occupation times of a ctrw on a lattice with anomalous sites abstract we develop formalism allowing us to derive results for the probability density of the occupation time of a set of sites on a lattice of a ctrw in which the pausing time density on the set can differ from those on the remaining lattice sites the problem is suggested by transillumination techniques used in optical imaging details are given for the case of a single site on the lattice and an anomalous pausing time density it is shown that if the random walk is transient i e in three or more dimensions when the variance of a single jump is finite the asymptotic density for the occupation time at the special point is a negative exponential in one dimension the random walk is recurrent here it is shown that the occupation time scales as t 1 2 these results extend to finite numbers of anomalous points

generation and monitoring of discrete stable random processes using multiple immigration population models some properties of classical population processes that comprise births deaths and multiple immigrations are investigated the rates at which the immigrants arrive can be tailored to produce a population whose steady state fluctuations are described by a pre selected distribution attention is focused on the class of distributions with a discrete stable law which have power law tails and whose moments and autocorrelation function do not exist the separate problem of monitoring and characterizing the fluctuations is studied analysing the statistics of individuals that leave the population the fluctuations in the size of the population are transferred to the times between emigrants that form an intermittent time series of events the emigrants are counted with a detector of finite dynamic range and response time this is modelled through clipping the time series or saturating it at an arbitrary but finite level whereupon its moments and correlation properties become finite distributions for the time to the first counted event and for the time between events exhibit power law regimes that are characteristic of the fluctuations in population size the processes provide analytical models with which properties of complex discrete random phenomena can be explored and in addition provide generic means by which random time series encompassing a wide range of intermittent and other discrete random behaviour may be generated

level crossing rate and average fade duration of egc systems with cochannel interference in rayleigh fading both the first order signal statistics e g the outage probability and the second order signal statistics e g the average level crossing rate lcr and the average fade duration afd are important design criteria and performance measures for wireless communication systems including the equal gain combining egc systems in the presence of the cochannel interference cci although the analytical expressions for the outage probability of the coherent egc systems are exposed to cci and various fading channels are already known the respective expressions for the average lcr and the afd are not available in the literature this paper presents such analytical expressions for the rayleigh fading channel which are obtained by utilizing a novel analytical approach that does not require the explicit expression for the joint probability density function pdf of the instantaneous output signal to interference ratio and its time derivative applying the characteristic function method and the beaulieu series we determined the average lcr and the afd at the output of an interference limited egc system with an arbitrary diversity order and an arbitrary number of cochannel interferers in the form of an infinite integral and infinite series for the dual diversity case the respective expressions are derived in closed forms in terms of the gamma and beta functions

residence time distribution for a class of gaussian markov processes we study the distribution of residence time or equivalently that of mean magnetization for a family of gaussian markov processes indexed by a positive parameter alpha the persistence exponent for these processes is simply given by theta alpha but the residence time distribution is nontrivial the shape of this distribution undergoes a qualitative change as theta increases indicating a sharp change in the ergodic properties of the process we develop two alternate methods to calculate exactly but recursively the moments of the distribution for arbitrary alpha for some special values of alpha we obtain closed form expressions of the distribution function s1063 651x 99 03306 1

numerical solution to a sideways parabolic equation the inverse heat conduction problem can be considered to be a sideways parabolic equation in the quarter plane this is a model of a problem where one wants to determine the temperature on both sides of a thick wall but one side is inaccessible to measurements a numerical procedure for this severely ill posed problem is suggested which consists of two steps namely a mollification of the data and a marching difference scheme the numerical method is proved to be stable several computational results are presented and discussed copyright 2001 john wiley sons ltd

screw pitch precision measurement using simple linear regression and image analysis in this paper a novel and simple method of calculating the screw pitch from a screw image is proposed we combine following three techniques to synthesize the system a calibrating the camera parameters based on the principles of simple linear regression and geometry optics b hiring image processing techniques to extract the screw object from an image c using hotelling transform to rotate the principle axes of the extracted screw object image to coincide with the coordinate axes to explore the utility and demonstrate the efficiency of the proposed scheme simulations under various conditions are conducted the experiment results show that our proposed scheme can exactly measure the pitches of screws with an error of less than 0 1 m this precision is enough and suitable exactly in screw applications

power law relaxation in a complex system omori law after a financial market crash we study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value we show that the empirical observation of a power law evolution of the number of events exceeding the selected threshold a behavior known as the omori law in geophysics is consistent with the simultaneous occurrence of i a return probability density function characterized by a power law asymptotic behavior and ii a power law relaxation decay of its typical scale our empirical observation cannot be explained within the framework of simple and widespread stochastic volatility models

persistence of a continuous stochastic process with discrete time sampling non markov processes we consider the problem of discrete time persistence which deals with the zero crossings of a continuous stochastic process x t measured at discrete times t ndeltat for a gaussian stationary process the persistence no crossing probability decays as exp theta d t rho a n for large n where a exp deltat 2 and the discrete persistence exponent theta d is given by theta d ln rho 2 ln a using the independent interval approximation we show how theta d varies with deltat for small deltat and conclude that experimental measurements of persistence for smooth processes such as diffusion are less sensitive to the effects of discrete sampling than measurements of a randomly accelerated particle or random walker we extend the matrix method developed by us previously phys rev e 64 015101 r 2001 to determine rho a for a two dimensional random walk and the one dimensional random acceleration problem we also consider alternating persistence which corresponds to a 0 and calculate rho a for this case

large deviations and nontrivial exponents in coarsening systems we investigate the statistics of the mean magnetization of its large deviations and persistent large deviations in simple coarsening systems in particular we consider more specifically the case of the diffusion equation of the ising chain at zero temperature and of the two dimensional voter model for the diffusion equation at large times the mean magnetization has a limit law which is studied analytically using the independent interval approximation the probability of persistent large deviations defined as the probability that the mean magnetization was for all previous times greater than some level x decays algebraically at large times with an exponent continuously varying with x when x 1 is the usual persistence exponent similar behaviour is found for the glauber ising chain at zero temperature for the two dimensional voter model large deviations of the mean magnetization are algebraic while the probability of persistent large deviations seem to behave as the usual persistence probability

stability results for the heat equation backward in time abstract for the heat equation backward in time u t u x x x r t 0 t u t l p r subject to the constraint u 0 l p r e with t 0 l p r 0 e 1 p being given we prove that if u 1 and u 2 are two solutions of the problem then there is a constant c 0 such that u 1 t u 2 t l p r c t t e 1 t t t 0 t in case p 2 we establish stability estimates of holder type for all derivatives with respect to x and t of the solutions we suggest a useful strategy of choosing mollification parameters which provides a continuity at t 0 when an additional condition on the smoothness of u x 0 is given furthermore we propose a stable marching difference scheme for this ill posed problem and test several related numerical methods for it

determining surface temperatures from interior observations we consider the inverse heat transfer problem for the case of the one dimensional heat equation in a quarter plane and present a new solution algorithm together with error bounds of logarithmic convexity type our method is based on regularizing the initial value problem for the heat equation run sideways we describe a numerical experiment with rapidly varying temperature profiles and explain how the method can be extended to problems with temperature dependent thermal properties

a variety associated to an algebra with involution abstract a variety iv a is canonically associated to a central simple algebra a with orthogonal involution of the first kind the properties of this variety are the main topic of this paper the paper is divided into two parts we first define this variety to be the subvariety of the grassmannian of the n dimensional subspaces of the n2 dimensional vector space a consisting of all the n dimensional right ideals i of a such that i i 0 the geometric properties of iv a are investigated in particular the generic property of this variety is identified further the kernel of the scalar extension map br f br k where k is the function field of iv a is also computed lastly a criterion on the embeddability of the field k into the function field of the brauer severi variety of a is given in the second part the quillen k theory of iv a is computed the k theory result then leads to an index reduction formula for the function field k

l infty error bounds in partial deconvolution of the inverse gaussian pulse when a c infty approximation to the dirac 5 function in the form of an inverse gaussian pulse is used as input into a linear time invariant system the output waveform is an approximation to that system s green s function in which the singularities have been smoothed out the ill posed deconvolution problem for the output signal aims at reconstructing these singularities by exploiting the smoothing properties of the inverse gaussian kernel we prove that partial deconvolution of the output waveform given l 2 a priori bounds on the data noise and the unknown green s function results in l infty error bounds for the regularized solution and its derivatives consequently when the l 2 norm of the output noise is sufficiently small partial deconvolution is a pointwise reliable c infty function which in turn approximates the desired green s function in many applications

analytical level crossing rates and average fade durations for diversity techniques in nakagami fading channels the level crossing rates lcrs and average fade durations afds of a fading channel find diverse applications in the evaluation and design of wireless communication systems analytical expressions for these quantities are available in the literature for certain diversity reception techniques but are generally limited to the rayleigh fading channel with few exceptions moreover the methods employed are usually specific to a certain channel diversity pair and thus cannot be applied to all cases of interest using a unified methodology we derive analytical expressions for the lcrs and afds for three diversity reception techniques and a general nakagami 1960 fading channel we provide novel analytical expressions for selection combining sc and equal gain combining egc and rederive in a more general manner the case of maximal ratio combining mrc it is shown that our general results reduce to some specific cases previously published these results are used to examine the effects of the diversity technique the number of receiving branches and severity of the fading on the concerned quantities it is observed that as the nakagami m parameter and the diversity order increase the behavior of the combined received envelope for egc follows closely the one for mrc and distances itself from sc

the group of k1 zero cycles on the second generalized severi brauer variety of an algebra of index 4 abstract in this manuscript it is shown that the group of k 1 zero cycles on the second generalized severi brauer variety of an algebra a of index 4 is given by elements of the group k 1 a together with a square root of their reduced norm utilizing results of krashen concerning exceptional isomorphisms we translate our problem to the computation of cycles on involution varieties work of chernousov and merkurjev then gives a means of describing such cycles in terms of clifford and spin groups and corresponding r equivalence classes we complete our computation by giving an explicit description of these algebraic groups

contour based corner detection via angle difference of principal directions of anisotropic gaussian directional derivatives this paper presents a contour based corner detector using the angle difference of the principal directions of anisotropic gaussian directional derivatives andds on contours the noise robust andds can characterize fine directional intensity variations around edge pixels and corners the proposed corner detector consists of three steps extraction of edge map by the canny edge detector improvement of contours by the douglas peucker d p polygonal approximation and filling small gaps between contours and finding corners from contours by using the angle difference of the principal directions of the andds as the corner measure different from the existing contour based detectors where corner measures correspond to the geometric properties of a contour the new corner measure utilizes the directional intensity variations at the pixels on a contour and thus has high angular resolution good localization and noise robustness the proposed detector is compared with the three state of the art detectors from two aspects two test images with ground truths are used to assess its detection capability and localization accuracy twenty four test images with various scenes and without ground truths are used to evaluate its repeatability under affine transforms jpeg compression and noise degradation the experimental results show that the proposed detector attains better overall performance anisotropic directional derivatives are applied to corner detection of images a corner detector using the principal direction of the anisotropic directional derivatives is presented the detector is compared with the three state of the art corner detector the detector behaves better in detection localization repeatability and noise robustness

diffusive persistence and the sign time distribution we present a new method for extracting the persistence exponent theta for the diffusion equation based on the distribution p of sign times with the aid of a numerically verified ansatz for p we derive an exact formula for theta in arbitrary spatial dimension d our results are in excellent agreement with previous numerical studies furthermore our results indicate a qualitative change in p above d 36 signalling the existence of a sharp change in the ergodic properties of the diffusion field

statistics of the occupation time for a class of gaussian markov processes we revisit the work of dhar and majumdar 1999 phys rev e 59 6413 on the limiting distribution of the temporal mean mt t 1 0tdu sign yu for a gaussian markovian process yt depending on a parameter which can be interpreted as brownian motion in the time scale t t2 this quantity the mean magnetization is simply related to the occupation time of the process that is the length of time spent on one side of the origin up to time t using the fact that the intervals between sign changes of the process form a renewal process on the time scale t we determine recursively the moments of the mean magnetization we also find an integral equation for the distribution of mt this allows a local analysis of this distribution in the persistence region mt 1 as well as its asymptotic analysis in the regime where is large finally we put the results thus found in perspective with those obtained by dhar and majumdar by another method based on a formalism due to kac

infinitely divisible pulses continuous deconvolution and the characterization of linear time invariant systems this paper addresses the problem of determining the impulse response of a linear time invariant system by probing the system with a causal c infty approximation to the dirac delta function we analyze the ill posed deconvolution problem which results from a wide choice of possibly multimodal infinitely divisible probe pulses the notion of infinite divisibility is shown to play a key role when the system s response is suspected of having nondifferentiable singularities we reformulate the volterra integral equation as a cauchy problem for a linear partial differential equation in two independent variables and introduce the concepts of partial and continuous deconvolution we then show that partial deconvolution of the output waveform results in l infty error bounds for the regularized solution and its derivatives under l 2 a priori bounds on the data noise and the unknown system response using the poisson summation formula and fft algorithms we construct an efficient computational alg

phase distribution and phase correlation of financial time series the scaling phase distribution and phase correlation of financial time series are investigated based on the dow jones industry average and nasdaq 10 min intraday data for a period from 1 aug 1997 to 31 dec 2003 the returns of the two indices are shown to have nice scaling behaviors and belong to stable distributions according to the criterion of l evy s ensuremath alpha stable distribution condition an approach catching characteristic features of financial time series based on the concept of instantaneous phase is further proposed to study the phase distribution and correlation analysis of the phase distribution concludes that return time series fall into a class which is different from other nonstationary time series the correlation between returns of the two indices probed by the distribution of phase difference indicates that there was a remarkable change of trading activities after the event of the 9 11 attack and this change persisted in later trading activities

persistence exponents for fluctuating interfaces numerical and analytic results for the exponent ensuremath theta describing the decay of the first return probability of an interface to its initial height are obtained for a large class of linear langevin equations the models are parametrized by the dynamic roughness exponent ensuremath beta with 0l ensuremath beta l1 for ensuremath beta frac 1 2 the time evolution is markovian using simulations of solid on solid models of the discretized continuum equations as well as of the associated zero dimensional stationary gaussian process we address two problems the return of an initially flat interface and the return to an initial state with fully developed steady state roughness the two problems are shown to be governed by different exponents for the steady state case we point out the equivalence to fractional brownian motion which has a return exponent ensuremath theta s 1 ensuremath ensuremath beta the exponent ensuremath theta 0 for the flat initial condition appears to be nontrivial we prove that ensuremath theta 0 ensuremath rightarrow ensuremath infty for ensuremath beta ensuremath rightarrow 0 ensuremath theta 0 g ensuremath theta s for ensuremath beta l frac 1 2 and ensuremath theta 0 l ensuremath theta s for ensuremath beta g frac 1 2 and calculate ensuremath theta 0 s perturbatively to first order in an expansion around the markovian case ensuremath beta frac 1 2 using the exact result ensuremath theta s 1 ensuremath ensuremath beta accurate upper and lower bounds on ensuremath theta 0 can be derived which show in particular that ensuremath theta 0 g 1 ensuremath ensuremath beta 2 ensuremath beta for small ensuremath beta

zero crossing rates of functions of gaussian processes formulas for the expected zero crossing rates of random processes that are monotone transformations of gaussian processes can be obtained by using two different techniques the first technique involves derivation of the expected zero crossing rate for discrete time processes and extends the result of the continuous time case by using an appropriate limiting argument the second is a direct method that makes successive use of r price s 1958 theorem the chain rule for derivatives and s o rice s 1954 formula for the expected zero crossing rate of a gaussian process a constant which depends on the variance of the transformed process and a second moment of its derivative is derived multiplying rice s original expression by this constant yields the zero crossing formula for the transformed process the two methods can be used for the general level crossing problem of random processes that are monotone functions of a gaussian process

spectral zero crossings localization properties and applications we present an analysis of the rate of sign changes in the discrete fourier spectrum of a sequence the sign changes of either the real or imaginary parts of the spectrum are considered and the rate of sign changes is termed as the spectral zero crossing rate szcr we show that szcr carries information pertaining to the locations of transients within the temporal observation window we show duality with temporal zero crossing rate analysis by expressing the spectrum of a signal as a sum of sinusoids with random phases this extension leads to spectral domain iterative filtering approaches to stabilize the spectral zero crossing rate and to improve upon the location estimates the localization properties are compared with group delay based localization metrics in a stylized signal setting well known in speech processing literature we show applications to epoch estimation in voiced speech signals using the szcr on the integrated linear prediction residue the performance of the szcr based epoch localization technique is competitive with the state of the art epoch estimation techniques that are based on average pitch period

new exact closed form pdf of the sum of nakagami m random variables with applications an exact closed form expression is developed for the probability density function pdf of the sum of independent but not necessarily identically distributed nakagami m random variables by utilizing the newly developed pdf and the associated developments new exact expressions of the bit error probability are presented for predetection equal gain combining diversity

analytical results for generalized persistence properties of smooth processes we present a general scheme to calculate within the independent interval approximation generalized level dependent persistence properties for processes having a finite density of zero crossings our results are especially relevant for the diffusion equation evolving from random initial conditions one of the simplest coarsening systems exact results are obtained in certain limits and rely on a new method to deal with constrained multiplicative processes an excellent agreement of our analytical predictions with direct numerical simulations of the diffusion equation is found

linear diversity combining on nakagami 0 5 fading channels the nakagami 0 5 distribution is an important special case of the nakagami distribution as it represents a worst case fading scenario this scenario is of particular significance for wireless applications with high quality of service requirements the bit error probability bep performances of three basic diversity combining schemes in nakagami 0 5 fading are considered it is shown that the error rate performances of dual branch equal gain and selection combining sc diversity are identical regardless of modulation format it is also shown that l branch maximal ratio combining diversity in nakagami 0 5 fading has the same bep performance as single branch reception in nakagami l 2 fading with l times the transmission power of each branch a useful upper bound for the bep of l branch sc diversity in nakagami 0 5 fading is also derived the performance degradation for the worst case nakagami 0 5 fading relative to rayleigh fading can be as much as 24 6 db for a dual diversity receiver at target bep of 10 6 the additional resources required to restore a specified performance level as increased channel signal to noise ratio and as number of additional diversity branches are quantified it is concluded that worst case nakagami channels can result in dramatically poorer performance than rayleigh channels making proper system design and evaluation essential to achieve a required transmission quality

dynamics of absorption of a randomly accelerated particle consider a randomly accelerated particle moving on the half line x 0 with a boundary condition at x 0 that respects the scale invariance of the equations of motion under x 3x v v t 2t if the boundary condition leads to absorption of the particle at x 0 and if the probability q x v t that the particle has not yet been absorbed at time t decays for long times as a power law with exponent then the power law must have the specific form q x v t cx2 3u 2 3 2 3 v3 9x t this is a consequence of scale invariance and the fokker planck equation here c is a constant and u a b z is a confluent hypergeometric function the persistence exponents for several boundary conditions of physical interest follow directly from this result

from doubly stochastic representations of k distributions to random walks and back again an optics tale a random walk model with a negative binomially fluctuating number of steps is considered in the case where the mean of the number fluctuations is finite the asymptotic behaviour of the resultant statistics in the large limit is derived and shown to give the k distribution the equivalence of this model to the hitherto unrelated doubly stochastic representation of the k distribution is also demonstrated the convergence to the k distribution of the probability density function generated by a random walk with a finite mean number of steps is examined along with the moments and the non gaussian statistics are shown to be a direct result of discreteness and bunching effects

average level crossing rate and average outage duration of generalized selection combining the paper presents an analytical methodology for the evaluation of the average level crossing rate and the average outage duration of generalized selection combining more specifically it presents a general approach when this scheme is employed over independent but not necessarily identically distributed fading channels the general approach is then specialized to independent identically distributed rayleigh fading paths selected numerical examples and plots are also provided and discussed

nodal domains statistics a criterion for quantum chaos we consider the distribution of the properly normalized numbers of nodal domains of wave functions in 2d quantum billiards we show that these distributions distinguish clearly between systems with integrable separable or chaotic underlying classical dynamics and for each case the limiting distribution is universal system independent thus a new criterion for quantum chaos is provided by the statistics of the wave functions which complements the well established criterion based on spectral statistics

sign time distributions for interface growth we apply the recently introduced distribution of sign times dst to nonequilibrium interface growth dynamics we are able to treat within a unified picture the persistence properties of a large class of relaxational and noisy linear growth processes and prove the existence of a nontrivial scaling relation a critical dimension is found relating to the persistence properties of these systems we also illustrate by means of numerical simulations the different types of dst to be expected in both linear and nonlinear growth mechanisms

on the distribution of the sum of nakagami m random variables in this paper we investigate the classical problem of finding the probability density function pdf of the sum of nakagami m random variables exact infinite series representations are derived for the sum of three and four identically and independently distributed i i d nakagami m random variables and subsequently it is extended to the sum of general number of random variables a useful pattern emerged as a result of these extensions and a new fourier transform pair that involves parabolic cylinder function and gauss hypergeometric function is obtained bounds on the error resulting from truncation of the infinite series of pdfs are also presented these pdfs are used to analyze the performance of dual triple and quadruple branch predetection equal gain combining egc receivers over nakagami m fading environment furthermore a hypergeometric relation is derived as a result of those derivations subsequently the analysis is extended to the case of l branch egc receiver performance as well selected simulation plots are provided to compare the results with the approximate results available in the literature and to illustrate the validity of the formulation

lacunarity of the zero crossings of gaussian processes a lacunarity analysis of the zero crossings derived from gaussian stochastic processes with oscillatory autocorrelation functions is evaluated and reveals distinct multiscaling signatures depending on the smoothness and degree of anticorrelation of the process these bear qualitative similarities and quantitative distinctions from an oscillatory deterministic signal and a poisson random process both possessing the same mean interval size between crossings at very small and large scales compared with the correlation length of the random processes the lacunarity is similar to the poisson but exhibits significant departures from poisson behavior if there is a zero frequency component to the process s power spectrum a comparison of exact results with the gliding box technique that is frequently used to determine lacunarity demonstrates its inherent bias

persistence of a continuous stochastic process with discrete time sampling we introduce the concept of discrete time persistence which deals with zero crossings of a continuous stochastic process x t measured at discrete times t n delta t for a gaussian markov process with relaxation rate mu we show that the persistence no crossing probability decays as rho a n for large n where a exp mu delta t and we compute rho a to high precision we also define the concept of alternating persistence which corresponds to a 1 corresponding to motion in an unstable potential mu 0 there is a nonzero probability of having no zero crossings in infinite time and we show how to calculate it

generalized pollaczek khinchin formula for markov channels the wireless fading channels with finite input buffer poisson arrivals and two state markov modulated service processes mmsp are modeled as m mmsp 1 k queues in this paper the existing performance analyses of markov channels are almost all based on the matrix geometric method which provides little physical insights for system design by contrast we focus on deriving closed form analytic expressions with physical interpretations in terms of system parameters of interest our main contribution is to derive the generalized pollaczek khinchin p k formula of m mmsp 1 k queue from start service probability to explore the impact of state transitions on the queueing behavior of markov channels this generalized p k formula reveals that the performance of wireless channels with varying rates can be fully characterized by a newly defined system parameter called state transition factor which clearly explains the reason that the channel with slow state transition rate owns a larger delay for the same channel capacity in the extreme case when the state transition factor approaches 0 we show that the channel under consideration can be approximately modeled as an m g 1 queue we use the type i hybrid arq system with a fixed data rate as an example in this paper to illustrate our results

statistics of return intervals in long term correlated records we consider long term correlated data with several distribution densities gaussian exponential power law and log normal and various correlation exponents ensuremath gamma 0l ensuremath gamma l1 and study the statistics of the return intervals r j between events above some threshold q we show that irrespective of the distribution the return intervals are long term correlated in the same way as the original record but with additional uncorrelated noise due to this noise the correlations are difficult to observe by the detrended fluctuation analysis which exhibits a crossover behavior but show up very clearly in the autocorrelation function the distribution p q r of the return intervals is characterized at large scales by a stretched exponential with exponent ensuremath gamma and at short scales by a power law with exponent ensuremath gamma ensuremath 1 we discuss in detail the occurrence of finite size effects for large threshold values for all considered distributions we show that finite size effects are most pronounced in exponentially distributed data sets where they can even mask the stretched exponential behavior in records of up to 10 6 data points finally in order to quantify the clustering of extreme events due to the long term correlations in the return intervals we study the conditional distribution function and the related moments we find that they show pronounced memory effects irrespective of the distribution of the original data

persistence of non markovian gaussian stationary processes in discrete time the persistence of a stochastic variable is the probability that it does not cross a given level during a fixed time interval although persistence is a simple concept to understand it is in gener

zero cycles on homogeneous varieties abstract in this paper we study the group a 0 x of zero dimensional cycles of degree 0 modulo rational equivalence on a projective homogeneous algebraic variety x to do this we translate rational equivalence of 0 cycles on a projective variety into r equivalence on symmetric powers of the variety for certain homogeneous varieties we then relate these symmetric powers to moduli spaces of etale subalgebras of central simple algebras which we construct this allows us to show a 0 x 0 for certain classes of homogeneous varieties for groups of each of the classical types extending previous results of swan karpenko of merkurjev and of panin

characterization of structural reorganization in rice piles diagnostics applied to a rice pile cellular automaton reveal different mechanisms producing power law behaviors of statistical attributes of grains which are germane to self organised critical phenomena the probability distributions for these quantities can be derived from two distinct random walk models that account for correlated clustered behavior through incorporating fluctuations in the number of steps in the walk the first model describes the distribution for a spatial quantity the resultant flight length of grains this has a power law tail caused by grains moving through a discrete power law distributed number of random steps of finite length developing this model into a random walk obtains distributions for the resultant flight length with characteristics similar to l evy distributions the second random walk model is devised to explain a temporal quantity the distribution of trapping or residence times of grains at single locations in the pile diagnostics reveal that the trapping time can be constructed as a sum of subtrapping times which are described by a l evy distribution where the number of terms in the sum is a discrete random variable accurately described by a negative binomial distribution the infinitely divisible two parameter limit distribution for the resultant of such a random walk is discussed and describes a dual scale power law behavior if the number fluctuations are strongly clustered the form for the distribution of transit times of grains results as a corollary

a mollification method for a noncharacteristic cauchy problem for a parabolic equation abstract in this paper the noncharacteristic cauchy problem ncp formula is considered with lp r p 1 it is proved that a solution of ncp exists if and only if is infinitely differentiable and n lp r c 2n s2n n n for certain constantscands ncp is well known to be severely ill posed a small perturbation in the cauchy data may cause a dramatically large error in the solution the following mollification method is suggested for solving ncp in a stable way if lp r is given inexactly by lp r then we mollify by convolutions with the dirichlet kernel and the de la vallee poussin kernel the exact solution of ncp is approximated by the solution of the mollified problem with a reasonable choice of mollification parameters which yields error estimates of the holder type by the method we can work with the data inlp r p 1 and obtain several sharp stability estimates inlp andl norms of the holder type for the solution of the problem the method can easily be implemented numerically using the fast fourier transform a stable marching difference scheme based on this method is suggested several numerical examples are given which show that the method is effective

differentiation by the f transform and application to edge detection in this contribution we consider integrable functions of many in particular two variables and extend for them the technique of f transform to f1 transform we prove that linear coefficients in the representation of the f1 transform component approximate the first partial derivatives we give estimates for this approximation finally we discuss the application to the edge detection problem we propose a new algorithm where the technique of f1 transform is combined with the canny detector a theoretical justification and advantages of the proposed approach are emphasized and illustrative examples are presented

statistics of multiple sign changes in a discrete non markovian sequence we study analytically the statistics of multiple sign changes in a discrete non markovian sequence psi i phi i phi i 1 i 1 2 em leader n where phi i s are independent and identically distributed random variables each drawn from a symmetric and continuous distribution rho phi we show that the probability p m n of m sign changes up to n steps is universal i e independent of the distribution rho phi the mean and variance of the number of sign changes are computed exactly for all n 0 we show that the generating function tilde p p n summation operator infinity m 0 p m n p m approximately exp theta d p n for large n where the discrete partial survival exponent theta d p is given by a nontrivial formula theta d p ln sin 1 square root of 1 p 2 square root of 1 p 2 for 0 infinity n infinity but keeping x m n fixed p m n approximately exp n phi x where the large deviation function phi x is computed the implications of these results for ising spin glasses are discussed

close form solution and parameter selection for convex minimization based edge preserving smoothing this work presents a new approach for the analysis of convex minimization based edge preserving image smoothing and the parameter selection therein the global solution that is the response of a convex smoothing model to the ideal step edge is derived in close form by analyzing the close form solution insights are drawn into how the optimal solution responds to edges in the data and how the parameter values affect resultant edges in the solution based on this a scheme is proposed for selecting parameters to achieve desirable responses at edges the theoretic results are substantiated by experiments

robust ellipse detection with gaussian mixture models the euclidian distance between gaussian mixtures has been shown to be robust to perform point set registration jian and vemuri 2011 we propose to extend this idea for robustly matching a family of shapes ellipses optimisation is performed with an annealing strategy and the search for occurrences is repeated several times to detect multiple instances of the shape of interest we compare experimentally our approach to other state of the art techniques on a benchmark database for ellipses and demonstrate the good performance of our approach highlightswe extend the framework based on l2 to estimate a parametric family of curves we propose a non isotropic and multidimensional modeling for the density functions we propose a method for detecting multiple instances of an ellipse

generalized framework for the level crossing analysis of ordered random processes this paper investigates the following general problem relating to ordered random processes given n independent but not necessarily identical random processes how frequently on average does any given process become one of the pth p 1 2 n 1 largest processes this is a fundamental problem arising in the design and analysis of contemporary multidimensional wireless communication systems e g multiantenna multiuser employing opportunistic selection we formulate this problem as one involving the level crossing rate lcr of a carefully defined ordered random process across the zero threshold which we solve by developing a new mathematical framework based on the theory of permanents for the case where the processes correspond to time varying rayleigh fading channels we present exact closed form formulas for the lcr simplified tight upper bounds as well as asymptotic results for n and p approaching infinity but with fixed ratio these results reveal interesting fundamental limits for the lcr and are shown to given meaningful insight even for small values of n and p we further use our mathematical framework to characterize the required per branch and overall switching rate of a generalized selection combining diversity receiver allowing for different average powers for each branch with the aid of majorization theory we demonstrate that the overall switching rate is maximized when the power delay profile is uniform

return times for stochastic processes with power law scaling an analytical study of the return time distribution of extreme events for stochastic processes with power law correlation has been carried out the calculation is based on an expansion in the correlation exponent c t ensuremath mid t ensuremath mid ensuremath 1 the fixed point of the theory is associated with stretched exponential scaling of the distribution analytical expressions have been provided in the preasymptotic regime also the permanence time distribution appears to be characterized by stretched exponential scaling the conditions for application of the theory to non gaussian processes have been analyzed and the relations with the issue of return times in the case of multifractal measures have been discussed

persistence in a stationary time series we study the persistence in a class of continuous stochastic processes that are stationary only under integer shifts of time we show that under certain conditions the persistence of such a continuous process reduces to the persistence of a corresponding discrete sequence obtained from the measurement of the process only at integer times we then construct a specific sequence for which the persistence can be computed even though the sequence is non markovian we show that this may be considered as a limiting case of persistence in the diffusion process on a hierarchical lattice

a novel edge detection method with application to the fat content prediction in marbled meat intramuscular fat is an important quality criterion notably juiciness in meat grading but traditional visual inspectors are time consuming and destructive however edge detection techniques characterize meat surface in consistence rapid and non destructive approach in this paper novel edge detection method applied on intramuscular fat is presented based on the energy and skewness as two smoothed versions of the image parametric analyses were investigated and the method was tested on several images producing minimum improvements of 6 451 1 667 and 7 826 in signal to noise ratio mean square error and edges localization respectively in comparison to roberts prewitt sobel and canny detectors

motivic decomposition of isotropic projective homogeneous varieties we give a decomposition of the chow motive of an isotropic projective homogeneous variety of a semisimple algebraic group in terms of twisted motives of simpler projective homogeneous varieties as an application we prove a generalization of rost s nilpotence theorem

zero crossing statistics for non markovian time series in applications spanning from image analysis and speech recognition to energy dissipation in turbulence and time to failure of fatigued materials researchers and engineers want to calculate how often a stochastic observable crosses a specific level such as zero at first glance this problem looks simple but it is in fact theoretically very challenging and therefore few exact results exist one exception is the celebrated rice formula that gives the mean number of zero crossings in a fixed time interval of a zero mean gaussian stationary process in this study we use the so called independent interval approximation to go beyond rice s result and derive analytic expressions for all higher order zero crossing cumulants and moments our results agree well with simulations for the non markovian autoregressive model

a mollification method for ill posed problems a mollification method for a class of ill posed problems is suggested the idea of the method is very simple and natural if the data are given inexactly then we try to find a sequence of mollification operators which map the improper data into well posedness classes of the problem mollify the improper data within these mollified data our problem becomes well posed and when these facts are in hand we try to obtain error estimates and optimal or quasi optimal mollification parameters the method is working not only for problems in hilbert spaces but also for problems in banach spaces applications of the method to concrete problems like numerical differentiation parabolic equations backwards in time the cauchy problem for the laplace equation one and multidimensional non characteristic cauchy problems for parabolic equations in infinite or finite domains give us very sharp stability estimates of h older continuous type in these cases the method is optimal in the sense that it gives the same order of h older continuous dependence on the data as for the regularized problems furthermore the method may be implemented numerically using fast fourier transforms for the first time a uniform stability estimate of h older continuous type of the solution of the heat equation backwards in time in the space l p bbb r for all p in 1 infty could be established by our mollification method a new simple sharp pointwise estimate of h older type for the weak solution of a non characteristic cauchy problem for parabolic equations in a finite domain is established

exact occupation time distribution in a non markovian sequence and its relation to spin glass models we compute exactly the distribution of the occupation time in a discrete non markovian toy sequence that appears in various physical contexts such as the diffusion processes and ising spin glass chains the non markovian property makes the results nontrivial even for this toy sequence the distribution is shown to have non gaussian tails characterized by a nontrivial large deviation function that is computed explicitly an exact mapping of this sequence to an ising spin glass chain via a gauge transformation raises an interesting question for a generic finite sized spin glass model at a given temperature what is the distribution over disorder of the thermally averaged number of spins that are aligned to their local fields we show that this distribution remains nontrivial even at infinite temperature and can be computed explicitly in few cases such as in the sherrington kirkpatrick model with gaussian disorder

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

a novel particle swarm optimisation approach to detecting continuous thin and smooth edges in noisy images detection of continuous edges is a hard problem and most edge detection algorithms produce jagged and thick edges particularly in noisy images this paper firstly presents a novel constrained optimisation model for detecting continuous thin and smooth edges in such images then two particle swarm optimisation based algorithms are applied to search for good solutions these two algorithms utilise two different constraint handling methods penalising and preservation the algorithms are examined and compared with a modified version of the canny algorithm as a gaussian filter based edge detector and the robust rank order rro based algorithm as a statistical based edge detector on two sets of images with different types and levels of noise pratt s figure of merit as a measure of localisation accuracy is used for the comparison of these algorithms experimental results show that the proposed edge detectors are more robust under noisy conditions and their performances are better than the canny and rro algorithms for the images corrupted by impulsive and gaussian noise the proposed algorithm based on the penalising method is faster than the algorithm using the preservation method to handle the constraints

power law distributed level crossings define fractal behavior a relationship is established between the autocorrelation function of continuous gaussian and non gaussian stochastic processes and the discrete process that describes their zero or level crossings random fractals occur when the distribution for the number of crossings is described by a class of markov processes whose singlefold statistics are the discrete analog of the levy stable continuous probability densities

on the second order statistics of the multihop rayleigh fading channel second order statistics provides a dynamic representation of a fading channel and plays an important role in the evaluation and design of the wireless communication systems in this paper we present a novel analytical framework for the evaluation of important second order statistical parameters as the level crossing rate lcr and the average fade duration afd of the amplify and forward multihop rayleigh fading channel more specifically motivated by the fact that this channel is a cascaded one and can be modeled as the product of n fading amplitudes we derive novel analytical expressions for the average lcr and the afd of the product of n rayleigh fading envelopes or of the recently so called nrayleigh channel furthermore we derive simple and efficient closed form approximations to the aforementioned parameters using the multivariate laplace approximation theorem it is shown that our general results reduce to the corresponding ones of the specific dual hop case previously published numerical and computer simulation examples verify the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations

persistence exponents and the statistics of crossings and occupation times for gaussian stationary processes we consider the persistence probability the occupation time distribution and the distribution of the number of zero crossings for discrete or equivalently discretely sampled gaussian stationary processes gsps of zero mean we first consider the ornstein uhlenbeck process finding expressions for the mean and variance of the number of crossings and the partial survival probability we then elaborate on the correlator expansion developed in an earlier paper g c m a ehrhardt and a j bray phys rev lett 88 070602 2002 to calculate discretely sampled persistence exponents of gsps of known correlator by means of a series expansion in the correlator we apply this method to the processes d n x dt n ensuremath eta t with ng 3 incorporating an extrapolation of the series to the limit of continuous sampling we then extend the correlator method to calculate the occupation time and crossing number distributions as well as their partial survival distributions and the means and variances of the occupation time and number of crossings we apply these general methods to the d n x dt n ensuremath eta t processes for n 1 random walk n 2 random acceleration and larger n and to simple diffusion from random initial conditions in one to three dimensions the results for discrete sampling are extrapolated to the continuum limit where possible

renewal theory with fat tailed distributed sojourn times typical versus rare renewal processes with heavy tailed power law distributed sojourn times are commonly encountered in physical modeling and so typical fluctuations of observables of interest have been investigated in detail to describe rare events the rate function approach from large deviation theory does not hold and new tools must be considered here we investigate the large deviations of the number of renewals the forward and backward recurrence times the occupation time and the time interval straddling the observation time we show how non normalized densities describe these rare fluctuations and how moments of certain observables are obtained from these limiting laws numerical simulations illustrate our results showing the deviations from arcsine dynkin darling kac l evy and lamperti laws

rationally connected varieties over local fields let x be a proper variety defined over a field k following ma we say that two points x x x k are r equivalent if they can be connected by a chain of rational curves defined over k cf 4 1 in essence two points are r equivalent if they are obviously rationally equivalent several authors have proved finiteness results over local and global fields cubic hypersurfaces ma sd linear algebraic groups ct sa vo1 gi vo2 rational surfaces ct co ct1 ct sk1 quadric bundles and intersections of two quadrics ct sa sd pa su r equivalence is only interesting if there are plenty of rational curves on x at least over k such varieties have been studied in the series of papers komi mo1 ko mi mo3 see also ko1 there are many a priori different ways of defining what plenty of rational curves should mean fortunately many of these turn out to be equivalent and this leads to the notion of rationally connected varieties see ko mi mo2 ko1 iv 3 ko2 4 1 2

on the canny edge detector abstract the canny edge detector is widely used in computer vision to locate sharp intensity changes and to find object boundaries in an image the canny edge detector classifies a pixel as an edge if the gradient magnitude of the pixel is larger than those of pixels at both its sides in the direction of maximum intensity change in this paper we will show that defining edges in this manner causes some obvious edges to be missed we will also show how to revise the canny edge detector to improve its detection accuracy

large deviation functions for nonlinear functionals of a gaussian stationary markov process we introduce a general method based on a mapping onto quantum mechanics for investigating the large t limit of the distribution p r t of the nonlinear functional r v 1 t ensuremath int 0 t mathrm dt ensuremath v x t ensuremath where v x is an arbitrary function of the stationary gaussian markov process x t for stackrel ensuremath rightarrow t ensuremath infty at fixed r we obtain p r t ensuremath sim mathrm exp ensuremath ensuremath theta r t where ensuremath theta r is a large deviation function we present explicit results for a number of special cases including v x xh x where h x is the heaviside function which is related to the cooling and the heating degree days relevant to weather derivatives

fluctuations in the zeros of differentiable gaussian processes the stochastic point processes formed by the zero crossings or extremal points of differentiable stationary gaussian processes are studied as a function of their autocorrelation function the properties of these point processes are mapped to the space formed by the parameters appearing in the autocorrelation function their adopted form being sensitive to the structure of the autocorrelation function principally in the vicinity of the origin the distribution for the number of zeros occurring in an asymptotically large interval are approximately negative binomial or binomial depending upon whether the relative variance or fano factor is greater or less than unity the correlation properties of the zeros are such that they are repelled from each other or are antibunched if the autocorrelation function of the gaussian process is characterized by a single scale size but occur in clusters if more than one characteristic scale size is present the intervals between zeros can be interpreted in terms of the autocorrelation function of the zeros themselves when bunching occurs the interval density becomes bimodal indicating the interval sizes within and between the clusters the interevent periods are statistically dependent on one another with densities whose asymptotic behavior is governed by that of the autocorrelation function of the gaussian process at large delay times poisson distributed fluctuations of the zeros occur only exceptionally but never form a poisson process

rationally connected varieties over finite fields let x be a geometrically rational or more generally separably rationally connected variety over a finite field k we prove that if k is large enough then x contains many rational curves defined over k as a consequence we prove that r equivalence is trivial on x if k is large enough these results imply the following conjecture of j l colliot thelene let y be a rationally connected variety over a number field f for a prime p let y p denote the corresponding variety over the local field f p then for almost all primes p the chow group of 0 cycles on y p is trivial and r equivalence is trivial on y p