estimating dimension from small samples abstract details of a new algorithm to estimate the dimension of a measure from point samples are described the new algorithm emphasizes that dimension need not be the same at all scales that is there need not be a scaling region the algorithm is verified with gaussian measures and is found to be reliable and have less demanding data requirements than conventional estimators using certain convergence properties of gaussian measures it is shown that good estimates can be made from very small samples

weighted ordinal means the concept of weighted ordinal arithmetic means and other related weighted ordinal means is studied based on the relevant results on the scale 0 1 new types of weighted ordinal means are proposed in some cases these ordinal means coincide with those proposed by godo and torra but not in the case when ordinal means introduced by them are not idempotent based on divisible ordinal t conorms and modifying the approach of godo and torra we show how the previously introduced weighted ordinal means can be obtained without exploiting the formal similarity of the structure of continuous t conorms on 0 1 and divisible ordinal t conorms

distortions of reconstruction for chaotic attractors abstract we consider the problem of quality evaluation for delay reconstruction of chaotic attractors from scalar time series the proposed approach is based upon local linear analysis of the reconstruction mapping it is shown that some linear distortions in principle could be corrected but usually nonlinear distortions make it dificult to efficiently apply this technique the new algorithms of estimating the scale of nonlinear distortion and irrelevance time upper limit for the reconstruction window from a time series are proposed both of them do not require pricise knowledge of minimal embedding dimension for the attractor studied

characters of the borel and sylow subgroups of classical groups abstract let g be a classical group over the field with q p d elements we prove that if p is an odd prime then the irreducible characters of the sylow p subgroup of g have degrees that are powers of q moreover we prove that if p is odd and g is not the unitary group then the borel subgroup of g is an m group and its character degrees as well as the sizes of the conjugacy classes can be written in the form q r q 1 s 2 k

fundamental limitations for estimating dimensions and lyapunov exponents in dynamical systems we show that values of the correlation dimension estimated over a decade from the grassberger procaccia algorithm cannot exceed the value 2 log10n if n is the number of points in the time series when this bound is saturated it is thus not legitimate to conclude that low dimensional dynamics is present the estimation of lyapunov exponents is also discussed

counting irreducible representations of large degree of the upper triangular groups abstract let u n q be the upper triangular group of degree n over the finite field f q with q elements in this paper we present constructions of large degree complex irreducible representations of u n q where n 7 and then determine the number of irreducible representations of largest second largest and third largest degrees

supercharacters and superclasses for algebra groups we study certain sums of irreducible characters and compatible unions of conjugacy classes in finite algebra groups these groups generalize the unimodular upper triangular groups over a finite field and the supercharacter theory we develop extends results of carlos andre and ning yan that were originally proved in the upper triangular case this theory sometimes allows explicit computations in situations where it would be impractical to work with the full character table we discuss connections with the kirillov orbit method and with gelfand pairs and we give conditions for a supercharacter or a superclass to be an ordinary irreducible character or conjugacy class respectively we also show that products of supercharacters are positive integer combinations of supercharacters

a nonlinear dynamical systems analysis of fricative consonants acoustic waveforms of the strident fricatives s z sh and yog spoken by two native american english speakers are analyzed using modern chaotic analysis techniques fricative data are extracted from both intervocalic and sustained utterances for comparison acoustic waveforms of the vowels a i and u are also analyzed for 44 of the unvoiced fricative tokens in vcv contexts and 59 of the sustained voiced fricatives indications of low dimensional dynamics could be found with the given limitations of stationarity the low dimensional chaotic behavior is exhibited by a correlation dimension d2 ranging between 3 and 7 2 and by positive maximum lyapunov exponents les for the remaining fricatives results suggest that the dimensional complexity therein is greater than the maximum d2 value that could be reliably estimated from the available data about 7 8 for the intervocalic cases and 9 for the sustained cases intervocalic voiced fricatives are excluded from the analysis due to stat

characters of the sylow p subgroups of the chevalley groups d4 pn abstract let u q be a sylow p subgroup of the chevalley groups d 4 q where q is a power of a prime p we describe a construction of all complex irreducible characters of u q and obtain a classification of these irreducible characters via the root subgroups which are contained in the center of these characters furthermore we show that the multiplicities of the degrees of these irreducible characters are given by polynomials in q 1 with nonnegative integer coefficients

on the irreducible characters of a sylow 2 subgroup of the finite symplectic group in characteristic 2 abstract we show that if p m is a sylow 2 subgroup of the finite symplectic group sp 2 m q where q is a power of 2 then p m has irreducible complex characters of degree 2 t q m m 1 2 where t is any integer satisfying 0 t m 2 and that q m m 1 2 is the largest possible degree of an irreducible complex character of p m we include related results on the degrees of the irreducible characters of a sylow 2 subgroup of the split special orthogonal group so 2 m q when q is a power of 2

constructing characters of sylow p subgroups of finite chevalley groups abstract let q be a power of a prime p let g be a finite chevalley group over f q and let u be a sylow p subgroup of g we assume that p is not a very bad prime for g we explain a procedure of reduction of irreducible complex characters of u which leads to an algorithm whose goal is to obtain a parametrization of the irreducible characters of u along with a means to construct these characters as induced characters a focus in this paper is determining the parametrization when g is of type f 4 where we observe that the parametrization is uniform over good primes p 3 but differs for the bad prime p 3 we also explain how it has been applied for all groups of rank 4 or less

danco an intrinsic dimensionality estimator exploiting angle and norm concentration abstract in the past decade the development of automatic intrinsic dimensionality estimators has gained considerable attention due to its relevance in several application fields however most of the proposed solutions prove to be not robust on noisy datasets and provide unreliable results when the intrinsic dimensionality of the input dataset is high and the manifold where the points are assumed to lie is nonlinearly embedded in a higher dimensional space in this paper we propose a novel intrinsic dimensionality estimator danco and its faster variant fastdanco which exploit the information conveyed both by the normalized nearest neighbor distances and by the angles computed on couples of neighboring points the effectiveness and robustness of the proposed algorithms are assessed by experiments on synthetic and real datasets by the comparative evaluation with state of the art methodologies and by significance tests

difficulties in detecting chaos in a complex system abstract the sequences given by a 7d map are analysed by means of the methods widely used to detect chaos in the real world in order to test their sensitivity to chaotic features of a non linear system determined by comparatively high number of parameters the same diagnostic approaches are applied to the 3d lorenz map for comparison the results show that for some of the sequences yielded from the 7d map the adopted methods are not able to give a straightforward answer to the question if the system is chaotic as in the 3d case since the sequences subject to the analysis are not contaminated by noise and are sufficiently long it could be assumed that such difficulties arise likely due to specific internal features of the more complex system it is found also that an increase from 0 01 to 0 5 of the sampling step determining the sequences obtained from the 7d map masks the chaos in some of them

nonlinear analysis of the fracture surface of a single crystal brittle solid abstract the dynamical behavior of a spatial fracture mechanism in a rapid crack in a single crystal brittle solid was under investigation wide thin strips like specimens were fractured under three point bending the spatial mechanism was photographed and digitized and the results were then studied using nonlinear analysis the nonlinear tools used were correlation dimension false nearest neighbor null hypothesis surrogate data and the dominant lyapunov exponent the governing equation of motion in the analyzed region is a differential equations with a minimum of seven independent dynamical variables in contrast to a single independent variable used in analytical calculations

nonlinearity in high frequency stock returns evidence from the athens stock exchange abstract this study investigates empirically the presence of nonlinearities in the athens composite share price index high frequency returns a preliminary analysis indicates that volatility exhibits a periodic intraday inverse j shaped pattern associated with the opening and closing of the market periodicity is then removed employing a flexible fourier form subsequently an arma figarch model over several frequencies yields that return volatility is long memory and self similar nonlinear analysis with the use of the embedding dimension suggests that the filtered return process does not exhibit deterministic or higher order stochastic nonlinearity rather it is reminiscent of a random process we conclude that the acspi data are nonlinear however nonlinearity is attributed to persistent arch effects

use of recurrence plot and recurrence quantification analysis in taiwan unemployment rate time series abstract the aim of the article is to answer the question if the taiwan unemployment rate dynamics is generated by a non linear deterministic dynamic process this paper applies a recurrence plot and recurrence quantification approach based on the analysis of non stationary hidden transition patterns of the unemployment rate of taiwan the case study uses the time series data of the taiwan s unemployment rate during the period from 1978 01 to 2010 06 the results show that recurrence techniques are able to identify various phases in the evolution of unemployment transition in taiwan

aggregation under uncertainty basic uncertain information bui in the form langle x c rangle where x in 0 1 is an observed datum and c in 0 1 is its reliability is discussed and studied the concept of bui s aggregation is introduced and some construction methods are proposed and exemplified the connection with interval valued data and their aggregation is also discussed

generalized phi transformations of aggregation functions abstract in this paper we present a new method of construction of aggregation functions based on the so called bijective chains that generalizes the standard isomorphic transforms of aggregation functions it covers among others several known construction methods such as the construction of copulas based on ultramodular copulas or particular ordinal sums of aggregation functions e g of t norms copulas t conorms several properties of the proposed construction method are discussed and exemplified

properties making a chaotic system a good pseudo random number generator we discuss the properties making a deterministic algorithm suitable to generate a pseudo random sequence of numbers high value of kolmogorov sinai entropy high dimensionality of the parent dynamical system and very large period of the generated sequence we propose the multidimensional anosov symplectic cat map as a pseudo random number generator we show what chaotic features of this map are useful for generating pseudo random numbers and investigate numerically which of them survive in the discrete state version of the map testing and comparisons with other generators are performed

correlation integral as a tool for distinguishing between dynamics and statistics in time series data abstract we propose a new test for time series data for proper choice of processing technique dynamical or statistical it is based upon the normalized slope of the correlation integral m m 1 d ln c d ln where m is the embedding dimension it is shown that when does not tend to 0 on the resolved range of scales as m grows then there will be serious limitations for dynamical methods even if the data are dynamical by nature in the latter case it means that the length of time series does not allow to resolve small scales and on large scales the delay reconstruction for any m mixes true and false neighbours of points and therefore restricts the application of dynamical techniques such as estimating lyapunov exponents or predicting time series

super characters of finite unipotent groups of types b n c n and d n abstract we define and study super characters over the complex field of the classical finite unipotent groups of types b n c n and d n under the assumption that the prime is sufficiently large we extend the known results for the unitriangular group proved by the first author in the papers c a m andre basic characters of the unitriangular group j algebra 175 1995 287 319 and c a m andre basic characters of the unitriangular group for arbitrary primes proc amer math soc 130 7 2002 1943 1954 in particular we prove that every irreducible complex character occurs as a constituent of a unique super character we also give a combinatorial description of all the irreducible characters of maximum degree

slow and fast dynamics in coupled systems a time series analysis view abstract we study the dynamics of systems with different timescales when access only to the slow variables is allowed we use the concept of finite size lyapunov exponent fsle and consider both the cases when the equations of motion for the slow components are known and the situation when a scalar time series of one of the slow variables has been measured a discussion on the effects of parametrizing the fast dynamics is given we show that although the computation of the largest lyapunov exponent can be practically infeasible in complex dynamical systems the computation of the fsle allows to extract information on the characteristic time and on the predictability of the large scale slow time dynamics even with moderate statistics and unresolved small scales

the necessity for a time local dimension in systems with time varying attractors abstract we show that a simple non linear system for ordinary differential equations may possess a time varying attractor dimension this indicates that it is infeasible to characterize eeg and meg time series with a single time global dimension we suggest another measure for the description of non stationary attractors

calculating conjugacy classes in sylow p subgroups of finite chevalley groups abstract in s m goodwin on the conjugacy classes in maximal unipotent subgroups of simple algebraic groups transform groups 11 1 2006 51 76 8 the first author outlined an algorithm for calculating a parametrization of the conjugacy classes in a sylow p subgroup u q of a finite chevalley group g q valid when q is a power of a good prime for g q in this paper we develop this algorithm and discuss an implementation in the computer algebra language gap using the resulting computer program we are able to calculate the parametrization of the conjugacy classes in u q when g q is of rank at most 6 in these cases we observe that the number of conjugacy classes of u q is given by a polynomial in q with integer coefficients

a new method to estimate the kolmogorov entropy from recurrence plots its application to neuronal signals recurrence plots are a useful graphic tool for studying dynamical systems a new variable is proposed to quantify their deterministic structure it allows an easy computation of the k2 entropy since the distance between points needs to be calculated only once instead of every time for each new embedding dimension and it bypasses some of the limitations inherent to the classical grassberger and procaccia method it is valuable for biological data as illustrated here by tests with various dynamical models and its application to experimental signals recorded from neurons

nonlinear dynamic analysis of voices before and after surgical excision of vocal polyps phase space reconstruction correlation dimension and second order entropy methods from nonlinear dynamics are used to analyze sustained vowels generated by patients before and after surgical excision of vocal polyps two conventional acoustic perturbation parameters jitter and shimmer are also employed to analyze voices before and after surgery presurgical and postsurgical analyses of jitter shimmer correlation dimension and second order entropy are statistically compared correlation dimension and second order entropy show a statistically significant decrease after surgery indicating reduced complexity and higher predictability of postsurgical voice dynamics there is not a significant postsurgical difference in shimmer although jitter shows a significant postsurgical decrease the results suggest that jitter and shimmer should be applied to analyze disordered voices with caution however nonlinear dynamic methods may be useful for analyzing abnormal vocal function and quantitatively evaluating the effects of surgical excision of vocal polyps

nonlinear determinism in time series measurements of two dimensional turbulence experiments on two dimensional and three dimensional turbulent flows in a rotating annulus are analyzed using linear and nonlinear time series predictors the models are used to predict the time series a time s ahead and to calculate the velocity incrementu s u sn s u sn between the current value of the time series sn and a point time s apart for two dimensional flow the nonlinear model provides superior predictions to the linear model foru s positive and large in contrast for three dimensional turbulence the prediction of the nonlinear model is no better than the linear model for two dimensional turbulence the probability density functions for the predictedu s from the linear model have an exponential tail while for the nonlinear model the tail exhibits power law decay the scaling exponent of this power law can be explained using arguments of the kolmogorov 1941 theory our findings contradict the common assumption that two dimensional turbulence shares the unpredictability properties of three dimensional turbulent flows 2002 elsevier science b v all rights reserved