a fast and accurate algorithm for solving bernstein vandermonde linear systems abstract a fast and accurate algorithm for solving a bernstein vandermonde linear system is presented the algorithm is derived by using results related to the bidiagonal decomposition of the inverse of a totally positive matrix by means of neville elimination the use of explicit expressions for the determinants involved in the process serves to make the algorithm both fast and accurate

transfer functions of regular linear systems part ii the system operator and the lax phillips semigroup this paper is a sequel to a paper by the second author on regular linear systems 1994 referred to here as part i we introduce the system operator of a well posed linear system which for a finite dimensional system described by x ax bu y cx du would be the s dependent matrix s s a si c b d in the general case s s is an unbounded operator and we show that it can be split into four blocks as in the finite dimensional case but the splitting is not unique the upper row consists of the uniquely determined blocks a si and b as in the finite dimensional case but the lower row is more problematic for weakly regular systems which are introduced and studied here there exists a special splitting of s s where the right lower block is the feedthrough operator of the system using s 0 we give representation theorems which generalize those from part i to well posed linear systems and also to the situation when the initial time is we also introduce the lax phillips semigroup t induced by a well posed linear system which is in fact an alternative representation of a system used in scattering theory our concept of a lax phillips semigroup differs in several respects from the classical one for example by allowing an index r which determines an exponential weight in the input and output spaces this index allows us to characterize the spectrum of a and also the points where s s is not invertible in terms of the spectrum of the generator of for various values of the system is dissipative if and only if with index zero is a contraction semigroup

characterizations of input to state stability for infinite dimensional systems we prove characterizations of input to state stability iss for a large class of infinite dimensional control systems including some classes of evolution equations over banach spaces time delay systems ordinary differential equations ode and switched systems these characterizations generalize well known criteria of iss proved by sontag and wang for ode systems for the special case of differential equations in banach spaces we prove even broader criteria for iss and apply these results to show that under some mild restrictions the existence of a noncoercive iss lyapunov functions implies iss we introduce the new notion of strong iss siss that is equivalent to iss in the ode case but is strictly weaker than iss in the infinite dimensional setting and prove several criteria for the siss property at the same time we show by means of counterexamples that many characterizations which are valid in the ode case are not true for general infinite dimensional systems

dynamics and spatial organization in two species competition the authors investigate the time evolution of a prototypical population biology reaction which involves reproduction self regulation and competitive annihilation of two distinct species in one dimension the authors use a quasistatic analysis to argue that for a system with equal initial densities of two strongly competing species an alternating pattern of domains forms whose lengths grow logarithmically with time a scaling analysis of the underlying master equation as well as numerical integration of the reaction diffusion equations support this result for unequal initial densities the concentration of the minority species undergoes a power law decay with a non universal exponent the authors generalize the model by allowing for a nonlinear self regulation term in the rate equations as a function of the exponent of this nonlinearity the typical domain size may grow either as a power law with time or saturate at a finite value this general approach also suggests that a coarsening domain mosaic occurs in arbitrary spatial dimensions in two dimensions numerical integration of the reaction diffusion equations indicates that the average domain area grows approximately as t0 84

phase ordering and persistence in a class of stochastic processes interpolating between the ising and voter models we study the dynamics of a class of two dimensional stochastic processes depending on two parameters which may be interpreted as two different temperatures respectively associated to interfacial and to bulk noise special lines in the plane of parameters correspond to the ising model voter model and majority vote model the dynamics of this class of models may be described formally in terms of reaction diffusion processes for a set of coalescing annihilating and branching random walkers we use the freedom allowed by the space of parameters to measure by numerical simulations the persistence probability of a generic model in the low temperature phase where the system coarsens this probability is found to decay at large times as a power law with a seemingly constant exponent we also discuss the connection between persistence and the nature of the interfaces between domains

discrete opinion dynamics on networks based on social influence a model of opinion dynamics based on social influence on networks was studied the opinion of each agent can have integer values i 1 2 i and opinion exchanges are restricted to connected agents it was found that for any i 2 and self confidence parameter 0 u 1 when u is a degree independent constant the weighted proportion qi of the population that hold a given opinion i is a martingale and the fraction qi of opinion i will gradually converge to qi the tendency can slow down with the increase of degree assortativity of networks when u is degree dependent qi does not possess the martingale property however qi still converges to it in both cases for a finite network the states of all agents will finally reach consensus further if there exist stubborn persons in the population whose opinions do not change over time it was found that for degree independent constant u both qi and qi will converge to fixed proportions which only depend on the distribution of initial obstinate persons and naturally the final equilibrium state will be the coexistence of diverse opinions held by the stubborn people the analytical results were verified by numerical simulations on barabasi albert ba networks the model highlights the influence of high degree agents on the final consensus or coexistence state and captures some realistic features of the diffusion of opinions in social networks

regular linear systems governed by neutral fdes the aim of this paper is to prove that a class of distributed parameter systems governed by neutral fdes provides regular linear systems employing the well established theory of representation transfer function and feedback of these later we then give new representations of the state and the output function of the neutral systems

speed and fluctuations of n particle branching brownian motion with spatial selection we consider branching brownian motion on the real line with the following selection mechanism every time the number of particles exceeds a large given number n only the n right most particles are kept and the others killed after rescaling time by log 3n we show that the properly recentred position of the lceil alpha n rceil th particle from the right alpha in 0 1 converges in law to an explicitly given spectrally positive levy process this behaviour has been predicted to hold for a large class of models falling into the universality class of the fkpp equation with weak multiplicative noise brunet et al in phys rev e 73 5 056126 2006 and is proven here for the first time for such a model

how to get a conservative well posed linear system out of thin air part ii controllability and stability let a0 be a possibly unbounded positive operator on the hilbert space h which is boundedly invertible let c0 be a bounded operator from cal d a 0 1 2 with the norm z 1 2 2 langle

optimal linear glauber model contrary to the actual nonlinear glauber model the linear glauber model lgm is exactly solvable although the detailed balance condition is not generally satisfied this motivates us to address the issue of writing the transition rate w j in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least the advantage of this work is that by studying the lgm analytically we will be able to anticipate how the kinetic properties of an arbitrary ising system depend on the temperature and the coupling constants the analytical expressions for the optimal values of the parameters involved in the linear w j are obtained using a simple moore penrose pseudoinverse matrix this approach is quite general in principle applicable to any system and can reproduce the exact results for one dimensional ising system in the continuum limit we get a linear time dependent ginzburg landau equation from the glauber s microscopic model of non conservative dynamics we analyze the critical and dynamic properties of the model and show that most of the important results obtained in different studies can be reproduced by our new mathematical approach we will also show in this paper that the effect of magnetic field can easily be studied within our approach in particular we show that the inverse of relaxation time changes quadratically with weak magnetic field and that the fluctuation dissipation theorem is valid for our model

survey paper well posed systems the lti case and beyond this survey is an introduction to well posed linear time invariant lti systems for non specialists we recall the more general concept of a system node classical and generalized solutions of system equations criteria for well posedness the subclass of regular linear systems some of the available linear feedback theory motivated by physical examples we recall the concepts of impedance passive and scattering passive systems conservative systems and systems with a special structure that belong to these classes we illustrate this theory by examples of systems governed by heat and wave equations we develop local and global well posedness results for lti systems with nonlinear in particular bilinear feedback by extracting the abstract idea behind various proofs in the literature we apply these abstract results to derive well posedness results for the burgers and navier stokes equations

funnel control in the presence of infinite dimensional internal dynamics abstract we consider output trajectory tracking for a class of uncertain nonlinear systems whose internal dynamics may be modelled by infinite dimensional systems which are bounded input bounded output stable we describe under which conditions these systems belong to an abstract class for which funnel control is known to be feasible as an illustrative example we show that for a system whose internal dynamics are modelled by a transport equation which is not exponentially stable we obtain prescribed performance of the tracking error

a stationary fleming viot type brownian particle system we consider a system x 1 ldots x n of n particles in a bounded d dimensional domain d during periods in which none of the particles x 1 ldots x n hit the boundary partial d the system behaves like n independent d dimensional brownian motions when one of the particles hits the boundary partial d then it instantaneously jumps to the site of one of the remaining n 1 particles with probability n 1 1 for the system x 1 ldots x n the existence of an invariant measure nu mskip 12mu nu has been demonstrated in burdzy et al comm math phys 214 3 679 703 2000 we provide a structural formula for this invariant measure nu mskip 12mu nu in terms of the invariant measure m of the markov chain xi which returns the sites the process x x 1 ldots x n jumps to after hitting the boundary partial d n in addition we characterize the asymptotic behavior of the invariant measure m of xi when n using the methods of the paper we provide a rigorous proof of the fact that the stationary empirical measure processes frac1n sum i 1 n delta x i converge weakly as n to a deterministic constant motion this motion is concentrated on the probability measure whose density with respect to the lebesgue measure is the first eigenfunction of the dirichlet laplacian on d this result can be regarded as a complement to a previous one in grigorescu and kang stoch process appl 110 1 111 143 2004

conditions for robustness and nonrobustness of thestability of feedback systems with respect to small delays inthe feedback loop it has been observed that for many stable feedback control systems the introduction of arbitrarily small time delays into the loop causes instability in this paper we present a systematic frequency domain treatment of this phenomenon for distributed parameter systems we consider the class of all matrix valued transfer functions which are bounded on some right half plane and which have a limit at spinfty along the real axis such transfer functions are called regular under the assumption that a regular transfer function is stabilized by unity output feedback we give sufficient conditions for the robustness and for the nonrobustness of the stability with respect to small time delays in the loop these conditions are given in terms of the high frequency behavior of the open loop system moreover we discuss robustness of stability with respect to small delays for feedback systems with dynamic compensators in particular we show that if a plant with infinitely many poles in the closed right half plane is stabilized by a controller then the stability is not robust with respect to delays we show that the instability created by small delays is itself robust to small delays three examples are given to illustrate these results

configurational transition in a fleming viot type model and probabilistic interpretation of laplacian eigenfunctions we analyse and simulate a two dimensional brownian multi type particle system with death and branching birth depending on the position of particles of different types the system is confined in a two dimensional box whose boundaries act as the sink of brownian particles the branching rate matches the death rate so that the total number of particles is kept constant in the case of m types of particle in a rectangular box of size and elongated shape we observe that the stationary distribution of particles corresponds to the mth laplacian eigenfunction for smaller elongations a b we find a configurational transition to a new limiting distribution the ratio a b for which the transition occurs is related to the value of the mth eigenvalue of the laplacian with rectangular boundaries

factorizations of cauchy vandermonde matrices abstract this paper analyzes the factorization of the inverse of a cauchy vandermonde matrix as a product of bidiagonal matrices factorizations of cauchy vandermonde matrices are also considered the results are applied to derive a fast algorithm for solving linear systems whose coefficient matrices are cauchy vandermonde matrices

funnel control for the boundary controlled heat equation we consider an output regulation problem for a single input single output system with dynamics described by the heat equation on some bounded domain omega subset mathbb r d with sufficiently smooth boundary the input is formed by neumann boundary control and the output is the surface integral of the state at the boundary we show that the funnel controller can be applied to this system in order to track a given output reference signal within a prespecified performance funnel

on the hot spots conjecture of j rauch rodrigo banuelos research partially supported by nsf grant dms 9400854 krzysztof burdzy s research partially supported by nsf grant dms 9322689

total positivity and neville elimination abstract neville elimination is described in terms of schur complements of matrices and used to improve some well known characterizations of totally positive and strictly totally positive matrices

the byrnes isidori form for infinite dimensional systems we define a byrnes isidori form for a class of infinite dimensional systems with relative degree r and show that any system belonging to this class can be transformed into this form we also analyze the concept of stable zero dynamics and show that it is together with the byrnes isidori form instrumental for static proportional high gain output feedback stabilization moreover we show that funnel control is feasible for any system with relative degree one and with exponentially stable zero dynamics a funnel controller is a time varying proportional output feedback controller which ensures for a large class of reference signals that the error between the output and the reference signal evolves within a prespecified funnel therefore transient behavior of the error is obeyed

critical branching brownian motion with absorption survival probability we consider branching brownian motion on the real line with absorption at zero in which particles move according to independent brownian motions with the critical drift of sqrt 2 kesten stoch process 7 9 47 1978 showed that almost surely this process eventually dies out here we obtain upper and lower bounds on the probability that the process survives until some large time t these bounds improve upon results of kesten stoch process 7 9 47 1978 and partially confirm nonrigorous predictions of derrida and simon epl 78 60006 2007

an annihilating branching particle model for the heat equation with average temperature zero we consider two species of particles performing random walks in a domain in d with reflecting boundary conditions which annihilate on contact in addition there is a conservation law so that the total number of particles of each type is preserved when the two particles of different species annihilate each other particles of each species chosen at random give birth we assume initially equal numbers of each species and show that the system has a diffusive scaling limit in which the densities of the two species are well approximated by the positive and negative parts of the solution of the heat equation normalized to have constant l1 norm in particular the higher neumann eigenfunctions appear as asymptotically stable states at the diffusive time scale

proof of the honeycomb asymptotics for optimal cheeger clusters abstract we prove that in the limit as k the hexagonal honeycomb solves the optimal partition problem in which the criterion is minimizing the largest among the cheeger constants of k mutually disjoint cells in a planar domain as a by product the same result holds true when the cheeger constant is replaced by the first robin eigenvalue of the laplacian

performance funnels and tracking control tracking of an absolutely continuous reference signal assumed bounded with essentially bounded derivative is considered in the context of a class of non linear single input single output dynamical systems modelled by functional differential equations satisfying certain structural hypotheses which interpreted in the highly specialised case of linear systems translate into assumptions of i relative degree one ii positive high frequency gain and iii stable zero dynamics the control objective is evolution of the tracking error within a prespecified funnel thereby guaranteeing prescribed transient performance and prescribed asymptotic tracking accuracy this objective is achieved by a control which takes the form of linear error feedback with time varying gain the gain is generated by a non linear feedback law in which the reciprocal of the distance of the tracking error to the funnel boundary plays a central role in common with many established adaptive control methodologies the overall f

model of cluster growth and phase separation exact results in one dimension we present exact results for a lattice model of cluster growth in one dimension the growth mechanism involves interface hopping and pairwise annihilation supplemented by spontaneous creation of the stable phase 1 regions by overturning the unstable phase 1 spins with probabilityp for cluster coarsening at phase coexistence p 0 the conventional structure factor scaling applies in this limit our model falls in the class of diffusion limited reactions a a inert the 1 cluster size grows diffusively t and the two point correlation function obeys scaling however forp 0 i e for the dynamics of formation of stable phase from unstable phase we find that structure factor scaling breaks down the length scale associated with the size of the growing 1 clusters reflects only the short distance properties of the two point correlations

transfer functions of regular linear systems part i characterizations of regularity we recall the main facts about the representation of regular linear systems essentially that they can be described by equations of the form x t ax t bu t y t cx t du t like finite dimensional systems but now a b and c are in general unbounded operators regular linear systems are a subclass of abstract linear systems we define transfer functions of abstract linear systems via a generalization of a theorem of foures and segal we prove a formula for the transfer function of a regular linear system which is similar to the formula in finite dimensions the main result is a simple to state but hard to prove necessary and sufficient condition for an abstract linear system to be regular in terms of its transfer function other conditions equivalent to regularity are also obtained the main result is a consequence of a new tauberian theorem which is of independent interest

measure valued branching diffusions with spatial interactions a strong equation driven by a historical brownian motion is used to construct and characterize measure valued branching diffusions in which the spatial motions obey an ito equation with drift and diffusion depending on the position of an individual and the entire population

coprime factorization for regular linear systems mild sufficient conditions are given for the existence of a doubly coprime factorization of the transfer function of a regular linear system as well as formulae for such a factorization the results are illustrated by two examples of delay systems one of which has infinitely many unstable poles

the noisy voter model under the influence of contrarians abstract the influence of contrarians on the noisy voter model is studied at the mean field level the noisy voter model is a variant of the voter model where agents can adopt two opinions optimistic or pessimistic and can change them by means of an imitation herding and an intrinsic noise mechanisms an ensemble of noisy voters undergoes a finite size phase transition upon increasing the relative importance of the noise to the herding form a bimodal phase where most of the agents share the same opinion to a unimodal phase where almost the same fraction of agent are in opposite states by the inclusion of contrarians we allow for some voters to adopt the opposite opinion of other agents anti herding we first consider the case of only contrarians and show that the only possible steady state is the unimodal one more generally when voters and contrarians are present we show that the bimodal unimodal transition of the noisy voter model prevails only if the number of contrarians in the system is smaller than four and their characteristic rates are small enough for the number of contrarians bigger or equal to four the voters and the contrarians can be seen only in the unimodal phase moreover if the number of voters and contrarians as well as the noise and herding rates are of the same order then the probability functions of the steady state are very well approximated by the gaussian distribution

input constrained funnel control with applications to chemical reactor models error feedback control in the presence of input constraints is considered for a class of exothermic chemical reactor models the primary control objective is regulation of a setpoint temperature t with prescribed accuracy given 0 arbitrarily small ensure that for every admissible system and reference setpoint the regulation error e t t is ultimately smaller than that is e t i for all t su4ciently large the second objective is guaranteed transient performance the evolution of the regulation error should be contained in a prescribed performance funnel f around the setpoint temperature t a simple error feedback control with input constraints of the form u t sat u 6 u k t t t t u u an o9set is introduced which achieves the objective in the presence of disturbances corrupting the measurement the gain k t is a function of the error e t t t t and its distance to the funnel boundary the input constraints u 6 u have to satisfy certain feasibility assumptions in terms of the model data and the operating point t

diffusive clustering in the two dimensional voter model on donne des resultats de simulation et une enquete concernant les resultats connus sur le modele du votant dans trois cas distincts trois ou plusieurs dimensions une dimension et deux dimensions

bernstein bezoutian matrices and curve implicitization a new application of bernstein bezoutian matrices a type of resultant matrices constructed when the polynomials are given in the bernstein basis is presented in particular the approach to curve implicitization through sylvester and bezout resultant matrices and bivariate interpolation in the usual power basis is extended to the case in which the polynomials appearing in the rational parametric equations of the curve are expressed in the bernstein basis avoiding the basis conversion from the bernstein to the power basis the coefficients of the implicit equation are computed in the bivariate tensor product bernstein basis and their computation involves the bidiagonal factorization of the inverses of certain totally positive matrices

splitting the voter potts model critical point recently some two dimensional models with double symmetric absorbing states were shown to share the same critical behavior that was called the voter universality class we show that for an absorbing states potts model with finite but further than nearest neighbor range of interactions the critical point is split into two critical points one of the ising type and the other of the directed percolation universality class similar splitting takes place in the three dimensional nearest neighbor model

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

a note on superprocesses subject to a mild restriction ona generator of the one particle motion we show thea fleming viot superprocess can be obtained from thea dawson watanabe superprocess by conditioning the latter to have constant total mass

well posedness and exact controllability of fourth order schrodinger equation with boundary control and collocated observation in this paper we study the well posedness and exact controllability of a system described by a fourth order schrodinger equation on a bounded domain of mathbb r n n geqslant 2 with boundary control and collocated observation the neumann boundary control problem is first discussed it is shown that the system is well posed in the sense of d salamon this implies the exponential stability of the closed loop system under proportional output feedback control the well posedness result is then generalized to the dirichlet boundary control problem in particular in order to conclude feedback stabilization from well posedness we discuss the exact controllability with the dirichlet boundary control which is similar to the neumann boundary control case in addition we show that both systems are regular in the sense of g weiss and their feedthrough operators are zero

infinite dimensional input to state stability and orlicz spaces in this work the relation between input to state stability and integral input to state stability is studied for linear infinite dimensional systems with an unbounded control operator although a special focus is laid on the case l infty general function spaces are considered for the inputs we show that integral input to state stability can be characterized in terms of input to state stability with respect to orlicz spaces since we consider linear systems the results can also be formulated in terms of admissibility for parabolic diagonal systems with scalar inputs both stability notions with respect to l infty are equivalent

time varying regular bilinear systems the theory of infinite dimensional systems introduced and developed by salamon trans amer math soc 300 1987 pp 383 431 and weiss siam j control optim 27 1989 pp 527 545 has been recently applied for various systems see e g the jacob partington survey current trends in operator theory and its applications birkhauser boston 2004 in the same spirit schnaubelt in his recent work siam j control optim 41 2002 pp 1141 1165 has extended their approach to the time varying linear systems in this paper we follow this spirit and prove that one can extend the results recently obtained for infinite dimensional time invariant bilinear systems to the time varying setting in particular we show that the absolute regularity and detectability assumptions ensure the existence of an observer for this kind of systems

bernstein bezoutian matrices several computational and structural properties of bezoutian matrices expressed with respect to the bernstein polynomial basis are shown the exploitation of such properties allows the design of fast algorithms for the solution of bernstein bezoutian linear systems without never making use of potentially ill conditioned reductions to the monomial basis in particular we devise an algorithm for the computation of the greatest common divisor gcd of two polynomials in bernstein form a series of numerical tests are reported and discussed which indicate that bernstein bezoutian matrices are much less sensitive to perturbations of the coefficients of the input polynomials compared to other commonly used resultant matrices generated after having performed the explicit conversion between the bernstein and the power basis

hydrodynamics of the voter model we study the voter model on mathbb z d d geqq 3 for a sequence mu varepsilon of initial states which have a gradient in the mean magnetization of the order varepsilon varepsilon rightarrow 0 we prove that the magnetization field m varepsilon f t varepsilon d sum f varepsilon x eta x varepsilon 2 t tends to a deterministic field m f t int dqf q m q t as varepsilon rightarrow 0 m q t is the solution of the diffusion equation the fluctuations of m varepsilon f t around its mean are given by an infinite dimensional non homogeneous ornstein uhlenbeck process in the limit as varepsilon rightarrow 0 locally i e around varepsilon 1 q varepsilon 2 t the voter model is in equilibrium with parameter m q t

two spin majority cellular automaton as a model of 2d cluster and interface growth a new probabilistic cellular automaton model is introduced to simulate cluster and interface growth in two dimensions the dynamics of this model is an extension to higher dimensions of the compact directed percolation studied by essam numerical results indicate that the two dimensional cluster coarsening and growth can be described only approximately by the conventional cluster size scaling due to a crossover in the growth mode the spreading of the initially flat interface follows a purely diffusional t1 2 law

displacement structure theory and applications in this survey paper we describe how strands of work that are important in two different fields matrix theory and complex function theory have come together in some work on fast computational algorithms for matrices with what we call displacement structure in particular a fast triangularization procedure can be developed for such matrices generalizing in a striking way an algorithm presented by schur 1917 j reine angew math 147 1917 pp 205 232 in a paper on checking when a power series is bounded in the unit disc this factorization algorithm has a surprisingly wide range of significant applications going far beyond numerical linear algebra we mention among others inverse scattering analytic and unconstrained rational interpolation theory digital filter design adaptive filtering and state space least squares estimation

voter dynamics on an ising ladder coarsening and persistence coarsening and persistence of ising spins on a ladder is examined under voter dynamics the density of domain walls decreases algebraically with time as t 1 2 for sequential as well as parallel dynamics the persistence probability decreases as under sequential dynamics and as under parallel dynamics where p 2 s 0 88 numerical values of the exponents are explained the results are compared with the voter model on one and two dimensional lattices as well as ising model on a ladder under zero temperature glauber dynamics

a matricial description of neville elimination with applications to total positivity abstract the neville elimination process used by the authors in some previous papers in connection with totally positive matrices is studied in detail in the case of nonsingular matrices a wide class of matrices is found where neville elimination has a lower computational cost than gauss elimination finally some new characterizations are obtained for strictly totally positive and nonsingular totally positive matrices in terms of their neville elimination and that of their inverses

a fleming viot particle representation of the dirichlet laplacian we consider a model with a large number n of particles which move according to independent brownian motions a particle which leaves a domain d is killed at the same time a different particle splits into two particles for large n the particle distribution density converges to the normalized heat equation solution in d with dirichlet boundary conditions the stationary distributions converge as n to the first eigenfunction of the laplacian in d with the same boundary conditions

competition and cooperation in one dimensional stepping stone models mutualism is a major force driving evolution and sustaining ecosystems although the importance of spatial degrees of freedom and number fluctuations is well known their effects on mutualism are not fully understood with range expansions of microbes in mind we show that even when mutualism confers a selective advantage it persists only in populations with high density and frequent migrations when these parameters are reduced mutualism is generically lost via a directed percolation dp process with a phase diagram strongly influenced by an exceptional symmetric dp dp2 transition

well posedness and controllability of a class of coupled linear systems we consider coupled systems consisting of an infinite dimensional part and a finite dimensional part connected in feedback such as for example the well known scole system a beam with a rigid body attached at one end the external world interacts with the coupled system via the finite dimensional part which receives the external input and sends out the output the infinite dimensional part is assumed to be such that it becomes well posed and strictly proper when connected in cascade with an integrator under several assumptions we derive well posedness and exact controllability results for such coupled systems the first main result concerns the case when the input signal of the finite dimensional part is the difference between the external input and the feedback signal the second main result allows a more general structure for the finite dimensional part we also prove a result for the approximate controllability of coupled systems

a soluble kinetic model for spinodal decomposition we compare the two dimensional voter model with approximate theories for spinodal decomposition the cluster size distribution and the short time dynamics of the voter model are studied by means of a monte carlo simulation the time dependent structure factor and the long time scaling of the voter dynamics are known analytically