optimal estimation of a general regression function let e be a convex subset of rd and for each 0 e e let f 0 dt be a probability on the line for any vector an an an2 ann where anl e e let xn1 xnn be independent observations the distribution of xn being f an dt the main results give a method of estimating the unknown regression function an based on a minimum distance recipe under regularity assumptions the proposed estimators are shown in an appropriate framework to be asymptotically normal locally asymptotically minimax and robust the abstract results are illustrated by application to the linear model and to exponential response models in general nothing at all is assumed about the form of the regression function accordingly this forces the limiting normal distributions of the proposed estimators to be located on infinite dimensional linear spaces

the discrete time h control problem with measurement feedback this paper is concerned with the discrete time h infty control problem with measurement feedback it follows that as in the continuous time case the existence of an internally stabilizing controller that makes the h infty norm strictly less than 1 is related to the existence of stabilizing solutions to two algebraic riccati equations however in the discrete time case the solutions of these algebraic riccati equations must satisfy extra conditions

existence and stability of propagating fronts for an autocatalytic reaction diffusion system we study a one dimensional reaction diffusion system which describes an isothermal autocatalytic chemical reaction involving both a quadratic a b 2b and a cubic a 2b 3b autocatalysis the parameters of this system are in the ratio d d b d a of the diffusion constants of the reactant a and the autocatalyst b and the relative activity ii of the cubic reaction first for all values of d 0 and k greater than or equal to 0 we prove the existence of a family of propagating fronts or travelling waves describing the advance of the reaction in particular in the quadratic case k 0 we recover the results of billingham and needham phil trans r sec london a 334 1991 1 24 then if d is close to 1 and k is sufficiently small we prove using energy functionals that these propagating fronts are stable against small perturbations in exponentially weighted sobolev spaces this extends part of the results that are known for the scalar equation to which our system reduces when d 1 c 1998 elsevier science b v

travelling waves of auto catalytic chemical reaction of general order an elliptic approach abstract in this paper we study the existence and non existence of travelling wave to parabolic system of the form a t a x x a f b b t d b x x a f b with f a degenerate nonlinearity in the context of an auto catalytic chemical reaction a is the density of a chemical species called reactant a b that of another chemical species b called auto catalyst and d d b d a 0 is the ratio of diffusion coefficients d b of b and d a of a respectively such a system also arises from isothermal combustion the nonlinearity is called degenerate since f 0 f 0 0 one case of interest in this article is the propagating wave fronts in an isothermal auto catalytic chemical reaction of order n a n b n 1 b with 1 n 2 and d 1 due to different molecular weights and or sizes of a and b the resulting nonlinearity is f b b n explicit bounds v and v that depend on d are derived such that there is a unique travelling wave of every speed v v and there does not exist any travelling wave of speed v v new to the literature it is shown that v v d when d 1 furthermore when d 1 it is shown rigorously that there exists a v min such that there is a travelling wave of speed v if and only if v v min estimates on v min improve significantly that of early works another case in which two different orders of isothermal auto catalytic chemical reactions are involved is also studied with interesting new results proved

stability of moving fronts in the ginzburg landau equation we use renormalization group ideas to study stability of moving fronts in the ginzburg landau equation in one spatial dimension in particular we prove stability of the real fronts under complex perturbations this extends the results of aronson and weinberger to situations where the maximum principle is inapplicable and constitutes a step in proving the general marginal stability hypothesis for the ginzburg landau equation

sequential determination of estimator as well as sample size on considere certains problemes d estimation ponctuelle ou par intervalles et on propose des methodes sequentielles pour le choix d un estimateur et de la taille de l echantillon sur lequel sera base l estimateur

on approximate solutions to the wavefront speed problem we propose an approximate method to obtain the speed of wavefronts it is built up from a known variational principle for a range of systems of biological and physical interest comparison to previously known solutions and to numerical simulations shows the powerfulness of our approximate technique for time delayed equations we also propose an alternative approximate solution based on the renormalization group approach and we compare both approximations

robust estimation via minimum distance methods given a fixed parametric family p it is desired to estimate however due to contaminations of various sorts the data actually collected by the statistician follow a distribution that is close to but possibly distinct from thep s it is proved that under these conditions and in an appropriate asymptotic framework the minimum distance estimators of the cramer von mises type are robust specification of a cramer von mises weight functionh defines a notion of distance each such choice ofh then delineates the kind of contamination possible and leads to an estimator which defends optimally against it when the theory is specialized to location models various choices ofh lead to estimators asymptotically equivalent to such familiar ones as trimmed mean median hodges lehmann estimator and so forth the framework developed herein provides some guidelines for choosing among the possible estimators and suggests that the standard cramer von mises estimator of location is probably as good a robust estimator as any

non generic connections corresponding to front solutions a classification of special nonlinear front solutions for certain one time and one space reaction diffusion equations is presented using the method of weiss tabor and carnevale wtc these results are related to known stability criteria in particular the steepness criterion of van saarloos 1989 the wtc method is shown to be equivalent to a special first order reduction and both of these methods are shown to work for reaction diffusion equations with special nonlinearities of particular interest is the fact that the special first order reduction is shown to give separatrices in appropriate phase spaces an example of reaction diffusion equation is presented without these special nonlinearities while this equation is shown to have a special nonlinear connection and resulting stability properties it is intractable for either a singular manifold expansion of a first order reduction a lie symmetry analysis is carried out and it is shown that equations with continuous groups other than translational invariance are only a subclass of equations which are amenable to the special solution techniques however the rescaling ansatz of cariello and tabor 1991 suggests that some symmetries are present

estimation in the general linear model when the accuracy is specified before data collection an estimator of is accurate with accuracy a and confidence ay o y 1 if p bfl ea y for all 3 given a sequence y1 y2 of independent vector valued homoscedastic normally distributed random variables generated via the general linear model yi xi e the k dimensional parameter d3 is accurately estimated using a sequential version of the maximum probability estimator developed by l weiss and j wolfowitz the procedure given also generalizes c stein s fixed width confidence sets to several dimensions

sources sinks and wavenumber selection in coupled cgl equations and experimental implications for counter propagating wave systems we study the coupled complex ginzburg landau cgl equations for traveling wave systems and show that sources and sinks are the important coherent structures that organize much of the dynamical properties of traveling wave systems we focus on the regime in which sources and sinks separate patches of left and right traveling waves i e the case that these modes suppress each other we present in detail the framework to analyze these coherent structures and show that the theory predicts a number of general properties which can be tested directly in experiments our counting arguments for the multiplicities of these structures show that independently of the precise values of the coefficients in the equations there generally exists a symmetric stationary source solution which sends out waves with a unique frequency and wave number sinks on the other hand occur in two parameter families and play an essentially passive role being sandwiched between the sources these simple but general results imply that sources are important in organizing the dynamics of the coupled cgl equations simulations show that the consequences of the wavenumber selection by the sources is reminiscent of a similar selection by spirals in the 2d complex ginzburg landau equations sources can send out stable waves convectively unstable waves or absolutely unstable waves we show that there exists an additional dynamical regime where both single and bimodal states are unstable the ensuing chaotic states have no counterpart in single amplitude equations a third dynamical mechanism is associated with the fact that the width of the sources does not show simple scaling with the growth rate e this is related to the fact that the standard coupled cgl equations are not uniform in e in particular when the group velocity term dominates over the linear growth term no stationary source can exist however sources displaying nontrivial dynamics can often survive here our results for the existence multiplicity wavelength selection dynamics and scaling of sources and sinks and the patterns they generate are easily accessible by experiments we therefore advocate a study of the sources and sinks as a means to probe traveling wave systems and compare theory and experiment in addition they bring up a large number of new research issues and open problems which are listed explicitly in the concluding section

chaotic step bunching during crystal growth abstract we study a simple model for step bunching during crystal growth by propagating a disturbance into an unstable system of equidistant steps the system exhibits a wide range of different bunching modes as a function of the initial step spacing leading to distinctive spatial patterns periodic with subharmonic bifurcations chaotic and intermittent linear and nonlinear marginal stability theory gives extremely accurate predictions of the velocity of the propagating front one of the bifurcations is identified as a transition from a regime where linear marginal stability applies to a nonlinear marginal stability regime the location of this bifurcation is determined accurately

coalescence of low viscosity fluids in air an electrical method is used to study the early stages of coalescence of two low viscosity drops a drop of aqueous nacl solution is suspended in air above a second drop of the same solution which is grown until the drops touch at that point a rapidly widening bridge forms between them by measuring the resistance and capacitance of the system during this coalescence event one can obtain information about the time dependence of the characteristic bridge radius and its characteristic height at early times a new asymptotic regime is observed that is inconsistent with previous theoretical predictions the measurements at several drop radii and approach velocities are consistent with a model in which the two liquids coalesce with a slightly deformed interface

on the turing patterns in one dimensional gradient skew gradient dissipative systems in this article fundamental properties concerning the turing patterns are considered in one dimensional dissipative systems with gradient skew gradient structure introduced in m kuwamura and e yanagida phys d 175 2003 pp 185 195 it is a natural extension of free energy which covers reaction diffusion systems of activator inhibitor type the theory based on this concept provides a new perspective on a fundamental problem of what unique turing pattern is to be selected among many

pattern propagation in nonlinear dissipative systems abstract we discuss the problem of pattern selection in situations where a stable nonuniform state of a nonlinear dissipative system propagates into an initially unstable homogeneous region our strategy is to consider this process as a generalization of front propagation in a nonlinear diffusion problem for which rigorous results are known and we point out that these known properties are consistent with a marginal stability hypothesis that has been suggested in the theory of dendritic crystal growth we then describe a more general interpretation of the marginal stability hypothesis and finally present numerical evidence for its validity from three different pattern forming models

spontaneously ordered motion of self propelled particles we study a biologically inspired inherently non equilibrium model consisting of self propelled particles in the model particles move on a plane with a velocity of constant magnitude they locally interact with their neighbours by choosing at each timestep a velocity direction equal to the average direction of their neighbours thus in the limit of vanishing velocities the model becomes analogous to a monte carlo realization of the classical xy ferromagnet we show by large scale numerical simulations that unlike in the equilibrium xy model a long range ordered phase characterized by non vanishing net flow emerges in this system in a phase space domain bordered by a critical line along which the fluctuations of the order parameter diverge the corresponding phase diagram as a function of two parameters the amplitude of noise and the average density of the particles is calculated and is found to have the form we also find that scales as a function of the external bias h field or wind according to a power law in the ordered phase the system shows long range correlated fluctuations and 1 f noise

information and asymptotic efficiency in parametric nonparametric models asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems for regular estimates and asymptotic minimax bounds the methods used involve i the notion of a hellinger differentiable root density where part of the differentiation is with respect to the nonparametric part of the model to obtain appropriate scores and ii calculation of the effective score for the real or vector finite dimensional parameter of interest as that component of the score function orthogonal to all nuisance parameter scores perhaps infinite dimensional the resulting asymptotic information for estimation of the parametric component of the model is just 4 times the squared l 2 norm of the effective score a corollary of these results is a simple necessary condition for adaptive estimation adaptation is possible only if the scores for the parameter of interest are orthogonal to the scores for the nuisance function or nonparametric part of the model examples considered include the one sample location model with and without symmetry mixture models the two sample shift model and cox s proportional hazards model

traveling spike autosolitons in the gray scott model abstract we developed singular perturbation techniques based on the strong separation of time and length scales to construct the solutions in the form of the traveling spike autosolitons self sustained solitary waves in the gray scott model of an autocatalytic reaction we found that when the inhibitor diffusion is sufficiently slow the ultrafast traveling spike autosolitons are realized in a wide range of parameters when the diffusion of the inhibitor is sufficiently fast the slower traveling spike autosolitons with the diffusion precursor are realized we asymptotically calculated the main parameters such as speed and amplitude of these autosolitons as well as the regions of their existence in the gray scott model we also showed that in certain parameter regions the traveling spike autosolitons coexist with static

state space approach to discrete time h control abstract state space solutions to a discrete time problem are given for a given number 0we give a characterization of all controllers such that the norm of the closed loop transfer function is less than the approach taken is based on the solution of two riccati equations using the stable deflating subspace of a symplectic pencil this ensures that no unnecessary assumptions on the a matrix on the realization of the transfer function are needed while the results are the direct analogues of those in the continuous time the state space derivation is considerably more difficult

j lossless conjugation and factorization for discrete time systems the j j lossless factorization plays an important role in h control theory just like the wiener hopf factorization does in lqg theory for continuous time systems in this paper the theory of j lossless factorization is extended to discrete time systems the notion j lossless conjugation which is a powerful tool for computing j lossless factorization in continuous time systems is also extended to discrete time systems these extensions are far from trivial the discrete time version j lossless conjugations and factorizations turns out to be much more complicated reflecting the complicated nature of the discrete time riccati equations

negative regret optional stopping and the elimination of outliers abstract this article examines the phenomenon of negative regret in sequential point estimation in which a stopping rule used in ignorance of the variance of the distribution sometimes performs better than the best fixed sample size when the variance is known an explanation in terms of a certain robustifying effect of the stopping rule is given results of simulation studies illustrating both negative regret and its explanation are also given suppose x 1 x 2 are iid with mean and variance 2 one may stop observing the sequence of x i s after any number of observations n and estimate by the sample mean subject to the loss if is known then the best fixed i e nonrandom sample size in the sense of minimum risk can be used if is unknown the best fixed sample size is unknown necessitating a sequential procedure for a sequential procedure of the type first proposed by robbins 1959 the regret expected additional loss from not knowing and using the sequential procedure instead

front propagation into unstable states universal algebraic convergence towards uniformly translating pulled fronts fronts that start from a local perturbation and propagate into a linearly unstable state come in two classes pulled fronts and pushed fronts the term pulled front expresses that these fronts are pulled along by the spreading of linear perturbations about the unstable state accordingly their asymptotic speedv equals the spreading speed of perturbations whose dynamics is governed by the equations linearized about the unstable state the central result of this paper is the analysis of the convergence of asymptotically uniformly traveling pulled fronts towardsv we show that when such fronts evolve from sufficiently steep initial conditions which initially decay faster than e x forx 1 t hey have auniversal relaxation behavioras timet 1 the velocity of a pulled front always relaxes algebraically like v t d v 3 2t c 3 p d d 2 t 3 2 c o 1 t 2 the parametersv and d are determined through a saddle point analysis from the equation of motion linearized about the unstable invaded state this front velocity is independent of the precise value of the front amplitude which one tracks to measure the front position the interior of the front is essentially slaved to the leading edge and develops universally as x t d8v t x rt dt 0 v t 0 c o 1 t 2 where8v x vt is a uniformly translating front solution with velocity v v our result which can be viewed as a general center manifold result for pulled front propagation is derived in detail for the well known nonlinear diffusion equation of type t d 2 x c 3 where the invaded unstable state is d 0 even for this simple case the subdominant t 3 2 term extends an earlier result of bramson our analysis is then generalized to more general sets of partial differential equations with higher spatial or temporal derivatives to pdes with memory kernels and also to difference equations such as those that occur in numerical finite difference codes our universal result for pulled fronts thus implies independence i of the level curve which is used to track the front position ii of the precise nonlinearities iii of the precise form of the linear operators in the dynamical equation and iv of the precise initial conditions as long as they are sufficiently steep the only remainders of the explicit form of the dynamical equation are the nonlinear solutions 8v and the three saddle point parameters v and d as our simulations confirm all our analytical predictions in every detail it can be concluded that we have a complete analytical understanding of the propagation mechanism and relaxation behavior of pulled fronts if they are uniformly translating for t 1 an immediate consequence of the slow algebraic relaxation is that the standard moving boundary approximation breaks down for weakly curved pulled fronts in two or three dimensions in addition to our main result for pulled fronts we also discuss the propagation and convergence of fronts emerging from

second order approximation to the risk of a sequential procedure given x 1 x 2 cdots i i d with mean mu and variance sigma 2 suppose that at stage n one wishes to estimate mu by the sample mean bar x n subject to the loss function l n a bar x n mu 2 n a 0 if sigma is known the optimal fixed sample size n 0 approx a 1 2 sigma can be used with corresponding risk r n 0 but if sigma is unknown there is no fixed sample size procedure that will achieve the risk r n 0 for the sequential estimation procedure with stopping rule t inf n geq n a n 1 sum n 1 x i bar x n 2 leq a 1 n 2 the second order approximation of woodroofe 1977 to the risk r t for normal x i is extended to the distribution free case specifically if the x i have finite moments of order greater than eight and are non lattice under certain conditions on the delay n a it is shown that the regret r t r n 0 c o 1 as a rightarrow infty where c depends on the first four moments of the distribution of the x i for the lattice case bounds of the form c 1 o 1 leq r t r n 0 leq c 2 o 1 are obtained where the c j are c pm 3 it follows from these approximations that the regret can take arbitrarily large negative values as the distribution of the x i varies in contrast to previous results for normal and gamma cases

a generalized chain scattering representation and its algebraic system properties presents a generalization of the chain scattering representation to the case of general plants through the notion of input output consistency the conditions under which the generalized chain scattering representation gcsr and the dual generalized chain scattering representation dgcsr exist are proposed the generalized chain scattering matrices are formulated into a general parameterized form by using the generalized inverse of matrices some algebraic system properties such as the cascade structure property the symmetry duality of the gcsr s and dgcsr s are studied

bacterial wisdom godel s theorem and creative genomic webs this paper is devoted to presenting an alternative approach to the darwinian one the basic assumption is that the creativity observed in nature is not an illusion but part of an objective reality in the new picture evolutionary progress is not a result of successful accumulation of mistakes but is rather the outcome of designed creative processes in the genome

holotransformations of bacterial colonies and genome cybernetics we present a study of colony transformations during growth of bacillus subtilis under adverse environmental conditions it is a continuation of our pilot study of adaptive self organization during growth of bacterial colonies physica a 187 1992 378 first we identify and describe the transformations pathway i e the excitation of the branching modes from bacillus subtilis 168 grown under diffusion limited conditions and the phase transformations between the tip splitting phase phase t and the chiral phase phase c which belong to the same mode this pathway shows the evolution of complexity as the bacteria are exposed to adverse growth conditions we present the morphology diagram of phases t and c as a function of agar concentration and pepton level as expected the growth of phase t is ramified fractal like or dla like at low pepton level about 1 g 1 and turns compact at high pepton level about 10 g 1 the growth of phase c is also ramified at low pepton level and turns denser and finally compact as the pepton level increases generally speaking the colonies develop more complex patterns and higher micro level organization for more adverse environments we use the growth velocity as a response function to describe the growth at low agar concentration and low pepton level phase c grows faster than phase t and for a high agar concentration about 2 phase t grows faster we observe colony transformations between the two phases phase transformations they are found to be consistent with the fastest growing morphology selection principle adopted from azoic systems the transformations are always from the slower phase to the faster one hence we observe t c transformations at low agar concentrations and c t transformations at high agar concentrations we have observed both localized and extended transformations usually the transformations are localized for more adverse growth conditions and extended for growth conditions close to the boundaries between morphologies we have observed also transformations between different branching modes as well as transformations via virtual states motivated by the contemporary knowledge about phages and plasmids we postulate a theoretical framework to comply with our experimental findings we explain our observations using these assumptions as well as our proposal of co mutations and auto catalytic mutations as presented in the above mentioned pilot paper this theoretical framework is a part of the new evolving picture of genome cybernetics we also discuss the concept of adaptive genome changes which are based on pre existing knowledge as well as the concept of genetic learning i e changes in response to a new problem which develop the potential for adaptive genome changes these concepts follow naturally if the picture of genome cybernetics is accepted we conclude with a discussion of the implications and with further predictions to be tested experimentally derived from our assumptions

fractal growth by local sensitive epidemic model lsem simulating the internal feeding systems ifs abstract the fractal systems may be classified into two families which are distinguishable by a different nutrient feeding during their growth process for the internal feeding systems ifs the source is directly connected to the growing interface while for the external feeding systems efs it is placed far away so that the released particles have to execute random walks before adhering to the aggregate a generalized model nicknamed local sensitive epidemic model lsem is developed to unify the main models simulating the growth of the ifsystems by combining all their growth parameters gp and growth rules gr this model considers in addition i a particle interaction extended to the kth neighbour which may be attractive or repulsive ii a continuous updating of the local characteristics of the surrounding medium and iii an aggregate relaxation which tends to optimize the total energy during or after the growth process the coupled effects of all these parameters allow one to simulate the main fractal phases observed experimentally and to discuss the conditions under which they may be obtained as well as their different morphological transitions

sequentially deciding between two experiments for estimating a common success probability abstract to estimate a success probability p two experiments are available individual bernoulli p trials or the product of individual bernoulli p trials this problem has its roots in reliability where either single components can be tested or a system of identical components can be tested a total of n experiments can be performed and the problem is to sequentially select some combination allocation of these two experiments along with an estimator of p to achieve low mean squared error mse of the final estimate this scenario is similar to that of the better known group testing problem but here the goal is to estimate failure rates rather than to identify defective units the problem also arises in epidemiological applications such as estimating disease prevalence information maximization considerations and analysis of the asymptotic mse of several estimators lead to the following adaptive procedure use the maximum likelihood estimator mle to estimate p and if this estimator is b

travelling kinks in schlogl s second model for non equilibrium phase transitions using the separation technique developed by osborne and stuart 1980 travelling wave solutions are written down for the nonlinear reaction diffusion equation of schlogl s second model assuming that the necessary conditions for the static phase coexistence are satisfied

sequential estimation of the mean of a first order stationary autoregressive process on considere un estimateur ponctuel sequentiel base sur une moyenne d echantillon et on montre qu il est asymptotiquement efficace en risque lorsque le cout par observation tend vers zero

speed selection for traveling wave solutions to the diffusion reaction equation with cubic reaction term and burgers nonlinear convection the problem of traveling wave tw speed selection for solutions to a generalized murray burgers kpp fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results depending on the magnitude of a parameter inherent in the reaction term i the term is either a concave function or a function with the inflection point and ii transition from pulled to pushed tw solution occurs due to interplay of two nonlinear terms the reaction term and the burgers convection term explicit pushed tw solutions are derived it is shown that physically observable tw solutions i e solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition can be determined by seeking the tw solution characterized by the maximum decay rate at its leading edge in the appendix the developed approach is applied to a non linear diffusion reaction equation that is widely used to model premixed turbulent combustion

convection front propagation and wavenumber selection abstract the propagation of convection front in a horizontal fluid layer heated from below is studied by the numerical integration of both the newell whitehead segel amplitude equation and the full boussinesq equations it is shown that the propagation speed before its steady state value is reached can lie within a wide range and vary depending on the width of the front profile time dependent regimes play an important role resulting in different wavenumbers of the roll pattern formed behind the front the rate of roll relaxation or tendency toward the optimal preferred wavenumber strongly depends on the width of the region occupied by the roll pattern and on the front propagation speed at large speeds the freezing of the wavenumbers is possible the effect of the rayleigh number r is mainly indirect by the variation of the speed of the front so that at lower r the relaxation is faster the evolution of the whole pattern may be complicated because of the combined effect of two competing mechanisms the role relaxation and the counteraction of the mass of other rolls the available results of the studies of front propagation do not contradict the possibility of the existence of the preferred wavenumber

existence of traveling waves of invasion for ginzburg landau type problems in infinite cylinders we study a class of systems of reaction diffusion equations in infinite cylinders which arise within the context of ginzburg landau theories and describe the kinetics of phase transformation in second order or weakly first order phase transitions with non conserved order parameters we use a variational characterization to study the existence of a special class of traveling wave solutions which are characterized by a fast exponential decay in the direction of propagation our main result is a simple verifiable criterion for existence of these traveling waves under the very general assumptions of non linearities we also prove boundedness regularity and some other properties of the obtained solutions as well as several sufficient conditions for existence or non existence of such traveling waves and give rigorous upper and lower bounds for their speed in addition we prove that the speed of the obtained solutions gives a sharp upper bound for the propagation speed of a class of disturbances which are initially sufficiently localized we give a sample application of our results using a computer assisted approach

extended symbolic dynamics in bistable cml existence and stability of fronts abstract we consider a diffusive coupled map lattice cml for which the local map is piecewise affine and has two stable fixed points by introducing a spatio temporal coding we prove the one to one correspondence between the set of global orbits and the set of admissible codes this relationship is applied to the study of the uniform fronts dynamics it is shown that for any given velocity in 1 1 there is a parameter set for which the fronts with that velocity exist and their shape is unique the dependence of the fronts velocity on the local map s discontinuity is proved to be a devil s staircase moreover the linear stability of the global orbits which do not reach the discontinuity follows directly from our simple map for the fronts this statement is improved and as a consequence the velocity of all the propagating interfaces is computed for any parameter the fronts are shown to be also nonlinearly stable under some restrictions on the parameters actually these restrictions follow from the co existence of uniform fronts and non uniformly travelling fronts for strong coupling finally these results are extended to some c local maps

existence and nonexistence of travelling waves of a reaction diffusion system abstract in this paper we study the existence and nonexistence of travelling waves of the reaction diffusion system a t a x x e a x a b k a b q b t d b x x d e b x a b k a b q where a b are concentration densities of the two chemical species d 0 is the ratio of diffusion coefficients of the two chemical species involved e is the strength of the electric field applied k 0 is a parameter and q 1 the system arises from the study of two dimensional iodate arsenous acid iaa reaction with a constant electric field applied iaa reaction is very much studied in experiments and demonstrates the interesting phenomenon of instability driven by buoyancy of travelling waves by using a novel approach explicit bounds c d e and c d e are derived such that there is a unique travelling wave of every speed c c d e and there does not exist any travelling wave of speed c c d e with q being fixed in addition c d e bears a close resemblance of the minimum travelling wave speed of the classical case of d 1 and e 0 when 0 e 1 and d 1

renormalization group and the ginzburg landau equation we use renormalization group methods to prove detailed long time asymptotics for the solutions of the ginzburg landau equations with initial data approaching asx different spiraling stationary solutions a universal pattern is formed depending only on this asymptotics at spatial infinity

a sequential procedure with asymptotically negative regret for estimating a normal mean rn e ln acr2 n n is minimized by taking n n ao 2 1 2 and the corresponding minimum fixed sample size risk is rn 2n since u2 is unknown robbins 1959 proposed the following type of sequential procedure let 1 1 t inf n m n avn n 1 2 i where m is the initial sample size and vn e n xn 2 and estimate u by xt woodroofe 1977 showed that if m 4 the regret of the procedure rt rn 1 2 o 1 as a oc the purpose of this article is to show that there does exist a sequential procedure for which the regret is negative at u 0 and 1 2 at u 0 asymptotically instead of vn n as an estimator of j 2 consider an estimator o n of the form

persistence of overflowing manifolds for semiflow this paper which is a sequel to a previous one 4 by the same authors is devoted to the persistence of overflowing manifolds and inflowing manifolds for a semiflow in a banach space we consider a c1 semiflow defined on a banach space x that is it is continuous on 0 x and for each t 0 t t x x is c1 and t t t x t t s x for all t s 0 and x x a typical example is the solution operator for a differential equation in 4 we proved that a compact normally hyperbolic invariant manifold m persists under small c1 perturbations in the semiflow we also showed that in a neighborhood of m there exist a center stable manifold and a center unstable manifold that intersect in the manifold m in 4 the compactness and invariance of the manifold m were important assumptions in the present paper we study the more general case where the manifold m is overflowing negatively invariant and the semiflow crosses the boundary transversally or inflowing positively invariant and the semiflow crosses the boundary transversally we do not assume that m is compact or finite dimensional also m is not necessarily an imbedded manifold but an immersed manifold as an example a local unstable manifold of an equilibrium point is an overflowing manifold in brief our main results on the overflowing manifolds may be summarized as follows the precise statements are given in section 2 we assume that the immersed manifoldm does not twist very much locally m is covered by the image under t t of a subset a positive distance away from boundary dt t contracts along the normal direction and does so more strongly than it does along the tangential direction and dt t has a certain uniform continuity in a neighborhood of m if the c1 perturbation t t of t t is sufficiently close to t t then t t has a unique c1 immersed overflowing manifold m nearm furthermore if t t isck and a spectral gap condition holds then m isck similar results for inflowing manifolds are also obtained and given in section 7

the dual algebraic riccati equations and the set of all solutions of the discrete time riccati equation abstractin this paper two new pairs of dual continuous time algebraic riccati equations cares and dual discrete time algebraic riccati equations dares are proposed the dual dares are first studied with some nonsingularity assumptions on the system matrix and the parameter matrix then in the case of singular matrices a generalised inverse is introduced to deal with the dual dare problem these dual ares can easily lead us to an iterative procedure for finding the anti stabilising solutions especially to dare by means of that for the stabilising solutions furthermore we provide the counterpart results on the set of all solutions to dare inspired by the results for care two examples are presented to illustrate the theoretical results

variational principles and the shift in the front speed due to a cutoff we apply variational principles to reaction diffusion equations in order to predict for a general reaction term the sign of the shift in the front speed due to a cutoff we develop an improved variational principle to obtain the shift in the front speed for a wide range of reaction terms and the theoretical results so obtained are in excellent agreement with numerical solutions this work proves that variational principles are an optimal framework to deal with fronts propagating into unstable and metastable states under cutoff

j factorizations of a general discrete time system abstract the problems of extending the j lossless conjugation the j j spectral factorization and the j j lossless factorization to a completely general discrete time system are considered existence conditions together with a numerically sound prototype algorithm for computing the factors are provided for a system having any type of singularity including arbitrary normal rank poles and zeros at infinity at zero or on the unit circle

pushed global modes in weakly inhomogeneous subcritical flows abstract a new type of nonlinear global mode or fully nonlinear synchronized solution arising in the dynamics of open shear flows which behave as oscillators annu rev fluid mech 22 1990 473 and in optical parametric oscillators j opt soc am b 17 2000 997 is identified in the context of the real subcritical ginzburg landau equation with slowly varying coefficients the nonlinear global modes satisfy a boundary condition accounting for the inlet of the flow we show that the spatial structure of these new nonlinear global modes consists of a localized state limited by a pushed upstream front that withstand the mean advection and a fast return to zero downstream achieved either by a second stationary front facing backward or by a saddle node bifurcation driven by the non parallelism of the flow we derive scaling laws for the slope of the nonlinear global modes at the inlet and for the position of the maximum amplitude which are in agreement with similar scaling obtained in experiments with a shear layer in a hele shaw cell phys rev lett 82 1999 1442 extension to the complex ginzburg landau equation is discussed in a large region of parameters the nonlinear global modes have the same spatial structure as in the real case and oscillate at a global frequency selected at threshold by the pushed front in parameters region where these pushed global modes are not selected new states with a non periodic in time behavior are exhibited

studies of bacterial branching growth using reaction diffusion models for colonial development abstract various bacterial strains exhibit colonial branching patterns during growth on poor substrates these patterns reflect bacterial cooperative self organization and cybernetic processes of communication regulation and control employed during colonial development one method of modeling is the continuous or coupled reaction diffusion approach in which continuous time evolution equations describe the bacterial density and the concentration of the relevant chemical fields in the context of branching growth this idea has been pursued by a number of groups we present an additional model which includes a lubrication fluid excreted by the bacteria we also add fields of chemotactic agents to the other models we then present a critique of this whole enterprise with focus on the models potential for revealing new biological features

finite size effects in random energy models and in the problem of polymers in a random medium by the use of traveling wave equations we calculate the finite size corrections to the free energy of random energy models in their low temperature phases and in the neighborhood of the transition temperature we find that although the extensive part of the free energy does not show any critical behavior when the temperature approaches its transition value the finite size corrections signal the transition by becoming singular we obtain a scaling form for these finite size corrections valid in the limitn andt t c by considering a generalized random energy model in the limit of a very large number of steps we obtain results for the finite size corrections in the problem of a polymer in a random medium

instabilities and propagation properties in a fourth order reaction diffusion equation in this paper we investigate the instability and the propagation properties of a class of reaction diffusion equations of fourth order two examples are introduced the extended fisher kolmogorov equation efk and the swift hohenberg equation sh both have been studied before by related methods see for example peletier and rottschafer 2004 19 van saarloos 2003 24 but the analysis here will support the introduced linear mechanism in front selection these two equations support a patterned front solutions and the double eigenvalue mechanism is used to provide evidence for that and to determine a minimal front speed

j lossless and extended j lossless factorizations approach for domain h control the paper addresses problems of numerical conditioning of the discrete time h x control design based on j lossless factorizations of the chain scattering representation of a plant it is demonstrated that for a sufficiently small sampling period forward shift operator techniques may become ill conditioned and numerical robustness and reliability of design procedures can be significantly improved by utilizing a so called i operator form of the source problem state space models of all i domain controllers are given the solutions are obtained by considering two coupled i domain algebraic riccati equations that can be solved by applying a generalized eigenproblem formulation numerical conditioning of these solutions can effectively be evaluated by using a suitable relative condition number an extended j lossless factorization for generalized plants with zeros on the stability boundary circle is also given a so called zero compensator technique adapted to the i domain models is utilized to cancel suc

microscopic origin of hydrodynamic equations derivation and consequences abstract we describe some recent progress in deriving autonomous hydrodynamic type equations for macroscopic variables from model stochastic microscopic dynamics of particles on a lattice the derivations also yield the microscopic fluctuations about the deterministic macroscopic evolution these grow with time to become infinite when the deterministic solution is unstable a form of microscopic pattern selection is also found

scaling and universality in animate and inanimate systems we illustrate the general principle that in biophysics econophysics and possibly even city growth the conceptual framework provided by scaling and universality may be of use in making sense of complex statistical data specifically we discuss recent work on dna sequences heartbeat intervals avalanche like lung inflation urban growth and company growth although our main focus is on data we also discuss statistical mechanical models

variational characterization of the speed of propagation of fronts for the nonlinear diffusion equation we give an integral variational characterization for the speed of fronts of the nonlinear diffusion equationut uxx f u withf 0 f 1 0 andf 0 in 0 1 which permits in principle the calculation of the exact speed for arbitraryf

front stability in mean field models of diffusion limited growth we present calculations of the stability of planar fronts in two mean field models of diffusion limited growth the steady state solution for the front can exist for a continuous family of velocities and we show that the selected velocity is given by marginal stability theory we find that a naive mean field theory has no instability to transverse perturbations while a threshold mean field theory has a mullins sekerka instability these results place on firm theoretical ground the observed lack of the dendritic morphology in naive mean field theory and its presence in threshold models the existence of a mullins sekerka instability is related to the behavior of the mean field theories in the zero undercooling limit textcopyright 1996 the american physical society

a bacterial colony is not self similar abstract the geometry of complex bacterial colonies has been studied different values of the exponent in scaling law have been recorded on different length scales thus a colony is not a self similar object and has a multiple fractal structure

contest based on a directed polymer in a random medium we introduce a simple one parameter game derived from a model describing the properties of a directed polymer in a random medium at his turn each of the two players picks a move among two alternatives in order to maximize his final score and minimize opponent s return for a game of length n we find that the probability distribution of the final score s n develops a traveling wave form rm prob s n m f m v n with the wave profile f z unusually decaying as a double exponential for large positive and negative z in addition as the only parameter in the game is varied we find a transition where one player is able to get his maximum theoretical score by extending this model we suggest that the front velocity v is selected by the nonlinear marginal stability mechanism arising in some traveling wave problems for which the profile decays exponentially and for which standard traveling wave theory applies

conjugation interpolation and model matching in h abstract the notion of conjugation is introduced to give a unified framework of algebraic operations connected to the analytic aspects of transfer functions two classes of conjugations are shown to be important one is the lossless conjugation that performs inner outer factorization and the other is the j lossless conjugation that solves the model matching problem related to h 8 control the solution of the model matching problem obtained by j lossless conjugation is regarded as the state space version of the directional interpolation theory and is much simpler than those obtained via the nehari approximation

improving the fully sequential sampling scheme of anscombe chow robbins a new sequential sampling scheme is proposed in which after an initial batch sample sampling is continued in batches of data dependent sizes at most k such batches and then one at a time with a data dependent stopping rule this new scheme requires about the same sample size as the fully sequential anscombe chow robbins acr sampling scheme but substantially fewer sampling operations the problem of constructing fixed width confidence intervals for the mean of a normal population with unknown variance is used as an illustration

travelling waves in radially symmetric parabolic systems on montre que toutes les solutions ondes planes de propagation ou stationnaire de certains systemes paraboliques a symetrie radiale peuvent etre trouvees en resolvant une equation differentielle scalaire associee

speed of wave front solutions to hyperbolic reaction diffusion equations the asymptotic speed problem of front solutions to hyperbolic reaction diffusion hrd equations is studied in detail we perform linear and variational analyses to obtain bounds for the speed in contrast to what has been done in previous work here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds for some functions it is possible to determine the speed without any uncertainty this is also achieved for some systems of hrd i e time delayed lotka volterra equations that take into account the interaction among different species an analytical analysis is performed for several systems of biological interest and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently s1063 651x 99 06211 x

conjugation and h control of discrete time systems we establish conjugation notion in discrete time systems first introduced into the h control theory of continuous time systems by kimura 1989 in discrete time systems conjugation is a very elementary operation on rational transfer functions that replaces some of their poles by their reflections with respect to the unit circle with the aid of j lossless conjugation conjugation by a j lossless system it is shown that the parametrization of sub optimal solutions of h model matching problems is reduced to a lyapunov type equation the parametrization of all solutions is given in an extremely simple way it is further proved that the j lossless conjugation of the h model matching problem is a natural state space representation of classical interpolation in discrete time systems

selection stability and renormalization abstract we illustrate how to extend the concept of structural stability through applying it to the front propagation speed selection problem this consideration leads us to a renormalization group study of the problem the study illustrates two very general conclusions 1 singular perturbations in applied mathematics are best understood as renormalized perturbation methods and 2 amplitude equations are renormalization group equations

on sigma lossless transfer functions and related questions abstract this paper is concerned with a systematic approach to the properties of lossless rational transfer functions in the discrete as well as in the continuous time case as a result a unifying framework is revealed where several known results fit naturally special attention is given to the embedding problem of the lyapunov equation in view of its direct application to generalized levinson algorithms

invariant painleve analysis and coherent structures of two families of reaction diffusion equations exact closed form coherent structures pulses fronts domain walls having the form of complicated traveling waves are constructed for two families of reaction diffusion equations by the use of invariant painleve analysis these analytical solutions which are derived directly from the underlying pde s are investigated in the light of restrictions imposed by the ode that any traveling wave reduction of the corresponding pde must satisfy in particular it is shown that the coherent structures a asymptotically satisfy the ode governing traveling wave reductions and b are accessible to the pde from compact support initial conditions the solutions are compared with each other and with previously known solutions of the equations

state space formulae for discrete time h optimization abstract state space formulae and proofs are given for ail the important steps in discrete time h 8 optimization the steps closely follow the algorithms for continuous time systems but there are some technically involved differences in the detail that make their derivation non trivial

a rigorous upper bound on the propagation speed for the swift hohenberg and related equations we prove that if the initial condition of the swift hohenberg equation partial t u x t varepsilon 2 1 partial x 2 2 text u x t u 3 x t is bounded in modulus by ce x as x the solution cannot propagate to the right with a speed greater than mathop sup limits 0 gamma leqslant beta gamma 1 varepsilon 2 4 gamma 2 8 gamma 4 this settles a long standing conjecture about the possible asymptotic propagation speed of the swift hohenberg equation the proof does not use the maximum principle and is simple enough to generalize easily to other equations we illustrate this with an example of a modified ginzburg landau equation where the critical speed is not determined by the linearization alone

piecewise linear emulation of propagating fronts as a method for determining their speeds we use piecewise linear terms to emulate the polynomial nonlinear terms in a typical reaction diffusion equation replacing it thus with a set of simple linear inhomogeneous differential equations the resulting analytic solution constitutes an excellent approximation to the exact propagating front as is explicitly shown in the case of cubic and quintic nonlinearities yielding also the correct value for the physically selected speed of the observable front such a piecewise linear emulation can be used for any nonlinearity giving therefore a very reliable and accurate method for determining the selected speed of fronts invading unstable states especially pushed fronts

absolute and convective instabilities front velocities and global modes in nonlinear systems abstract we study the existence of self sustained saturated solutions of the real ginzburg landau equation subject to a boundary condition at x 0 such solutions are called nonlinear global ng modes the ng instability referring to the existence of these solutions is rigorously determined and the scaling behavior of the ng modes close to threshold is derived the ng instability is first compared to the linear concept of convective absolute c a instability characterizing whether the impulse response of an unstable flow in an infinite domain is asymptotically damped or amplified at a fixed location ng modes are shown to exist while at the same time the flow may be linearly stable convectively unstable or absolutely unstable the growth size of the ng modes is shown to be proportional to 1 2 when ng and a instabilities exist simultaneously being the criticality parameter whereas a ln 1 scaling is found when the ng instability occurs while the flow is c unstable or linearly stable the nonlinear convective absolute nc na instability defined chomaz 1992 by considering in infinite homogeneous domains whether the front separating a bifurcated state from the basic state moves downstream or upstream is determined using van saarloos and hohenberg 1992 results for the selected front velocity remarkably the na domain and the ng domain are shown to coincide similar results are presented for supercritical bifurcating systems for the van der pol duffing system and for a transcritical model in all the cases the a instability is only a sufficient condition for the existence of an ng mode and these simple models demonstrate that a system may be nonlinearly absolutely unstable whereas it is linearly convectively unstable this property should be generic if one accepts the conjecture that the selected front velocity is always larger than the linear front velocity response to a constant forcing applied at the origin is also studied it is shown that in the ng region the system possesses intrinsic dynamics which cannot be removed by the forcing by contrast the behavior of a nonlinear spatial amplifier is observed in a domain larger than the nc region nc instability is only a sufficient condition to trigger the system with forcing

efficient robust estimates in parametric models let p n an open subset ofr k be a regular parametric model for a sample ofn independent identically distributed observations this paper describes estimates t n n 1 of which are asymptotically efficient under the parametric model and are robust under small deviations from that model in essence the estimates are adaptively modified one step maximum likelihood estimates which adjust themselves according to how well the parametric model appears to fit the data when the fit seems poor t n discounts observations that would have large influence on the value of the usual one step mle the estimates t n are shown to be asymptotically minimax in the hajek lecam sense for a hellinger ball contamination model an alternative construction of robust asymptotically minimax estimates as modified mle s is described for canonical exponential families

fronts pulses sources and sinks in generalized complex ginzberg landau equations an important clement in the long time dynamics of pattern forming systems is a class of solutions we will call coherent structures these are states that are either themselves localized or that consist of domains of regular patterns connected by localized defects or interfaces this paper summarizes and extends recent work on such coherent structures in the one dimensional complex ginzburg landau equation and its generalizations for which rather complete information can be obtained on the existence and competition of fronts pulses sources and sinks for the special subclass of uniformly translating structures the solutions are derived from a set of ordinary differential equations that can be interpreted as a flow in a three dimensional phase space fixed points of the flow correspond to the two basic building blocks of coherent structures uniform amplitude states and evanescent waves whose amplitude decreases smoothly to zero a study of the stability of the fixed points under the flow leads to results on the existence and multiplicity of the different coherent structures the dynamical analysis of the original partial differential equation focusses on the competition between pulses and fronts and is expressed in terms of a set of conjectures for front propagation that generalize the marginal stability and pinch point approaches of earlier authors these rules together with an exact front solution whose dynamics plays an important role in the selection of patterns yield an analytic expression for the upper limit of the range of existence of pulse solutions as well as a determination of the regions of parameter space where uniformly translating fron t solutions can exist extensive numerical simulations show consistency with these rules and conjectures for the existence of fronts and pulses in the parameter ranges where no uniformly translating fronts can exist examples are shown of irregularly spreading fronts that generate strongly chaotic regions as well as nonuniformly translating fronts that lead to uniform amplitude states recent perturbative treatments based on expansions about the nonlinear schr6dinger equation are generalized to perturbations of the cubic quintic and derivative schr idinger equations for which both pulses and fronts exist in the unperturbed system comparison of the results with the exact solutions shows that the perturbation theory only yields a subset of the relevant solutions nevertheless those that are obtained are found to be consistent with the general conjectures and in particular they provide an analytic demonstration of front pulse competition while the discussion of the competition between fronts and pulses focusses on the complex ginzburg landau equation with quintic terms and a subcritical bifurcation a number of results are also presented for the cubic equation in particular the existence of a family of moving source solutions derived by bekki and nozaki for this equation contradicts the naive counting arguments we attribute this contradiction to a hidden symmetry of the solution but have not been able to show explicitly how this symmetry affects the phase space orbits

sequential confidence bands for densities this paper proposes a fully sequential procedure for constructing a fixed width confidence band for an unknown density on a finite interval and shows the procedure has the desired coverage probability asymptotically as the width of the band approaches zero the procedure is based on a result of bickel and rosenblatt its implementation in the sequential setting cannot be obtained using anscombe s theorem because the normalized maximal deviations between the kernel estimate and the true density are not uniformly continuous in probability u c i p instead we obtain a slightly weaker version of the u c i p property and a correspondingly stronger convergence property of the stopping rule these together yield the desired results