the concept of duality for automata over a changing alphabet and generation of a free group by such automata in the paper we deal with the notion of an automaton over a changing alphabet which generalizes the concept of a mealy type automaton we modify the methods based on the idea of a dual automaton and its action used by b steinberg et al 2011 and m vorobets and ya vorobets 2007 2010 16 18 and adapt them to automata over a changing alphabet we show that this modification provides some naturally defined automaton representations of a free nonabelian group by a 2 state automaton over a changing alphabet

orbit automata as a new tool to attack the order problem in automaton groups abstract we introduce a new tool called the orbit automaton that describes the action of an automaton group g on the subtrees corresponding to the orbits of g on levels of the tree the connection between g and the groups generated by the orbit automata is used to find elements of infinite order in certain automaton groups for which other methods failed to work

automatic algorithm for monotone trend removal the available numerical algorithms for trend removal require a direct subjective intervention in choosing critical parameters in this paper an algorithm is presented which needs no initial subjective assumptions monotone trends are approximated by piecewise linear curves obtained by dividing into subintervals the signal values interval not the time interval the slope of each linear segment of the estimated trend is proportional to the average one step displacement of the signal values included into the corresponding subinterval the evaluation of the trend removal is performed on statistical ensembles of artificial time series with the random component given by realizations of autoregressive of order one stochastic processes or by fractional brownian motions the accuracy of the algorithm is compared with that of two well tested methods polynomial fitting and a nonparametric method based on moving average for stationary noise the results of the algorithm are slightly better but for nonstationary noise the preliminary results indicate that the polynomial fitting has the best accuracy as a verification on a real time series the time periods with monotone variation of global average temperature over the last 1800 phantom rule 0 3em 0ex text years are established the removal of a nonmonotone trend is also briefly discussed

on centralizers in locally finite groups abstract the main result of the paper is the following theorem let g be a locally finite group containing a finite p subgroup a such that cg a is finite and a non cyclic subgroup b of order p2 such that cg b has finite exponent for all b b then g is almost locally solvable and has finite exponent

automata generating free products of groups of order 2 abstract we construct a family of automata with n states n 4 acting on a rooted binary tree that generate the free products of cyclic groups of order 2

fractal just infinite nil lie superalgebra of finite width abstract the grigorchuk and gupta sidki groups play fundamental role in modern group theory they are natural examples of self similar finitely generated periodic groups as their natural analogues there are constructions of nil lie p algebras over a field of characteristic 2 40 and arbitrary positive characteristic 52 in characteristic zero similar examples of lie algebras do not exist by a result of martinez and zelmanov 32 the second author constructed analogues of the grigorchuk and gupta sidki groups in the world of lie superalgebras of arbitrary characteristic the virtue of that construction is that the lie superalgebras have clear monomial bases 41 that lie superalgebras have slow polynomial growth and are graded by multidegree in the generators in particular a self similar lie superalgebra q is z 3 graded by multidegree in 3 generators its z 3 components lie inside an elliptic paraboloid in space the components are at most one dimensional thus the z 3 grading of q is fine an analogue of the periodicity is that homogeneous elements of the grading q q 0 q 1 are ad nilpotent in particular q is a nil finely graded lie superalgebra which shows that an extension of the mentioned result of martinez and zelmanov 32 to the lie superalgebras of characteristic zero is not valid but computations with q are rather technical in this paper we construct a similar but simpler and smaller example namely we construct a 2 generated fractal lie superalgebra r over arbitrary field we find a clear monomial basis of r and unlike many examples studied before we find also a clear monomial basis of its associative hull a the latter has a quadratic growth the algebras r and a are z 2 graded by multidegree in the generators positions of their z 2 components are bounded by pairs of logarithmic curves on plane the z 2 components of r are at most one dimensional thus the z 2 grading of r is fine as an analogue of periodicity we establish that homogeneous elements of the grading r r 0 r 1 are ad nilpotent in case of n graded algebras a close analogue to being simple is being just infinite unlike previous examples of lie superalgebras we are able to prove that r is just infinite but not hereditary just infinite our example is close to the smallest possible example because r has a linear growth with a growth function r m 3 m as m moreover r is of finite width 4 char k 2 in case char k 2 we obtain a lie algebra of width 2 that is not thin thus we have got a more handy analogue of the grigorchuk and gupta sidki groups the constructed lie superalgebra r is of linear growth of finite width 4 and just infinite it also shows that an extension of the result of martinez and zelmanov 32 to the lie superalgebras of characteristic zero is not valid

automata groups limit spaces and tilings abstract we explore the connections between automata groups limit spaces of self similar actions and tilings in particular we show how a group acting nicely on a tree gives rise to a self covering of a topological groupoid and how the group can be reconstructed from the groupoid and its covering the connection is via finite state automata these define decomposition rules or self similar tilings on leaves of the solenoid associated with the covering

the conjugacy problem in automaton groups is not solvable abstract free abelian by free self similar groups generated by finite self similar sets of tree automorphisms and having unsolvable conjugacy problem are constructed along the way finitely generated orbit undecidable free subgroups of gl d z for d 6 and aut f d for d 5 are constructed as well

a nonparametric trend test for seasonal data with serial dependence statistical tests for monotonic trend in seasonal e g monthly hydrologic time series are commonly confounded by some of the following problems nonnormal data missing values seasonality censoring detection limits and serial dependence an extension of the mann kendall test for trend designed for such data is presented here because the test is based entirely on ranks it is robust against nonnormality and censoring seasonality and missing values present no theoretical or computational obstacles to its application monte carlo experiments show that in terms of type i error it is robust against serial correlation except when the data have strong long term persistence e g arma 1 1 monthly processes with 0 6 or short records 5 years when there is no serial correlation it is less powerful than a related simpler test which is not robust against serial correlation

on subgroups of finite index in branch groups we give a structural description of the normal subgroups of subgroups of finite index in branch groups in terms of rigid stabilizers this gives further insight into the structure lattices of branch groups introduced by the second author we derive a condition concerning abstract commensurability of branch groups acting on the p ary tree for any prime p

examples of self iterating lie algebras abstract we construct examples of self iterating lie algebras similar to the grigorchuk group in case of characteristic 2 we construct a two generated restricted lie algebra of polynomial growth that has a nil p mapping

large hereditarily just infinite groups abstract it is shown that there is a hereditarily just infinite group in which all countably based profinite groups can be embedded and also that there exist hereditarily just infinite prosoluble groups that are not topologically finitely generated

large scale properties for bounded automata groups abstract in this paper we study some large scale properties of the mother groups of bounded automata groups first we give two methods to prove every mother group has infinite asymptotic dimension then we study the decomposition complexity of certain subgroup in the mother group we prove the subgroup belongs to d

estimation of nonlinear trends in water quality an improved approach using generalized additive models 1 this paper advocates the use of generalized additive models gams for the estimation of nonlinear trends in water quality in the presence of serially correlated errors the gam methodology is applicable to a range of physical chemical and biological water quality variates comparison with the estimate based on seasonal kendall s slope and robust regression is discussed an example is given concerning log transformed stream electrical conductivity which is adjusted for flow the monthly data have first order autocorrelation exceeding 0 5 and the trend is markedly nonlinear seasonal effects are shown to have been changing over time

on self similarity of p adic analytic pro p groups of small dimension abstract given a torsion free p adic analytic pro p group g with dim g p we show that the self similar actions of g on regular rooted trees can be studied through the virtual endomorphisms of the associated z p lie lattice we explicitly classify 3 dimensional unsolvable z p lie lattices for p odd and study their virtual endomorphisms together with lazard s correspondence this allows us to classify 3 dimensional unsolvable torsion free p adic analytic pro p groups for p 5 and to determine which of them admit a faithful self similar action on a p ary tree in particular we show that no open subgroup of s l 1 1 p admits such an action on the other hand we prove that all the open subgroups of s l 2 z p admit faithful self similar actions on regular rooted trees

on a 2 generated infinite 3 group subgroups and automorphisms this is the second paper dedicated to a detailed study of the infinite 3 group j 74 r 1 3 rr 3 1 y y ct 2 l a recursive definition to be explained later which was introduced by the author and narain gupta in 2 as a group of automorphisms of an infinite regular tree f as was shown in 4 y has the remarkable properties of containing a copy of every finite 3 group and having all its proper quotients finite the first paper s in this detailed study 99 dealt with the presentation problem here we study further aspects of its subgroup structure our prime objective though is to determine the group of automorphisms of 9 this task represents a large portion of our present paper the main results are as follows

some remarks on cohen lenstra heuristics cohen and lenstra have given a heuristic model which predicts the fraction of imaginary quadratic fields with class number divisible by a given odd prime p and of those whose class groups have a given p rank we show that these numbers also arise by

self similar associative algebras abstract famous self similar groups were constructed by grigorchuk gupta and sidki these examples lead to interesting examples of associative algebras the authors suggested examples of self similar lie algebras in terms of differential operators recently sidki introduced an example of an associative algebra of self similar matrices we construct families of self similar associative algebras c d generalizing the example of sidki we prove that our algebras are z z graded and have polynomial growth our approach is the weight strategy developed by the authors for self similar lie algebras and their envelopes in particular we obtain similar triangular decompositions into direct sums of three subalgebras c c c 0 c d d d 0 d we prove that some of our algebras are direct sums of two locally nilpotent subalgebras c c c d d d we show that in some cases the zero components c 0 d 0 are nontrivial and not nil algebras we show that our construction includes the example of sidki and the examples of self similar lie algebras and their associative hulls constructed by the authors before

stein s method and the rank distribution of random matrices over finite fields withqq n the distribution of n minus the rank of a matrix chosen uniformly the collection of all n n m matrices over the nite eld fq of size q 2 andqq the distributional limit ofqq n as n 1 we apply stein s method to prove the total variation bound 1 8q n m 1 jjq q nq qjjtv 3 q n m 1 in addition we obtain similar sharp results for the rank distributions of symmetric symmetric with zero diagonal skew symmetric skew cen trosymmetric and hermitian matrices

a language hierarchy and kitchens type theorem for self similar groups abstract we generalize the notion of self similar groups of infinite tree automorphisms to allow for groups which are defined on a tree but may not act faithfully on it the elements of such a group correspond to labeled trees which may be recognized by a tree automaton e g rabin buchi etc or considered as elements of a tree shift e g of finite type sofic as in symbolic dynamics we give examples to show how self similar groups defined in this way can be separated into different tree language hierarchies as the main result extending the classical result of kitchens on one dimensional group shifts we provide a sufficient condition for a self similar group whose elements form a sofic tree shift to be a tree shift of finite type as an application we show that the closures of certain self similar groups of rooted k ary tree automorphisms that satisfy an algebraic law are not rabin recognizable that is they can not be described within the second order theory of k successors in both the main result and in the application a crucial role is played by a distinguished branched subgroup structure of the groups under consideration

a nonparametric multivariate test for monotone trend with pharmaceutical applications abstract during a drug trial each subject may have many blood constituents measured at regular time intervals the traditional method of evaluating such data using normal ranges has undergone much controversy in the clinical chemistry literature we propose a new multivariate test for monotone trend based on kendall s statistic as a way to test for change in blood constituents over the course of a drug experiment the new test avoids the unrealistic assumptions and repeated testing problem of the normal range method an example illustrates the new procedure

techniques of trend analysis for monthly water quality data some of the characteristics that complicate the analysis of water quality time series are non normal distributions seasonality flow relatedness missing values values below the limit of detection and serial correlation presented here are techniques that are suitable in the face of the complications listed above for the exploratory analysis of monthly water quality data for monotonie trends the first procedure described is a nonparametric test for trend applicable to data sets with seasonality missing values or values reported as less than the seasonal kendall test under realistic stochastic processes exhibiting seasonality skewness and serial correlation it is robust in comparison to parametric alternatives although neither the seasonal kendall test nor the alternatives can be considered an exact test in the presence of serial correlation the second procedure the seasonal kendall slope estimator is an estimator of trend magnitude it is an unbiased estimator of the slope of a linear trend and has considerably higher precision than a regression estimator where data are highly skewed but somewhat lower precision where the data are normal the third procedure provides a means for testing for change over time in the relationship between constituent concentration and flow thus avoiding the problem of identifying trends in water quality that are artifacts of the particular sequence of discharges observed e g drought effects in this method a flow adjusted concentration is defined as the residual actual minus conditional expectation based on a regression of concentration on some function of discharge these flow adjusted concentrations which may also be seasonal and non normal can then be tested for trend by using the seasonal kendall test

relatively free semigroups of intermediate growth abstract the problem of calculating the growth of a finitely generated f g semigroup satisfying the given system of identities is considered examples of relatively free semigroups having intermediate growth new growth criteria and constructions are given the main ideas employed in the proofs are based on some new points of view on growth our method is also useful for constructing various examples of f g nilpotent and nil semigroups having intermediate growth and arbitrarily small gelfand kirillov superdimension

applicability of prewhitening to eliminate the influence of serial correlation on the mann kendall test 1 prewhitening has been used to eliminate the influence of serial correlation on the mann kendall mk test in trend detection studies of hydrological time series however its ability to accomplish such a task has not been well documented this study investigates this issue by monte carlo simulation simulated time series consist of a linear trend and a lag 1 autoregressive ar 1 process with a noise simulation results demonstrate that when trend exists in a time series the effect of positive negative serial correlation on the mk test is dependent upon sample size magnitude of serial correlation and magnitude of trend when sample size and magnitude of trend are large enough serial correlation no longer significantly affects the mk test statistics removal of positive ar 1 from time series by prewhitening will remove a portion of trend and hence reduces the possibility of rejecting the null hypothesis while it might be false contrarily removal of negative ar 1 by prewhitening will inflate trend and leads to an increase in the possibility of rejecting the null hypothesis while it might be true therefore prewhitening is not suitable for eliminating the effect of serial correlation on the mk test when trend exists within a time series

groups acting on rooted trees and their representations on the boundary abstract we consider groups that act on spherically symmetric rooted trees and study the associated representation of the group on the space of locally constant functions on the boundary of the tree we introduce and discuss the new notion of locally 2 transitive actions assuming local 2 transitivity our main theorem yields a precise decomposition of the boundary representation into irreducible constituents the method can be used to study gelfand pairs and enables us to answer a question of grigorchuk to provide examples we analyse in detail the local 2 transitivity of ggs groups moreover our results can be used to determine explicit formulae for zeta functions of induced representations defined by klopsch and the author

local pinsker inequalities via stein s discrete density approach pinsker s inequality states that the relative entropy between two random variables x and y dominates the square of the total variation distance between x and y in this paper we introduce generalized fisher information distances and prove that these also dominate the square of the total variation distance to this end we introduce a general discrete stein operator for which we prove a useful covariance identity we illustrate our approach with several examples whenever competitor inequalities are available in the literature the constants in ours are at least as good and in several cases better

amenability via random walks we use random walks to show that the basilica group is amenable answering an open question of grigorchuk and zuk our results separate the class of amenable groups from the closure of subexponentially growing groups under the operations of group extension and direct limits these classes are separated even within the realm of finitely presented groups

serial correlation in water quality variables estimation and implications for trend analysis 1 serial correlation in water quality time series invalidates tests of significance such as seasonal kendall analysis that assume independence one approach to analyzing such data is to estimate the magnitude of the serial correlation and then use the degree of serial correlation to adjust the variance and make valid inferences four methods for estimating serial correlation lag parameters are evaluated r estimation outperformed the alternative methods considered in case studies of water quality time series the nonparametric rank von neumann s ratio test of randomness is used to test for the presence of serial correlation and r estimation is used to estimate the severity of the serial correlation case study results demonstrate that serial correlation is common in monthly water quality data and does not disappear when bimonthly intervals are used adjustment for flow and seasonal effects generally reduced estimates of serial correlation however even after flow adjustment and deseasonalization the assumption of independence was often unreasonable

statistical estimation and interpretation of trends in water quality time series three approaches to trend analysis of water quality time series are discussed 1 seasonal model with a test for trend based on ranks of observations with observations assumed to be m dependent 2 transfer function noise model in which covariate series may be included by means of transfer functions with the remaining noise modeled as a seasonal autoregressive moving average process and 3 component model with the noise decomposed into series which describe trends and irregular and seasonal variation models are studied with regards to their ability to include covariate series possibility of interpretation of trends treatment of seasonal variation and serial dependence and robustness for outliers we regard the component model being the most realistic and the most informative of the three approaches models are applied to series of monthly phosphorus concentration in the ljungbyan river in southern sweden

on the burnside problem for periodic groups narain gupta 1 and said sidki 2 1 university of manitoba department of mathematics winnipeg manitoba r3t 2n2 canada 2 university of brasilia department of mathematics brasilia d f brazil introduction the generalized burnside problem refers to the question are finitely generated periodic groups finite this was answered in the negative by golod 1 who proved that for each prime p there exists a finitely generated infinite p group golod s construction in not however direct and is based on his celebrated work with safarevi recently grigor uk 2 has given a direct and elegant construction of an infinite 2 group which is generated by three elements of order 2 in this paper we give for each odd prime p a direct construction of an infinite p group on two generators each of order p our group is a subgroup of the automorphism group of a regular tree of degree p and as might be expected it is residually finite and has infinite exponent preliminaries let p be an odd prime and let t 0 be the infinite regular tree of degree p with vertex 0 so that through each vertex u of t 0 there are p regular subtrees

an automaton group with undecidable order and engel problems abstract for every turing machine we construct an automaton group that simulates it precisely starting from an initial configuration of the turing machine we explicitly construct an element of the group such that the turing machine stops if and only if this element is of finite order if the turing machine is universal the corresponding automaton group has an undecidable order problem this solves a problem raised by grigorchuk the above group also has an undecidable engel problem there is no algorithm that given g h in the group decides whether there exists an integer n such that the n iterated commutator g h h h is the identity or not this solves a problem raised by bartholdi

on the isolated points in the space of groups we investigate the isolated points in the space of finitely generated groups we give a workable characterization of isolated groups and study their hereditary properties various examples of groups are shown to yield isolated groups we also discuss a connection between isolated groups and solvability of the word problem

inequalities for integrals of modified bessel functions and expressions involving them abstract simple inequalities are established for some integrals involving the modified bessel functions of the first and second kind in most cases we show that we obtain the best possible constant or that our bounds are tight in certain limits we apply these inequalities to obtain uniform bounds for several expressions involving integrals of modified bessel functions such expressions occur in stein s method for variance gamma approximation and the results obtained in this paper allow for technical advances in the method we also present some open problems that arise from this research

multivariate tests for trend in water quality several methods of testing for multivariate trend have been discussed in the statistical and water quality literature we review both parametric and nonparametric approaches and compare their performance using synthetic data a new method based on a robust estimation and testing approach suggested by sen and puri performed very well for serially independent observations a modified version of the covariance inversion approach presented by dietz and killeen also performed well for serially independent observations for serially correlated observations the covariance eigenvalue method suggested by lettenmaier was the best performer