reconstruction of the spatio temporal dynamics of a human magnetoencephalogram abstract we reconstruct the entire experimentally observed spatio temporal signal of a human magnetoencephalogram meg observed in a sensori motor coordination experiment by kelso et al in this experiment when an acoustic stimulus frequency is changed systematically a spontaneous transition in coordination occurs at a critical frequency in both the motor behavior and brain signals here we present a stepwise approach for the reconstruction of the spatio temporal signal first we identify the order parameters and recall a theoretical model by the present authors and kelso which reproduces the temporal dynamics of the order parameters second we use the variational method by uhl et al in order to determine the spatial modes of the order parameters third we present a variational method for the reconstruction of the remaining spatio temporal signal and determine the spatial modes and temporal dynamics of the enslaved variables and possible order parameter modifications the obtained set of spatial modes proves to be a fixed spatial base system of the observed temporal dynamics in the brain

topology identification of weighted complex dynamical networks abstract recently various papers investigated the geometry features synchronization and control of complex network provided with certain topology while the exact topology of a network is sometimes unknown or uncertain using lyapunov theory we propose an adaptive feedback controlling method to identify the exact topology of a rather general weighted complex dynamical network model by receiving the network nodes evolution the topology of such kind of network with identical or different nodes or even with switching topology can be monitored experiments show that the methods presented in this paper are of high accuracy with good performance

discontinuous galerkin approximations of the stokes and navier stokes equations numerical schemes to compute approximate solutions of the evolutionary stokes and navier stokes equations are studied the schemes are discontinuous in time and conforming in space and of arbitrarily high order fully discrete error estimates are derived and dependence of the viscosity constant is carefully tracked it is shown that the errors are bounded by projection errors of the exact solution which exhibit optimal rates when the solutions are smooth

on a higher order accurate fully discrete galerkin approximation to the navier stokes equations we consider approximating the solution of the initial and boundary value problem for the navier stokes equations in bounded twoand three dimensional domains using a nonstandard galerkin finite element method for the space discretization and the third order accurate three step backward differentiation method coupled with extrapolation for the nonlinear terms for the time stepping the resulting scheme requires the solution of one linear system per time step plus the solution of five linear systems for the computation of the required initial conditions all these linear systems have the same matrix the resulting approximations of the velocity are shown to have optimal rate of convergence in l2 under suitable restrictions on the discretization parameters of the problem and the size of the solution in an appropriate function space

adaptive weak approximation of diffusions with jumps this work develops adaptive time stepping algorithms for the approximation of a functional of a diffusion with jumps based on a jump augmented monte carlo euler maruyama method which achieve a prescribed precision the main result is the derivation of new expansions for the time discretization error with computable leading order term in a posteriori form which are based on stochastic flows and discrete dual backward functions combined with proper estimation of the statistical error they lead to efficient and accurate computation of global error estimates extending the results by a szepessy r tempone and g e zouraris comm pure appl math 54 2001 pp 1169 1214 adaptive algorithms for either deterministic or trajectory dependent time stepping are proposed numerical examples show the performance of the proposed error approximations and the adaptive schemes

on the stability of the l 2 projection in h 1 ω we prove the stability in h1 of the l2 projection onto a family of finite element spaces of conforming piecewise linear functions satisfying certain local mesh conditions we give explicit formulae to check these conditions for a given finite element mesh in any number of spatial dimensions in particular stability of the l2 projection in h1 holds for locally quasiuniform geometrically refined meshes as long as the volume of neighboring elements does not change too drastically

compact families of piecewise constant functions in lp 0 t b abstract a strong compactness result in the spirit of the lions aubin simon lemma is proven for piecewise constant functions in time u with values in a banach space the main feature of our result is that it is sufficient to verify one uniform estimate for the time shifts u u instead of all time shifts u u h for h 0 as required in simon s compactness theorem this simplifies significantly the application of the rothe method in the existence analysis of parabolic problems

synchronization based topology identification of weighted general complex dynamical networks with time varying coupling delay abstract many existing papers investigated the geometric features control and synchronization of complex dynamical networks provided with certain topology however the exact topology of a network is sometimes unknown or uncertain based on lasalle s invariance principle we propose an adaptive feedback technique to identify the exact topology of a weighted general complex dynamical network model with time varying coupling delay by receiving the network nodes evolution the topology of such a kind of network with identical or different nodes or even with varying topology can be monitored in comparison with previous methods time delay is taken into account in this simple analytical and systematic synchronization based technique particularly the weight configuration matrix is not necessarily symmetric or irreducible and the inner coupling matrix need not be symmetric illustrative simulations are provided to verify the correctness and effectiveness of the proposed scheme

an eulerian description of fluids containing visco elastic particles equations governing the flow of fluid containing visco hyperelastic particles are developed in an eulerian framework the novel feature introduced here is to write an evolution equation for the strain it is envisioned that this will simplify numerical codes which typically compute the strain on lagrangian meshes moving through eulerian meshes existence results for the flow of linear visco hyperelastic particles in a newtonian fluid are established using a galerkin scheme

global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays by employing the lyapunov krasovskii functional and linear matrix inequality lmi approach the problem of global asymptotical stability is studied for recurrent neural networks with both discrete time varying delays and distributed time varying delays some sufficient conditions are given for checking the global asymptotical stability of recurrent neural networks with mixed time varying delay the proposed lmi result is computationally efficient as it can be solved numerically using standard commercial software two examples are given to show the usefulness of the results

error estimates for discontinuous galerkin approximations of implicit parabolic equations we analyze the classical discontinuous galerkin method for implicit parabolic equations symmetric error estimates for schemes of arbitrary order are presented the ideas developed allow certain assumptions frequently required in previous work to be relaxed for example different discrete spaces are allowed at each time step and the spatial operator is not required to be self adjoint or independent of time error estimates are posed in terms of projections of the exact solution onto the discrete spaces and are valid under the minimal regularity guaranteed by the natural energy estimate these projections are local and enjoy optimal approximation properties when the solution is sufficiently regular

optimization based structure identification of dynamical networks abstract the topological structure of a dynamical network plays a pivotal part in its properties dynamics and control thus understanding and modeling the structure of a network will lead to a better knowledge of its evolutionary mechanisms and to a better cottoning on its dynamical and functional behaviors however in many practical situations the topological structure of a dynamical network is usually unknown or uncertain thus exploring the underlying topological structure of a dynamical network is of great value in recent years there has been a growing interest in structure identification of dynamical networks as a result various methods for identifying the network structure have been proposed however in most of the previous work few of them were discussed in the perspective of optimization in this paper an optimization algorithm based on the projected conjugate gradient method is proposed to identify a network structure it is straightforward and applicable to networks with or without observation noise furthermore the proposed algorithm is applicable to dynamical networks with partially observed component variables for each multidimensional node as well as small scale networks with time varying structures numerical experiments are conducted to illustrate the good performance and universality of the new algorithm

finite element approximation of the nonstationary navier stokes problem i regularity of solutions and second order error estimates for spatial discretization this is the first part of a work dealing with the rigorous error analysis of finite element solutions of the nonstationary navier stokes equations second order error estimates are proven for spatial discretization using conforming or nonconforming elements the results indicate a fluid like behavior of the approximations even in the case of large data so long as the solution remains regular the analysis is based on sharp a priori estimates for the solution particularly reflecting its behavior as t to 0 and as t to infty it is shown that the regularity customarily assumed in the error analysis for corresponding parabolic problems cannot be realistically assumed in the case of the navier stokes equations as it depends on nonlocal compatibility conditions for the data the results which are presented here are independent of such compatibility conditions which cannot be verified in practice

optimal convergence for the implicit space time discretization of parabolic systems with p structure parabolic systems with p structure are considered on convex polyhedral domains under dirichlet boundary conditions a fully discrete scheme is studied using c 0 piecewise linear finite elements in space and the backward euler difference scheme in time a priori error estimates in quasi norms are proved and optimal convergence rates are obtained

global synchronization criteria of linearly coupled neural network systems with time varying coupling in this paper global synchronization of linearly coupled neural network nn systems with time varying coupling is investigated the dynamical behavior of the uncoupled system at each node is general which can be chaotic or others the coupling configuration is time varying i e the coupling matrix is not a constant matrix based on lyapunov function method and the specific property of householder transform some criteria for the global synchronization are obtained by these criteria one can verify whether the coupled system with time varying coupling is globally synchronized which is important and useful for both understanding and interpreting synchronization phenomena and designing coupling configuration finally two simulations are given to demonstrate the effectiveness of the theoretical results

pinning control of scale free dynamical networks abstract recently it has been demonstrated that many large complex networks display a scale free feature that is their connectivity distributions have the power law form in the present work control of a scale free dynamical network by applying local feedback injections to a fraction of network nodes is investigated the specifically and randomly pinning schemes are considered the specifically pinning of the most highly connected nodes is shown to require a significantly smaller number of local controllers as compared to the randomly pinning scheme the method is applied to an array of chua s oscillators as an example

finite element approximations of the nonstationary navier stokes problem part iv error estimates for second order time discretization this paper provides an error analysis for the crank nicolson method of time discretization applied to spatially discrete galerkin approximations of the nonstationary navier stokes equations second order error estimates are proven locally in time under realistic assumptions about the regularity of the solution for approximations of an exponentially stable solution these local error estimates are extended uniformly in time as text t to infty

exponential stability of discrete time genetic regulatory networks with delays discrete time versions of the continuous time genetic regulatory networks grns with sum regulatory functions are formulated and studied in this letter sufficient conditions are derived to ensure the global exponential stability of the discrete time grns with delays an illustrative example is given to demonstrate the effectiveness of the obtained results

approximation of liquid crystal flows the numerical solution of the flow of a liquid crystal governed by a particular instance of the ericksen leslie equations is considered convergence of finite element approximations is established under appropriate regularity hypotheses and numerical experiments exhibiting the interaction of singularities and the coupling of the director and momentum equations are presented

optimal rates of convergence for degenerate parabolic problems in two dimensions fully discrete implicit schemes for the solution of degenerate parabolic equations in two dimensions are shown to satisfy error estimates of the form o tau ln 1 h alpha h where tau is the time step size and h is the mesh size these results apply to both the stefan problem and the porous medium equation

compactness properties of the dg and cg time stepping schemes for parabolic equations for a broad class of parabolic equations it is shown that numerical solutions computed using the discontinuous galerkin or the continuous galerkin time stepping schemes of arbitrary order will inherit the compactness properties of the underlying equation convergence of numerical schemes for a phase field approximation of the flow of two fluids with surface tension is presented to illustrate these results

consensus analysis of multiagent networks via aggregated and pinning approaches in this paper the consensus problem of multiagent nonlinear directed networks mndns is discussed in the case that a mndn does not have a spanning tree to reach the consensus of all nodes by using the lie algebra theory a linear node and node pinning method is proposed to achieve a consensus of a mndn for all nonlinear functions satisfying a given set of conditions based on some optimal algorithms large size networks are aggregated to small size ones then by applying the principle minor theory to the small size networks a sufficient condition is given to reduce the number of controlled nodes finally simulation results are given to illustrate the effectiveness of the developed criteria

parameter identification of dynamical systems from time series in this paper synchronization based parameter identification of dynamical systems from time series is carefully revisited it is shown based on rigorous theoretical analysis and concrete counterexamples that some recent research reports on this issue are incomplete or even incorrect a linear independence condition is pointed out which is sufficient for such parameter identification of general dynamical systems

measuring interregional functional connectivity using coherence and partial coherence analyses of fmri data understanding functional connectivity within the brain is crucial to understanding neural function even the simplest cognitive operations are supported by highly distributed neural circuits we developed a novel method to measure task related functional interactions between neural regions by applying coherence and partial coherence analyses to functional magnetic resonance imaging fmri data coherence and partial coherence are spectral measures that estimate the linear time invariant lti relationship between time series they can be used to generate maps of task specific connectivity associated with seed regions of interest rois these maps may then be compared across tasks revealing nodes with task related changes of connectivity to the seed roi to validate the method we applied it to an event related fmri data set acquired while subjects performed two sequence tapping tasks one of which required more bimanual coordination areas showing increased functional connectivity with both tasks were the same as those showing increased activity furthermore though there were no significant differences in mean activity between the two tasks significant increases in interhemispheric coherence were found between the primary motor m1 and premotor pm regions for the task requiring more bimanual coordination this increase in interhemispheric connectivity is supported by other brain imaging techniques as well as patient studies

identifying the topology of a coupled fitzhugh nagumo neurobiological network via a pinning mechanism topology identification of a network has received great interest for the reason that the study on many key properties of a network assumes a special known topology different from recent similar works in which the evolution of all the nodes in a complex network need to be received this brief presents a novel criterion to identify the topology of a coupled fitzhugh nagumo fhn neurobiological network by receiving the membrane potentials of only a fraction of the neurons meanwhile although incomplete information is received the evolution of all the neurons including membrane potentials and recovery variables are traced based on schur complement and lyapunov stability theory the exact weight configuration matrix can be estimated by a simple adaptive feedback control the effectiveness of the proposed approach is successfully verified by neural networks with fixed and switching topologies

fully discrete finite element approximations of the navier stokes cahn hilliard diffuse interface model for two phase fluid flows this paper develops and analyzes some fully discrete finite element methods for a parabolic system consisting of the navier stokes equations and the cahn hilliard equation which arises as a diffuse interface model for the flow of two immiscible and incompressible fluids in the model the two sets of equations are coupled through an extra phase induced stress term in the navier stokes equations and a fluid induced transport term in the cahn hilliard equation fully discrete mixed finite element methods are proposed for approximating the coupled system it is shown that the proposed numerical methods satisfy a mass conservation law and a discrete energy law which is analogous to the basic energy law for the phase field model the convergence of the numerical solutions to the solutions of the phase field model and its sharp interface limit is established by utilizing the discrete energy law as a by product the convergence result also provides a constructive proof of the existence of weak solutions to the navier stokes cahn hilliard phase field model numerical experiments are also presented to validate the theory and to show the effectiveness of the combined phase field and finite element approach

merging the bramble pasciak steinbach and the crouzeix thome criterion for h 1 stability of the l 2 projection onto finite element spaces suppose s h1 is a finite dimensional linear space based on a triangulation t of a domain and let l2 l2 denote the l2 projection onto s provided the mass matrix of each element t t and the surrounding mesh sizes obey the inequalities due to bramble pasciak and steinbach or that neighboring element sizes obey the global growth condition due to crouzeix and thomee is h1 stable for all u h1 we have u h1 c u h1 with a constant c that is independent of e g the dimension of s this paper provides a more flexible version of the bramble pasciak steinbach criterion for h1 stability on an abstract level in its general version i the criterion is applicable to all kind of finite element spaces and yields in particular h1 stability for nonconforming schemes on arbitrary shape regular meshes ii it is weaker than i e implied by either the bramble pasciak steinbach or the crouzeix thomee criterion for regular triangulations into triangles iii it guarantees h1 stability of a priori for a class of adaptively refined triangulations into right isosceles triangles

error estimates for the discontinuous galerkin methods for parabolic equations the classical discontinuous galerkin method for a general parabolic equation is analyzed symmetric error estimates for schemes of arbitrary order are presented the ideas developed below relax many assumptions required in previous work for example different discrete spaces may be used at each time step and the spatial operator need not be self adjoint or independent of time our error estimates are posed in terms of projections of the exact solution onto the discrete spaces and are valid under the minimal regularity guaranteed by the natural energy estimate these projections are local and enjoy optimal approximation properties when the solution is sufficiently regular

functional structure of cortical neuronal networks grown in vitro we apply an information theoretic treatment of action potential time series measured with microelectrode arrays to estimate the connectivity of mammalian neuronal cell assemblies grown in vitro we infer connectivity between two neurons via the measurement of the mutual information between their spike trains in addition we measure higher point multi information between any two spike trains conditional on the activity of a third cell as a means to identify and distinguish classes of functional connectivity among three neurons the use of a conditional three cell measure removes some interpretational shortcomings of the pairwise mutual information and sheds light on the functional connectivity arrangements of any three cells we analyze the resultant connectivity graphs in light of other complex networks and demonstrate that despite their ex vivo development the connectivity maps derived from cultured neural assemblies are similar to other biological networks and display nontrivial structure in clustering coefficient network diameter and assortative mixing specifically we show that these networks are weakly disassortative small world graphs which differ significantly in their structure from randomized graphs with the same degree we expect our analysis to be useful in identifying the computational motifs of a wide variety of complex networks derived from time series data