universal amplitude ratios for self avoiding walks on the kagome lattice we have calculated exactly the number the mean square end to end distance the mean square radius of gyration and the mean square distance of a monomer from the origin for n step self avoiding walks on the kagome lattice up to 30 steps we have estimated the connective constant and the critical amplitudes our numerical results are consistent with the theoretical prediction by cardy and saleur 1989 on the universality for certain amplitude ratios

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

universal amplitude combinations for self avoiding walks and polygons on the honeycomb lattice abstract we have calculated exactly the mean square end to end distance the mean square radius of gyration and the mean square distance of a monomer from the origin for n step self avoiding walks on the honeycomb lattice up to 46 steps we also calculated the mean square radius of gyration and moments of area for n step self avoiding polygons on the honeycomb lattice up to 60 steps we estimated the critical amplitudes and our numerical results are consistent with the theoretical predictions by the universality for certain amplitude combinations

test for equality of intraclass correlation coefficients under unequal family sizes the likelihood ratio test the large sample z test and the large sample z test have been proposed to test for the equality of two intraclass correlation coefficients under unequal family sizes based on two independent multinomial samples it has been found on the basis of simulation studies that the likelihood ratio test consistently and reliably produces results superior to those of the large sample z test and large sample z test in terms of power for various combinations of intraclass correlation coefficient values

universal distance ratios for 2d saws series results the mean square distance of a monomer to the origin and the mean square distance of the centre of mass to the origin are studied by exact enumeration on the square and triangular lattices the numerical results are inconsistent with the theoretical prediction of cardy and saleur 1989 by more than fifteen times the numerical uncertainty in the authors calculation

universal amplitude ratios for three dimensional self avoiding walks we have calculated exactly the number the mean square end to end distance the mean square radius of gyration and the mean square distance of a monomer from the origin for n step self avoiding walks on the simple cubic diamond body centred cubic and face centred cubic lattices respectively up to 20 30 16 and 13 steps by a computer two universal amplitude ratios are estimated

estimation for a common correlation coefficient in bivariate normal distributions with missing observations summary the maximum likelihood ml estimate and the restricted or residual maximum likelihood reml estimate are considered for a common correlation coefficient among several bivariate normal distributions with different variances when some observations on either of the variables are missing the use of incomplete data in ml and reml estimation reduces mean squared errors of the correlation estimates reduction is large when the absolute value of a common correlation is large or numbers of paired observations are small an example and some simulation results are given to illustrate the characteristics of the estimates

resistivity exponent of two dimensional lattice animals we calculate the average resistancer l of lattice animals spanningl l cells on the square lattice using exact and monte carlo methods the dynamical resistivity exponent defined asr l l is found to be 1 36 0 07 this contradicts the alexander orbach conjecture which predicts 0 8 our value for differs from earlier measurements of this quantity by other methods yielding 1 17 0 05 and 1 22 0 08 by havlin et al

universal amplitude combinations for self avoiding walks polygons and trails the authors give exact relations for a number of amplitude combinations that occur in the study of self avoiding walks polygons and lattice trails in particular they elucidate the lattice dependent factors which occur in those combinations which are otherwise universal show how these are modified for oriented lattices and give new results for amplitude ratios involving even moments of the area of polygons they also survey numerical results for a wide range of amplitudes on a number of oriented and regular lattices and provide some new ones

critical exponents hyperscaling and universal amplitude ratios for two and three dimensional self avoiding walks we make a high precision monte carlo study of two and three dimensional self avoiding walks saws of length up to 80 000 steps using the pivot algorithm and the karp luby algorithm we study the critical exponents v and 2 triangle sub 4 gamma as well as several universal amplitude ratios in particular we make an extremely sensitive test of the hyperscaling relation dv 2 triangle sub 4 gamma in two dimensions we confirm the predicted exponent v 3 4 and the hyperscaling relation we estimate the universal ratios 0 14026 0 00007 0 43961 0 00034 and psi 0 66296 0 00043 68 confidence limits in three dimensions we estimate v 0 5877 0 0006 with a correction to scaling exponent triangle sub 1 0 56 0 03 subjective 68 confidence limits this value for v agrees excellently with the field theoretic renormalization group prediction but there is some discrepancy for triangle 1 earlier monte carlo estimates of v which were approximately 0 592 are now seen to be biased by corrections to scaling we estimate the universal ratios 0 1599 0 0002 and psi 0 2471 0 0003 since psi 0 hyperscaling holds the approach to psi is from above contrary to the prediction of the two parameter renormalization group theory we critically reexamine this theory and explain where the error lies in an appendix we prove rigorously modulo some standard scalingmore assumptions the hyperscaling relation dv 2 triangle sub 4 gamma for two dimensional saws less

universal amplitude combinations for self avoiding walks and polygons on directed lattices two directed lattices the l lattice and manhattan lattice are studied we have calculated exactly the number the mean square end to end distance the mean square radius of gyration and the mean square distance of a monomer from the origin for n step self avoiding walks on the l lattice and manhattan lattice for up to 60 and 50 steps respectively we have also computed the number and mean square radius of gyration for self avoiding polygons on the l lattice and manhattan lattice for up to 80 and 60 steps respectively we have estimated the critical amplitudes and our numerical results are consistent with the conjecture of universality for certain amplitude combinations however some amplitude combinations have values different from the corresponding values for undirected lattices

testing the effect of sex differences on sib sib correlations procedures for testing the effect of sex differences on sib sib correlations are studied it is demonstrated that a simple procedure for testing the equality of a pair of brother brother and sister sister correlations the modified z test is comparable in power to the likelihood ratio test in moderately large samples drawn from sibship size distributions that are likely to occur in practice in small samples the modified z test is preferable to the likelihood ratio test since the latter tends to be anti conservative

comment on the universality class of self avoiding walks on a two layer square lattice abstract we have calculated exactly the mean square radius of gyration and the mean square distance of a monomer from the origin for n step self avoiding walks on a two layer square lattice up to 24 steps we estimated two universal amplitude ratios and the results provide additional evidence that self avoiding walks on a two layer lattice belongs to the same universality class as the self avoiding walk on a planar lattice

inferences concerning a common intraclass correlation coefficient the maximum likelihood estimator rhom of a common intraclass correlation rho is derived in two independent samples drawn from multivariate normal populations a likelihood ratio statistic for testing the assumption of a common rho is also derived and examples are given comparisons are made with a procedure based on fisher s transformation

maximum likelihood estimation of intraclass correlation in the analysis of familial data estimating equation approach summary we introduce a generalized model for estimating intraclass correlation in the analysis of familial data this model incorporates the models of donner koval 1980 donner bull 1983 rosner 1984 and miunoz rosner carey 1986 as special cases we then obtain the maximum likelihood estimates of the parameters of the model in particular we obtain a single estimating equation to be solved iteratively for the estimation of the intraclass correlation p and discuss all the special cases asymptotic variance for the estimate of the intraclass correlation is obtained for all the models and some examples are given

generating functions for connected embeddings in a lattice i strong embeddings the method of partial generating functions developed to derive high field expansions for the ising model enumerates unrestricted strong embeddings in a lattice the method is modified to enumerate connected embeddings only an explicit general receipt is given for the relation between unrestricted and restricted generating functions for the body centred cubic lattice the number of connected strong embeddings of clusters with up to 13 sites is derived

on confidence intervals of a common intraclass correlation coefficient this study presents a novel approach for the confidence interval estimation of a common intraclass correlation coefficient derived from several samples under unequal family sizes this approach is developed using the concept of generalized pivots comparisons are made with a large sample procedure on the coverage probabilities

enumeration of self avoiding walks on the square lattice we describe a new algorithm for the enumeration of self avoiding walks on the square lattice using up to 128 processors on a hp alpha server cluster we have enumerated the number of self avoiding walks on the square lattice to length 71 series for the metric properties of mean square end to end distance mean square radius of gyration and mean square distance of monomers from the end points have been derived to length 59 an analysis of the resulting series yields accurate estimates of the critical exponents and confirming predictions of their exact values likewise we obtain accurate amplitude estimates yielding precise values for certain universal amplitude combinations finally we report on an analysis giving compelling evidence that the leading non analytic correction to scaling exponent 1 3 2

assessing interrater agreement from dependent data estimation of interrater agreement for ordered categorical data is examined when the same sample is being assessed by various raters with different methods we investigate the use of a latent model proposed by qu piedmonte and medendorp 1995 biomerics 51 268 275 to estimate the correlation between raters for each method and test for their equality for each of the assessment methods these correlations can be interpreted as the variance components of random effects representing subject and rater this method is applied to an hiv study in which the amount of ectopy on a woman s cervix is measured by both direct visual assessment and a computer planimetry method

optimal pointwise control for a parallel system of euler bernoulli beams abstract the optimal control of a distributed system consisting of two euler bernoulli beams coupled in parallel with pointwise controllers is considered an index of performance is formulated which consists of a modified energy functional of two coupled structures at a specified time and penalty functions involving the point control forces the minimization of the performance index over these forces is subject to the equation of motion governing the structural vibrations the imposed initial condition as well as the boundary conditions a maximum principle is derived for optimal point controls of one dimensional coupled structures undergoing transverse vibrations the optimal control law is obtained using a maximum principle and the applicability of the results is demonstrated a method of solution for such a type of structure is suggested by using the eigenfunction expansion and the maximum principle the solution involves reducing the original problem to a system of ordinary differential equations the effectiveness of this approach is illustrated numerically by comparing the behavior of the controlled and uncontrolled problem

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

collapse of two dimensional linear polymers we study the collapse transition of a two dimensional very long polymer the model we consider is a lattice model where the chain is represented by a self avoiding walk with nearest neighbor attraction by using the transfer matrix technique we calculate exactly the thermal and geometrical properties of the polymer on strips of finite width we then use finite size scaling to determine the values of the tricritical point exponentsv1 0 55 0 01vu 1 15 0 15 1 v1 1 80 0 05 we compare these results to the other values already proposed in the literature

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

an extension of the maximum principle for a class of optimal control problems in infinite dimensional spaces an extension of the pontryagin maximum principle and of the transversality conditions for a class of optimal control problems for a system of a parabolic equation and an ordinary differential equation in a hilbert space are given in particular the time optimal problem for some of these systems is considered as an application the optimal control of the diffusion of a class of epidemics is studied

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

self avoiding rings on the triangular lattice the finite lattice method of series expansion is used to extend the enumeration of self avoiding polygons on the triangular lattice through to rings of 35 steps the authors also give the enumeration of these triangular polygons grouped by perimeter and area of up to 21 unit triangles for perimeters up to 24 steps

a pontryagin maximum principle for infinite dimensional problems a basic idea of the classical approach for obtaining necessary optimality conditions in optimal control is to construct suitable needle like control variations we use this idea to prove the main result of the present paper a pontryagin maximum principle for infinite dimensional optimal control problems with pointwise terminal constraints in arbitrary banach state space by refining the classical variational technique we are able to replace the differentiability of the norm of the state space guaranteed by the strict convexity of its dual norm which is assumed in the known results by a separation argument we also drop another key assumption which is common in the existing literature on infinite dimensional control problems that the set of variations in the state space of the state trajectory s endpoint resulting from the control variations be finite codimensional instead we require only that it has nonempty interior in its closed affine hull as an application of the abstract result we present an illustrative example an optimal control problem for an age structured system with pointwise terminal state constraints

universal amplitude in the sizes of rings in two dimensions for self avoiding rings of n steps in two dimensions the limiting value as n to infinity of the combination npn r2 nxcn where pn is the number of distinct rings r2 n is their mean square radius of gyration and xc is the critical fugacity is equal to a calculable lattice dependent number times a universal amplitude this latter quantity is calculated exactly using methods of conformal invariance the value is in good agreement with the results of enumeration studies

universal amplitudes ratio at the collapse transition of polymers in two dimensions first values of the universal ratio of the mean square radius of gyration and the mean square end to end distance for 2d linear polymers at their collapse transition are calculated by the scanning simulation method two models are considered i self avoiding walks saws with nearest neighbour attractions for which this ratio is found to be 0 179 or 0 003 at the theta point ii self intersecting trails at their tricritical point for which the value 0 166 or 0 002 is obtained this provides yet another indication that these models may belong to different tricritical universality classes the authors have also computed this ratio for trails at the high temperature limit with non interacting intersections and found 0 141 or 0 001 in excellent agreement with earlier estimates of this ratio for saws in their swollen phase

the winding angle of planar self avoiding walks the problem of understanding the asymptotic statistical behaviour of the winding angle on of a self avoiding walk of n steps on a planar lattice is posed exact series expansion data for the square lattice up to n 21 are reported these data and monte carlo estimates up to n g 170 steps are fitted well by a logarithmic growth law for 06 the ratio oh appears to approach a limit of 2 9 to 3 2 which is close to the gaussian value 3 heuristic scaling arguments are consistent with simple logarithmic growth and also illuminate the logarithmic behaviour known rigorously for free brownian motion

universal distance ratios for two dimensional polymers by using a quantitative version of the c theorem in conformal theories the authors determine some universal geometrical features of two dimensional critical systems with emphasis on the ratios of mean square distances for polymers

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

universal distance ratios for 2d saws monte carlo and exact series results the mean square distance of a monomer to the origin and the mean square distance of the centre of mass to the origin are studied by monte carlo and exact series methods on the square and lattice the numerical results give strong evidence of a discrepancy with the theoretical prediction of cardy and saleur 1989 based on conformal invariance theory

universal distance ratios for interacting two dimensional polymers we present the hypothesis that at the theta temperature of a single interacting polymer in two dimensions a particular combination of universal distance amplitude ratios is given exactly by a simple formula in terms of critical indices only this generalizes a similar claim for noninteracting self avoiding walks which was derived from conformal invariance considerations we support our hypothesis with a series analysis of interacting self avoiding walks on the square lattice high precision simulations of interacting self avoiding walks on the manhattan lattice at the exact theta point and similar simulations of interacting trails on the square lattice

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

tests of hyperuniversality for self avoiding walks a universal combination of amplitudes for the end to end distance of n step self avoiding walks and for the number of n step self avoiding polygons is estimated numerically for various lattices in d 2 universality of this amplitude combination is confirmed to good accuracy while in d 3 the data are consistent with universality but the error limits are rather large for finite width square lattice strips the authors calculate universal critical point correlation amplitudes by fixed fugacity monte carlo simulations in addition these amplitudes are calculated analytically either exactly or approximately by cardy s conformal mapping approach numerical values agree well with the theoretical predictions

pontryagin s principle for local solutions of control problems with mixed control state constraints this paper deals with optimal control problems of semilinear parabolic equations with pointwise state constraints and coupled integral state control constraints we obtain necessary optimality conditions in the form of a pontryagin s minimum principle for local solutions in the sense of l p p leq infty

combined maximum likelihood estimates for the equicorrelation coefficient combined maximum likelihood estimates for equicorrelation covariance matrices are considered the case of a common equicorrelation rho and possibly different standard deviations sigma 1 sigma k among k experimental groups is examined first and the estimation of rho sigma 1 sigma k is discussed second under the assumption of a common standard deviation and possibly different equicorrelations the estimation of rho 1 rho k sigma is considered in each case maximum likelihood solutions and corresponding large sample variances are presented