survey paper research on probabilistic methods for control system design a novel approach based on probability and randomization has emerged to synergize with the standard deterministic methods for control of systems with uncertainty the main objective of this paper is to provide a broad perspective on this area of research known as probabilistic robust control and to address in a systematic manner recent advances the focal point is on design methods based on the interplay between uncertainty randomization and convex optimization and on the illustration of specific control applications

computer simulation of geometric stable distributions we present a new method for computer simulation of strictly geometric stable random variables the method is based on their representation as a product of two independent random variables with explicit distribution functions coupled with the inversion method we also extend the method to the multivariate case by deriving new representation and simulation algorithm for multivariate linnik distribution

analytic and asymptotic properties of linnik s probability densities ii abstract in 1953 linnik introduced the probability density p x defined in terms of its characteristic function t 1 1 t 0 recently this density has received several applications in this paper the expansions of p x into convergent series in terms involving log x x k x k k 0 1 2 are obtained and the asymptotic behaviour of p x at 0 and is investigated with respect to these expansions and to the asymptotic behaviour at 0 the cases i 1 is an integer ii 1 is a non integer rational number and iii is an irrational number are quite distinct the first part of the paper dealt with preliminaries asymptotic behavior at and case i the second part deals with cases ii and iii

analytic and asymptotic properties of generalized linnik probability densities is a characteristic function of a symmetric probability density p since a 4 then the family of symmetric linnik densities p a g 0 2 had several a w x probabilistic applications see e g 2 7 analytic and asymptotic properw x ties of the densities p were studied in 8 a w x in 1984 klebanov maniya and melamed 9 introduced the concept of geometric strict stability and proved that the family of geometrically strictly stable densities coincides with the family of densities with characteristic functions

on the rate of convergence to rosenblatt type distribution the main result of the article is the rate of convergence to the rosenblatt type distributions in non central limit theorems specifications of the main theorem are discussed for several scenarios in particular special attention is paid to the cauchy generalized linnik s and local global distinguisher random processes and fields direct analytical methods are used to investigate the rate of convergence in the uniform metric

new lower bounds for constant weight codes some new lower bounds are given for a n 4 w the maximum number of codewords in a binary code of length n minimum distance 4 and constant weight w in a number of cases the results significantly improve on the best bounds previously known

an improvement of the gilbert bound for constant weight codes corresp using the goppa codes as outer codes in a construction devised by kautz and singleton an improvement of the gilbert bound for constant weight codes is obtained

a 16 9 6 5 4 error correcting dc free block code a 2n k l c d dc free binary block code is a code of length 2n constant weight n 2 sup k codewords maximum runlength of a symbol l maximum accumulated charge c and minimum distance d the purpose of this code is to achieve dc freeness and error correction at the same time the goal is to keep the rate k 2n and d large and l and c small of course these are conflicting goals h c ferreira ieee trans magn vol mag 20 no 5 p 881 3 1984 presented a 16 8 8 5 4 dc free code here a 16 9 6 5 4 dc free code is presented easy encoding and decoding algorithms are also given

girsanov s transformation based variance reduced monte carlo simulation schemes for reliability estimation in nonlinear stochastic dynamics the study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems attention is focused on importance sampling strategies based on the application of girsanov s transformation method controls which minimize the distance function as in the first order reliability method form are shown to minimize a bound on the sampling variance of the estimator for the probability of failure two schemes based on the application of calculus of variations for selecting control signals are proposed the first obtains the control force as the solution of a two point nonlinear boundary value problem and the second explores the application of the volterra series in characterizing the controls the relative merits of these schemes visa vis the method based on ideas from the form are discussed illustrative examples involving archetypal single degree of freedom dof nonlinear oscillators and a multi degree of freedom nonlinear dynamical system are presented the credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct monte carlo simulations c 2017 elsevier inc all rights reserved

upper bounds for constant weight codes let a n d w denote the maximum possible number of codewords in an n d w constant weight binary code we improve upon the best known upper bounds on a n d w in numerous instances for n spl les 24 and d spl les 12 which is the parameter range of existing tables most improvements occur for d 8 10 where we reduce the upper bounds in more than half of the unresolved cases we also extend the existing tables up to n spl les 28 and d spl les 14 to obtain these results we develop new techniques and introduce new classes of codes we derive a number of general bounds on a n d w by means of mapping constant weight codes into euclidean space this approach produces among other results a bound on a n d w that is tighter than the johnson bound a similar improvement over the best known bounds for doubly constant weight codes studied by johnson and levenshtein is obtained in the same way furthermore we introduce the concept of doubly bounded weight codes which may be thought of as a generalization of the doubly constant weight codes subsequently a class of euclidean space codes called zonal codes is introduced and a bound on the size of such codes is established this is used to derive bounds for doubly bounded weight codes which are in turn used to derive bounds on a n d w we also develop a universal method to establish constraints that augment the delsarte inequalities for constant weight codes used in the linear programming bound in addition we present a detailed survey of known upper bounds for constant weight codes and sharpen these bounds in several cases all these bounds along with all known dependencies among them are then combined in a coherent framework that is amenable to analysis by computer this improves the bounds on a n d w even further for a large number of instances of n d and w

approximate bayesian computation by subset simulation a new approximate bayesian computation abc algorithm for bayesian updating of model parameters is proposed in this paper which combines the abc principles with the technique of subset simulation for efficient rare event simulation first developed in s k au and j l beck probabilistic engrg mech 16 2001 pp 263 277 it has been named abc subsim the idea is to choose the nested decreasing sequence of regions in subset simulation as the regions that correspond to increasingly closer approximations of the actual data vector in observation space the efficiency of the algorithm is demonstrated in two examples that illustrate some of the challenges faced in real world applications of abc we show that the proposed algorithm outperforms other recent sequential abc algorithms in terms of computational efficiency while achieving the same or better measure of accuracy in the posterior distribution we also show that abc subsim readily provides an estimate of the evidence marginal likelihood for posterior model class assessment as a by product

perfect constant weight codes in his pioneering work from 1973 delsarte conjectured that there are no nontrivial perfect codes in the johnson scheme many attempts were made during the years which followed to prove delsarte s conjecture but only partial results have been obtained we survey all these attempts and prove some new results having the same flavor we also present a new method taking a different approach which we hope can lead to the settling of this conjecture we show how this new method rules out sets of parameters as well as specific given parameters

approximate optimization of systems with high dimensional uncertainties and multiple reliability constraints a novel approach is proposed to solve reliability based optimization rbo problems where the uncertainty dimension can be large and where there may be many reliability constraints the basic idea is to transform all reliability constraints in the target rbo problem into non probabilistic ordinary ones by a pilot analysis it will be shown that such a pilot analysis only requires a single run of the modified subset simulation called the parallel subset simulation regardless the number of the reliability constraints once the reliability constraints are approximated by the ordinary ones the rbo problem can be solved as if it is an ordinary optimization problem the resulting optimal solution should be approximately feasible and the corresponding objective function value is minimized under the approximate constraints three numerical examples are investigated to verify the proposed novel approach the results show that the approach may be capable of finding approximate solutions that are usually close to the actual solution of the target rbo problem

reliability estimation for dynamical systems subject to stochastic excitation using subset simulation with splitting a new subset simulation approach is proposed for reliability estimation for dynamical systems subject to stochastic excitation the basic idea of subset simulation is to factor a small failure probability into a product of larger failure probabilities conditional on intermediate failure events the new method proposed in this work does not require markov chain monte carlo simulation in contrast to the original method to estimate the conditional probabilities instead only direct monte carlo simulation is needed the method employs splitting of a trajectory that reaches an intermediate failure level into multiple trajectories subsequent to the corresponding first passage time the new approach still enjoys most of the advantages of the original subset simulation e g it is applicable to general causal dynamical systems and it is robust with respect to the dimension of the uncertain input variables the statistical properties of the failure probability estimators are presented where it is shown that they are unbiased and formulas are derived to assess the error of estimation including the coefficient of variation we also discuss the selection of intermediate failure events and the number of samples for each failure level the resulting algorithm is simple and easy to implement two examples are presented to demonstrate the effectiveness of the new approach and the results are compared with the original subset simulation and with direct monte carlo simulation

multiscale conservation laws driven by levy stable and linnik diffusions asymptotics shock creation preservation and dissolution recent work has shown that the solutions of the fractal conservation laws driven by levy alpha stable diffusions exhibit shocks for bounded odd and convex on the positive half line initial data when the parameter alpha 1 we study the analogous situation for the levy alpha linnik diffusions in which case the local behavior is strikingly different although we are able to establish analytically that the large time behavior of the two types of conservation laws are similar but the main new insights obtained via large scale numerical experiments is that for any 0 alpha le 2 the conservation laws driven by alpha linnik diffusions display shocks that do not dissipate over time while those for alpha stable diffusion 0 alpha le 1 do we formulate rigorous conjectures based on these numerical experiments

generalized whittle matern random field as a model of correlated fluctuations this paper considers a generalization of the gaussian random field with covariance function of the whittle matern family such a random field can be obtained as the solution to the fractional stochastic differential equation with two fractional orders asymptotic properties of the covariance functions belonging to this generalized whittle matern family are studied which are used to deduce the sample path properties of the random field the whittle matern field has been widely used in modeling geostatistical data such as sea beam data wind speed field temperature and soil data in this paper we show that the generalized whittle matern field provides a more flexible model for wind speed data

local time of levy random walks a path integral approach the local time of a stochastic process quantifies the amount of time that sample trajectories x spend in the vicinity of an arbitrary point x for a generic hamiltonian we employ the phase space path integral representation of random walk transition probabilities in order to quantify the properties of the local time for time independent systems the resolvent of the hamiltonian operator proves to be a central tool for this purpose in particular we focus on the local times of levy random walks levy flights which correspond to fractional diffusion equations

constructions of error correcting dc free block codes two dc free codes are presented with distance 2d b or 1 length 2n 2r d 1 for d 3 where r is the least integer or log sub 2 2n 1 for the first code l 4 c 2 and the asymptotic rate of this code is 0 7925 for the second code l 6 c 3 and the asymptotic rate of this code is 0 8858 asymptotically these rates achieve the channel capacity for small values of n these codes do not achieve the best rate as an example of codes of short length with good rate the author presents a 30 10 6 4 dc free block code with 2 sup 21 codewords a construction is presented for which from a given code c sub 1 of length n even weight and distance 4 the author obtains a 4n l c 4 dc free block code c sub 2 where l is 4 5 or 6 and c is not greater than n 1 but usually significantly smaller the codes obtained by this method have good rates for small lengths the encoding and decoding procedures for all the codes are discussed

a generalized cauchy process and its application to relaxation phenomena we study some of the basic properties of a generalized cauchy process indexed by two parameters the application of the lamperti transformation to the generalized cauchy process leads to a self similar process which preserves the long range dependence the asymptotic properties of spectral density of the process are derived possible application of this process to model relaxation phenomena is considered

a new table of constant weight codes a table of binary constant weight codes of length nl28 is presented explicit constructions are given for most of the 600 codes in the table the majority of these codes are new the known techniques for constructing constant weight codes are surveyed and a table of unrestricted binary codes of length nl28 is given

a lower bound for a n 4 w corresp an explicit lower bound is given for a n 4 w the maximum number of codewords in a binary code of length n minimum distance four and constant weight w