a monte carlo method for series expansions the authors describe a simple and general algorithm to calculate series expansions in enumeration problems to large orders approximately by a monte carlo method it can be used to generate unbiased samples in cluster studies e g linear or branched polymers random surfaces etc in any dimension they calculate the number of site animals of size n on the square lattice for n or 50 and their average size to better than 1 accuracy

monte carlo study of the point for collapsing trees we investigate the collapse transition of lattice trees with nearest neighbor attraction in two and three dimensions two methods are used 1 a stochastic optimization process of the robbins monro type which is designed solely to locate the maximum value of the specific heat and 2 umbrella sampling which is designed to sample data over a wide temperature range as well as to combat the quasiergodicity of metropolis algorithms in the collapsed phase we find good evidence that the transition is second order with a divergent specific heat and that the divergence of the specific heat coincides with the metric collapse

density of states and dynamic scaling on the vicsek snowflake fractal real space rescaling techniques have been employed to obtain recursion relations for the parameters characterising the dynamics of both the heisenberg ferromagnet and antiferromagnet on the infinite vicsek snowflake fractal the authors have calculated the associated dynamic exponents zf and za by linearising about the respective fixed points of the ferromagnetic antiferromagnetic recursion relations and find them to satisfy the relation za zf 2 in addition using a functional integral method both the ferromagnetic and antiferromagnetic density of states rho f omega and rho a omega have been calculated exactly and the resulting spectra were found to satisfy the scaling equation rho alpha omega approximately bz alpha df rho lambda alpha omega near their respective fixed points alpha a f df denoting the fractal dimension finally the amplitudes galpha omega appearing in the solution to the scaling equation rho alpha omega approximately galpha omega omega dfz alpha 1 for the density of states rho alpha omega were found to be periodic functions of ln omega with period ln lambda alpha where lambda alpha is the eigenvalue associated with ferromagnetic alpha f or antiferromagnetic alpha a fixed point

rigid animals in three dimensions the number of rigid clusters c n is enumerated for the central force model on a site diluted fcc lattice the exponent vr governing the growth of the radius of gyration of the rigid animal is also calculated it is found that c n approximately n0 333n and vr 0 32 or 0 02

a nonlocal monte carlo algorithm for lattice trees a new nonlocal algorithm for the simulation of trees on the lattice zd is proposed the authors study the implementation and the properties of the algorithm and show that it is decisively better than an algorithm which performs only local moves they use the new algorithm to investigate the properties of lattice trees in two three four eight and nine dimensions

metropolis monte carlo simulation of lattice animals we propose and study a metropolis monte carlo algorithm for the simulation of weighted lattice animals in in the canonical ensemble with a fixed number of edges we examine the implementation and performance of the algorithm data obtained by sampling uniformly weighted animals and animals weighted as critical percolation clusters are reported and analysed in particular we estimate autocorrelation times and dynamical exponents to study the efficiency of the algorithm and estimate the metric and branch exponents of lattice animals in two and three dimensions

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

monte carlo test of a hyperscaling relation for the two dimensional self avoiding walk the authors simulated self avoiding walks on the square lattice with fixed endpoints by means of a dynamic monte carlo algorithm from these data they obtain an evaluation of the effective coordination number mu and the critical exponents alpha and v they can therefore test the hyperscaling relation 2 alpha dv with a careful estimate of systematic and statistical errors

topological properties of percolation clusters percolation properties including the total cluster mass s the shell mass b and the linear geometrical size r are studied as a function of the topological chemical distance parameter l all critical exponents are shown to be related to an apparently new exponent nu defined by r approximately lv critical exponents are calculated exactly for percolation clusters on the cayley tree a model for 6d percolation for which s approximately l2 b approximately l and r2 approximately l for diffusion on such clusters one finds that l3 approximately t numerical estimates of the exponents are obtained for other dimensions a conjecture which relates nu to beta and nu is discussed

computer simulation of a model for irreversible gelation a random mixture of bifunctional and tetrafunctional units is placed on a simple cubic lattice permanent bonds between these units are then formed by the random motion of active centres radicals resulting in a model for the gelation of polyacrylamide and similar processes the largest of the clusters formed by this kinetic percolation process is identified with the gel fraction the mean cluster size with the weight average degree of polymerisation the critical exponent gamma of the mean cluster size is roughly the same as for random percolation that is different from that of the classical theory of flory 1941 and stockmayer 1943 but the corresponding amplitude ratio that is the ratio of average molecular weight on both sides of the gel point differs strongly from its value in random percolation thus this kinetic gelation model seems to belong to a universality class of its own different from both that of random percolation and that of classical gelation theories

on the geometry of classifying spaces and horizontal slices we study the local properties of the moduli space of a polarized calabi yau manifold let u be a neighborhood of the moduli space then we know the universal covering space v of u is a smooth manifold suppose d is the classifying space of a polarized calabi yau manifold with the automorphism group g then we prove that the map from v to d induced by the period map is a pluriharmonic map we also give a kahler metric on v which is called the hodge metric we prove that the ricci curvature of the hodge metric is negative away from zero we also proved the nonexistence of the kahler metric on the classifying space of a calabi yau threefold which is invariant under a cocompact lattice of g 1 introduction let x be a polarized simply connected calabi yau manifold that is x is a simply connected compact kahler manifold of dimension n with zero first chern class and is akform of x such that h 2 x z in this paper we study the local properties of the moduli space of the polarized calabi yau manifold x by definition is the parameter space of the complex structures over x for the fixed polarization is a quasi projective variety by a theorem of viehweg 17 suppose x is a calabi yau manifold let n d im h 1 x tx 0

on the weil petersson volume and the first chern class of the moduli space of calabi yau manifolds in this paper we proved that the weil petersson volume of calabi yau moduli is a rational number we also proved that the integrations of the invariants of the ricci curvature of the weli petersson metric with respect to the weil petersson volume form are all rational numbers

graph animals subgraph sampling and motif search in large networks we generalize a sampling algorithm for lattice animals connected clusters on a regular lattice to a monte carlo algorithm for graph animals i e connected subgraphs in arbitrary networks as with the algorithm in n kashtan et al bioinformatics 20 1746 2004 it provides a weighted sample but the computation of the weights is much faster linear in the size of subgraphs instead of superexponential this allows subgraphs with up to ten or more nodes to be sampled with very high statistics from arbitrarily large networks using this together with a heuristic algorithm for rapidly classifying isomorphic graphs we present results for two protein interaction networks obtained using the tandem affinity purification tap method one of escherichia coli with 230 nodes and 695 links and one for yeast saccharomyces cerevisiae with roughly ten times more nodes and links we find in both cases that most connected subgraphs are strong motifs z scores 10 or antimotifs z scores 10 when the null model is the ensemble of networks with fixed degree sequence strong differences appear between the two networks with dominant motifs in e coli being nearly bipartite graphs and having many pairs of nodes that connect to the same neighbors while dominant motifs in yeast tend towards completeness or contain large cliques we also explore a number of methods that do not rely on measurements of z scores or comparisons with null models for instance we discuss the influence of specific complexes like the 26s proteasome in yeast where a small number of complexes dominate the k cores with large k and have a decisive effect on the strongest motifs with 6 8 nodes we also present zipf plots of counts versus rank they show broad distributions that are not power laws in contrast to the case when disconnected subgraphs are included

perimeter polynomials for bond percolation processes perimeter polynomials are given for the bond percolation problem on the following lattices the triangular up to d9 simple quadratic d13 honeycomb d17 face centred cubic d7 body centred cubic d8 simple cubic d9 and diamond d13 the total number of bond clusters grouped by size is given to two further orders in each case

particle approximation of the intensity measures of a spatial branching point process arising in multitarget tracking the aim of this paper is twofold first we analyze the sequence of intensity measures of a spatial branching point process arising in a multiple target tracking context we study its stability properties characterize its long time behavior and provide a series of weak lipschitz type functional contraction inequalities second we design and analyze an original particle scheme to approximate numerically these intensity measures under appropriate regularity conditions we obtain uniform and nonasymptotic estimates and a functional central limit theorem to the best of our knowledge these are the first sharp theoretical results available for this class of spatial branching point processes

a new simulation of branched polymers the scanning method for the simulation of linear chain is extended to general models of branched polymers without loops a branched chain grows in time namely a number of steps from the origin therefore i in contrast to other simulation techniques which are of a relaxation type the chains are statistically independent and the statistical error can reliably be estimated ii the probability of a chain is known and hence the entropy and iii the scanning construction enables one to study geometrical properties which depend on time for self avoiding trees on a square lattice the author obtains the relatively accurate estimates for the static critical exponents nu 0 640 or 0 004 and theta 1 003 or 0 02 and for the connective constant mu 5 1419 or 0 003 the author also obtains critical exponents gamma t approximately 1 26 and nu t approximately 0 83 which characterise the growth in time of the number of bonds and the gyration radius respectively application of the scanning method to more complex branched polymers is discussed

graph matching with a dual step em algorithm this paper describes a new approach to matching geometric structure in 2d point sets the novel feature is to unify the tasks of estimating transformation geometry and identifying point correspondence matches unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the em algorithm according to our em framework the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters these gating probabilities measure the consistency of the matched neighborhoods in the graphs the recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log likelihood function we evaluate the technique on two real world problems

monte carlo test of dimensional reduction for branched polymers in three dimensions by a monte carlo simulation of a grand canonical ensemble for a lattice tree model of branched polymers in three dimensions the author obtains the estimates theta 1 501 or 0 043 nu 0 495 or 0 013 for the critical exponents these estimates strongly support the exact conjecture theta 3 2 nu 1 2 by parisi and sourlas 1981 obtained using dimensional reduction the attrition constant mu is also estimated

generalized hodge metrics and bcov torsion on calabi yau moduli we establish an unexpected relation among the weil petersson metric the generalized hodge metrics and the bcov torsion using this relation we prove that certain kind of moduli spaces of polarized calabi yau manifolds do not admit complete subvarieties that is there is no complete family for certain class of polarized calabi yau manifolds we also give an estimate of the complex hessian of the bcov torsion using the relation after establishing a degenerate version of the schwarz lemma of yau we prove that the complex hessian of the bcov torsion is bounded by the poincare metric

on the number of lattice animals embeddable in the square lattice enumeration of lattice animals embeddable in a square lattice has been extended to 24 cell animals by redelmeier 1981 it is shown that the number of animals per site an approximately 0 317 4 0626 nn 1 exp 0 465 n 0 87 to a high degree of accuracy

high precision canonical monte carlo determination of the growth constant of square lattice trees exponent in this paper we show that l and u can be determined to high accuracy by using a canonical monte carlo algorithm we find thatl55 143960 0025 u51 01460 022 where the error bars are a combined 95 statistical confidence interval and an estimated systematic error due to uncertainties in modeling corrections to scaling if one assumes the exact value u51 and then determines l then the above estimate improves to l55 143 3960 000 72 in addition we also determine the longest path exponent r and the metric exponent n from our data r50 7400060 00062 n50 643760 0035 with error bars similarly a combined 95 statistical confidence interval and an estimate of the systematic error

simulations of lattice animals and trees the scaling behaviour of randomly branched polymers in a good solvent is studied in two to nine dimensions using as microscopic models lattice animals and lattice trees on simple hypercubic lattices as a stochastic sampling method we use a biased sequential sampling algorithm with re sampling similar to the pruned enriched rosenbluth method perm used extensively for linear polymers essentially we start simulating percolation clusters either site or bond re weigh them according to the animal tree ensemble and prune or branch the further growth according to a heuristic fitness function in contrast to previous applications of perm this fitness function is not the weight with which the actual configuration would contribute to the partition sum but is closely related to it we obtain high statistics of animals with up to several thousand sites in all dimension 2 d 9 in addition to the partition sum number of different animals we estimate gyration radii and numbers of perimeter sites in all dimensions we verify the parisi sourlas prediction and we verify all exactly known critical exponents in dimensions 2 3 4 and 8 in addition we present the hitherto most precise estimates for growth constants in d 3 for clusters with one site attached to an attractive surface we verify for d 3 the superuniversality of the cross over exponent at the adsorption transition predicted by janssen and lyssy but not for d 2 there we find 0 480 4 instead of the conjectured 1 2 finally we discuss the collapse of animals and trees arguing that our present version of the algorithm is also efficient for some of the models studied in this context but showing that it is not very efficient for the classical model for collapsing animals

critical dynamics in heisenberg ferromagnets and antiferromagnets near the percolation threshold the critical spin wave dynamics of dilute ferromagnetic and antiferromagnetic heisenberg systems near the percolation threshold is studied on a two dimensional regular fractal model for bond percolation which captures the relevant geometric features of the cluster structure the dynamic critical exponent and spectral dimension for both the ferromagnetic and antiferromagnetic systems are calculated the treatment of the dynamics in these systems requires the use of generalised scaling techniques for sublattice systems which involve an extension of the parameter space

numerical evidence of the critical percolation probability pc 1 for site problems on sierpinski gaskets the authors propose a new method the alternating translational dilation method atdm and use it in combination with the monte carlo technique to calculate the critical percolation probability for sierpinski gaskets sg they obtain numerical evidence of the critical percolation probability pc 1 for site problems on sg and an approximate relation pc 1 1 n in two dimensions where n is the number of stages of sg

symmetric differentials and the fundamental group helene esnault asked whether a smooth complex projective variety x with infinite fundamental group must have a nonzero symmetric differential meaning that h x s x 6 0 for some i 0 this was prompted by the second author s work 23 in fact severi had wondered in 1949 about possible relations between symmetric differentials and the fundamental group 34 p 36 we know from hodge theory that the cotangent bundle x has a nonzero section if and only if the abelianization of 1x is infinite the geometric meaning of other symmetric differentials is more mysterious and it is intriguing that they may have such a direct relation to the fundamental group in this paper we prove the following result on esnault s question in the slightly broader setting of compact kahler manifolds

universality in branched polymers on d dimensional hypercubic lattices the authors have derived series for weakly and strongly embeddable trees in d dimensional simple hypercubic lattices for arbitrary integral d for d 2 3 9 they present series evidence that such trees are in the same universality class as lattice animals in addition they have derived expansions in inverse powers of sigma 2d 1 for the growth parameters for bond and site trees and compare these with the corresponding results for animals

the pivot algorithm and polygons results on the fcc lattice the authors consider the pivot algorithm for polygons on the face centred cubic lattice and prove ergodicity a numerical study of the algorithm is carried out in particular the authors look at the acceptance fraction of the elementary moves and find that it goes only slowly to zero as the length of the polygons is increased the numerical properties of polygons on the fcc lattice are also considered they calculate the exponent nu by considering the mean square radius of gyration of the polygons and compare the result to the expected value from field theory they also consider the mean span of the polygons and discuss corrections to scaling and their influence on the numerical calculation of critical exponents

extrapolation of transfer matrix data for percolation and lattice animals by the romberg beleznay algorithm using beleznay s modified romberg algorithm the author re analyses the transfer matrix data for the two dimensional problems of derrida and stauffer 1985 he gets for percolation pc 0 59273 6 for the threshold of the square site problem nu 1 3330 7 for the correlation length exponent and omega 1 9 3 for the correction exponent in the case of lattice animals xc 0 246152 4 square lattice xc 0 19294 1 triangular lattice critical fugacity and nu 0 64062 10 radius exponent

cluster renormalisation study of site lattice animals in two and three dimensions the author studies site lattice animals using the cluster renormalisation cr approach previously applied to bond animals the exponent v characterising the asymptotic behaviour of the mean square radius of gyration of site animals and the fractal dimension df 1 v are determined in two and three dimensions he finds v 0 649 or 0 009 and v approximately 0 51 in two and three dimensions respectively in addition he studies restricted valence site animals on a triangular lattice using a single parameter cr approach

regional variance for multi object filtering recent progress in multi object filtering has led to algorithms that compute the first order moment of multi object distributions based on sensor measurements the number of targets in arbitrarily selected regions can be estimated using the first order moment in this work we introduce explicit formulae for the computation of the second order statistic on the target number the proposed concept of regional variance quantifies the level of confidence on target number estimates in arbitrary regions and facilitates information based decisions we provide algorithms for its computation for the probability hypothesis density phd and the cardinalized probability hypothesis density cphd filters we demonstrate the behaviour of the regional statistics through simulation examples

collapse transition and asymptotic scaling behavior of lattice animals low temperature expansion a low temperature expansion for the free energy density of lattice animals is derived analysis of the series yields a collapse transition temperature oftc 0 54 in close agreement with previous estimates it is demonstrated that p k the number ofp particle p bond animals obeys the asymptotic scaling law log p k pg k p o p the low temperature series and numerical data are used to estimate the scaling function

relaxation monte carlo for 3d branched polymers the leading confluence exponent a relaxation study of simple cubic site trees taking 18 months of cdc cyber computer time is used to estimate the radius of gyration dependence on the size both as regards the correlation exponent and the confluent correction the latter is found to be compatible with an analytic term within the uncertainty limits the radius prefactor is estimated as 0 542 0 005 and the limiting site perimeter to size ratio as 2 905 0 005

dynamic scaling on fractals with sublattices dynamic scaling techniques are developed for antiferromagnets and multiatomic lattices the methods are applied to antiferromagnets and triatomic lattices on sierpinski gasket fractals and to ferro and antiferromagnets on berker hierarchical lattices relationships between the frequencies of ferro and antiferromagnets on the same fractal and of mono and multiatomic fractal systems are given in particular the dynamic exponents za and zf of antiferromagnetic and ferromagnetic sierpinski gaskets or berker lattice fractals are shown to satisfy za 1 2zf

analytic torsion for calabi yau threefolds after bershadsky cecotti ooguri vafa we introduce an invariant of calabi yau threefolds which we call the bcov invariant and which we obtain using analytic torsion we give an explicit formula for the bcov invariant as a function on the compactified moduli space when it is isomorphic to a projective line as a corollary we prove the formula for the bcov invariant of quintic mirror threefolds conjectured by bershadsky cecotti ooguri vafa

monte carlo and series study of corrections to scaling in two dimensional percolation corrections to scaling for percolation cluster numbers in two dimensions are studied by monte carlo simulations of very large systems up to 17 109 lattice sites and by series analysis both series and monte carlo work suggests that the value of the correction to scaling exponent is slightly lower at the percolation threshold than away from it moreover the corrections to scaling observed at pc omega equivalent to 0 64 might be due to the mixing of scaling fields rather than to the irrelevant scaling fields the monte carlo results are compatible with finite size scaling and finite size scaling corrections are estimated technical problems associated with monte carlo simulation of very large systems are discussed in an appendix

on anisotropic spiral self avoiding walks we report on a monte carlo study of so called two choice spiral self avoiding walks on the square lattice these have the property that their geometric size such as is measured by the radius of gyration scales anisotropically with exponent values that seem to defy rational fraction conjectures this polymer model was previously understood to be in a universality class different to ordinary self avoiding walks directed walks which are also anisotropic and symmetric spiral walks in two dimensions our monte carlo study concurs with those previous exact enumeration studies in that respect however we estimate substantially different values for the scaling exponents associated with the geometric size of the walks we give arguments that explain this difference in terms of a turning point in the local exponent values and in turn explain this by arguing for the existence of probable logarithmic corrections we also supply numerical evidence supporting a conjecture concerning the angle of anisotropy in the model

asymptotics of degenerations of mixed hodge structures abstract we construct a hermitian metric on the classifying spaces of graded polarized mixed hodge structures and prove analogs of the strong distance estimate 6 between an admissible period map and the approximating nilpotent orbit we also consider the asymptotic behavior of the biextension metric introduced by hain 12 analogs of the norm estimates of 19 and the asymptotics of the naive limit hodge filtration considered in 21

on the number of trees in zd the number of trees weakly embedded in the hypercubic lattice tn is considered it is known that limn to infinity tn1n lambda 0 and that tn or lambda 0n these facts are proven by noting that trees satisfy a supermultiplicative inequality tntm or tn m a submultiplicative property is derived for trees of the form tn m or n m 3 alpha log n m tntm consequently there exists a constant delta such that o exp delta logn 2 lambda 0n or tn or lambda 0n

computer simulations of randomly branching polymers annealed versus quenched branching structures we present computer simulations of three systems of randomly branching polymers in d 3 dimensions ideal trees and self avoiding trees with annealed and quenched connectivities in all cases we performed a detailed analysis of trees connectivities spatial conformations and statistical properties of linear paths on trees and compare the results to the corresponding predictions of flory theory we confirm that overall the theory predicts correctly that trees with quenched ideal connectivity exhibit less overall swelling in good solvent than corresponding trees with annealed connectivity even though they are more strongly stretched on the path level at the same time we emphasize the inadequacy of the flory theory in predicting the behaviour of other and equally relevant observables like contact probabilities between tree nodes we show then that contact probabilities can be aptly characterized by introducing a novel critical exponent which accounts for how they decay as a function of the node to node path distance on the tree

tournaments flags and harmonic maps twistor space constructions have shown that under quite general hypotheses harmonic maps of riemann surfaces into riemannian manifolds can be represented by holomorphic curves with respect to almost complex structures which are often non integrable see for example 19 17 5 for maps into complex grassmannians the almost complex structures are invariant ones on flag manifolds and can be identified with tournaments i e digraphs in which any two nodes are joined by exactly one oriented edge elementary properties of tournaments are summarised in sect i the basic references are moon 14 and reid and beineke 18 emphasis is given to certain types of tournament which are interpreted in sect 2 in terms of the homogeneous structure of complex flag manifolds holomorphic curves in such flag manifolds are described in sect 3 by collections of subbundles of a trivial bundle over a riemann surface whose second fundamental forms define a tournament this approach relies on techniques of burstall and wood 6 and gives rise naturally to harmonic maps into grassmannians when the riemann surface has genus zero a result from algebraic geometry namely the birkhoff grothendieck decomposition theorem for holomorphic vector bundles fits into the scheme and allows one to reconstruct a tournament from a harmonic map into a grassmannian in sect 4 we use such techniques to show that harmonic maps of tl2p 1 into a complex grassmannian can be built up successively from holomorphic data this last result extends results of burstall and wood 6 and is closely related to recent work of uhlenbeck 21 and wolfson 23

derivation of the phd and cphd filters based on direct kullback leibler divergence minimization in this paper we provide novel derivations of the probability hypothesis density phd and cardinalised phd cphd filters without using probability generating functionals or functional derivatives we show that both the phd and cphd filters fit in the context of assumed density filtering and implicitly perform kullback leibler divergence kld minimizations after the prediction and update steps we perform the kld minimizations directly on the multitarget prediction and posterior densities

a second order phd filter with mean and variance in target number the probability hypothesis density phd and cardinalized phd cphd filters are popular solutions to the multitarget tracking problem due to their low complexity and ability to estimate the number and states of targets in cluttered environments the phd filter propagates the first order moment i e mean of the number of targets while the cphd propagates the cardinality distribution in the number of targets albeit for a greater computational cost introducing the panjer point process this paper proposes a second order phd so phd filter propagating the second order moment i e variance of the number of targets alongside its mean the resulting algorithm is more versatile in the modeling choices than the phd filter and its computational cost is significantly lower compared to the cphd filter this paper compares the three filters in statistical simulations which demonstrate that the proposed filter reacts more quickly to changes in the number of targets i e target births and target deaths than the cphd filter in addition a new statistic for multiobject filters is introduced in order to study the correlation between the estimated number of targets in different regions of the state space and propose a quantitative analysis of the spooky effect for the three filters

new monte carlo method for the self avoiding walk we introduce a new monte carlo algorithm for the self avoiding walk saw and show that it is particularly efficient in the critical region long chains we also introduce new and more efficient statistical techniques we employ these methods to extract numerical estimates for the critical parameters of the saw on the square lattice we find 2 63820 0 00004 0 00030 1 352 0 006 0 025 v 0 7590 0 0062 0 0042 where the first error bar represents systematic error due to corrections to scaling subjective 95 confidence limits and the second bar represents statistical error classical 95 confidence limits these results are based on saws of average length 166 using 340 hours cpu time on a cdc cyber 170 730 we compare our results to previous work and indicate some directions for future research

relation between size and shape of isotropic and directed percolation clusters and lattice animals shows that the generalised lattice animal model of family and coniglio 1980 naturally leads to a unified scaling picture for percolation and lattice animals in which the fugacity for occupied elements plays the dual role of a temperature like and a field like variable within this single scaling field description of percolation there is only one independent exponent from which all others can be obtained the author defines a new set of exponents alpha beta and gamma for percolation and finds that they are all related to the cluster number exponent theta through the relation alpha gamma 1 beta 3 theta in analogy with lattice animals to relate the cluster radius exponent nu to the other exponents he uses the generalised ginzburg criteria to obtain a modified hyperscaling relation for isotropic and directed percolation and lattice animals using this relation he finds that theta 1 nu sub perpendicular to d 1 for directed percolation and theta nu perpendicular to d 1 for directed lattice animals where nu sub and nu perpendicular to are exponents characterising the parallel and perpendicular cluster radii respectively using the same approach he obtains the stauffer relation theta 1 d nu and the parisi sourlas relation theta 1 d 2 nu for isotropic percolation and lattice animals respectively the above relations give the following expressions for theta within the flory theory theta percolation 3d 2 d 2 theta directed percolation 6d 5 2d 4 theta animals 7d 6 2d 4 and theta directed animals 9 d 1 4d 8

the scaling limit of lattice trees in high dimensions we prove that above eight dimensions the scaling limit of sufficiently spread out lattice trees is the variant of super brownian motion known as integrated super brownian excursion ise as conjectured by aldous the same is true for nearest neighbour lattice trees in sufficiently high dimensions the proof uses the lace expansion

monte carlo results for projected self avoiding polygons a two dimensional model for knotted polymers we introduce a two dimensional lattice model for the description of knotted polymer rings a polymer configuration is modelled by a closed polygon drawn on the square diagonal lattice with possible crossings describing pairs of strands of polymer passing on top of each other each polygon configuration can be viewed as the two dimensional projection of a particular knot we study numerically the statistics of large polygons with a fixed knot type using a generalization of the bfacf algorithm for self avoiding walks this new algorithm incorporates both the displacement of crossings and the three types of reidemeister transformations preserving the knot topology its ergodicity within a fixed knot type is not proven here rigorously but strong arguments in favour of this ergodicity are given together with a tentative sketch of proof assuming this ergodicity we obtain numerically the following results for the statistics of knotted polygons in the limit of a low crossing fugacity we find a localization along the polygon of all the primary factors forming the knot increasing the crossing fugacity gives rise to a transition from a self avoiding walk to a branched polymer behaviour

studies of the spectral dimension of the vicsek snowflake fractal by an exact real space renormalization group method the authors obtain the spectral dimension of the vicsek snowflake fractal the result seems to cast some doubt on the range of validity of the einstein relation on the deterministic fractal

two dimensional lattice tree exponents and amplitudes simulation algorithms versus series we use a local monte carlo algorithm to simulate lattice trees in two dimensions for the site and bond problem we investigate the properties of radius of gyration perimeter to site ratio and vertex degree in a tree adding some new results in the site problem compare our results on their noncritical properties with those obtained from earlier reversible and slightly nonreversible algorithms and combine our determinations with new exact series expansion data on the controversy surrounding the possible lack of universality for the first confluent singularity for the gyration radius we feel that conclusions must be guarded

percolation fractals and anomalous diffusion both the infinite cluster and its backbone are self similar at the percolation threshold pc this self similarity also holds at concentrationsp nearpc for length scalesl which are smaller than the percolation connectedness length forl the number of bonds on the infinite cluster scales asld where the fractal dimensionalityd is equal to d v geometrical fractal models which imitate the backbone and on which physical models are exactly solvable are presented above six dimensions one has d 4 and an additional scaling length must be included the effects of the geometrical structure of the backbone on magnetic spin correlations and on diffusion at percolation are also discussed

generalized atmospheric rosenbluth methods garm we show that the classical rosenbluth method for sampling self avoiding walks hammersley and morton 1954 j r stat soc b 16 23 rosenbluth and rosenbluth 1955 j chem phys 23 356 can be extended to a general algorithm for sampling many families of objects including self avoiding polygons the implementation relies on an elementary move which is a generalization of kinetic growth rather than only appending edges to the endpoint edges may be inserted at any vertex provided the resulting objects still lie within the same family this gives for the first time a kinetic growth algorithm for sampling self avoiding polygons we implement this method using pruning and enrichment grassberger 1997 phys rev e 56 3682 to sample self avoiding walks and polygons the algorithm can be further extended by mixing it with length preserving moves such as pivots and crank shaft moves

the cauchy schwarz divergence for poisson point processes in this paper we extend the notion of cauchy schwarz divergence to point processes and establish that the cauchy schwarz divergence between the probability densities of two poisson point processes is half the squared l 2 distance between their intensity functions extension of this result to mixtures of poisson point processes and in the case where the intensity functions are gaussian mixtures closed form expressions for the cauchy schwarz divergence are presented our result also implies that the bhattacharyya distance between the probability distributions of two poisson point processes is equal to the square of the hellinger distance between their intensity measures we illustrate the result via a sensor management application where the system states are modeled as point processes

models for point processes observed with noise summary consider a pair of point processes x and y where x is regarded as a true point process and y is an imperfect observation of x for the transformation from x to y we consider a number of disturbance mechanisms covering random thinning displacement censoring of the displaced points and superposition of extra points we present the conditional likelihood of y given x when both point processes are observed the likelihood may be used for inference about the disturbance mechanisms the likelihood is a sum typically with very many terms and we discuss an approximation with a small number of terms the results are applied to an example where x denotes a set of true positions of tree tops and y denotes tree top positions estimated by template matching in a digital image obtained by high resolution aerial photography the parameters governing the various disturbance mechanisms are estimated from the conditional likelihood

a new method for simulation of real chains scanning future steps a new method for simulating real polymer chains is developed and applied to self avoiding walks saws of length 49 599 on a three choice square lattice very good results for the entropy are obtained which deviate from the series expansion estimates by 0 1 2 the author also discusses how to extend the method to models of polymer chains with both excluded volume and finite interactions attractive or repulsive the author s method is expected to be more efficient than other simulation methods for treating self interacting saws and chains which are subject to various lattice constraints

filters for spatial point processes we study the general problem of estimating a hidden point process mathbf x given the realization of an observed point process mathbf y possibly defined in different spaces with known joint distribution we characterize the posterior distribution of mathbf x under marginal poisson and gauss poisson priors and when the transformation from mathbf x to mathbf y includes thinning displacement and augmentation with extra points these results are then applied in a filtering context when the hidden process evolves in discrete time in a markovian fashion the dynamics of mathbf x considered are general enough for many target tracking applications

gauss bonnet chern theorem on moduli space in this paper we prove a gauss bonnet chern type theorem in full generality for the chern weil forms of hodge bundles that is the chern weil forms compute the corresponding chern classes this settles a long standing problem second we apply the result to calabi yau moduli and proved the corresponding gauss bonnet chern type theorem in the setting of weil petersson geometry as an application of our results in string theory we prove that the number of flux vacua of type ii string compactified on a calabi yau manifold is finite and their number is bounded by an intrinsic geometric quantity

convergence and extrapolation in finite size scaling renormalization abstract finite size renormalization technique is studied by examining a test model which is exactly solvable and the problem of lattice animals and self avoiding walks bulk estimates of the leading irrelevant rg eigenvalue are found and compared with independent estimates from finite size data we introduce an extrapolation technique which is applicable to non monotonic sequences of exponent approximants

critical exponents and corrections to scaling for bond trees in two dimensions the author has analysed the newly obtained series of the radius of gyration rn and the number of clusters nn for n bond trees i e branch polymers without loops on the square n or 14 and triangular n or 11 lattices to estimate the critical parameters respective estimates of the exponents nu and theta for rn and nn are consistent with the corresponding values for lattice animals while the correction to scaling exponent delta 1 is inconsistent with the animal value in addition delta 1 has different values for rn delta 1 0 635 and nn delta 1 1 3 for bond trees he has also estimated an exponent delta characterising the density distribution delta 2 69 for the triangular lattice

convergence of finite size scaling renormalisation techniques abstract the rate of convergence of the transfer matrix finite size scaling or phenomenological renormalisation method is studied it is shown both heuristically and numerically that the convergence of estimates for exponents etc is governed asymptotically by the leading irrelevant variable scaling exponent the more rapid apparent convergence rates observed in many practical calculations for two dimensional lattices of widths up to ten lattice spacings are attributed to cancellation between various correction terms

a new monte carlo simulation for two models of self avoiding lattice trees in two dimensions by means of a new monte carlo sampling of a grand canonical ensemble we verify universality for the critical exponents and of two models of lattice trees constrained to be self avoiding on sites or on bonds the attrition constants are also obtained this algorithm a generalization of that recently proposed by berretti and sokal for random walks appears to optimize the critical slowing down in the scaling region systematic and statistical errors are carefully estimated

the pivot algorithm a highly efficient monte carlo method for the self avoiding walk the pivot algorithm is a dynamic monte carlo algorithm first invented by lal which generates self avoiding walks saws in a canonical fixed n ensemble with free endpoints heren is the number of steps in the walk we find that the pivot algorithm is extraordinarily efficient one effectively independent sample can be produced in a computer time of ordern this paper is a comprehensive study of the pivot algorithm including a heuristic and numerical analysis of the acceptance fraction and autocorrelation time an exact analysis of the pivot algorithm for ordinary random walk a discussion of data structures and computational complexity a rigorous proof of ergodicity and numerical results on self avoiding walks in two and three dimensions our estimates for critical exponents are 0 7496 0 0007 ind 2 and 0 592 0 003 ind 3 95 confidence limits based on saws of lengths 200 n 10000 and 200 n 3000 respectively

scaling treatment of anisotropic diffusion exact scaling treatments are given of anisotropic diffusion in pure and diluted chains and in a fractal a dynamic decimation method is used to obtain detailed dynamic scaling descriptions the results for chains show crossover to drift or localised behaviour induced by anisotropy or dilution the fractal results include bias induced crossover with exponent unity from anomalous diffusion behaviour exponent log2 5 to drift behaviour and scaling corrections exponent log2 5 3 arising from rotational anisotropy

the number and size of branched polymers in high dimensions we consider two models of branched polymers lattice trees on thed dimensional hypercubic lattice i the nearest neighbor model in sufficiently high dimensions and ii a spread out or long range model ford 8 in which trees are constructed from bonds of length less than or equal to a large parameterl we prove that for either model the critical exponent for the number of branched polymers exists and equals 5 2 and that the critical exponentv for the radius of gyration exists and equals 1 4 this improves our earlier results for the corresponding generating functions the proof uses the lace expansion together with an analysis involving fractional derivatives which has been applied previously to the self avoiding walk in a similar context

the gaussian mixture probability hypothesis density filter a new recursive algorithm is proposed for jointly estimating the time varying number of targets and their states from a sequence of observation sets in the presence of data association uncertainty detection uncertainty noise and false alarms the approach involves modelling the respective collections of targets and measurements as random finite sets and applying the probability hypothesis density phd recursion to propagate the posterior intensity which is a first order statistic of the random finite set of targets in time at present there is no closed form solution to the phd recursion this paper shows that under linear gaussian assumptions on the target dynamics and birth process the posterior intensity at any time step is a gaussian mixture more importantly closed form recursions for propagating the means covariances and weights of the constituent gaussian components of the posterior intensity are derived the proposed algorithm combines these recursions with a strategy for managing the number of gaussian components to increase efficiency this algorithm is extended to accommodate mildly nonlinear target dynamics using approximation strategies from the extended and unscented kalman filters

efficiency of the incomplete enumeration algorithm for monte carlo simulation of linear and branched polymers we study the efficiency of the incomplete enumeration algorithm for linear and branched polymers there is a qualitative difference in the efficiency in these two cases the average time to generate an independent sample of configuration of polymer with n monomers varies as n2 for linear polymers for large n but as exp cn for branched undirected and directed polymers where 0 1 on the binary tree our numerical studies for n of order 104 gives 0 333 0 005 we argue that 1 3 exactly in this case

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

diffusivity and radius of random animals percolation clusters and compact clusters defines a cluster diffusivity ds by introducing a random rearrangement between arbitrary cluster and perimeter sites such that the cluster remains connected monte carlo simulation is used on the square and simple cubic lattices to determine the dependence of ds and the radius of gyration rs on s the number of cluster sites three limiting cases are considered random animals p 0 percolation clusters p pc and compact clusters p pc the results for the exponent rho of rs are consistent with the best experimental and theoretical values the authors develop an elementary scaling theory for the observed power law dependence of ds in terms of different mechanisms dominant for small and large clusters a position space renormalisation group calculation in two dimensions yields corrections to the elementary theory for random animals and percolation clusters the predictions are consistent with the monte carlo results for ds