percolation processes in monomer polyatomic mixtures in this paper the percolation of mixtures of monomers and polyatomic species kk mers on a square lattice is studied by means of a finite size scaling analysis the critical exponents and the scaling collapsing of the fraction of percolating lattices are found a phase diagram separating a percolating from a non percolating region is determined the main features of the phase diagram are discussed in order to predict its evolution for larger kk mer sizes

random sequential addition a distribution function approach random sequential addition rsa of hard objects is an irreversible process defined by three rules objects are introduced on a surface or ad dimensional volume randomly and sequentially two objects cannot overlap and once inserted an object is clamped in its position the configurations generated by an rsa can be characterized in the macroscopic limit by a unique set of distribution functions and a density we show that these nonequilibrium rsa configurations can be described in a manner which in many respects parallels the usual statistical mechanical treatment of equilibrium configurations kirkwood salsburg like hierarchies for the distribution functions zero separation theorems diagrammatic expansions and approximate equations for the pair distribution function approximate descriptions valid for low to intermediate densities can be combined with exact results already derived for higher densities close to the jamming limit of the process similarities and differences between the equilibrium and the rsaconfigurations are emphasized finally the potential application of rsa processes to the study of glassy phases is discussed

time dependent perturbation theory for nonequilibrium lattice models we develop a time dependent perturbation theory for nonequilibrium interacting particle systems we focus on models such as the contact process which evolve via destruction and autocatalytic creation of particles at a critical value of the destruction rate there is a continuous phase transition between an active steady state and the vacuum state which is absorbing we present several methods for deriving series for the evolution starting from a single seed particle including expansions for the ultimate survival probability in the super and subcritical regions expansions for the average number of particles in the subcritical region and short time expansions algorithms for computer generation of the various expansions are presented rather long series 24 terms or more and precise estimates of critical parameters are presented

random cuts in binary mixtures of spheres three dimensional 3d disordered media may be studied by performing random planar cuts through the material and trying to go back to 3d geometry from two dimensional information we have studied from this point of view numerical packings of spheres of two sizes for which the radii of the spheres and the composition of the mixtures have been obtained from the cuts we have also studied the froths generated by the related laguerre voronoi tessellation of the packings and their cuts stereological relations in this specific frame are derived in both cases

competitive random sequential adsorption of point and fixed sized particles analytical results we study the kinetics of competitive random sequential adsorption rsa of particles of binary mixture of points and fixed sized particles within the mean field approach the present work is a generalization of the random car parking problem in the sense that it considers the case when either a car of fixed size is parked with probability q or the parking space is partitioned into two smaller spaces with probability 1 q at each time event this allows an interesting interplay between the classical rsa problem at one extreme q 1 and the kinetics of fragmentation processes at the other extreme q 0 we present exact analytical results for coverage for a whole range of q values and physical explanations are given for different aspects of the problem in addition a comprehensive account of the scaling theory emphasizing dimensional analysis is presented and the exact expression for the scaling function and exponents are obtained

kalman filtering with intermittent observations weak convergence to a stationary distribution the paper studies the asymptotic behavior of discrete time random riccati equations rre arising in kalman filtering when the arrival of the observations is described by a bernoulli independent and identically distributed i i d process we model the rre as an order preserving strongly sublinear random dynamical system rds under a sufficient condition stochastic boundedness and using a limit set dichotomy result for order preserving strongly sublinear rds we establish the asymptotic properties of the rre the sequence of random prediction error covariance matrices converges weakly to a unique invariant distribution whose support exhibits fractal behavior for stabilizable and detectable systems stochastic boundedness and hence weak convergence holds for any nonzero observation packet arrival probability and in particular we can establish weak convergence at operating arrival rates well below the critical probability for mean stability the resulting invariant measure in that situation does not possess a first moment we apply the weak feller property of the markov process governing the rre to characterize the support of the limiting invariant distribution as the topological closure of a countable set of points which in general is not dense in the set of positive semi definite matrices we use the explicit characterization of the support of the invariant distribution and the almost sure a s ergodicity of the sample paths to easily compute statistics of the invariant distribution a one dimensional example illustrates that the support is a fractured subset of the non negative reals with self similarity properties

random sequential adsorption of spheres of different sizes the random sequential adsorption of spheres selected from monodisperse binary and polydisperse distributions on a three dimensional substrate has been studied by computer simulations in the monodisperse case the adsorbed particle density algebraically approaches an asymptotic value of 0 384 0 001 according to feder s law feder j theor biol 87 1980 237 for the case of spheres of two different sizes the large sphere density approaches its asymptotic value exponentially while the small sphere density increases according to feder s law if the sphere radii ri are uniformly distributed over the range ra ri rb before testing for overlaps then the approach to the asymptotic density is algebraic but the effective exponent depends on the model parameter r rb ra

random sequential adsorption relationship to dead leaves and characterization of variability a new construction for the planar unbounded random sequential adsorption rsa model is presented which allows for a direct comparison with matheron s dead leaves model furthermore for the case of disks with random radii the problem of statistical determination of the proposal radius distribution is discussed finally second order characteristics related to the pair correlation function are suggested for describing the variability of the rsa disk systems

quantitative description and numerical simulation of random microstructures of composites and their effective elastic moduli abstract a digital image processing technique is used for measurement of centroid coordinates of fibers with forthcoming estimation of statistical parameters and functions describing the stochastic structure of a real fiber composite comparative statistical analysis of the real and numerically simulated structure are performed accompanying of known methods of the generation of random configurations by the random shaking procedure allows creating of the most homogenized and mixed structures that do not depend on the initial protocol of particle generation we consider a linearly elastic composite medium which consists of a homogeneous matrix containing a statistically homogeneous set of ellipsoidal inclusions the multiparticle effective field method see for references buryachenko appl mech rev 2001a 54 1 47 based on the theory of functions of random variables and green s functions is used for demonstration of the dependence of effective elastic moduli of fiber composites on the radial distribution functions estimated from the real experimental data as well as from the ensembles generated by the method proposed

kalman filtering with random coefficients and contractions the riccati transformation of linear filtering control theory is shown to be a contraction on the space of positive symmetric matrices this is used to describe the asymptotic behavior of the filter for systems with stochastic stationary parameters

precise algorithm to generate random sequential adsorption of hard polygons at saturation random sequential adsorption rsa is a time dependent packing process in which particles of certain shapes are randomly and sequentially placed into an empty space without overlap in the infinite time limit the density approaches a saturation limit although this limit has attracted particular research interest the majority of past studies could only probe this limit by extrapolation we have previously found an algorithm to reach this limit using finite computational time for spherical particles and could thus determine the saturation density of spheres with high accuracy in this paper we generalize this algorithm to generate saturated rsa packings of two dimensional polygons we also calculate the saturation density for regular polygons of three to ten sides and obtain results that are consistent with previous extrapolation based studies

geometry of random sequential adsorption by sequentially adding line segments to a line or disks to a surface at random positions without overlaps we obtain configurations of the one and two dimensional random sequential adsorption rsa problem we have simulated the one and two dimensional problem with periodic boundary condition the one dimensional simulations are compared with the exact analytical solutions to give an estimate of the accuracy of the simulation in two dimensions the geometrical properties of the rsa configuration are discussed and in addition known results of the rsa process are reproduced various statistical distributions of the voronoi dirichlet vd network corresponding to the rsa disk configuration are analyzed in order to characterize pores in the rsa configuration we introduce circular holes there is a direct correspondence between vertices of the vd network and these holes and also between direct indirect geometrical neighbors and these holes the hole size distribution is found to be a parabola we also find general relations that connect the asymptotic behavior of the surface coverage the correlation function and the hole size distribution

random sequential adsorption with restructuring in two dimensions a modified version of the random sequential adsorption model for the deposition of spherical particles onto a plane is presented successive particles are added via randomly positioned vertical trajectories and if they do not stick to the plane at first contact follow the path of steepest descent on the previously deposited particles before being adsorbed all particles reaching a stable position in contact with three previously adsorbed particles are removed the limiting coverage is found to be 0 610 56 or 0 000 05 larger than that of the standard rsa model and is shown to be reached exponentially with the number of trials the size distribution of connected clusters of spheres is analysed and is found to exhibit an exponential decay for large cluster sizes

random sequential adsorption of polydisperse mixtures asymptotic kinetics and structure the authors study the asymptotic kinetics of the random sequential adsorption rsa of a mixture of particles with a continuous distribution of sizes their results provide further support for the idea that the power law exponent for the approach to the jamming limit is simply related to the number of degrees of freedom of the adsorbing species they also predict the behaviour of the mean radial distribution function in the asymptotic regime

on estimation error outage for scalar gauss markov signals sent over fading channels measurements of a scalar linear gauss markov process are sent over a fading channel the fading channel is modeled as independent and identically distributed random variables with known realization at the receiver the optimal estimator at the receiver is the kalman filter in contrast to the classical kalman filter theory given a random channel the kalman gain and the error covariance become random then the probability distribution function of expected estimation error and its outage probability can be chosen for estimation quality assessment in this paper and in order to get the estimation error outage we provide means to characterize the stationary probability density function of the random expected estimation error furthermore and for the particular case of the i i d rayleigh fading channels upper and lower bounds for the outage probability are derived which provide insight and simpler means for design purposes we also show that the bounds are tight for the high snr regime and that the outage probability decreases linearly with the inverse of the average channel snr

random sequential adsorption on a 3 infinity lattice an exact solution the dynamics of a random sequential adsorption process on a quasi one dimensional lattice with three rows is solved exactly the long time behaviour of the coverage density is rho t 1 3 2 exp 2 3 t 9 it is shown that the number of connected lattice animals increases like n 23 indicating that most two dimensional lattice animals are non compact

an overlapping detection algorithm for random sequential packing of elliptical particles abstract random sequential packing of particles is a subject of intense research in many branches of physics and engineering the preponderance of preview work has focused on spherical particles and little is known about non overlapping elliptical particles in the present work a new numerical algorithm is developed to detect overlapping of ellipses by a series of sequential coordinate transformations and a novel golden section search algorithm the accuracy and efficiency of the numerical algorithm are tested and compared with algorithms developed in previous literature its stability is verified by visualizations of random sequential packing of monodispersed and polydispersed ellipses with different boundary conditions then the algorithm is applied to investigate the influence of the shape of ellipses on the random packing fraction as well as to study the influence of the shape and size of ellipses on the wall effect in the particle packing structure and some numerical results are demonstrated finally the reliability of the numerical algorithm extended to the three dimensional space is also evaluated by checking overlapping of ellipsoidal particles

some relations between extended and unscented kalman filters the unscented kalman filter ukf has become a popular alternative to the extended kalman filter ekf during the last decade ukf propagates the so called sigma points by function evaluations using the unscented transformation ut and this is at first glance very different from the standard ekf algorithm which is based on a linearized model the claimed advantages with ukf are that it propagates the first two moments of the posterior distribution and that it does not require gradients of the system model we point out several less known links between ekf and ukf in terms of two conceptually different implementations of the kalman filter the standard one based on the discrete riccati equation and one based on a formula on conditional expectations that does not involve an explicit riccati equation first it is shown that the sigma point function evaluations can be used in the classical ekf rather than an explicitly linearized model second a less cited version of the ekf based on a second order taylor expansion is shown to be quite closely related to ukf the different algorithms and results are illustrated with examples inspired by core observation models in target tracking and sensor network applications

random sequential adsorption of lines and ellipses infinitely many lines of zero thickness may be adsorbed onto a plane without overlap and it is shown that the number of lines adsorbed should scale as 13 where is the number of adsorption trials per unit area of surface this is confirmed by numerical simulation the adsorption of ellipses with major and minor axes 2a 2b respectively is also studied the area coverage theta approaches its maximum value theta max as alpha as to infinity where alpha is typically 1 3 as b a decreases from unity theta max first increases to a maximum value 0 58 or 0 01 when b approximately 0 5 and then decreases a feature not noted in previous work

distortion outage analysis for joint space time coding and kalman filtering in this paper we consider the scenario of transmitting a first order gauss markov vector signal over a multi input multi output mimo rayleigh nonfrequency selective fading channel the signal is reconstructed at the receiver side with the help of a kalman filter in order to minimize the mean squared error orthogonal space time codes are utilized in order to increase the quality of estimation and mitigate the destructing effects of the fading channel as a criterion for estimation quality assessment we use the distortion outage probability we first obtain upper and lower bounds for the outage probability as a function of system parameters we then perform high snr analysis of the bounds through which we prove the achievability of the maximum diversity order for a n times k mimo fading channel in addition we obtain upper and lower bounds for the coding gain of the distortion outage probability in the high snr regime and outline the relation between system parameters and the coding gain

saturation coverage in random sequential adsorption of very elongated particles abstract in the random sequential adsorption rsa of unoriented anisotropic objects onto a flat uniform surface the saturation coverage goes to zero when the aspect ratio of the objects becomes infinite by scaling arguments we show that follows a power law p where p 1 1 2 2 the fractal dimension of the system of adsorbed needles is also discussed

generalized fs w versus dyson s classification of irreducible representations we study the characterization of the 13 cases obtained in the classification of the irreducible linear antilinear representations of semigroups in a finite dimensional vector space x over an algebraically closed field k with a conjugation j generalized frobenius schur wigner or fs w classification it has already been shown that each case can be characterized by various equivalent properties some of which can be endowed with a physical interpretation we show here that whenever k is the complex field c each case can be characterized by the structure in the sense specified by the weyl theorem on the structure of the matrix algebras and their commutators of a pair of suitable operator algebras over the real field r this characterization coincides with the one given by dyson for each case of his classification of symmetry groups thus the latter classification is recovered under more general assumptions and in a generalized framework and its one to one correspondence with the generalized fs w cla

joint source channel codes for mimo block fading channels we consider transmission of a continuous amplitude source over an l block rayleigh fading mt x mr multiple input multiple output mimo channel when the channel state information is only available at the receiver since the channel is not ergodic shannon s source channel separation theorem becomes obsolete and the optimal performance requires a joint source channel approach our goal is to minimize the expected end to end distortion particularly in the high signal to noise ratio snr regime the figure of merit is the distortion exponent defined as the exponential decay rate of the expected distortion with increasing snr we provide an upper bound and lower bounds for the distortion exponent with respect to the bandwidth ratio among the channel and source bandwidths for the lower bounds we analyze three different strategies based on layered source coding concatenated with progressive superposition or hybrid digital analog transmission in each case by adjusting the system parameters we optimize the distortion exponent as a function of the bandwidth ratio we prove that the distortion exponent upper bound can be achieved when the channel has only one degree of freedom that is l 1 and min mt mr 1 when we have more degrees of freedom our achievable distortion exponents meet the upper bound for only certain ranges of the bandwidth ratio we demonstrate that our results which were derived for a complex gaussian source can be extended to more general source distributions as well

a precise algorithm to detect voids in polydisperse circle packings computer simulations are the primary tool for studying polydisperse particle packings quanti tatively for the problem of packing n unequal circles in a larger container circle nothing is known a priori about the optimal packing i e the packing with the highest packing fraction simulations usually start from a random initial configuration with the aim to finish with a dense final packing unfortunately smaller circles often get stuck in trapped positions and prevent the rest of the packing from growing larger hence the knowledge of the structure of unoccupied areas or holes inside a packing is important to be able to move trapped circles into free circular places or voids a novel algorithm is proposed for detecting such voids in two dimensional arbitrary circle packings by a decomposition of the contact graph combined with a clever object jumping strategy and together with other heuristic methods like swaps and shifts this approach increases the packing fraction significantly its effectiveness for jumping across the maximally random jammed barrier mrj 0 8575 in the large n limit for small benchmark instances as well as for large problem sizes up to n 103 is demonstrated

pair correlation function in random sequential adsorption processes an analytical expression of the pair distribution function is derived for the car parking problem and for the random sequential adsorption of k mers onto a one dimensional lattice both on a lattice and in the continuum limit super exponential decay of the distribution function is observed a comparison of the spatial correlations with those at equilibrium demonstrates the influence of the irreversibility of the rsa process

diversity effects in kalman filtering over rayleigh fading channels a scalar first order gauss markov signal is sent over d parallel i i d rayleigh fading channels using uncoded transmission assuming perfect channel estimation at the receiver the optimal mmse estimator is the kalman filter with random instantaneous estimation error variance statistical characteristics of the instantaneous estimation error variance are studied to characterize the estimation quality one such characteristic is the estimation error outage which probabilistically depicts how often the value of the instantaneous estimation error variance exceeds a certain threshold in this paper we study the effect of channel diversity on the estimation error outage probability we show that for a certain range of outage thresholds the estimation error outage probability decreases with inverse of d th power of the average signal to noise ratio at the receiver side this means that analogous to the context of digital communication over fading channels our result implies a diversity order of d in estimating the input process

irreducible linear antilinear representations and internal symmetries we reconsider a well known classification due to wigner of the unitary antiunitary finite dimensional irreducible group representations within a somewhat generalized mathematical framework where in particular any algebraically closed field k with an involutory automorphism j is considered in place of the complex field c we show that each case of the classification can be characterized by the set u l of the linear mappings that commute with the given set u which is now assumed to be an irreducible semigroup of linear and antilinear i e j semilinear mappings and explicitly exhibit u l then this classification is crossed with the classification of the sets of linear and antilinear mappings that has been obtained in some previous work and that generalizes the old classification of the unitary representations introduced by frobenius and schur we obtain a new classification in which every case can be characterized by the group uc of the invertible linear and antilinear mappings which commute with

kinetics and fractal properties of the random sequential adsorption of line segments the random sequential adsorption rsa of infinitely thin line segments is studied by computer simulation it is shown that the exponent for the time dependence of the surface coverage increases beyond the value 0 33 reported by sherwood 1990 to a value of 0 38 at later times it is also argued that the fractal dimension of the adsorbed lines is about 1 8 making use of a previous result on the rsa of rectangular objects

path integral representation for a stochastic sandpile we introduce an operator description for a stochastic sandpile model with a conserved particle density and develop a path integral representation for its evolution the resulting exact expression for the effective action highlights certain interesting features of the model for example it is nominally massless and the dynamics is via cooperative diffusion using the path integral formalism we construct a diagrammatic perturbation theory yielding a series expansion for the activity density in powers of time

scaling properties of the number of random sequential adsorption iterations needed to generate saturated random packing the properties of the number of iterations in random sequential adsorption protocol needed to generate finite saturated random packing of spherically symmetric shapes were studied numerical results obtained for one two and three dimensional packings were supported by analytical calculations valid for any dimension d it has been shown that the number of iterations needed to generate finite saturated packing is subject to pareto distribution with exponent 1 1 d and the median of this distribution scales with packing size according to the power law characterized by exponent d obtained results can be used in designing effective random sequential adsorption simulations

a framework for state space estimation with uncertain models develops a framework for state space estimation when the parameters of the underlying linear model are subject to uncertainties compared with existing robust filters the proposed filters perform regularization rather than deregularization it is shown that under certain stabilizability and detectability conditions the steady state filters are stable and that for quadratically stable models the filters guarantee a bounded error variance moreover the resulting filter structures are similar to various time and measurement update prediction and information forms of the kalman filter albeit ones that operate on corrected parameters rather than on the given nominal parameters simulation results and comparisons with spl hscr sub spl infin guaranteed cost and set valued state estimation filters are provided

robust extended kalman filtering linearization errors inherent in the specification of an extended kalman filter ekf can severely degrade its performance this correspondence presents a new approach to the robust design of a discrete time ekf by application of the robust linear design methods based on the h sub spl infin norm minimization criterion the results of simulations are presented to demonstrate an advantage for signal demodulation and nonlinear equalization applications

mean square stability for kalman filtering with markovian packet losses this paper studies the stability of kalman filtering over a network subject to random packet losses which are modeled by a time homogeneous ergodic markov process for second order systems necessary and sufficient conditions for stability of the mean estimation error covariance matrices are derived by taking into account the system structure while for certain classes of higher order systems necessary and sufficient conditions are also provided to ensure stability of the mean estimation error covariance matrices all stability criteria are expressed by simple inequalities in terms of the largest eigenvalue of the open loop matrix and transition probabilities of the markov process their implications and relationships with related results in the literature are discussed

packing of spheroids in three dimensional space by random sequential addition packings of spheroidal particles with semi axes of length a b b were generated by random sequential addition rsa simulations as the jamming limit is approached the volume fraction occupied by particles tends towards an asymptote which was determined as a function of aspect ratio this asymptote has a local minimum at spheres with local maxima at prolate spheroids and oblate values of agree with results from rsa simulations of sphere packings but lie below volume fractions obtained in simulations of near spheres packed under gravity volume fractions reported for simulations of spheroids packed under gravity vary widely when the aspect ratio is very large or small differences between these results and the predictions of rsa are discussed

on the dynamics of random sequential absorption the dynamics of random sequential absorption on d dimensional lattices is represented by a simple graphical expansion results for the entire filling process and in particular its saturation limit are easily obtained it is shown that the large d limit of the saturation density is ln 2d 2d the expression gives an accurate approximation for d or 3

random sequential adsorption line segments on the square lattice we study kinetics of the rmgle layer random sequenrisl adsorption of lint segments of ked kn5h on the square iatijcc by a monte carlo srmulatton the area covered b the line segments grows with time and finally reacher a jamming limit when no more adsorption is possible the jamming coverage depends on the segment length and 11s vanation is studted at the late stage approach of the coverage to the jamming limit is arymptotieally exponential with a rate found to be independent of the segment length based on our monte carlo data an act expression for the late stage deposition kinettcs 15 conjectured random sequential adsorption rsa has been the subject of much recent experimental and theoretical investigation objects of figte size are randomly deposited adsorbed on an initially empty substrate so that no two objects overlap the quantity of interest is the fraction of the total area b f in time i covered by the depositing particles due to the blocking of the area by the already randomly adsorbed particles the limiting 3amming coverage co is less than the close packing the emergence of this jammed state is iduenced by the infiuite memory effects consequently its formation cannot he described by mean field theory except for very early times when 6 t af experimental studies 11 41 include e g adhesion of colloidal particles 131 and proteins 2 on homogeneous substrates with relaxation times much longer than the formation time of deposits theoretical studies s 171 of rsa include series expansions is l j numerical monte carlo mc simulations 9 14 16 and some analytical results 1171 mostly for one dimensional systems in such studies it was shown that the precise form of the long time behaviour of b r depends on the shape and orientational freedom of the adsorbing particles earlier studies have focused on continuum deposition models for which a power law behaviour of the late stage deposition 1171

monte carlo simulation of the percolation process caused by the random sequential adsorption of k mers on heterogeneous triangular lattices abstract mixed site bond percolation is studied for a random sequential adsorption process of k mers on heterogeneous lattices with variable connectivity by means of monte carlo simulation the percolation phase diagrams are built to render evidence about complex structures critical exponents are also calculated to show that the universality class corresponding to ordinary percolation in two dimensions is preserved

lattice free models of directed cell motility directed cell migration often occurs when individual cells move in response to an external chemical stimulus cells can respond by moving in either the direction of increasing chemoattraction or decreasing chemorepulsion concentration many previous models of directed cell migration use a lattice based framework where agents undergo a lattice based random walk and the direction of nearest neighbour motility events is biased in a preferred direction such lattice based models can lead to unrealistic configurations of agents since the agents always move on an artificial lattice structure which is never observed experimentally we present a lattice free model of directed cell migration that incorporates two key features first agents move on a continuous domain with the possibility that there is some preferred direction of motion second to be consistent with experimental observations we enforce a crowding mechanism so that motility events that would lead to agent overlap are not permitted we compare simulation data from the new lattice free model with a more traditional lattice based model to provide additional insight into the lattice free model we construct an approximate conservation statement which corresponds to a nonlinear advection diffusion equation in the continuum limit the solution of this mean field model compares well with averaged data from the individual based model

probability distribution function for the random sequential adsorption of hard disks abstract the distribution of the number of hard core objects deposited in a finite region through a random sequential adsorption process is analyzed three idealized model probability distributions for this problem are tested by comparing them with computer simulation distributions for the random sequential adsorption of hard disks on a flat surface a hypergeometric distribution where the effects of mutual exclusion between particles are incorporated by a coverage dependent effective volume per particle is shown to give best agreement with simulation results this effective volume is derived in terms of the fluctuations in the particle number finite size effects in the fluctuations are taken into account

irreversible random and cooperative process on lattices direct determination of density expansions abstract for processes where events occur irreversibly and in general cooperatively at the sites of a lattice hierarchies of rate equations for the probabilities of configurations of events can be written down immediately provided the cooperative effects have finite range mostly truncation methods of solution have been implemented here we present a direct method of determination of formal density expansions and investigate some properties of the solution of these hierarchies the basic technique is demonstrated by several explicit examples and is readily applied to handle lattices which are finite semi infinite of infinite uniform periodic or with defective sites and to processes involving monomer or polyatomic filling or competing events

quaternionic representations of magnetic groups we study magnetic groups which contain a time inversion operator besides spatial symmetries in the framework of quaternionic group representation theory we obtain a classification of these groups depending on the reducibility of their spatial part and then we cross it with the generalized frobenius schur classification that has been obtained by ourselves elsewhere ten distinct cases arise but only five of them apply to factorizable groups i e groups in which the time inversion operator appears alone and not multiplied by a spatial symmetry we supply examples for these five cases and determine which of them apply to bosonic or fermionic systems respectively finally we discuss the degeneracy of energy levels in the presence of a time reversal symmetry kramers degeneracy in quaternionic quantum mechanics obtaining right values in all cases

on the distortion snr exponent of hybrid digital analog space time coding we consider the transmission of a real independent and identically distributed i i d analog source over a quasi static m input n output multiple input multiple output mimo block fading channel the relevant performance criterion is end to end average quadratic distortion d versus channel signal to noise ratio snr for given spectral efficiency eta defined as the ratio of the source bandwidth over the channel bandwidth in the limit of high snr we define the distortion snr exponent a eta as the largest a such that d esdot snr a over all possible source channel coding schemes of spectral efficiency eta we find a simple upper bound on a eta an achievable lower bound asep eta achievable by separated tandem source channel coding and a tighter lower bound ahybrid eta achievable by new hybrid digital analog space time coding schemes as a corollary we have that a eta is completely determined for the scalar case m n 1 and for the bandwidth compression case eta ges 2 min m n expiicit and simple construction of hybrid space time codes achieving ahybrid eta are also given

equilibrium versus random sequential addition of dimers on a lattice the statistical mechanical properties of particles forming dimers are compared with the results obtained on a two dimensional lattice through a random sequential addition rsa experiment the relation between the most likely fraction of dimers filling the lattice at equilibrium in the disordered phase and the corresponding non equilibrium jamming limit attained through rsa is explored some implications relevant for the physics of the liquid state are also discussed

an algorithm for series expansions based on hierarchical rate equations we propose a computational method to obtain series expansions in powers of time for general dynamical systems described by a set of hierarchical rate equations the method is generally applicable to problems in both equilibrium and non equilibrium statistical mechanics such as random sequential adsorption diffusion reaction dynamics and ising dynamics a new result for random sequential adsorption of dimers on a square lattice is presented

on the random filling of rd by non overlapping d dimensional cubes abstract we compute the time dependent coverage in the random sequential adsorption of aligned d dimensional cubes in r d using time series expansions the seventh order series in 2 3 and 4 dimensions is resummed in order to predict the coverage at jamming the result is in agreement with monte carlo simulations a simple argument based on a property of the pertubative expansion valid at arbitrary orders allows us to analytically derive some generalizations of the palasti approximation

exact bounds from a new series expansion method for random sequential adsorption we present a new series expansion method for the analysis of the covering fraction theta in a random sequential adsorption process with nearest neighbour exclusion on a lattice it is the first method to yield sequences of increasing lower bounds and decreasing upper bounds on theta it is illustrated by numerical calculations for the hexagonal lattice

adaptive kalman filtering in networked systems with random sensor delays multiple packet dropouts and missing measurements in this paper adaptive filtering schemes are proposed for state estimation in sensor networks and or networked control systems with mixed uncertainties of random measurement delays packet dropouts and missing measurements that is all three uncertainties in the measurement have certain probability of occurrence in the network the filter gains can be derived by solving a set of recursive discrete time riccati equations examples are presented to demonstrate the applicability and performances of the proposed schemes

effect of packing method on the randomness of disc packings the randomness of disc packings generated by random sequential adsorption rsa random packing under gravity rpg and mason packing mp which gives a packing density close to that of the rsa packing has been analysed based on the delaunay tessellation and is evaluated at two levels i e the randomness at individual subunit level which relates to the construction of a triangle from a given edge length distribution and the randomness at network level which relates to the connection between triangles from a given triangle frequency distribution the delaunay tessellation itself is also analysed and its almost perfect randomness at the two levels is demonstrated which verifies the proposed approach and provides a random reference system for the present analysis it is found that i the construction of a triangle subunit is not random for the rsa mp and rpg packings with the degree of randomness decreasing from the rsa to mp and then to rpg packing ii the connection of triangular subunits in the network is almost perfectly random for the rsa packing acceptable for the mp packing and not good for the rpg packing packing method is an important factor governing the randomness of disc packings

random sequential adsorption series expansion and monte carlo simulation abstract random sequential adsorption is an irreversible surface deposition of extended objects in systems with continuous degrees of freedom coverage follows a power law t j ct where the exponent depends on the geometric shape symmetry of the objects lattice models give typically exponential saturation to jamming coverage we discuss how such function t can be computed by series expansions and analyzed with pade approximations we consider the applications of efficient monte carlo computer simulation method event driven method to random sequential adsorptions with high precision and at very long time scale

kinetics of random sequential parking on a line we study the kinetics of irreversible random sequential parking of intervals of different sizes on an infinite line for the simplest fixed length parking distribution the model reduces to the known car parking problem and we present an alternate solution to this problem we also consider the general homogeneous case when the parking distribution varies asx 1 atx 1 with the lengthx of the filling interval we develop a scaling theory describing such mixture deposition processes and show that the scaled hole size distribution with xtz a scaling variable decays with the scaled mass as exp const 1 as we determine scaling exponentsz and and find that at large times the coverage t has a power law form 1 t t v with nonuniversal exponent 2 1 depending on the homogeneity index

kinetics of growing and coalescing droplets a class of mean field models for the patterns formed by growing and coalescing droplets on a line is introduced and solved all the models are found to have a scale invariant regime where the patterns are self similar in time

stability of a random riccati equation with markovian binary switching this paper is concerned with the boundedness of the solution of a random riccati difference equation arising from kalman filtering with observation losses characterized by a markovian binary jump parameter a new sufficient condition for stability in the peak covariance sense is obtained which has a simpler form and is shown to be less conservative for systems with the observability index of two than existing works meanwhile we give some conditions under which the covariance matrix is bounded or unbounded in the usual sense then the equivalence between the peak covariance stability and the usual covariance stability is established for systems with the observability index of one and independent and identically distributed i i d observation losses

random sequential addition of hard spheres in high euclidean dimensions sphere packings in high dimensions have been the subject of recent theoretical interest employing numerical and theoretical methods we investigate the structural characteristics of random sequential addition rsa of congruent spheres in d dimensional euclidean space mathbb r d in the infinite time or saturation limit for the first six space dimensions 1 ensuremath le d ensuremath le 6 specifically we determine the saturation density pair correlation function cumulative coordination number and the structure factor in each of these dimensions we find that for 2 ensuremath le d ensuremath le 6 the saturation density ensuremath phi s scales with dimension as ensuremath phi s c 1 2 d c 2 d 2 d where c 1 0 202 phantom rule 0 2em 0ex 048 and c 2 0 973 phantom rule 0 2em 0ex 872 we also show analytically that the same density scaling is expected to persist in the high dimensional limit albeit with different coefficients a byproduct of this high dimensional analysis is a relatively sharp lower bound on the saturation density for any d given by ensuremath phi s ensuremath ge d 2 1 ensuremath s 0 2 d 1 where s 0 0 1 is the structure factor at k 0 i e infinite wavelength number variance in the high dimensional limit we demonstrate that a pal asti type conjecture the saturation density in mathbb r d is equal to that of the one dimensional problem raised to the d th power cannot be true for rsa hyperspheres we show that the structure factor s k must be analytic at k 0 and that rsa packings for 1 ensuremath le d ensuremath le 6 are nearly hyperuniform consistent with the recent decorrelation principle we find that pair correlations markedly diminish as the space dimension increases up to six we also obtain kissing contact number statistics for saturated rsa configurations on the surface of a d dimensional sphere for dimensions 2 ensuremath le d ensuremath le 5 and compare to the maximal kissing numbers in these dimensions we determine the structure factor exactly for the related ghost rsa packing in mathbb r d and demonstrate that its distance from hyperuniformity increases as the space dimension increases approaching a constant asymptotic value of 1 2 our work has implications for the possible existence of disordered classical ground states for some continuous potentials in sufficiently high dimensions