated by numerical example

evaluation of the exact union bound for trellis coded modulations over fading channels an analytical technique is presented for computing the exact union bound on the average bit error probability of trellis coded modulation schemes over rayleigh rician or shadowed rician fading channels to this end an integral expression is derived for the pairwise error event probability pep existing bounds can be obtained as special cases of this expression it turns out that a gauss chebyshev quadrature rule offers excellent accuracy for this integral by extension the exact union bound i e the weighted sum of an exact peps of a code can readily be evaluated this method has the same complexity as the union chernoff bound and a few examples are given to show its application

on reachability and controllability of switched boolean control networks this paper investigates the reachability and controllability of switched boolean control networks bcns by using the semi tensor product method first a kind of switching input state transfer graph is defined based on which and the algebraic expression of switched bcns we thus propose a new kind of switching input state incidence matrix that contains the complete information of the switching input state transfer graph second by the switching input state incidence matrix several necessary and sufficient conditions are obtained for the reachability and controllability of switched bcns finally an algorithm is established to find a switching sequence and a control scheme to realize the reachability of switched bcns in the shortest time the study of an illustrative example shows that the new results obtained in this paper are very effective in investigating the reachability and controllability of switched bcns

interfaces in multidimensional diffusion equations with absorption terms we study the properties of interfaces in solutions of the cauchy problem for the nonlinear degenerate parabolic equation ut um aup in rn 0 t n 1 2 3 with the parameters m 1 p 0 a 0 satisfying the condition m p 2 we show that the velocity of the interface t supp u x t is given by the formula v m m 1 um 1 t where is the solution of the degenerate elliptic equation div u aup 0 0 on t the first term expresses the classical darcy law while the second one models the presence of an external force that makes the interface to move in the inward direction we give explicit formulas which represent the interface t as a bijection from 0 it is proved that the solution u and its interface t are analytic functions of time t and that they preserve the initial regularity in the spatial variables we also show that the regularity of the interface velocity v with respect to the spatial variables is better than it was at the initial instant the analysis is based on a special coordinate transformation a local version of lagrangian coordinates that renders the free boundary stationary

a linear representation of dynamics of boolean networks a new matrix product called semi tensor product of matrices is reviewed using it a matrix expression of logic is proposed where a logical variable is expressed as a vector a logical function is expressed as a multiple linear mapping under this framework a boolean network equation is converted into an equivalent algebraic form as a conventional discrete time linear system analyzing the transition matrix of the linear system formulas are obtained to show a the number of fixed points b the numbers of cycles of different lengths c transient period for all points to enter the set of attractors and d basin of each attractor the corresponding algorithms are developed and used to some examples

symbol mapping diversity design for multiple packet transmissions in this paper we present a simple but effective method of enhancing and exploiting diversity from multiple packet transmissions in systems that employ nonbinary linear modulations such as phase shift keying psk and quadrature amplitude modulation qam this diversity improvement results from redesigning the symbol mapping for each packet transmission by developing a general framework for evaluating the upper bound of the bit error rate ber with multiple transmissions a criterion to obtain optimal symbol mappings is attained the optimal adaptation scheme reduces to solutions of the well known quadratic assignment problem qap symbol mapping adaptation only requires a small increase in receiver complexity but provides very substantial ber gains when applied to additive white gaussian noise awgn and flat fading channels

normalization and solvability of dynamic algebraic boolean networks in this brief we first study the normalization of dynamic algebraic boolean networks dabns a new expression for the normalized dabns is obtained as applications of this result the solvability and uniqueness of the solution to dabns are then investigated necessary and sufficient conditions for the solvability and the uniqueness are obtained in addition pinning control to ensure the solvability and uniqueness of the solution to dabns is also studied numerical examples are given to illustrate the efficiency of the proposed results

convergence of gauge method for incompressible flow a new formulation a gauge formulation of the incompressible navier stokes equations in terms of an auxiliary field a and a gauge variable u a was proposed recently by e and liu this paper provides a theoretical analysis of their formulation and verifies the computational advantages we discuss the implicit gauge method which uses backward euler or crank nicolson in time discretization however the boundary conditions for the auxiliary field a are implemented explicitly vertical extrapolation the resulting momentum equation is decoupled from the kinematic equation and the computational cost is reduced to solving a standard heat and poisson equation moreover such explicit boundary conditions for the auxiliary field a will be shown to be unconditionally stable for stokes equations for the full nonlinear navier stokes equations the time stepping constraint is reduced to the standard cfl constraint t x c we also prove first order convergence of the gauge method when we use mac grids as our spatial discretization the optimal error estimate for the velocity field is also obtained

a study on moving mesh finite element solution of the porous medium equation an adaptive moving mesh finite element method is studied for the numerical solution of the porous medium equation with and without variable exponents and absorption the method is based on the moving mesh partial differential equation approach and employs its newly developed implementation the implementation has several improvements over the traditional one including its explicit compact form of the mesh velocities ease to program and less likelihood of producing singular meshes three types of metric tensor that correspond to uniform and arclength based and hessian based adaptive meshes are considered the method shows first order convergence for uniform and arclength based adaptive meshes and second order convergence for hessian based adaptive meshes it is also shown that the method can be used for situations with complex free boundaries emerging and splitting of free boundaries and the porous medium equation with variable exponents and absorption two dimensional numerical results are presented

finite time stability analysis and h control for a class of nonlinear time delay hamiltonian systems this paper investigates the finite time stability fts analysis and finite time h control design for a class of nonlinear time delay hamiltonian systems and proposes some delay dependent results on both the fts and finite time control design first a criterion on the fts is proposed for general time delay nonlinear systems via the razumikhin approach then based on the criterion some delay independent and delay dependent conditions on the fts are derived for the nonlinear time delay hamiltonian systems by constructing a suitable lyapunov function third we use the obtained fts results to investigate the finite time h control problem and present a control design procedure for a class of nonlinear time delay port controlled hamiltonian systems by the energy shaping approach study of two illustrative examples shows that the results obtained in this paper work very well in the fts analysis and control design of some nonlinear time delay hamiltonian systems

function perturbations on singular boolean networks abstract this paper is devoted to studying function perturbations on the transition matrix and topological structure of a singular boolean network sbn via the semi tensor product of matrices first the algebraic form of an sbn is given and we discuss how the transition matrix of the sbn changes under function perturbations then the local uniqueness of solutions to the sbn is studied under which the impacts of function perturbations on the topological structure are investigated finally examples are given to show the effectiveness of the obtained results

numerical simulation of diffusive and aggregation phenomena in nonlinear continuity equations by evolving diffeomorphisms we propose a numerical algorithm for solving nonlinear continuity equations written in lagrangian coordinates this transformation is intimately related to variational approaches for the well posedness of gradient flows of energy functionals with respect to the quadratic transportation distance in optimal transport theory these schemes allow the numerical approximation of both diffusive and aggregation regimes of different models positivity energy decreasing and mesh adaptation are built in in the numerical scheme and thus we are capable of capturing blow up densities and of dealing with vacuum regions and merging of mass patches in a natural way

strategy optimization for static games based on stp method abstract in this paper we consider the choice behavior of players in a static game and discuss solutions to static games of complete information problem via semi tensor product stp method some properties of the dominant behaviors are obtained based on which choosing the dominant strategies deleting the dominated strategies are used to optimize the strategy sets so as to obtain solutions to the considered game examples are given to show the effectiveness of the results

delay dependent stabilization of stochastic interval delay systems with nonlinear disturbances in this paper a delay dependent approach is developed to deal with the robust stabilization problem for a class of stochastic time delay interval systems with nonlinear disturbances the system matrices are assumed to be uncertain within given intervals the time delays appear in both the system states and the nonlinear disturbances and the stochastic perturbation is in the form of a brownian motion the purpose of the addressed stochastic stabilization problem is to design a memoryless state feedback controller such that for all admissible interval uncertainties and nonlinear disturbances the closed loop system is asymptotically stable in the mean square where the stability criteria are dependent on the length of the time delay and therefore less conservative by using ito s differential formula and the lyapunov stability theory sufficient conditions are first derived for ensuring the stability of the stochastic interval delay systems then the controller gain is characterized in terms of the solution to a delay dependent linear matrix inequality lmi which can be easily solved by using available software packages a numerical example is exploited to demonstrate the effectiveness of the proposed design procedure