analysis of fronts in reaction dispersal processes the existence of traveling wave front solutions with a minimum speed selected for reaction dispersal processes is studied we obtain a general existence condition in terms of the waiting time and dispersal distance probability distribution functions and we detail this result for situations of ecological interest in particular when particles disperse according to jumps of short length and any waiting time probability distribution function we show that the minimum speed selection for traveling wave fronts is not always possible so the waiting time and the dispersal distance distributions cannot be arbitrarily chosen

random walk in chemical space of cantor dust as a paradigm of superdiffusion we point out that the chemical space of a totally disconnected cantor dust k n ensuremath subset e n is a compact metric space c n with the spectral dimension d s d ensuremath ell ngd where d and d ensuremath ell n are the fractal and chemical dimensions of k n respectively hence we can define a random walk in the chemical space as a markovian gaussian process the mapping of a random walk in c n into k n ensuremath subset e n defines the quenched l evy flight on the cantor dust with a single step duration independent of the step length the equations describing the superdiffusion and diffusion reaction front propagation ruled by the local quenched l evy flight on k n ensuremath subset e n are derived the use of these equations to model superdiffusive phenomena observed in some physical systems in which propagators decay faster than algebraically is discussed

non regular maximum likelihood problems four non regular estimation problems are reviewed and discussed one the unbounded likelihood problem involves distributions with infinite spikes for which maximum likelihood can fail to give consistent estimators a comparison is made with modified likelihood and spacings methods which do give efficient estimators in this case an application to the box cox shifted power transform is given the other three problems occur when the true parameter lies in some special subregion in one the constrained parameter problem the subregion is a boundary the other two the embedded model and the indeterminate parameters problems occur when the model takes on a special form in the subregion these last two problems have previously been investigated separately we show that they are equivalent in some situations both often arise in non linear models and we give a directed graph approach which allows for their occurrence in nested model building it is argued that many non regular problems can be handled systematically without having to resort to elaborate technical assumptions relatively uncomplicated methods may be used provided that the underlying nature of the non regularity is understood

estimation in a cox regression model with a change point according to a threshold in a covariate we consider a nonregular cox model for independent and identically distributed right censored survival times with a change point according to the unknown threshold of a covariate the maximum partial likelihood estimators of the parameters and the estimator of the baseline cumulative hazard are studied we prove that the estimator of the change point is n consistent and the estimator of the regression parameters are n 1 2 consistent and we establish the asymptotic distributions of the estimators the estimators of the regression parameters and of the baseline cumulative hazard are adaptive in the sense that they do not depend on the knowledge of the change point

a monte carlo approach for change point detection in the cox proportional hazards model detecting a time lag of treatment effect or identifying change points in a hazard function is of great interest and importance in survival analysis the testing procedures hereto are primarily based on analytical approximations for the asymptotic null distribution of either the likelihood ratio test or the score test in the presence of random censoring and or covariates however the justification for the limiting distribution often requires some technical assumptions and conditions that are difficult to verify in practice moreover a satisfactory asymptotic theory for testing the existence of multiple change points in hazard function has not emerged in this paper we consider maximal score tests for detecting change point s in the cox proportional hazards model with censored data we propose to use a simple monte carlo approach for assessing the statistical significance of tests the proposed approach is applicable for testing a single change point in the cox model with covariates and sample stratifications over various types of candidate regions including discrete time point sets or disjoint intervals we also show that the proposed test statistics and the monte carlo procedure are well applicable under situations with multiple change points simulation studies and an analysis of a real data from a randomized cancer trial are conducted to demonstrate the finite sample performance of the proposed approach

probabilistic approach to a proliferation and migration dichotomy in tumor cell invasion the proliferation and migration dichotomy of the tumor cell invasion is examined within a two component continuous time random walk ctrw model the balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration are derived the transport of tumor cells is formulated in terms of the ctrw with an arbitrary waiting time distribution law while proliferation is modeled by a logistic growth the overall rate of tumor cell invasion for normal diffusion and subdiffusion is determined

tests for a change point summary the problem considered is that of testing a sequence of independent normal random variables with constant known or unknown variance for no change in mean versus alternatives with a single change point various tests such as those based on the likelihood ratio and recursive residuals are studied power approximations are developed by integrating approximations for conditional boundary crossing probabilities a comparison of several tests is made

likelihood ratio tests for a changepoint with survival data summary we consider the likelihood ratio test for a changepoint or lag of the effect of some covariates e g treatment in regression modelling of survival data subject to right censoring asymptotic distributions under null hypotheses are derived numerical examples are used to illustrate the implementation of the procedure finally we apply the theory to data from a large randomised cancer prevention trial

inference for a hazard rate change point summary we discuss inference based on the likelihood ratio process for a hazard rate change point a random change of time scale transforms the empirical process into a poisson process which enables us to derive large deviation approximations to the significance level of the likelihood ratio test we derive approximate confidence regions for the change point and joint confidence regions for the change point and size of change the effect of censorship is also discussed the methods are illustrated using stanford heart transplant data for which the 70 days following the transplant are found to be most critical

relationships between dmp relation and some partial orders let h be an infinite dimensional complex hilbert space and let b h be the algebra of all bounded linear operators on h the equivalent definition of the dmp relation on b h using operator block matrices is introduced we present a new interpretation of this relation which allows to generalize many known results for matrices to general hilbert spaces regarding the dmp relation and its relationship with the star order and minus partial order also some properties of dmp relation defined with the help of idempotent operators are investigated

exact percentage points of the likelihood ratio test for a change point hazard rate model we wish to test that the hazard rate of survival or failure time data is constant against the alternative of a change in hazard after an unspecified time the likelihood ratio is unbounded but the exact null distribution of a restricted likelihood ratio test statistic is found this distribution is not affected by type ii censoring but it does depend very strongly on the interval in which the unknown change point is assumed to lie some exact percentage points are given which are much larger than simulated points that have been reported in the literature

regular markov chains for which the transition matrix has large exponent abstract in this paper we analyze properties of transition matrices t r n n of regular markov chains whose exponent index of primitivity is bounded below by n 1 2 1 2 2 our investigation leads to a proof that for such a t the corresponding condition number k t max 1 i j n q i j where q i t we go on to show that if e r n n is a perturbation of t such that t e is also a transition matrix for a regular markov chain and and are the stationary distribution vectors of t and t e respectively then and 1 1 many of the techniques used to establish these results are combinatorial in nature

likelihood ratio test for a piecewise continuous weibull model with an unknown change point abstract in this paper we consider the likelihood ratio test for the scale and shape parameters in a piecewise continuous weibull model with an unknown change point under the null hypothesis of no change in scale and shape parameters we derive that the likelihood ratio process converges weakly to the squared euclidian norm of a weighted mean zero gaussian vector process

biased random walks and propagation failure the critical value of the reaction rate able to sustain the propagation of an invasive front is obtained for general non markovian biased random walks with reactions from the hamilton jacobi equation corresponding to the mean field equation we find that the critical reaction rate depends only on the mean waiting time and on the statistical properties of the jump length probability distribution function and is always underestimated by the diffusion approximation if the reaction rate is larger than the jump frequency invasion always succeeds even in the case of maximal bias numerical simulations support our analytical predictions

anomalous diffusion with linear reaction dynamics from continuous time random walks to fractional reaction diffusion equations we have revisited the problem of anomalously diffusing species modeled at the mesoscopic level using continuous time random walks to include linear reaction dynamics if a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term if the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a nonstandard diffusion term results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term we have also developed further extensions of the ctrw model to include more general reaction dynamics

testing for change point in the covariate effects based on the cox regression model models with change point in covariates have wide applications in cancer research with the response being the time to a certain event a cox model with change point in covariate is considered at which the pattern of the change point effects can be flexibly specified to test for the existence of the change point effects three statistical tests namely the maximal score maximal normalized score and maximal wald tests are proposed the asymptotic properties of the test statistics are established monte carlo approaches to simulate the critical values are suggested a large scale simulation study is carried out to study the finite sample performance of the proposed test statistics under the null hypothesis of no change points and various alternative hypothesis settings each of the proposed methods provides a natural estimate for the location of the change point but it is found that the performance of the maximal score test can be sensitive to the true location of the change point in some cases while the performance of the maximal wald test is very satisfactory in general even in cases with moderate sample size for illustration the proposed methods are applied to two medical datasets concerning patients with primary biliary cirrhosis and breast cancer respectively

anomalous subdiffusion with multispecies linear reaction dynamics we have introduced a set of coupled fractional reaction diffusion equations to model a multispecies system undergoing anomalous subdiffusion with linear reaction dynamics the model equations are derived from a mesoscopic continuous time random walk formulation of anomalously diffusing species with linear mean field reaction kinetics the effect of reactions is manifest in reaction modified spatiotemporal diffusion operators as well as in additive mean field reaction terms one consequence of the nonseparability of reaction and subdiffusion terms is that the governing evolution equation for the concentration of one particular species may include both reactive and diffusive contributions from other species the general solution is derived for the multispecies system and some particular special cases involving both irreversible and reversible reaction dynamics are analyzed in detail we have carried out monte carlo simulations corresponding to these special cases and we find excellent agreement with theory

front propagation in hyperbolic fractional reaction diffusion equations from the continuous time random walk scheme and assuming a l evy waiting time distribution typical of subdiffusive transport processes we study a hyperbolic reaction diffusion equation involving time fractional derivatives the linear speed selection of wave fronts in this equation is analyzed when the reaction diffusion dimensionless number and the fractional index satisfy a certain condition we find fronts exhibiting an unphysical behavior they travel faster in the subdiffusive than in the diffusive regime

asymptotic score statistic processes and tests for constant hazard against a change point alternative the problem of testing for a constant failure rate against alternatives with failure rates involving a single change point is considered the asymptotic significance level for tests based on maximal score statistics are shown to involve the solution to a first passage time problem for an ornstein uhlenbeck process an example illustrates the methodology

on graphs with equal algebraic and vertex connectivity let g be an undirected unweighted graph on n vertices let l be its laplacian matrix and let l l i j be the group inverse of l it is known that for z l 1 2 max1 i j n s 1n li s lj s the quantity 1 z l is a lower bound on the algebraic connectivity a g of g while the vertex connectivity of g v g is an upper bound on a g we characterize the graphs g for which v g a g and subsequently prove that if n v g 2 then v g a g holds if and only if 1 z l a g v g we close with an example showing that the equality 1 z l a g does not necessarily imply that 1 z l a g v g

aalen additive hazards change point model we study a test comparing the full aalen additive hazards model and the change point model and suggest how to estimate the parameters of the change point model we also study a test for no change point effect both tests are provided with large sample properties and a resampling method is applied to obtain p values the finite sample properties of the proposed inference procedures and estimators are assessed through a simulation study the methods are further applied to a dataset concerning myocardial infarction

the generalized cattaneo equation for the description of anomalous transport processes the cattaneo equation which describes a diffusion process with a finite velocity of propagation is generalized to describe anomalous transport three possible generalizations are proposed each one supported by a different scheme continuous time random walks non local transport theory and delayed flux force relation the properties of these generalizations are studied in both the long time and the short time regimes in the long time limit we recover the mean square displacement which is characteristic for these anomalous processes as expected the short time behaviour is modified in comparison to generalized diffusion equations

mathematical modeling of time fractional reaction diffusion systems we study a fractional reaction diffusion system with two types of variables activator and inhibitor the interactions between components are modeled by cubical nonlinearity linearization of the system around the homogeneous state provides information about the stability of the solutions which is quite different from linear stability analysis of the regular system with integer derivatives it is shown that by combining the fractional derivatives index with the ratio of characteristic times it is possible to find the marginal value of the index where the oscillatory instability arises the increase of the value of fractional derivative index leads to the time periodic solutions the domains of existing periodic solutions for different parameters of the problem are obtained a computer simulation of the corresponding nonlinear fractional ordinary differential equations is presented for the fractional reaction diffusion systems it is established that there exists a set of stable spatio temporal structures of the one dimensional system under the neumann and periodic boundary conditions the characteristic features of these solutions consist of the transformation of the steady state dissipative structures to homogeneous oscillations or space temporary structures at a certain value of fractional index and the ratio of characteristic times of system

continuous time random walks and traveling fronts we present a geometric approach to the problem of propagating fronts into an unstable state valid for an arbitrary continuous time random walk with a fisher kolmogorov petrovski piskunov growth reaction rate we derive an integral hamilton jacobi type equation for the action functional determining the position of reaction front and its speed our method does not rely on the explicit derivation of a differential equation for the density of particles in particular we obtain an explicit formula for the propagation speed for the case of anomalous transport involving non markovian random processes

front propagation in reaction dispersal models with finite jump speed the continuous time random walk and the hamilton jacobi method are used to reach analytical expressions for the speed of traveling fronts in reaction dispersal models in this work the waiting time and jump length are assumed to be coupled random variables the jump length for any jump is selected according to the waiting time at the end of the previous jump and in consequence jumps of finite speed are performed we study the effect of finite jump speed of the particles on the speed of the traveling fronts and find that in the parabolic and hyperbolic limits it can exceed the jump speed of the particles we report analytical expressions for different probability distribution functions finally we introduce the possibility that several particle speeds are allowed so different dispersal mechanisms can be considered simultaneously

nonparametric analysis of changes in hazard rates for censored survival data an alternative to change point models summary as a nonparametric estimator for the point of the most rapid change of a hazard rate we propose the location of an extremum of a nonparametric estimate of the derivative or equivalently of a zero of a nonparametric estimate of the second derivative using the kernel method for the nonparametric estimation of derivatives of the hazard rate the asymptotic local limiting distribution and uniform consistency are applied to prove consistency and to find the limiting distribution of these estimators under random censoring and to construct confidence intervals both for the derivatives of the hazard rate and for the point of most rapid change an application to leukaemia data illustrates this concept and we discuss its relations to change point modelling the monte carlo method is used to assess the reliability of finite sample analyses and in particular of the given example

the restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics fractional dynamics has experienced a firm upswing during the past few years having been forged into a mature framework in the theory of stochastic processes a large number of research papers developing fractional dynamics further or applying it to various systems have appeared since our first review article on the fractional fokker planck equation metzler r and klafter j 2000a phys rep 339 1 77 it therefore appears timely to put these new works in a cohesive perspective in this review we cover both the theoretical modelling of sub and superdiffusive processes placing emphasis on superdiffusion and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function we also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems

an exactly solvable model of subdiffusion reaction front propagation the propagation of a reaction front is considered in the framework of the seki lindenberg reaction subdiffusion model which is appropriate in the case of a diffusion limited reaction typically this kind of problem is solved using approximate approaches or numerical methods we apply a model piecewise linear reaction function which allows for exact analytical solutions for a front between two stable homogeneous states a unique value of the front velocity is found in the case of fronts between a stable and an unstable state a family of traveling wave solutions is revealed the conditions for the existence of a special pushed front are considered the influence of advection on the front velocity is also analyzed

change points in nonparametric regression analysis an otherwise smooth regression model are proposed the assumptions needed are much weaker than those made in parametric models the proposed estimators apply as well to the detection of discontinuities in derivatives and therefore to the detection of change points of slope and of higher order curvature the proposed estimators are based on a comparison of left and right one sided kernel smoothers weak convergence of a stochastic process in local differences to a gaussian process is established for properly scaled versions of estimators of the location of a change point the continuous mapping theorem can then be invoked to obtain asymptotic distributions and corresponding rates of convergence for change point estimators these rates are typically faster than n 1 2 rates of global lp convergence of curve estimates with appropriate kernel modifications adapting to estimated change points are derived as a consequence it is shown that these rates of convergence are the same as if the location of the change point was known the methods are illustrated by means of the well known data on the annual flow volume of the nile river between 1871 and 1970 1 introduction nonparametric regression methods are usually applied in order to obtain a smooth fit of a regression curve without having to specify a parametric class of regression functions sometimes a generally smooth curve might contain an isolated discontinuity or change point in the curve or in a possibly higher order derivative and in many cases interest focuses on the occurrence of such change points in parametric approaches to the regression change point problem simple linear regressions before and after a possible change point are assumed and then the possibility of a discontinuity in the form of a jump or of a jump in the first derivative or equivalently a slope change is incorporated into the model see for instance hinkley 1969 and brown durbin and evans 1975 the analysis of change points which describe sudden localized changes typically occurring in economics medicine and the physical sciences has recently found increasing interest general smoothness assumptions allowing for a large class of regression functions to be considered seem to be more appropriate in a variety of applied problems than parametric modelling an

dynamical features of reaction diffusion fronts in fractals the speed of front propagation in fractals is studied by using i the reduction of the reaction transport equation into a hamilton jacobi equation and ii the local equilibrium approach different equations proposed for describing transport in fractal media together with logistic reaction kinetics are considered finally we analyze the main features of wave fronts resulting from this dynamic process i e why they are accelerated and what is the exact form of this acceleration