sensor location for discrete mode observability of switching linear systems with unknown inputs this paper deals with the problem of additional sensor placement in order to recover the discrete mode observability of switching structured linear systems with unknown inputs such a property is quite important for designing control laws observers fault detection and isolation schemes when the fault occurrence implies a commutation between two modes and so on the proposed method based on a graph theoretic approach assumes only the knowledge of the system s structure we express in graphical terms new necessary and sufficient conditions for discrete mode generic observability when these conditions are not satisfied we propose a sensor placement procedure which allows us to recover the mode observability our approach can be implemented by classical and quite simple graph theory algorithms

noise induced escape from bifurcating attractors symplectic approach in the weak noise limit the effect of noise is studied in one dimensional maps undergoing transcritical tangent and pitchfork bifurcations the attractors of the noiseless map become metastable states in the presence of noise in the weak noise limit a symplectic two dimensional map is associated with the original one dimensional map the consequences of their noninvertibility on the phase space structures are discussed heteroclinic orbits are identified which play a key role in the determination of the escape rates from the metastable states near bifurcations the critical slowing down justifies the use of a continuous time approximation replacing maps by flows which allows the analytic calculation of the escape rates this method provides the universal scaling behavior of the escape rates at the bifurcations

generalized covariations local time and stratonovich ito s formula for fractional brownian motion with hurst index h 1 4 given a locally bounded real function g we examine the existence of a 4 covariation g b h b h b h b h where b h is a fractional brownian motion with a hurst index h ge tfrac 1 4 we provide two essential applications first we relate the 4 covariation to one expression involving the derivative of local time in the case h tfrac 1 4 generalizing an identity of bouleau yor type well known for the classical brownian motion a second application is an ito formula of stratonovich type for f b h the main difficulty comes from the fact b h has only a finite 4 variation

forward backward and symmetric stochastic integration we define three types of non causal stochastic integrals forward backward and symmetric our approach consists in approximating the integrator two optics are considered the first one is based on traditional usual stochastic calculus and the second one on wiener distributions

a countable representation of the fleming viot measure valued diffusion the fleming viot measure valued diffusion arises as the infinite population limit of various discrete genetic models with general type space the paper gives a countable construction of the process as the empirical measure carried by a certain interactive particle system this explicit representation facilitates the study of various properties of the fleming viot process the construction also carries versions of the familiar genealogical processes from population genetics in particular kingman s coalescent thus unifying the genealogical and measure valued approaches to the subject

particle representations for measure valued population models models of populations in which a type or location represented by a point in a metric space e is associated with each individual in the population are considered a population process is neutral if the chances of an individual replicating or dying do not depend on its type measurevalued processes are obtained as infinite population limits for a large class of neutral population models and it is shown that these measure valued processes can be represented in terms of the total mass of the population and the de finetti measures associated with an e valued particle model

sensor location and classification for disturbance rejection by measurement feedback in this paper a new necessary and sufficient condition is proposed for the solvability of the disturbance rejection by measurement feedback drmf problem involving linear structured systems the associated system graph can be used to easily check whether or not the condition holds in relation to the drmf problem two issues related to the available sensor set have been investigated sensor number and location when the drmf problem is not solvable with the given sensor set how many sensors are needed and where should they be located to make the drmf problem solvable sensor classification when the drmf problem is solvable with the given sensor set what is the impact of the failure of a sensor on the solvability based on the new condition a lower bound can be determined for the number of sensors required moreover measuring state variables outside a given subset is found to be of no use to solve the drmf problem it is sufficient to measure state variables sufficiently close to the disturbances in the associated system graph sensor classification is used to distinguish between essential sensors i e sensors for which failure leads to unsolvability and useless sensors that have no impact on solvability partial classification results are provided for the general case and a complete characterization of essential and useless sensors is provided for the single disturbance case

stopping time resampling for sequential monte carlo methods summary motivated by the statistical inference problem in population genetics we present a new sequential importance sampling with resampling strategy the idea of resampling is key to the recent surge of popularity of sequential monte carlo methods in the statistics and engineering communities but existing resampling techniques do not work well for coalescent based inference problems in population genetics we develop a new method called stopping time resampling which allows us to compare partially simulated samples at different stages to terminate unpromising partial samples and to multiply promising samples early on to illustrate the idea we first apply the new method to approximate the solution of a dirichlet problem and the likelihood function of a non markovian process then we focus on its application in population genetics all our examples show that the new resampling method can significantly improve the computational efficiency of existing sequential importance sampling methods

simultaneous finite and infinite zero assignments of linear systems abstract a simultaneous finite and infinite zero assignment problem via sensor selection for linear multivariable systems is proposed by sensor selection we mean an appropriate choice of the output matrix c here by utilizing the well known burnovsky canonical form for a linear system characterized by the matrix pair a b we obtain an explicit construction algorithm that generates a non empty set c of output matrices such that for any member c of this set the corresponding system characterized by the triple a b c has the prescribed finite and infinite zero structures two examples are also given to illustrate our results

semi martingale inequalities via the garsia rodemich rumsey lemma and applications to local times abstract with the help of the garsia rodemich rumsey lemma some improvements of the burkholder davis gundy inequalities for continuous martingales are obtained as well as certain estimates of the l p norm of the supremum of a the local times of a continuous semi martingale and b the difference of the local times of two continuous martingales

survival of contact processes on the hierarchical group we consider contact processes on the hierarchical group where sites infect other sites at a rate depending on their hierarchical distance and sites become healthy with a constant recovery rate if the infection rates decay too fast as a function of the hierarchical distance then we show that the critical recovery rate is zero on the other hand we derive sufficient conditions on the speed of decay of the infection rates for the process to exhibit a nontrivial phase transition between extinction and survival for our sufficient conditions we use a coupling argument that compares contact processes on the hierarchical group with freedom two with contact processes on a renormalized lattice an interesting novelty in this renormalization argument is the use of a result due to rogers and pitman on markov functionals

assignment of complete structural properties of linear systems via sensor selection for x ax bu the problem of structural assignment via sensor selection is to find an output equation y cx du such that the resulting system a b c d has the pre specified structural properties such as the finite and infinite zero structures as well as the invertibility properties in this paper we establish a set of necessary and sufficient conditions under which a complete set of system structural properties can be assigned and an explicit algorithm for constructing the required matrix pair c d

joint convergence along different subsequences of the signed cubic variation of fractional brownian motion the purpose of this paper is to study the convergence in distribution of two subsequences of the signed cubic variation of the fractional brownian motion with hurst parameter h 1 6 we prove that under some conditions on both subsequences the limit is a two dimensional brownian motion whose components may be correlated and we find explicit formulae for its covariance function

a change of variable formula with ito correction term we consider the solution u x t to a stochastic heat equation for fixed x the process f t u x t has a nontrivial quartic variation it follows that f is not a semimartingale so a stochastic integral with respect to f cannot be defined in the classical ito sense we show that for sufficiently differentiable functions g x t a stochastic integral g f t t d f t exists as a limit of discrete midpoint style riemann sums where the limit is taken in distribution in the skorokhod space of cadlag functions moreover we show that this integral satisfies a change of variable formula with a correction term that is an ordinary ito integral with respect to a brownian motion that is independent of f

a change of variable formula for the 2d fractional brownian motion of hurst index bigger or equal to 1 4 we prove a change of variable formula for the 2d fractional brownian motion of index h bigger of equal to 1 4 for h strictly bigger than 1 4 our formula coincides with that obtained by using the rough paths theory for h 1 4 the more interesting case there is an additional term that is a classical wiener integral against an independent standard brownian motion

trace formulas for stochastic evolution operators weak noise perturbation theory periodic orbit theory is all effective tool for the analysis of classical and quantum chaotic systems in this paper we extend this approach to stochastic systems in particular to mappings with additive noise the theory is cast in the standard field theoretic formalism and weak noise perturbation theory written in terms of feynman diagrams the result is a stochastic analog of the next to leading h corrections to the gutzwiller trace formula with long time averages calculated from periodic orbits of the deterministic system the perturbative corrections are computed analytically and tested numerically on a simple 1 dimensional system

survey generic properties and control of linear structured systems a survey in this survey paper we consider linear structured systems in state space form where a linear system is structured when each entry of its matrices like a b c and d is either a fixed zero or a free parameter the location of the fixed zeros in these matrices constitutes the structure of the system indeed a lot of man made physical systems which admit a linear model are structured a structured system is representative of a class of linear systems in the usual sense it is of interest to investigate properties of structured systems which are true for almost any value of the free parameters therefore also called generic properties interestingly a lot of classical properties of linear systems can be studied in terms of genericity moreover these generic properties can in general be checked by means of directed graphs that can be associated to a structured system in a natural way we review here a number of results concerning generic properties of structured systems expressed in graph theoretic terms by properties we mean here system specific properties like controllability the finite and infinite zero structure and so on as well as solvability issues of certain classical control problems like disturbance rejection input output decoupling and so on in this paper we do not try to be exhaustive but instead by a selection of results we would like to motivate the reader to appreciate what we consider as a wonderful modelling and analysis tool we emphasize the fact that this modelling technique allows us to get a number of important results based on poor information on the system only moreover the graph theoretic conditions are intuitive and are easy to check by hand for small systems and by means of well known polynomially bounded combinatorial techniques for larger systems

macroscopic limits for stochastic partial differential equations of mckean vlasov type a class of quasilinear stochastic partial differential equations spdes driven by spatially correlated brownian noise is shown to become macroscopic i e deterministic as the length of the correlations tends to 0 the limit is the solution of a quasilinear partial differential equation the quasilinear spdes are obtained as a continuum limit from the empirical distribution of a large number of stochastic ordinary differential equations sodes coupled though a mean field interaction and driven by correlated brownian noise the limit theorems are obtained by application of a general result on the convergence of exchangeable systems of processes we also compare our approach to sodes with the one introduced by kunita

the generic number of invariant zeros of a structured linear system in this paper we consider a structured linear system represented by means of a directed graph we present a graph theoretic method to compute the generic number of invariant zeros of the corresponding rosenbrock matrix the method is based on a fundamental decomposition of the directed graph representing the structured system the generic number of invariant zeros is important in generic versions of problems involving controllability and pole placement

the tree length of an evolving coalescent a well established model for the genealogy of a large population in equilibrium is kingman s coalescent for the population together with its genealogy evolving in time this gives rise to a time stationary tree valued process we study the sum of the branch lengths briefly denoted as tree length and prove that the suitably compensated sequence of tree length processes converges as the population size tends to infinity to a limit process with cadlag paths infinite infinitesimal variance and a gumbel distribution as its equilibrium

spectrum of stochastic evolution operators local matrix representation approach a matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum in the weak noise limit a perturbative expansion for the spectrum is formulated in terms of local matrix representations of the evolution operator centered on classical periodic orbits the evaluation of perturbative corrections is easier to implement in this framework than in the standard feynman diagram perturbation theory the results are perturbative corrections to a stochastic analog of the gutzwiller semiclassical spectral determinant computed to several orders beyond what has so far been attainable in stochastic and quantum mechanical applications

smaller population size at the mrca time for stationary branching processes we consider an elementary model of random size varying population governed by a stationary continuous state branching process we compute the distributions of various variables related to the most recent common ancestor mrca the time to the mrca the size of the current population and the size of the population just before the mrca in particular we observe a natural mild bottleneck effect as the size of the population just before the mrca is stochastically smaller than the size of the current population we also compute the number of individuals involved in the last coalescent event of the genealogical tree that is the number of individuals at the time of the mrca who have descendants in the current population by studying more precisely the genealogical structure of the population we get asymptotics for the number of ancestors just before the current time we give explicit computations in the case of the quadratic branching mechanism in this case the size of the population at the mrca is in mean 2 3 of the size of the current population we also provide in this case the fluctuations for the renormalized number of ancestors

weak noise approach to the logistic map using a nonperturbative weak noise approach we investigate the interference of noise and chaos in simple 1d maps we replace the noise driven 1d map by an area preserving 2d map modelling the poincare sections of a conserved dynamical system with unbounded energy manifolds we analyze the properties of the 2d map and draw conclusions concerning the interference of noise on the nonlinear time evolution we apply this technique to the standard period doubling sequence in the logistic map from the 2d area preserving analogue we in addition to the usual period doubling sequence obtain a series of period doubled cycles which are elliptic in nature these cycles are spinning off the real axis at parameters values corresponding to the standard period doubling events

canonical phase space approach to the noisy burgers equation probability distributions we present a canonical phase space approach to stochastic systems described by langevin equations driven by white noise mapping the associated fokker planck equation to a hamilton jacobi equation in the nonperturbative weak noise limit we invoke a principle of least action for the determination of the probability distributions we apply the scheme to the noisy burgers and kardar parisi zhang equations and discuss the time dependent and stationary probability distributions in one dimension we derive the long time skew distribution approaching the symmetric stationary gaussian distribution in the short time region we discuss heuristically the nonlinear soliton contributions and derive an expression for the distribution in accordance with the directed polymer replica and asymmetric exclusion model results we also comment on the distribution in higher dimensions

soliton approach to the noisy burgers equation steepest descent method the noisy burgers equation in one spatial dimension is analyzed by means of the martin siggia rose technique in functional form in a canonical formulation the morphology and scaling behavior are accessed by means of a principle of least action in the asymptotic nonperturbative weak noise limit the ensuing coupled saddle point field equations for the local slope and noise fields replacing the noisy burgers equation are solved yielding nonlinear localized soliton solutions and extended linear diffusive mode solutions describing the morphology of a growing interface the canonical formalism and the principle of least action also associate momentum energy and action with a soliton diffusive mode configuration and thus provide a selection criterion for the noise induced fluctuations in a quantum mechanical representation of the path integral the noise fluctuations corresponding to different paths in the path integral are interpreted as quantum fluctuations and the growth morphology represented by a landau type quasiparticle gas of quantum solitons with gapless dispersion e ensuremath propto p 3 2 and quantum diffusive modes with a gap in the spectrum finally the scaling properties are discussed from a heuristic point of view in terms of a quantum spectral representation for the slope correlations the dynamic exponent z 3 2 is given by the gapless soliton dispersion law whereas the roughness exponent ensuremath zeta 1 2 follows from a regularity property of the form factor in the spectral representation a heuristic expression for the scaling function is given by a spectral representation and has a form similar to the probability distribution for l evy flights with index z

an analytic approach to fleming viot processes with interactive selection we study a class of nonsymmetric dirichlet forms e d e having a space of measures as state space e and derive some general results about them we show that under certain conditions they generate diffusion processes m in particular if m is ergodic and e d e is symmetric w r t quasi every starting point the large deviations of the empirical distribution of m are governed by e we apply all of this to construct fleming viot processes with interactive selection and prove some results on their behavior among other things we show some support properties for these processes using capacitary methods

resolvent estimates for fleming viot operators with brownian drift abstract this article is a supplement to the paper of d a dawson and p march j funct anal 132 1995 417 472 we define a two parameter scale of banach spaces of functions defined on m 1 r d the space of probability measures on d dimensional euclidean space using weighted sums of the classical sobolev norms we prove that the resolvent of the fleming viot operator with constant diffusion coefficient and brownian drift acts boundedly between certain members of the scale these estimates gauge the degree of smoothing performed by the resolvent and separate the contribution due to the diffusion coefficient and that due to the drift coefficient

observer based fault detection and isolation for structured systems fault detection and isolation fdi problems are here consid ered for linear systems with faults and disturbances we design a set of ob server based residuals in such a way that the transfer from the disturbances to the residuals is zero and the transfer from the faults to the residuals al lows fault isolation we are interested in obtaining a transfer function from faults to residuals with either a diagonal structure i e a dedicated struc tured residuals set or a triangular one we deal with this problem when the system under consideration is structured that is the entries of the system matrices are either fixed zeros or free parameters to a structured system one can associate in a natural way a directed graph we can then provide necessary and sufficient conditions under which the fdi problems have a solution for almost any value of the free parameters these conditions are simply expressed in terms of input output paths in the associated graph index terms fault detection and isolation graph theory model based approach structured residuals structured systems

inference in molecular population genetics full likelihood based inference for modern population genetics data presents methodological and computational challenges the problem is of considerable practical importance and has attracted recent attention with the development of algorithms based on importance sampling is and markov chain monte carlo mcmc sampling here we introduce a new is algorithm the optimal proposal distribution for these problems can be characterized and we exploit a detailed analysis of genealogical processes to develop a practicable approximation to it we compare the new method with existing algorithms on a variety of genetic examples our approach substantially outperforms existing is algorithms with efficiency typically improved by several orders of magnitude the new method also compares favourably with existing mcmc methods in some problems and less favourably in others suggesting that both is and mcmc methods have a continuing role to play in this area we offer insights into the relative advantages of each approach and we discuss diagnostics in the is framework

variations of the solution to a stochastic heat equation we consider the solution to a stochastic heat equation this solution is a random function of time and space for a fixed point in space the resulting random function of time f t has a nontrivial quartic variation this process therefore has infinite quadratic variation and is not a semimartin gale it follows that the classical ito calculus does not apply motivated by heuristic ideas about a possible new calculus for this process we are led to study modifications of the quadratic variation namely we modify each term in the sum of the squares of the increments so that it has mean zero we then show that these sums as functions of t converge weakly to brownian motion

asymptotic expansions for the escape rate of stochastically perturbed unimodal maps abstract the escape rate of a stochastic dynamical system can be found as an expansion in powers of the noise strength in the previous work the coefficients of such an expansion for a one dimensional map were fitted to a general form containing a few parameters these parameters were found to be related to the fractal structure of the repeller of the system the parameter the noise dimension remains to be interpreted this report presents new data for showing that the relation to the dimensions is more complicated than predicted in the earlier work and oscillates as a function of the map parameter in contrast to other dimension like quantities

tree valued resampling dynamics martingale problems and applications the measure valued fleming viot process is a diffusion which models the evolution of allele frequencies in a multi type population in the neutral setting the kingman coalescent is known to generate the genealogies of the individuals in the population at a fixed time the goal of the present paper is to replace this static point of view on the genealogies by an analysis of the evolution of genealogies we encode the genealogy of the population as an isometry class of an ultra metric space which is equipped with a probability measure the space of ultra metric measure spaces together with the gromov weak topology serves as state space for tree valued processes we use well posed martingale problems to construct the tree valued resampling dynamics of the evolving genealogies for both the finite population moran model and the infinite population fleming viot diffusion we show that sufficient information about any ultra metric measure space is contained in the distribution of the vector of subtree lengths obtained by sequentially sampled individuals we give explicit formulas for the evolution of the laplace transform of the distribution of finite subtrees under the tree valued fleming viot dynamics

long time behaviour and regularity properties of transition semigroups of fleming viot processes let a be a feller generator on a compact space and l be the corresponding fleming viot fv operator with no selection and no recombination in this paper we give conditions on a implying that the semigroup t t generated by l i converges towards equilibrium with exponential rate moreover we determine explicit bounds on the rate of convergence in terms of a ii is hypercontractive iii is strong feller and iv is compact we give applications of the last result to the existence of invariant measures for fv operators with interactive selection

a graph theoretic approach to fault detection and isolation for structured bilinear systems in this paper using a graph theoretic approach we address some issues related to the fault detection and isolation for structured bilinear systems considering a structured bilinear system submitted to faults and disturbances we give necessary and sufficient conditions to the solvability of the so called bilinear fundamental problem of residual generation we also treat the cases where the system is submitted to multiple failures occurring simultaneously or only one at a time one of the main advantages of the proposed analysis tool is that all the given conditions are easy to check because they deal with finding paths in a digraph this makes our approach well suited to studying large scale systems

asymptotic behavior of weighted quadratic variations of fractional brownian motion the critical case h 1 4 we derive the asymptotic behavior of weighted quadratic variations of fractional brow nian motion b with hurst index h 1 4 this completes the only missing case in a very recent work by i nourdin d nualart and c a tudor moreover as an application we solve a recent conjecture of k burdzy and j swanson on the asymptotic behavior of the riemann sums with alternating signs associated to b

poisson representations of branching markov and measure valued branching processes representations of branching markov processes and their measure valued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates each particle has a location and a level but unlike earlier constructions the levels change with time in fact death of a particle occurs only when the level of the particle crosses a specified level r or for the limiting models hits infinity for branching markov processes at each time t conditioned on the state of the process the levels are independent and uniformly distributed on 0 r for the limiting measure valued process at each time t the joint distribution of locations and levels is conditionally poisson distributed with mean measure k t x lambda where lambda denotes lebesgue measure and k is the desired measure valued process the representation simplifies or gives alternative proofs for a variety of calculations and results including conditioning on extinction or nonextinction harris s convergence theorem for supercritical branching processes and diffusion approximations for processes in random environments

optimal sensor location for detecting changes in dynamical behavior we address the problem of optimal sensor location for monitoring the eigenstructure of a multivariable dynamical system the criterions which are optimized are the power of new tests designed for detecting and diagnosing changes in the eigencharacteristics of a system 3 12 the key points are the choice of the parameterization for computing the criterion and the comparison of designs with a different number of sensors the discussion of the numerical results for sensor location includes the analysis of the effect of the geometry of the unknown excitation

fleming viot processes in population genetics fleming and viot indiana univ math j 28 1979 pp 817 843 introduced a class of probability measure valued diffusion processes that has attracted the interest of both pure and applied probabilists this paper surveys the subject of fleming viot processes as it relates to population genetics topics include 1 introduction 2 some measure valued markov chains 2 1 a diploid model 2 2 the wright fisher model 2 3 a moran model 3 the fleming viot process characterization 4 convergence 5 ergodicity 6 an infinite particle system 7 bounded mutation operators 8 reversibility 9 examples 9 1 continuous state stepwise mutation model 9 2 infinitely many neutral alleles model 9 3 infinitely many neutral alleles model with ages 9 4 two locus model with recombination 9 5 n locus model with gene conversion 9 6 infinitely many sites model without recombination 9 7 infinitely many neutral alleles model with allelic genealogies

central limit theorem for a stratonovich integral with malliavin calculus this is the publisher s version also available electronically from http projecteuclid org euclid aop 1372859768

sensor location for diagnosis in linear systems a structural analysis we consider here the fault detection and isolation fdi problem for linear systems we are interested in designing a set of observer based residuals in such a way that the transfer from the faults to the residuals is diagonal and the transfer from the disturbances to the residuals is zero we deal with this problem when the system under consideration is structured that is the entries of the system matrices are either fixed zeros or free parameters this problem can be solved in terms of the graph that can be associated in a natural way with a structured system when the fdi solvability conditions are not satisfied we assume that internal variables can be measured at a cost and look into the question of wether the problem is solvable with these new measurements we give solvability conditions for a solution with a minimal number of additional sensors and among such solutions provide a minimal cost solution for the sensor location problem under consideration we pay particular attention to the internal analysis of the system and we propose a structural decomposition of the system associated graph based on some particular separators this analysis leads to the definition of a reduced system we prove that some potential additional sensors are inefficient for solving our fdi problem and that the fdi problem can be solved using only measurements on the reduced system

calcul stochastique non adapte pour des processus a deux parametres formules de changement de variables de type stratonovitch et de type skorohod nous etablissons une formule de changement de variables de type stratonovitch pour des processus non adaptes indexes par 0 1 2 qui est analogue a celle existant en calcul deterministe pour cela nous definissons une integrale de stratonovitch simple resp double nous en deduisons une formule de changement de variables de type skorohod ne contenant pas d integrale curviligne nous utilisons des regularisations du processus de wiener obtenues par convolution avec une approximation de l unite

solitons in the noisy burgers equation we investigate numerically the coupled diffusion advective type field equations originating from the canonical phase space approach to the noisy burgers equation or the equivalent kardar parisi zhang equation in one spatial dimension the equations support stable right hand and left hand solitons and in the low viscosity limit a long lived soliton pair excitation we find that two identical pair excitations scatter transparently subject to a size dependent phase shift and that identical solitons scatter on a static soliton transparently without a phase shift the soliton pair excitation and the scattering configurations are interpreted in terms of growing step and nucleation events in the interface growth profile finally we show that growing steps perform an anomalous random walk with dynamic exponent z 3 2

noise induced escape from attractors the author deals with several aspects of kautz 1987 1988 minimum principle for the noise induced escape from attractors he presents a slightly simpler derivation points out a connection with lyapunov exponents and invariant manifolds and generalises to chaotic maps

continuum sites stepping stone models coalescing exchangeable partitions and random trees analogues of stepping stone models are considered where the sitespace is continuous the migration process is a general markov process and the type space is infinite such processes were defined in previous work of the second author by specifying a feller transition semigroup in terms of expectations of suitable functionals for systems of coalescing markov processes an alternative representation is obtained here in terms of a limit of interacting particle systems it is shown that under a mild condition on the migration process the continuum sites stepping stone process has continuous sample paths the case when the migration process is brownian motion on the circle is examined in detail using a duality relation between coalescing and annihilating brownian motion this duality relation is also used to show that a tree like random compact metric space that is naturally associated to an in nite family of coalescing brownian motions on the circle has hausdorff and packing dimension both almost surely equal to 1 2 and moreover this space is capacity equivalent to the middle 1 2 cantor set and hence also to the brownian zero set

brief paper state and input observability recovering by additional sensor implementation a graph theoretic approach this paper deals with the problem of additional sensor location in order to recover the state and input observability for structured linear systems the proposed method is based on a graph theoretic approach and assumes only the knowledge of the system s structure it allows one to provide the minimal number of the required sensors and either their pertinent location or a necessary and sufficient condition which allows one to check if a sensor location is adequate or not we obtain a sensor placement procedure based on classical and well known graph theory algorithms which have polynomial complexity orders

decay of metastable states with discrete dynamics we consider the escape from invariant sets of one dimensional piecewise linear maps which are additively disturbed by weak gaussian white noise the escape rates from point attractors and from strange invariant sets in the vicinity of the crisis at fully developed chaos are analytically determined and compared with results from numerical simulations both situations are combined resulting in a model with a point attractor which has a strange invariant set as basin boundary numerically a nonexponential decay of the attractor is found that can be described by a markovian three state model with transition rates known from the previous analysis