low firing rates in a compartmental model neuron a nonlinear relationship is obtained between the membrane potential of a compartmental model neuron as a function of input stimulation this is used to show how shunting effects can lead to low output firing rates in associative memory networks

winding of planar brownian curves the authors compute the joint probability for a closed brownian curve to wind n times around a prescribed point and to enclose a given algebraic area an estimate from below of the arithmetic area is obtained

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

moments of inertia and the shapes of brownian paths we compute the joint probability law of the principal moments of inertia of brownian paths open or closed using constrained path integrals and random matrix theory the case of two dimensional paths is discussed in detail in particular we show that the ratio of the average values of the largest and smallest moments is equal to 4 99 open paths and 3 07 closed paths we also present results of numerical simulations which include investigation of the relationships between the moments of inertia and the arithmetic area enclosed by a path

shapes and sizes of arbitrary random walks at o 1 d3 ii asphericity and prolateness parameters abstract for arbitrary random walks in any d dimensional space expansions in powers of 1 d of asphericity and prolateness parameters and moments of the inverse size ratio have been developed which at o 1 d 3 yield very good approximations to exact values of the parameters for chains rings dumbbells and 3 and 5 arm regular stars the 1 d expansions have also been used to obtain an estimate of these shape asymmetry parameters for 3d edwards chains rings dumbbells and 3 arm stars and to give a mathematical proof that infinitely large random nets such as bethe lattice or starburst and mckay s net exhibit spherical symmetry for arbitrary random walks at d it is proved that these parameters coincide with their corresponding factors while for an end looped self avoiding walk it is found that its shape asymmetry is even larger than that of an open saw an 1 f expansion of the parameters for f arm regular stars has also been obtained and a comparison of the dimensionality dependence of the parameters with that of the corresponding factors has been made for the four types of random walks

viral dynamics of an htlv i infection model with intracellular delay and ctl immune response delay abstract we have developed a model of htlv i infection with two time delays an intracellular delay and a ctl immune response delay the basic reproduction number r 0 which depends on the intracellular delay is shown to determine stability conditions of the model steady states if r 0 1 using a suitable lyapunov function we show that the infection free steady state is globally asymptotically stable including both time delays if r 0 1 the unique infected steady state exists and we analyze our model in two cases a the model only with the intracellular delay that has an infected steady state that is globally asymptotically stable for every intracellular delay shown using suitable lyapunov functions b the model with the immune response delay only that experiences a destabilization of the infected steady state leading to hopf bifurcation and periodic solutions furthermore we employ latin hypercube sampling lhs to investigate the possibility of the occurrence of the hopf bifurcation and determine the key parameters that affect the stability of the infected steady state under realistic parameter space numerical simulations indicate that an increase of the intracellular delay can cause the infected steady state to stabilize while an increase of the immune delay can cause it to destabilize

practical poissonian gaussian noise modeling and fitting for single image raw data we present a simple and usable noise model for the raw data of digital imaging sensors this signal dependent noise model which gives the pointwise standard deviation of the noise as a function of the expectation of the pixel raw data output is composed of a poissonian part modeling the photon sensing and gaussian part for the remaining stationary disturbances in the output data we further explicitly take into account the clipping of the data over and under exposure faithfully reproducing the nonlinear response of the sensor we propose an algorithm for the fully automatic estimation of the model parameters given a single noisy image experiments with synthetic images and with real raw data from various sensors prove the practical applicability of the method and the accuracy of the proposed model

the aspherity of random walks the asphericity a of a random walk is defined and calculated for non self avoiding walks the definition of a generalises to self avoiding walks percolating clusters and other fractal objects and thus provides a generalised quantitative measure of the departure from spherical symmetry of the gross shape of these objects

a simple dynamical model of two dimensional vesicles two dimensional vesicles are modelled as pressurized self intersecting rings the fluctuating motion of the bounding walls of the vesicle when it is subjected to the random collisions of fluid molecules is treated along the lines suggested by rouse 1953 in his study of dilute polymer solutions within the model exact solutions of the dynamical equation governing the probability distribution of shapes when expressed in an appropriate set of normal coordinates is obtained numerical simulations of the dynamical evolution of the distribution of the principal components of the square of the radius of gyration are also presented

study of the shape of random walks a comprehensive study of the shape of discrete random walks considering the general case of arbitrary length and any space dimension is presented the probability distributions for several magnitudes such as the principal inertia moments the asphericity and the angle between the principal axis of inertia and the end to end vector are evaluated numerically in most cases and especially in low dimensional spaces these probability distributions spread widely and possess a non zero skewness this implies that any description of the shapes of random walks which is based only on mean values of related magnitudes is incomplete this situation does nor vary when random walks of large lengths are considered since the relative fluctuations ratio between the standard deviation and the mean value do not go to zero in that limit on the other hand when the space dimension grows the distributions become more peaked reaching the expected asymptotic limit for infinite dimension the present study also indicates that the probability distributions for the principal inertia moments have approximately the form of chi squared distributions analysing the probability distribution for the asphericity it is shown that the distributions for the different moments are not completely independent

the shapes and sizes of two dimensional pressurized self intersecting rings as models for two dimensional vesicles two dimensional vesicles are modelled as pressurized unrestricted closed random walks the model though suffering from undesirable physical characteristics has the decided advantage of yielding exact analytical statistical analysis of the size and shapes of these objects closed form expressions for the average of the square of the radius of gyration and the asphericity are derived in addition exact expressions for the full probability distribution are also obtained numerical computations of the probability function for several pressures are presented the authors arrive at a new exact formula for the distribution function p r12 r22 of the principal components of the square of the radius of gyration for two dimensional rings

the shapes of open and closed random walks a 1 d expansion a new technique for calculating the shapes of random walks is presented the method is used to derive an exact analytical expression for the asphericity of an unrestricted closed or ring walk embedded in d spatial dimensions a graphical procedure is developed to systematise a 1 d series expansion for the individual principal radii of gyration and their respective probability distribution functions p r2i 1 or i or d the average principal radii of gyration are calculated to o 1 d2 for both open and closed walks and selected terms in the 1 d expansion are summed to all orders in 1 d in the determination of p r2i this leads to an explicit analytical form for p r2i for open walks the distribution of the largest eigenvalue is compared with a distribution obtained from numerical simulations of walks in three dimensions the agreement between the two is extremely good other predictions for various parameters that characterise the average shape of open and closed walks in three dimensions are also found to agree remarkably well with the results of simulations the error being of the order of 5

indirect estimation of signal dependent noise with nonadaptive heterogeneous samples we consider the estimation of signal dependent noise from a single image unlike conventional algorithms that build a scatterplot of local mean variance pairs from either small or adaptively selected homogeneous data samples our proposed approach relies on arbitrarily large patches of heterogeneous data extracted at random from the image we demonstrate the feasibility of our approach through an extensive theoretical analysis based on mixture of gaussian distributions a prototype algorithm is also developed in order to validate the approach on simulated data as well as on real camera raw images

the shapes of high dimensional random walks the individual principal radii of gyration are computed for unrestricted random walks in a large number of spatial dimensions a low order expansion in one over the dimensionality yields useful information regarding the distribution and average of these measures of the extent and spatial anisotropy of high dimensional random walks such an expansion may well prove useful in the study of the shapes of other random fractal objects

a measure of the symmetry of random walks we derive the probability density for a simple measure of the asymmetry of a one dimensional random walk namely the ratio of the minimum of the two maximum displacements in the positive and negative directions to the maximum we show that in the diffusion limit the asymmetry is independent of time these results are shown to apply to random walks in which individual steps have a stable law distribution as well as to multidimensional random walks

complex dynamic behavior in a viral model with delayed immune response the rich dynamics of a viral infection model is studied under the assumption that the immune response is retarded it is shown that if the basic reproductive ratio of the virus is less than one the infection free equilibrium is globally asymptotically stable analytical and numerical results show that if the basic reproductive ratio of the virus is greater than one the combined effect of the strength of the lytic component the time delay of the immune response and the birth rate of susceptible host cells is to create a rich dynamics which includes the occurrence of stable periodic solutions and chaotic dynamical behavior the route from periodic oscillations to chaos is investigated these results can be used to explain irregular real time series data on the immune state of patients

universality and time scale invariance for the shape of planar levy processes for a broad class of planar markov processes viz l evy processes satisfying certain conditions valid e g in the case of brownian motion and l evy flights we establish an exact universal formula describing the shape of the convex hull of sample paths we show indeed that the average number of edges joining paths points separated by a time lapse ensuremath delta ensuremath tau ensuremath in left ensuremath delta ensuremath tau 1 ensuremath delta ensuremath tau 2 right is equal to 2 phantom rule 0 16em 0ex text ln left ensuremath delta ensuremath tau 2 ensuremath delta ensuremath tau 1 right regardless of the specific distribution of the process s increments and regardless of its total duration t the formula also exhibits invariance when the time scale is multiplied by any constant apart from its theoretical importance our result provides insights regarding the shape of two dimensional objects e g polymer chains modeled by the sample paths of stochastic processes generally more complex than brownian motion in particular for a total time or parameter duration t the average number of edges on the convex hull cut off to discard edges joining points separated by a time lapse shorter than some ensuremath delta ensuremath tau lt will be given by 2 phantom rule 0 16em 0ex text ln frac t ensuremath delta ensuremath tau thus it will only grow logarithmically rather than at some higher pace

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

global stability of a delayed htlv i infection model with a class of nonlinear incidence rates and ctls immune response in this paper applying new lyapunov functional techniques to a delayed htlv i infection model with a class of nonlinear incidence rates and ctls immune response we establish that the global dynamics are completely determined by two basic reproduction numbers r 0 r 0 as follows if r 0 1 then a viral free equilibrium is globally asymptotically stable if r 0 11 then there exists a unique endemic equilibrium which is globally asymptotically stable in particular to obtain concrete eventual lower bounds for positive solutions of the model we offer some new techniques

study of the shape of random walks ii inertia moment ratios and the two dimensional asphericity a study of some features of the quantities used to describe the shape of random walks focusing on the probability distribution of the asphericity of discrete random walks in two dimensions is presented a connection is established between the asphericity distribution and the probability distribution corresponding to the ratio of the principal inertia moments the probability distributions of arbitrary inertia moment ratios are analysed for varying spatial dimension and an analytic expression for them is found which presents excellent agreement with monte carlo data in all the cases considered this function is then used to obtain the corresponding two dimensional asphericity distribution which also proved to be a very good approximation to the true distribution obtained from an independent monte carlo simulation

shapes of random walks at order 1 d2 the authors calculate various parameters which characterize the size and shape of random walks utilizing a recently developed 1 d expansion technique where d is the spatial dimension in which the random walk takes place a new procedure for extracting the averages of the principal radii of gyration is presented and the calculation is carried out to order 1 d2 which is one order higher than previous work comparison with the results of numerical simulations provides new insights regarding the accuracy of the 1 d expansion procedure

new approaches to shapes of arbitrary random walks abstract the problem of the shape of a random object such as a flexible polymer chain was first tackled by kuhn nearly thirty years after the answer to the probability distribution of its size was publicly sought for by pearson in 1905 since then significant progress in the field has been made but the important task of evaluatin both analytically and accurately averaged individual principal components of the shape or inertia tensor for a walk of a certain architectural type remains unfinished we have recently developed a new and general formalism for both exact and approximate calculations of these and other averages such as asphericity and prolateness parameters which is illustrated here for an end looped random walk and a self avoiding or edwards chain we find that this combined open and closed random walks has surprisingly larger shape asymmetry than a simply open walk despite its smaller size

the shape of self avoiding walks an exhaustive analysis of the shape properties of discrete self avoiding random walks is presented the dependence of the main parameters of the probability distributions from the length of the walk and the differences between these distributions for conventional and self avoiding walks are studied by means of high precision monte carlo simulations it is shown that the characteristics of the shape of self avoiding random walks when regarded as a function of the walk length present the expected asymptotic behaviour the differences with conventional random walks depend upon the observable considered the probability distributions of the principal inertia eigenvalues of self avoiding walks spread around the most probable value more widely than the corresponding distributions for unrestricted walks while in the cases of the asphericity or ratios of inertia eigenvalues the distributions for self avoiding walks are somewhat more peaked than their counterparts for conventional random walks analytical expressions for the probability distributions of inertia moment ratios and the two dimensional asphericity are given for common random walks there is an excellent agreement between these analytical distributions and the monte carlo data in this work it is established that this concordance is maintained if the same analytical distributions are applied to the self avoiding case this means that within the precision of the simulations the functional form of the mentioned distributions does not vary when passing from conventional to self avoiding walks

universal shape ratios for open and closed random walks exact results for all d the mean asphericities ad of open and closed gaussian polymer chains are computed exactly and analytically up to simple quadratures for arbitrary space dimensions d excellent agreement is found with existing simulation data for d 2 3 and 4 the authors technique can also be used to compute other averages of ratios of fluctuating variables as well as extended to include the effects of self avoiding walk interactions

pure let image deconvolution we propose a non iterative image deconvolution algorithm for data corrupted by poisson or mixed poisson gaussian noise many applications involve such a problem ranging from astronomical to biological imaging we parameterize the deconvolution process as a linear combination of elementary functions termed as linear expansion of thresholds this parameterization is then optimized by minimizing a robust estimate of the true mean squared error the poisson unbiased risk estimate each elementary function consists of a wiener filtering followed by a pointwise thresholding of undecimated haar wavelet coefficients in contrast to existing approaches the proposed algorithm merely amounts to solving a linear system of equations which has a fast and exact solution simulation experiments over different types of convolution kernels and various noise levels indicate that the proposed method outperforms the state of the art techniques in terms of both restoration quality and computational complexity finally we present some results on real confocal fluorescence microscopy images and demonstrate the potential applicability of the proposed method for improving the quality of these images

universal features of the shapes of percolation clusters and lattice animals the shapes of percolation clusters and lattice animals are investigated the universal quantities delta d and sd which were introduced to measure the average asymmetry and degree of prolate or oblateness respectively of long chain polymers are here computed in an in expansion for percolation clusters and for lattice animals delta d is computed to o in while sd is computed to o 1 the clusters are shown to be on average anisotropic and prolate but less so than polymers percolation clusters and lattice animals have identical shapes above eight dimensions below d 8 animals are slightly more anisotropic than percolation clusters

stability properties and hopf bifurcation of a delayed viral infection model with lytic immune response a class of more general delayed viral infection model with lytic immune response is proposed based on some important biological meanings the effect of time delay on stabilities of the equilibria is given the sufficient criteria for local and global asymptotic stabilities of the viral free equilibrium and the local asymptotic stabilities of the no immune response equilibrium are given we also get the sufficient criteria for stability switch of the positive equilibrium numerical simulations are carried out to explain the mathematical conclusions

on the asymmetry of a random walk in the presence of a field any ensemble of random walks with symmetric transition probabilities will have symmetric properties however any single realization of such a random walk may be asymmetric in an earlier paper weiss and weissman developed a measure of asymmetry and applied it to random walks in the absence of a field showing that the degree of asymmetry in the diffusion limit is independent of time and that the most probable degree of asymmetry corresponds to the maximum possible we show in the present paper how the presence of a symmetric field can change this result both in making the degree of asymmetry depend on time and driving the random walk toward a more symmetric state

global stability in a viral infection model with lytic and nonlytic immune responses this paper investigates the global stability of a viral infection model with lytic and nonlytic immune responses if the basic reproductive ratio of the virus is less than or equal to one by the lasalle s invariance principle and center manifold theorem the disease free steady state is globally asymptotically stable if the basic reproductive ratio of the virus is greater than one then the virus persists in the host and the disease steady state is locally asymptotically stable furthermore by the method of lyapunov function the global stability of the disease steady state is established at the same time if we neglect the efficacy of the lytic component using a geometrical approach we obtain a different type of conditions for the global stability of the disease steady state