two view multibody structure from motion we present an algebraic geometric approach to 3 d motion estimation and segmentation of multiple rigid body motions from noise free point correspondences in two perspective views our approach exploits the algebraic and geometric properties of the so called multibody epipolar constraint and its associated multibody fundamental matrix which are natural generalizations of the epipolar constraint and of the fundamental matrix to multiple motions we derive a rank constraint on a polynomial embedding of the correspondences from which one can estimate the number of independent motions as well as linearly solve for the multibody fundamental matrix we then show how to compute the epipolar lines from the first order derivatives of the multibody epipolar constraint and the epipoles by solving a plane clustering problem using generalized pca gpca given the epipoles and epipolar lines the estimation of individual fundamental matrices becomes a linear problem the clustering of the feature points is then automatically obtained from either the epipoles and epipolar lines or from the individual fundamental matrices although our approach is mostly designed for noise free correspondences we also test its performance on synthetic and real data with moderate levels of noise

a class of k sample tests for comparing the cumulative incidence of a competing risk in this paper for right censored competing risks data a class of tests developed for comparing the cumulative incidence of a particular type of failure among different groups the tests are based on comparing weighted averages of the hazards of the subdistribution for the failure type of interest asymptotic results are derived by expressing the statistics in terms of counting processes and using martingale central limit theory it is proposed that weight functions very similar to those for the g p tests from ordinary survival analysis be used simulation results indicate that the asymptotic distributions provide adequate approximations in moderate sized samples

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

generalized langevin equation with a three parameter mittag leffler noise abstract the relaxation functions for a given generalized langevin equation in the presence of a three parameter mittag leffler noise are studied analytically the results are represented by three parameter mittag leffler functions exact results for the velocity and displacement correlation functions of a diffusing particle are obtained by using the laplace transform method the asymptotic behavior of the particle in the short and long time limits are found by using the tauberian theorems it is shown that for large times the particle motion is subdiffusive for 1 and superdiffusive for many previously obtained results are recovered due to the many parameters contained in the noise term the model considered in this work may be used to improve the description of data and to model anomalous diffusive processes in complex media

unified continuum description for sub diffusion random walks on multi dimensional comb model abstract the anisotropic sub diffusion random walks on multi dimensional comb structure model have been studied in the continuum approximation the problem is that in the considered model mean square displacements on different directions have different power temporal dependencies so this case essentially differs from usual anisotropic diffusion case and it is not obviously how to describe such a diffusion by a unified way nevertheless the unified continuum description for such random walks has been developed as result the new generalization of fick s law for diffusion current has been obtained for anisotropic anomalous sub diffusion random walks in multi dimensional case namely it has been shown that the effective diffusion coefficient in the generalized fick s law has new operator form components of diffusion tensor instead of constant values have the fractional order temporal derivatives

time dependent solutions for a fractional schrodinger equation with delta potentials we investigate for an arbitrary initial condition the time dependent solutions for a fractional schrodinger equation in the presence of delta potentials by using the green function approach the solutions obtained show an anomalous spreading asymptotically characterized by a power law behavior which is governed by the order of the fractional spatial operator present in the schrodinger equation

relative affine structure canonical model for 3d from 2d geometry and applications we propose an affine framework for perspective views captured by a single extremely simple equation based on a viewer centered invariant we call relative affine structure via a number of corollaries of our main results we show that our framework unifies previous work including euclidean projective and affine in a natural and simple way and introduces new extremely simple algorithms for the tasks of reconstruction from multiple views recognition by alignment and certain image coding applications

dependent competing risks and summary survival curves summary in many contexts where there is interest in inferring the marginal distribution of a survival time t subject to censoring embodied in a latent waiting time c the times t and c may not be independent this paper presents a new class of nonparametric assumptions on the conditional distribution of t given c and shows how they lead to consistent generalizations of the kaplan meier 1958 survival curve estimator the new survival curve estimators are used under weak assumptions to construct bounds on the marginal survival which can be much narrower than those of peterson 1976 in stratified populations where t and c are independent only within strata examples indicate that the kaplan meier estimator is often approximately consistent

bounds on net survival probabilities for dependent competing risks bounds on the marginal survival function based on data from a competing risks experiment are obtained these bounds require an investigator to specify a range of possible concordances for the times to occurrences of the competing risks these bounds are tighter than those of peterson 1976 proceedings of the national academy of sciences 73 11 13

independent motion detection in 3d scenes this paper presents an algorithmic approach to the problem of detecting independently moving objects in 3d scenes that are viewed under camera motion there are two fundamental constraints that can be exploited for the problem 1 two multiview camera motion constraint for instance the epipolar trilinear constraint and 2 shape constancy constraint previous approaches to the problem either use only partial constraints or rely on dense correspondences or flow we employ both the fundamental constraints in an algorithm that does not demand a priori availability of correspondences or flow our approach uses the plane plus parallax decomposition to enforce the two constraints it is also demonstrated that for a class of scenes called sparse 3d scenes in which genuine parallax and independent motions may be confounded how the plane plus parallax decomposition allows progressive introduction and verification of the fundamental constraints results of the algorithm on some difficult sparse 3d scenes are promising

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

detecting motion regions in the presence of a strong parallax from a moving camera by multiview geometric constraints we present a method for detecting motion regions in video sequences observed by a moving camera in the presence of a strong parallax due to static 3d structures the proposed method classifies each image pixel into planar background parallax or motion regions by sequentially applying 2d planar homographies the epipolar constraint and a novel geometric constraint called the structure consistency constraint the structure consistency constraint being the main contribution of this paper is derived from the relative camera poses in three consecutive frames and is implemented within the plane parallax framework unlike previous planar parallax constraints proposed in the literature the structure consistency constraint does not require the reference plane to be constant across multiple views it directly measures the inconsistency between the projective structures from the same point under camera motion and reference plane change the structure consistency constraint is capable of detecting moving objects followed by a moving camera in the same direction a so called degenerate configuration where the epipolar constraint fails we demonstrate the effectiveness and robustness of our method with experimental results of real world video sequences

estimates of marginal survival for dependent competing risks based on an assumed copula summary when time to death and time to censoring are associated one may be appreciably misled when the marginal survival functions are estimated using the product limit estimators which assume independent censoring if no assumption about the relationship between the two times is made the marginal survival functions are not identifiable a natural function that defines the association between the two random variables is the copula we show that if this function is known then the competing risks data are sufficient to identify the marginal survival functions and construct a suitable estimator this estimator is consistent and reduces to the kaplan meier estimator when death and censoring times are independent this statistic can be used to provide bounds on the marginal survival functions based on a range of possible associations between the competing risks

the fundamental matrix theory algorithms and stability analysis in this paper we analyze in some detail the geometry of a pair of cameras i e a stereo rig contrarily to what has been done in the past and is still done currently for example in stereo or motion analysis we do not assume that the intrinsic parameters of the cameras are known coordinates of the principal points pixels aspect ratio and focal lengths this is important for two reasons first it is more realistic in applications where these parameters may vary according to the task active vision second the general case considered here captures all the relevant information that is necessary for establishing correspondences between two pairs of images this information is fundamentally projective and is hidden in a confusing manner in the commonlyused formalism of the essential matrix introduced by longuet higgins 1981 this paper clarifies the projective nature of the correspondence problem in stereo and shows that the epipolar geometry can be summarized in one 3 x 3 matrix of rank 2 which we propose to call the fundamental matrix after this theoretical analysis we embark on the task of estimating the fundamental matrix from point corre spondences a task which is of practical importance we analyze theoretically and compare experimentally using synthetic and real data several methods of estimation the problem of the stability of the estimation is studied from two complementary viewpoints first we show that there is an interesting relationship between the fundamental matrix and three dimensional planes which induce homographies between the images and create unstabilities in the estimation procedures second we point to a deep relation between the unstability of the estimation procedure and the presence in the scene of so called critical surfaces which have been studied in the context of motion analysis finally we conclude by stressing the fact that we believe that the fundamental matrix will play a crucial role in future applications of three dimensional computer vision by greatly increasing its versatility robustness and hence applicability to real difficult problems

generalized fractional diffusion equations for accelerating subdiffusion and truncated levy flights fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time for processes lacking such scaling the corresponding description may be given by diffusion equations with fractional derivatives of distributed order such equations were introduced in a v chechkin r gorenflo and i sokolov phys rev e 66 046129 2002 for the description of the processes getting more anomalous in the course of time decelerating subdiffusion and accelerating superdiffusion here we discuss the properties of diffusion equations with fractional derivatives of the distributed order for the description of anomalous relaxation and diffusion phenomena getting less anomalous in the course of time which we call respectively accelerating subdiffusion and decelerating superdiffusion for the former process by taking a relatively simple particular example with two fixed anomalous diffusion exponents we show that the proposed equation effectively describes the subdiffusion phenomenon with diffusion exponent varying in time for the latter process we demonstrate by a particular example how the power law truncated levy stable distribution evolves in time to the distribution with power law asymptotics and gaussian shape in the central part the special case of two different orders is characteristic for the general situation in which the extreme orders dominate the asymptotics

generalized time dependent schrodinger equation in two dimensions under constraints we investigate a generalized two dimensional time dependent schrodinger equation on a comb with a memory kernel a dirac delta term is introduced in the schrodinger equation so that the quantum motion along the x direction is constrained at y 0 the wave function is analyzed by using green s function approach for several forms of the memory kernel which are of particular interest closed form solutions for the cases of dirac delta and power law memory kernels in terms of fox h function as well as for a distributed order memory kernel are obtained further a nonlocal term is also introduced and investigated analytically it is shown that the solution for such a case can be represented in terms of infinite series in fox h functions green s functions for each of the considered cases are analyzed and plotted for the most representative ones anomalous diffusion signatures are evident from the presence of the power law tails the normalized green s functions obtained in this work are of broader interest

fractional schrodinger equation some properties of the fractional schrodinger equation are studied we prove the hermiticity of the fractional hamilton operator and establish the parity conservation law for fractional quantum mechanics as physical applications of the fractional schrodinger equation we find the energy spectra of a hydrogenlike atom fractional bohr atom and of a fractional oscillator in the semiclassical approximation an equation for the fractional probability current density is developed and discussed we also discuss the relationships between the fractional and standard schrodinger equations

applications of crude incidence curves crude incidence curves display the cumulative number of failures of interest as a function of time with competing causes of failure they are distinct from cause specific incidence curves that treat secondary types of failures as censored observations after briefly reviewing their definition and estimation we present five applications of crude incidence curves to show their utility in a broad range of studies in some of these applications it is helpful to model survival time distributions with use of two different time metameters for example time from diagnosis and age of the patient we describe how one can incorporate published vital statistics into the models when secondary types of failure correspond to common causes of death

competing risks with frailty models when treatment affects only one failure type summary using a model in which treatment affects only the failure type of primary clinical interest the use of a cause specific analysis is examined when the latent failure times are derived from a frailty model the relationship between the cause specific hazard ratio and the marginal hazard ratio is expressed in terms of a local dependence measure of the latent failure times frequently in clinical trials the treatment being tested is expected to affect only one of several clinical outcomes for example radiation treatment to a tumour site may affect the local but not distant recurrence rates adjuvant cancer chemotherapy given to an elderly population may affect the probability of dying from cancer but not from other causes competing risks problems arise when occurrence of a secondary outcome makes the subsequent occurrence of the primary outcome unobservable or uninterpretable for reviews of various approaches to the analysis of survival data with competing risks see gail 1975 or prentice et al 1978 one approach postulates latent failure times for each possible outcome the minimum of these latent failure times and an indicator of failure type are observed possible parameters of interest include the marginal survival curve or the crude cumulative incidence curve associated with the latent failure type of primary interest and the survival curve associated with the minimum of latent failure times the choice of parameter should depend on the clinical question korn dorey 1992 since we will assume that the treatment affects only the latent failure times associated with the primary outcome we concentrate on inference for the marginal survival distribution of that latent failure time however as is well known peterson 1976 the marginal survival distribution associated with a latent failure time is not identifiable without further assumptions frequently a cause specific survival curve for the primary failure type is constructed by treating failures of other types as censored observations if the latent failure times are statistically independent then the cause specific survival curve will estimate the marginal survival curve in this paper we examine one implication of performing a cause specific analysis of a treatment when the latent failure times are not independent in particular for two types of failure we will compare the cause specific hazard ratio with the marginal hazard ratio for the primary failure type of interest our underlying model will specify that the treatment affects only the primary latent failure times we allow for non independence of the latent failure times by specifying their bivariate distribution in terms of an archimedean copula genest mackay 1986 these bivariate distri butions subsume the frailty models of clayton 1978 and hougaard 1984 1986 see oakes 1989 a general approach to identifiable marginal survival using a specified copula is given by zheng

determining the epipolar geometry and its uncertainty a review two images of a single scene object are related by the epipolar geometry which can be described by a 3 3 singular matrix called the essential matrix if images internal parameters are known or the fundamental matrix otherwise it captures all geometric information contained in two images and its determination is very important in many applications such as scene modeling and vehicle navigation this paper gives an introduction to the epipolar geometry and provides a complete review of the current techniques for estimating the fundamental matrix and its uncertainty a well founded measure is proposed to compare these techniques projective reconstruction is also reviewed the software which we have developed for this review is available on the internet

fractional diffusion on a fractal grid comb a grid comb model is a generalization of the well known comb model and it consists of n backbones for n 1 the system reduces to the comb model where subdiffusion takes place with the transport exponent 1 2 we present an exact analytical evaluation of the transport exponent of anomalous diffusion for finite and infinite number of backbones we show that for an arbitrarily large but finite number of backbones the transport exponent does not change contrary to that for an infinite number of backbones the transport exponent depends on the fractal dimension of the backbone structure