the becker doring equations at large times and their connection with the lsw theory of coarsening a systematic procedure is given for obtaining the asymptotic late time behavior of the becker doring equations describing the time evolution of a population of clusters of particles in lowest order of approximation the distribution of the sizes of the largest clusters satisfies the equations of the lifshitz slyozov wagner theory of coarsening

asymptotic behavior of solutions to the coagulation fragmentation equations ii weak fragmentation the discrete coagulation fragmentation equations are a model for the kinetics of cluster growth in which clusters can coagulate via binary interactions to form larger clusters or fragment to form smaller ones the assumptions made on the fragmentation coefficients have the physical interpretation that surface effects are important our results on the asymptotic behavior of solutions generalize the corresponding results of ball carr and penrose for the becker doring equation

the becker doring equations and the lifshitz slyozov theory of coarsening in this paper the relation between the kinetic set of becker doring bd equations and the classical lifshitz slyozov ls theory of coarsening is studied a model that resembles the ls theory but keeps some of the nucleation effects is derived for this model a solution is described that shows how the kinetic effects explain the particular solution selected in the ls theory by means of a renormalization procedure a discrete group of transformations is shown to play an important role in describing the structure of the solution near the critical size of the ls theory

randomness in distribution protocols randomness is a useful computation resource due to its ability to enhance the capabilities of other resources its interaction with resources such as time space interaction with provers and its role in several areas of computer science has been extensively studied in this paper we give a systematic analysis of the amount of randomness needed by secret sharing schemes and secure key distribution schemes we give both upper and lower bounds on the number of random bits needed by secret sharing schemes the bounds are tight for several classes of secret sharing schemes for secure key distribution schemes we provide a lower bound on the amount of randomness needed thus showing the optimality of a recently proposed key distribution protocol

universally ideal secret sharing schemes given a set of parties 1 spl middot spl middot spl middot n an access structure is a monotone collection of subsets of the parties for a certain domain of secrets a secret sharing scheme for an access structure is a method for a dealer to distribute shares to the parties these shares enable subsets in the access structure to reconstruct the secret while subsets not in the access structure get no information about the secret a secret sharing scheme is ideal if the domains of the shares are the same as the domain of the secrets an access structure is universally ideal if there exists an ideal secret sharing scheme for it over every finite domain of secrets an obvious necessary condition for an access structure to be universally ideal is to be ideal over the binary and ternary domains of secrets the authors prove that this condition is also sufficient they also show that being ideal over just one of the two domains does not suffice for universally ideal access structures finally they give an exact characterization for each of these two conditions

some early statistical contributions to the theory and practice of linear algebra abstract we outline the history of some of the concepts and techniques of linear algebra which are intimately connected with the development of the method of least squares and related fitting procedures our study concentrates on contributions made during the early years of the nineteenth century but it is not entirely restricted to this period

the becker doring equations with exponentially size dependent rate coefficients this paper is concerned with an analysis of the becker doring equations which lie at the heart of a number of descriptions of non equilibrium phase transitions and related complex dynamical processes the becker doring theory describes growth and fragmentation in terms of stepwise addition or removal of single particles to or from clusters of similar particles and has been applied to a wide range of problems of physicochemical and biological interest within recent years here we consider the case where the aggregation and fragmentation rates depend exponentially on cluster size these choices of rate coefficients at least qualitatively correspond to physically realistic molecular clustering scenarios such as occur in for example simulations of simple fluids new similarity solutions for the constant monomer becker doring system are identified and shown to be generic in the case of aggregation and fragmentation rates that depend exponentially on cluster size

zero error capacity under list decoding shannon s zero error channel capacities c sub of c sub o with and without noiseless feedback are generalized to list decoding the receiver lists l messages erring if the correct one is not listed the corresponding capacities c sub of l c sub o l are nondecreasing in l for an i letter input alphabet c sub of l attains its maximum at l i 1 a lower bound to c sub o l approaches that maximum as l increases

decomposition constructions for secret sharing schemes the paper describes a very powerful decomposition construction for perfect secret sharing schemes the author gives several applications of the construction and improves previous results by showing that for any graph g of maximum degree d there is a perfect secret sharing scheme for g with information rate 2 d 1 as a corollary the maximum information rate of secret sharing schemes for paths on more than three vertices and for cycles on more than four vertices is shown to be 2 3

l 1 statistical analysis and related methods prologue thoughts on real data and statistics y dodge some statistical tools for the analysis of complex molecular spectra a f ruckstuhl estimation testing and property characterization the gauss markov property for the median g w basset jr a class of estimators based on adaptative convex combinations of two estimation procedures y dodge j jureckova robustness of l1 regression in the light of linear programming j dupacova a linear model with a pseudoisotropic distribution of errors s kotz y g kuritsyn l1 estimation and testing in conditionally contaminated linear models c h muller explicit scale estimators with high breakdown point p j rousseeuw c croux m type tests in linear models some comments on studentizing and a small simulation w a stahel p hartmann high breakdown estimators in nonlinear regression a stromberg graphical analysis regression plotting based on quadratic predictors r d cook the notion of sphericity for finite l1 figures of data analysis b fichet the interpretation of residuals based on l1 estimation s j sheather j w mckean graphical methods for model comparison s weisberg nonparametric estimation in linear models generalized regression quantiles forming a useful toolkit for robust linear regression p chaudhuri efficient l estimators in semiparametric linear heteroscedastic models c gutenbrunner bounded influence and high breakdown point regression with linear combinations of order statistics and rank statistics s heiler nonparametric estimation of conditional quantile functions r koenker s portnoy p ng time series analysis recursive time series methods in l1 norm t cipra m r romera asymptotics of boscovich type parameter estimates for infinite variance autoregressive processes k knight l1 norm estimation of regression models with serially dependent error terms h nyquist multivariate analysis on multivariate notions of sign and rank t p hettmansperger j nyblom h oja data depth and multivariate rank tests r y liu a two sample extension of the multivariate interdirection sign test r h randles computational procedures generating median graphs from boolean matrices h j bandelt computational algorithms for least absolute value regression t e dielman algorithms for non linear lp estimation h ekblom k madsen the geometrical foundations of a class of estimation procedures which minimise sums of euclidean distances and related quantities r w farebrother computing p values in robust inference location scale c field testing software for robust regression j e gentle s c narula v a sposito a continuation method for linear l1 estimation k madsen h b nielsen the calculation of the oja multivariate median a o niinimaa distributions and density estimation

metastable states for the becker doring cluster equations the becker doring equations in whichc l t can represent the concentration ofl particle clusters or droplets in say a condensing vapour at timet are begin array 20 c dc l t mathord left vphantom dc l t dt right kern nulldelimiterspace dt j l 1 t j l t l 2 3 end array with j l t a l c 1 t c l t b l 1 c l 1 t and eitherc1 const case a or rho sum limits 1 infty lc l const case b the equilibrium solutions arec l q l z l where q l prod limits 2 l a r 1 mathord left vphantom a r 1 b r right kern nulldelimiterspace b r the density of the saturated vapour defined as rho s sum limits 1 infty lq l z s l wherez s is the radius of convergence of the series is assumed finite it is proved here that subject to some further plausible conditions on the kinetic coefficientsa l andb l there is a class of metastable solutions of the equations withc1 z s small and positive which take an exponentially long time to decay to their asymptotic steady states an exponentially long time means one that increases more rapidly than any negative power of the given value ofc1 z s or in caseb s as the latter tends to zero the main ingredients in the proof are i a time independent upper bound on the solution of the kinetic equations this upper bound is a steady state solution of case a of the equations of the type used in the becker doring theory of nucleation and ii an upper bound on the total concentration of particles in clusters greater than a certain critical size which with suitable initial conditions remains exponentially small until the time becomes exponentially large

randomness in secret sharing and visual cryptography schemes secret sharing schemes allow a secret to be shared among a group of participants so that only qualified subsets of participants can recover the secret a visual cryptography scheme vcs is a special kind of secret sharing scheme in which the secret to share consists of an image and the shares consist of xeroxed transparencies which are stacked to recover the shared image in this paper we analyze the relationship between secret sharing schemes and vcss focusing our attention on the amount of randomness required to generate the shares we prove that secret sharing schemes for a set of secrets of size two bsss and vcss are equivalent with respect to the randomness indeed we show how to transform a bss for a given access structure into a vcs for the same access structure while preserving the randomness of the original scheme we provide both upper and lower bounds on the randomness of bsss all vcss presented in this paper allow a perfect reconstruction of black pixels

dealing with the multiplicity of solutions of the l1 and l regression models abstract it is well known that the least absolute value l and the least sum of absolute deviations l1 algorithms produce estimators that are not necessarily unique in this paper it is shown how the set of all solutions of the l1 and l regression problems for moderately large sample sizes can be obtained in addition if the multiplicity of solutions wants to be avoided two new methods giving the same optimal l1 and l values but supplying unique solutions are proposed the idea consists of using two steps in the first step the optimal values of the l1 and l errors are calculated and in the second step in case of non uniqueness of solutions one of the multiple solutions is selected according to a different criterion for the l the procedure is used sequentially but removing in each iteration the data points with maximum absolute residual and adding the corresponding constraints for keeping these residuals and this process is repeated until no change in the solution is obtained in this way not only the maximum absolute residual values are minimized in the modified method but also the maximum absolute residual values of the remaining points sequentially until no further improvement is possible in the l1 case a least squares criterion is used but restricted to the l1 residual condition thus in the modified l1 method not only the l1 residual is minimized but also the sum of squared residuals subject to the l1 residual the methods are illustrated by their application to some well known examples and their performances are tested by some simulations which show that the lack of uniqueness problem cannot be corrected for some experimental designs by increasing the sample size

numerical approximation of the lifshitz slyozov wagner equation the lifshitz slyozov wagner theory of coarsening ostwald ripening describes the late stages of the growth by diffusional mass transfer of the grains of a new phase from a supersaturated solution it results in a nonlinear transport equation with a nonlocal nonlinearity for the volume distribution function of the grains a time explicit finite volume numerical scheme is proposed to solve this equation in self similar variables and is shown to converge under a cfl condition numerical simulations are also presented

renormalization theoretic analysis of non equilibrium phase transitions i the becker doring equations with power law rate coefficients we study in detail the application of renormalization theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes we investigate the becker d oring equations originally formulated to describe and analyse non equilibrium phase transitions and more recently generalized to describe a wide range of physicochemical problems in this paper we analyse how the systematic coarse graining renormalization of the becker d oring system of equations affects the aggregation and fragmentation rate coefficients we consider the case of power law size dependent cluster rate coefficients which we show lead to only three classes of system that require analysis coagulation dominated systems fragmentation dominated systems and those where coagulation and fragmentation are exactly balanced we analyse the late time asymptotics associated with each class

cluster growth poised on the edge of break up size distributions with small exponent power laws abstract in many naturally occurring growth processes cluster size distributions of power law form n s s with small exponents 0 1 are observed we suggest here that such distributions emerge naturally from cluster growth where size dependent aggregation is counterbalanced by size dependent break up the model used in the study is a simple reaction kinetic model including only monomer cluster processes it is shown that under such conditions power law size distributions with small exponents are obtained therefore the results suggest that the ubiquity of small exponent power law distributions is related to the growth process where aggregation driven cluster growth is poised on the edge of cluster break up

long time behavior of a modified becker doring system a modification based on asymptotic behavior of the becker doring system is introduced in which the concentration of monomers is slaved to the concentrations of the other clusters this modified system has the same continuum limit as the usual becker doring system for one member of the modified systems it is proved for compact initial data that all solutions will converge to the same self similar form as time tends to infinity

non crossing non parametric estimates of quantile curves in this paper a new nonparametric estimate of conditional quantiles is proposed that avoids the problem of crossing quantile curves calculated for various p 2 0 1 the method uses an initial estimate of the conditional distribution function in a flrst step and solves the problem of inversion and monotonization with respect to p 2 0 1 simultaneously it is demonstrated that the new estimates are asymptotically normal distributed and asymptotically flrst order equivalent to quantile estimates obtained by local constant or local linear smoothing of the conditional distribution function the performance of the new procedure is illustrated by means of a simulation study and some comparisons with the currently available procedures which are similar in spirit with the proposed method are presented

the becker doring cluster equations basic properties and asymptotic behaviour of solutions existence and uniqueness results are established for solutions to the becker doring cluster equations the density is shown to be a conserved quantity under hypotheses applying to a model of a quenched binary alloy the asymptotic behaviour of solutions with rapidly decaying initial data is determined denoting the set of equilibrium solutions byc 0 s the principal result is that if the initial density 0 s then the solution converges strongly toc o while if 0 s the solution converges weak toc s in the latter case the excess density 0 s corresponds to the formation of larger and larger clusters i e condensation the main tools for studying the asymptotic behaviour are the use of a lyapunov function with desirable continuity properties obtained from a known lyapunov function by the addition of a special multiple of the density and a maximum principle for solutions