selection of variables in cluster analysis an empirical comparison of eight procedures eight different variable selection techniques for model based and non model based clustering are evaluated across a wide range of cluster structures it is shown that several methods have difficulties when non informative variables i e random noise are included in the model furthermore the distribution of the random noise greatly impacts the performance of nearly all of the variable selection procedures overall a variable selection technique based on a variance to range weighting procedure coupled with the largest decreases in within cluster sums of squares error performed the best on the other hand variable selection methods used in conjunction with finite mixture models performed the worst

cohomological dimension cofiniteness and abelian categories of cofinite modules abstract let r be a commutative noetherian ring i j be ideals of r and m be a finitely generated r module in this paper it is shown that q j m q i m cd j m i m furthermore it is shown that for any ideal i of r and any finitely generated r module m with q i m 1 the local cohomology modules h i i m are i cofinite for all integers i 0 as a consequence of this result it is shown that if q i r 1 then for any finitely generated r module m the local cohomology modules h i i m are i cofinite for all integers i 0 finally it is shown that the category of all i cofinite r modules c r i c o f is an abelian subcategory of the category of all r modules whenever r m is a complete noetherian local ring and i is an ideal of r with q i r 1 these assertions answer affirmatively two questions raised by r hartshorne in 16 in the some special cases

cofiniteness with respect to ideals of dimension one we prove that the category of modules cofinite with respect to an ideal of dimension one in a noetherian ring is a full abelian subcategory of the category of modules the proof is based on a criterion for cofiniteness with respect to an ideal of dimension one namely for such ideals it suffices that the two first ext modules in the definition for cofiniteness are finitely generated this criterion is also used to prove very simply that all local cohomology modules of a finitely generated module with respect to an ideal of dimension one in an arbitrary noetherian ring are cofinite with respect to the ideal

sample function properties of multi parameter stable processes the almost sure behaviour of the sample functions of the vectorvalued n parameter wiener process and its stable analogues is investigated especially their small fluctuations in particular laws of the simple and of the iterated logarithm are established for the supremum of the local time increments or sojourn times these results give precise information about the minimum oscillation of the sample functions in addition the hausdorff measure problem for the graph and the range of these processes is solved

probabilistic measures of adequacy of a numerical search for a global maximum abstract measures of the probability of all unobserved species are applied to the problem of assessing the adequacy of a search for a global maximum using random starting points the measures as used here estimate the probability that an iterative algorithm using a randomly selected starting point will find a solution not observed in previous random starting points the probability of an unobserved global maximum is less than or equal to this probability we used these measures to evaluate the adequacy of our search procedure for the maximum likelihood estimates of the parameters of a mixture of two normals these measures indicated that for most problems generated there was little chance that there were unobserved domains of convergence occasional problems however had appreciable estimated probabilities in such problems examination of the data suggested regions where a more focused search for unobserved domains of convergence was warranted

cofiniteness of local cohomology modules for ideals of small dimension abstract let r be a commutative noetherian ring and let m be a non zero finitely generated r module let i be an ideal of r and t a non negative integer such that dim supp h i i m 1 for all i t it is shown that the r modules h i 0 m h i 1 m h i t 1 m are i cofinite and the r module hom r r i h i t m is finitely generated this immediately implies that if i has dimension one i e dim r i 1 then h i i m is i cofinite for all i 0 this is a generalization of the main results of delfino and marley d delfino t marley cofinite modules and local cohomology j pure appl algebra 121 1997 45 52 and yoshida k i yoshida cofiniteness of local cohomology modules for ideals of dimension one nagoya math j 147 1997 179 191 for an arbitrary noetherian ring r also we prove that if r is local and dim supp h i i m 2 for all i t then the r modules ext r j r i h i i m and hom r r i h i t m are weakly laskerian for all i t and all j 0 as a consequence it follows that the set of associated primes of h i i m is finite for all i 0 whenever dim r i 2

solution and estimation of linear rational expectations models abstract this paper addresses the issue of solution and estimation of linear rational expectations models it confirms via the method of undetermined coefficients the finding that these models do not in general imply unique solutions for the variables they explain but it provides evidence in the form of a monte carlo experiment that one may recover accurate estimates of the parameters that characterize the solution set with which the data were generated the estimation strategy proposed and implemented is fiml subject to the restrictions placed on the final form by the structural equations the hypothesis of rational expectations and the assumption of a stable multivariate moving average representation for the endogenous variables

a hybrid shuffled complex evolution approach based on differential evolution for unconstrained optimization numerous optimization methods have been proposed for the solution of the unconstrained optimization problems such as mathematical programming methods stochastic global optimization approaches and metaheuristics in this paper a metaheuristic algorithm called modified shuffled complex evolution msce is proposed where an adaptation of the downhill simplex search strategy combined with the differential evolution method is proposed the efficiency of the new method is analyzed in terms of the mean performance and computational time in comparison with the genetic algorithm using floating point representation gaf and the classical shuffled complex evolution sce ua algorithm using six benchmark optimization functions simulation results and the comparisons with sce ua and gaf indicate that the msce improves the search performance on the five benchmark functions of six tested functions

an extended mind evolutionary computation model for optimizations the paper makes an analysis on the simulated mechanisms of mind evolutionary computation mec firstly and proposes an extended computation model for mec emec emec manipulates the search based on the behavior space and the information space all operations in the behavior space are processed based on groups that symbolize the solution area while the operations in the information space are done based on the billboards that are used to record the evolutionary information all components of emec are formulated in details including the similar taxis operation the cooperation operation and a simulated annealing based dissimilation operation sado emec emphasizes on the share and the guide of the information in the search and gets a performance superior to the simple mec the proposed emec was performed on some well known benchmark problems the experimental results show emec is a robust global optimization algorithm and can alleviate the premature convergence validly

generalized simulated annealing for function optimization a generalized simulated annealing method has been developed and applied to the optimization of functions possibly constrained having many local extrema the method is illustrated in some difftcult pedagogical examples and used to solve a problem analyzed by bates technometrics 25 pp 373 376 1983 for which we identify an improved optimum the sensitivity of the solution to changes in the constraints and in other specifications of the problem is analyzed and discussed

modifications of real code genetic algorithm for global optimization a series of modifications to the real coded genetic algorithm for the task of locating the global minimum of multidimensional functions are presented here these modifications include a new stopping rule a novel mutation mechanism and a periodically application of a local search procedure the proposed modifications are tested on a series of optimization problems and the results are reported

fernique type inequalities and moduli of continuity for anisotropic gaussian random fields this paper is concerned with sample path properties of anisotropic gaussian random fields we establish fernique type inequalities and utilize them to study the global and local moduli of continuity for anisotropic gaussian random fields applications to fractional brownian sheets and to the solutions of stochastic partial differential equations are investigated

on a category of cofinite modules which is abelian let a be a noetherian local ring and i an ideal of a of dimension one our purpose of this paper is to prove that the category mathcal m a i cof of cofinite modules is abelian consequently this assertion answers affirmatively the questions given by hartshorne invent math 9 147 1970 cf sect 2 four questions and one theorem for an ideal of dimension one over a local ring

global optimization by an improved differential evolutionary algorithm a hybrid differential evolutionary de algorithm for global optimization is proposed in the new algorithm the stochastic properties of chaotic systems are used to spread the individuals in search spaces as much as possible the pattern search method is employed to speed up the local exploiting and the de operators are used to jump to a better point the global convergence is proved three typical chaotic systems are investigated in detail numerical experiments on benchmark examples including 13 high dimensional functions demonstrate that the new method achieved an improved success rate and final solution with less computational effort

stochastic global optimization methods part 1 clustering methods in this stochastic approach to global optimization clustering techniques are applied to identify local minima of a real valued objective function that are potentially global three different methods of this type are described their accuracy and efficiency are analyzed in detail

hausdorff measure of trajectories of multiparameter fractional brownian motion consider 0 1 and the gaussian process y t on r n with covariance e y t y s t 2 s 2 t s 2 where t is the euclidean norm of t consider independent copies x 1 x d of y and the process x t x 1 t x d t valued in r d in the transient case n d we show that a s for each compact set l of r n with nonempty interior we have 0 x l where denotes the hausdorff measure associated with the function e e n log log 1 e this result extends work of a goldman in the case 1 2 the proofs are considerably simpler

a filled function method for finding a global minimizer of a function of several variables the concept of a filled function is introduced we construct a particular filled function and analyze its properties an algorithm for global minimization is generated based on the concept and properties of the filled function some typical examples with 1 to 10 variables are tested and computational results show that in most cases this algorithm works better than the tunneling algorithm the advantages and disadvantages are analyzed and further research directions are discussed

stochastic global optimization methods part 11 multi level methods in part ii of our paper two stochastic methods for global optimization are described that with probability 1 find all relevant local minima of the objective function with the smallest possible number of local searches the computational performance of these methods is examined both analytically and empirically

local times of fractional brownian sheets let b0h b0h t t i mathbb r n be a real valued fractional brownian sheet consider the n d gaussian random field bh defined by bh t bh1 t bhd t t i mathbb r n where bh1 bhd are independent copies of b0h in this paper the existence and joint continuity of the local times of bh are established

sloped muscle excitation waveforms improve the accuracy of forward dynamic simulations abstract mathematical models of the muscle excitation are useful in forward dynamic simulations of human movement tasks one objective was to demonstrate that sloped as opposed to rectangular excitation waveforms improve the accuracy of forward dynamic simulations a second objective was to demonstrate the differences in simulated muscle forces using sloped versus rectangular waveforms to fulfill these objectives surface emg signals from the triceps brachii and elbow joint angle were recorded and the intersegmental moment of the elbow joint was computed from 14 subjects who performed two cyclic elbow extension experiments at 200 and 300 deg s additionally the surface emg signals from the leg musculature joint angles and pedal forces were recorded and joint intersegmental moments were computed during a more complex pedaling task 90 rpm at 250 w using forward dynamic simulations four optimizations were performed in which the experimental intersegmental moment was tracked for the elbow extension tasks and four optimizations were performed in which the experimental pedal angle pedal forces and joint intersegmental moments were tracked for the pedaling task in these optimizations the three parameters onset and offset time and peak excitation defining the sloped triangular quadratic and hanning and rectangular excitation waveforms were varied to minimize the difference between the simulated and experimentally tracked quantities for the elbow extension task the intersegmental elbow moment root mean squared error onset timing error and offset timing error were less from simulations using a sloped excitation waveform compared to a rectangular excitation waveform p 0 001 the average and peak muscle forces were from 7 to 16 larger and 20 28 larger respectively when using a rectangular excitation waveform the tracking error for pedaling also decreased when using a sloped excitation waveform with the quadratic waveform generating the smallest tracking errors for both tasks these results support the use of sloped over rectangular excitation waveforms to establish greater confidence in the results of forward dynamic simulations

global optimization of statistical functions with simulated annealing abstract many statistical methods rely on numerical optimization to estimate a model s parameters unfortunately conventional algorithms sometimes fail even when they do converge there is no assurance that they have found the global rather than a local optimum we test a new optimization algorithm simulated annealing on four econometric problems and compare it to three common conventional algorithms not only can simulated annealing find the global optimum it is also less likely to fail on difficult functions because it is a very robust algorithm the promise of simulated annealing is demonstrated on the four econometric problems

local cohomology and serre subcategories the membership of the local cohomology modules h a n m of a module m in certain serre subcategories of the category of modules is studied from below i n generalizations of depth and regular

precision and approximate flatness in artificial neural networks several of the major classes of artificial neural networks output functions are linear combinations of elements of approximately flat sets this gives a tool for understanding the precision problem as well as providing a rationale for mixing types of networks approximate flatness also helps explain the power of artificial neural network techniques relative to series regressions series regressions take linear combinations of flat sets while neural networks take linear combinations of the much larger class of approximately flat sets

mixed fractional brownian sheets and their applications let x x t t r n be an n d mixed fractional brownian sheet that is x t b t ab t for all t r n where b and b are two independent n d fractional brownian sheets with hurst indices 1 n 0 1 n and 1 n 0 1 n respectively and where a r is a nonzero constant in this paper we obtain the hausdorff and packing dimensions of the range x 0 1 n the graph grx 0 1 n and the level sets for the mixed fractional brownian sheet x we then establish the exact uniform and local moduli of continuity for the real valued mixed fractional brownian sheet x0 as an application we study the regularity of the collision local times of two independent fractional brownian sheets and provide a sufficient condition for the collision local times having a joint continuous version we also determine the hausdorff and packing dimensions of the set of collision times

monte carlo tests with nuisance parameters a general approach to finite sample inference and nonstandard asymptotics abstract the technique of monte carlo mc tests dwass 1957 annals of mathematical statistics 28 181 187 barnard 1963 journal of the royal statistical society series b 25 294 provides a simple method for building exact tests from statistics whose finite sample distribution is intractable but can be simulated when no nuisance parameter is involved we extend this method in two ways first by allowing for mc tests based on exchangeable possibly discrete test statistics second by generalizing it to statistics whose null distribution involves nuisance parameters maximized mc mmc tests simplified asymptotically justified versions of the mmc method are also proposed these provide a simple way of improving standard asymptotics and dealing with nonstandard asymptotics

holder conditions for the local times and the hausdorff measure of the level sets of gaussian random fields let y t t n be a real valued strongly locally nondeterministic gaussian random field with stationary increments and y 0 0 consider the n d gaussian random field defined by where x 1 x d are independent copies of y the local and global holder conditions in the set variable for the local time of x t are established and the exact hausdorff measure of the level set x 1 x is evaluated

a new approximate point optimal test of a composite null hypothesis in this paper we use the generalized neyman pearson lemma to introduce a new approximate point optimal test that can be used for testing a composite null hypothesis against a composite alternative the new test involves finding multiple critical values two methods for obtaining these critical values are outlined we report simulations of the application of this test to two composite non nested testing problems namely testing for first order moving average ma 1 errors against first order autoregressive ar 1 errors in the linear regression model and testing for ar 1 errors against integrated ma 1 ima 1 1 errors in the linear model we compare the performance of the new test with silvapulle and king s 1991 approximate point optimal test and some asymptotic tests and find that the new test has a clear advantage over the other tests particularly for the second testing problem

principal component analysis combined with truncated newton minimization for dimensionality reduction of chemical databases the similarity and diversity sampling problems are two challenging optimization tasks that arise in the analysis of chemical databases as a first step to their solution we propose an efficient projection refinement protocol based on the principal component analysis pca and the truncated newton minimization method implemented by our package tnpack pca tnpack we show that pca can provide the same initial guess as the singular value decomposition svd for the optimization task of solving the distance geometry optimization problem if each column of a database matrix has a mean of zero hence our pca tnpack approach is analogous to the svd tnpack projection refinement protocol that we developed recently for visualizing large chemical databases using pca tnpack and the merck mddr database mdl drug data report we further investigate the projection refinement procedure with regards to the preservation of the original clusters of chemical compounds the accuracy of similarity and diversity sampling of chemical compounds and the potential application in the study of structure activity relationships we also explore by simple experiments accuracy and efficiency aspects of the pca tnpack procedure compared to those of a global optimization algorithm simulated annealing as implemented by the program package simann in terms of producing the projection mapping of a database numerical results show that the 2d pca tnpack mapping can preserve the distance relationships of the original database and is thus valuable as a first step in similarity and diversity applications of course the generation of a global rather than local minimizer and its interpretation in terms of pharameceutical applications remains a challenge since all numerical tests are performed on the merck mddr database results are representative of realistic cases encountered in the field of drug design and may help analyze properties of medicinal compounds

a theoretical analysis of preferred pedaling rate selection in endurance cycling one objective of this study was to investigate whether neuromuscular quantities were associated with preferred pedaling rate selection during submaximal steady state cycling from a theoretical perspective using a musculoskeletal model with an optimal control analysis specific neuromuscular quantities of interest were the individual muscle activation force stress and endurance to achieve this objective a forward dynamic model of cycling and optimization framework were used to simulate pedaling at three different rates of 75 90 and 105 rpm at 265 w the pedaling simulations were produced by optimizing the individual muscle excitation timing and magnitude to reproduce experimentally collected data the results from these pedaling simulations indicated that all neuromuscular quantities were minimized at 90 rpm when summed across muscles in the context of endurance cycling these results suggest that minimizing neuromuscular fatigue is an important mechanism in pedaling rate selection a second objective was to determine whether any of these quantities could be used to predict the preferred pedaling rate by using the quantities with the strongest quadratic trends as the performance criterion to be minimized in an optimal control analysis these quantities were analyzed to assess whether they could be further minimized at 90 rpm and produce normal pedaling mechanics the results showed that both the integrated muscle activation and average endurance summed across all muscles could be further minimized at 90 rpm indicating that these quantities cannot be used individually to predict preferred pedaling rates

a genetic algorithm approach to find the best regression econometric model among the candidates although statistical modeling is a common task in different fields of science it is still difficult to estimate the best model that can accurately describe inherent characteristics of a system for which historical or experimental data are available since we may classify estimating techniques as optimizations we can model this problem as an optimization problem and solve it by a new heuristic algorithm like neural networks genetic algorithms and tabu search or by classic ones such as regression and econometric models in this paper we propose a new type of genetic algorithm to find the best regression model among all suggested and evaluate its performances by an economical case study

diagnostic analysis and computational strategies for estimating discrete time duration models a monte carlo study abstract this paper uses monte carlo analysis to study important and contentious issues in estimating single spell discrete time duration models we find simulated annealing dominates gradient methods for recovering true models we recommend a partially flexible step function for duration dependence combined with likelihood ratio tests for determining support points of unobserved heterogeneity we find that ignoring time changing features of explanatory variables introduces substantial biases in model coefficient and average partial effect estimates these biases do not diminish as sample size increases

a stopping rule for the computation of generalized method of moments estimators to obtain consistency and asymptotic normality a generalized method of moments gmm estimator typically is defined to be an approximate global minimizer of a gmm criterion function to compute such an estimator however can be problematic because of the difficulty of global optimization in consequence practitioners usually ignore the problem and take the gmm estimator to be the result of a local optimization algorithm this yields an estimator that is not necessarily consistent and asymptotically normal the use of a local optimization algorithm also can run into the problem of instability due to flats or ridges in the criterion function which makes it difficult to know when to stop the algorithm to alleviate these problems of global and local optimization we propose a stopping rule sr procedure for computing gmm estimators the sr procedure eliminates the need for global search with high probability and it provides an explicit sr for problems of stability that may arise with local optimization problems

small values of gaussian processes and functional laws of the iterated logarithm we estimate small ball probabilities for locally nondeterministic gaussian processes with stationary increments a class of processes that includes the fractional brownian motions these estimates are used to prove chung type laws of the iterated logarithm

enhancing pso methods for global optimization the particle swarm optimization pso method is a well established technique for global optimization during the past years several variations of the original pso have been proposed in the relevant literature because of the increasing necessity in global optimization methods in almost all fields of science there is a great demand for efficient and fast implementations of relative algorithms in this work we propose three modifications of the original pso method in order to increase the speed and its efficiency that can be applied independently in almost every pso variant these modifications are a a new stopping rule b a similarity check and c a conditional application of some local search method the proposed were tested using three popular pso variants and a variety test functions we have found that the application of these modifications resulted in significant gain in speed and efficiency