robust optimal control of regular languages this paper presents an algorithm for robust optimal control of regular languages under specified uncertainty bounds on the event cost parameters of the language measure that has been recently reported in literature the performance index for the proposed robust optimal policy is obtained by combining the measure of the supervised plant language with uncertainty the performance of a controller is represented by the language measure of the supervised plant and is minimized over the given range of event cost uncertainties synthesis of the robust optimal supervisory control policy requires at most n iterations where n is the number of states of the deterministic finite state automaton dfsa model generated from the regular language of the unsupervised plant behavior the computational complexity of the control synthesis method is polynomial in n

estimation of von bertalanffy growth curve parameters from recapture data a simple method of constructing estimating functions for parameters in the von bertalanffy growth model e y t l 1 exp kt is presented for tag recapture data when the age of the animal is unknown the estimating functions are unbiased under very general distributional assumptions provided k does not vary between animals simulations of growth in lobsters and whelks indicate that the method performs well provided the initial capture times and recapture intervals vary over reasonable ranges comparison is made with methods based on least squares which have been shown to be generally inconsistent

invariance principle for the random conductance model with unbounded conductances we study a continuous time random walk x in an environment of i i d random conductances e 1 we obtain heat kernel bounds and prove a quenched invariance principle for x this holds even when e e

dirac operators and the calculation of the connes metric on arbitrary infinite graphs as an outgrowth of our investigation of non regular spaces within the context of quantum gravity and non commutative geometry we develop a graph hilbert space framework on arbitrary infinite graphs and use it to study spectral properties of graph laplacians and graph dirac operators we define a spectral triplet sharing most of the properties of what connes calls a spectral triple with the help of this scheme we derive an explicit expression for the connes distance function on general directed or undirected graphs we derive a series of a priori estimates and calculate it for a variety of examples of graphs as a possibly interesting side we show that the natural setting for approaching such problems may be the framework of non linear programming or optimization we compare our results arrived at within our particular framework with those of other authors and show that the seeming differences depend on the use of different graph geometries and or dirac operators

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

determination of the unknown age at first capture of western rock lobsters panulims cygnus by random effects model summary we propose a method for fitting growth curves to multiple recapture data of lobsters when the age at first capture is unknown the von bertalanffy growth curve is used to model the growth to account for individual variability the unknown age in logarithmic scale of a lobster at first capture the individual asymptotic size and the individual growth coefficient of its carapace length are modeled as random effects with a trivariate normal distribution unlike previously suggested models the present model permits correlation between the growth coefficient and the age at first capture and can be fitted readily using existing software the error structures between consecutive recaptures of a lobster are assumed to be a first order autoregressive process with unequally spaced time points a comparison between this model and the fabens growth equation is given the proposed method is a flexible method and can be applied to fit different growth equations when the age at first capture is unknown

superderivations and symmetric markov semigroups unbounded superderivations are used to construct non commutative elliptic operators on semi finite von neumann algebras the method exploits the interplay between dynamical semigroups and dirichlet forms the elliptic operators may be viewed as generators of irreversible dynamics for fermion systems with infinite degrees of freedom

dirac operators and spectral triples for some fractal sets built on curves abstract we construct spectral triples and in particular dirac operators for the algebra of continuous functions on certain compact metric spaces the triples are countable sums of triples where each summand is based on a curve in the space several fractals like a finitely summable infinite tree and the sierpinski gasket fit naturally within our framework in these cases we show that our spectral triples do describe the geodesic distance and the minkowski dimension as well as more generally the complex fractal dimensions of the space furthermore in the case of the sierpinski gasket the associated dixmier type trace coincides with the normalized hausdorff measure of dimension log 3 log 2

volume growth and spectrum for general graph laplacians we prove estimates relating exponential or sub exponential volume growth of weighted graphs to the bottom of the essential spectrum for general graph laplacians the volume growth is computed with respect to a metric adapted to the laplacian and use of these metrics produces better results than those obtained from consideration of the graph metric only conditions for absence of the essential spectrum are also discussed these estimates are shown to be optimal or near optimal in certain settings and apply even if the laplacian under consideration is an unbounded operator

spectral properties of the two photon absorption and emission process the quantum markov semigroup of the two photon absorption and emission process has two extremal normal invariant states starting from an arbitrary initial state it converges toward some convex combination of these states as time goes to infinity approach to equilibrium we compute the exact exponential rate of this convergence showing that it depends only on the emission rates moreover we show that off diagonal matrix elements of any initial state go to zero with an exponential rate which is smaller than the exponential rate of convergence of the diagonal part in other words quantum features of a state survive longer than the relaxation time of its classical part

robust and nonblocking supervisory control of nondeterministic discrete event systems using trajectory models this note considers the robust supervisory control problems of uncertain nondeterministic discrete event systems dess the uncertain des to be controlled is assumed to be modeled as a set of some possible nondeterministic automata then the control objective is to achieve a given language specification and guarantee the nonblockingness of any nondeterministic automata of the set which are controlled by a robust nonblocking supervisor based on trajectory models this note presents the necessary and sufficient conditions for the existence of a robust nonblocking supervisor for a given uncertain nondeterministic des

dirichlet forms and markovian semigroups on standard forms of von neumann algebras we characterize w continuous markovian semigroups on a von neumann algebra m which are 0 symmetric w r t a faithful normal state 0in m in terms of quadratic forms on the hilbert space h of a standard form m h p j we characterize also symmetric strongly continuous contraction semigroups on a real hilbert space h which leave invariant a closed convex set in h in terms of a contraction property of the associated quadratic forms we apply the results to give criteria of essential selfadjointness for quadratic form sums and to give a characterization of w continuous markovian semigroups on m which commute with the modular automorphism group 0t

ergodic property of markovian semigroups on standard forms of von neumann algebras we give sufficient conditions for ergodicity of the markovian semigroups associated to dirichlet forms on standard forms of von neumann algebras constructed by the method proposed by park we apply our result to show that the diffusion type markovian semigroups for quantum spin systems are ergodic in the region of high temperatures where the uniqueness of the kms state holds

estimation of growth parameters from multiple recapture data this article develops a method for analysis of growth data with multiple recaptures when the initial ages for all individuals are unknown the existing approaches either impute the initial ages or model them as random effects assumptions about the initial age are not verifiable because all the initial ages are unknown we present an alternative approach that treats all the lengths including the length at first capture as correlated repeated measures for each individual optimal estimating equations are developed using the generalized estimating equations approach that only requires the first two moment assumptions explicit expressions for estimation of both mean growth parameters and variance components are given to minimize the computational complexity simulation studies indicate that the proposed method works well two real data sets are analyzed for illustration one from whelks dicathais aegaota and the other from southern rock lobster jasus edwardsii in south australia

dirac and magnetic schrodinger operators on fractals abstract in this paper we define local dirac operators and magnetic schrodinger hamiltonians on fractals and prove their essential self adjointness to do so we use the concept of 1 forms and derivations associated with dirichlet forms as introduced by cipriani and sauvageot and further studied by the authors jointly with rockner ionescu and rogers for simplicity our definitions and results are formulated for the sierpinski gasket with its standard self similar energy form we point out how they may be generalized to other spaces such as the classical sierpinski carpet

intrinsic metrics for non local symmetric dirichlet forms and applications to spectral theory we present a study of what may be called an intrinsic metric for a general regular dirichlet form for such forms we then prove a rademacher type theorem for strongly local forms we show existence of a maximal intrinsic metric under a weak continuity condition and for dirichlet forms with an absolutely continuous jump kernel we characterize intrinsic metrics by bounds on certain integrals we then turn to applications on spectral theory and provide for measure perturbation of general regular dirichlet forms an allegretto piepenbrinck type theorem which is based on a ground state transform and a shnol type theorem our setting includes laplacian on manifolds on graphs and stable processes

supervisory control of nondeterministic systems with driven events via prioritized synchronization and trajectory models the supervisory control of nondeterministic discrete event dynamical systems dedss with driven events in the setting of prioritized synchronization and trajectory models introduced by heymann are studied prioritized synchronization captures the notions of controllable uncontrollable and driven events in a natural way and the authors use it for constructing supervisory controllers the trajectory model is used for characterizing the behavior of nondeterministic dedss since it is a sufficiently detailed model in contrast to the less detailed language or failures models and serves as a language congruence with respect to the operation of prioritized synchronization results concerning controllability and observability in this general setting are obtained

robust nonblocking supervisory control of discrete event systems under partial observation in this paper we extend previous results on robust nonblocking supervisory control of discrete event systems with full observation to the case of control under partial observation where only a subset of events are observable and can be monitored the exact model of the plant is not known but is assumed to be among a finite set of possible models for each plant model a legal marked behavior is assumed given we manage to characterize the entire set of solutions of the robust control problem and obtain a set of necessary and sufficient conditions for the existence of a solution for the robust control problem

verification of robust diagnosability for partially observed discrete event systems in this paper we study robust failure diagnosis of discrete event systems given a set of possible models each of which has its own nonfailure specification we consider the existence of a single diagnoser such that for all possible models it detects any occurrence of a failure within a uniformly bounded number of steps we call such a diagnoser a robust diagnoser we introduce a notion of robust diagnosability and prove that it serves as a necessary and sufficient condition for the existence of a robust diagnoser we then present an algorithm for verifying the robust diagnosability condition

spectral analysis and feller property for quantum ornstein uhlenbeck semigroups a class of dynamical semigroups arising in quantum optics models of masers and lasers is investigated the semigroups are constructed by means of noncommutative dirichlet forms on the full algebra of bounded operators on a separable hilbert space the explicit action of their generators on a core in the domain is used to demonstrate the feller property of the semigroups with respect to the c subalgebra of compact operators the dirichlet forms are analysed and the c 2 spectrum together with eigenspaces are found when reduced to certain maximal abelian subalgebras the semigroups give rise to the markov semigroups of classical ornstein uhlenbeck processes on the one hand and of classical birth and death processes on the other

analysis on graphs and noncommutative geometry abstract we study the form of the continuous time heat kernel for a second order discrete laplacian on a weighted graph the analysis is shown to be closely related to the theory of symmetric markov semigroups on noncommutative l p spaces and to the noncommutative geometry of connes the paper obtains better pointwise upper bounds on the heat kernels than those previously known by the use of a novel metric on the graph in certain cases it is shown that the new estimates are optimal of their type the metric is investigated at some length and compared with other known metrics on graphs

dirichlet forms and symmetric markovian semigroups on ccr algebras with respect to quasi free states employing the construction method of dirichlet forms on standard forms of von neumann algebras developed in infinite dimensional analysis quantum probability and related topics 2000 vol 3 no 1 pp 1 14 ref 1 we construct dirichlet forms and associated symmetric markovian semigroups on ccr algebras with respect to quasi free states more precisely let a h0 be the ccr algebra over a complex separable pre hilbert space h0 and let be a quasi free state on a h0 for any normalized admissible function f and complete orthonormal system cons gn h0 we construct a dirichlet form and corresponding symmetric markovian semigroup on the natural standard form associated to the gns representation of a h0 it turns out that the form is independent of admissible function f and cons gn chosen by analyzing the spectrum of the generator dirichlet operator of the semigroup we show that the semigroup is ergodic and tends to the equilibrium exponentially fast

robustness of supervisors for discrete event systems supervisory control in the context of spl omega languages is considered the nominal supervisor design problem is to find a non blocking supervisor for a nominal plant such that the closed loop infinite behavior equals a specified closed loop behavior the robustness of solutions to the nominal problem is defined with respect to variations in the plant it is shown there exists a supervisor solving the nominal problem which maximizes the set of plants for which the closed loop languages for all other plants in the set satisfy lower and upper bounds in the sense of language containment computational issues are discussed and the theoretical results are illustrated with an example

construction of a family of quantum ornstein uhlenbeck semigroups for a given quasi free state on the ccr algebra over one dimensional hilbert space a family of markovian semigroups which leave the quasi free state invariant is constructed by means of noncommutative elliptic operators and dirichlet forms on von neumann algebras the generators dirichlet operators of the semigroups are analyzed and the spectrums together with eigenspaces are found when restricted to a maximal abelian subalgebra the semigroups are reduced to a unique markovian semigroup of classical ornstein uhlenbeck process

gradient flow and entropy inequalities for quantum markov semigroups with detailed balance abstract we study a class of ergodic quantum markov semigroups on finite dimensional unital c algebras these semigroups have a unique stationary state and we are concerned with those that satisfy a quantum detailed balance condition with respect to we show that the evolution on the set of states that is given by such a quantum markov semigroup is gradient flow for the relative entropy with respect to in a particular riemannian metric on the set of states this metric is a non commutative analog of the 2 wasserstein metric and in several interesting cases we are able to show in analogy with work of otto on gradient flows with respect to the classical 2 wasserstein metric that the relative entropy is strictly and uniformly convex with respect to the riemannian metric introduced here as a consequence we obtain a number of new inequalities for the decay of relative entropy for ergodic quantum markov semigroups with detailed balance

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

modular implementation of robust supervisory controllers for discrete event systems in this paper the problem of designing robust supervisory controllers for uncertain discrete event systems is studied it is assumed that both the plant behavior and the design specifications can be represented by regular languages it is also assumed that the unknown model of the uncertain plant belongs to a finite set of possibilities to solve the problem a modular approach based on a general recursive robust control scheme is developed the contribution of the present paper consists in deriving a maximally permissive modular robust supervisory controller for the case of prefix closed languages having the advantage of linear complexity in the number of models as opposed to the exponential complexity of the worst case scenario in the direct implementation of standard supervisors for augmented systems

a reduction method for noncommutative l_p spaces and applications we consider the reduction of problems on general noncommutative l p spaces to the corresponding ones on those associated with finite von neumann algebras the main tool is an unpublished result of the first named author which approximates any noncommutative l p space by tracial ones we show that under some natural conditions a map between two von neumann algebras extends to their crossed products by a locally compact abelian group or to their noncommutative l p spaces we present applications of these results to the theory of noncommutative martingale inequalities by reducing most recent general noncommutative martingale ergodic inequalities to those in the tracial case

lipschitz algebras and derivations ii exterior differentiation abstract basic aspects of differential geometry can be extended to various non classical settings lipschitz manifolds rectifiable sets sub riemannian manifolds banach manifolds wiener space etc although the constructions differ in each of these cases one can define a module of measurable 1 forms and a first order exterior derivative we give a general construction which applies to any metric space equipped with a finite measure and produces the desired result in all of the above cases it agrees with cheeger s construction when the latter is defined it also applies to an important class of dirichlet spaces where however the known first order differential calculus in general differs from ours although the two are related

derivations as square roots of dirichlet forms abstract the aim of this work is to analyze the structure of a tracially symmetric dirichlet form on a c algebra in terms of a killing weight and a closable derivation taking values in a hilbert space with a bimodule structure it is shown that the generator of the associate markovian semigroup always appears in a natural way as the divergence of a closable derivation applications are shown to the decomposition of dirichlet forms and to the construction of differential calculus on metric spaces

quantum ito s formula and stochastic evolutions using only the boson canonical commutation relations and the riemann lebesgue integral we construct a simple theory of stochastic integrals and differentials with respect to the basic field operator processes this leads to a noncommutative ito product formula a realisation of the classical poisson process in fock space which gives a noncommutative central limit theorem the construction of solutions of certain noncommutative stochastic differential equations and finally to the integration of certain irreversible equations of motion governed by semigroups of completely positive maps the classical ito product formula for stochastic differentials with respect to brownian motion and the poisson process is a special case

remarks on the decomposition of dirichlet forms on standard forms of von neumann algebras for a bounded generator g of a weakly continuous completely positive kms symmetric markovian semigroup on a von neumann algebra m acting on a separable hilbert space h let h be the operator induced by g via the symmetric embedding of m into h we decompose the dirichlet form associated with h into a direct integral of forms whose associated generators are divergences of derivations moreover if the derivations are inner then the dirichlet form can be written as the form given by park infinite dimen anal quantum probab relat top 3 1 2000 8 179 2005

nonblocking supervisory control of nondeterministic systems via prioritized synchronization shayman and kumar 1995 showed that supervisory control of nondeterministic discrete event systems in the presence of driven events can be achieved using prioritized synchronous composition as a mechanism of control and trajectory models as a modeling formalism first introduced by heymann 1990 the specifications considered in this earlier work were given by prefix closed languages in this paper we extend this work to include markings so that nonclosed specifications and issues such as blocking can be addressed it is shown that the usual notion of nonblocking called language model nonblocking may not be adequate in the setting of nondeterministic systems and a stronger notion called trajectory model nonblocking is introduced necessary and sufficient conditions for the existence of language model nonblocking as well as trajectory model nonblocking supervisors are obtained for nondeterministic systems in the presence of driven events in terms of extended controllability and relative closure conditions and a new condition called the trajectory closure condition

non symmetric dirichlet forms on semifinite von neumann algebras abstract the theory of non symmetric dirichlet forms is generalized to the non abelian setting also establishing the natural correspondences among dirichlet forms sub markovian semigroups and sub markovian resolvents within this context some results on the allowed functional calculus for closed derivations on hilbert algebras are obtained examples of non symmetric dirichlet forms given by derivations on hilbert algebras are studied

unequally spaced longitudinal data with ar 1 serial correlation this paper discusses longitudinal data analysis when each subject is observed at different unequally spaced time points observations within subjects are assumed to be either uncorrelated or to have a continuous time first order autoregressive structure possibly with observation error the random coefficients are assumed to have an arbitrary between subject covariance matrix covariates can be included in the fixed effects part of the model exact maximum likelihood estimates of the unknown parameters are computed using the kalman filter to evaluate the likelihood which is then maximized with a nonlinear optimization program an example is presented where a large number of subjects are each observed at a small number of observation times hypothesis tests for selecting the best model are carried out using wald s test on contrasts or likelihood ratio tests based on fitting full and restricted models

the haagerup approximation property for von neumann algebras via quantum markov semigroups and dirichlet forms the haagerup approximation property for a von neumann algebra equipped with a faithful normal state is shown to imply existence of unital preserving and kms symmetric approximating maps this is used to obtain a characterisation of the haagerup approximation property via quantum markov semigroups extending the tracial case result due to jolissaint and martin and further via quantum dirichlet forms

application of nonlinear models with random coefficients to growth data summary the application of nonlinear random coefficient models to the analysis of growth curve data is described the approach is further developed for the estimation of mean growth curves and their variability from mark recapture data when the age of an animal at first capture is unknown but the time between successive captures is known these methods are of wide applicability as shown by the analysis of data on the growth of emus dromaius novaehollandiae noisy scrub birds atrichornis clamosus and whelks dicathais aegaota simulations of a mark recapture experiment on the rock spiny lobster panulirus argus in mexico using a known growth curve showed the effectiveness of the approach in estimating both the population s growth curve and the variability in individual growth

robust and nonblocking supervisory control of nondeterministic discrete event systems with communication delay and partial observation for an uncertain nondeterministic discrete event system des modelled as a set of possible nondeterministic finite state automata uncontrollable events may subsequently occur before a control action issued by a robust supervisor is applied to the system due to delays in sensing communicating and actuating for an uncertain nondeterministic des under such communication delays and partial observation this article presents necessary and sufficient conditions for the existence of a robust and nonblocking supervisor to achieve a given language specification for any nondeterministic model in the set moreover this article addresses a synthesis problem of a robust and nonblocking supervisor