monte carlo renormalization of the three dimensional ising model abstract we have investigated the simple cubic ising model by means of the monte carlo renormalization technique the emphasis of our study concerns the influence of truncation i e the dimensionality of the coupling subspace in which the analysis of the correlation functions generated by the monte carlo and spin blocking algorithms is performed to this purpose we have included up to 36 even and 21 odd couplings in our analysis we find that the increase in the number of couplings has a significant influence on the largest eigenvalues of the linearized renormalization transformation matrices these eigenvalues serve to estimate the renormalization exponents yi and yh remarkably we find no significant finite size effect on these eigenvalues when the maximum number of couplings is included in the analysis except for the smallest system sizes 83 43 after a suitable extrapolation to the fixed point we find good agreement with existing results for the critical exponents we have determined the critical point of the simple cubic ising model as k 0 221652 6 also in agreement with existing results

backward bifurcation analysis of epidemiological model with partial immunity this paper presents a two stage sis epidemiological model in animal population with bovine tuberculosis btb in african buffalo as a guiding example the proposed model is rigorously analyzed the analysis reveals that the model exhibits the phenomenon of backward bifurcation where a stable disease free equilibrium dfe coexists with a stable endemic equilibrium ee when the associated reproduction number r v is less than unity it is shown under two special cases of the presented model that this phenomenon of backward bifurcation does not arise depending on vaccination coverage and efficacy of vaccine numerical simulations of the model show that the use of an imperfect vaccine can lead to effective control of the disease if the vaccination coverage and the efficacy of vaccine are high enough

vectorized search for single clusters breadth first search for a single cluster on a regular lattice is shown to be vectorizable it is applied to construct clusters in the single cluster variant of the swendsen wang algorithm on a cray ymp total cpu time has been reduced by factors of 3 5 7 in large scale applications a multiple cluster version is also described

the capacity region of the gaussian multiple input multiple output broadcast channel the gaussian multiple input multiple output mimo broadcast channel bc is considered the dirty paper coding dpc rate region is shown to coincide with the capacity region to that end a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequality to show that a superposition of gaussian codes is optimal for the degraded vector broadcast channel and that dpc is optimal for the nondegraded case furthermore the capacity region is characterized under a wide range of input constraints accounting as special cases for the total power and the per antenna power constraints

causes of backward bifurcations in some epidemiological models abstract the phenomenon of backward bifurcation in disease transmission models where a stable endemic equilibrium co exists with a stable disease free equilibrium when the associated reproduction number is less than unity has been observed in a number of disease transmission models the epidemiological consequence of backward bifurcation is that the classical requirement of the reproduction number being less than unity becomes only a necessary but not sufficient for disease elimination hence the presence of this phenomenon in the transmission dynamics of a disease makes its effective control in the community difficult this paper addresses the problem of finding the causes of backward bifurcation in some standard deterministic models for the spread of some emerging and re emerging diseases it contains a brief review of some common causes as well as some new causes of backward bifurcation in some standard disease transmission models it is shown that in addition to the usual causes such as the use of imperfect vaccine and exogenous re infection in tb disease a number of other biological or epidemiological mechanisms such as vaccine derived immunity waning at a slower rate than natural immunity disease induced mortality in vector borne diseases and differential susceptibility in risk structured models could also cause backward bifurcation in disease transmission models

remote vector gaussian source coding with decoder side information under mutual information and distortion constraints let x y z be zero mean jointly gaussian random vectors of dimensions nx ny and nz respectively let p be the set of random variables w such that w harr y harr x z is a markov string we consider the following optimization problem wisinp min i y z subject to one of the following two possible constraints 1 i x w z ges ri and 2 the mean squared error between x and xcirc e x w z is less than d the problem under the first kind of constraint is motivated by multiple input multiple output mimo relay channels with an oblivious transmitter and a relay connected to the receiver through a dedicated link while for the second case it is motivated by source coding with decoder side information where the sensor observation is noisy in both cases we show that jointly gaussian solutions are optimal moreover explicit water filling interpretations are given for both cases which suggest transform coding approaches performed in different transform domains and that the optimal solution for one problem is in general suboptimal for the other

system size dependence of the autocorrelation time for the swendsen wang ising model abstract we present monte carlo simulation results of the autocorrelation time for the swendsen wang method for the simulation of the ising model we have calculated the exponential and the integrated autocorrelation time at the critical point t c of the two dimensional ising model our results indicate that both autocorrelation times depend logarithmically on the linear system size l instead of a power law the simulations were carried out on the parallel computer of the condensed matter theory group at the university of mainz

the dynamical critical exponent of the two three and five dimensional kinetic ising model abstract we present monte carlo simulation results for the dynamical critical exponent z of the two three and five dimensional kinetic ising model we used glauber as well as metropolis dynamics both type of dynamics lead to the same z values in two and three dimensions the z values were calculated from the magnetization relaxation from an ordered state into the equilibrium state at tc for very large systems up to 169984 2 3072 3 and 48 5 for the two dimensional case we obtain z 2 21 0 03 and for the three dimensional case z 2 08 0 03 for the five dimensional glauber case the requirement z 2 gives a critical point j kbtc 0 11391 from monte carlo simulations whereas new series expansions with four more terms give 0 113935 0 000015 for this ratio

simulation of mandelbrot s self similarity for square site critical percolation clusters and random walks abstract each site visited by a walker or occupied by an incipient infinite percolation cluster is surrounded by a neighborhood of size b the total area within a square of size r covered by these neighborhoods then is found to obey self similarity if 1 b r l where l is the linear dimension of lattice or walk

on the optimality of binning for distributed hypothesis testing we study a hypothesis testing problem in which data are compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data the aim is to characterize all achievable encoding rates and exponents of the type 2 error probability when the type 1 error probability is at most a fixed value for related problems in distributed source coding schemes based on random binning perform well and are often optimal for distributed hypothesis testing however the use of binning is hindered by the fact that the overall error probability may be dominated by errors in the binning process we show that despite this complication binning is optimal for a class of problems in which the goal is to test against conditional independence we then use this optimality result to give an outer bound for a more general class of instances of the problem

rate region of the vector gaussian ceo problem with the trace distortion constraint we establish a new extremal inequality which is further leveraged to give a complete characterization of the rate region of the vector gaussian ceo problem with the trace distortion constraint the proof of this extremal inequality hinges on a careful analysis of the karush kuhn tucker necessary conditions for the non convex optimization problem associated with the berger tung scheme which enables us to integrate the perturbation argument by wang and chen and the distortion projection method by rahman and wagner

a parallel multigrid algorithm for percolation clusters a new parallel cluster finding algorithm is formulated by using multigrid relaxation methods very similar to those used for differential equation solvers for percolation clusters this approach drastically reduces critical slowing down relative to local or scan relaxation methods numerical studies of scaling properties with system size are presented in the case of the 2d percolation clusters of the swendsen wang ising dynamics running on the connection machine

cluster monte carlo algorithms abstract the swendsen wang and wolff monte carlo algorithms are described in some detail using the potts model as an example various generalizations are then reviewed and some applications are discussed two complete fortran programs for the algorithms are provided

non equilibrium critical relaxation of the three dimensional ising model abstract the non equilibrium relaxation process at the critical point is studied using monte carlo simulation for the ferromagnetic ising model on a cubic lattice it was observed that the time dependent magnetization decayed following a power law t from the all up initial condition three kinds of single spin flip dynamics were studied for several lattices up to 1536 3 the system size dependences are also studied the value of was estimated to be 0 250 2 this value of leads to the estimation of the dynamical exponent z to be 2 06 2 if we assume z where and denote the critical exponents for spontaneous magnetization and correlation length in equilibrium state respectively and 0 515 the result of the non equilibrium relaxation in the ordered phase is also given

energy relaxation in ising models starting with all spins parallel simulations show the energy to relax at the critical point as t 1 z with z near 2 2 for 1699802 no logarithm and 2 1 for 28003

non equilibrium relaxation and interface energy of the ising model abstract from the non equilibrium critical relaxation study of the two dimensional ising model the dynamical critical exponent z is estimated to be 2 165 0 010 for this model the relaxation in the ordered phase of this model is consistent with exp t behavior the interface energy of the three dimensional ising model is studied and the critical exponent of the correlation length and the critical amplitude of the surface tension 0 are estimated to be 0 6250 0 0025 and 1 42 0 04 respectively a dynamic monte carlo renormalization group method is successfully applied to the equilibrium properties of the three dimensional ising model

single cluster monte carlo dynamics for the ising model we present an extensive study of a new monte carlo acceleration algorithm introduced by wolff for the ising model it differs from the swendsen wang algorithm by growing and flipping single clusters at a random seed in general it is more efficient than swendsen wang dynamics ford 2 giving zero critical slowing down in the upper critical dimension monte carlo simulations give dynamical critical exponentszw 0 33 0 05 and 0 44 0 10 ind 2 and 3 respectively and numbers consistent withzw 0 ind 4 and mean field theory we present scaling arguments which indicate that the wolff mechanism for decorrelation differs substantially from swendsen wang despite the apparent similarities of the two methods

rate region of the gaussian scalar help vector source coding problem we determine the rate region of the gaussian one helper source coding problem in which the helper observes a scalar the main encoder observes a vector and the distortion constraint is a positive semidefinite upper bound on the error covariance matrix of the main source the rate region is achieved by a gaussian achievable scheme we introduce a novel outer bounding technique to establish the converse our approach is to create a reduced dimensional problem by projecting the main source and the distortion constraint in certain directions determined by the optimal gaussian scheme we also provide an outer bound to the rate region of the more general problem in which there are distortion constraints on both sources this outer bound is partially tight in general and completely tight in some nontrivial cases

gaussian state amplification with noisy observations we consider the problem of channel state amplification in a gaussian channel with additive gaussian channel states where the encoder observes noncausally a noisy version of these states a complete characterization is provided for the minimum reconstruction distortion under a transmitter power constraint and it is shown that a simple analog scheme with power control is optimal more precisely if the power available to the encoder is below certain threshold the analog scheme using full power is optimal however when the power available to the encoder is above that threshold analog transmission using only a fixed amount of the available power is optimal furthermore the problem of simultaneous message transmission and gaussian state amplification with noisy observations is studied for which an inner bound and two nontrivial outer bounds to the optimal tradeoff between the transmission rate and the state reconstruction distortion are provided the coding scheme underlying the inner bound combines analog signaling and gelfand pinsker coding where the latter deviates from the operating point of costa s dirty paper coding the first outer bound is obtained by extending the channel decomposition technique while the second outer bound requires a strategic analysis of the covariance matrix of the relevant random variables

global results for an epidemic model with vaccination that exhibits backward bifurcation vaccination of both newborns and susceptibles is included in a transmission model for a disease that confers immunity the interplay of the vaccination strategy together with the vaccine efficacy and waning is studied in particular it is shown that a backward bifurcation leading to bistability can occur under mild parameter constraints compound matrices are used to show that each orbit limits to an equilibrium in the case of bistability this global result requires a novel approach since there is no compact absorbing set

the distributed karhunen loeve transform the karhunen loeve transform klt is a key element of many signal processing and communication tasks many recent applications involve distributed signal processing where it is not generally possible to apply the klt to the entire signal rather the klt must be approximated in a distributed fashion this paper investigates such distributed approaches to the klt where several distributed terminals observe disjoint subsets of a random vector we introduce several versions of the distributed klt first a local klt is introduced which is the optimal solution for a given terminal assuming all else is fixed this local klt is different and in general improves upon the marginal klt which simply ignores other terminals both optimal approximation and compression using this local klt are derived two important special cases are studied in detail namely the partial observation klt which has access to a subset of variables but aims at reconstructing them all and the conditional klt which has access to side information at the decoder we focus on the jointly gaussian case with known correlation structure and on approximation and compression problems then the distributed klt is addressed by considering local klts in turn at the various terminals leading to an iterative algorithm which is locally convergent sometimes reaching a global optimum depending on the overall correlation structure for compression it is shown that the classical distributed source coding techniques admit a natural transform coding interpretation the transform being the distributed klt examples throughout illustrate the performance of the proposed distributed klt this distributed transform has potential applications in sensor networks distributed image databases hyper spectral imagery and data fusion

an extremal inequality motivated by multiterminal information theoretic problems we prove a new extremal inequality motivated by the vector gaussian broadcast channel and the distributed source coding with a single quadratic distortion constraint problems as a corollary this inequality yields a generalization of the classical entropy power inequality epi as another corollary this inequality sheds insight into maximizing the differential entropy of the sum of two dependent random variables

efficient parallelization of the 2d swendsen wang algorithm we established a fast swendsen wang algorithm for the two dimensional ising model on parallel computers with a high efficiency on an intel paragon with 140 processors we reached spin update times of only 14 ns with an efficiency of 89 this algorithm was used to examine the non equilibrium relaxation of magnetization and energy in large ising systems of a size up to 17920 17920 spins nevertheless we observed still a strong finite size effect for the magnetization we assume both magnetization and energy decay to behave like t e bt in an infinitely large system thus for long times magnetization and energy show an exponential asymtotic time dependence implying a critical dynamic exponent z of zero

mathematical analysis of a disease transmission model with quarantine isolation and an imperfect vaccine a new mathematical model for the transmission dynamics of a disease subject to the quarantine of latent cases and isolation of symptomatic cases and an imperfect vaccine is designed and analyzed the model undergoes a backward bifurcation where a stable disease free equilibrium co exists with a stable endemic equilibrium when the associated reproduction threshold is less than unity it is shown that the backward bifurcation phenomenon can be removed if the vaccine is perfect or if mass action incidence instead of standard incidence is used in the model formulation further the model has a unique endemic equilibrium when the threshold quantity exceeds unity a nonlinear lyapunov function of the goh volterra type is used to show that the endemic equilibrium is globally asymptotically stable for a special case numerical simulations of the model show that the singular use of a quarantine isolation strategy may lead to the effective disease control or elimination if its effectiveness level is at least moderately high enough the combined use of the quarantine isolation strategy with a vaccination strategy will eliminate the disease even for the low efficacy level of the universal strategy considered in this study it is further shown that the imperfect vaccine could induce a positive or negative population level impact depending on the size or sign of a certain associated epidemiological threshold

relaxation to equilibrium of single cluster dynamics of the ising model abstract the approach to equilibrium at the critical temperature of the two dimensional ising model from an initial ordered spin configuration is investigated using the single cluster monte carlo dynamics introduced by wolff an initial configuration of all up spins and its dual a checkerboard state are considered we give simple mean field and scaling arguments for the existence of power law decay because the usual arguments for time rescaling might not be applicable when the system is approaching equilibrium we directly determine the relation of the number of cluster flips to the number of monte carlo steps per spin for both initial configurations we find that the effective dynamical critical exponent determined from the power law behavior and the proper time rescaling differs from the estimates of the equilibrium dynamical exponent and depends on the initial conditions for the system sizes and times we have investigated

non equilibrium critical relaxation of the wolff dynamics of the ising model abstract the non equilibrium critical relaxation of the single cluster dynamics is studied for the ferromagnetic ising model on the square and cubic lattices power law behavior is observed in the energy relaxation process starting from an all up spin configuration from this power decay the dynamical exponent z is estimated to be 0 50 0 05 and 1 3 0 1 for the square and cubic lattices respectively where the time is defined by the number of cluster flip trials if the time scale is normalized by cluster mass they are 0 25 0 05 and 0 3 0 1 respectively