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

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

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

global solvability of a free boundary three dimensional incompressible viscoelastic fluid system with surface tension motivated by beale commun pure appl math 34 359 392 1981 arch ration mech anal 84 307 352 1983 1984 we investigate the global well posedness of a free boundary problem of a three dimensional incompressible viscoelastic fluid system in an infinite strip and with surface tension on the upper free boundary provided that the initial data is sufficiently close to the equilibrium state

exponential decay of benard convection problem with surface tension abstract we consider the dynamics of an boussinesq approximation benard convection fluid evolving in a three dimensional domain bounded below by a fixed flatten boundary and above by a free moving surface the domain is horizontally periodic and the effect of the surface tension is on the free surface by developing a priori estimates for the model we prove the exponential decay of solutions in the framework of high regularity

local existence theorems for the first and second initial boundary value problems for a weakly non newtonian fluid we prove an existence and uniqueness theorem for three dimensional motions of a certain class of simple incompressible materials the constitutive equation is assumed to have in addition to a newtonian part a viscoelastic part given by a smooth bounded functional of the history of the displacement gradient both displacement and traction boundary conditions are considered

observability of boolean networks via matrix equations from the new perspective of logical matrix equations observability of boolean networks bns is investigated in this paper first it is shown that one bn is locally observable on the set of reachable states if and only if the constructed matrix equations have a unique canonical solution then combining with an equivalence relation a novel condition is established to verify global observability finally an example is worked out to illustrate the obtained results

general purpose computation with neural networks a survey of complexity theoretic results we survey and summarize the literature on the computational aspects of neural network models by presenting a detailed taxonomy of the various models according to their complexity theoretic characteristics the criteria of classification include the architecture of the network feedforward versus recurrent time model discrete versus continuous state type binary versus analog weight constraints symmetric versus asymmetric network size finite nets versus infinite families and computation type deterministic versus probabilistic among others the underlying results concerning the computational power and complexity issues of perceptron radial basis function winner take all and spiking neural networks are briefly surveyed with pointers to the relevant literature in our survey we focus mainly on the digital computation whose inputs and outputs are binary in nature although their values are quite often encoded as analog neuron states we omit the important learning issues

state space analysis of boolean networks this paper provides a comprehensive framework for the state space approach to boolean networks first it surveys the authors recent work on the topic using semitensor product of matrices and the matrix expression of logic the logical dynamic equations of boolean control networks can be converted into standard discrete time dynamics to use the state space approach the state space and its subspaces of a boolean network have been carefully defined the basis of a subspace has been constructed particularly the regular subspace y friendly subspace and invariant subspace are precisely defined and the verifying algorithms are presented as an application the indistinct rolling gear structure of a boolean network is revealed

observability of boolean networks a graph theoretic approach boolean networks bns are discrete time dynamical systems with boolean state variables and outputs bns are recently attracting considerable interest as computational models for genetic and cellular networks we consider the observability of bns that is the possibility of uniquely determining the initial state given a time sequence of outputs our main result is that determining whether a bn is observable is np hard this holds for both synchronous and asynchronous bns thus unless p np there does not exist an algorithm with polynomial time complexity that solves the observability problem we also give two simple algorithms with exponential complexity that solve this problem our results are based on combining the algebraic representation of bns derived by d cheng with a graph theoretic approach some of the theoretical results are applied to study the observability of a bn model of the mammalian cell cycle

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

brief paper controllability of probabilistic boolean control networks this paper deals with the controllability of probabilistic boolean control networks first a survey on the semi tensor product approach to probabilistic boolean networks is given second the controllability of probabilistic boolean control networks via two kinds inputs is studied finally examples are given to show the efficiency of the obtained results

a finite element analysis of a linearized problem of the navier stokes equations with surface tension a finite element analysis is performed for a stationary linearized problem of the navier stokes equations with surface tension since the surface tension brings about a second order derivative of the velocity in the boundary condition the velocity space is equipped with a stronger topology than in the conventional case under the strong topology conditions of the uniform solvability and the approximation are verified on some pairs of finite element spaces for the velocity and the pressure thus an optimal error estimate is derived some numerical results are shown which agree well with theoretical ones

fitting semi markov models to interval censored data with unknown initiation times in a semi markov model the hazard of making a transition between stages depends on the time spent in the current stage but is independent of time spent in other stages if the initiation time time of entry into the network is not known for some persons and if transition time data are interval censored i e if transition times are not known exactly but are known only to have occurred in some interval then the length of time these persons spent in any stage is not known we show how a semi markov model can still be fit to interval censored data with missing initiation times for the special case of models in which all persons enter the network at the same initial stage and proceed through the same succession of stages to a unique absorbing stage we present discrete time nonparametric maximum likelihood estimators of the waiting time distributions for this type of data

the analysis of panel data under a markov assumption abstract methods for the analysis of panel data under a continuous time markov model are proposed we present procedures for obtaining maximum likelihood estimates and associated asymptotic covariance matrices for transition intensity parameters in time homogeneous models and for other process characteristics such as mean sojourn times and equilibrium distributions generalizations to handle covariance analysis and to the fitting of certain nonhomogeneous models are presented and an example based on a longitudinal study of the smoking habits of school children is discussed questions of embeddability and estimation are examined

realization of boolean control networks based on the linear expression of the dynamics of boolean networks the coordinate transformation of boolean variables is defined it follows that the state space coordinate transformation for the dynamics of boolean networks is revealed using it the invariant subspace for a boolean control network is defined then the structure of a boolean control network is analyzed and the controllable and observable normal forms and the kalman decomposition form are presented finally the realization problem including minimum realization of boolean control networks is investigated

optimal control of logical control networks this paper considers the infinite horizon optimal control of logical control networks including boolean control networks as a special case using the framework of game theory the optimal control problem is formulated in the sight of the algebraic form of a logical control network its cycles can be calculated algebraically then the optimal control is revealed over a certain cycle when the games using memory 1 which means the players only consider previous steps action at each step are considered the higher order logical control network is introduced and its algebraic form is also presented which corresponds to a conventional logical control network i e 1 then it is proved that the optimization technique developed for conventional logical control networks is also applicable to this memory case

global regularity of 2d density patches for inhomogeneous navier stokes this paper is about lions open problem on density patches lions in mathematical topics in fluid mechanics vol 1 volume 3 of oxford lecture series in mathematics and its applications clarendon press oxford university press new york 1996 whether or not inhomogeneous incompressible navier stokes equations preserve the initial regularity of the free boundary given by density patches using classical sobolev spaces for the velocity we first establish the propagation of c 1 gamma regularity with 0 gamma 1 in the case of positive density furthermore we go beyond this to show the persistence of a geometrical quantity such as the curvature in addition we obtain a proof for c 2 gamma regularity

aggregation algorithm towards large scale boolean network analysis the analysis of large scale boolean network dynamics is of great importance in understanding complex phenomena where systems are characterized by a large number of components the computational cost to reveal the number of attractors and the period of each attractor increases exponentially as the number of nodes in the networks increases this paper presents an efficient algorithm to find attractors for medium to large scale networks this is achieved by analyzing subnetworks within the network in a way that allows to reveal the attractors of the full network with little computational cost in particular for each subnetwork modeled as a boolean control network the input state cycles are found and they are composed to reveal the attractors of the full network the proposed algorithm reduces the computational cost significantly especially in finding attractors of short period or any periods if the aggregation network is acyclic also this paper shows that finding the best acyclic aggregation is equivalent to finding the strongly connected components of the network graph finally the efficiency of the algorithm is demonstrated on two biological systems namely a t cell receptor network and an early flower development network

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

discrete time nonparametric estimation for semi markov models of chain of events data subject to interval censoring and truncation chain of events data are longitudinal observations on a succession of events that can only occur in a prescribed order one goal in an analysis of this type of data is to determine the distribution of times between the successive events this is difficult when individuals are observed periodically rather than continuously because the event times are then interval censored chain of events data may also be subject to truncation when individuals can only be observed if a certain event in the chain e g the final event has occurred we provide a nonparametric approach to estimate the distributions of times between successive events in discrete time for data such as these under the semi markov assumption that the times between events are independent this method uses a self consistency algorithm that extends turnbull s algorithm 1976 journal of the royal statistical society series b 38 290 295 the quantities required to carry out the algorithm can be calculated recursively for improved computational efficiency two examples using data from studies involving hiv disease are used to illustrate our methods

symbolic dynamics of boolean control networks we consider boolean control networks bcns and in particular boolean networks bns in the framework of symbolic dynamics sd we show that the set of state space trajectories of a bcn is a shift space of finite type sft this observation allows us to extend two important analysis tools from sd namely the artin mazur zeta function and the topological entropy to bns and bcns some of the theoretical results are illustrated using a bcn model of the core network regulating the mammalian cell cycle

semi markov models with phase type sojourn distributions continuous time multistate models are widely used for categorical response data particularly in the modeling of chronic diseases however inference is difficult when the process is only observed at discrete time points with no information about the times or types of events between observation times unless a markov assumption is made this assumption can be limiting as rates of transition between disease states might instead depend on the time since entry into the current state such a formulation results in a semi markov model we show that the computational problems associated with fitting semi markov models to panel observed data can be alleviated by considering a class of semi markov models with phase type sojourn distributions this allows methods for hidden markov models to be applied in addition extensions to models where observed states are subject to classification error are given the methodology is demonstrated on a dataset relating to development of bronchiolitis obliterans syndrome in post lung transplantation patients

stability and stabilization of boolean networks with impulsive effects abstract this paper investigates the stability and stabilization of boolean networks with impulsive effects after giving a survey on semi tensor product of matrices we convert a boolean network with impulsive effects into impulsive discrete time dynamics then some necessary and sufficient conditions are given for the stability and stabilization of boolean networks with impulsive effects finally examples are provided to illustrate the efficiency of the obtained results

on controllability of delayed boolean control networks this paper is devoted to studying the trajectory and state controllability of boolean control networks bcns with time delay in contrast to bcns without time delay the dynamics of delayed bcns are determined by a sequence of initial states named here trajectories trajectory controllability means that there exists a control signal steering a system from an initial trajectory to a desired trajectory while state controllability means that there exists a control signal steering an initial state to a given state here both trajectory controllability and state controllability will be studied it should be noted that in this paper trajectory controllability does not mean tracking or following a given trajectory in fact it means to control bcns to a destination trajectory of length mu at the k th step using the semi tensor product of matrices the delayed bcns are first converted into an equivalent algebraic description and then some necessary and sufficient conditions are derived for the trajecto

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

on boolean control networks with maximal topological entropy boolean control networks bcns are discrete time dynamical systems with boolean state variables and inputs that are interconnected via boolean functions bcns are recently attracting considerable interest as computational models for genetic and cellular networks with exogenous inputs the topological entropy of a bcn with m inputs is a nonnegative real number in the interval 0 m log 2 roughly speaking a larger topological entropy means that asymptotically the control is more powerful we derive a necessary and sufficient condition for a bcn to have the maximal possible topological entropy our condition is stated in the framework of cheng s algebraic state space representation of bcns this means that verifying this condition incurs an exponential time complexity we also show that the problem of determining whether a bcn with n state variables and m n inputs has a maximum topological entropy is np hard suggesting that this problem cannot be solved in general using a polynomial time algorithm

a remark on scalar equations for synchronous boolean networks with biological applications by c farrow j heidel j maloney and j rogers the problem of finding all cycles in the exponentially growing state space of synchronous boolean networks was studied in the paper by c farrow j heidel j maloney and j r scalar equations for synchronous boolean networks with biological applications ieee trans neural networks vol 15 no 2 pp 348 354 mar 2004 no efficient algorithm was given to solve the problem we show that even the determination of the number of fixed points cycles of length 1 for monotone boolean networks and the determination of the existence of fixed points for general boolean networks are both strong np complete

global solvability of the navier stokes equations with a free surface in the maximal lp lq regularity class abstract we consider the motion of incompressible viscous fluids bounded above by a free surface and below by a solid surface in the n dimensional euclidean space for n 2 the aim of this paper is to show the global solvability of the navier stokes equations with a free surface describing the above mentioned motion in the maximal l p l q regularity class our approach is based on the maximal l p l q regularity with exponential stability for the linearized equations and also it is proved that solutions to the original nonlinear problem are exponentially stable

small time existence for the three dimensional navier stokes equations for an incompressible fluid with a free surface in 1980 beale 2 studied the problem of describing the motion of a layer of heavy viscous incompressible fluid lying above an infinite rigid bottom and having a non compact free surface with no surface tension he proved its local solvability in an anisotropic sobolev space for any initial data its global solvability was discussed by sylv sxer 20 but a crucial point of her proof does not appear clear to me the regularity of the free surface with surface tension taken into account beale 31 and beale nishida 4 respectively studied the large time existence and regularity and the large time behavior of the solution to this problem with initial data near equilibrium teramoto 24 25 considered these problems for fluids lying above an inclined plane for any initial data the same problem was solved locally in time by allain 11 in the two dimensional case the aim of this paper is to establish the analogous result in the three dimensional case a similar problem describing the motion of a finite isolated mass of incompressible viscous fluid was studied thoroughly by solonnikov he proved local solvability in a h61der space in 12 and global solvability in the space w 2 1 p n where n is the dimension of the domain in 16 without surface tension and in 13 15 17 19 21 with surface tension let us formulate our problem given an initial domain f r 3 with x3 being the vertical component and an initial velocity vector field vo in f we want to know the domain f t t 0 occupied by the fluid which is bounded by the fixed bottom sb and the free surface se t the velocity vector field v v x t vl v2 v3 and the pressure p p x t so that

discontinuous galerkin method for coupling hydrostatic free surface flows to saturated subsurface systems abstract we formulate a coupled surface subsurface flow model that relies on hydrostatic equations with free surface in the free flow domain and on darcy s law in the subsurface the model is discretized using the local discontinuous galerkin method and a statement of discrete energy stability is proved for the fully non linear coupled system the performance of the proposed scheme is illustrated by a numerical convergence study and a realistic example

state feedback stabilization for probabilistic boolean networks abstract a probabilistic boolean network pbn is a discrete time system composed of a family of boolean networks bns between which the pbn switches in a stochastic fashion studying control related problems in pbns may provide new insights into the intrinsic control in biological systems and enable us to develop strategies for manipulating complex biological systems using exogenous inputs this paper investigates the problem of state feedback stabilization for pbns based on the algebraic representation of logic functions a necessary and sufficient condition is derived for the existence of a globally stabilizing state feedback controller and a control design method is proposed when the presented condition holds it is shown that the controller designed via the proposed procedure can simultaneously stabilize a collection of pbns that are composed of the same constituent bns

disturbance decoupling of boolean control networks disturbance decoupling problem ddp of boolean control networks is considered using semi tensor product of matrices and the matrix expression of logical functions a working procedure is proposed to solve the problem this procedure consists of two key design steps first how to convert a system into an output friendly coordinate frame an algorithm is provided to calculate the output friendly subspaces secondly it was shown how to find proper controllers to solve the problem if it is solvable a state variable separation form is introduced to guide the design of controllers based on the design technique necessary and sufficient conditions are obtained for the solvability of ddp