asymptotical stability of probabilistic boolean networks with state delays this paper devotes to establishing a bridge between asymptotical stability of a probabilistic boolean network pbn and a solution to its induced equations which are induced from the pbn s transition matrix by utilizing the semitensor product technique routinely the dynamics of a pbn with coincident state delays can be equivalently converted into that of a higher dimensional pbn without delays subsequently several novel stability criteria are derived from the standpoint of equations solution the most significant finding is that a pbn is globally asymptotically stable at a predesignated one point distribution if and only if a vector obtained by adding 1 at the bottom of this distribution is the unique nonnegative solution to pbn s induced equations moreover the influence of coincident state delays on pbn s asymptotical stability is explicitly analyzed without consideration of the convergence rate consequently such bounded state delays are verified to have no impact on pbn s stability albeit delays are time varying based on this worthwhile observation the time computational complexity of the aforementioned approach can be reduced by removing delays directly furthermore this universal procedure is summarized to reduce the time complexity of some previous results in the literature to a certain extent two examples are employed to demonstrate the feasibility and effectiveness of the obtained theoretical results

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

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

state analysis of boolean control networks with impulsive and uncertain disturbances in this paper we put forward a method for the state analysis of boolean control networks with impulsive and uncertain disturbances in detail we introduce the probability in the analysis of the state of boolean networks mathematically the stp as the analytical tool has be used for the modeling of uncertainty in addition we give a mathematical proof for the model lastly we conduct some simulations which validate the efficiency for this model

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

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

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

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

modulation of estimators and confidence sets an unknown signal plus white noise is observed at n discretetime points within a large convex class of linear estimators of the signal we choose the one which minimizes estimated quadratic risk by construction the resulting estimator is nonlinear this estimation is done after orthogonal transformation of the data to a reasonable coordinate system the procedure adaptively tapers the coefficients of the transformed data if the class of candidate estimators satisfies a uniform entropy condition then our estimator is asymptotically minimax in pinsker s sense over certain ellipsoids in the parameter space and dominates the james stein estimatorasymptotically we describe computational algorithms for the modulation estimator and construct confidence sets for the unknown signal these confidence sets are centered at the estimator have correctasymptotic coverage probability and have relatively small risk asset valued estimators of the signal

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

optimal infinite horizon control for probabilistic boolean networks external control of a genetic regulatory network is used for the purpose of avoiding undesirable states such as those associated with disease heretofore intervention has focused on finite horizon control i e control over a small number of stages this paper considers the design of optimal infinite horizon control for context sensitive probabilistic boolean networks pbns it can also be applied to instantaneously random pbns the stationary policy obtained is independent of time and dependent on the current state this paper concentrates on discounted problems with bounded cost per stage and on average cost per stage problems these formulations are used to generate stationary policies for a pbn constructed from melanoma gene expression data the results show that the stationary policies obtained by the two different formulations are capable of shifting the probability mass of the stationary distribution from undesirable states to desirable ones

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

sampled data state feedback stabilization of boolean control networks in this letter we investigate the sampled data state feedback control sdsfc problem of boolean control networks bcns some necessary and sufficient conditions are obtained for the global stabilization of bcns by sdsfc different from conventional state feedback controls new phenomena observed the study of sdsfc based on the controllability matrix we derive some necessary and sufficient conditions under which the trajectories of bcns can be stabilized to a fixed point by piecewise constant control pcc it is proved that the global stabilization of bcns under sdsfc is equivalent to that by pcc moreover algorithms are given to construct the sampled data state feedback controllers numerical examples are given to illustrate 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

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

brief paper an integer programming approach to optimal control problems in context sensitive probabilistic boolean networks a boolean network is one of the models of biological networks such as gene regulatory networks and has been extensively studied in particular a probabilistic boolean network pbn is well known as an extension of boolean networks but in the existing methods to solve the optimal control problem of pbns it is necessary to compute the state transition diagram with 2 n nodes for a given pbn with n states to avoid this computation an integer programming based approach is proposed for a context sensitive pbn cs pbn which is a general form of pbns in the proposed method a cs pbn is transformed into a linear system with binary variables and the optimal control problem is reduced to an integer linear programming problem by a numerical example the effectiveness of the proposed method is shown

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

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

a minimum time control for boolean control networks with impulsive disturbances this paper investigates a mayer type optimal control and minimum time control of a boolean control network bcn with impulsive disturbances using the semi tensor product the bcn with impulsive disturbances is converted into algebraic discrete time impulsive dynamic systems and several necessary conditions for optimality are derived then we consider the problem of steering a bcn with impulsive disturbances from a given initial state to a desired state in minimal time and a necessary condition stated in the form of maximum principle is obtained for a control to be time optimal it shows that the impulsive disturbances play an important role in the optimal control problem for bcns at last a biological example is given to illustrate the effectiveness and advantage of the obtained results

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

bisimulations of boolean control networks a framework for analyzing bisimulation relations of boolean control networks bcns is set up in this paper bisimulation relations are natural objectives in control systems theory a bisimulation relation between a pair of control systems defines a relation on their state spaces or state sets explaining how a trajectory or transition of one system can be paired with a trajectory or transition of the other system and vice versa the paper first formalizes the notion of bi simulation in bcns and presents detailed results characterizing bi simulation relations for bcns then as an application of the notion of bisimulation it considers the propagation of the fundamental properties of macro controllability and stabilizability through a bisimulation relation it thereby suggests the possibility that certain control properties of a bcn can be inferred by analyzing a potentially simpler bcn the analysis developed in this paper is based on the semitensor product approach which gives algorithms that have e

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

on reducible state variables of logical control networks abstract reducible state variables are important for the study of reduced order observer and control design of logical control networks lcns this paper studies the number of reducible state variables of lcns based on the upper bound of reducible state variables several sufficient necessary conditions are presented for the number of reducible state variables in addition using the regular subspace theory the coordinate transformation as well as the swap matrix are constructed and some new criteria are proposed to calculate reducible state variables

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

reachability of higher order logical control networks via matrix method this paper investigates the reachability of higher order logical control networks first with semi tensor product method the matrix expression of a higher order logical control network is given then a partitioned matrix is constructed which intuitively shows the input state mapping information with this matrix some conditions are obtained for the reachability of higher order logical control networks finally an algorithm is designed to find control sequences that drive a given initial state to a given destination state

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

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

confidence balls in gaussian regression starting from the observation of an r n gaussian vector of mean f and covariance matrix sigma 2 i n i n is the identity matrix we propose a method for building a euclidean confidence ball around f with prescribed probability of coverage for each n we describe its nonasymptotic property and show its optimality with respect to some criteria

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

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

adaptive wavelet estimation a block thresholding and oracle inequality approach we study wavelet function estimation via the approach of block thresh olding and ideal adaptation with oracle oracle inequalities are derived and serve as guides for the selection of smoothing parameters based on an oracle inequality and motivated by the data compression and localization properties of wavelets an adaptive wavelet estimator for nonparametric re gression is proposed and the optimality of the procedure is investigated we show that the estimator achieves simultaneously three objectives adaptiv ity spatial adaptivity and computational efficiency specifically it is proved that the estimator attains the exact optimal rates of convergence over a range of besov classes and the estimator achieves adaptive local minimax rate for estimating functions at a point the estimator is easy to imple ment at the computational cost of on simulation shows that the es timator has excellent numerical performance relative to more traditional wavelet estimators 1 introduction wavelet methods have demonstrated considerable suc cess in nonparametric function estimation in terms of spatial adaptivity com putational efficiency and asymptotic optimality in contrast to the traditional linear procedures wavelet methods achieve near optimal convergence rates over large function classes such as besov classes and enjoy excellent mean squared error properties when used to estimate functions that are spatially inhomogeneous for example as shown by donoho and johnstone 1998 wavelet methods can outperform optimal linear methods even at the level of convergence rate over certain besov classes standard wavelet methods achieve adaptivity through term by term thresholding of the empirical wavelet coefficients there each individual empirical wavelet coefficient is compared with a predetermined threshold a wavelet coefficient is retained if its magnitude is above the threshold level and is discarded otherwise a well known example of term by term thresholding is donoho and johnstone s visushrink donoho and johnstone 1994 visushrink is spatially adaptive and the estimator is within a log arithmic factor of the optimal convergence rate over a wide range of besov classes visushrink achieves a degree of tradeoff between variance and bias contributions to the mean squared error however the tradeoff is not optimal visushrink reconstruction is often over smoothed hall kerkyacharian and picard 1999 considered block thresholding for wavelet function estimation which thresholds empirical wavelet coefficients in

confidence sets for nonparametric wavelet regression we construct nonparametric confidence sets for regression functions using wavelets that are uniform over besov balls we consider both thresholding and modulation estimators for the wavelet coefficients the confidence set is obtained by showing that a pivot process constructed from the loss function converges uniformly to a mean zero gaussian process inverting this pivot yields a confidence set for the wavelet coefficients and from this we obtain confidence sets on functionals of the regression curve

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

adaptive nonparametric confidence sets we construct honest confidence regions for a hilbert space valued parameter in various statistical models the confidence sets can be centered at arbitrary adaptive estimators and have diameter which adapts optimally to a given selection of models the latter adaptation is necessarily limited in scope we review the notion of adaptive confidence regions and relate the optimal rates of the diameter of adaptive confidence regions to the minimax rates for testing and estimation applications include the finite normal mean model the white noise model density estimation and regression with random design institute of mathematical statistics 2006

adaptive confidence bands for nonparametric regression functions this article proposes a new formulation for the construction of adaptive confidence bands cbs in nonparametric function estimation problems cbs which have size that adapts to the smoothness of the function while guaranteeing that both the relative excess mass of the function lying outside the band and the measure of the set of points where the function lies outside the band are small it is shown that the bands adapt over a maximum range of lipschitz classes the adaptive cb can be easily implemented in standard statistical software with wavelet support we investigate the numerical performance of the procedure using both simulated and real datasets the numerical results agree well with the theoretical analysis the procedure can be easily modified and used for other nonparametric function estimation models supplementary materials for this article are available online

adaptive confidence sets in l 2 the problem of constructing confidence sets that are adaptive in l 2 loss over a continuous scale of sobolev classes of probability densities is considered adaptation holds where possible with respect to both the radius of the sobolev ball and its smoothness degree and over maximal parameter spaces for which adaptation is possible two key regimes of parameter constellations are identified one where full adaptation is possible and one where adaptation requires critical regions be removed techniques used to derive these results include a general nonparametric minimax test for infinite dimensional null and alternative hypotheses and new lower bounds for l 2 adaptive confidence sets

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

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

minimax estimation via wavelet shrinkage we attempt to recover an unknown function from noisy sampled data using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coefficients the shrinkage can be tuned to be nearly minimax over any member of a wide range of triebel and besov type smoothness constraints and asymptotically minimax over besov bodies with p q linear estimates cannot achieve even the minimax rates over triebel and besov classes with p 2 so the method can significantly outperform every linear method e g kernel smoothing spline sieve in a minimax sense variants of our method based on simple threshold nonlinear estimators are nearly minimax our method possesses the interpretation of spatial adaptivity it reconstructs using a kernel which may vary in shape and bandwidth from point to point depending on the data least favorable distributions for certain of the triebel and besov scales generate objects with sparse wavelet transforms many real objects have similarly sparse transforms which suggests that these minimax results are relevant for practical problems sequels to this paper which was first drafted in november 1990 discuss practical implementation spatial adaptation properties universal near minimaxity and applications to inverse problems

adaptive confidence balls adaptive confidence balls are constructed for individual resolution levels as well as the entire mean vector in a multiresolution framework finite sample lower bounds are given for the minimum expected squared radius for confidence balls with a prespecified confidence level the confidence balls are centered on adaptive estimators based on special local block thresholding rules the radius is derived from an analysis of the loss of this adaptive estimator in addition adaptive honest confidence balls are constructed which have guaranteed coverage probability over all of r n and expected squared radius adapting over a maximum range of besov bodies

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

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

locally adaptive confidence bands we develop honest and locally adaptive confidence bands for probability densities they provide substantially improved confidence statements in case of inhomogeneous smoothness and are easily implemented and visualized the article contributes conceptual work on locally adaptive inference as a straightforward modification of the global setting imposes severe obstacles for statistical purposes among others we introduce a statistical notion of local holder regularity and prove a correspondingly strong version of local adaptivity we substantially relax the straightforward localization of the self similarity condition in order not to rule out prototypical densities the set of densities permanently excluded from the consideration is shown to be pathological in a mathematically rigorous sense on a technical level the crucial component for the verification of honesty is the identification of an asymptotically least favorable stationary case by means of slepian s comparison inequality

stabilization controllability and optimal control of boolean networks with impulsive effects and state constraints the present note investigates the stabilization controllability and optimal control problem of boolean networks with impulsive effects and state constraints by using the semi tensor product method the algebraic form of the boolean networks with impulsive effects and state constraints is derived the stabilization and controllability issues of the systems are investigated and some necessary and sufficient conditions are obtained in addition the mayer type optimal control problem is also studied and algorithms are provided to design the control sequence furthermore examples are given to illustrate the main results

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

generalized fiducial inference for wavelet regression we apply fisher s fiducial idea to conduct statistical inference for wavelet regression we first develop a general methodology for handling model selection problems within the fiducial framework with this new methodology we then propose fiduical based methods for performing wavelet curve estimation as well as constructing both pointwise and curvewise confidence intervals it is shown that under some mild regularity conditions both the new fiducial based pointwise and curvewise confidence intervals have asymptotically correct coverage furthermore simulation results show that these new fiducial based methods especially for constructing pointwise confidence intervals also possess promising empirical properties to the best of our knowledge this is the first time that the fiducial idea has been applied to a nonparametric estimation problem

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

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

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

set stability and set stabilization of boolean control networks based on invariant subsets this study addresses the set stability of boolean networks bns and set stabilization of boolean control networks bcns set stability determines whether a bn converges to a given subset whereas set stabilizability addresses the issue of whether a bcn can be stabilized to a given subset many problems can be viewed as special cases of set stability and set stabilization including synchronization partial stability and partial stabilization problems the concepts of invariant subset and control invariant subset are introduced then algorithms for the largest invariant subset and the largest control invariant subset contained in a given subset are proposed based on the invariant subsets obtained the necessary and sufficient conditions for set stability and set stabilizability are established and formulae are provided to calculate the shortest transient periods for respective initial states a design procedure is proposed for finding all the time optimal set stabilizers finally an example is used to show the application of the proposed results to the synchronization problem of bns

automatic inversion of magnetic anomalies from two height levels using finite difference similarity transforms we solve the inverse magnetic problem for the depth and shape of simple sources in the presence of a regional field and truly random noise we do not use noise generating derivatives nor are we forced to solve complex systems of equations our inverse operator applies a new geometric type of field transform the finite difference similarity transform fdst that is based on a postulated degree of homogeneity in the potential field magnetic data from two height levels are required for the calculation of the fdsts the fdsts are generated for an assumed central point of similarity cps and a trial value index for the coefficient of similarity and they are sensitive to the distance between the source and the cps and to the agreement between the index and the degree of homogeneity in the data when the cps converges to a singular point in the potential field say the center or the topedge of the source and when the trial index converges on the degree of homogeneity present in the data the fdst drops

output feedback stabilization of boolean control networks in the paper output feedback control of boolean control networks bcns is investigated first necessary and sufficient conditions for the existence of a time invariant output feedback tiof law stabilizing the bcn to some equilibrium point are given and constructive algorithms to test the existence of such a feedback law are proposed two sufficient conditions for the existence of a stabilizing time varying output feedback tvof are then given finally an example concerning the lac operon in the bacterium escherichia coli is presented to illustrate the effectiveness of the proposed techniques