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

computing orthogonal polynomials in sobolev spaces numerical methods are considered for generating polynomials orthogonal with respect to an inner product of sobolev type i e one that involves derivatives up to some given order each having its own positive measure associated with it the principal objective is to compute the coefficients in the increasing order recurrence relation that these polynomials satisfy by virtue of them forming a sequence of monic polynomials with degrees increasing by 1 from one member to the next as a by product of this computation one gains access to the zeros of these polynomials via eigenvalues of an upper hessenberg matrix formed by the coefficients generated two methods are developed one is based on the modified moments of the constitutive measures and generalizes what for ordinary orthogonal polynomials is known as modified chebyshev algorithm the other a generalization of stieltjes s procedure expresses the desired coefficients in terms of a sobolev inner product involving the orthogonal polynomials in question whereby the inner product is evaluated by numerical quadrature and the polynomials involved are computed by means of the recurrence relation already generated up to that point the numerical characteristics of these methods are illustrated in the case of sobolev orthogonal polynomials of old as well as new types based on extensive numerical experimentation a number of conjectures are formulated with regard to the location and interlacing properties of the respective zeros

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 finite convergence criterion for the discounted optimal control of stochastic logical networks stochastic logical networks slns are discrete time stochastic dynamical systems with boolean or multivalued logical state variables the discounted infinite horizon optimal control problem for sln is addressed in this paper by resorting to the equivalent markov decision process description the infinite horizon optimization problem is presented in algebraic form then using the increasing dimension technique an improved finite convergence criterion which can find the optimal stationary policy is derived for value iteration approach to demonstrate the theoretical value of this approach it is applied to the optimization problems of the human machine game and the p53 mdm2 gene network

an asymptotic result for laguerre sobolev orthogonal polynomials abstract let s n denote the sequence of polynomials orthogonal with respect to the sobolev inner product f g s 0 f x g x x e x d x 0 f x g x x e x d x where 1 0 and the leading coefficient of the s n is equal to the leading coefficient of the laguerre polynomial l n then if x c s 0 lim n s n x l n 1 x is a constant depending on

on finite potential games a linear system called the potential equation pe is presented it is proved that a finite game is potential if and only if its potential equation has solution some properties of the potential equation are obtained based on these properties a closed form solution of the pe is obtained moreover a formula based on the solution of the pe is obtained to calculate the potential function finally it is proved that a networked evolutionary game is potential if and only if its fundamental network game is potential some interesting examples are presented to illustrate the theoretical results

behavior of sensitivities in the one dimensional advection dispersion equation implications for parameter estimation and sampling design the spatial and temporal variability of sensitivities has a significant impact on parameter estimation and sampling design for studies of solute transport in porous media physical insight into the behavior of sensitivities is offered through an analysis of analytically derived sensitivities for the one dimensional form of the advection dispersion equation when parameters are estimated in regression models of one dimensional transport the spatial and temporal variability in sensitivities influences variance and covariance of parameter estimates several principles account for the observed influence of sensitivities on parameter uncertainty 1 information about a physical parameter may be most accurately gained at points in space and time with a high sensitivity to the parameter 2 as the distance of observation points from the upstream boundary increases maximum sensitivity to velocity during passage of the solute front increases and the consequent estimate of velocity tends to have lower variance 3 the frequency of sampling must be in phase with the s shape of the dispersion sensitivity curve to yield the most information on dispersion 4 the sensitivity to the dispersion coefficient is usually at least an order of magnitude less than the sensitivity to velocity 5 the assumed probability distribution of random error in observations of solute concentration determines the form of the sensitivities 6 if variance in random error in observations is large trends in sensitivities of observation points may be obscured by noise and thus have limited value in predicting variance in parameter estimates among designs 7 designs that minimize the variance of one parameter may not necessarily minimize the variance of other parameters 8 the time and space interval over which an observation point is sensitive to a given parameter depends on the actual values of the parameters in the underlying physical system

receding horizon based feedback optimization for mix valued logical networks the optimization of mix valued probabilistic logical networks is a natural extension of optimization of boolean networks in this study we have first obtained a recursive solution for the finite horizon case then we have proved that when the filter length is large enough the obtained optimal control sequence coincides with the one for the infinite horizon case using the reeding horizon technique this result turns searching an infinite sequence of controls into finding an optimal feedback matrix by solving a finite horizon optimization problem as examples its applications to human machine game and to metastatic melanoma are investigated

on polynomials orthogonal with respect to an inner product involving differences abstract in this paper we consider the inner product r x g x d x c g c where c r and is a distribution function with infinite spectrum such that has no points of increase in the interval c c 1 furthermore 0 and g are functions on r and c c 1 c let qn x be the sequence of monic orthogonal polynomials with respect to this inner product and pn x pnc x the sequences of monic standard orthogonal polynomials 0 with respect to d x and x c x c 1 d x respectively we derive an explicit representation for qn x in terms of pn x and pnc x and we present some results on the distribution of the zeros of qn x in relation to the zeros of pn x finally we treat the special case where pn x are charlier polynomials and c 0

orthogonal polynomials and approximation in sobolev spaces abstract this paper discusses the density of polynomials in sobolev type function spaces defined on the compact interval 1 1 of the real line r the problems considered are motivated by consideration of the spectral representation of certain jacobi type orthogonal polynomials

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

zeros of sobolev orthogonal polynomials following from coherent pairs let sn denote the monic orthogonal polynomial sequence with respect to the sobolev inner product f g s fgd 0 f g d 1 where d 0 d 1 is a so called coherent pair and 0 then sn has n different real zeros the position of these zeros with respect to the zeros of other orthogonal polynomials in particular laguerre and jacobi polynomials is investigated coherent pairs are found where the zeros of sn 1 separte the zeros of sn

reduced order parameter estimation using quasilinearization and quadratic programming 1 the ability of a particular model to accurately predict how a system responds to forcing is predicated on various model parameters that must be appropriately identified there are many algorithms whose purpose is to solve this inverse problem which is often computationally intensive in this study we propose a new algorithm that significantly reduces the computational burden associated with parameter identification the algorithm is an extension of the quasilinearization approach where the governing system of differential equations is linearized with respect to the parameters the resulting inverse problem therefore becomes a linear regression or quadratic programming problem qp for minimizing the sum of squared residuals the solution becomes an update on the parameter set this process of linearization and regression is repeated until convergence takes place this algorithm has not received much attention as the qps can become quite large often infeasible for real world systems to alleviate this drawback proper orthogonal decomposition is applied to reduce the size of the linearized model thereby reducing the computational burden of solving each qp in fact this study shows that the snapshots need only be calculated once at the very beginning of the algorithm after which no further calculations of the reduced model subspace are required the proposed algorithm therefore only requires one linearized full model run per parameter at the first iteration followed by a series of reduced order qps the method is applied to a groundwater model with about 30 000 computation nodes where as many as 15 zones of hydraulic conductivity are estimated

zeros of sobolev orthogonal polynomials of hermite type let s n n denote a set of polynomials orthogonal with respect to the sobolev inner product s f x g x d j 0 x l f x g x d j 1 where l 0 and d j 0 d j 1 is a so called symmetrically coherent pair with d j 0 or d j 1 the hermite measure e x 2dx if d j 1 is the hermite measure then s n has n different real zeros if d j 0 is the hermite measure then s n has at least n 2 different real zeros we determine conditions for s n to have complex zeros

connection coefficients for laguerre sobolev orthogonal polynomials laguerre sobolev polynomials are orthogonal with respect to an inner product of the form p qs 0 p x q x x e x dx 0 p x q x d x w here 1 0 and p q p the linear space of polynomials with real coefficients if d x x e x dx the corresponding sequence of monic orthogonal polynomials q x has been studied by marcellan et al j com put appl math 71 1996 245 265 while if d x x dx the sequence of monic orthog onal polynomials l x was introduced by koekoek and meijer siam j math anal 24 1993 768 782 for each of these two families of laguerre sobolev polynomials here we give the explicit expression of the connection coefficients in their expansion as a series of standard la guerre polynomials the inverse connection problem of expanding laguerre polynomials in series of laguerre sobolev polynomials and the connection problem relating two families of laguerre sobolev polynomials with different parameters are also considered

incorporation of prior information on parameters into nonlinear regression groundwater flow models 1 theory prior information on the parameters of a groundwater flow model can be used to improve parameter estimates obtained from nonlinear regression solution of a modeling problem two scales of prior information can be available 1 prior information having known reliability that is bias and random error structure and 2 prior information consisting of best available estimates of unknown reliability a regression method that incorporates the second scale of prior information assumes the prior information to be fixed for any particular analysis to produce improved although biased parameter estimates approximate optimization of two auxiliary parameters of the formulation is used to help minimize the bias which is almost always much smaller than that resulting from standard ridge regression it is shown that if both scales of prior information are available then a combined regression analysis may be made

sobolev orthogonal polynomials on product domains orthogonal polynomials on the product domain a 1 b 1 a 2 b 2 with respect to the inner product f g s a 1 b 1 a 2 b 2 f x y g x y w 1 x w 2 y d x d y f c 1 c 2 g c 1 c 2 are constructed where w i is a weight function on a i b i for i 1 2 0 and c 1 c 2 is a fixed point the main result shows how an orthogonal basis for such an inner product can be constructed for certain weight functions in particular for product laguerre and product gegenbauer weight functions which serve as primary examples

an algebraic expression of finite horizon optimal control algorithm for stochastic logical dynamical systems abstract this paper investigates the finite horizon optimal control problem for the stochastic logical dynamical systems with finite states after giving the equivalent descriptions of stochastic logical dynamical system in term of markov process the finite horizon optimization problem is presented in an algebraic form based on semi tensor product of matrix and the increasing dimensional technique a succinct algebraic expression of dynamic programming algorithm is derived to solve the optimal control problem examples including an application on stochastic kleene s logical optimization problem are presented to show the effectiveness of our main result

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

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

controllability and observability of boolean control networks the controllability and observability of boolean control networks are investigated after a brief review on converting a logic dynamics to a discrete time linear dynamics with a transition matrix some formulas are obtained for retrieving network and its logical dynamic equations from this network transition matrix based on the discrete time dynamics the controllability via two kinds of inputs is revealed by providing the corresponding reachable sets precisely then the problem of observability is also solved by giving necessary and sufficient conditions

hermite sobolev and closely connected orthogonal polynomials abstract in this paper a bilinear functional a g m o n m c m m g m which corresponds to the hermite sobolev and closely connected orthogonal polynomials is studied the domain of m m 1 n in which a is positive definite is given and the hermite sobolev and closely connected formal orthogonal polynomials are given in the nonnormal case

structure relations for orthogonal polynomials on the unit circle structure relations for orthogonal polynomials with respect to hermitian linear functionals are studied firstly we prove that semi classical orthogonal polynomials satisfy structure relations of the following type k 0s1 n kpn s1 k k 0s2 n kzkpn 1 k k 0r1 n kpn s1 k 1 k 0r2 n kpn r2 k where s1 s2 r1 r2 are integers specified in the text pn is the reversed polynomial of pn pn 1 pn 1 n 1 and n k n k n k n k are complex numbers then we study the semi classical character of sequences of orthogonal polynomials rn pn connected through a structure relation of the following type k 0s1 n krn s1 k k 0s2 n krn s2 k k 0r1 n kpn r1 k 1 k 0r2 n kpn r2 k where the integers s1 s2 r1 r2 satisfy some natural conditions specified in the text

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

δ sobolev orthogonal polynomials of meixner type asymptotics and limit relation let qn x n be the sequence of monic polynomials orthogonal with respect to the sobolev type inner product p x r x s u0 p x r x u1 p x r x where 0 f x f x 1 f x denotes the forward difference operator and u0 u1 is a coherent pair of positive definite linear functionals being u1 the meixner linear functional in this paper relative asymptotics for the qn x n sequence with respect to meixner polynomials on compact subsets of c 0 is obtained this relative asymptotics is also given for the scaled polynomials in both cases we deduce the same asymptotics as we have for the self coherent pair that is when u0 u1 is the meixner linear functional furthermore we establish a limit relation between these orthogonal polynomials and the laguerre sobolev orthogonal polynomials which is analogous to the one existing between meixner and laguerre polynomials in the askey scheme

inner products involving q differences the little q laguerre sobolev polynomials in this paper polynomials which are orthogonal with respect to the inner product p r s k 0 p qk r qk aq k aq q q q k k 0 dqp qk dqr qk aq k aq q q q k where dq is the q difference operator 0 0 q 1 and 0 aq 1 are studied for these polynomials algebraic properties and q difference equations are obtained as well as their relation with the monic little q laguerre polynomials some properties about the zeros of these polynomials are also deduced finally the relative asymptotics qn x pn x a q n on compact subsets of c 0 1 is given where qn x is the nth degree monic orthogonal polynomial with respect to the above inner product and pn x a q denotes the monic little q laguerre polynomial of degree n

coupled inverse problems in groundwater modeling 1 sensitivity analysis and parameter identification some basic concepts and methods for solving the coupled inverse problem in groundwater modeling are presented in a series of two papers because there are crossover effects between state variables and parmeters coupled inverse problems are different from single inverse problems in several aspects especially in the selection of objective functions identifiability and experimental design this paper discusses the general definition of coupled inverse problems posed in the framework of multiobjective optimization in order to obtain gradient vectors of objective functions as well as all sensitivity coefficients a general procedure for deriving the adjoint state equations and their associated conditions is described using the rules of adjoint operation presented in this paper the derivation of adjoint problems becomes very easy even for nonlinear and transient coupled problems as examples the adjoint problem of flow mass transport or flow heat transport the adjoint problem of saltwater intrusion and the adjoint problem of two phase flow are derived numerical experiments on a two dimensional flow mass transport problem are given to explain the procedure of sensitivity analysis and parameter identification for coupled problems the hydraulic conductivity can be identified by using observations of head and or solute concentration

asymptotics of sobolev orthogonal polynomials for coherent pairs of laguerre type abstract let s n n denote a sequence of polynomials orthogonal with respect to the sobolev inner product f g s f x g x d 0 x f x g x d 1 x where 0 and d 0 d 1 is a so called coherent pair with at least one of the measures d 0 or d 1 a laguerre measure we investigate the asymptotic behaviour of sn x outside the supports of d 0 and d 1 and n

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

asymptotics of sobolev orthogonal polynomials for coherent pairs of jacobi type abstract let sn n denote a sequence of polynomials orthogonal with respect to the sobolev inner product f g s f x g x d 0 x f x g x d 1 x where 0 and d 0 d 1 is a so called coherent pair with at least one of the measures d 0 or d 1 a jacobi measure we investigate the asymptotic behaviour of sn x for n and x fixed x c 1 1 as well as x 1 1

on sobolev orthogonal polynomials with coherent pairs the laguerre case type 1 we study the asymptotic properties of orthogonal polynomials with sobolev inner product formula the pair d d is called a coherent pair if there exists nonzero constantsdnsuch that formula wherepn x andqn x are thenth monic orthogonal polynomials with respect tod andd respectively one can divide the coherent pairs into two cases the jacobi case and the laguerre case there are two types in each case we consider thenth root asymptotics and the zero distribution for the laguerre case type 1

theq laguerre polynomials and related moment problems abstract we study two indeterminate hamburger moment problems associated with q laguerre polynomials the coefficients in their recurrence relations are of exponential growth this completes earlier work started by d moak some of the measures that the polynomials are orthogonal with respect to are found and lead to the evaluation of certain integrals a symmetric set of orthogonal polynomials is also considered

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

connection problems for polynomial solutions of nonhomogeneous differential and difference equations abstract we consider nonhomogeneous hypergeometric type differential difference and q difference equations whose nonhomogeneity is a polynomial q n x the polynomial solution of these problems is expanded in the q n x basis and also in a basis p n x related in a natural way with the homogeneous hypergeometric equation we give an algorithm building a recurrence relation for the expansion coefficients in both bases that we solve explicitly in many cases involving classical orthogonal polynomials finally some concrete applications and extensions are given

a comparison of several methods of solving nonlinear regression groundwater flow problems computational efficiency and computer memory requirements for four methods of minimizing functions were compared for four test nonlinear regression steady state groundwater flow problems the fastest methods were the marquardt and quasi linearization methods which required almost identical computer times and numbers of iterations the next fastest was the quasi newton method and last was the fletcher reeves method which did not converge in 100 iterations for two of the problems the fastest method per iteration was the fletcher reeves method and this was followed closely by the quasi newton method the marquardt and quasi linearization methods were slower for all four methods the speed per iteration was directly related to the number of parameters in the model however this effect was much more pronounced for the marquardt and quasi linearization methods than for the other two hence the quasi newton and perhaps fletcher reeves method might be more efficient than either the marquardt or quasi linearization methods if the number of parameters in a particular model were large although this remains to be proven the marquardt method required somewhat less central memory than the quasi linearization metilod for three of the four problems for all four problems the quasi newton method required roughly two thirds to three quarters of the memory required by the marquardt method and the fletcher reeves method required slightly less memory than the quasi newton method memory requirements were not excessive for any of the four methods

orthogonal polynomials on sobolev spaces old and new directions abstract during the last years orthogonal polynomials on sobolev spaces have attracted considerable attention algebraic properties distribution of their zeros and fourier expansions as well as their relevance in the analysis of spectral methods for partial differential equations provide a very large field to explore and to compare with the standard case in this paper we present an introductory survey about the subject the origin of the problems and their development show the interest and the promising future of this field

sobolev orthogonal polynomial in the complex plane sobolev orthogonal polynomials with respect to measures supported on compact subsets of the complex plane are considered for a wide class of such sobolev orthogonal polynomials it is proved that their zeros are contained in a compact subset of the complex plane and their asymptotic zero distribution is studied we also find the nth root asymptotic behavior of the corresponding sequence of sobolev orthogonal polynomials

variational sensitivity analysis data requirements and parameter identification in a leaky aquifer system the adjoint state sensitivity method is developed to aid the analysis of a pumping test design for parameter identification in a leaky aquifer system the system considered consists of an unconfined aquifer overlaying an aquitard which overspreads a confined aquifer the adjoint equations are derived in the continuous form without discretizing the governing equations and are expressed in terms of convection diffusion equations with time dependent coefficients the multiple cell balance mcb method is used to solve the nonlinear governing equations as well as their adjoint equations algorithms are developed for calculating sensitivity coefficients of heads in each layer of an aquifer with respect to various parameters a concept called contribution of an observation is introduced which can be used to measure the usefulness of an observation in connection with data requirements for parameter identification it links experimental design with observation errors and the requirement of model application the sufficiency of an observation system for parameter identification can be evaluated at the design stage before extensive resources are committed to data collection a numerical example is given to verify the proposed method and to explain its applicability to the design of a pumping test

aquifer parameter identification with optimum dimension in parameterization this paper presents a systematic procedure whereby the functional coefficients imbedded in a two dimensional partial differential equation which governs unsteady groundwater flow are optimally identified the coefficients to be identified are transmissivities which vary spatially finite elements are used to represent the unknown transmissivity function parametrically in terms of nodal values over a suitable discretization of a flow region a modified gauss newton algorithm is used for parameter optimization covariance analysis is used to estimate the reliability of the estimated parameters as the dimension of the unknown parameter increases the modeling error represented by a least squares criterion will generally decrease but errors in data would be propagated to a greater degree into the estimated parameters thus reducing the reliability of estimation the reliability of the estimated parameters is characterized by a norm of the covariance matrix this information is used for the determination of the optimum dimension in parameterization

analytic aspects of sobolev orthogonal polynomials revisited this paper surveys some recent achievements in the analytic theory of polynomials orthogonal with respect to inner products involving derivatives asymptotic properties zero location approximation and moment theory are some of the topic considered

what is beyond coherent pairs of orthogonal polynomials abstract usually coherent pairs of orthogonal polynomials have been considered in the wider context of sobolev orthogonality in this paper we focus our attention on the problem of coherence between two orthogonal polynomial sequences in terms of the corresponding linear functionals we deduce some conditions about the linear functionals in order that the corresponding orthogonal polynomial sequences constitute a coherent pair

some properties of the sobolev laguerre polynomials abstract in this paper we study the case 0 of the sobolev laguerre polynomials we determine a generating function for the polynomials and an expansion formula

coupled estimation of flow and solute transport parameters a methodology for solving the coupled linear flow and transport inverse problem is presented it allows the estimation of aquifer parameters transmissivity storativity recharge boundary heads and flows leakage dispersivity molecular diffusion porosity retardation linear decay boundary concentrations using their prior estimates as well as head and concentration measurements as basic information transient flow and transport equations are solved using the finite element method in space and a weighted finite difference scheme in time flow and transport domains can be one two or quasi three dimensional applying linear one dimensional elements linear two dimensional triangles or bilinear two dimensional rectangles mixed at will time regimes can be transient or steady state in any equation flow or transport parameters are estimated on the basis of maximum likelihood theory which allows us to obtain information about parameters uncertainty minimization of the negative log likelihood is performed using marquardt s method the applicability of the method is shown by means of two real examples they illustrate that the proposed approach can successfully address model selection parameter uncertainty and nontrivial identifiability problems estimation of time dependent sources and the role of prior estimates are also addressed in the examples while the formulation of the problem leaves room for both stochastic and deterministic treatment of hydraulic parameters the latter has been adopted in both examples limitations of the approach are also apparent

smallest zeros of some types of orthogonal polynomials asymptotics we establish mehler heine type formulas for orthogonal polynomials related to rational modifications of hermite weight on the real line and for hermite sobolev orthogonal polynomials these formulas give us the asymptotic behaviour of the smallest zeros of the corresponding orthogonal polynomials furthermore we solve a conjecture posed in a previous paper about the asymptotics of the smallest zeros of the hermite sobolev polynomials as well as an open problem concerning the asymptotics of these sobolev orthogonal polynomials

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

q coherent pairs and q orthogonal polynomials in this paper we introduce the concept of q coherent pair of linear functionals we prove that if u 0 u 1 is a q coherent pair of linear functionals then at least one of them has to be a q classical linear functional moreover we present the classification of all q coherent pairs of positive definite linear functionals when u 0 or u 1 is either the little q jacobi linear functional or the little q laguerre wall linear functional finally by using limit processes we recover the classification of coherent pairs of linear functionals stated by meijer

ratio and plancherel rotach asymptotics for meixner sobolev orthogonal polynomials abstract we study the analytic properties of the monic meixner sobolev polynomials qn orthogonal with respect to the inner product involving differences p q s i 0 p i q i p i q i i i i 0 0 where 0 is the forward difference operator f x f x 1 f x and n denotes the pochhammer symbol relative asymptotics for meixner sobolev polynomials with respect to meixner polynomials is obtained this relative asymptotics is also given for the scaled polynomials moreover a zero distribution for the scaled meixner sobolev polynomials and plancherel rotach asymptotics for qn are deduced

coherent pairs of measures and markov bernstein inequalities abstract all the coherent pairs of measures associated to linear functionals c 0 and c 1 introduced by iserles et al in 1991 have been given by meijer in 1997 there exist seven kinds of coherent pairs all these cases are explored in order to give three term recurrence relations satisfied by polynomials the smallest zero 1 n of each of them of degree n has a link with the markov bernstein constant m n appearing in the following markov bernstein inequalities c 1 p 2 m n 2 c 0 p 2 p p n where m n 1 1 n the seven kinds of three term recurrence relations are given in the case where c 0 e x d x 0 and c 1 e x d x explicit upper and lower bounds are given for 1 n and the asymptotic behavior of the corresponding markov bernstein constant is stated except in a part of one case lim n 1 n 0 is proved in all the cases

laguerre sobolev orthogonal polynomials abstract in this paper polynomials that are orthogonal with respect to the inner product f g s 0 f x g x x e x dx 0 f x g x x e x dx where 1 and 0 are studied for these nonstandard orthogonal polynomials algebraic and differential properties as well as the relation with the classical laguerre polynomials are obtained finally some properties concerning the localization and separation of the zeros of these polynomials are deduced

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 positivity of some bilinear functionals in sobolev spaces abstract the positivity of a bilinear functional a a f g n m 0 m c m f m g m is studied as a function of coefficients m the concerned cases are those of laguerre gegenbauer and jacobi for c m c 0 m 1 n the domain m m 1 n where a is positive definite is given as a consequence when n 1 the corresponding markov bernstein inequalities are given

incorporation of prior information on parameters into nonlinear regression groundwater flow models 2 applications this paper investigates factors influencing the degree of improvement in estimates of parameters of a nonlinear regression groundwater flow model by incorporating prior information of unknown reliability consideration of expected behavior of the regression solutions and results of a hypothetical modeling problem lead to several general conclusions first if the parameters are properly scaled linearized expressions for the mean square error mse in parameter estimates of a nonlinear model will often behave very nearly as if the model were linear second by using prior information the mse in properly scaled parameters can be reduced greatly over the mse of ordinary least squares estimates of parameters third plots of estimated mse and the estimated standard deviation of mse versus an auxiliary parameter the ridge parameter specifying the degree of influence of the prior information on regression results can help determine the potential for improvement of parameter estimates fourth proposed criteria can be used to make appropriate choices for the ridge parameter and another parameter expressing degree of overall bias in the prior information results of a case study of truckee meadows reno sparks area washoe county nevada conform closely to the results of the hypothetical problem in the truckee meadows case incorporation of prior information did not greatly change the parameter estimates from those obtained by ordinary least squares however the analysis showed that both sets of estimates are more reliable than suggested by the standard errors from ordinary least squares

model inversion of transient nonlinear groundwater flow models using model reduction despite increasing computational resources many high dimensional applications are impractical for model inversions in this paper two methods are presented that are promising for high dimensional model inversion the methods draw on proper orthogonal decomposition pod and yield reduced models that describe a truncated behavior of the original model we utilize pod differently for the two methods which differ in efficiency and implementation the first method rigm applies a pod to an existing partial differential equation the second method rism applies it to an autoregressive formulation of a discrete model both methods were applied to several synthetic cases and a real world case with synthetic measurements and by comparing them to classic inverse methodologies i e the method of finite differences and the adjoint method the two pod methods appeared to be computationally robust and more efficient for a wide range of prior estimates moreover the implementation of an adjoint for the rism method is easy

asymptotic properties of sobolev orthogonal polynomials abstract in this report we will survey some of the main ideas and tools which appeared recently in the study of the analytic properties of polynomials orthogonal with respect to inner products involving derivatives although some results on weak asymptotics are mentioned the strong outer asymptotics constitutes the core of the paper both the discrete and the continuous cases are considered and several open problems and conjectures are posed

some asymptotics for sobolev orthogonal polynomials involving gegenbauer weights we consider the sobolev inner product email protected 1 1f x g x 1 x 2 a 1 email protected f x g x email protected x a 12 where email protected is a measure involving a gegenbauer weight and with mass points outside the interval 1 1 we study the asymptotic behaviour of the polynomials which are orthogonal with respect to this inner product we obtain the asymptotics of the largest zeros of these polynomials via a mehler heine type formula these results are illustrated with some numerical experiments

some remarks on a paper by l carlitz we study a family of orthogonal polynomials which generalizes a sequence of polynomials considered by l carlitz we show that they are a special case of the sheffer polynomials and point out some interesting connections with certain sobolev orthogonal polynomials

exact scheffe type confidence intervals for output from groundwater flow models 1 use of hydrogeologic information a new method is developed to efficiently compute exact scheffe type confidence intervals for output or other function of parameters g beta derived from a groundwater flow model the method is general in that parameter uncertainty can be specified by any statistical distribution having a log probability density function log pdf that can be expanded in a taylor series however for this study parameter uncertainty is specified by a statistical multivariate beta distribution that incorporates hydrogeologic information in the form of the investigator s best estimates of parameters and a grouping of random variables representing possible parameter values so that each group is defined by maximum and minimum bounds and an ordering according to increasing value the new method forms the confidence intervals from maximum and minimum limits of g beta on a contour of a linear combination of 1 the quadratic form for the parameters used by cooley and vecchia 1987 and 2 the log pdf for the multivariate beta distribution three example problems are used to compare characteristics of the confidence intervals for hydraulic head obtained using different weights for the linear combination different weights generally produced similar confidence intervals whereas the method of cooley and vecchia 1987 often produced much largermore confidence intervals less

inverse modeling of groundwater flow using model reduction numerical groundwater flow models often have a very high number of model cells greater than a million such models are computationally very demanding which is disadvantageous for inverse modeling this paper describes a low dimensional formulation for groundwater flow that reduces the computational burden necessary for inverse modeling the formulation is a projection of the original groundwater flow equation on a set of orthogonal patterns i e a galerkin projection the patterns empirical orthogonal functions are computed by a decomposition of the covariance matrix over an ensemble of model solutions those solutions represent the behavior of the model as a result of model impulses and the influence of a chosen set of parameter values for an interchangeable set of parameter values the patterns yield a low dimensional model as the number of patterns is often small an advantage of this model is that the adjoint is easily available and most accurate for inverse modeling for several synthetical cases the low dimensional model was able to find the global minimum efficiently and the result was comparable to that of the original model for several cases our model even converged where the original model failed our results demonstrate that the proposed procedure results in a 60 time reduction to solve the groundwater flow inverse problem greater efficiencies can be expected in practice for large scale models with a large number of grid cells that are used to compute transient simulations

new steps on sobolev orthogonality in two variables sobolev orthogonal polynomials in two variables are defined via inner products involving gradients such a kind of inner product appears in connection with several physical and technical problems matrix second order partial differential equations satisfied by sobolev orthogonal polynomials are studied in particular we explore the connection between the coefficients of the second order partial differential operator and the moment functionals defining the sobolev inner product finally some old and new examples are given

a computationally efficient parallel levenberg marquardt algorithm for highly parameterized inverse model analyses inverse modeling seeks model parameters given a set of observations however for practical problems because the number of measurements is often large and the model parameters are also numerous conventional methods for inverse modeling can be computationally expensive we have developed a new computationally efficient parallel levenberg marquardt method for solving inverse modeling problems with a highly parameterized model space levenberg marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large scale problems our novel method projects the original linear problem down to a krylov subspace such that the dimensionality of the problem can be significantly reduced furthermore we store the krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters the efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques we apply this new inverse modeling method to invert for random transmissivity fields in 2 d and a random hydraulic conductivity field in 3 d our algorithm is fast enough to solve for the distributed model parameters transmissivity in the model domain the algorithm is coded in julia and implemented in the mads computational framework http mads lanl gov by comparing with levenberg marquardt methods using standard linear inversion techniques such as qr or svd methods our levenberg marquardt method yields a speed up ratio on the order of 101 to 102 in a multicore computational environment therefore our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate to large scale problems