on errors in variables for binary regression models summary we consider binary regression models when some of the predictors are measured with error for normal measurement errors structural maximum likelihood estimates are considered we show that if the measurement error is large the usual estimate of the probability of the event in question can be substantially in error especially for high risk groups in the situation of large measurement error we investigate a conditional maximum likelihood estimator and its properties

an infinite number of effectively infinite clusters in critical percolation an infinite number of effectively infinite clusters are predicted at the percolation threshold if effectively infinite means that a cluster s mass increases with a positive power of the lattice size l all these cluster masses increase as ld with the fractal dimension d d v while the mass of the rth largest cluster for fixed l decreases as 1 r with d d in d dimensions these predictions are confirmed by computer simulations for the square lattice where d 91 48 and 91 96

reducing measurement error in student achievement estimation the achievement level is a variable measured with error that can be estimated by means of the rasch model teacher grades also measure the achievement level but they are expressed on a different scale this paper proposes a method for combining these two scores to obtain a synthetic measure of the achievement level based on the theory developed for regression with covariate measurement error in particular the focus is on ordinal scaled grades using the simex method for measurement error correction the result is a measure comparable across subjects with smaller measurement error variance an empirical application illustrates the method

nonlinear and nonparametric regression and instrumental variables we consider regression when the predictor is measured with error and an instrumental variable iv is available the regression function can be modeled linearly nonlinearly or nonparametrically our major new result shows that the regression function and all parameters in the measurement error model are identified under relatively weak conditions much weaker than previously known to imply identifiability in addition we exploit a characterization of the iv estimator as a classical correction for attenuation method based on a particular estimate of the variance of the measurement error this estimate of the measurement error variance allows us to construct functional nonparametric regression estimators making no assumptions about the distribution of the unobserved predictor and structural estimators that use parametric assumptions about this distribution the functional estimators uses simulation extrapolation or deconvolution kernels and the structural method uses bayesian markov chain monte carlo

biased and greedy random walks on two dimensional lattices with quenched randomness the greedy ant within a disordered environment the main characteristics of biased greedy random walks bgrws on two dimensional lattices with real valued quenched disorder on the lattice edges are studied here the disorder allows for negative edge weights in previous studies considering the negative weight percolation nwp problem this was shown to change the universality class of the existing static percolation transition in the presented study four different types of bgrws and an algorithm based on the ant colony optimization heuristic were considered regarding the bgrws the precise configurations of the lattice walks constructed during the numerical simulations were influenced by two parameters a disorder parameter ensuremath rho that controls the amount of negative edge weights on the lattice and a bias strength b that governs the drift of the walkers along a certain lattice direction the random walks are greedy in the sense that the local optimal choice of the walker is to preferentially traverse edges with a negative weight associated with a net gain of energy for the walker here the pivotal observable is the probability that after termination a lattice walk exhibits a total negative weight which is here considered as percolating the behavior of this observable as function of ensuremath rho for different bias strengths b is put under scrutiny upon tuning ensuremath rho the probability to find such a feasible lattice walk increases from zero to 1 this is the key feature of the percolation transition in the nwp model here we address the question how well the transition point ensuremath rho mathrm c resulting from numerically exact and static simulations in terms of the nwp model can be resolved using simple dynamic algorithms that have only local information available one of the basic questions in the physics of glassy systems

approximate quasi likelihood estimation in models with surrogate predictors abstract we consider quasi likelihood estimation with estimated parameters in the variance function when some of the predictors are measured with error we review and extend four approaches to estimation in this problem all of them based on small measurement error approximations a taxonomy of the data sets likely to be available in measurement error studies is developed an asymptotic theory based on this taxonomy is obtained and includes measurement error and berkson error models as special cases

global attractor for a chemotaxis model with prevention of overcrowding abstract chemotaxis model with volume filling introduced by painter and hillen is studied under no flux or dirichlet boundary conditions existence of global in time solution to a full model is proved for some cases existence of a global attractor in the space w 1 p r 2 p n r n is shown

blow up in a higher dimensional chemotaxis system despite logistic growth restriction abstract we study radially symmetric solutions of a class of chemotaxis systems generalizing the prototype u t u u v u u x t 0 0 v m t u x t 0 in a ball r n with parameters 0 0 0 and 1 and m t 1 u x t d x it is shown that when n 5 and 3 2 1 2 n 2 then there exist initial data such that the smooth local in time solution of blows up in finite time this indicates that even superlinear growth restrictions may be insufficient to rule out a chemotactic collapse as is known to occur in the corresponding system without any proliferation

mean field behavior of the negative weight percolation model on random regular graphs we investigate both analytically and numerically the ensemble of minimum weight loops in the negative weight percolation model on random graphs with fixed connectivity and bimodal weight distribution this allows us to study the mean field behavior of this model the analytical study is based on a conjectured equivalence with the problem of self avoiding walks in a random medium the numerical study is based on a mapping to a standard minimum weight matching problem for which fast algorithms exist both approaches yield results that are in agreement on the location of the phase transition on the value of critical exponents and on the absence of any sizable indications of a glass phase by these results the previously conjectured upper critical dimension of d u 6 is confirmed

model of chemotaxis with threshold density and singular diffusion abstract a quasilinear singular parabolic system corresponding to recent models of chemotaxis in which 1 there is an impassable threshold for the density of cells and 2 the diffusion of cells becomes singular fast or superdiffusion when the density approaches the threshold it is proved that for some range of parameters describing the relation between the diffusive and the chemotactic component of the cell flux there are global in time classical solutions which in some cases are separated from the threshold uniformly in time global in time weak solutions in the case of fast diffusion and the set of stationary states are studied as well the applications of the general results to particular models are shown

finite time blowup and global in time unbounded solutions to a parabolic parabolic quasilinear keller segel system in higher dimensions abstract in this paper we consider quasilinear keller segel type systems of two kinds in higher dimensions in the case of a nonlinear diffusion system we prove an optimal with respect to possible nonlinear diffusions generating explosion in finite time of solutions finite time blowup result in the case of a cross diffusion system we give results which are optimal provided one assumes some proper non decay of a nonlinear chemical sensitivity moreover we show that once we do not assume the above mentioned non decay our result cannot be as strong as in the case of nonlinear diffusion without nonlinear cross diffusion terms to this end we provide an example interesting by itself of global in time unbounded solutions to the nonlinear cross diffusion keller segel system with chemical sensitivity decaying fast enough in a range of parameters in which there is a finite time blowup result in a corresponding case without nonlinear cross diffusion

invasion percolation and global optimization invasion bond percolation ibp is mapped exactly into prim close quote s algorithm for finding the shortest spanning tree of a weighted random graph exploring this mapping which is valid for arbitrary dimensions and lattices we introduce a new ibp model that belongs to the same universality class as ibp and generates the minimal energy tree spanning the ibp cluster copyright ital 1996 the american physical society

recursive sampling of random walks self avoiding walks in disordered media the author presents a new algorithm for simulating random walks which is simple versatile and efficient it uses recursive function calls and can be used to obtain unbiased samples with any given length distribution this makes it particularly useful in disordered geometries where the effective connectivity constant is not known a priori when applying it to self avoiding random walks on two dimensional media with quenched randomness he finds evidence for at least two new renormalization group fixed points

stationary solutions of chemotaxis systems the keller segel model is a system of partial differential equations modelling a mutual attraction of amoebae caused by releasing a chemical substance chemotaxis this paper analyzes the stationary solutions of the system with general nonlinearities via bifurcation techniques and gives a criterion for bifurcation of stable nonhomogeneous aggregation patterns examples are discussed with various kinds of nonlinearities modelling the sensitivity of the chemotaxis response

non existence of stationary pattern of a chemotaxis model with logistic growth abstract in this paper we study the non existence of non constant steady state i e stationary pattern for a chemotaxis model with the volume filling effect and logistic cell growth we establish the critical value of the chemotactic coefficient between the existence and the non existence of stationary pattern the proofs mainly rely on the maximum principle the implicit function theorem and the finite covering theorem this work is a supplement and perfection of the known reference

directed polymers in a random medium abstract the problem of a polymer in a random medium can be formulated as follows consider a regular lattice with on each bond ij a random energy ij the energy e w of a self avoiding walk w on this lattice is the sum of the energies of all the bonds visited by the walk then the problem is to compute the partition function z w exp e w t several recent results will be presented 1 the mean field version of this problem can be solved exactly and one observes a low temperature phase similar to the spin glass phase 2 for finite dimensional lattices one can derive bounds on the transition temperature in high enough dimension 3 for hierarchical lattices the problem can be reduced to finding stable laws when one combines random variables in a non linear way for example z z 1 z 2 z 3 z 4

stationary solutions of a volume filling chemotaxis model with logistic growth and their stability in this paper we derive the conditions for the existence of stationary solutions i e nonconstant steady states of a volume filling chemotaxis model with logistic growth over a bounded domain subject to homogeneous neumann boundary conditions at the same time we show that the same system without the chemotaxis term does not admit pattern formations moreover based on an explicit formula for the stationary solutions which is derived by asymptotic bifurcation analysis we establish the stability criteria and find a selection mechanism of the principal wave modes for the stable stationary solution by estimating the leading term of the principal eigenvalue we show that all bifurcations except the one at the first location of the bifurcation parameter are unstable and if the pattern is stable then its principal wave mode must be a positive integer which minimizes the bifurcation parameter for a special case where the carrying capacity is one half we find a necessary and sufficient condition for th

percolation thresholds on planar euclidean relative neighborhood graphs in the present article statistical properties regarding the topology and standard percolation on relative neighborhood graphs rngs for planar sets of points considering the euclidean metric are put under scrutiny rngs belong to the family of proximity graphs i e their edgeset encodes proximity information regarding the close neighbors for the terminal nodes of a given edge therefore they are e g discussed in the context of the construction of backbones for wireless ad hoc networks that guarantee connectedness of all underlying nodes here by means of numerical simulations we determine the asymptotic degree and diameter of rngs and we estimate their bond and site percolation thresholds which were previously conjectured to be nontrivial we compare the results to regular 2d graphs for which the degree is close to that of the rng finally we deduce the common percolation critical exponents from the rng data to verify that the associated universality class is that of standard 2d percolation

asymptotic behavior of solutions to a quasilinear nonuniform parabolic system modelling chemotaxis abstract in this paper we study a quasilinear nonuniform parabolic system modelling chemotaxis and taking the volume filling effect into account the results on the existence of a unique global classical solution was obtained in cie lak 2007 4 however the convergence to equilibrium was not considered in that paper in this paper we first obtain the crucial uniform boundedness of the solution then with the help of a suitable non smooth simon ojasiewicz approach we obtain the results on convergence to equilibrium and the decay rate

correction of logistic regression relative risk estimates and confidence intervals for systematic within person measurement error errors in the measurement of exposure that are independent of disease status tend to bias relative risk estimates and other measures of effect in epidemiologic studies toward the null value two methods are provided to correct relative risk estimates obtained from logistic regression models for measurement errors in continuous exposures within cohort studies that may be due to either random unbiased within person variation or to systematic errors for individual subjects these methods require a separate validation study to estimate the regression coefficient lambda relating the surrogate measure to true exposure in the linear approximation method the true logistic regression coefficient beta is estimated by beta lambda where beta is the observed logistic regression coefficient based on the surrogate measure in the likelihood approximation method a second order taylor series expansion is used to approximate the logistic function enabling closed form likelihood estimation of beta confidence intervals for the corrected relative risks are provided that include a component representing error in the estimation of lambda based on simulation studies both methods perform well for true odds ratios up to 3 0 for higher odds ratios the likelihood approximation method was superior with respect to both bias and coverage probability an example is provided based on data from a prospective study of dietary fat intake and risk of breast cancer and a validation study of the questionnaire used to assess dietary fat intake

simex variance component tests in generalized linear mixed measurement error models in the analysis of clustered data with covariates measured with error a problem of common interest is to test for correlation within clusters and heterogeneity across clusters we examined this problem in the framework of generalized linear mixed measurement error models we propose using the simex method to construct a score test for the null hypothesis that all variance components are zero a key feature of this simex score test is that no assumptions need to be made regarding the distributions of the random eects and the unobserved covariates we illustrate this test by analyzing framingham heart disease data and evaluate its performance by simulation we also propose individual simex score tests for testing the variance components separately both tests can be easily implemented using existing statistical software

measurement error instrumental variables and corrections for attenuation with applications to meta analyses macmahon et al present a meta analysis of the effect of blood pressure on coronary heart disease as well as new methods for estimation in measurement error models for the case when a replicate or second measurement is made of the fallible predictor the correction for attenuation used by these authors is compared to others already existing in the literature as well as to a new instrumental variable method the assumptions justifying the various methods are examined and their efficiencies are studied via simulation compared to the methods we discuss the method of macmahon et al may have bias in some circumstances because it does not take into account i possible correlations among the predictors within a study ii possible bias in the second measurement or iii possibly differing marginal distributions of the predictors or measurement errors across studies a unifying asymptotic theory using estimating equations is also presented

asymptotics for the simex estimator in nonlinear measurement error models abstract cook and stefanski have described a computer intensive method the simex method for approximately consistent estimation in regression problems with additive measurement error in this article we derive the asymptotic distribution of their estimators and show how to compute estimated standard errors these standard error estimators can either be used alone or as prepivoting devices in a bootstrap analysis we also give theoretical justification to some of the phenomena observed by cook and stefanski in their simulations

finite size scaling for percolation above six dimensions we consider percolation in d dimensions for finite samples of linear size l theoretical arguments are presented to show that for d 6 the shift in the percolation threshold pc l pc behaves like a l2 b ld3 for periodic boundary conditions a 0 these predictions are consistent with recent simulations is seven dimensions

low order approximations in deconvolution and regression with errors in variables summary we suggest two new methods which are applicable to both deconvolution and regression with errors in explanatory variables for nonparametric inference the two approaches involve kernel or orthogonal series methods they are based on defining a low order approximation to the problem at hand and proceed by constructing relatively accurate estimators of that quantity rather than attempting to estimate the true target functions consistently of course both techniques could be employed to construct consistent estimators but in many contexts of importance e g those where the errors are gaussian consistency is from a practical viewpoint an unattainable goal we rephrase the problem in a form where an explicit interpretable low order approximation is available the information that we require about the error distribution the error in variables distribution in the case of regression is only in the form of low order moments and so is readily obtainable by a rudimentary analysis of indirect measurements of errors e g through repeated measurements in particular we do not need to estimate a function such as a characteristic function which expresses detailed properties of the error distribution this feature of our methods coupled with the fact that all our estimators are explicitly defined in terms of readily computable averages means that the methods are particularly economical in computing time

boundedness and global existence in the higher dimensional parabolic parabolic chemotaxis system with without growth source abstract in this paper we are concerned with a general class of quasilinear parabolic parabolic chemotaxis systems with without growth source under homogeneous neumann boundary conditions in a smooth bounded domain r n with n 2 it is recently known that blowup is possible even in the presence of superlinear growth restrictions here we derive new and interesting characterizations on the growth versus the boundedness we show that the hard task of proving the l boundedness of the cell density can be reduced to proving its l r boundedness in other words we show that the l r boundedness of the cell density can successfully guarantee its l boundedness and hence its global boundedness where r n or n 2 depending on whether the growth restriction is essentially linear including no growth or superlinear hence a blowup solution also blows up in l p norm for any suitably large p more detailed information on how the growth source affects the boundedness of the solution is derived these results reveal deep understandings of blowup mechanism for chemotaxis models then we use these criteria to establish uniform boundedness and hence global existence of the underlying models logistic source in 2 d cubic source as initially proposed by mimura and tsujikawa in 3 d n 1 st source in n d with n 4 as a consequence in a chemotaxis growth model blowup is impossible if the growth effect is suitably strong finally we underline that our results remove the commonly assumed convexity on the domain

directed negative weight percolation we consider the negative weight percolation model on directed graphs in particular we study the model on a two dimensional weighted periodic centered square lattice bond weights are taken from a distribution that allows for both positive and negative values for a given realization of the disorder a minimally weighted directed loop and path configuration is determined by performing a nontrivial transformation of the original lattice into a minimum weight perfect matching problem for this problem fast polynomial time algorithms are available thus we could study large systems with high accuracy depending on the fraction of negatively and positively weighted bonds on the lattice a continuous phase transition is identified and its characterizing critical exponents are estimated by means of a finite size scaling analysis we observe a strong change of the universality class with respect to standard directed percolation as well as with respect to undirected negative weight percolation furthermore the relation to directed polymers in random media is illustrated

boundedness in a quasilinear parabolic parabolic keller segel system with subcritical sensitivity abstract we consider the quasilinear parabolic parabolic keller segel system u t d u u s u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a convex smooth bounded domain r n with n 1 it is proved that if s u d u c u with 2 n and some constant c 0 for all u 1 then the classical solutions to the above system are uniformly in time bounded provided that d u satisfies some technical conditions such as algebraic upper and lower growth resp decay estimates as u this boundedness result is optimal according to a recent result by the second author winkler 2010 27 which says that if s u d u c u for u 1 with c 0 and some 2 n n 2 then for each mass m 0 there exist blow up solutions with mass u 0 m in addition this paper also proves a general boundedness result for quasilinear non uniformly parabolic equations by modifying the iterative technique of moser alikakos alikakos 1979 1

parameter estimation for differential equation models using a framework of measurement error in regression models differential equation de models are widely used in many scientific fields including engineering physics and biomedical sciences the so called forward problem the problem of simulations and predictions of state variables for given parameter values in the de models has been extensively studied by mathematicians physicists engineers and other scientists however the inverse problem the problem of parameter estimation based on the measurements of output variables has not been well explored using modern statistical methods although some least squares based approaches have been proposed and studied in this article we propose parameter estimation methods for ordinary differential equation ode models based on the local smoothing approach and a pseudo least squares psls principle under a framework of measurement error in regression models the asymptotic properties of the proposed psls estimator are established we also compare the psls method to the corresponding simulation extrapolation

universality of the optimal path in the strong disorder limit we study numerically the optimal paths in two and three dimensions on various disordered lattices in the limit of strong disorder we find that the length l of the optimal path scales with geometric distance r as l approximately r d opt with d opt 1 22 0 01 for d 2 and 1 44 0 02 for d 3 independent of whether the optimization is on a path of weighted bonds or sites and independent of the lattice or its coordination number our finding suggests that the exponent d opt is universal depending only on the dimension of the system

global dynamics of a hyperbolic parabolic model arising from chemotaxis we prove global existence and qualitative behavior of classical solutions for a hyperbolic parabolic system describing chemotaxis on bounded domains it is shown that classical solutions to the initial boundary value problem of the one dimensional model exist globally in time for large initial data and the solutions converge to constant equilibrium states exponentially in time which rigorously demonstrates the collapsing of cell populations in chemotaxis moreover similar results are established for the multidimensional model when the initial data are small

simulation extrapolation the measurement error jackknife abstract this article provides theoretical support for our simulation based estimation procedure simex for measurement error models we do so by establishing a strong relationship between simex estimation and jackknife estimation a result of our investigation is the identification of a variance estimation method for simex that parallels jackknife variance estimation data from the framingham heart study are used to illustrate the variance estimation procedure in logistic regression measurement error models

upper critical dimension of the negative weight percolation problem by means of numerical simulations we investigate the geometric properties of loops on hypercubic lattice graphs in dimensions d 2 through 7 where edge weights are drawn from a distribution that allows for positive and negative weights we are interested in the appearance of system spanning loops of total negative weight the resulting negative weight percolation nwp problem is fundamentally different from conventional percolation as we have seen in previous studies of this model for the two dimensional case here we characterize the transition for hypercubic systems where the aim of the present study is to get a grip on the upper critical dimension d u of the nwp problem for the numerical simulations we employ a mapping of the nwp model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms we characterize the loops via observables similar to those in percolation theory and perform finite size scaling analyses e g three dimensional hypercubic systems with side length up to l 56 sites in order to estimate the critical properties of the nwp phenomenon we find our numerical results consistent with an upper critical dimension d u 6 for the nwp problem

long time behaviour of solutions to a chemotaxis model with volume filling effect the lyapunov functional is constructed for a quasilinear parabolic system which models chemotaxis and takes into account a volume filling effect for some typical case it is proved that the limit set of any trajectory consists of regular stationary solutions some lower and upper bounds on the stationary solutions are found for a given range of parameters there are stationary solutions which are inhomogeneous in space

critical properties of loop percolation models with optimization constraints we study loop percolation models in two and in three space dimensions in which configurations of occupied bonds are forced to form a closed loop we show that the uncorrelated occupation of elementary plaquettes of the square and the simple cubic lattice by elementary loops leads to a percolation transition that is in the same universality class as the conventional percolation in contrast to this an optimization constraint for the loop configurations which then have to minimize a particular generic energy function leads to a percolation transition that constitutes a universality class for which we report the critical exponents implication for the physics of solid on solid and vortex glass models are discussed

theoretical comparison of bootstrap confidence intervals we develop a unified framework within which many commonly used bootstrap critical points and confidence intervals may be discussed and compared in all seven different bootstrap methods are examined each being usable in both parametric and nonparametric contexts emphasis is on the way in which the methods cope with first and second order departures from normality percentile t and accelerated bias correction emerge as the most promising of existing techniques certain other methods are shown to lead to serious errors in coverage and position of critical point an alternative approach based on shortest bootstrap confidence intervals is developed we also make several more technical contributions in particular we confirm efron s conjecture that accelerated bias correction is second order correct in a variety of multivariate circumstances and give a simple interpretation of the acceleration constant

blow up criterion for a hyperbolic parabolic system arising from chemotaxis abstract in this paper we investigate a hyperbolic parabolic system arising from chemotaxis a blow up criterion of local strong solutions to the model in r d is established based on the scaling invariance of the system as a by product we prove a global in time well posedness result when d 1 for large initial data

largest and second largest cluster statistics at the percolation threshold of hypercubic lattices we investigate the scale invariance of the average ratio between the masses of the largest and second largest clusters at percolation we employ a finite size scaling method to estimate percolation thresholds based on the simulations of relatively small lattices and report on estimates for p c in hypercubic lattices with d 2 7 in full agreement with the best literature estimates also we find the critical mass ratio to be strongly dependent on the boundary conditions decreasing with the lattice dimension further we compute several relevant mass distribution functions associated with the two largest clusters which approach to limiting distributions for dg6 finally we discuss the main relevant features of the mass distributions in light of the relative role played by the spanning and nonspanning clusters

optimal path in two and three dimensions we apply the dijkstra algorithm to generate optimal paths between two given sites on a lattice representing a disordered energy landscape we study the geometrical and energetic scaling properties of the optimal path where the energies are taken from a uniform distribution our numerical results for both two and three dimensions suggest that the optimal path for random uniformly distributed energies is in the same universality class as the directed polymers we present physical realizations of polymers in a disordered energy landscape for which this result is relevant s1063 651x9808212 9

simulation extrapolation estimation in parametric measurement error models we describe a simulation based method of inference for parametric measurement error models in which the measurement error variance is known or at least well estimated the method entails adding add

nonparametric methods for solving the berkson errors in variables problem summary it is common in errors in variables problems in regression to assume that the errors are incurred after the experiment in that the observed value of the explanatory variable is an independent perturbation of its true value however if the errors are incurred before the experiment then the true value of the explanatory variable equals a perturbation of its observed value this is the context of the berkson model which is increasingly attracting attention in parametric and semiparametric settings we introduce and discuss nonparametric techniques for analysing data that are generated by the berkson model our approach permits both random and regularly spaced values of the target doses in the absence of data on dosage error it is necessary to propose a distribution for the latter but we show numerically that our method is robust against that assumption the case of dosage error data is also discussed a practical method for smoothing parameter choice is suggested our techniques for errors in variables regression are shown to achieve theoretically optimal convergence rates

phase transitions in diluted negative weight percolation models we investigate the geometric properties of loops on two dimensional lattice graphs where edge weights are drawn from a distribution that allows for positive and negative weights we are interested in the appearance of spanning loops of total negative weight the resulting percolation problem is fundamentally different from conventional percolation as we have seen in a previous study of this model for the undiluted case here we investigate how the percolation transition is affected by additional dilution we consider two types of dilution either a certain fraction of edges exhibits zero weight or a fraction of edges is even absent we study these systems numerically using exact combinatorial optimization techniques based on suitable transformations of the graphs and applying matching algorithms we perform a finite size scaling analysis to obtain the phase diagram and determine the critical properties of the phase boundary we find that the first type of dilution does not change the universality class compared to the undiluted case whereas the second type of dilution leads to a change in the universality class

exact ground states of large two dimensional planar ising spin glasses studying spin glass physics through analyzing their ground state properties has a long history although there exist polynomial time algorithms for the two dimensional planar case where the problem of finding ground states is transformed to a minimum weight perfect matching problem the reachable system sizes have been limited both by the needed cpu time and by memory requirements in this work we present an algorithm for the calculation of exact ground states for two dimensional ising spin glasses with free boundary conditions in at least one direction the algorithmic foundations of the method date back to the work of kasteleyn from the 1960s for computing the complete partition function of the ising model using kasteleyn cities we calculate exact ground states for huge two dimensional planar ising spin glass lattices up to 3000 2 spins within reasonable time according to our knowledge these are the largest sizes currently available kasteleyn cities were recently also used by thomas and middleton in the context of extended ground states on the torus moreover they show that the method can also be used for computing ground states of planar graphs furthermore we point out that the correctness of heuristically computed ground states can easily be verified finally we evaluate the solution quality of heuristic variants of the l bieche et al approach

minimum spanning trees on random networks we show that the geometry of minimum spanning trees mst on random graphs is universal because of this geometric universality we are able to characterize the energy of mst using a scaling distribution p epsilon found using uniform disorder we show that the mst energy for other disorder distributions is simply related to p epsilon we discuss the relationship to invasion percolation to the directed polymer in a random media to uniform spanning trees and also the implications for the broader issue of universality in disordered systems

corrected score estimation via complex variable simulation extrapolation a monte carlo method of computing unbiased estimating equations for the analysis of data measured with error is described asymptotic distribution results are obtained for estimators derived from the monte carlo estimating equations the method is illustrated with examples applications and simulation studies the monte carlo estimating equations are corrected scores in the sense of nakamura and the proposed methods are closely related to the simulation method described by cook and stefanski