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

a note on tree gatekeeping procedures in clinical trials dmitrienko et al statist med 2007 26 2465 2478 proposed a tree gatekeeping procedure for testing logically related hypotheses in hierarchically ordered families which uses weighted bonferroni tests for all intersection hypotheses in a closure method by marcus et al biometrika 1976 63 655 660 an algorithm was given to assign weights to the hypotheses for every intersection the purpose of this note is to show that any weight assignment algorithm that satisfies a set of sufficient conditions can be used in this procedure to guarantee gatekeeping and independence properties the algorithm used in dmitrienko et al statist med 2007 26 2465 2478 may fail to meet one of the conditions namely monotonicity of weights which may cause it to violate the gatekeeping property an example is given to illustrate this phenomenon a modification of the algorithm is shown to rectify this problem

the complexity of fault detection problems for combinational logic circuits in this correspondence we analyze the computational complexity of fault detection problems for combinational circuits and propose an approach to design for testability although major fault detection problems have been known to be in general np complete they were proven for rather complex circuits in this correspondence we show that these are still np complete even for monotone circuits and thus for unate circuits we show that for k level k 3 monotone unate circuits these problems are still np complete but that these are solvable in polynomial time for 2 level monotone unate circuits a class of circuits for which these fault detection problems are solvable in polynomial time is presented ripple carry adders decoder circuits linear circuits etc belong to this class a design approach is also presented in which an arbitrary given circuit is changed to such an easily testable circuit by inserting a few additional test points

a mapping approach for handling sloping interfaces a mapping approach for handling sloping interfaces in parabolic equation solutions is developed and tested at each range the medium is rigidly translated vertically so that a sloping interface becomes horizontal to simplify the approach the slope is assumed to be small and the extra terms that arise in the wave equation under the mapping are neglected the effects of these terms can be approximately accounted for by applying a leading order correction to the phase the mapping introduces variations in topography which are relatively easy to handle for the case of a pressure release boundary condition the accuracy of the approach is demonstrated for problems involving fluid sediments the approach should also be accurate for problems involving elastic sediments and should be useful for solving three dimensional problems involving variable topography

mixtures of multiple testing procedures for gatekeeping applications in clinical trials this paper proposes a general framework for constructing gatekeeping procedures for clinical trials with hierarchical objectives such problems frequently exhibit complex structures including multiple families of hypotheses and logical restrictions the proposed framework is based on combining multiple procedures across families it enables the construction of powerful and flexible gatekeeping procedures that account for general logical restrictions among the hypotheses of interest a clinical trial in patients with schizophrenia is used to illustrate the approach for parallel gatekeeping whereas another clinical trial in patients with hypertension is used to illustrate the approach for gatekeeping with general logical restrictions

tree structured gatekeeping tests in clinical trials with hierarchically ordered multiple objectives this paper discusses a new class of multiple testing procedures tree structured gatekeeping procedures with clinical trial applications these procedures arise in clinical trials with hierarchically ordered multiple objectives for example in the context of multiple dose control tests with logical restrictions or analysis of multiple endpoints the proposed approach is based on the principle of closed testing and generalizes the serial and parallel gatekeeping approaches developed by westfall and krishen j statist planning infer 2001 99 25 41 and dmitrienko et al statist med 2003 22 2387 2400 the proposed testing methodology is illustrated using a clinical trial with multiple endpoints primary secondary and tertiary and multiple objectives superiority and non inferiority testing as well as a dose finding trial with multiple endpoints

powerful short cuts for multiple testing procedures with special reference to gatekeeping strategies in this paper we present a general testing principle for a class of multiple testing problems based on weighted hypotheses under moderate conditions this principle leads to powerful consonant multiple testing procedures furthermore short cut versions can be derived which simplify substantially the implementation and interpretation of the related test procedures it is shown that many well known multiple test procedures turn out to be special cases of this general principle important examples include gatekeeping procedures which are often applied in clinical trials when primary and secondary objectives are investigated and multiple test procedures based on hypotheses which are completely ordered by importance we illustrate the methodology with two real clinical studies

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

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

fault detection analysis of boolean control networks in this technical note we address the fault detection problem for boolean control networks bcns we first investigate completeness and t completeness of the set of input output trajectories next we introduce the concept of meaningful fault and prove necessary and sufficient conditions under which meaningful faults can be detected from the input output trajectories of the bcn two fault detection algorithms are provided

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

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

boolean derivatives weighted chow parameters and selection probabilities of stack filters the theory of boolean derivatives the activities of the arguments of a boolean function bf and chow 1961 parameters are studied from the point of view of their application in the statistical analysis of a class of nonlinear filters stack filters the connection between the partial derivatives of a positive bf pbf and the selection probabilities of stack filters is established the notions of the weighted activities of the variables of the pbf and weighted chow parameters are introduced for the analysis the computation of the joint selection probability matrix and the sample selection probability vector of a continuous stack filter spectral approaches to the selection probabilities of stack filters are derived in particular spectral algorithms with computational complexity o 2 sup n where n is the number of input samples within an input window are given for the computation of sample selection probability vectors the difference of the spectral algorithms presented from the nonspectral ones is that spectral algorithms are universal i e their complexities are independent of the pbf which is used as the base for stack filtering they are also straightforward to implement and fast spectral transforms exist

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

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

an explicit analytical solution for sound propagation in a three dimensional penetrable wedge with small apex angle a problem of sound propagation in a shallow water waveguide with a weakly sloping penetrable bottom is considered the adiabatic mode parabolic equations are used to approximate the solution of the three dimensional 3d helmholtz equation by modal decomposition of the acoustic pressure field the mode amplitudes satisfy parabolic equations that admit analytical solutions in the special case of the 3d wedge using the analytical formula for modal amplitudes an explicit and remarkably simple expression for the acoustic pressure in the wedge is obtained the proposed solution is validated by the comparison with a solution of the 3d penetrable wedge problem obtained using a fully 3d parabolic equation that includes a leading order cross term correction

brief paper boolean derivative calculation with application to fault detection of combinational circuits via the semi tensor product method using the semi tensor product method this paper investigates the boolean derivative calculation with application to fault detection of combinational circuits and presents a number of new results first a new set of formulas is obtained to calculate the boolean derivative by the semi tensor product method then the obtained new results are applied to detecting the multiple faults of combinational circuits and a new detection method is proposed finally two illustrative examples are studied by using the results obtained in this paper the study of illustrative examples shows that the new detection method can be used for detection of more than two faults effectively

nonsingularity of feedback shift registers in this paper the multi valued feedback shift register fsr is studied and a new approach is present to analyze its nonsingularity number of cycles and cycle synthesis firstly the fsr is expressed in an algebraical form based on which several necessary and sufficient conditions are given for the nonsingularity secondly the structural matrix of fsr is defined and a new method is introduced to determine the number of cycles with different lengths for arbitrarily given fsr thirdly the problem on cycle decomposition and synthesis of an fsr is investigated and some new results are obtained finally an illustrative example is studied to support our new results

higher order pade approximations for accurate and stable elastic parabolic equations with application to interface wave propagation higher order pade approximations are applied to derive accurate and stable parabolic equations for sound propagation in oceans bounded below by an elastic bottom or bounded above by ice cover accuracy is achieved by placing constraints on the derivatives of the pade approximations at the point corresponding to the reference wave number stability is achieved by requiring that the pade approximations map part of the lower left quadrant of the complex plane into the upper half of the complex plane elastic parabolic equations based on these pade series can handle problems involving compressional shear and interface waves very wide propagation angles and large depth variations and weak range variations in the seismoacoustic parameters a finite difference spectral solution is developed for generating reference solutions and starting fields the rotated elastic parabolic equation is used to investigate the accuracy of the elastic parabolic equation for range dependent problems

a single scattering correction for large contrasts in elastic layers the single scattering solution is implemented in a formulation that makes it possible to accurately handle solid solid interfaces with the parabolic equation method problems involving large contrasts across sloping stratigraphy can be handled by subdividing a vertical interface into a series of two or more scattering problems the approach can handle complex layering and is applicable to a large class of seismic problems the solution of the scattering problem is based on an iteration formula which has improved convergence in the new formulation and the transverse operator of the parabolic wave equation which is implemented efficiently in terms of banded matrices accurate solutions can often be obtained by using only one iteration

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

a single scattering correction for the seismo acoustic parabolic equation an efficient single scattering correction that does not require iterations is derived and tested for the seismo acoustic parabolic equation the approach is applicable to problems involving gradual range dependence in a waveguide with fluid and solid layers including the key case of a sloping fluid solid interface the single scattering correction is asymptotically equivalent to a special case of a single scattering correction for problems that only have solid layers kusel et al j acoust soc am 121 808 813 2007 the single scattering correction has a simple interpretation conservation of interface conditions in an average sense that facilitated its generalization to problems involving fluid layers promising results are obtained for problems in which the ocean bottom interface has a small slope

rational operators for filtering the parabolic equation pe method has been applied to approximate the wave equation construct radiation conditions solve scattering problems construct initial conditions and derive energy flux conditions a new application of the pe method filters based on rational approximations of depth operators is described and tested the rational approximation is designed to act as the identity operator on the desired part of the spectrum of the depth separated wave equation and to annihilate other parts of the spectrum this approach does not require explicit knowledge of the spectrum the applications of the filter include directly solving eigenvalue problems annihilating components of the wave number spectrum generating initial conditions at the source range and eliminating gibbs oscillations that arise in energy conserving pe solutions

controllability of higher order boolean control networks using the semi tensor product method this paper investigates the controllability of a th order boolean control network after a brief introduction on semi tensor product of matrices to th order boolean control networks the controllability issue is studied first a systematic procedure to reconstruct the logical dynamic of a th order boolean control network from its network transition matrix is presented for design purpose then the controllability via two types of controls is considered necessary and sufficient conditions are provided for each case the application of input state incidence matrix to the controllability of th order boolean control networks is studied finally as an application examples are given to illustrate the effectiveness of the obtained results

transparent boundary conditions for split step pade approximations of the one way helmholtz equation in this paper we generalize the nonlocal discrete transparent boundary condition introduced by f schmidt and p deuflhard 1995 comput math appl 29 53 76 and by f schmidt and d yevick 1997 j comput phys 134 96 107 to propagation methods based on arbitrary pade approximations of the two dimensional one way helmholtz equation our approach leads to a recursive formula for the coefficients appearing in the nonlocal condition which then yields an unconditionally stable propagation method

complex pade approximants for wide angle acoustic propagators procedures for constructing wide angle propagators that attenuate evanescent modes in parabolic equation pe models of underwater sound propagation are examined in this context two new split step pade approximations to exponentiated square root operators are proposed the first method involves a propagator derived from a pade approximant of a square root operator that has been rotated in the complex plane while the propagator of the second method is obtained from a complex coefficient rational approximation of the square root operator numerical evidence confirms that these proposed methods yield improved behavior compared to previously suggested techniques in selected areas of the spectral domain

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

sparse source identification of linear diffusion advection equations by adjoint methods abstract we present an algorithm for the time inversion of diffusion advection equations based on the adjoint methodology given a final state distribution our main aim is to recover sparse initial conditions constituted by a finite combination of kronecker deltas identifying their location and mass we discuss the strengths of the adjoint machinery and the difficulties that are to be faced in particular when the diffusivity coefficient or the time horizon is large

energy conserving and reciprocal solutions for higher order parabolic equations conservation of sound energy in nonabsorbing media and acoustical reciprocity in stationary fluids at rest are the fundamental properties of the acoustic field preserving these properties in parabolic approximations is essential for accurate modeling of sound propagation in shallow water environments recently godin proposed a family of wide angle parabolic equations pe s for motionless fluid which are energy conserving reciprocal and allow improved description of mode coupling without adversely affecting phase accuracy for moving media a generalized claerbout pe was also derived its solutions preserve the acoustic energy in the absence of dissipation and satisfy the flow reversal theorem frt which is an extension of reciprocity principle to moving media the report presents a numerical scheme for solving the proposed pe s the algorithm preserves the conservational properties of the original pseudo differential equations implicit finite difference solutions satisfy discrete analogs of the e

wave number sampling at short range the self starter is an efficient approach for solving geoacoustic inverse problems involving a vertical array of receivers located on the order of ten wavelengths from a source r j cederberg and m d collins j acoust soc am 22 102 109 1997 with this approach accurate solutions can be obtained by sampling the wave number spectrum at approximately ten points there have been unsubstantiated claims that the spectral solution provides similar efficiency when implemented with an approach that involves perturbing the integration contour off the real line f b jensen et al computational ocean acoustics american institute of physics new york 1994 pp 231 240 it is demonstrated that this quadrature scheme breaks down at short ranges and that the self starter solution is about an order of magnitude faster these conclusions are based on comparisons of the rational approximations associated with the self starter and the quadrature scheme comparisons of acoustic fields for particular proble

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

investigation of the global dynamics of cellular automata using boolean derivatives global dynamics of a non linear cellular automaton ca is in general irregular asymmetric and unpredictable as opposed to that of a linear ca which is highly systematic and tractable in this paper efforts have been made to systematize non linear ca evolutions in the light of boolean derivatives and jacobian matrices a few new theorems on hamming distance between boolean functions as well as on jacobian matrices of cellular automata are proposed and proved moreover a classification of boolean functions based on the nature of deviation from linearity has been suggested with a view to grouping them together to classes subclasses such that the members of a class subclass satisfy certain similar properties next an error vector which cannot be captured by the jacobian matrix is identified and systematically classified this leads us to the concept of modified jacobian matrix whereby a quasi affine representation of a non linear cellular automaton is introduced