probabilistic generation of finite simple groups ii abstract in earlier work it was shown that each nonabelian finite simple group g has a conjugacy class c such that whenever 1 x g the probability is greater than 1 10 that g x y for a random y c much stronger asymptotic results were also proved here we show that allowing equality the bound 1 10 can be replaced by 13 42 and excluding an explicitly listed set of simple groups the bound 2 3 holds we use these results to show that any nonabelian finite simple group g has a conjugacy class c such that if x 1 x 2 are nontrivial elements of g then there exists y c such that g x 1 y x 2 y similarly aside from one infinite family and a small explicit finite set of simple groups g has a conjugacy class c such that if x 1 x 2 x 3 are nontrivial elements of g then there exists y c such that g x 1 y x 2 y x 3 y we also prove analogous but weaker results for almost simple groups

generation and random generation from simple groups to maximal subgroups abstract let g be a finite group and let d g be the minimal number of generators for g it is well known that d g 2 for all non abelian finite simple groups we prove that d h 4 for any maximal subgroup h of a finite simple group and that this bound is best possible we also investigate the random generation of maximal subgroups of simple and almost simple groups by applying a recent theorem of jaikin zapirain and pyber we show that the expected number of random elements generating such a subgroup is bounded by an absolute constant we then apply our results to the study of permutation groups in particular we show that if g is a finite primitive permutation group with point stabilizer h then d g 1 d h d g 4

finite index subgroups of mapping class groups let g 3 and n 0 and let mg n be the mapping class group of a surface of genus g with n boundary components we prove that mg n contains a unique subgroup of index 2g 1 2g 1 up to conjugation a unique subgroup of index 2g 1 2g 1 up to conjugation and the other proper subgroups ofmg n are of index greater than 2g 1 2g 1 in particular the minimum index for a proper subgroup of mg n is 2g 1 2g 1 ams subject classification primary 57m99 secondary 20g40 20e28 0 introduction and statement of results the interaction between mapping class groups and finite groups has long been a topic of interest the famous hurwitz bound of 1893 showed that the mapping class group of a closed riemann surface of genus g has an upper bound of 84 g 1 for the order of its finite subgroups and kerckhoff showed that the order of finite cyclic subgroups is bounded above by 4g 2 19 20 the subject of finite index subgroups of mapping class groups was brought into focus by grossman s discovery that the mapping class group mg n 0 homeo g n of an oriented surface g n of genus g and n boundary components is residually finite and thus well endowed with subgroups of finite index 15 homeo g n denotes the space of those homeomorphisms of g n that preserve the orientation and are the identity on the boundary this prompts the dual question what is the minimum index mi mg n of a proper subgroup of finite index in mg n results to date have suggested that like the maximum finite order question the minimum index question should have an answer that is linear in g the best previously published bound is mi mg n 4g 4 for g 3 see 26 this inequality is used by aramayona and souto to prove that if g 6 and g 2g 1 then any nontrivial homomorphism mg n mg n is induced by an embedding 1 it is also an important ingredient in the proof of zimmermann 33 that for g 3 and 4 the minimal nontrivial quotient of mg 0 is sp2g f2 the headline result of this paper is the following exact exponential bound theorem 0 1 for g 3 and n 0 mi mg n mi sp2g z mi sp2g f2 2g 1 2g 1 this exponential bound is all the more surprising since in similar questions we get linear expected bounds for instance bridson 5 6 has proved that a mapping class group of a surface

a comparison of simulated annealing cooling strategies using computer experiments on a simple three state system and an np complete system of permanents we compare different proposed simulated annealing schedules in order to find the cooling strategy which has the least total entropy production during the annealing process for given initial and final states and fixed number of iterations the schedules considered are constant thermodynamic speed exponential logarithmic and linear cooling schedules the constant thermodynamic speed schedule is shown to be the best we are actually considering two different schedules with constant thermodynamic speed the original one valid for near equilibrium processes and a version based on the natural timescale valid also at higher speeds the latter one delivers better results especially in case of fast cooling or when the system is far from equilibrium also with the lowest energy encountered during the entire optimization the best so far energy as the indicator of merit constant thermodynamic speed is superior finally we have compared two different estimators of the relaxation time one estimator is using the second largest eigenvalue of the thermalized form of the transition probability matrix and the other is using a simpler approximation for small deviations from equilibrium these two different expressions only agree at high temperatures

a test of weak separability for multi way functional data with application to brain connectivity studies this paper concerns the modeling of multi way functional data where double or multiple indices are involved we introduce a concept of weak separability the weakly separable structure supports the use of factorization methods that decompose the signal into its spatial and temporal components the analysis reveals interesting connections to the usual strongly separable covariance structure and provides insights into tensor methods for multi way functional data we propose a formal test for the weak separability hypothesis where the asymptotic null distribution of the test statistic is a chi square type mixture the method is applied to study brain functional connectivity derived from source localized magnetoencephalography signals during motor tasks

on the orders of primitive groups with restricted nonabelian composition factors we prove that given c0 there exists c such that the following holds if g is a primitive permutation group of degree n no composition factor of which is an alternating group of degree greater than c0 or a classical group of dimension greater than c0 then g nc in particular if the nonabelian composition factors of g have bounded order then g is polynomially bounded

transitive projective planes and insoluble groups suppose that a group g acts transitively on the points of p a finite non desarguesian projective plane we prove first that the sylow 2subgroups of g are cyclic or generalized quaternion we then prove that if g is insoluble then g o g is isomorphic to sl2 5 or sl2 5 2 msc 2000 20b25 51a35

overgroups in gl nr f of certain subgroups of sl n k i for any pair of division rings k and f with k f and dimfk r we determine all the overgroups of sl n k in gl nr f as well as the overgroups of sp n k in gl nr f for commutative k and even n the overgroups of su n k f and n k q in gl nr f will be determined in another paper overgroups in gl nr f of certain subgroups of sl n k ii

subgroups of maximal rank in finite exceptional groups of lie type the purpose of this paper is to investigate a large and natural class of maximal subgroups of the finite exceptional groups of lie type which we call subgroups of maximal rank these subgroups play a prominent role both in the classification of local maximal subgroups in 9 theorem 1 and in the reduction theorem for subgroups in 28 theorem 2 in 9 it is shown that any local maximal subgroup of a finite exceptional group of lie type is either a subgroup of maximal rank or one of a small list of exceptions and in 28 using this result it is proved that any maximal subgroup is either of maximal rank or almost simple or in a known list to describe these subgroups we require the following notation let g be a simple adjoint algebraic group over an algebraically closed field k of characteristic p 0 and let o be an endomorphism of g such that l ga is a finite exceptional simple group of lie type over fq where q p let a be a group such that f x l the group aut l is generated by ga together with field and graph automorphisms see 5 38 all of which extend to morphisms of the abstract group g commuting with o thus there is a subgroup x of caut c a such that x x o and so x acts on the set of a stable subsets of g for a a stable subset y we write nx y for the stabilizer in x of y if d is a a stable closed connected reductive subgroup of g containing a maximal torus t of g and m nx d we call m a subgroup of maximal rank in x in this paper we determine the structure and conjugacy classes of those subgroups of maximal rank which are maximal in x

a characterization of solvability for finite groups in terms of their frame abstract the frame of a group is the poset of conjugacy classes of all its proper subgroups in this paper we will prove that a finite group is solvable if and only if every collection of maximal elements of its frame has a well defined meet and the poset consisting of all such meets including the meet of the empty set is a modular lattice

random generation of finite and profinite groups and group enumeration the following article appeared in annals of mathematics 173 2 2011 769 814 and may be found at http annals math princeton edu 2011 173 2 p04

explicit surjectivity of galois representations for abelian surfaces and gl 2 varieties abstract let a be an absolutely simple abelian variety without potential complex multiplication defined over the number field k suppose that either dim a 2 or a is of gl 2 type we give an explicit bound l 0 a k such that for every prime l l 0 a k the image of gal k k in aut t l a is as large as it is allowed to be by endomorphisms and polarizations

testing differential networks with applications to the detection of gene gene interactions model organisms and human studies have led to increasing empirical evidence that interactions among genes contribute broadly to genetic variation of complex traits in the presence of gene by gene interactions the dimensionality of the feature space becomes extremely high relative to the sample size this imposes a significant methodological challenge in identifying gene by gene interactions in the present paper through a gaussian graphical model framework we translate the problem of identifying gene by gene interactions associated with a binary trait d into an inference problem on the difference of two high dimensional precision matrices which summarize the conditional dependence network structures of the genes we propose a procedure for testing the differential network globally that is particularly powerful against sparse alternatives in addition a multiple testing procedure with false discovery rate control is developed to infer the specific structure of the differential network theoretical justification is provided to ensure the validity of the proposed tests and optimality results are derived under sparsity assumptions a simulation study demonstrates that the proposed tests maintain the desired error rates under the null and have good power under the alternative the methods are applied to a breast cancer gene expression study

joint testing and false discovery rate control in high dimensional multivariate regression multivariate regression with high dimensional covariates has many applications in genomic and genetic research in which some covariates are expected to be associated with multiple responses this paper considers joint testing for regression coefficients over multiple responses and develops simultaneous testing methods with false discovery rate control the test statistic is based on inverse regression and bias corrected group lasso estimates of the regression coefficients and is shown to have an asymptotic chi squared null distribution a row wise multiple testing procedure is developed to identify the covariates associated with the responses the procedure is shown to control the false discovery proportion and false discovery rate at a prespecified level asymptotically simulations demonstrate the gain in power relative to entrywise testing in detecting the covariates associated with the responses the test is applied to an ovarian cancer dataset to identify the microrna regulators that regulate protein expression

explicit representations of maximal subgroups of the monster abstract most of the maximal subgroups of the monster are now known but in many cases they are hard to calculate in we produce explicit small representations of all the maximal subgroups which are not 2 local the representations we construct are available on the world wide web at http brauer maths qmul ac uk atlas

hybrid evolutionary fuzzy learning scheme in the applications of traveling salesman problems abstract this study develops a hybrid evolutionary fuzzy learning algorithm that automatically determines the near optimal traveling path in large scale traveling salesman problems lstsps identifying solutions for lstsps is one of the most complicated topics in the field of global combinatorial optimization problems the proposed hybrid evolutionary fuzzy learning scheme combines the advantages of the adaptive fuzzy c means fcm simple max min merging concept simulated annealing sa learning algorithm and an efficient table transform based particle swarm optimization tpso this study uses the proposed method to deal with the large size tsp routing system the evolutionary tpso learning algorithm is applied to optimize the traveling table which in turn extracts the appropriate traveling table sequence codes for approaching the shorter traveling path the sa local optimal learning algorithm works after the tpso learning scheme using three operators to acquire the optimal traveling solution inversion translation and switching the other considerable notation is to divide the large scale cities into suitable subgroup cities to improve the efficiency of training machine the popular fcm algorithm is a valid unsupervised clustering method that identifies the relational grades of a given traveling city dataset separating them into popular categories based on the critical issue in maximal city number to break the city nodes of the traveling loop and reconnect suitable nodes again with the minimal distance searching procedure the proposed simple but powerful max min merging algorithm to rebuild the new traveling path various sizes of tsp testing instances reveal that the developed hybrid evolutionary fuzzy learning algorithm achieves better results than other learning methods in both the quality of routing and computing time

confidence regions for entries of a large precision matrix we consider the statistical inference for high dimensional precision matrices specifically we propose a data driven procedure for constructing a class of simultaneous confidence regions for a subset of the entries of a large precision matrix the confidence regions can be applied to test for specific structures of a precision matrix and to recover its nonzero components we first construct an estimator for the precision matrix via penalized node wise regression we then develop the gaussian approximation to approximate the distribution of the maximum difference between the estimated and the true precision coefficients a computationally feasible parametric bootstrap algorithm is developed to implement the proposed procedure the theoretical justification is established under the setting which allows temporal dependence among observations therefore the proposed procedure is applicable to both independent and identically distributed data and time series data numerical results with both simulated and real data confirm the good performance of the proposed method

a computer assisted analysis of some matrix groups abstract we use algorithms developed recently for the study of linear groups to investigate a sequence of matrix groups defined over gf 2 these are images of representations of certain finitely presented groups considered by soicher in a study of simplicial complexes related to the suzuki sequence graphs

on conjugacy classes of maximal subgroups of finite simple groups and a related zeta function we prove that the number of conjugacy classes of maximal subgroups of bounded order in a finite group of lie type of bounded rank is bounded for exceptional groups this solves a longstanding open problem the proof uses among other tools some methods from geometric invariant theory using this result we provide a sharp bound for the total number of conjugacy classes of maximal subgroups of lie type groups of fixed rank drawing conclusions regarding the behaviour of the corresponding zeta function g s m maxg g m s which appears in many probabilistic applications more specifically we are able to show that for simple groups g and for any fixed real number s 1 g s 0 as g this confirms a conjecture made in 27 we also apply these results to prove the conjecture made in 29 that the symmetric group sn has n o 1 conjugacy classes of primitive maximal subgroups 2000 mathematics classification numbers 20e28 20g15 20d06

gaussian and bootstrap approximations for high dimensional u statistics and their applications this paper studies the gaussian and bootstrap approximations for the probabilities of a nondegenerate u statistic belonging to the hyperrectangles in mathbb r d when the dimension d is large a two step gaussian approximation procedure that does not impose structural assumptions on the data distribution is proposed subject to mild moment conditions on the kernel we establish the explicit rate of convergence uniformly in the class of all hyperrectangles in mathbb r d that decays polynomially in sample size for a high dimensional scaling limit where the dimension can be much larger than the sample size we also provide computable approximation methods for the quantiles of the maxima of centered u statistics specifically we provide a unified perspective for the empirical bootstrap the randomly reweighted bootstrap and the gaussian multiplier bootstrap with the jackknife estimator of covariance matrix as randomly reweighted quadratic forms and we establish their validity we show that all three methods are inferentially first order equivalent for high dimensional u statistics in the sense that they achieve the same uniform rate of convergence over all d dimensional hyperrectangles in particular they are asymptotically valid when the dimension d can be as large as o e n c for some constant c in 0 1 7 the bootstrap methods are applied to statistical applications for high dimensional non gaussian data including i principled and data dependent tuning parameter selection for regularized estimation of the covariance matrix and its related functionals ii simultaneous inference for the covariance and rank correlation matrices in particular for the thresholded covariance matrix estimator with the bootstrap selected tuning parameter we show that for a class of sub gaussian data error bounds of the bootstrapped thresholded covariance matrix estimator can be much tighter than those of the minimax estimator with a universal threshold in addition we also show that the gaussian like convergence rates can be achieved for heavy tailed data which are less conservative than those obtained by the bonferroni technique that ignores the dependency in the underlying data distribution

subgroup growth and congruence subgroups letk be a global field o its ring of integers g an almost simple simply connected connected algebraic subgroups ofgl m defined overk and g o which is assumed to be infinite let n resp n be the number of all resp congruence subgroups of index at mostn in we show a if char k 0 then i c 1 frac log 2 n log log n leqq log gamma n gamma leqq c 2 frac log 2 n log log n for suitable constantsc1 andc2 under some mild assumptions we also have ii has the congruence subgroup property if and only if log n o log2n iii if is boundedly generated the has the congruence subgroup property this confirms a conjecture of rapinchuk r1 which was also proved by platonov and rapinchuk pr3 b if char k 0 and under somewhat stronger conditions ong then for suitable constantsc3 andc4 c3 log2n log n c4log3n

two sample tests for high dimensional covariance matrices we propose two tests for the equality of covariance matrices between two high dimensional populations one test is on the whole variance covariance matrices and the other is on offdiagonal sub matrices which define the covariance between two non overlapping segments of the high dimensional random vectors the tests are applicable i when the data dimension is much larger than the sample sizes namely the large p small n situations and ii without assuming parametric distributions for the two populations these two aspects surpass the capability of the conventional likelihood ratio test the proposed tests can be used to test on covariances associated with gene ontology terms

a note on the solvability of groups abstract let m be a maximal subgroup of a finite group g and k l be a chief factor such that l m while k m we call the group m k l a c section of m and we define sec m to be the abstract group that is isomorphic to a c section of m for every maximal subgroup m of g assume that sec m is supersolvable then any composition factor of g is isomorphic to l 2 p or z q where p and q are primes and p 1 mod 8 this result answer a question posed by y wang s li c sections of maximal subgroups of finite groups j algebra 229 2000 86 94

cyclic quotients of transitive groups abstract let a be a transitive subgroup of s n we show that the largest cyclic quotient of a has order at most n this can be interpreted as an equivalent result about extensions of constants in the galois closure of a covering of curves over a finite field we also prove that the point stabilizer in a finite primitive permutation group always has a faithful orbit

a high dimensional nonparametric multivariate test for mean vector this work is concerned with testing the population mean vector of nonnormal high dimensional multivariate data several tests for high dimensional mean vector based on modifying the classical hotelling t2 test have been proposed in the literature despite their usefulness they tend to have unsatisfactory power performance for heavy tailed multivariate data which frequently arise in genomics and quantitative finance this article proposes a novel high dimensional nonparametric test for the population mean vector for a general class of multivariate distributions with the aid of new tools in modern probability theory we proved that the limiting null distribution of the proposed test is normal under mild conditions when p is substantially larger than n we further study the local power of the proposed test and compare its relative efficiency with a modified hotelling t2 test for high dimensional data an interesting finding is that the newly proposed test can have even more substantial power gain with l

finite groups admitting grassmannian 4 designs abstract let v be a finite dimensional euclidean space we classify finite subgroups of go v that admit grassmannian 4 designs we also classify zariski closed subgroups g of go v over which sym 2 v 1 g is irreducible

the maximality of monomial subgroups of linear groups over division rings abstract the monomial subgroups are proved to be maximal in gl n k or sl n k for arbitrary division rings k with some exceptions

the primitive permutation groups of degree less than 2500 abstract in this paper we use the o nan scott theorem and aschbacher s theorem to classify the primitive permutation groups of degree less than 2500

comparing large covariance matrices under weak conditions on the dependence structure and its application to gene clustering comparing large covariance matrices has important applications in modern genomics where scientists are often interested in understanding whether relationships e g dependencies or co regulations among a large number of genes vary between different biological states we propose a computationally fast procedure for testing the equality of two large covariance matrices when the dimensions of the covariance matrices are much larger than the sample sizes a distinguishing feature of the new procedure is that it imposes no structural assumptions on the unknown covariance matrices hence the test is robust with respect to various complex dependence structures that frequently arise in genomics we prove that the proposed procedure is asymptotically valid under weak moment conditions as an interesting application we derive a new gene clustering algorithm which shares the same nice property of avoiding restrictive structural assumptions for high dimensional genomics data using an asthma gene expression dataset we illustrate how the new test helps compare the covariance matrices of the genes across different gene sets pathways between the disease group and the control group and how the gene clustering algorithm provides new insights on the way gene clustering patterns differ between the two groups the proposed methods have been implemented in an r package hdtest and are available on cran

enumerating finite groups of given order let f n denote the number of isomorphism classes of groups of order n let n hw p9ig be the prime factorization of n and let a a n ek and u ii n maxkl1 gi the function f n has been subject to considerable study g higman 15 and c c sims 26 showed that if n is a prime power say n p then f n n 2 27 o l a2 for a x oc p m neumann 22 proved that if the number of isomorphism classes of simple groups of order n is bounded by nca2 for some constant c then f n n 1 c a2 holds in general combining the methods of 22 with some consequences of the classification theorem of finite simple groups a mciver and neumann 21 obtained that in fact the estimates f n na2 2 and f n n1 2 1 2 hold recently d f holt 16 found a rather elegant proof for the bound

primitive permutation groups of bounded orbital diameter we give a description of infinite families of finite primitive permutation groups for which there is a uniform finite upper bound on the diameter of all orbital graphs this is equivalent to describing families of finite permutation groups such that every ultraproduct of the family is primitive a key result is that in the almost simple case with socle of fixed lie rank apart from very specific cases there is such a diameter bound this is proved using recent results on the model theory of pseudofinite fields and difference fields

primitive permutation groups with a solvable 2 transitive subconstituent for a permutation group g acting on a finite set and a point a suborbit is an orbit of the point stabilizer g on the permutation group induced by g on is called a subconstituent of g moreover g is said to be uniprimitive if g is primitive but not 2 transitive in this paper we investigate uniprimitive permutation groups which have a solvable 2 transitive subconstituent we determine all such groups g which have a simple socle the affine case that is g has an elementary abelian socle are also discussed and an infinite family of affine primitive groups with non self paired 2 transitive subconstituents are presented

on fixed points of elements in primitive permutation groups abstract the fixity of a finite permutation group is the maximal number of fixed points of a non identity element we study the fixity of primitive groups of degree n showing that apart from a short list of exceptions the fixity of such groups is at least n 1 6 we also prove that there is usually an involution fixing at least n 1 6 points

topological generation of exceptional algebraic groups abstract let g be a simple algebraic group over an algebraically closed field k and let c 1 c t be non central conjugacy classes in g in this paper we consider the problem of determining whether there exist g i c i such that g 1 g t is zariski dense in g first we establish a general result which shows that if is an irreducible subvariety of g t then the set of tuples in generating a dense subgroup of g is either empty or dense in in the special case c 1 c t by considering the dimensions of fixed point spaces we prove that this set is dense when g is an exceptional algebraic group and t 5 assuming k is not algebraic over a finite field in fact for g g 2 we only need t 4 and both of these bounds are best possible as an application we show that many faithful representations of exceptional algebraic groups are generically free we also establish new results on the topological generation of exceptional groups in the special case t 2 which have applications to random generation of finite exceptional groups of lie type in particular we prove a conjecture of liebeck and shalev on the random r s generation of exceptional groups

maximal subgroups in finite and profinite groups we prove that if a finitely generated profinite group g is not generated with positive probability by finitely many random elements then every finite group f is obtained as a quotient of an open subgroup of g the proof involves the study of maximal subgroups of profinite groups as well as techniques from finite permutation groups and finite chevalley groups confirming a conjecture from ann of math 137 1993 203 220 we then prove that a finite group g has at most igic maximal soluble subgroups and show that this result is rather useful in various enumeration problems

annealing markov chain monte carlo with applications to ancestral inference abstract markov chain monte carlo mcmc the metropolis hastings algorithm has been used for many statistical problems including bayesian inference likelihood inference and tests of significance though the method generally works well doubts about convergence often remain here we propose mcmc methods distantly related to simulated annealing our samplers mix rapidly enough to be usable for problems in which other methods would require eons of computing time they simulate realizations from a sequence of distributions allowing the distribution being simulated to vary randomly over time if the sequence of distributions is well chosen then the sampler will mix well and produce accurate answers for all the distributions even when there is only one distribution of interest these annealing like samplers may be the only known way to get a rapidly mixing sampler these methods are essential for attacking very hard problems which arise in areas such as statistical genetics we illustrate the methods wi

the control of the false discovery rate in multiple testing under dependency benjamini and hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems a simple procedure was given there as an fdr controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate we prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses this condition for positive dependency is general enough to cover many problems of practical interest including the comparisons of many treatments with a single control multivariate normal test statistics with positive correlation matrix and multivariate t furthermore the test statistics may be discrete and the tested hypotheses composite without posing special difficulties for all other forms of dependency a simple conservative modification of the procedure controls the false discovery rate thus the range of problems for which a procedure with proven fdr control can be offered is greatly increased 1 1 simultaneous hypotheses testing the control of the increased type i error when testing simultaneously a family of hypotheses is a central issue in the area of multiple comparisons rarely are we interested only in whether all hypotheses are jointly true or not which is the test of the intersection null hypothesis in most applications we infer about the individual hypotheses realizing that some of the tested hypotheses are usually true we hope not all and some are not we wish to decide which ones are not true indicating statistical discoveries an important such problem is that of multiple endpoints in a clinical trial a new treatment is compared with an existing one in terms of a large number of potential benefits endpoints

hybrid parallel tempering and simulated annealing method in this paper we propose a new hybrid scheme of parallel tempering and simulated annealing hybrid pt sa within the hybrid pt sa scheme a composite system with multiple conformations is evolving in parallel on a temperature ladder with various transition step sizes the simulated annealing sa process uses a cooling scheme to decrease the temperature values in the temperature ladder to the target temperature the parallel tempering pt scheme is employed to reduce the equilibration relaxation time of the composite system at a particular temperature ladder configuration in the sa process the hybrid pt sa method reduces the waiting time in deep local minima and thus leads to a more efficient sampling capability on high dimensional complicated objective function landscapes compared to the approaches pt and parallel sa with the same temperature ladder transition step sizes and cooling scheme parallel sa configurations our preliminary results obtained with the hybrid pt sa method confirm the expected improvements in simulations of several test objective functions including the rosenbrock s function and the rugged funnel like function and several instantiations of the traveling salesman problem the hybrid pt sa may have slower convergence than genetic algorithms ga with good crossover heuristics but it has the advantage of tolerating bad initial values and displaying robust sampling capability even in the absence of additional information moreover the hybrid pt sa has natural parallelization potential

investigation of temperature parallel simulated annealing for optimizing continuous functions with application to hyperspectral tomography abstract the simulated annealing sa algorithm is a well established optimization technique which has found applications in many research areas however the sa algorithm is limited in its application due to the high computational cost and the difficulties in determining the annealing schedule this paper demonstrates that the temperature parallel simulated annealing tpsa algorithm a parallel implementation of the sa algorithm shows great promise to overcome these limitations when applied to continuous functions the tpsa algorithm greatly reduces the computational time due to its parallel nature and avoids the determination of the annealing schedule by fixing the temperatures during the annealing process the main contributions of this paper are threefold first this paper explains a simple and effective way to determine the temperatures by applying the concept of critical temperature t c second this paper presents systematic tests of the tpsa algorithm on various continuous functions demonstrating comparable performance as well established sequential sa algorithms third this paper demonstrates the application of the tpsa algorithm on a difficult practical inverse problem namely the hyperspectral tomography problem the results and conclusions presented in this work provide are expected to be useful for the further development and expanded applications of the tpsa algorithm

constructive recognition of finite alternating and symmetric groups acting as matrix groups on their natural permutation modules we present a las vegas algorithm which for a given matrix group known to be isomorphic modulo scalars to a finite alternating or symmetric group acting on the fully deleted permutation module produces an explicit isomorphism with the standard permutation representation of the group this algorithm exploits information available from the matrix representation and thereby is faster than existing black box recognition algorithms applied to these groups in particular it uses the fact that certain types of elements in these groups can be identified and constructed from the structure of their characteristic polynomials the algorithm forms part of a large scale program for computing with groups of matrices over finite fields when combined with existing black box recognition algorithms the results of this paper prove that any d dimensional absolutely irreducible matrix representation of a finite alternating or symmetric group over a finite field can be recognised with o d1 2 random group elements and o d1 2 matrix multiplications up to some logarithmic factors

two point stabilisers of partition actions of linear groups a partition of a kl dimensional vector space v is a set of l subspaces each of dimension k such that their direct sum is the original space v in this paper we show that unless l 2 the action of a group l such that psl v l pgl v on the set of partitions of v into l subspaces of dimension k is base two there exist two partitions v and w such that l v w 1 we will also show that given any finite group g there exist k l and partitions v w such that l v w g these results complement work the author has done with partition actions of the symmetric groups

on the number of generators of finite images of free products of finite groups abstract we prove that the analog of the grushko neumann theorem does not hold for profinite free products of profinite groups to do that we bound the number of generators of a finite group generated by a family of subgroups of pairwise coprime orders

asymptotic results for primitive permutation groups abstract we prove that the number of conjugacy classes of primitive permutation groups of degreenis at mostnc n where n denotes the maximal exponent occurring in the prime factorization ofn this result is applied to investigating maximal subgroup growth of infinite groups we then proceed by showing that if the point stabilizerg of a primitive groupgof degreendoes not have the alternating group alt d as a section then the order ofgis bounded by a polynomial inn this result extends a well known theorem of babai cameron and palfy it is used to prove for example that ifhis a subgroup of indexnin a groupg andhis a product ofbcyclic groups then g hg ncwherecdepends onb

a two sample test for high dimensional data with applications to gene set testing we proposed a two sample test for means of high dimensional data when the data dimension is much larger than the sample size the classical hotelling s t 2 test does not work for this large p small n situation the proposed test does not require explicit conditions on the relationship between the data dimension and sample size this offers much flexibility in analyzing high dimensional data an application of the proposed test is in testing significance for sets of genes which we demonstrate in an empirical study on a leukemia data set

a classification of the maximal subgroups of the finite alternating and symmetric groups following the classification of finite simple groups one of the major problems in finite group theory today is the determination of the maximal subgroups of the almost simple groups that is of groups x such that x0 u x aut x for some finite non abelian simple group x0 the problem has been solved for most sporadic groups and groups of lie type of low rank see 19 sects 3 43 for discussion and references this paper is a contribution to the case where x0 is an alternating group a so that for n 6 x is a or s the maximal subgroups of a and s are known for several classes of degrees n

two sample covariance matrix testing and support recovery in high dimensional and sparse settings in the high dimensional setting this article considers three interrelated problems a testing the equality of two covariance matrices and b recovering the support of and c testing the equality of and row by row we propose a new test for testing the hypothesis h 0 and investigate its theoretical and numerical properties the limiting null distribution of the test statistic is derived and the power of the test is studied the test is shown to enjoy certain optimality and to be especially powerful against sparse alternatives the simulation results show that the test significantly outperforms the existing methods both in terms of size and power analysis of a prostate cancer dataset is carried out to demonstrate the application of the testing procedures when the null hypothesis of equal covariance matrices is rejected it is often of significant interest to further investigate how they differ from each other motivated by applications in genomics we also consider recovering the support of and

testing matrix groups for primitivity abstract we describe an algorithm which seeks to decide whether or not a matrix group defined over a finite field acts to preserve blocks of imprimitivity and if so to find a block system implementations of the algorithm are publicly available

fixed point ratios in actions of finite classical groups iii abstract this is the first in a series of four papers on fixed point ratios in actions of finite classical groups our main result states that if g is a finite almost simple classical group and is a faithful transitive non subspace g set then either fpr x x g 1 2 for all elements x g of prime order or g is one of a small number of known exceptions here fpr x denotes the proportion of points in which are fixed by x in this introductory note we present our results and describe an application to the study of minimal bases for primitive permutation groups a further application concerning monodromy groups of covers of riemann surfaces is also outlined

classical groups probabilistic methods and the 2 3 generation problem we study the probability that randomly chosen elements of prescribed type in a finite simple classical group g generate g in particular we prove a conjecture of kantor and lubotzky in this area the probabilistic approach is then used to determine the finite simple classical quotients of the modular group psl2 z up to finitely many exceptions

factorizations of almost simple groups with a factor having many nonsolvable composition factors abstract this paper classifies the factorizations of almost simple groups with a factor having at least two nonsolvable composition factors this together with a previous classification result of the authors reduces the factorization problem of almost simple groups to the case where both factors have a unique nonsolvable composition factor

a theory for dynamic weighting in monte carlo computation this article provides a first theoretical analysis of a new monte carlo approach the dynamic weighting algorithm proposed recently by wong and liang in dynamic weighting monte carlo one augments the original state space of interest by a weighting factor which allows the resulting markov chain to move more freely and to escape from local modes it uses a new invariance principle to guide the construction of transition rules we analyze the behavior of the weights resulting from such a process and provide detailed recommendations on how to use these weights properly our recommendations are supported by a renewal theory type analysis our theoretical investigations are further demonstrated by a simulation study and applications in neural network training and ising model simulations