structural properties of dendrite groups let g be the homeomorphism group of a dendrite we study the normal subgroups of g for instance there are uncountably many non isomorphic such groups g that are simple groups moreover these groups can be chosen so that any isometric g action on any metric space has a bounded orbit in particular they have the fixed point property fh

simplicity of some automorphism groups abstract let m be a countably infinite first order relational structure which is homogeneous in the sense of fraisse we show under the assumption that the class of finite substructures of m has the free amalgamation property along with the assumption that aut m is transitive on m but not equal to sym m that aut m is a simple group this generalises results of truss rubin and others the proof uses the polish group structure of the automorphism group and generalises to certain other homogeneous structures with prospects for further application

on the predictability of discrete dynamical systems iii abstract given an integer n 2 a metrizable compact topological n manifold x with boundary and a finite positive borel measure on x we prove that most homeomorphisms f x x are non sensitive almost everywhere on x moreover we also prove that for most homeomorphisms f x x the non wandering set f has measure zero

generic stationary measures and actions let g be a countably infinite group and let be a generating probability measure on g we study the space of stationary borel probability measures on a topological g space and in particular on z g where z is any perfect polish space we also study the space of stationary measurable g actions on a standard nonatomic probability space equip the space of stationary measures with the weak topology when has finite entropy we show that a generic measure is an essentially free extension of the poisson boundary of g when z is compact this implies that the simplex of stationary measures on z g is a poulsen simplex we show that this is also the case for the simplex of stationary measures on 0 1 g we furthermore show that if the action of g on its poisson boundary is essentially free then a generic measure is isomorphic to the poisson boundary next we consider the space of stationary actions equipped with a standard topology known as the weak topology here we show that when g has property t the ergodic actions are meager we also construct a group g without property t such that the ergodic actions are not dense for some finally for a weaker topology on the set of actions which we call the very weak topology we show that a dynamical property e g ergodicity is topologically generic if and only if it is generic in the space of measures there we also show a glasner king type 0 1 law stating that every dynamical property is either meager or residual

homeomorphic measures on stationary bratteli diagrams we study the set s of ergodic probability borel measures on stationary non simple bratteli diagrams which are invariant with respect to the tail equivalence relation r equivalently the set s is formed by ergodic probability measures invariant with respect to aperiodic substitution dynamical systems the paper is devoted to the classification of measures from s with respect to a homeomorphism the properties of the clopen values set s are studied it is shown that for every measure s there exists a subgroup g r such that s g 0 1 a criterion of goodness is proved for such measures based on this result the measures from s are classified up to a homeomorphism we prove that for every good measure s there exist countably many measures i i n s such that the measures and i are homeomorphic but the tail equivalence relations on the corresponding bratteli diagrams are not orbit equivalent

a structure theorem for actions of semisimple lie groups we consider a connected semisimple lie group g with finite center an admissible probability measure on g and an ergodic g u space x v we first note lemma 0 1 that x v has a unique maximal projective factor of the form g q vo where q is a parabolic subgroup of g and then prove 1 theorem 1 if every noncompact simple factor of g has real rank at least two then the maximal projective factor is nontrivial unless v is a g

an improved bonferroni procedure for multiple tests of significance summary a modification of the bonferroni procedure for testing multiple hypotheses is presented the method based on the ordered p values of the individual tests is less conservative than the classical bonferroni procedure but is still simple to apply a simulation study shows that the probability of a type i error of the procedure does not exceed the nominal significance level a for a variety of multivariate normal and multivariate gamma test statistics for independent tests the procedure has type i error probability equal to a the method appears particularly advantageous over the classical bonferroni procedure when several highly correlated test statistics are involved

turbulence amalgamation and generic automorphisms of homogeneous structures we study topological properties of conjugacy classes in polish groups with emphasis on automorphism groups of homogeneous countable structures we first consider the existence of dense conjugacy classes the topological rokhlin property we then characterize when an automorphism group admits a comeager conjugacy class answering a question of truss and apply this to show that the homeomorphism group of the cantor space has a comeager conjugacy class answering a question of akin hurley and kennedy finally we study polish groups that admit comeager conjugacy classes in any dimension in which case the groups are said to admit ample generics we show that polish groups with ample generics have the small index property generalizing results of hodges hodkinson lascar and shelah and arbitrary homomorphisms from such groups into separable groups are automatically continuous moreover in the case of oligomorphic permutation groups they have uncountable cofinality and the bergman property these results in particular apply to automorphism groups of many stable 0 categorical structures and of the random graph in this connection we also show that the infinite symmetric group s has a unique non trivial separable group topology for several interesting groups we also establish serre s properties fh and fa

the simes method for multiple hypothesis testing with positively dependent test statistics abstract the simes method for testing intersection of more than two hypotheses is known to control the probability of type i error only when the underlying test statistics are independent although this method is more powerful than the classical bonferroni method it is not known whether it is conservative when the test statistics are dependent this article proves that for multivariate distributions exhibiting a type of positive dependence that arise in many multiple hypothesis testing situations the simes method indeed controls the probability of type i error this extends some results established very recently in the special case of two hypotheses

on homeomorphic bernoulli measures on the cantor space let be the bernoulli measure on the cantor space given as the infinite product of two point measures with weights and it is a long standing open problem to characterize those and such that and are topologically equivalent i e there is a homeomorphism from the cantor space to itself sending to the possibly weaker property of and being continuously reducible to each other is equivalent to a property of and called binomial equivalence in this paper we define an algebraic property called refinability and show that if and are refinable and binomially equivalent then and are topologically equivalent next we show that refinability is equivalent to a fairly simple algebraic property finally we give a class of examples of binomially equivalent and refinable numbers in particular the positive numbers and such that and are refinable so the corresponding measures are topologically equivalent

independence in topological and c dynamics we develop a systematic approach to the study of independence in topological dynamics with an emphasis on combinatorial methods one of our principal aims is to combinatorialize the local analysis of topological entropy and related mixing properties we also reframe our theory of dynamical independence in terms of tensor products and thereby expand its scope to c dynamics

a stagewise rejective multiple test procedure based on a modified bonferroni test summary simes 1986 has proposed a modified bonferroni procedure for the test of an overall hypothesis which is the combination of n individual hypotheses in contrast to the classical bonferroni procedure it is not obvious how statements about individual hypotheses are to be made for this procedure in the present paper a multiple test procedure allowing statements on individual hypotheses is proposed it is based on the principle of closed test procedures marcus peritz gabriel 1976 and controls the multiple level a

sensitivity analysis of flexible multibody systems using composite materials components in this paper a general formulation for the computation of the first order analytical sensitivities based on the direct method using automatic differentiation of flexible multibody systems is presented the direct method for sensitivity calculation is obtained by differentiating the equations that define the response of the flexible multibody systems of composite materials with respect to the design variables which are the ply orientations of the laminated in order to appraise the benefits of the approach suggested and to highlight the risks of the procedure the analytical sensitivities are compared with the numerical results obtained by using the finite difference method for the beam composite material elements the section properties and their sensitivities are found using an asymptotic procedure that involves a two dimensional 2 d finite element analysis of their cross section the equations of the sensitivities are obtained by automatic differentiation and integrated in time simultaneously with the equations of motion of the multibody systems the equations of motion and the sensitivities of the flexible multibody system are solved and the accelerations velocities and the sensitivities of accelerations and velocities are integrated in time using a multi step multi order integration algorithm through the application of the methodology to two simple flexible multibody systems the difficulties and benefits of the procedure with respect to finite difference approaches or to the direct implementation of the analytic sensitivities are discussed copyright 2008 john wiley sons ltd

a change point approach for phase i analysis in multistage processes we study the phase i analysis of a multistage process where the input of the current process stage may be closely related to the output s of the earlier stage s we frame univariate observations from each of the stages in a multistage process as a single vector and recognize that the directions in which these vectors can shift are limited when attention is restricted to a single step shift in the mean of one stage this allows us to focus detection power on a limited subspace with improved sensitivity taking advantage of this particular characteristic we propose a change point approach that integrates the classical binary segmentation test with the directional information based on the state space model for testing the stability of a batch of historical data we give an accurate approximation for the significance level of the proposed test our simulation results show that the proposed approach consistently outperforms existing methods for multistage processes

some probability inequalities for ordered rm mtp sb 2 random variables a proof of the simes conjecture some new probability inequalities involving the ordered components of an mtp 2 random vector are derived which provide an analytical proof of an important conjecture in the field of multiple hypothesis testing this conjecture has been mostly validated so far using simulation

approximate and real trajectories for generic dynamical systems abstract in this paper we show that generic dynamical systems have a weak shadowing property namely that for a generic dynamical system in the space of discrete continuous dynamical systems on a compact manifold m with the usual c 0 topology given 0 there exists a 0 such that trajectories are close to real trajectories there are no dimensional restrictions on this result we also give some results on the inverse problem of tracing real trajectories by trajectories these problems are motivated by questions regarding the validity of numerical solutions of differential equations

on li yorke pairs the li yorke definition of chaos proved its value for interval maps in this paper it is considered in the setting of general topological dynamics we adopt two opposite points of view on the one hand sufficient conditions for li yorke chaos in a topological dynamical system are given we solve a long standing open question by proving that positive entropy implies li yorke chaos on the other hand properties of dynamical systems without li yorke pairs are investigated in addition to having entropy 0 they are minimal when transitive and the property is stable under factor maps arbitrary products and inverse limits finally it is proved that minimal systems without li yorke pairs are disjoint from scattering systems

limit sets of typical continuous functions abstract given a metrizable compact topological n manifold x with boundary and a finite positive borel measure on x we prove that for the typical continuous function f x x it is true that for every point x in a full measure subset of x the limit set f x is a cantor set of hausdorff dimension zero f maps f x homeomorphically onto itself each point of f x has a dense orbit in f x and f is non sensitive at each point of f x moreover the function x f x is continuous almost everywhere

on weighted hochberg procedures summary we consider different ways of constructing weighted hochberg type step up multiple test procedures including closed procedures based on weighted simes tests and their conservative step up short cuts and step up counterparts of two weighted holm procedures it is shown that the step up counterparts have some serious pitfalls such as lack of familywise error rate control and lack of monotonicity in rejection decisions in terms of p values therefore an exact closed procedure appears to be the best alternative its only drawback being lack of simple stepwise structure a conservative step up short cut to the closed procedure may be used instead but with accompanying loss of power simulations are used to study the familywise error rate and power properties of the competing procedures for independent and correlated p values although many of the results of this paper are negative they are useful in highlighting the need for caution when procedures with similar pitfalls may be used

dynamical entropy in banach spaces we introduce a version of voiculescu brown approximation entropy for isometric automorphisms of banach spaces and develop within this framework the connection between dynamics and the local theory of banach spaces as discovered by glasner and weiss our fundamental result concerning this contractive approximation entropy or ca entropy characterizes the occurrence of positive values both geometrically and topologically this leads to various applications for example we obtain a geometric description of the topological pinsker factor and show that a c algebra is type i if and only if every multiplier inner automorphism has zero ca entropy we also examine the behaviour of ca entropy under various product constructions and determine its value in many examples including isometric automorphisms of l p for 1 p and noncommutative tensor product shifts

graph theoretic structure of maps of the cantor space abstract in this paper we develop unifying graph theoretic techniques to study the dynamics and the structure of spaces h 0 1 n and c 0 1 n the space of homeomorphisms and the space of self maps of the cantor space respectively using our methods we give characterizations which determine when two homeomorphisms of the cantor space are conjugate to each other we also give a new characterization of the comeager conjugacy class of the space h 0 1 n the existence of this class was established by kechris and rosendal and a specific element of this class was described concretely by akin glasner and weiss our characterization readily implies many old and new dynamical properties of elements of this class for example we show that no element of this class has a li yorke pair implying the well known glasner weiss result that there is a comeager subset of h 0 1 n each element of which has topological entropy zero our analogous investigation in c 0 1 n yields a surprising result there is a comeager subset of c 0 1 n such that any two elements of this set are conjugate to each other by an element of h 0 1 n our description of this class also yields many old and new results concerning dynamics of a comeager subset of c 0 1 n

weakly almost periodic functions model theoretic stability and minimality of topological groups we investigate the automorphism groups of aleph 0 categorical structures and prove that they are exactly the roelcke precompact polish groups we show that the theory of a structure is stable if and only if every roelcke uniformly continuous function on the automorphism group is weakly almost periodic analysing the semigroup structure on the weakly almost periodic compactification we show that continuous surjective homomorphisms from automorphism groups of stable aleph 0 categorical structures to hausdorff topological groups are open we also produce some new wap trivial groups and calculate the wap compactification in a number of examples

good measures on cantor space while there is up to homeomorphism only one cantor space i e one zero dimensional perfect compact nonempty metric space there are many measures on cantor space which are not topologically equivalent the clopen values set for a full nonatomic measure is the countable dense subset u u is clopen of the unit interval it is a topological invariant for the measure for the class of good measures it is a complete invariant a full nonatomic measure is good if whenever u v are clopen sets with u v there exists w a clopen subset of v such that w u these measures have interesting dynamical properties they a re exactly the measures which arise from uniquely ergodic minimal systems on cantor space for some of them there is a unique generic measure preserving homeomorphism that is within the polish group of such homeomorphisms there is a dense g conjugacy class

generically there is but one self homeomorphism of the cantor set we describe a self homeomorphism r of the cantor set x and then show that its conjugacy class in the polish group h x of all homeomorphisms of x forms a dense g subset of h x we also provide an example of a locally compact second countable topological group which has a dense conjugacy class

homogeneous probability measures on the cantor set abstract we show that every homeomorphism between closed measure zero subsets extends to a measure preserving auto homeomorphism whenever the cantor set is endowed with a suitable probability measure this is valid both for the standard product measure as well as for the universal homogeneous rational measure

amenable actions of groups the equivalence between different characterizations of amenable actions of a locally compact group is proved in particular this answers a question raised by r j zimmer in 1977

a step up multiple test procedure abstract we consider the problem of simultaneously testing k 2 hypotheses on parameters 1 k in a typical application the s may be a set of contrasts for instance a set of orthogonal contrasts among population means or a set of differences between k treatment means and a standard treatment mean it is assumed that least squares estimators 1 k are available that are jointly normally distributed with a common variance known up to a scalar namely the error variance 2 and a common known correlation an independent 2 distributed unbiased estimator of 2 is also assumed to be available we propose a step up multiple test procedure for this problem which tests the t statistics for the k hypotheses in order starting with the least significant one and continues as long as an acceptance occurs by contrast the step down approach which is usually used starts with the most significant and continues as long as a rejection occurs critical constants required by this step up procedure to co

ordered structures and large conjugacy classes abstract this article is a contribution to the following problem does there exist a polish non archimedean group equivalently automorphism group of a fraisse limit that is extremely amenable and has ample generics as fraisse limits whose automorphism groups are extremely amenable must be ordered i e equipped with a linear ordering we focus on ordered fraisse limits we prove that automorphism groups of the universal ordered boron tree and the universal ordered poset have a comeager conjugacy class but no comeager 2 dimensional diagonal conjugacy class we formulate general conditions implying that there is no comeager conjugacy class comeager 2 dimensional diagonal conjugacy class or non meager 2 dimensional topological similarity class in the automorphism group of an ordered fraisse limit we also provide a number of applications of these results

weak shadowing for discrete dynamical systems on nonsmooth manifolds abstract in j math anal appl 189 1995 409 423 corless and pilyugin proved that weak shadowing is a c 0 generic property in the space of discrete dynamical systems on a compact smooth manifold m in our paper we give another proof of this theorem which does not assume that m has a differential structure moreover our method also works for systems on some compact metric spaces that are not manifolds such as a hilbert cube or generally a countably infinite cartesian product of manifolds with boundary and a cantor set

shifts of finite type as fundamental objects in the theory of shadowing shifts of finite type and the notion of shadowing or pseudo orbit tracing are powerful tools in the study of dynamical systems in this paper we prove that there is a deep and fundamental relationship between these two concepts let x be a compact totally disconnected space and f x rightarrow x a continuous map we demonstrate that f has shadowing if and only if the system f x is conjugate to the inverse limit of a directed system satisfying the mittag leffler condition and consisting of shifts of finite type in particular this implies that in the case that x is the cantor set f has shadowing if and only if f x is the inverse limit of a sequence satisfying the mittag leffler condition and consisting of shifts of finite type moreover in the general compact metric case where x is not necessarily totally disconnected we prove that f has shadowing if f x is a factor of the inverse limit of a sequence satisfying the mittag leffler condition and consisting of shifts of finite type by a quotient that almost lifts pseudo orbits

random walks on random coset spaces with applications to furstenberg entropy we determine the range of furstenberg entropy for stationary ergodic actions of nonabelian free groups by an explicit construction involving random walks on random coset spaces

a characterization of homeomorphic bernoulli trial measures we give conditions which given two bernoulli trial measures determine whether there exists a homeomorphism of cantor space which sends one measure to the other answering a question of oxtoby we then provide examples relating these results to the notions of good and refinable measures on cantor space

on characters of inductive limits of symmetric groups abstract in the paper we completely describe characters central positive definite functions of simple locally finite groups that can be represented as inductive limits of products of symmetric groups under block diagonal embeddings each such group g defines an infinite graded graph that encodes the embedding scheme the group g acts on the space x of infinite paths of the associated graph by changing initial edges of paths assuming the finiteness of the set of ergodic measures for the system x g we establish that each non regular indecomposable character g c is uniquely determined by the formula g 1 fix g 1 k fix g k where 1 k are g ergodic measures fix g x x g x x and 1 k 0 1 we illustrate our results on the group of rational permutations of the unit interval

multiplicity adjustment for multiple endpoints in clinical trials with multiple doses of an active treatment frequently multiple doses of an active treatment and multiple endpoints are simultaneously considered in the designs of clinical trials for these trials traditional multiplicity adjustment procedures such as bonferroni hochberg and hommel procedures can be applied when treating the comparisons of different doses to the control on all endpoints at the same level however these approaches will not take into account the possible dose response relationship on each endpoint and therefore are less specific and may have lower power to gain power in this paper we consider the problem as a two dimensional multiplicity problem one dimension concerns the multiple doses and the other dimension concerns the multiple endpoints we propose procedures which consider the dose order to form the closure of the procedures and control the family wise type i error rate in a strong sense for this two dimensional problem numerical examples show that procedures proposed in this paper in general have higher power than the commonly used procedures e g the regular hochberg procedure especially for comparing the higher dose to the control

validity of the hochberg procedure revisited for clinical trial applications there is much interest in using the hochberg procedure hp for statistical tests on primary endpoints of confirmatory clinical trials the procedure is simple to use and enjoys more power than the bonferroni and the holm procedures however the hp is not assumption free like the other two procedures it controls the familywise type i error rate when test statistics used for statistical tests are independent or if dependent satisfy a conditionally independent formulation otherwise its properties for dependent tests at present are not fully understood consequently its use for confirmatory trials especially for their primary endpoints remains worrisome confirmatory trials are typically designed with 1 2 primary endpoints therefore a question was raised at the food and drug administration as to whether the hp is a valid test for the simple case of performing treatment to control comparisons on two primary endpoints when their test statistics are not independent confirmatory trials for statistical tests normally use simple test statistics such as the normal z student s t and chi square the literature does include some work on the hp for dependent cases covering these test statistics but concerns remain regarding its use for confirmatory trials for which endpoint tests are mostly of the dependent kind the purpose of this paper is therefore to revisit this procedure and provide sufficient details for better understanding of its performance for dependent cases related to the aforementioned question published 2015 this article is a u s government work and is in the public domain in the usa

dynamic analysis of spatial flexible multibody systems using joint co ordinates this paper presents a systematic method for deriving the minimum number of equations of motion for spatial flexible multibody systems relative kinematics are developed using relative joint co ordinates and relative joint velocities to formulate a minimum number of equations of motion the present method takes advantage of the simplicity of the absolute co ordinate formulation and computational efficiency of the relative joint co ordinate formulation the system equations of motion are first formulated in terms of a coupled set of absolute reference co ordinates and elastic modal co ordinates these equations are transformed to the joint co ordinate space by use of a velocity transformation matrix including the elastic modal velocities a computer algorithm is proposed and extended to closed loop mechanisms one example of a flexible vehicle is presented and the results are discussed to illustrate the computational efficiency of the method

hommel s bonferroni type inequality for unequally spaced levels summary hommel 1983 established a sharp upper bound to the overall significance level for a generalization of the bonferroni inequality based upon equally spaced critical levels for the successive ordered p values this note generalizes the sharp upper bound to unequally spaced critical levels

the topological rohlin property and topological entropy for a compact metric space x let g h x denote the group of self homeomorphisms with the topology of uniform convergence the group g acts on itself by conjugation and we say that x satisfies the topological rohlin property if this action has dense orbits we show that the hilbert cube the cantor set and with a slight modification also even dimensional spheres satisfy this property we also show that zero entropy is generic for homeomorphisms of the cantor set whereas it is infinite entropy which is generic for homeomorphisms of cubes of dimension d 2 and the hilbert cube

generic automorphisms of homogeneous structures let g be a permutation group on the set usually we take n o we seek a notion of genericity for members of g the idea is that a member of g should be generic if it is in some sense typical we argue that the following is the correct definition suppose that g is endowed with a metric so that it becomes a complete metric space it follows that the baire category theorem holds and we may use the notions of meagre and comeagre sets

chaos among self maps of the cantor space glasner and weiss have shown that a generic homeomorphism of the cantor space has zero topological entropy hochman has shown that a generic transitive homeomorphism of the cantor space has the property that it is topologically conjugate to the universal odometer and hence far from being chaotic in any sense we show that a generic self map of the cantor space has zero topological entropy moreover we show that a generic self map of the cantor space has no periodic points and hence is not devaney chaotic nor devaney chaotic on any subsystem however we exhibit a dense subset of the space of all self maps of the cantor space each element of which has infinite topological entropy and is devaney chaotic on some subsystem

sensitivity analysis for the cross match test with applications in genomics the cross match test is an exact distribution free test of no treatment effect on a high dimensional outcome in a randomized experiment the test uses optimal nonbipartite matching to pair 2i subjects into i pairs based on similar outcomes and the cross match statistic a is the number of times that a treated subject was paired with a control rejecting for small values of a if the test is applied in an observational study in which treatments are not randomly assigned then it may be comparing treated and control subjects who are not comparable and thus may falsely reject a true null hypothesis of no treatment effect we develop a sensitivity analysis for the cross match test and apply it in an observational study of the effects of smoking on gene expression levels in addition we develop a sensitivity analysis for several multiple testing procedures using the cross match test and apply it to 1627 molecular function categories in gene ontology

is the simes improved bonferroni procedure conservative summary simes 1986 proposed a modified bonferroni procedure for conducting multiple tests of significance he proved that when the n test statistics are independent his procedure has exact size a already hommel 1983 had considered a similar procedure and shown that it need not be conservative he gave an attainable upper bound for its anticonservativeness here we show that for one sided tests based on positively correlated bivariate normal test statistics the procedure is conservative and for negatively correlated such variables it is anticonservative two sided tests based on bivariate normal variables are always conservative some numerical values are given which show that for all practical purposes the nominal a value can be used