scalar equations for synchronous boolean networks with biological applications one way of coping with the complexity of biological systems is to use the simplest possible models which are able to reproduce at least some nontrivial features of reality although two value boolean models have a long history in technology it is perhaps a little bit surprising that they can also represent important features of living organizms in this paper the scalar equation approach to boolean network models is further developed and then applied to two interesting biological models in particular a linear reduced scalar equation is derived from a more rudimentary nonlinear scalar equation this simpler but higher order two term equation gives immediate information about both cycle and transient structure of the network

synchronization of arbitrarily switched boolean networks this paper investigates the complete synchronization problem for the drive response switched boolean networks sbns under arbitrary switching signals where the switching signals of the response sbn follow those generated by the drive sbn at each time instant first the definition of complete synchronization is introduced for the drive response sbns under arbitrary switching signals second the concept of switching reachable set starting from a given initial state set is put forward based on it a necessary and sufficient condition is derived for the complete synchronization of the drive response sbns last we give a simple algebraic expression for the switching reachable set in a given number of time steps and two computable algebraic criteria are obtained for the complete synchronization of the sbns a biological example is given to demonstrate the effectiveness of the obtained main results

transient boundary element algorithm for elastoplastic building floor slab analysis a direct boundary element algorithm is developed for the dynamic analysis of thin elastoplastic building floor slabs directly supported by columns the formulation employs the classical boundary element methodology dedicated to the analysis of elastoplastic plates the method uses the static fundamental solution of the thin elastic plate problem in this case boundary as well as interior elements are used in the space descritization of the problem this is due to the presence of plasticity and inertial effects in the integral formulation an explicit time integration algorithm employed on the incremental form of the matrix equation of motion leads to the solution of the problem simple practical examples illustrate the accuracy and the efficiency of the proposed algorithm

the generalized morse oscillator in the so 4 2 dynamical group scheme a family of the morse oscillators with certain quantized coupling constants are described as composite objects in the framework of the so 4 2 dynamical group scheme although a single morse oscillator can be solved by the subgroup so 2 1 of so 4 2 this so 2 1 is not the spectrum generating group the set of all energy levels is given by the representation of another particular one parameter subgroup of so 4 2 which is the dynamical group of a single morse oscillator the continuous spectra of this oscillator and other variations of the morse potential are also discussed by making an analytic continuation from the morse potential well to the morse barrier

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

output feedback stabilization control design for boolean control networks this paper investigates the output feedback stabilization of boolean control networks bcns by using the semi tensor product method and presents a number of new results first based on the algebraic expression of bcns a necessary and sufficient condition is presented for the existence of output feedback stabilizers second a constructive procedure is proposed to design output feedback stabilization controllers for bcns the study of an illustrative example shows that the new results obtained in this paper are very effective in designing output feedback stabilizers for bcns

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

synchronization of stochastically coupled cellular automata we analyze the dynamics of two coupled elementary cellular automata with complex spatiotemporal dynamics the coupling mechanism characterized by a probability p is stochastic from numerical simulations we find that a sharp transition to full synchronization of the two cellular automata occurs at a critical value of p this transition admits an approximate semianalytical description in terms of the evolution of the difference automaton and is found both for symmetric and asymmetric coupling it is argued that the behavior of cellular automata under coupling may inspire a classification of their individual dynamics s1063 651x 98 51407 9

synchronization of boolean networks with time delays abstract this paper studies analytically synchronization of two deterministic boolean networks with time delays which are unidirectionally coupled in the drive response configuration necessary and sufficient conditions of synchronization are established based on the algebraic representations of logical dynamics in terms of the semi tensor product of matrices the synchronization conditions show that for drive response boolean networks different relations between the inherent state delay and the unidirectional coupling delay may result in distinct synchronization phenomena and both kinds of time delays that ensure synchronization if existent are not unique examples are worked out to illustrate the present results

system decomposition with respect to inputs for boolean control networks abstract in this paper the problem of system decomposition with respect to inputs is investigated for boolean control networks bcns first based on the linear representation of bcns some algebraic equivalent conditions for the decomposability are obtained second the concept of perfect equal vertex partition pevp is proposed for bcns a necessary and sufficient graphical condition for the decomposability i e the existence of a pevp is proposed third for calculating a pevp an algorithm called vertex set uniting algorithm vsua is designed finally a biological example is analyzed to show the effectiveness of the proposed method

cellular automaton model for the simulation of laser dynamics the classical modeling approach for laser study relies on the differential equations in this paper a cellular automaton model is proposed as an alternative for the simulation of population dynamics even though the model is simplified it captures the essence of laser phenomenology i there is a threshold pumping rate that depends inversely on the decaying lifetime of the atoms and the photons and ii depending on these lifetimes and on the pumping rate a constant or an oscillatory behavior can be observed more complex behaviors such as spiking and pattern formation can also be studied with the cellular automaton model

boundary element modelling of flat plate floors under vertical loading the present paper develops a boundary element model for flat plate floors the floor slab is modelled using the shear deformable plate bending theory internal columns or walls are treated using internal collocation technique where three interaction generalized forces are considered at the slab column connection two bending moments in two directions and shear force in the vertical direction such forces are considered to be constant over the column cross sections the present technique takes into account the realistic geometric modelling of the column cross sections the effect of considering such geometry in the analysis of the bending moments transferred from slab to columns is studied several examples including solution of practical building slab are presented the results are compared to those obtained from other numerical methods to demonstrate the accuracy and the reliability of the present formulation the present formulation can be considered as an accurate tool to predict moment transferred from the slab to the column copyright 2004 john wiley sons ltd

boundary integration and interpolation procedures for plate bending in the direct boundary element method dbem for thin plate bending analysis the integration of the kernel shape function products can lead to complications due to a combination of factors the first is the existence of a singularity at the source point leading to the singular kernel which increases in strength as the integral equation is differentiated once for rotation again for moment and yet again for shear the second factor arises from the use of piecewise interpolation polynomials in the first part of the dbem analysis where the unspecified boundary values are computed the numerical procedures are fairly straightforward it is found in this paper that special care must be taken in calculating internal actions at domain points the problems which can be encountered are demonstrated and a modified boundary interpolation procedure is described examples are given which show the superiority of the recommended approach

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

contact between plates by a new direct boundary integral equation formulation abstract the unilateral contact between two plates according to kirchhoff s theory is solved by using a boundary integral equation method a discretization leading to a matrix formulation is proposed to solve this problem an elimination of boundary unknowns is performed an iterative method proves successful with the example treated

correspondence between neural threshold networks and kauffman boolean cellular automata for an asymmetric version of the mcculloch pitts neural network 1943 and for kauffman s infinite range boolean network model 1984 the time evolution of the hamming distances between two different initial configurations are compared in the thermodynamic limit it is shown that in both models phase transitions occur for corresponding values of the transition parameters and that their hamming distances can have the same time evolution leading to quantitatively the same dynamics as known from time dependent landau theory for phase transitions

simultaneous stabilization for a set of boolean control networks abstract this paper investigates simultaneous stabilization of a collection of boolean control networks bcns by using the semi tensor product method and presents a number of new results first an algebraic expression of the bcns is obtained by the semi tensor product based on which some necessary and sufficient conditions are presented to solve the simultaneous stabilization problem by a free control sequence a state feedback control and an output feedback control respectively second using the column stacking form of matrices a new procedure is established to design both state feedback and output feedback controllers for the simultaneous stabilization problem the study of two illustrative examples shows that the new results obtained in this paper are very effective in solving simultaneous stabilization of a collection of bcns

the direct boundary element method in plate bending the direct boundary element method based on the rayleigh green identity is employed for the static analysis of kirchhoff plates the starting point is a slightly modified version of stern s equations the focus is on the implementation of the method for linear elements and a hermitian interpolation for the deflection w the concept of element matrices is developed and the cauchy principal values of the singular integrals are given in detail the treatment of domain integrals the handling of internal supports the properties of the solution and the effect of singularities are discused numerical examples illustrate the various techniques in the appendix the influence functions for the second and third derivatives of the deflection w are given

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

on a time dependent extension of the morse potential a time dependent extension of a morse potential is formulated both the bound and unbound state wave functions are obtained algebraically for the resulting time dependent schrodinger equations based upon the representations of su 2 and su 1 1 respectively the method of r separation of variables is instrumental in the analysis

bounded h_ infty synchronization and state estimation for discrete time varying stochastic complex networks over a finite horizon in this paper new synchronization and state estimation problems are considered for an array of coupled discrete time varying stochastic complex networks over a finite horizon a novel concept of bounded h synchronization is proposed to handle the time varying nature of the complex networks such a concept captures the transient behavior of the time varying complex network over a finite horizon where the degree of bounded synchronization is quantified in terms of the h norm a general sector like nonlinear function is employed to describe the nonlinearities existing in the network by utilizing a timevarying real valued function and the kronecker product criteria are established that ensure the bounded h synchronization in terms of a set of recursive linear matrix inequalities rlmis where the rlmis can be computed recursively by employing available matlab toolboxes the bounded h state estimation problem is then studied for the same complex network where the purpose is to design a state estimator to estimate the network states through available output measurements such that over a finite horizon the dynamics of the estimation error is guaranteed to be bounded with a given disturbance attenuation level again an rlmi approach is developed for the state estimation problem finally two simulation examples are exploited to show the effectiveness of the results derived in this paper

a new boundary integral formulation for stream function and vorticity in axisymmetric stokes flow a boundary integral equation approach is presented to solve the flow stream function and vorticity in the axisymmetric stokes problem without swirl the governing equations expressed in these variables require that the fundamental solutions of the involved differential operators be found the fundamental solutions in a closed form suitable for numerical treatment of integral equations are obtained and their equivalent forms in infinite integral are derived by using fourier and hankel transforms a coupled system of boundary integral equations for the stream function and the vorticity is formulated by employing new fundamental solutions solution of these equations is realized by the collocation method numerical results are included for several bounded and unbounded domain problems to validate and demonstrate the effectiveness of the proposed approach

unilateral buckling of thin elastic plates by the boundary integral equation method the unilateral buckling of thin elastic plates according to kirchhoff s theory is studied by using a boundary integral method a representation for the second member of the equation is given in the matrix formulatiea boundary unknowns are eliminated therefore the unilateral buckling problem reduces to compute the eigenvalues and the eigenvectors of a matrix depending on the contact zone with the rigid foundation an iterative process allows this zone and the buckling load to be computed the capacities of the proposed method are illustrated by four examples

complete synchronization of boolean networks we examine complete synchronization of two deterministic boolean networks bns coupled unidirectionally in the drive response configuration a necessary and sufficient criterion is presented in terms of algebraic representations of bns as a consequence we show that complete synchronization can occur only between two conditionally identical bns when the transition matrix of the drive network is nonsingular two examples are worked out to illustrate the obtained results

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

evaluation of boundary integrals for plate bending the alternative to quadrature as a procedure for dealing with the integrations required in the direct boundary element method dbem is to carry out the integration analytically and code the results directly the potential benefits are efficient computer programs the avoidance of numerical instability and generally better accuracy the technique is developed in this paper serious problems arise when gauss quadrature is employed for the integration of functions which contain or are close to singularities a numerical integration approach may fail at the first stage of the analysis that is during the assembly of the discrete equations or it may fail at the subsequent stage of computing domain points near the boundary the severity of the problem is dependent both on the strength of the singularity and on geometry these points are illustrated with examples

synchronization and maximum lyapunov exponents of cellular automata we study the synchronization of totalistic one dimensional cellular automata ca the ca with a nonzero synchronization threshold exhibit complex nonperiodic space time patterns and vice versa this synchronization transition is related to directed percolation we also study the maximum lyapunov exponent for ca defined analogous to continuous dynamical systems as the exponential rate of expansion of the linear map induced by the evolution rule of ca constructed with the aid of the boolean derivatives the synchronization threshold is strongly correlated to the maximum lyapunov exponent and we propose approximate relations between these quantities the value of this threshold can be used to parametrize the space time complexity of ca

lie algebras for systems with mixed spectra i the scattering poschl teller potential starting from an n body quantum space we consider the lie algebraic framework where the poschl teller hamiltonian 1 2 2 c sech2 s csch2 is the single sp 2 r casimir operator the spectrum of this system is mixed it contains a finite number of negative energy bound states and a positive energy continuum of free states it is identified with the clebsch gordan series of the d d representation coupling the wave functions are the sp 2 r clebsch gordan coefficients of that coupling in the parabolic basis using only lie algebraic techniques we find the asymptotic behavior of these wave functions for the special pure trough potential s 0 we derive thus the transmission and reflection amplitudes of the scattering matrix

r separation of variables for the time dependent hamilton jacobi and schrodinger equations the theory of r separation of variables is developed for the time dependent hamilton jacobi and schrodinger equations on a riemannian manifold v n where time dependent vector and scalar potentials are permitted as an application it is shown how to obtain all r separable coordinates for the n sphere and euclidean n space

redefined observability matrix for boolean networks and distinguishable partitions of state space this paper redefines the observability matrix and defines the observability index for boolean networks bns in the new definition a bn is observable if and only if the observability matrix is of full rank the observability matrix is calculated by a simple algorithm and is applied to the problem of distinguishability of partitions a partition of the state space is said to be distinguishable if any two distinct subsets are distinguishable and the finest distinguishable partition fdp is finer than any other distinguishable partition a necessary and sufficient condition is proposed for checking the distinguishability of any given partition and an algorithm is proposed for calculating the fdp the proposed results are illustrated by examples

synchronization of kauffman networks we analyze the synchronization transition for a pair of coupled identical kauffman networks in the chaotic phase the annealed model for kauffman networks shows that synchronization appears through a transcritical bifurcation and provides an approximate description for the whole dynamics of the coupled networks we show that these analytical predictions are in good agreement with numerical results for sufficiently large networks and study finite size effects in detail preliminary analytical and numerical results for partially disordered networks are also presented

a boundary integral equation method for plate flexure with conditions inside the domain a method for solving boundary value problems for thin plate flexure as described by kirchhoff s theory is proposed an integral formulation leads to a system of boundary integral equations involving values of deflection slope bending moment and transverse shear force along the edge a discretization leading to a matrix formulation is proposed to solve problems with inner conditions in the plate domain an elimination of boundary unknowns proves successful the degenerate case where the boundary is free which leads to a non invertible matrix is investigated three examples illustrate the efficiency of the method

a boundary element method for dynamic plate bending problems abstract in this paper the fundamental solution for kirchhoff plate in the laplace transform domain is deduced and the boundary element formulation is established to study plate bending problem by use of the moment integral equation the dual boundary element equation is developed to solve the cracked plate problem subjected to dynamic loads durbin s laplace transform inversion method is used and the dynamic stress intensity factors are determined by equivalent stress technique an infinite plate containing an isolated crack or two cracks or one set of parallel cracks under heaviside load on the crack surfaces is studied the numerical results obtained demonstrate the efficiency and accuracy of the proposed formulation

model construction of boolean network via observed data in this paper a set of data is assumed to be obtained from an experiment that satisfies a boolean dynamic process for instance the dataset can be obtained from the diagnosis of describing the diffusion process of cancer cells with the observed datasets several methods to construct the dynamic models for such boolean networks are proposed instead of building the logical dynamics of a boolean network directly its algebraic form is constructed first and then is converted back to the logical form firstly a general construction technique is proposed to reduce the size of required data the model with the known network graph is considered motivated by this the least in degree model is constructed that can reduce the size of required data set tremendously next the uniform network is investigated the number of required data points for identification of such networks is independent of the size of the network finally some principles are proposed for dealing with data with errors

symmetry of time dependent schrodinger equations i a classification of time dependent potentials by their maximal kinematical algebras potentials for the time dependent schrodinger equation 1 2 xx v x t x t i t x t are classified according to their space time or kinematical algebras in a search for exactly solvable time dependent models in addition it is shown that their dynamical algebras are isomorphic to their kinematical algebras on the solution space of the schrodinger equation

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

state feedback controller design for the synchronization of boolean networks with time delays abstract state feedback control design to make the response boolean network synchronize with the drive boolean network is far from being solved in the literature motivated by this this paper studies the feedback control design for the complete synchronization of two coupled boolean networks with time delays a necessary condition for the existence of a state feedback controller is derived first then the feedback control design procedure for the complete synchronization of two coupled boolean networks is provided based on the necessary condition finally an example is given to illustrate the proposed design procedure

symmetry of time dependent schrodinger equations ii exact solutions for the equation xx 2i t 2g2 t x2 2g1 t x 2g0 t ψ x t 0 the maximal kinematical algebra of the schrodinger equation xx 2i t 2g2 t x2 2g1 t x 2 g0 t x t 0 is known to be the schrodinger algebra s1 the kinematical symmetries are realized as first order differential operators in the space and time variables a subalgebra g of s1 is chosen and from g and its invariants a complete set of commuting observables are constructed the solution space of the schrodinger equation is identified with the appropriate irreducible representation space of g the wave functions simultaneous eigenvectors of the compatible observables are computed as explicit functions of space and time the properties of a system with a potential v x t g2 t x2 g1 t x g0 t are discussed

robust synchronization of an array of coupled stochastic discrete time delayed neural networks this paper is concerned with the robust synchronization problem for an array of coupled stochastic discrete time neural networks with time varying delay the individual neural network is subject to parameter uncertainty stochastic disturbance and time varying delay where the norm bounded parameter uncertainties exist in both the state and weight matrices the stochastic disturbance is in the form of a scalar wiener process and the time delay enters into the activation function for the array of coupled neural networks the constant coupling and delayed coupling are simultaneously considered we aim to establish easy to verify conditions under which the addressed neural networks are synchronized by using the kronecker product as an effective tool a linear matrix inequality lmi approach is developed to derive several sufficient criteria ensuring the coupled delayed neural networks to be globally robustly exponentially synchronized in the mean square the lmi based conditions obtained are dependent not only on the lower bound but also on the upper bound of the time varying delay and can be solved efficiently via the matlab lmi toolbox two numerical examples are given to demonstrate the usefulness of the proposed synchronization scheme

emergence of complex dynamics in a simple model of signaling networks various physical social and biological systems generate complex fluctuations with correlations across multiple time scales in physiologic systems these long range correlations are altered with disease and aging such correlated fluctuations in living systems have been attributed to the interaction of multiple control systems however the mechanisms underlying this behavior remain unknown here we show that a number of distinct classes of dynamical behaviors including correlated fluctuations characterized by 1 f scaling of their power spectra can emerge in networks of simple signaling units we found that under general conditions complex dynamics can be generated by systems fulfilling the following two requirements i a small world topology and ii the presence of noise our findings support two notable conclusions first complex physiologic like signals can be modeled with a minimal set of components and second systems fulfilling conditions i and ii are robust to some degree of degradation i e they will still be able to generate 1 f dynamics