choquet weak convergence of capacity functionals of random sets the results in this paper are about the convergence of capacity functionals of random sets the motivation stems from asymptotic aspects in inference and decision making with coarse data in biostatistics set valued observations as well as connections between random sets with several emerging uncertainty calculi in intelligent systems such as fuzziness belief functions and possibility theory specifically we study the counter part of billingsley s portmanteau theorem for weak convergence of probability measures namely convergence of capacity functionals of random sets in terms of choquet integrals

the design of trellis coded mpsk for fading channels set partitioning for optimum code design a previous work on criteria for designing trellis coded mpsk modulation to achieve minimum error probability performance on the rician fading channel see ibid vol 36 no 9 p 1004 1012 sep 1988 is extended it is demonstrated that allowing for multiple symbols per trellis branch i e multiple trellis coded modulation mtcm provides an additional degree of freedom for designing a code to meet the optimization on the fading channel diversities larger than those achievable with conventional trellis codes having the same number of trellis states are now attainable it is under these conditions that mtcm achieves its full potential

set partitioning for multilevel codes on a rayleigh fading channel on a rayleigh fading channel multilevel codes achieve larger hamming distances than single level codes at comparable decoder complexity and bandwidth efficiency by employing a multistage decoder typically multilevel codes are designed using ungerboeck s 1982 set partitioning this results in a large path multiplicity that degrades the code performance significantly in order to overcome the performance degradation we propose a set partitioning method that greatly reduces the path multiplicity

on the convergence in distribution of measurable multifunctions random sets normal integrands stochastic processes and stochastic infima the concept of the distribution function of a closed valued measurable multifunction is introduced and used to study the convergence in distribution of sequences of multifunctions and the epi convergence in distribution of normal integrands and stochastic processes in particular various compactness criteria are exhibited the connections with the classical convergence theory for stochastic processes are analyzed and for purposes of illustration we apply the theory to sketch out a modified derivation of donsker s theorem brownian motion as a limit of normalized random walks we also suggest the potential application of the theory to the study of the convergence of stochastic infima

differentiability of relations and differential stability of perturbed optimization problems several new concepts of differentiability of multifunctions are introduced special attention is paid to relations given by perturbed inequalities applications are given to the study of the value or marginal function of a perturbed nonlinear program

monte carlo study of the ising model phase transition in terms of the percolation transition of physical clusters finite squarel l ising lattices with ferromagnetic nearest neighbor interaction are simulated using the swendsen wang cluster algorithm both thermal properties internal energyu specific heatc magnetization m susceptibility and percolation cluster properties relating to the physical clusters namely the fortuin kasteleyn clusters percolation probability p percolation susceptibility p cluster size distributionnl are evaluated paying particular attention to finite size effects it is shown that thermal properties can be expressed entirely in terms of cluster properties p being identical to m in the thermodynamic limit while finite size corrections differ in contrast p differs from even in the thermodynamic limit since a fluctuation in the size of the percolating net contributes to but not to p neartc the cluster size distribution has the scaling properties as hypothesized by earlier phenomenological theories we also present a generalization of the swendsen wang algorithm allowing one to cross over continuously to the glauber dynamics

isotropic majority vote model on a square lattice the stationary critical properties of the isotropic majority vote model on a square lattice are calculated by monte carlo simulations and finite size analysis the critical exponents and are found to be the same as those of the ising model and the critical noise parameter is found to beqc 0 075 0 001

multilevel trellis coded modulations for the rayleigh fading channel the authors present coded 8 phase shift keyed 8 psk modulations for the rayleigh fading channel the schemes are based on multilevel trellis coded modulation constructions and utilize maximum free hamming distance binary convolutional codes as building blocks a suboptimal multistage decoder that utilizes interstage interleaving and iterative decoding is proposed and evaluated examples are constructed to show that the proposed schemes outperform the best modified codes of the ungerboeck type due to significantly higher implicit time diversity yielding seven branches of built in time diversity whereas the ungerboeck code yields four branches of time diversity for a 64 state system the transmission delay is higher however the new schemes can provide three levels of unequal error protection when 8 psk or 8 differential phase shift keying 8 dpsk modulations are used they provide 10 14 db channel signal to noise ratio gain over uncoded 4 dpsk at a bit error rate of 10 sup 3 for a modest decoding complexity

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

nonequilibrium spin models with ising universal behaviour the properties of a family of nonequilibrium spin models with up down symmetry on a square lattice are determined by a mean field pair approximation and by monte carlo simulation the phase diagram in the parameter space displays a critical line that terminates at a first order critical point it is found that the critical exponents are the same as those of the equilibrium ising model

convergence of dynamic programming models weak conditions are presented for approximating dynamic programming models for a sequence of these models continuous convergence of the sequence of associated optimal value functions is obtained under the condition that state and action space converge in the sense of kuratowski and that the mappings of admissible actions as well as the transition law the discount factors and the reward functions converge continuously further a relation for the associated sets of optimal actions is given the analysis is based on results about convergence preserving properties of supremum value functions and integrals the approximation results are extended to so called upper semi continuous convergent sequences and are related to discretization procedures by using projections

scaling properties of the cluster distribution of a critical nonequilibrium model abstract a geometric approach to critical fluctuations of a nonequilibrium model is reported the two dimensional majority vote model was investigated by monte carlo simulations on square lattices of various sizes and a detailed scaling analysis of cluster statistical and geometric properties was performed the cluster distribution exponents and fractal dimension were found to be the same as those of the two dimensional ising model this result which cannot be derived purely from the known bulk critical behaviour widens our knowledge about the range of validity of the ising universality class for nonequilibrium systems

coset codes ii binary lattices and related codes for pt i see ibid vol 34 no 5 p 1123 51 1988 the family of barnes wall lattices including d sub 4 and e sub 8 of lengths n 2 sup n and their principal sublattices which are useful in constructing coset codes are generated by iteration of a simple construction called the squaring construction the closely related reed muller codes are generated by the same construction the principal properties of these codes and lattices are consequences of the general properties of iterated squaring constructions which also exhibit the interrelationships between codes and lattices of different lengths an extension called the cubing construction generates good codes and lattices of lengths n 3 2 sup n including the golay code and leech lattice with the use of special bases for 8 space another related construction generates the nordstrom robinson code and an analogous 16 dimensional nonlattice packing these constructions are represented by trellis diagrams that display their structure and interrelationships and that lead to efficient maximum likelihood decoding algorithms

second order directional derviatives in parametric optimization problems we characterize the second order directional derivative in the sense of ben tal and zowe of a marginal function of the following general form x inf f x y y x this requires us to introduce some geometrical notions as for example the first and second order tangent directions to a multifunction the main results are then applied to some particular types of marginal functions

variational inclusions for contingent derivative of set valued maps in this paper we give two versions of ky fan s inequality for set valued maps acting between normed vector spaces and we consider sufficient conditions to solve a variational inclusion problem concerning derivatives of set valued maps a selection result for set valued maps between finite dimensional vector spaces and its contingent derivative is obtained as well from this result we derive some conditions for the existence of a solution of a generalized variational inequality problem

wijsman convergence of convex sets under renorming let x p be a metric space a natural way to define convergence for a sequence of nonempty closed subsets a of x to a nonempty closed subset a is to insist that we have pointwise convergence of the associated sequence of distance functionals for the sets a to the distance functional for the set a for each x e x c x a lim d x a convergence in this sense is just convergence with respect to the weak topology on the nonempty closed subsets cl x of x determined by the family of distance functionals d x e x e x the so called wijsman topology z l 8 determined by the metric p here of course each functional of the form d x 0 is a function of a closed set variable unfortunately different metrics may give rise to different wijsman topologies even if the metrics are uniformly equivalent see e g 4 section 41 it turns out 6 theorem 3 11 that if we vary our metrics over the class c x of metrics that give rise to the topology of x as well as varying x over x the resulting family

existence and differentiability of metric projections in hilbert spaces this paper considers metric projections onto a closed subset s of a hilbert space if the set s is convex then it is well known that the corresponding metric projections always exist unique and directionally differentiable at boundary points of s these properties of metric projections are considered for possibly nonconvex sets s in particular existence and directional differentiability of metric projections for certain classes of sets are established and will be referred to as nearly convex sets

calculus rules on a new set valued second order derivative for convex functions etant donnee une fonction convexe f qui a ete construite a partir d autres fonctions f i dont les differentielles secondes sont aisees a determiner on cherche a exprimer les differentielles secondes de f en fonction des 2 f i

a dual approach to inference for partially identified econometric models abstract this paper considers inference for the set i of parameter values that minimize a criterion function chernozhukov et al 2007 cht develop a general theory of estimation and inference using the level set of a criterion function we establish a dual relationship between the level set estimator and its support function and show that the properly normalized support function provides alternative wald type inference methods these methods can be used to obtain confidence sets for i and points inside it for models with finitely many moment inequalities we show that our wald type statistic is asymptotically equivalent to cht s statistic under regularity conditions

bulk surface and hull fractal dimension of critical ising clusters in d 2 the authors present accurate numerical calculations of the fractal dimension d and surface dimension ds of the critical ising cluster in d 2 the results clearly support the values d 187 96 ds 5 6 which are consistent with ising clusters being described by tricritical q 1 potts model exponents from this the hull dimension dh of critical ising clusters is found to be dh 11 8 consistent with numerical work of other authors

on the convergence of closed valued measurable multifunctions in this paper we study the convergence almost everywhere and in measure of sequences of closed valued multifunctions we first give a number of criteria for the convergence of sequences of closed subsets these results are used to obtain various characterizations for the convergence of measurable multifunctions in particular we are interested in the convergence properties of measurable selections

critical behaviour of non equilibrium q state systems we present two classes of non equilibrium models with critical behaviour each model is characterized by an integer q 1 and is defined on configurations of q valued spins on regular lattices the definitions of the models are very similar to the updating rules in wolff s algorithm for the potts model but both classes break detailed balance except for q 2 and q infinity in the first case both models reduce to the ising model while one of them reduces to percolation more precisely to the general epidemic process for q infinity locations of the critical point and critical exponents are estimated in two dimensions

convergence of functions equi semicontinuity the ever increasing complexity of the systems to be modeled and analyzed taxes the existing mathematical and numerical techniques far beyond our present day capabilities by their intrinsic nature some problems are so difficult to solve that at best we may hope to find a solution to an approximation of the original problem stochastic optimization problems except in a few special cases are typical examples of this class this however raises the question of what is a valid approximate to the original problem the design of the approximation must be such that i the solution to the approximate provides approximate solutions to the original problem and ii a refinement of the approximation yields a better approximate solution the classical techniques for approximating functions are of little use in this setting in fact very simple examples show that classical approximation techniques dramatically fail in meeting the objectives laid out above what is needed at least at a theoretical level is to design the approximates to the original problem in such a way that they satisfy an epi convergence criterion the convergence of the functions defining the problem is to be replaced by the convergence of the sets defined by these functions that type of convergence has many properties but for our purpose the main one is that it implies the convergence of the optimal solutions this article is devoted to the relationship between the epi convergence and the classical notion of pointwise convergence a strong semicontinuity condition is introduced and it is shown to be the link between these two types of convergences it provides a number of useful criteria which can be used in the design of approximates to difficult problems

on the convergence in probability of random sets measurable multifunctions it is shown that the convergence in probability of random sets introduced by salinetti and wets is consistent with the more standard definitions of convergence in probability and is metric invariant

directional differentiability of metric projections onto moving sets at boundary points soient x y des espaces normes de dimension finie et x y une multifonction assignant a chaque xex un ensemble ferme x cy a x sont associees la fonction distance d x y r et la projection metrique a valeur d ensemble x y y on etudie les proprietes differentielles de au voisinage d un point x 0 y 0 avec y 0 point limite de l ensemble x 0

short time dynamics of a two dimensional majority vote model short time monte carlo methods are used to study the nonequilibrium ferromagnetic phase transition in a majority vote model in two dimensions the existence of an initial critical slip regime is verified the measured values of dynamic exponents z 2 170 5 and ensuremath theta 0 191 2 are in excellent agreement with those of the kinetic ising model universality class

fractal dimensions of potts clusters potts clusters are connected sets of nearest neighbour sites for which the potts variable is in the same state at criticality there exists a fractal cluster using arguments from the renormalization group conformal invariance and numerical simulations the author determines the bulk surface hull and red bond dimension of these clusters as a function of the number of potts states

the design of trellis coded mpsk for fading channels performance criteria it has been well established that the appropriate criterion for optimum trellis coded modulation design on the additive white gaussian noise channel is maximization of the free euclidean distance it is shown that when the trellis coded modulation is used on a rician fading channel with interleaving deinterleaving the design of the code of optimum performance is guided by other factors in particular the length of the shortest error event path and the product of branch distances possibly normalized by the euclidean distance of the path along the path although maximum free distance d sub free is still an important consideration it plays a less significant role the more severe the fading is on the channel these considerations lead to the definition of a new distance measure of optimization of trellis codes transmitted over rician fading channels if no interleaving deinterleaving is used then once again the design of the trellis code is guided by maximizing d sub free