finite time stability analysis of stochastic switched boolean networks with impulsive effect abstract this paper analyzes the finite time stability of stochastic switched boolean networks sbns with impulsive effect using the algebraic state space representation assr approach the dynamics of sbns with impulsive effect is converted to an algebraic form based on the algebraic form some necessary and sufficient conditions are presented for the finite time stability of stochastic sbns with impulsive effect including probabilistic switching signal case and markov jump switching signal case the study of an illustrative example shows that the obtained new results are effective

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

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

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

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

output regulation of boolean control networks this note investigates the output regulation of boolean control networks bcns by using the semi tensor product of matrices and presents a number of new results firstly based on an algebraic state space representation of bcns a necessary and sufficient condition is presented for the solvability of the output regulation problem secondly an effective method is proposed for the control design of the output regulation problem by using an augmented system approach the study of an illustrative example shows that the obtained new results are effective in dealing with the output regulation of bcns

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

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

control design for output tracking of delayed boolean control networks abstract this paper investigates the output tracking control of delayed boolean control networks dbcns by using the algebraic state space representation method firstly the output tracking control problem of dbcns is formulated and the dynamics of dbcns is converted into an equivalent algebraic form secondly based on the algebraic form and controllability of dbcns a necessary and sufficient condition is presented for the output tracking control of dbcns without state constraints thirdly a necessary and sufficient condition is presented for the output tracking control of dbcns with state constraints by constructing a constrained reachability matrix the study of an illustrative example shows the effectiveness of the obtained new results

disturbance decoupling control design for switched boolean control networks abstract this paper investigates a kind of disturbance decoupling problems ddps for switched boolean control networks bcns that is the disturbance independent output decoupling problem via the semi tensor product of matrices by converting the dynamics of switched bcns into an algebraic form and using the redundant variable separation technique all possible state feedback controllers are designed for the disturbance independent output decoupling problem then based on the obtained state feedback disturbance decoupling controllers and the system s output equation a constructive procedure is proposed to design all possible output feedback disturbance decoupling controllers the study of two illustrative examples shows that the new results obtained in this paper are effective in designing disturbance decoupling controllers for switched bcns

function perturbation impact on feedback stabilization of boolean control networks function perturbation analysis of boolean networks is an important topic in the study of gene regulation due to gene mutation or immeasurable variables this brief studies the function perturbation impact on feedback stabilization of boolean control networks bcns by using the algebraic state space representation approach first the state feedback stabilization control design of bcns is recalled and the function perturbation problem is formulated second given a state feedback stabilizer it is robust to the considered function perturbation if one of the following three cases happens 1 the block where the function perturbation occurs is different from the block which is affected by the state feedback stabilizer case 1 2 when case 1 does not happen the perturbed column converges to the equilibrium faster than the original column case 2 3 when cases 1 and 2 do not happen the perturbed column does not belong to the reachable set of the original column case 3 third when the perturbed column belongs to the reachable set of the original column a constructive procedure is proposed to modify the given state feedback stabilizer to be robust to the function perturbation finally the obtained new results are applied to the function perturbation analysis of lactose operon in escherichia coli the main novelty of this brief is to develop a new theoretical framework for the robustness of feedback controllers of bcns with respect to function perturbation which is not solved in the existing literature

the equivalence issue of two kinds of controllers in boolean control networks abstract in this paper the equivalence issue between state feedback controller and free sequence controller in boolean control network bcn is investigated based on the algebraic representation of boolean networks we prove that a boolean control network can be stabilized to a cycle or a fixed point via free sequence controller if and only if there is a state feedback controller which can derive the boolean control network to the cycle or the fixed point then two algorithms are provided to find the state feedback controller after that we prove that a bcn can be globally controllable by free sequence controller while the bcn is not necessarily globally controllable by state feedback controller at last an example is given to illustrate the results

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

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

asymptotic model matching for nonlinear systems this paper investigates the problem of designing a compensating control law for a square invertible nonlinear plant so that the response of the closed loop system asymptotically matches that of a prescribed driven nonlinear model a set of necessary conditions for achieving asymptotic model matching is established one of these involves the stability properties for subdynamics which are common to every model matching closed loop these subdynamics called the fixed dynamics are intrinsically characterized based on these results a new set of sufficient conditions for achieving asymptotic model matching is given the interrelation between the minimum phase and vector relative degree properties of a plant and a matchable model are studied

convergence theorems for least change secant update methods the purpose of this paper is to present a convergence analysis of least change secant methods in which part of the derivative matrix being approximated is computed by other means the theorems and proofs given here can be viewed as generalizations of those given by broyden dennis more j inst math appl 12 1973 pp 223 246 and by dennis more math comp 28 1974 pp 549 560 the analysis is done in the orthogonal projection setting of dennis schnabel siam rev 21 1980 pp 443 459 and many readers might feel that it is easier to understand the theorems here readily imply local and q superlinear convergence of all the standard methods in addition to proving these results for the first time for the sparse symmetric method of marwil and toint and the nonlinear least squares method of dennis gay welsch

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

on preconditioned uzawa methods and sor methods for saddle point problems this paper studies convergence analysis of a preconditioned inexact uzawa method for nondifferentiable saddle point problems the sor newton method and the sor bfgs method are special cases of this method we relax the bramble pasciak vassilev condition on preconditioners for convergence of the inexact uzawa method for linear saddle point problems the relaxed condition is used to determine the relaxation parameters in the sor newton method and the sor bfgs method furthermore we study global convergence of the multistep inexact uzawa method for nondifferentiable saddle point problems

automata boolean matrices and ultimate periodicity abstract this paper presents a boolean matrix based method to automata theory with an application to the study of regularity preserving functions a new characterization of such functions is derived in terms of the property of ultimate periodicity with respect to powers of boolean matrices this characterization reveals the intrinsic algebraic nature of regularity preserving functions it facilitates a concise proof of known as well as previously unknown properties of regularity preserving functions leading to the solution of the subtraction problem left open by kosaraju

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

state feedback based output tracking control of probabilistic boolean networks abstract this paper studies the state feedback based output tracking control of probabilistic boolean control networks pbcns by using the semi tensor product of matrices a series of reachable sets with probability 1 is defined inductively for pbcns and some useful properties are obtained for the reachable sets based on the properties of the reachable sets a necessary and sufficient condition is presented for the state feedback based output tracking control of pbcns meanwhile a constructive procedure is proposed to design state feedback laws for pbcns to track a constant reference signal the study of two illustrative examples shows that the obtained new results are very effective

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

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

a maximum principle for single input boolean control networks boolean networks have recently been attracting considerable interest as computational models for genetic and cellular networks we consider a mayer type optimal control problem for a single input boolean network and derive a necessary condition for a control to be optimal this provides an analog of pontryagin s maximum principle for single input boolean networks

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

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

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

a survey of full length nonlinear shift register cycle algorithms shift registers have been used to generate sequences of 0 s and 1 s for over thirty years a wide variety of applications has been made of these sequences principally communications have made use of the sequences generated one particular class of shift register sequences for which applications exist is the full length nonlinear shift register sequences these sequences are periodic and of length 2 n and all 2 n different binary n tuples appear exactly one time in a periodic portion of the sequence in this paper we discuss various algorithms which have been suggested for generating these sequences

observability reconstructibility and state observers of boolean control networks the aim of this paper is to introduce and characterize observability and reconstructibility properties for boolean networks and boolean control networks described according to the algebraic approach proposed by d cheng and co authors in the series of papers 3 6 7 and in the recent monography a complete characterization of these properties based both on the boolean matrices involved in the network description and on the corresponding digraphs is provided finally the problem of state observer design for reconstructible bns and bcns is addressed and two different solutions are proposed

filtering for nonlinear genetic regulatory networks with stochastic disturbances in this paper the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition the stochastic perturbation is in the form of a scalar brownian motion and the time delays exist in both the translation process and the feedback regulation process the purpose of the addressed filtering problem is to estimate the true concentrations of the mrna and protein specifically we are interested in designing a linear filter such that in the presence of time delays stochastic disturbances as well as sector nonlinearities the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta by using the linear matrix inequality lmi technique sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model and the filter gain is then characterized in terms of the solution to an lmi which can be easily solved by using standard software packages a simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures

approximation of the constrained joint spectral radius via algebraic lifting this paper studies the linear constrained switching system which is a discrete time switched linear system whose switching sequences are constrained by a deterministic finite automaton the stability of a constrained switching system is characterized by its constrained joint spectral radius that is known to be difficult to compute or approximate using the semi tensor product of matrices the matrix form expression of a constrained switching system is shown to be equivalent to that of a lifted arbitrary switching system then the constrained joint generalized spectral radius of a constrained switching system is proved to be equal to the joint generalized spectral radius of its lifted arbitrary switching system which can be approximated by off the shelf algorithms

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

tensor methods for unconstrained optimization using second derivatives a new type of method for unconstrained optimization called a tensor method is introduced it is related in its basic philosophy to the tensor methods for nonlinear equations for schnabel and frank siam j numer anal 21 1984 pp 815 843 but beyond that the methods have significant differences the tensor method for unconstrained optimization bases each iteration upon a fourth order model of the objective function this model consists of the quadratic portion of the taylor series plus low rank third and fourth order terms that cause the model to interpolate already calculated function and gradient values from one or more previous iterates this paper also shows that the costs of forming storing and solving the tensor model are not significantly more than these costs for a standard method based upon a quadratic taylor series model test results are presented for sets of problems where the hessian at the minimizer is nonsingular and where it is singular on all the test sets the tensor method

mix valued logic based formation control the formation control fc problem is investigated via a mix valued logic based approach first a trajectory tracking algorithm of mix valued logic control networks is proposed then a new formulation of fc problems is established and a feedback control is designed to solve fc problems the mathematical description of partial formation control pfc problems is then designed as a structure of logical networks an interesting practical example of pfc is also presented and discussed in detail

output controllability and optimal output control of state dependent switched boolean control networks in the present paper we investigate the output controllability and optimal output control problems of a state dependent switched boolean control network by using the semi tensor product the algebraic form of the system is obtained then output controllability problems of the system are discussed and some necessary and sufficient conditions are given next the mayer type optimal output control issue is considered and an algorithm is provided to find out the control sequence at last an example is given to show the effectiveness of the main results

a characterisation of the proportional hazards model through a measure of discrimination between two residual life distributions summary a time dependent kullback leibler discrimination function is defined by comparing residual life distributions at each age t it is proved that the resulting kullback leibler discrimination function is constant in t if and only if the two survival distributions satisfy a proportional hazards model let x and y be two nonnegative random variables representing times to failure of two systems let f x pr x x and g y pr y y be the failure distributions of x and y with survival functions f x 1 f x and g y 1 g y respectively where f o g o 1 we assume that f and g are differentiable with densities f t f t and g t g t respectively and hazard rate functions af x f x f x and ag x g x g x the kullback leibler discrimination information i x y or i f g is defined as

on the index of convergence of a class of boolean matrices with structural properties boolean matrices are of prime importance in the study of discrete event systems des which allow us to model systems across a variety of applications the index of convergence i e the number of

confidence intervals for an effect size measure based on the mann whitney statistic part 1 general issues and tail area based methods for two random variables x and y pr y x pr y x is advocated as a general measure of effect size to characterize the degree of separation of their distributions it is estimated by u mn a generalization of the mann whitney u statistic derived by dividing u by the product of the two sample sizes it is equivalent to the area under the receiver operating characteristic curve it is readily visualized in terms of two gaussian distributions with appropriately separated peaks the effect of discretization of a continuous variable is explored tail area based confidence interval methods are developed which can be applied to very small samples or extreme outcomes copyright 2005 john wiley sons ltd

stability analysis for switched boolean networks under arbitrary switching signals this note investigates the stability of switched boolean networks sbns under arbitrary switching signal by using the tool of semi tensor product of matrices first an algebraic expression is given for the sbn via the semi tensor product based on it a necessary and sufficient condition is presented for the switching point reachability of the system second using the switching point reachability the pointwise stabilizability is studied and a necessary and sufficient condition is obtained finally the global stability of sbns under arbitrary switching signal is investigated and an easily verifiable necessary and sufficient condition is presented two illustrative examples are presented to show that the main results are effective in analyzing the stability of sbns

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

neural network based approximate output regulation of discrete time nonlinear systems the existing approaches to the discrete time nonlinear output regulation problem rely on the offline solution of a set of mixed nonlinear functional equations known as discrete regulator equations for complex nonlinear systems it is difficult to solve the discrete regulator equations even approximately moreover for systems with uncertainty these approaches cannot offer a reliable solution by combining the approximation capability of the feedforward neural networks nns with an online parameter optimization mechanism we develop an approach to solving the discrete nonlinear output regulation problem without solving the discrete regulator equations explicitly the approach of this paper can be viewed as a discrete counterpart of our previous paper on approximately solving the continuous time nonlinear output regulation problem

brief paper controllability of boolean control networks via the perron frobenius theory boolean control networks bcns are recently attracting considerable interest as computational models for genetic and cellular networks addressing control theoretic problems in bcns may lead to a better understanding of the intrinsic control in biological systems as well as to developing suitable protocols for manipulating biological systems using exogenous inputs we introduce two definitions for controllability of a bcn and show that a necessary and sufficient condition for each form of controllability is that a certain nonnegative matrix is irreducible or primitive respectively our analysis is based on a result that may be of independent interest namely a simple algebraic formula for the number of different control sequences that steer a bcn between given initial and final states in a given number of time steps while avoiding a set of forbidden states

optimal control of boolean control networks in this paper we address the optimal control problem for boolean control networks bcns we first consider the problem of finding the input sequences that minimize a given cost function over a finite time horizon the problem solution is obtained by means of a recursive algorithm that represents the analogue for bcns of the difference riccati equation for linear systems we prove that a significant number of optimal control problems for bcns can be easily reframed into the present setup in particular the cost function can be adjusted so as to include penalties on the switchings provided that we augment the size of the bcn state variable in the second part of the paper we address the infinite horizon optimal control problem and we provide necessary and sufficient conditions for the problem solvability the solution is obtained as the limit of the solution over the finite horizon 0 t and it is always achieved in a finite number of steps finally the average cost problem over the infinite horizon investigated in optimal control of logical control networks y zhao ieee trans autom control vol 56 no 8 pp 1766 1776 aug 2011 is addressed by making use of the results obtained in the previous sections

divergence estimation of continuous distributions based on data dependent partitions we present a universal estimator of the divergence d p spl par q for two arbitrary continuous distributions p and q satisfying certain regularity conditions this algorithm which observes independent and identically distributed i i d samples from both p and q is based on the estimation of the radon nikodym derivative dp dq via a data dependent partition of the observation space strong convergence of this estimator is proved with an empirically equivalent segmentation of the space this basic estimator is further improved by adaptive partitioning schemes and by bias correction the application of the algorithms to data with memory is also investigated in the simulations we compare our estimators with the direct plug in estimator and estimators based on other partitioning approaches experimental results show that our methods achieve the best convergence performance in most of the tested cases

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

a practical divergence measure for survival distributions that can be estimated from kaplan meier curves this paper introduces a new simple divergence measure between two survival distributions for two groups of patients the divergence measure between their associated survival distributions is based on the integral of the absolute difference in probabilities that a patient from one group dies at time t and a patient from the other group survives beyond time t and vice versa in the case of non crossing hazard functions the divergence measure is closely linked to the harrell concordance index c the mann whitney test statistic and the area under a receiver operating characteristic curve the measure can be used in a dynamic way where the divergence between two survival distributions from time zero up to time t is calculated enabling real time monitoring of treatment differences the divergence can be found for theoretical survival distributions or can be estimated non parametrically from survival data using kaplan meier estimates of the survivor functions the estimator of the divergence is shown to be generally unbiased and approximately normally distributed for the case of proportional hazards the constituent parts of the divergence measure can be used to assess the proportional hazards assumption the use of the divergence measure is illustrated on the survival of pancreatic cancer patients copyright 2016 john wiley sons ltd

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

on robust control invariance of boolean control networks this paper investigates the robust control invariance of boolean control networks bcns via the semi tensor product of matrices firstly based on an algebraic state space representation of bcns two necessary and sufficient conditions are presented to check whether or not a given set is a robust control invariant set under a given state feedback controller secondly by defining a series of suitable sets all possible state feedback gain matrices under which a given set is a robust control invariant set are characterized an illustrative example is presented to demonstrate the obtained new results

further results on feedback stabilization control design of boolean control networks abstract this paper investigates designing all possible feedback stabilizers for boolean control networks bcns some new results on the feedback stabilization control design of bcns are presented the main tool used in the paper is the semi tensor product of matrices first the complete family of reachable sets is defined for bcns then it is shown that all the complete families of reachable sets determine all possible state feedback stabilizers second using all the complete families of reachable sets all possible state feedback stabilizers are obtained third a necessary and sufficient condition is obtained for the existence of output feedback stabilizers based on this condition all possible output feedback stabilizers are designed for bcns finally the obtained new results are applied to the regulation of the lactose operon in escherichia coli

algebraic formulation and topological structure of boolean networks with state dependent delay abstract this paper investigates the algebraic formulation topological structure and set stability of boolean networks with state dependent delay sdd firstly using the algebraic state space representation assr method the dynamics of boolean networks with sdd is converted into an equivalent augmented system secondly based on the equivalent augmented system some necessary and sufficient conditions are presented to calculate fixed points and cycles of boolean networks with sdd thirdly it is proved that the set stability of boolean networks with sdd is equivalent to the set stability of augmented system and a necessary and sufficient condition is presented by constructing a kind of set stability matrix finally the obtained results are applied to the strategy consensus of networked evolutionary games with memories

logical matrix factorization with application to topological structure analysis of boolean network this note investigates the logical matrix factorization with application to the topological structure analysis of boolean networks first the concepts of both factorization and rank are defined for logical matrices and two factorization problems are then studied using nonsingular logical matrix transformations several necessary and sufficient conditions for the factorization of a given logical matrix are presented second the logical matrix factorization is applied to the topological structure analysis of a given boolean network and a size reduced structure equivalent logical network is constructed for the given system it is shown that the topological structure including all the fixed points and cycles of the resulting size reduced logical network is the same as that of the original boolean network the study of an illustrative example shows that the new results presented in this note are effective in analyzing the topological structure of boolean networks

the detection and stabilisation of limit cycle for deterministic finite automata abstractin this paper the topological structure properties of deterministic finite automata dfa under the framework of the semi tensor product of matrices are investigated first the dynamics of dfa are converted into a new algebraic form as a discrete time linear system by means of boolean algebra using this algebraic description the approach of calculating the limit cycles of different lengths is given second we present two fundamental concepts namely domain of attraction of limit cycle and prereachability set based on the prereachability set an explicit solution of calculating domain of attraction of a limit cycle is completely characterised third we define the globally attractive limit cycle and then the necessary and sufficient condition for verifying whether all state trajectories of a dfa enter a given limit cycle in a finite number of transitions is given fourth the problem of whether a dfa can be stabilised to a limit cycle by the state feedback controller is discussed criteri

controllability analysis and control design for switched boolean networks with state and input constraints this paper investigates the controllability analysis and the control design for switched boolean networks sbns with state and input constraints by using the semi tensor product method and presents a number of new results on their controllability optimal control and stabilization first the constrained incidence matrix is proposed for sbns based on which several necessary and sufficient conditions are obtained for the controllability second using the results on the controllability two algorithms are established to design proper switching sequence and controls that minimize the cost functional in a fixed designed shortest termination time third the constrained sbn is converted to an equivalent unconstrained one based on which some necessary and sufficient conditions are presented for the stabilization of the constrained sbn with open loop and closed loop controls respectively finally a practical example of the apoptosis network is studied by using the new results obtained in this paper the s

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 the local convergence of quasi newton methods for constrained optimization we consider the application of a general class of quasi newton methods to the solution of the classical equality constrained nonlinear optimization problem specifically we develop necessary and sufficient conditions for the q superlinear convergence of such methods and present a companion linear convergence theorem the essential conditions relate to the manner in which the hessian of the lagrangian function is approximated

controllability and observability of boolean control networks with time variant delays in states this brief investigates the controllability and observability of boolean control networks with not necessarily bounded time variant delays in states after a brief introduction to converting a boolean control network to an equivalent discrete time bilinear dynamical system via the semi tensor product of matrices the system is split into a finite number of subsystems constructed forest with no time delays by using the idea of splitting time that is proposed in this brief then the controllability and observability of the system are investigated by verifying any so called controllability constructed path and any so called observability constructed paths in the above forest respectively which generalize some recent relevant results matrix test criteria for the controllability and observability are given the corresponding control design algorithms based on the controllability theorems are given we also show that the computing complexity of our algorithm is much less than that of the existing algorithms

fixed point quasi newton methods this article studies iterative methods defined by x k 1 phi x k e k where x k in mathbb r n and e k lie on a space of parameters sufficient conditions are established for local convergence and for convergence at an ideal linear or superlinear rate a theory of least change secant update methods for this class of processes is developed several examples are given showing a wide range of applications of the new theory key words quasi

tensor methods for nonlinear equations a new class of methods for solving systems of nonlinear equations called tensor methods is introduced tensor methods are general purpose methods intended especially for problems where the jacobian matrix at the solution is singular or ill conditioned they base each iteration on a quadratic model of the nonlinear function the standard linear model augmented by a simple second order term the second order term is selected so that the model interpolates function values from several previous iterations as well as the current function value and jacobian the tensor method requires no more function and derivative information per iteration and hardly more storage or arithmetic per iteration than a standard method based on newton s method in extensive computational tests a tensor algorithm is significantly more efficient than a similar algorithm based on the standard linear model both on standard nonsingular test problems and on problems where the jacobian at the solution is singular

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

identification of boolean control networks in this paper the identification of boolean control networks is addressed first necessary and sufficient conditions are obtained for the identification of state equation from input state data then a necessary and sufficient condition for a controllable boolean network to be observable is presented based on these two results a necessary and sufficient condition for the identification from input output data is achieved to practically identify the model a numerical algorithm is proposed two particular cases i identification of systems with a known network graph ii identification of a higher order boolean network are also investigated finally the approximate identification for large size networks is explored

parallel projection methods and the resolution of ill posed problems abstract in this paper we consider a modification of the parallel projection method for solving overdetermined nonlinear systems of equations introduced recently by diniz ehrhardt and martinez 1 this method is based on the classical cimmino s algorithm for solving linear systems the components of the function are divided into small blocks as an attempt to correct the intrinsic ill conditioning of the system and the new iteration is a convex combination of the projections onto the linear manifolds defined by different blocks the modification suggested here was motivated by the application of the method to the resolution of a nonlinear fredholm first kind integral equation we prove convergence results and we report numerical experiments

team theory and person by person optimization with binary decisions in this paper we extend the notion of person by person pbp optimization to binary decision spaces the novelty of our approach is the adaptation to a dynamic team context of notions borrowed from the pseudo boolean optimization field as completely local global or unimodal functions and submodularity we also generalize the concept of pbp optimization to the case where groups of m decisions makers make joint decisions sequentially which we refer to as m b m optimization the main contribution is a description of sufficient conditions verifiable in polynomial time under which a pbp or an m b m optimization algorithm converges to the team optimum as a second contribution we present a local and greedy algorithm characterized by approximate decision strategies i e strategies based on a local state vector that return the same decisions as in the complete information framework where strategies are based on full state vector as a last contribution we also show that there exists a subclass of

probabilistic index an intuitive non parametric approach to measuring the size of treatment effects effect sizes es tell the magnitude of the difference between treatments and ideally should tell clinicians how likely their patients will benefit from the treatment currently used es are expressed in statistical rather than in clinically useful terms and may not give clinicians the appropriate information we restrict our discussion to studies with two groups one with n patients receiving a new treatment and the other with m patients receiving the usual or no treatment the standardized mean difference e g cohen s d is a well known index for continuous outcomes there is some intuitive value to d but measuring improvement in standard deviations sd is a statistical concept that may not help a clinician how much improvement is a half sd a more intuitive and simple to calculate es is the probability that the response of a patient given the new treatment x is better than the one for a randomly chosen patient given the old or no treatment y i e p x y larger values meaning better outcomes this probability has an immediate identity with the area under the curve auc measure in procedures for receiver operator characteristic roc curve comparing responses to two treatments it also can be easily calculated from the mann whitney u wilcoxon or kendall statistics we describe the characteristics of an ideal es we propose p x y as an alternative index summarize its correspondence with well known non parametric statistics compare it to the standardized mean difference index and illustrate with clinical data copyright 2005 john wiley sons ltd

brief paper complete controllability of impulsive stochastic integro differential systems this paper is concerned with the controllability of impulsive stochastic integro differential systems sufficient conditions of complete controllability for impulsive stochastic integro differential systems are obtained by using schaefer s fixed point theorem a numerical example is provided to show the effectiveness of the proposed results

stochastic stability and stabilization of n person random evolutionary boolean games abstract this paper studies the stochastic stability and stabilization of n person random evolutionary boolean games rebg firstly the n person rebg is converted to an algebraic form by using the semi tensor product of matrices secondly a necessary and sufficient condition is presented for the stochastic stability of n person rebg based on the algebraic form thirdly a constructive procedure is proposed for the state feedback stochastic stabilization control design of n person rebg by defining a series of stochastic reachable sets finally two illustrative examples are worked out to show the effectiveness of the obtained new results

an improved criterion for controllability of boolean control networks this paper tackles the controllability problem of boolean control networks bcns by resorting to the semi tensor product technique and the warshall algorithm several improved novel reachability and controllability criteria are obtained for the bcns through constructing a sequence of rigorous boolean matrices controllability matrix of the considered bcns is derived iteratively it is worth pointing out that the proposed method has lower computational complexity and thus facilitates the reachability and controllability analysis for bcns in addition the issue concerning controllability of bcns with undesirable interior states is investigated by checking a set of designated boolean matrices finally to test the effectiveness of the obtained theoretical results a genetic network model known as the lambda switch is used as an example for numerical simulation

minimum time control of boolean networks boolean networks bns are discrete time dynamical systems with boolean state variables bns have recently been attracting considerable interest as computational models for biological systems and in particular gene regulating networks boolean control networks bcns are boolean networks with boolean inputs we consider the problem of steering a bcn from a given state to a desired state in minimal time using the algebraic state space representation assr of bcns we derive several necessary conditions stated in the form of maximum principles mps for a control to be time optimal in the assr every state and input vector is a canonical vector using this special structure yields an explicit state feedback formula for all time optimal controls to demonstrate the theoretical results we develop a bcn model for the genetic switch controlling the lambda phage development upon infection of a bacteria our results suggest that this biological switch is designed in a way that guarantees minimal time respon

policy iteration algorithm for optimal control of stochastic logical dynamical systems this brief investigates the infinite horizon optimal control problem for stochastic multivalued logical dynamical systems with discounted cost applying the equivalent descriptions of stochastic logical dynamics in term of markov decision process the discounted infinite horizon optimal control problem is presented in an algebraic form then employing the method of semitensor product of matrices and the increasing dimension technique a succinct algebraic form of the policy iteration algorithm is derived to solve the optimal control problem to show the effectiveness of the proposed policy iteration algorithm an optimization problem of p53 mdm2 gene network is investigated

necessary and sufficient conditions for asymptotic model matching of switching linear systems this paper investigates the problem of designing a feedback controller to force the response of a given plant to match asymptotically that of a prescribed model in case both the plant and the model are switching linear systems matching has to be achieved with stability of the feedback loop for any initial conditions of the plant the model and the controller in case it is dynamic and for any choice of the switching law solvability of the problem is characterized in terms of necessary and sufficient conditions that in part refer to the geometric structure of the difference system which compares the output of the model and of the plant stability is considered both for slow switching and for arbitrary switching proofs of the solvability conditions provide viable procedures for synthesizing the static or dynamic controllers that achieve the matching respectively when the state of the model is measurable and when it is not weaker sufficient conditions that can be practically checked by simple algorithmic procedures are provided both in the general situation and under slightly restrictive hypotheses

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

estimation of the average hazard ratio summary simple estimators of the average hazard ratio are obtained for the two sample problem with censored failure time data these estimators are compared with estimators arising out of the partial likelihood within the proportional hazards class efficiency results are found to be generally quite favourable provided the hazard ratio is not too large some comments are made on extensions to the k sample problem

monitoring a general class of two sample survival statistics with applications summary this paper considers a general class of statistics for testing the equality of two survival distributions in clinical trials with sequential monitoring the tests can be expressed as lebesgue stieltjes integrals of a weight function with respect to the difference between two survival distributions prominent members of this class include the two sample difference in kaplan meier estimates the test of medians brookmeyer crowley 1982 a truncated version of efron s 1967 test and the pepe fleming statistic pepe fleming 1989 1991 statistics in this class are shown to converge to a gaussian process indexed by information time under both null and local alternatives even if different statistics are used at different information times properly standardised statistics in a subclass converge to gaussian processes with independent increments so that the usual group sequential techniques for monitoring a clinical trial can be applied the design of a trial comparing two treatments with respect to mother to newborn transmission of hiv is used to illustrate practical aspects of monitoring

output tracking control of boolean control networks via state feedback this paper investigates the state feedback based output tracking control of boolean control networks bcns with a constant reference signal by using the semi tensor product method based on the algebraic expression of bcns and by constructing a series of reachable sets a general procedure is proposed for the design of the state feedback laws for bcns to track a constant reference signal the study of an illustrative example shows that the obtained new results are effective in designing state feedback based output tracking controllers for bcns to track a constant reference signal

bi decomposition of multi valued logical functions and its applications abstract the bi decomposition of multi valued logical mvl functions including disjoint and non disjoint cases is considered using a semi tensor product an mvl function can be expressed in its algebraic form based on this form straightforward verifiable necessary and sufficient conditions are provided for each case respectively the constructive proofs also lead to constructing corresponding decompositions using these results the implicit function theorem ift of k valued functions as a special bi decomposition is obtained finally as an application the normalization of dynamic algebraic d a boolean networks is investigated using ift of k valued functions

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

the estimation of average hazard ratios by weighted cox regression often the effect of at least one of the prognostic factors in a cox regression model changes over time which violates the proportional hazards assumption of this model as a consequence the average hazard ratio for such a prognostic factor is under or overestimated while there are several methods to appropriately cope with non proportional hazards in particular by including parameters for time dependent effects weighted estimation in cox regression is a parsimonious alternative without additional parameters the methodology which extends the weighted k sample logrank tests of the tarone ware scheme to models with multiple binary and continuous covariates has been introduced in the nineties of the last century and is further developed and re evaluated in this contribution the notion of an average hazard ratio is defined and its connection to the effect size measure p x y is emphasized the suggested approach accomplishes estimation of intuitively interpretable average hazard ratios and provides tools for inference a monte carlo study confirms the satisfactory performance advantages of the approach are exemplified by comparing standard and weighted analyses of an international lung cancer study sas and r programs facilitate application

matrix approach to model matching of asynchronous sequential machines in this note we propose a matrix based approach for asynchronous sequential machines using semi tensor product of matrices we convert an asynchronous machine into a discrete time bilinear system and study its dynamics by investigating its structure matrices we give simple algorithms for cycle detection and reachability analysis and moreover provide a control design method for the model matching of two input state machines

model matching for finite state machines the problem of model matching for finite state machines fsms consists of finding a controller for a given open loop system so that the resulting closed loop system matches a desired input output behavior in this paper a set of model matching problems is addressed strong model matching where the reference model and the plant are deterministic fsms and the initial conditions are fixed strong model matching with measurable disturbances where disturbances are present in the plant and strong model matching with nondeterministic reference model where any behavior out of those in the reference model has to be matched by the closed loop system necessary and sufficient conditions for the existence of controllers for all these problems are given a characterization of all feasible control laws is derived and an efficient synthesis procedure is proposed further the well known supervisory control problem for discrete event dynamical systems dedss formulated in its basic form is shown to be solvable as a strong model matching problem with measurable disturbances and nondeterministic reference model

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