ergodic chaos based communication schemes recent studies have shown the applicability of synchronized chaotic systems to the area of communications in different ways at the same time synchronization based signal recovery and estimation of parameters severely suffer due to the presence of channel noise by exploiting the ergodic properties of chaotic signals effectively a simple technique called the mean value method is introduced this method is shown to be capable of estimating chaos system parameters from the transmitted chaotic signal efficiently for a low signal to noise ratio a suitable demodulator has been designed for ergodic chaotic parameter modulation scheme for digital signal communication further the mean value technique incorporates a noncoherent receiver to recover analog information signal from the chaos masked signal efficiently it is found that the proposed chaotic masking scheme is robust even in the presence of strong noise in addition this scheme has the potential advantage of a very simple hardware realization which promises enhanced signal recovery performances

estimating parameters of a nonlinear dynamical system a method based on a modified newton raphson scheme is presented to estimate parameters of a nonlinear dynamical system from the time series data of the variables the method removes some of the problems associated with the standard synchronization based methods an important achievement of this method is that it is possible to determine the exact form of dynamical equations for systems with quadratic nonlinearity

the structure of random partitions of large integers random partitions of integers are treated in the case where all partitions of an integer are assumed to have the same probability the focus is on limit theorems as the number being partitioned approaches the limiting probability distribution of the appropriately normalized number of parts of some small size is exponential the large parts are described by a particular markov chain a central limit theorem and a law of large numbers holds for the numbers of intermediate parts of certain sizes the major tool is a simple construction of random partitions that treats the number being partitioned as a random variable the same technique is useful when some restriction is placed on partitions such as the requirement that all parts must be distinct

beta coalescents and continuous stable random trees coalescents with multiple collisions also known as a coalescents were introduced by pitman and sagitov in 1999 these processes describe the evolution of particles that undergo stochastic coagulation in such a way that several blocks can merge at the same time to form a single block in the case that the measure a is the beta 2 a a distribution they are also known to describe the genealogies of large populations where a single individual can produce a large number of offspring here we use a recent result of birkner et al to prove that beta coalescents can be embedded in continuous stable random trees about which much is known due to the recent progress of duquesne and le gall our proof is based on a construction of the donnelly kurtz lookdown process using continuous random trees which is of independent interest this produces a number of results concerning the small time behavior of beta coalescents most notably we recover an almost sure limit theorem of the present authors for the number of blocks at small times and give the multifractal spectrum corresponding to the emergence of blocks with atypical size also we are able to find exact asymptotics for sampling formulae corresponding to the site frequency spectrum and the allele frequency spectrum associated with mutations in the context of population genetics

existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions abstract in this paper we present a general framework for solving stochastic functional differential equations in infinite dimensions in the sense of martingale solutions which can be applied to a large class of spde with finite delays e g d dimensional stochastic fractional navier stokes equations with delays d dimensional stochastic reaction diffusion equations with delays d dimensional stochastic porous media equations with delays moreover under local monotonicity conditions for the nonlinear terms we obtain the existence and uniqueness of strong solutions to spde with delays

the structure of a random graph at the point of the phase transition consider the random graph models g n edges m and g n prob edge p with m m n 1 n 1 3 n 2 and p p n 1 an 1 3 n for 1 1 define an i component of a random graph as a component which has exactly i more edges than vertices call an i component with i 1 a complex component for both models we show that when a is constant the expected number of complex components is bounded almost surely a s each of these components if any exist has size of order n2 3 and the maximum value of i is bounded in probability we prove that a s the largest suspended tree in each complex component has size of order n2 3 and deletion of all suspended trees results in a smoothed graph of size of order n 3 with the maximum vertex degree 3 the total number of branching vertices i e of degree 3 is bounded in probability thus each complex component is almost surely topologically equivalent to a 3 regular multigraph of a uniformly bounded size lengths of the shortest cycle and of the shortest path between two branching vertices of a smoothed graph are each of order n 3 we find a relatively simple integral formula for the limit distribution of the numbers of complex components which implies in particular that all values of the complexity spectrum have positive limiting probabilities we also answer questions raised by erdos and renyi back in 1960 it is proven that there exists p a the limiting planarity probability with 0 p a 1 p oo 1 p oo 0 in particular g n m g n p resp is almost surely nonplanar iff m n 2 n 213 00 np i n 1 3 oo resp

three dimensional navier stokes equations driven by space time white noise abstract in this paper we prove existence and uniqueness of local solutions to the three dimensional 3d navier stokes n s equation driven by space time white noise using two methods first the theory of regularity structures introduced by martin hairer in 16 and second the paracontrolled distribution proposed by gubinelli imkeller perkowski in 12 we also compare the two approaches

loop correlations in random wire models we introduce a family of loop soup models on the hypercubic lattice the models involve links on the edges and random pairings of the link endpoints on the sites we conjecture that loop correlations of distant points are given by poisson dirichlet correlations in dimensions three and higher we prove that in a specific random wire model that is related to the classical xy spin system the probability that distant sites form an even partition is given by the poisson dirichlet counterpart

a high resolution data adaptive time frequency representation a data adaptive time frequency representation is developed that overcomes some limitations of the short time fourier transform while avoiding the cross terms that make the wigner distribution and other bilinear representations difficult to interpret the adaptive time frequency representations uses gaussian basis functions but varies their time width and chirp rate with time and frequency to achieve high signal concentration everywhere a measure of local signal concentration allows fully automated determination of the optimal basis parameters the adaptive method is computationally expensive but may provide much better performance than any currently known technique

on time dynamics of coagulation fragmentation processes we establish a characterization of coagulation fragmentation processes such that the induced birth and death processes depicting the total number of groups at time t 0 are time homogeneous based on this we provide a characterization of mean field gibbs coagulation fragmentation models which extends the one derived by hendriks et al as a by product of our results the class of solvable models is widened and a question posed by n berestycki and pitman is answered under restriction to mean field models

occupancy distributions arising in sampling from gibbs poisson abundance models estimating the number n of unseen species from a k sample displaying only p k distinct sampled species has received attention for long it requires a model of species abundance together with a sampling model we start with a discrete model of iid stochastic species abundances each with gibbs poisson distribution a k sample drawn from the n species abundances vector is the one obtained while conditioning it on summing to k we discuss the sampling formulae species occupancy distributions frequency of frequencies in this context we then develop some aspects of the estimation of n problem from the size k of the sample and the observed value of pn k the number of distinct sampled species

kolmogorov equations in infinite dimensions well posedness and regularity of solutions with applications to stochastic generalized burgers equations we develop a new method to uniquely solve a large class of heat equations so called kolmogorov equations in infinitely many variables the equations are analyzed in spaces of sequentially weakly continuous functions weighted by proper lyapunov type functions this way for the first time the solutions are constructed everywhere without exceptional sets for equations with possibly nonlocally lipschitz drifts apart from general analytic interest the main motivation is to apply this to uniquely solve martingale problems in the sense of stroock varadhan given by stochastic partial differential equations from hydrodynamics such as the stochastic navier stokes equations in this paper this is done in the case of the stochastic generalized burgers equation uniqueness is shown in the sense of markov flows

time domain green s function for an infinite sequentially excited periodic planar array of dipoles the present paper is a continuation of previous explorations by the authors aimed at gaining a basic understanding of the time domain td behavior of large periodic phased i e sequentially turned on array antennas and related configurations our systematic investigation of the relevant canonical td dipole excited green s functions has so far included those for infinite and truncated sequentially pulsed line periodic arrays parameterized in terms of radiating propagating and nonradiating evanescent conical td floquet waves fw and truncation induced td fw modulated tip diffractions the present contribution extends these investigations to an infinite periodic sequentially pulsed planar array which generates pulsed plane propagating and evanescent fw starting from the familiar frequency domain fd transformation of the linearly phased element by element summation synthesis into summations of propagating and evanescent fws we access the time domain by fourier inversion the inversion integrals are manipulated in a unified fashion into exact closed forms which are parameterized by the single nondimensional quantity spl eta c v sup p sub u1 where v sup p sub u1 and c are the excitation phase speed along a preferred phasing direction u sub 1 in the array plane and the ambient wave speed respectively the present study deals with the practically relevant rapidly phased propagating case spl eta 1 regime for a future manuscript numerical reference data generated via element by element summation over the fields radiated by the individual dipoles with ultrawide band limited excitation are compared with results obtained much more efficiently by inclusion of a few td fws physical interpretation of the formal td fw solutions is obtained by recourse to asymptotics instantaneous frequencies and wavenumbers and related constructs of special interest is the demonstration that the td fws emerge along equal delay ellipses from the array plane this furnishes a novel and physically appealing interpretation of the planar array td fw phenomenology

permanental partition models and markovian gibbs structures we study both time invariant and time varying gibbs distributions for configurations of particles into disjoint clusters specifically we introduce and give some fundamental properties for a class of partition models called permanental partition models whose distributions are expressed in terms of the permanent of a similarity matrix parameter we show that in the time invariant case the permanental partition model is a refinement of the celebrated pitman ewens distribution whereas in the time varying case the permanental model refines the ewens cut and paste markov chains j appl probab 43 3 778 791 2011 by a special property of the permanent the partition function can be computed exactly allowing us to make several precise statements about this general model including a characterization of exchangeable and consistent permanental models

the phase transition in a random hypergraph we show that in the evolution of the random d uniform hypergraph gd n m the phase transition occurs when m n d d 1 o n2 3 we also prove local limit theorems for the distribution of the size of the largest component of gd n m in the subcritical and in the early supercritical phase

application of haar wavelet based multiresolution time domain schemes to electromagnetic scattering problems the multiresolution time domain mrtd algorithm is applied to the problem of general two dimensional electromagnetic scattering a haar wavelet expansion is utilized a parallel between haar mrtd and the classic yee finite difference time domain fdtd algorithm is discussed and results of simulations on canonical targets are shown for comparison we focus on the incident field implementation which in our case consists of a pulsed plane wave also we consider scattering in a half space environment with application to subsurface sensing the results illustrate the advantage of the haar mrtd method as compared with the classic fdtd which consists of reduced memory and execution time requirements without sacrificing accuracy

upper bound on the characters of the symmetric groups let c be a conjugacy class in the symmetric group s n and be a partition of n let f be the degree of the irreducible representation s c the character of s at c and r c the normalized character c f we prove that there exist constants b 0 and 1 q 0 such that for n 4 for every conjugacy class c in s n and every irreducible representation s of s n r c max q 1 n 1 n b supp c where supp c is the number of non fixed digits under the action of a permutation in c 1 is the size of the largest part in and 1 is the number of parts in the proof is obtained by enumeration of rim hook tableaux the hook formula and probabilistic arguments combinatorial algebraic and statistical applications follow this result in particular we estimate the rate of mixing of random walks on the alternating groups with respect to conjugacy classes

cutoff for conjugacy invariant random walks on the permutation group we prove a conjecture raised by the work of diaconis and shahshahani z wahrscheinlichkeitstheorie verwandte geb 57 2 159 179 1981 about the mixing time of random walks on the permutation group induced by a given conjugacy class to do this we exploit a connection with coalescence and fragmentation processes and control the kantorovich distance by using a variant of a coupling due to oded schramm as well as contractivity of the distance recasting our proof in the language of ricci curvature our proof establishes the occurrence of a phase transition which takes the following form in the case of random transpositions at time cn 2 the curvature is asymptotically zero for c le 1 and is strictly positive for c 1

on a recursive method for the estimation of unknown parameters of partially observed chaotic systems we investigate a recently proposed method for on line parameter estimation and synchronization in chaotic systems this novel technique has been shown effective to estimate a single unknown parameter of a primary chaotic system with known functional form that is only partially observed through a scalar time series it works by periodically updating the parameter of interest in a secondary system with the same functional form as the primary one but no explicit coupling between their dynamic variables in order to minimize a suitably defined cost function in this paper we review the basics of the method and investigate its robustness and new extensions in particular we study the performance of the novel technique in the presence of noise either observational i e an additive contamination of the observed time series or dynamical i e a random perturbation of the system dynamics and when there is a mismatch between the primary and secondary systems numerical results including comparisons with other techniques are presented finally we investigate the extension of the original method to perform the estimation of two unknown parameters and illustrate its effectiveness by means of computer simulations

a phase transition in the random transposition random walk our work is motivated by bourque pevzner s simulation study of the effectiveness of the parsimony method in studying genome rearrangement and leads to a surprising result about the random transposition walk in continuous time on the group of permutations on n elements starting from the identity let d t be the minimum number of transpositions needed to go back to the identity element from the location at time t d t undergoes a phase transition for 0 1 d cn 2 u c n where u is an explicit function satisfying u x x 2 moreover we describe the fluctuations of d cn 2 about its mean at each of the three stages subcritical critical and supercritical the techniques used involve viewing the cycles in the random permutation as a coagulation fragmentation process and relating the behavior to the erd s renyi random graph model

a note on stochastic semilinear equations and their associated fokker planck equations abstract the main purpose of this paper is to prove existence and uniqueness of probabilistically weak and strong solutions to stochastic differential equations sde on hilbert spaces under a new approximation condition on the drift recently proposed in 6 to solve fokker planck equations fpe extended in this paper to a considerably larger class of drifts as a consequence we prove existence of martingale solutions to the sde whose time marginals then solve the corresponding fpe applications include stochastic semilinear partial differential equations with white noise and a non linear drift part which is the sum of a burgers type part and a reaction diffusion part the main novelty is that the latter is no longer assumed to be of at most linear but of at most polynomial growth this case so far had not been covered by the existing literature we also give a direct and more analytic proof for existence of solutions to the corresponding fpe extending the technique from 6 to our more general framework which in turn requires to work on a suitable gelfand triple rather than just the hilbert state space

power laws for family sizes in a duplication model qian luscombe and gerstein j molecular biol 313 2001 673 681 introduced a model of the diversification of protein folds in a genome that we may formulate as follows consider a multitype yule process starting with one individual in which there are no deaths and each individual gives birth to a new individual at rate 1 when a new individual is born it has the same type as its parent with probability 1 r and is a new type different from all previously observed types with probability r we refer to individuals with the same type as families and provide an approximation to the joint distribution of family sizes when the population size reaches n we also show that if 1 s n 1 r then the number of families of size at least s is approximately cns 1 1 r while if n 1 r s the distribution decays more rapidly than any power

the poisson dirichlet law is the unique invariant distribution for uniform split merge transformations we consider a markov chain on the space of countable partitions of the interval 0 1 obtained first by size biased sampling twice allowing repetitions and then merging the parts if the sampled parts are distinct or splitting the part uniformly if the same part was sampled twice we prove a conjecture of vershik stating that the poisson dirichlet law with parameter 1 is the unique invariant distribution for this markov chain our proof uses a combination of probabilistic combinatoric and representation theoretic arguments

optimal time domain detection of a deterministic target buried under a randomly rough interface we consider pulsed plane wave scattering from targets buried under a rough air ground interface the properties of the interface are parametrized as a random process with known statistics and therefore the fields scattered from a particular surface constitute one realization of an ensemble characterized by corresponding statistics moreover since the fields incident upon a buried target must first penetrate the rough interface they and the subsequent scattered fields are random processes as well based on this understanding an optimal detector is formulated accounting for the clutter and target signature statistics the former due to scattering at the rough surface and the latter due to transmission the statistics of these two processes are in general different the detector performance is compared to that of a matched filter which assumes the target signature is known exactly i e nonrandom the results presented here as a function of angle and polarization demonstrate that there is often a significant gain in detector performance if the target signature is properly treated as a random process

network oriented dyadic time domain green s function for a sequentially excited infinite planar array of dipoles in free space during the past few years we have performed an effective wideband analysis for characterizing the electrodynamic behavior of phased array antennas infinite periodic structures frequency selective surfaces and related applications with emphasis on gaining physical insight into the phenomenology of short pulse radiation the present contribution shows the current status of our network oriented dyadic time domain green s function td gf for a planar array of sequentially excited dipoles that constitutes a prototype study of sequentially short pulsed radiation by infinite periodic arrays the dispersive effects of the td floquet waves fw and the consequences of a te and tm field decomposition are discussed in details in this network formulation the equivalent td transmission line tl voltages and currents excited by equivalent td current generators are determined an expression for the tm voltage tl gf is provided for the first time in terms of incomplete lipschitz hankel integrals and bessel functions together with some remarks for its evaluation as shown in previous publications for the scalar potentials real td physical observables are determined by pairing td floquet waves with positive and negative indices it is shown that the vectorial td radiated field is reconstructed at any time with the superposition of a few td fws

wavelet based linear system modeling and adaptive filtering it is shown how linear time varying systems can be modeled in several different ways by discrete time wavelets or more generally by some set of functions interpretation of physical meanings possible efficiency and other characteristics of the modeling are considered system identification minimizing the mean square output error is studied optimal coefficients and the corresponding minimum mean square error are found and they are in general time varying least mean square adaptive filtering algorithms are derived for on line filtering and system identification theoretically and by simulations the advantages of using wavelet based filtering are shown separation of adaptation effects from unknown time varying system behavior and fast convergence adaptive coefficients estimated by a recursive least square algorithm can tend toward constants even in the case of time varying systems time invariant system identification and adaptive filtering is given as a special case of the general time varying setting

time harmonic and transient scattering by finite periodic flat strip arrays hybrid ray floquet mode mom algorithm a frequency and short pulse sp time domain td study of two dimensional plane wave scattering from a finite periodic array of thin flat coplanar perfectly conducting strips is presented rigorous analytical numerical reference solutions are established by spatial spectral wave number decomposition and the method of moments mom followed by frequency inversion the analytical portion is approximated so as to yield via high frequency asymptotics for a sufficiently large number of strips a hybrid ray floquet mode mom algorithm that not only explains the phenomena in physical terms but is also numerically efficient and reasonably accurate when compared with the reference solution of special interest are the td floquet modes with their space time dependent frequencies and wave numbers by superposition they can synthesize the highly resolved pulse train return under sp conditions attention is given also to direct sp td synthesis and to processing options for sp td data

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

existence and uniqueness of martingale solutions for sdes with rough or degenerate coefficients abstract in this paper we extend recent results on the existence and uniqueness of solutions of odes with non smooth vector fields to the case of martingale solutions in the stroock varadhan sense of sdes with non smooth coefficients in the first part we develop a general theory which roughly speaking allows to deduce existence uniqueness and stability of martingale solutions for l d almost every initial condition x whenever existence and uniqueness is known at the pde level in the l setting and conversely if existence and uniqueness of martingale solutions is known for l d a e initial condition then existence and uniqueness for the pde holds in the second part of the paper we consider situations where on the one hand no pointwise uniqueness result for the martingale problem is known and on the other hand well posedness for the fokker planck equation can be proved thus the theory developed in the first part of the paper is applicable in particular we will study the fokker planck equation in two somehow extreme situations in the first one assuming uniform ellipticity of the diffusion coefficients and lipschitz regularity in time we are able to prove existence and uniqueness in the l 2 setting in the second one we consider an additive noise and assuming the drift b to have bv regularity and allowing the diffusion matrix a to be degenerate also identically 0 we prove existence and uniqueness in the l setting therefore in these two situations our theory yields existence uniqueness and stability results for martingale solutions

fokker planck equations and maximal dissipativity for kolmogorov operators with time dependent singular drifts in hilbert spaces we consider a kolmogorov operator l0 in a hilbert space h related to a stochastic pde with a time dependent singular quasi dissipative drift f f t h h defined on a suitable space of regular functions we show that l0 is essentially m dissipative in the space lp 0 t h p 1 where dt dx t dx dt and the family t t 0 t is a solution of the fokker planck equation given by l0 as a consequence the closure of l0 generates a markov c0 semigroup we also prove uniqueness of solutions to the fokker planck equation for singular drifts f applications to reaction diffusion equations with time dependent reaction term are presented this result is a generalization of the finite dimensional case considered in v bogachev g da prato m rockner existence of solutions to weak parabolic equations for measures proc london math soc 3 88 2004 753 774 v bogachev g da prato m rockner on parabolic equations for measures comm partial differential equations 33 3 2008 397 418 and v bogachev g da prato m rockner w stannat uniqueness of solutions to weak parabolic equations for measures bull london math soc 39 2007 631 640 to infinite dimensions

ricci curvature of markov chains on metric spaces abstract we define the coarse ricci curvature of metric spaces in terms of how much small balls are closer in wasserstein transportation distance than their centers are this definition naturally extends to any markov chain on a metric space for a riemannian manifold this gives back after scaling the value of ricci curvature of a tangent vector examples of positively curved spaces for this definition include the discrete cube and discrete versions of the ornstein uhlenbeck process moreover this generalization is consistent with the bakry emery ricci curvature for brownian motion with a drift on a riemannian manifold positive ricci curvature is shown to imply a spectral gap a levy gromov like gaussian concentration theorem and a kind of modified logarithmic sobolev inequality the bounds obtained are sharp in a variety of examples

the hyperbolic geometry of random transpositions turn the set of permutations of n objects into a graph g n by connecting two permutations that differ by one transposition and let t be the simple random walk on this graph in a previous paper berestycki and durrett in discrete random walks 2005 17 26 showed that the limiting behavior of the distance from the identity at time cn 2 has a phase transition at c 1 here we investigate some consequences of this result for the geometry of g n our first result can be interpreted as a breakdown for the gromov hyperbolicity of the graph as seen by the random walk which occurs at a critical radius equal to n 4 let t be a triangle formed by the origin and two points sampled independently from the hitting distribution on the sphere of radius an for a constant 0 0 whereas it is always o n thick when a 1 4 we also show that the hitting distribution of the sphere of radius an is asymptotically singular with respect to the uniform distribution finally we prove that the critical behavior of this gromov like hyperbolicity constant persists if the two endpoints are sampled from the uniform measure on the sphere of radius an however in this case the critical radius is a 1 log 2

optimize design of adaptive synchronization controllers and parameter observers in different hyperchaotic systems based on the lyapunov stability and adaptive synchronization theory optimization design of adaptive controllers and parameter observers with controllable gain coefficient are investigated in detail the linear errors of corresponding variables and parameters are used to construct different appropriate positive lyapunov functions v and the parameter observers and adaptive controllers are approached analytically by simplifying the differential inequality dv dt 0 particularly an optional gain coefficient is selected in the parameter observers and positive lyapunov function which decides the transient period to identify the unknown parameters and reach synchronization the scheme is used to study the synchronization of two non identical hyperchaotic rossler systems the theoretical and numerical results confirm that the four unknown parameters in the drive system are estimated exactly and the two hyperchaotic systems reach complete synchronization when the controllers and parameter observers work on the driven system to confirm the model independence of this scheme an alternative hyperchaotic system is investigated whereby the results confirm that the five unknown parameters are identified rapidly and exactly and that the two hyperchaotic systems reach complete synchronization as well

wave propagation and sampling theory part ii sampling theory and complex waves morlet et al 1982 this issue showed the advantages of using complex values for both waves and characteristics of the media we simulated the theoretical tools we present here using the goupillaud kunetz algorithm now we present sampling methods for complex signals or traces corresponding to received waves and sampling methods for complex characterization of multilayered or heterogeneous media regarding the complex signals we present a twodimecsional 2 d method of sampling in the time frequency domain using a special or extended gabor expansion on a set of basic wavelets adapted to phase preservation such a 2 d expansion permits us to handle in a proper manner instantaneous frequency spectra we show the differences between wavelet resolution and sampling grid resolution we also show the importance of phase preservation in high resolution seismic regarding the media we show how analytical studies of wave propagation in periodic structured layers could help when trying to characterize the physical properties of the layers and their large scale granularity as a result of complex deconvolution analytical studies of wave propagation in periodic structures are well known in solid state physics and lead to the so called bloch waves the introduction of complex waves leads to replacing the classical wave equation by a schriidinger equation finally we show that complex wave equations gabor expansion and bloch waves are three different ways of introducing the tools of quantum mechanics in highresolution seismic gabor 1946 kittel 1976 morlet 1975 and conversely the goupillaud kunetz algorithm and an extended gabor expansion may be of some use in solid state physics

parameter adaptive identical synchronization disclosing lorenz chaotic masking a parameter adaptive rule that globally synchronizes oscillatory lorenz chaotic systems with initially different parameter values is reported in principle the adaptive rule requires access to the three state variables of the drive system but it has been readapted to work with the exclusive knowledge of only one variable a potential message carrier the rule is very robust and can be used to trace parameter modulation conveying hidden messages the driven system is defined according to a drive driven type of coupling that guarantees synchronization if parameters are identical from any arbitrary initial state the parameters of the driven system are dynamically adapted to reach convergence to the drive parameter values at this point synchronization mismatch or parameter tracing is used to unmask any potential hidden message

mixing and concentration by ricci curvature abstract we generalise the coarse ricci curvature method of ollivier by considering the coarse ricci curvature of multiple steps in the markov chain this implies new spectral bounds and concentration inequalities we also extend this approach to the bounds for mcmc empirical averages obtained by joulin and ollivier we prove a recursive lower bound on the coarse ricci curvature of multiple steps in the markov chain making our method broadly applicable applications include the split merge random walk on partitions glauber dynamics with random scan and systemic scan for statistical physical spin models and random walk on a binary cube with a forbidden region

wave propagation and sampling theory part i complex signal and scattering in multilayered media from experimental studies in digital processing of seismic reflection data geophysicists know that a seismic signal does vary in amplitude shape frequency and phase versus propagation time to enhance the resolution of the seismic reflection method we must investigate these variations in more detail we present quantitative results of theoretical studies on propagation of plane waves for normal incidence through perfectly elastic multilayered media as wavelet shapes we use zero phase cosine wavelets modulated by a gaussian envelope and the corresponding complex wavelets a finite set of such wavelets for an appropriate sampling of the frequency domain may be taken as the basic wavelets for a gabor expansion of any signal or trace in a two dimensional 2 d domain time and frequency we can then compute the wave propagation using complex functions and thereby obtain quantitative results including energy and phase of the propagating signals these results appear as complex 2 d functions of time and frequency i e as instantaneous frequency spectra choosing a constant sampling rate on the logarithmic scale in the frequency domain leads to an appropriate sampling method for phase preservation of the complex signals or traces for this purpose we developed a gabor expansion involving basic wavelets with a constant time duration mean period ratio for layered media as found in sedimentary basins

gibbs distributions for random partitions generated by a fragmentation process in this paper we study random partitions of 1 n where every cluster of size j can be in any of wj possible internal states the gibbs n k w distribution is obtained by sampling uniformly among such partitions with k clusters we provide conditions on the weight sequence w allowing construction of a partition valued random process where at step k the state has the gibbs n k w distribution so the partition is subject to irreversible fragmentation as time evolves for a particular one parameter family of weight sequences wj the time reversed process is the discrete marcus lushnikov coalescent process with affine collision rate ki j a b i j for some real numbers a and b under further restrictions on a and b the fragmentation process can be realized by conditioning a galton watson tree with suitable offspring distribution to have n nodes and cutting the edges of this tree by random sampling of edges without replacement to partition the tree into a collection of subtrees suitable offspring distributions include the binomial negative binomial and poisson distributions

analysis of the rayleigh pulse seismologists make frequent use of wavelets also referred to as signals signatures or pulses particularly in such fields as seismic filtering wavelet processing wave propagation modeling and trace inversion whenever possible the actual seismic wavelet of the real source should be considered hosken 1988 however frequently particularly in wave propagation modeling one must consider a synthetic source wavelet this should if possible be given by a simple mathematical formula and possess an easy description for its most important spectral properties e g amplitude and phase spectrum main frequency hilbert transform etc moreover the mathematical expression should be such that with a minimum number of parameters a large flexibility in the form of the wavelet can be obtained

bayesian nonparametric estimation of the probability of discovering new species summary we consider the problem of evaluating the probability of discovering a certain number of new species in a new sample of population units conditional on the number of species recorded in a basic sample we use a bayesian nonparametric approach the different species proportions are assumed to be random and the observations from the population exchangeable we provide a bayesian estimator under quadratic loss for the probability of discovering new species which can be compared with well known frequentist estimators the results we obtain are illustrated through a numerical example and an application to a genomic dataset concerning the discovery of new genes by sequencing additional single read sequences of cdna fragments

brownian excursions critical random graphs and the multiplicative coalescent let b t s 0 s be reflecting inhomogeneous brownian motion with drift t s at time s started with b t 0 0 consider the random graph script g sign n n 1 tn 4 3 whose largest components have size of order n 2 3 normalizing by n 2 3 the asymptotic joint distribution of component sizes is the same as the joint distribution of excursion lengths of b t corollary 2 the dynamics of merging of components as t increases are abstracted to define the multiplicative coalescent process the states of this process are vectors x of nonnegative real cluster sizes x i and clusters with sizes x i and x j merge at rate x i x j the multiplicative coalescent is shown to be a feller process on l 2 the random graph limit specifies the standard multiplicative coalescent which starts from infinitesimally small clusters at time the existence of such a process is not obvious

continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models given any regularly varying dislocation measure we identify a natural self similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths as an application we obtain continuum random tree limits of aldous s beta splitting models and ford s alpha models for phylogenetic trees this confirms in a strong way that the whole trees grow at the same speed as the mean height of a randomly chosen leaf

transforming cabbage into turnip polynomial algorithm for sorting signed permutations by reversals genomes frequently evolve by reversals r i j that transform a gene order 1 i i 1 j 1 j n into 1 i j 1 i 1 j n reversal distance between permutations and sis the minimum number of reversals to transform into a analysis of genome rearrangements in molecular biology started in the late 1930 s when dobzhansky and sturtevant published a milestone paper presenting a rearrangement scenario with 17 inversions between the species of drosophilia analysis of genomes evolving by inversions leads to a combinatorial problem of sorting by reversals studied in detail recently we study sorting of signed permutations by reversals a problem that adequately models rearrangements in a small genomes like chloroplast or mitochondrial dna the previously suggested approximation algorithms for sorting signed permutations by reversals compute the reversal distance between permutations with an astonishing accuracy for both simulated and biological data we prove a duality theorem explaining this intriguing performance and show that there exists a hidden parameter that allows one to compute the reversal distance between signed permutations in polynomial time

an invariance principle for certain dependent sequences let x 1 x 2 cdots be a strictly stationary second order sequence which is associated i e is such that any two coordinatewise nondecreasing functions of the x i s of finite variance are nonnegatively correlated if sum j operatorname cov x 1 x j infty then the partial sum processes w n t defined in the usual way so that w n m n x 1 cdots x m me x 1 sqrt n for m 1 2 cdots converge in distribution on c lbrack 0 t rbrack to a wiener process this result is based on two general theorems concerning associated random variables which are of independent interest

frequency and time domain green s functions for a phased semi infinite periodic line array of dipoles we extend a previous prototype study of felsen and capolino see ibid vol 48 p 921 931 june 2000 of frequency domain fd and time domain td green s functions for an infinite periodic phased line array of dipoles to account for the effects of truncation as modeled by a semi infinite array these canonical problems are to be used eventually for the systematic analysis and synthesis of actual rectangular td plane phased arrays in the presentation we rely on the analytic results and phenomenologies pertaining to the infinite array which are reviewed major emphasis is then placed on the modifications introduced by the truncation finite poisson summation is used to convert the individual dipole radiations into collective truncated wavefields the fd and td floquet waves fw in the td exact closed form solutions are obtained and are examined asymptotically to extract fd and td periodicity matched conical truncated fw fields both propagating and nonpropagating corresponding tip diffracted periodicity matched spherical waves and uniform transition functions connecting both across the fd and td fw truncation boundaries these new effects can again be incorporated in a fw modulated geometrical theory of diffraction a numerical example of radiation from a finite phased td dipole array with band limited excitation demonstrates the accuracy and efficiency of the fw diffracted field asymptotic algorithm when compared with an element by element summation reference solution

martingale and stationary solutions for stochastic navier stokes equations we prove the existence of martingale solutions and of stationary solutions of stochastic navier stokes equations under very general hypotheses on the diffusion term the stationary martingale solutions yield the existence of invariant measures when the transition semigroup is well defined the results are obtained by a new method of compactness

mixing times for random k cycles and coalescence fragmentation chains let sn be the permutation group on n elements and consider a random walk on sn whose step distribution is uniform on k cycles we prove a well known conjecture that the mixing time of this process is 1 k nlog n with threshold of width linear in n our proofs are elementary and purely probabilistic and do not appeal to the representation theory of sn

the evolution of the random reversal graph genomes are typically represented as signed permutations where each integer corresponds to a single gene and its sign indicates the orientation of the gene in this paper we study genome rearrangements via reversals sankoff and blanchette 1999 20 flipping entire segments of genes and changing their orientations this abstraction leads to the notion of the reversal graph in which two signed permutations are neighbors if they differ by one reversal we identify the evolution of multiple genomes within the random reversal graph i e the probability space consisting of subgraphs over signed permutations obtained by selecting edges reversals with independent probability n which is an important framework for the analysis of genome rearrangements in the sense of relating the reversal rate n with the global evolution of genomes our main result shows that the structure of the random reversal graph changes dramatically at n 1 n 1 2 for n 1 n 1 2 the random graph consists of components of size at most o n ln n a s and for 1 n 1 2 there emerges a unique largest component of size 2 n n a s where is the survival probability of a certain branching process this giant component is furthermore dense in the reversal graph

lorenz like systems and classical dynamical equations with memory forcing an alternate point of view for singling out the origin of chaos an alternate view for the emergence of chaos in lorenz like systems is presented in this paper for such purpose the lorenz problem is reformulated in a classical mechanical form and it turns out to be equivalent to the problem of a damped and forced one dimensional motion of a particle in a two well potential with a forcing term depending on the memory of the particle past motion the dynamics of the original lorenz system in the proposed particle phase space can then be rewritten in terms of a one dimensional first exit time problem the emergence of chaos turns out to be due to the discontinuous solutions of the transcendental equation ruling the time for the particle to cross the intermediate potential wall the whole problem is tackled analytically deriving a piecewise linearized lorenz like system that preserves all the essential properties of the original model