generalized linear models for enzyme kinetic data ruppert cressie and carroll 1989 discuss various models for fitting the michaelismenten equations to data on enzyme kinetics i find it surprising that they do not include among the models they consider generalized linear models glms with an inverse link mccullagh and nelder 1989 chap 8 the advantages of glms over data transformation have often been rehearsed see e g nelder and pregibon 1987 the assumption of normality of errors is extended in glms to include any exponential family and is separated from the transformation required to produce additive effects of the systematic factors the data are analysed on the original scale which often makes more sense than the transformed scale in this paper i analyse the enzyme kinetic data quoted by ruppert et al as their table 8 the data are given here in table 1 the postulated relation their equation 3 1 is

finite size scaling in the p state mean field potts glass a monte carlo investigation the p state mean field potts glass with bimodal bond distribution j is studied by monte carlo simulations both for p 3 and p 6 states for system sizes from n 5 to n 120 spins considering particularly the finite size scaling behavior at the exactly known glass transition temperature t c it is shown that for p 3 the moments q k of the spin glass order parameter satisfy a simple scaling behavior q k alpha n k 3 tilde f k n 1 3 1 t t c text k 1 2 3 tilde f k being the appropriate scaling function and t the temperature also the specific heat maxima have a similar behavior c v max alpha text const n 1 3 while moments of the magnetization scale as m k alpha n k 2 the approach of the positions t max of these specific heat maxima to t c as n is nonmonotonic for p 6 the results are compatible with a first order transition q k q jump k as n but since the order parameter q jump at t c is rather small a behavior q k n k 3 as n also is compatible with the data thus no firm conclusions on the finite size behavior of the order parameter can be drawn the specific heat maxima c v max behave qualitatively in the same way as for p 3 consistent with the prediction that there is no latent heat a speculative phenomenological discussion of finite size scaling for such transitions is given for small n n 15 for p 3 n 12 for p 6 the monte carlo data are compared to exact partition function calculations and excellent agreement is found we also discuss ratios r x equiv langle x rangle t langle x rangle t text av 2 text av langle x rangle t text av 2 for various quantities x to test the possible lack of self averaging at t c

rational group decision making a random field ising model at t 0 abstract a modified version of a finite random field ising ferromagnetic model in an external magnetic field at zero temperature is presented to describe group decision making fields may have a non zero average a postulate of minimum inter individual conflicts is assumed interactions then produce a group polarization along one very choice which is however randomly selected a small external social pressure is shown to have a drastic effect on the polarization individual bias related to personal backgrounds cultural values and past experiences are introduced via quenched local competing fields they are shown to be instrumental in generating a larger spectrum of collective new choices beyond initial ones in particular compromise is found to results from the existence of individual competing bias conflict is shown to weaken group polarization the model yields new psychosociological insights about consensus and compromise in groups

some pitfalls for experimenters with random sat abstract we consider the use of random cnf formulas in evaluating the performance of sat testing algorithms and in particular the role that the phase transition phenomenon plays in this use examples from the literature illustrate the importance of understanding the properties of formula distributions prior to designing an experiment we expect this to be of increasing importance in the field

prediction and tolerance intervals with transformation and or weighting we consider estimation of quantiles and construction of prediction and tolerance intervals for a new response following a possibly nonlinear regression fit with transformation and or weighting we consider the case of normally distributed errors and to a lesser extent the nonparametric case in which the error distribution is unknown quantile estimation here follows standard theory although we introduce a simple computational device for likelihood ratio testing and confidence intervals prediction and tolerance intervals are somewhat more difficult to obtain we show that the effect of estimating parameters when constructing tolerance intervals can be expected to be greater than the effect in the prediction problem improved prediction and tolerance intervals are constructed based on resampling techniques in the tolerance interval case a simple analytical correction is introduced we apply these methods to the prediction of automobile stopping distances and salmon production using respectively a he

a quasi likelihood approach to nonnegative matrix factorization a unified approach to nonnegative matrix factorization based on the theory of generalized linear models is proposed this approach embeds a variety of statistical models including the exponential family within a single theoretical framework and provides a unified view of such factorizations from the perspective of quasi likelihood using this framework a family of algorithms for handling signal dependent noise is developed and its convergence proved using the expectation maximization algorithm in addition a measure to evaluate the goodness of fit of the resulting factorization is described the proposed methods allow modeling of nonlinear effects using appropriate link functions and are illustrated using an application in biomedical signal processing

mean field theory and fluctuations in potts spin glasses i a short range potts spin glass is studied a stable non marginal mean field theory is found with one level of replica symmetry breaking and a discontinuous transition for p 4 a complete stability analysis is provided and two different correlation lengths are found above eight dimensions the fluctuations in the ordered phase around this solution are incorporated in a renormalisation group approach and it is found that for a small range of the parameters they restore scaling close to the upper critical dimension for the three state case it appears that fluctuations destroy the stability of the solution for d or 8 and cause the system to undergo a first order phase transition non universal corrections to the equation of state above the upper critical dimension are discussed

a transformation weighting model for estimating michaelis menten parameters abstract there has been considerable disagreement about how best to estimate the parameters in michaelis menten models this document points out that many fitting methods are based on different stochastic models being weighted least squares estimates after appropriate transformation the authors propose a flexible model which can be used to help determine the proper transformation and choice of weights the method is illustrated by examples keywords nonlinear regression lineweaver burke transformation

a minimal algorithm for the 0 1 knapsack problem several types of large sized 0 1 knapsack problems kp may be easily solved but in such cases most of the computational effort is used for sorting and reduction in order to avoid this problem it has been proposed to solve the so called core of the problem a knapsack problem defined on a small subset of the variables the exact core cannot however be identified before kp is solved to optimality thus previous algorithms had to rely on approximate core sizes in this paper we present an algorithm for kp where the enumerated core size is minimal and the computational effort for sorting and reduction also is limited according to a hierarchy the algorithm is based on a dynamic programming approach where the core size is extended by need and the sorting and reduction is performed in a similar lazy way computational experiments are presented for several commonly occurring types of data instances experience from these tests indicate that the presented approach outperforms any known algorithm for kp

optimal designs for michaelis menten kinetic studies many reactions in enzymology are governed by the michaelis menten equation characterising these reactions requires the estimation of the parameters k m and v m a x which determine the michaelis menten equation and this is done by observing rates of reactions at a set of substrate concentrations the choice of substrate concentrations is investigated by determining bayesian d optimal designs for a model in which residuals have a normal distribution with constant variance designs which focus on alternative quantities such as k m or the ratio v m a x k m are also considered the effect on the optimal designs of alternative error distributions is also considered

transformations to symmetry and homoscedasticity abstract this article considers transformations in regression to eliminate skewness and heteroscedasticity of the response we work with the transform both sides model where the relationship between the median response and the independent variables has been identified at least tentatively to preserve this relationship the response and the regression model are transformed in the same way extending the work of others for the location parameter case we propose an estimator that eliminates skewness we also develop an estimator to eliminate heteroscedasticity and an estimator that attempts to induce both symmetry and homoscedasticity both and appear new by comparing and we develop a test of the null hypothesis that there exists a transformation to both symmetry and homoscedasticity we study the question when does the estimator of behave in terms of asymptotic variance as if the regression parameter were known and vice versa the results are of use for telling when the optimal estimator of do

phase transition in an optimal clusterization model abstract an optimal clusterization model resembling the infinite range potts glass type model with j bonds and unrestricted number of states p n is introduced and studied as a function of the q probability of j bonds it is found that the r relative size of the largest cluster or coalition shows a percolation like transition at q 1 2 by a simple renormalization approach and several optimization methods we investigate the r q curves for finite system sizes non trivial consequences for social percolation problems are discussed

performance prediction and preselection for optimization and heuristic solution procedures the operations research literature contains numerous studies on the design and application of optimization and heuristic solution procedures these studies identify a particular optimization problem suggest a general solution procedure and then customize that procedure to improve its efficiency and or accuracy in contrast this paper shows how to use existing solution procedures more effectively we develop a methodology for predicting the relative performance of alternative procedures using easily computed problem characteristics this methodology enables us for any given data set to preselect a solution procedure we apply this preselection methodology to the 0 1 knapsack problem for which two successful optimization procedures dynamic programming and branch and search are available extensive computational testing indicates that substantial savings in average computation time are achieved the benefits of our work include faster and cheaper identification of effective solution procedures as well as an improved understanding of the relationship between problem characteristics and the performance of various procedures our methodology can be applied to many optimization problems to develop easily implemented guidelines for selecting appropriate solution procedures

on the static and dynamical transition in the mean field potts glass we study the static as well as the glassy or dynamical transition in the mean field p state potts glass by numerical solution of the saddle point equations we investigate the static and dynamical transitions for all values of p in the non perturbative regime p 4 the static and dynamical edwards anderson parameter increase with p logarithmically this makes the glassy transition temperature lie very close to the static one we compare the main predictions of the theory with numerical simulations

finite size scaling in the p state mean field potts glass exact statistical mechanics for small samples the mean field potts glass with bimodal bond distribution is studied for p 3 and p 6 potts states via exact summation of the partition function of systems of up to n 15 sites averages over the disorder realizations are also done exactly up to n 8 while random bond configurations are generated for the larger systems our enumeration method is described in some detail and the applicability of finite size scaling fss for our very small systems is discussed for p 3 second order transition the data agree reasonably with the fss relations given by parisi et al for the p 2 ising case for p 6 no clear signs of the predicted first order behaviour could be observed this case is even more affected by finite size effects since the necessary antiferromagnetic bias of the bond distribution introduces an additional correction in the free energy for both p the data are compatible with a vanishing ground state entropy

double exponential families and their use in generalized linear regression abstract in one parameter exponential families such as the binomial and poisson the variance is a function of the mean double exponential families allow the introduction of a second parameter that controls variance independently of the mean double families are used as constituent distributions in generalized linear regressions in which both means and variances are allowed to depend on observed covariates the theory is applied to two examples a logistic regression and a large two way contingency table in such cases the binomial model of variance is often untrustworthy for example because genuine random sampling was infeasible the subjects may have been obtained in clumps so that the statistician should really be using smaller sample sizes clumped sampling is just one of many possible causes of overdispersion a habitual source of concern to users of binomial and poisson models this article concerns a class of regression families that allow the statistician to model overdispersion while carrying

an extended quasi likelihood function summary wedderburn s original definition of quasi likelihood for generalized linear models is extended to allow the comparison of variance functions as well as those of linear predictors and link functions the relationship between generalized linear models and the use of transformations of the response variable is explored and the ideas are illustrated by three examples generalized linear models by allowing the full distributional assumption about the random component in the model to be replaced by a much weaker assumption in which only the first and second moments were defined in making this extension wedderburn widened the scope of generalized linear models in a way very similar to that of gauss when he replaced the assumption of normality in classical linear models by that of equal variance for generalized linear models with distributions in the exponential family likelihood ratio and score tests are used for testing hypotheses concerning nested subsets of covariates in the linear predictor and for assessing hypothesized link functions these methods are also applicable with wedderburn s form of quasi likelihood however neither of these methods is suitable for the comparison of different variance functions in this paper we introduce an extended quasi likelihood function which allows for the comparison of various forms of all the components of a generalized linear model i e the linear predictor the link function and the variance function we then apply the ideas to the analysis of several sets of data

a new algorithm for the 0 1 knapsack problem we present a new algorithm for the optimal solution of the 0 1 knapsack problem which is particularly effective for large size problems the algorithm is based on determination of an appropriate small subset of items and the solution of the corresponding core problem from this we derive a heuristic solution for the original problem which with high probability can be proved to be optimal the algorithm incorporates a new method of computation of upper bounds and efficient implementations of reduction procedures the corresponding fortran code is available we report computational experiments on small size and large size random problems comparing the proposed code with all those available in the literature

nature s way of optimizing we propose a general purpose method for finding high quality solutions to hard optimization problems inspired by self organizing processes often found in nature the method called extremal optimization successively eliminates extremely undesirable components of sub optimal solutions drawing upon models used to simulate far from equilibrium dynamics it complements approximation methods inspired by equilibrium statistical physics such as simulated annealing with only one adjustable parameter its performance proves competitive with and often superior to more elaborate stochastic optimization procedures we demonstrate it here on two classic hard optimization problems graph partitioning and the traveling salesman problem 2000 elsevier science b v all rights reserved

correlation clustering on networks random networks with co existing positive and negative links are studied from the viewpoint of the np hard correlation clustering problem the task is to produce a clustering of the vertices which maximizes the number of positive edges within clusters and the number of negative edges between clusters simulated annealing monte carlo renormalization and molecular dynamics optimization are used to find the optimal cluster structure recently this problem was studied for globally coupled systems and an interesting phase transition like phenomenon was predicted in the thermodynamic limit the relative size of the largest cluster r exhibits a step like behavior as a function of the density of positive links q r 0 if q 1 2 here we prove that when considering random networks with a constant bond density the same phase transition is expected a totally different result emerges however when networks with a fixed average number of connections per node are considered in such cases a nontrivial spin glass type behavior is found where the location of the critical point shifts toward q 1 2 values the results also suggest that instead of the simple step like behavior the r q curve has a more complex shape which depends on the specific topology of the considered network

autocorrelation coefficient for the graph bipartitioning problem abstract local search and its variants simulated annealing and tabu search are widely used heuristics to approximately solve np hard optimization problems to use local search one simply has to specify a neighborhood structure and a cost function which has to be optimized however from a theoretical point of view many questions remain unanswered and one of the most important is which neighborhood structure will provide the best quality solutions the aim of this paper is to theoretically justify some results previously reported by johnson et al 1989 1991 in their extended empirical study concerning simulated annealing and the graph bipartitioning problem and to sharply tune the best landscape among the two reported in that study experimental results perfectly agree with the theoretical predictions

generating hard satisfiability problems abstract we report results from large scale experiments in satisfiability testing as has been observed by others testing the satisfiability of random formulas often appears surprisingly easy here we show that by using the right distribution of instances and appropriate parameter values it is possible to generate random formulas that are hard that is for which satisfiability testing is quite difficult our results provide a benchmark for the evaluation of satisfiability testing procedures

upper bounds and algorithms for hard 0 1 knapsack problems it is well known that many instances of the 0 1 knapsack problem can be effectively solved to optimality also for very large values of n the number of binary variables while other instances cannot be solved for n equal to only a few hundreds we propose upper bounds obtained from the mathematical model of the problem by adding valid inequalities on the cardinality of an optimal solution and relaxing it in a lagrangian fashion we then introduce a specialized iterative technique for determining the optimal lagrangian multipliers in polynomial time a branch and bound algorithm is finally developed computational experiments prove that several classes of hard instances are effectively solved even for large values of n

algorithms for scheduling a single machine to minimize the weighted number of late jobs this paper considers the problem of scheduling n jobs each having a processing time a due date and a weight on a single machine to minimize the weighted number of late jobs an o n log n algorithm is given for solving the linear programming problem obtained by relaxing the integrality constraints in a zero one programming formulation of the problem this linear programming lower bound is used in a reduction algorithm that eliminates jobs from the problem also a branch and bound algorithm that uses the linear programming lower bound is proposed computational results with branch and bound algorithms that use this and other lower bounds and with a dynamic programming algorithm for problems with up to 1000 jobs are given

a mixture of dynamic programming and branch and bound for the subset sum problem given n items each having a weight wi and a container of capacity w the subset sum problemssp is to select a subset of the items whose total weight is closest to without exceeding w the paper presents a mixed approach depth first search dynamic programming to the exact solution of the problem an extensive computational experience is presented comparing the proposed algorithm with that of ahrens finke as well as with the balas zemel algorithm for large problems both easy and hard problems with values of n up to 10 000 are considered

the effects of coefficient correlation structure in two dimensional knapsack problems on solution procedure performance this paper presents the results of an empirical study of the effects of coefficient correlation structure and constraint slackness settings on the performance of solution procedures on synthetic two dimensional knapsack problems 2kp the population correlation structure among 2kp coefficients the level of constraint slackness and the type of correlation product moment or rank are varied in this study representative branch and bound and heuristic solution procedures are used to investigate the influence of these problem parameters on solution procedure performance population correlation structure and in particular the interconstraint component of the correlation structure is found to be a significant factor influencing the performance of both the algorithm and the heuristic in addition the interaction between constraint slackness and population correlation structure is found to influence solution procedure performance

core problems in knapsack algorithms since balas and zemel in the 1980s introduced the so called core problem as an efficient tool for solving the knapsack problem all the most successful algorithms have applied this concept balas and zemel proved that if the weights in the core are uniformly distributed then there is a high probability for finding an optimal solution in the core items outside the core may be fathomed because of reduction rules this paper demonstrates that generally it is not reasonable to assume a uniform distribution of the weights in the core and it is experimentally shown that the heuristic proposed by balas and zemel does not find as good solutions as expected also other algorithms that solve some kind of core problem may be stuck by difficult cores this behavior has apparently not been noticed before because of unsufficient testing capacities leading to difficult problems are identified for several categories of instance types and it is demonstrated that the hitherto applied test instances are easier than the average as a consequence we propose a series of new randomly generated test instances and show how recent algorithms behave when applied to these problems