on the group of homotopy equivalences of a manifold we consider the group of homotopy equivalences s m of a simply connected manifold m which is part of the fundamental extension of groups due to barcus barratt we show that the kernel of this extension is always a finite group and we compute this kernel for various examples this leads to computations of the group s m for special manifolds m for example if m is a connected sum of products s x sm of spheres in particular the group s s x s is determined completely also the connection of s m with the group of isotopy classes of diffeomorphisms of m is studied the group x of homotopy equivalences of a space x is the set of homotopy classes of homotopy equivalences x x the group structure is induced by mapcomposition the group x i e the group of automorphisms of the homotopy type of x can be regarded as the homotopy symmetry group of the space x in the literature there has been a lot of interest in the computation of such groups compare for example the excellent survey article of m arkowitz 2 this paper is concerned with the structure of m in case m is a closed compact oriented manifold or more generally a poincare complex the computation of this group is an important step for the diffeomorphism classification of manifolds by surgery 40 the group m is also important for cooke s theory 17 of replacing homotopy actions by actions for a differential manifold m the group m is comparable with the group hodiff m of isotopy classes of diffeomorphisms of m in fact via the j homomorphism there is a striking similarity between these groups as is shown in 10 below still there is little known on the group m in the literature only very specific examples are computed see 2 this paper contains on the one hand general results on the structure of the group m see 1 5 on the other hand our methods are used for explicit computations see 6 10 let e be a small open cell of the simply connected m dimensional manifold m and let m m e be the complement the inclusion f sm 1 c m of the boundary is the attaching map for m we consider the fundamental extension of groups due to barcus barratt 42 m i m m 3 s m f here m i m is the subgroup of m consisting of all elements which can be represented by an orientation preserving map m m under m this group is received by the editors august 17 1994 1991 mathematics subject classification primary 55010 57050 1996 american mathematical society 4737 this content downloaded from 157 55 39 197 on wed 26 apr 2017 17 53 44 utc all use subject to http about jstor org terms

multirate digital signal processing algorithm to calculate complex acoustic pressure fields an efficient algorithm to compute complex magnitude and phase acoustic pressure field data that uses a multirate digital processing architecture is presented the algorithm is based on the discretization of the velocity potential function sampled at a rate that varies as a function of field point location and transducer geometry the algorithm can be used to determine accurate magnitude and phase information at any field point location and for any transducer geometry with a closed form velocity potential function including planar pistons spherically focused pistons and planar annular array transducers e g the nondiffracting or j0 bessel transducer numerical simulations based on this algorithm are presented together with exact field calculations wherever possible in order to make absolute error comparisons additionally results based on a standard gaussian quadrature integration scheme are presented in order to compare computational speed and accuracy in the near field results indicate improv

abelianisation of orthogonal groups and the fundamental group of modular varieties abstract we study the commutator subgroup of integral orthogonal groups belonging to indefinite quadratic forms we show that the index of this commutator is 2 for many groups that occur in the construction of moduli spaces in algebraic geometry in particular the moduli of k3 surfaces we give applications to modular forms and to computing the fundamental groups of some moduli spaces

a wavelet based joint estimator of the parameters of long range dependence a joint estimator is presented for the two parameters that define the long range dependence phenomenon in the simplest case the estimator is based on the coefficients of a discrete wavelet decomposition improving a wavelet based estimator of the scaling parameter abry and veitch 1998 as well as extending it to include the associated power parameter an important feature is its conceptual and practical simplicity consisting essentially in measuring the slope and the intercept of a linear fit after a discrete wavelet transform is performed a very fast o n operation under well justified technical idealizations the estimator is shown to be unbiased and of minimum or close to minimum variance for the scale parameter and asymptotically unbiased and efficient for the second parameter through theoretical arguments and numerical simulations it is shown that in practice even for small data sets the bias is very small and the variance close to optimal for both parameters closed form expressions are given for the covariance matrix of the estimator as a function of data length and are shown by simulation to be very accurate even when the technical idealizations are not satisfied comparisons are made against two maximum likelihood estimators in terms of robustness and computational cost the wavelet estimator is found to be clearly superior and statistically its performance is comparable we apply the tool to the analysis of ethernet teletraffic data completing an earlier study on the scaling parameter alone

the anomaly line bundle of the self dual field theory in this work we determine explicitly the anomaly line bundle of the abelian self dual field theory over the space of metrics modulo diffeomorphisms including its torsion part inspired by the work of belov and moore we propose a non covariant action principle for a pair of euclidean self dual fields on a generic oriented riemannian manifold the corresponding path integral allows one to study the global properties of the partition function over the space of metrics modulo diffeomorphisms we show that the anomaly bundle for a pair of self dual fields differs from the determinant bundle of the dirac operator coupled to chiral spinors by a flat bundle that is not trivial if the underlying manifold has middle degree cohomology and whose holonomies are determined explicitly we briefly sketch the relevance of this result for the computation of the global gravitational anomaly of the self dual field theory that will appear in another paper

infinite loop spaces and positive scalar curvature we study the homotopy type of the space of metrics of positive scalar curvature on high dimensional compact spin manifolds hitchin used the fact that there are no harmonic spinors on a manifold with positive scalar curvature to construct a secondary index map from the space of positive scalar metrics to a suitable space from the real k theory spectrum our main results concern the nontriviality of this map we prove that for 2n ge 6 the natural ko orientation from the infinite loop space of the madsen tillmann weiss spectrum factors up to homotopy through the space of metrics of positive scalar curvature on any 2n dimensional spin manifold for manifolds of odd dimension 2n 1 ge 7 we prove the existence of a similar factorisation when combined with computational methods from homotopy theory these results have strong implications for example the secondary index map is surjective on all rational homotopy groups we also present more refined calculations concerning integral homotopy groups to prove our results we use three major sets of technical tools and results the first set of tools comes from riemannian geometry we use a parameterised version of the gromov lawson surgery technique which allows us to apply homotopy theoretic techniques to spaces of metrics of positive scalar curvature secondly we relate hitchin s secondary index to several other index theoretical results such as the atiyah singer family index theorem the additivity theorem for indices on noncompact manifolds and the spectral flow index theorem finally we use the results and tools developed recently in the study of moduli spaces of manifolds and cobordism categories the key new ingredient we use in this paper is the high dimensional analogue of the madsen weiss theorem proven by galatius and the third named author

word maps isotopy and entropy on trouve des diffeomorphismes de basse entropie dans chaque classe d isotopie sur s 3 s 3

an annular superposition integral for axisymmetric radiators a fast integral expression for computing the nearfield pressure is derived for axisymmetric radiators this method replaces the sum of contributions from concentric annuli with an exact double integral that converges much faster than methods that evaluate the rayleigh sommerfeld integral or the generalized king integral expressions are derived for plane circular pistons using both continuous wave and pulsed excitations several commonly used apodization schemes for the surface velocity distribution are considered including polynomial functions and a smooth piston function the effect of different apodization functions on the spectral content of the wave field is explored quantitative error and time comparisons between the new method the rayleigh sommerfeld integral and the generalized king integral are discussed at all error levels considered the annular superposition method achieves a speed up of at least a factor of 4 relative to the point source method and a factor of 3 relative to the generalized king integral without increasing the computational complexity

an efficient grid sectoring method for calculations of the near field pressure generated by a circular piston an analytical expression is derived for time harmonic calculations of the near field pressure produced by a circular piston the near field pressure is described by an efficient integral that eliminates redundant calculations and subtracts the singularity which in turn reduces the computation time and the peak numerical error the resulting single integral expression is then combined with an approach that divides the computational grid into sectors that are separated by straight lines the integral is computed with gauss quadrature in each sector and the number of gauss abscissas in each sector is determined by a linear mapping function that prevents large errors from occurring in the axial region by dividing the near field region into 10 sectors the raw computation time is reduced by nearly a factor of 2 for each expression evaluated in this grid the grid sectoring approach is most effective when the computation time is reduced without increasing the peak error and this is consistently accomplished with the efficient integral formulation of the four single integral expressions evaluated with grid sectoring the efficient formulation that eliminates redundant calculations and subtracts the singularity demonstrates the smallest computation time for a specified value of the maximum error

simplified expansions for radiation from a baffled circular piston computation of acoustic radiation from a baffled circular piston continues to be an active area of investigation both as a canonical problem and because of numerous practical applications for time harmonic radiation exact series expansions are an attractive approach because they do not require numerical integration or limiting approximations here series expansions due to hasegawa inoue and matsuzawa j acoust soc am 74 1044 1047 1983 75 1048 1051 1984 are shown to reduce to simpler expressions suitable for numerical computations for the region r a where a is the piston radius and r is the distance from the piston center an exact solution is given by a series of spherical hankel functions and legendre polynomials with explicit closed form position independent coefficients for the paraxial region w a where w is the distance from the piston axis a second exact series expansion is valid for all axial distances z and reduces to the known analytic solution for w 0 these two expansions allow the radiated field to be computed at any point with rapid convergence except for points near the circle bounding the piston example numerical results illustrate application of this method to ultrasonic sources

a fast near field method for calculations of time harmonic and transient pressures produced by triangular pistons analytical expressions are demonstrated for fast calculations of time harmonic and transient near field pressures generated by triangular pistons these fast expressions remove singularities from the impulse response thereby reducing the computation time and the peak numerical error with a general formula that describes the near field pressure produced by any triangular piston geometry the time domain expressions are further accelerated by a time space decomposition approach that analytically separates the spatial and temporal components of the numerically computed transient pressure applied to a hanning weighted input pulse time space decomposition converts each spatio temporal integral into six spatial integral evaluations at each field point time harmonic and transient calculations are evaluated for an equilateral triangle with sides equal to four wavelengths and the resulting errors are compared to pressures obtained with exact and approximate implementations of the impulse response method the results show that the fast near field method achieves smaller maximum errors and is consistently faster than the impulse response and methods that approximate the impulse response

finite group actions on kervaire manifolds abstract let m k 4 k 2 be the kervaire manifold a closed piecewise linear pl manifold with kervaire invariant 1 and the same homology as the product s 2 k 1 s 2 k 1 of spheres we show that a finite group of odd order acts freely on m k 4 k 2 if and only if it acts freely on s 2 k 1 s 2 k 1 if m k is smoothable then each smooth structure on m k admits a free smooth involution if k 2 j 1 then m k 4 k 2 does not admit any free top involutions free exotic pl involutions are constructed on m k 30 m k 62 and m k 126 each smooth structure on m k 30 admits a free z 2 z 2 action

wavelet based estimations of fractional brownian sheet least squares versus maximum likelihood abstract the scaling behavior or self similarity and long range dependence has been studied in numerous fields such as computer telecommunication hydrology and economics and can be characterized by the hurst parameter h fractional brownian sheet plays an important role in modeling the scaling behavior in multi dimensional signals a wavelet based maximum likelihood estimator for the hurst parameter h h 1 h d of fractional brownian sheet is proposed it is asymptotically normal and compared with the wavelet based least squares estimators introduced in the previous article from theoretical analysis and numerical simulation the theoretical results show that the proposed estimator has the same asymptotic covariance as the least squares estimator of which the weight is equal to the number of available wavelet coefficients and the convergence rates of two estimators are both o 1 i 1 d t i t i is sample length in the i th dimension the simulation results show that the proposed estimator performs better than the least squares estimators in bias and costs less runtime than the generalized least squares estimator realized by the two step method

the picard group of the moduli space of curves with level structures for 4 l and g large we calculate the integral picard groups of the moduli spaces of curves and principally polarized abelian varieties with level l structures in particular we determine the divisibility properties of the standard line bundles over these moduli spaces and we calculate the second integral cohomology group of the level l subgroup of the mapping class group in a previous paper the author determined this rationally this entails calculating the abelianization of the level l subgroup of the mapping class group generalizing previous results of perron sato and the author finally along the way we calculate the first homology group of the mod l symplectic group with coefficients in the adjoint representation

on the mapping class groups of r sp sp for p 3 7 for m r sharp r s p times s p p 3 7 we calculate pi 0 rm diff m r theta 2p 1 and mathcal e m r respectively the group of isotopy classes of orientation preserving diffeomorphisms of mr modulo isotopy classes with representatives which are the identity outside a 2p disc and the group of homotopy classes of orientation preserving homotopy equivalences of mr

anisotropic discrete dual tree wavelet transform for improved classification of trabecular bone this paper deals with a new anisotropic discrete dual tree wavelet transform addtwt to characterize the anisotropy of bone texture more specifically we propose to extend the conventional discrete dual tree wavelet transform ddtwt by using the anisotropic basis functions associated with the hyperbolic wavelet transform instead of isotropic spectrum supports a texture classification framework is adopted to assess the performance of the proposed transform the generalized gaussian distribution is used to model the distribution of the sub band coefficients the estimated vector of parameters for each image is then used as input for the support vector machine classifier experiments were conducted on synthesized anisotropic fractional brownian motion fields and on a real database composed of osteoporotic patients and control cases results show that the addtwt outperforms most of the competing anisotropic transforms with an area under curve rate of 93

exponents of operator self similar random fields abstract if x c e t and c h x t have the same finite dimensional distributions for some pair of linear operators e and h we say that the random vector field x t is operator self similar the exponents e and h are not unique in general due to symmetry this paper characterizes the possible set of range exponents h for a given domain exponent and conversely the set of domain exponents e for a given range exponent

computerized flow field analysis oriented texture fields an approach to the solution of signal to symbol transformation in the domain of flow fields such as oriented texture fields and velocity vector fields is discussed the authors use the geometric theory of differential equations to derive a symbol set based on the visual appearance of phase portraits which are a geometric representation of the solution curves of a system of differential equations they also provide the computational framework to start with a given flow field and derive its symbolic representation specifically they segment the given texture derive its symbolic representation and perform a quantitative reconstruction of the salient features of the original texture based on the symbolic descriptors results of applying this technique to several real texture images are presented this technique is useful in describing complex flow visualization pictures defects in lumber processing defects in semiconductor wafer inspection and optical flow fields

wavelet based texture retrieval using generalized gaussian density and kullback leibler distance we present a statistical view of the texture retrieval problem by combining the two related tasks namely feature extraction fe and similarity measurement sm into a joint modeling and classification scheme we show that using a consistent estimator of texture model parameters for the fe step followed by computing the kullback leibler distance kld between estimated models for the sm step is asymptotically optimal in term of retrieval error probability the statistical scheme leads to a new wavelet based texture retrieval method that is based on the accurate modeling of the marginal distribution of wavelet coefficients using generalized gaussian density ggd and on the existence a closed form for the kld between ggds the proposed method provides greater accuracy and flexibility in capturing texture information while its simplified form has a close resemblance with the existing methods which uses energy distribution in the frequency domain to identify textures experimental results on a database of 640 texture images indicate that the new method significantly improves retrieval rates e g from 65 to 77 compared with traditional approaches while it retains comparable levels of computational complexity

theta functions and a presentation of 21 2g 1 sp 2g 2 abstract we investigate a curtis tits style group presentation based on the dynkin diagram c g in which the short root generators have order two while the long root generators have order four we prove that this describes a finite group with an almost extraspecial normal subgroup of order 2 2 g 2 and quotient isomorphic to the symplectic group sp 2 g 2 such an extension has to be non split if g 3 and was proved to exist in papers of bolt room and wall from 1961 2 and griess from 1973 our presentation proves that it is a double cover of a finite quotient of sp 2 g z we investigate a 2 g dimensional complex representation on a suitable space of theta functions and produce some consequences for the signatures of 4 manifolds described as surface bundles over surfaces in particular we prove that if the monodromy is contained in the theta subgroup sp q 2 g z sp 2 g z then the signature of the 4 manifold is divisible by eight

the kodaira dimension of the moduli of k3 surfaces the global torelli theorem for projective k3 surfaces was first proved by piatetskii shapiro and shafarevich 35 years ago opening the way to treating moduli problems for k3 surfaces the moduli space of polarised k3 surfaces of degree 2d is a quasi projective variety of dimension 19 for general d very little has been known hitherto about the kodaira dimension of these varieties in this paper we present an almost complete solution to this problem our main result says that this moduli space is of general type for d 61 and for d 46 50 54 57 58 60

homological stability for moduli spaces of high dimensional manifolds i s galatius was partially supported by nsf grants dms 1105058 and dms 1405001 the european research council erc under the european union s horizon 2020 research and innovation pro gramme grant agreement no 682922 as well as the danish national research foundation through the centre for symmetry and deformation dnrf92 and erc 682992 o randal williams was partially supported by the herchel smith fund and epsrc grant ep m027783 1

fractional brownian motion a maximum likelihood estimator and its application to image texture fractals have been shown to be useful in characterizing texture in a variety of contexts use of this methodology normally involves measurement of a parameter h which is directly related to fractal dimension in this work the basic theory of fractional brownian motion is extended to the discrete case it is shown that the power spectral density of such a discrete process is only approximately proportional to f a instead of in direct proportion as in the continuous case an asymptotic cramer rao bound is derived for the variance of an estimate of h subsequently a maximum likelihood estimator mle is developed to estimate h it is shown that the variance of this estimator nearly achieves the minimum bound a generation algorithm for discrete fractional motion is presented and used to demonstrate the capabilities of the mle when the discrete fractional brownian process is contaminated with additive gaussian noise the results show that even at signal to noise ratios of 30 db significant errors in estimation of h can result when noise is present the mle is then applied to x ray images of the human calcaneus to demonstrate how the line to line formulation can be applied to the two dimensional case these results indicate that it has strong potential for quantifying texture

multiple resolution texture analysis and classification textures are classified based on the change in their properties with changing resolution the area of the gray level surface is measured at serveral resolutions this area decreases at coarser resolutions since fine details that contribute to the area disappear fractal properties of the picture are computed from the rate of this decrease in area and are used for texture comparison and classification the relation of a texture picture to its negative and directional properties are also discussed

a statistical test for the time constancy of scaling exponents a statistical test is described for determining if scaling exponents vary over time it is applicable to diverse scaling phenomena including long range dependence and exactly self similar processes in a uniform framework without the need for prior knowledge of the type in question it is based on the special properties of wavelet based estimates of the scaling exponent strongly motivating an idealized inference problem the equality or otherwise of means of independent gaussian variables with known variances a uniformly most powerful invariant test exists for this problem and is described a separate uniformly most powerful invariant test is also given for when the scaling exponent undergoes a level change the power functions of both tests are given explicitly and compared using simulation the effect in practice of deviations from the idealizations made of the statistical properties of the wavelet detail coefficients are analyzed and found to be small the tests inherit the significant robustness and computational advantages of the underlying wavelet based estimator a detailed methodology is given describing its use in practical situations the use and benefits of the test are illustrated on the bellcore ethernet data sets

singularity spectrum of fractal signals from wavelet analysis exact results the multifractal formalism for singular measures is revisited using the wavelet transform for bernoulli invariant measures of some expanding markov maps the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima the generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures it is demonstrated that the hausdorff dimensiond h of the set of singularities of holder exponenth can be directly determined from the wavelet transform modulus maxima the singularity spectrum so obtained is shown to be not disturbed by the presence in the signal of a superimposed polynomial behavior of ordern provided one uses an analyzing wavelet that possesses at leastn n vanishing moments however it is shown that ac behavior generally induces a phase transition in thed h singularity spectrum that somewhat masks the weakest singularities this phase transition actually depends on the numbern of vanishing moments of the analyzing wavelet its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal these theoretical results are illustrated with numerical examples they are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional brownian motions and turbulent velocity signals

spatial impulse responses from a flexible baffled circular piston the theory of orthogonal polynomial zernike expansions of functions on a disk as used in the diffraction theory of optical aberrations is applied to obtain semi analytical expressions for the spatial impulse responses arising from a non uniformly moving baffled circular piston these expressions are in terms of the expansion coefficients of the non uniformity and the responses of the orthogonal expansion functions the latter impulse responses have a closed formas finite series involving legendre functions and the sinc function the method is compared with a similar method proposed in p r stepanishen j acoust soc am 70 1176 1181 1981 where zero th orderorthogonal bessel functions rather than zernike polynomials are used as expansion functions the method is also considered for retrieval of a non uniform velocity profile from measured spatial impulseresponses on the level of expansion coefficients which can be applied to acoustic holography for loudspeakers

a 2d fast near field method for calculating near field pressures generated by apodized rectangular pistons analytical two dimensional 2d integral expressions are derived for fast calculations of time harmonic and transient near field pressures generated by apodized rectangular pistons these 2d expressions represent an extension of the fast near field method fnm for uniformly excited pistons after subdividing the rectangular piston into smaller rectangles the pressure produced by each of the smaller rectangles is calculated using the uniformly excited fnm expression for a rectangular piston and the total pressure generated by an apodized rectangular piston is the superposition of the pressures produced by all of the subdivided rectangles by exchanging summation variables and performing integration by parts a 2d apodized fnm expression is obtained and the resulting expression eliminates the numerical singularities that are otherwise present in numerical models of pressure fields generated by apodized rectangular pistons a simplified time space decomposition method is also described and this method further reduces the computation time for transient pressure fields the results are compared with the rayleigh sommerfeld integral and the field ii program for a rectangular source with each side equal to four wavelengths for time harmonic calculations with a 0 1 normalized root mean square error nrmse the apodized fnm is 4 14 times faster than the rayleigh sommerfeld integral and 59 43 times faster than the field ii program and for a 0 01 nrmse the apodized fnm is 12 50 times faster than the rayleigh sommerfeld integral and 155 06 times faster than the field ii program for transient calculations with a 0 1 nrmse the apodized fnm is 2 31 times faster than the rayleigh sommerfeld integral and 4 66 times faster than the field ii program and for a 0 01 nrmse the apodized fnm is 11 90 times faster than the rayleigh sommerfeld integral and 24 04 times faster than the field ii program thus the 2d apodized fnm is ideal for fast pressure calculations and for accurate reference calculations in the near field region

statistical texture characterization from discrete wavelet representations we conjecture that texture can be characterized by the statistics of the wavelet detail coefficients and therefore introduce two feature sets 1 the wavelet histogram signatures which capture all first order statistics using a model based approach and 2 the wavelet co occurrence signatures which reflect the coefficients second order statistics the introduced feature sets outperform the traditionally used energy best performance is achieved by combining histogram and co occurrence signatures

homological stability and stable moduli of flat manifold bundles abstract we prove that the group homology of the diffeomorphism group of g s n s n int d 2 n as a discrete group is independent of g in a range provided that n 2 this answers the high dimensional version of a question posed by morita about surface diffeomorphism groups made discrete the stable homology is isomorphic to the homology of a certain infinite loop space related to the haefliger s classifying space of foliations one geometric consequence of this description of the stable homology is a splitting theorem that implies certain classes called generalized mumford morita miller classes lift to a secondary r z invariants for flat g s n s n bundles provided g 0

stable moduli spaces of high dimensional manifolds we prove an analogue of the madsen weiss theorem for high dimensional manifolds in particular we explicitly describe the ring of characteristic classes of smooth fibre bundles whose fibres are connected sums of g copies of sn sn in the limit g to infty rationally it is a polynomial ring in certain explicit generators giving a high dimensional analogue of mumford s conjecture

vector field analysis for oriented patterns presents a method based on the properties of vector fields for the estimation of a set of symbolic descriptors node saddle star node improper node center and spiral from linear orientation fields planar first order phase portraits are used to model the linear orientation fields a weighted linear estimator is developed to estimate linear phase portraits using only the flow orientation a classification scheme for planar first order phase portraits based on their local properties curl divergence and deformation is developed the authors present results of experiments on noise added synthetic flow patterns and real oriented textures

modular lagrangians and the theta multiplier let v be a free module over z 4 of rank 2 n and let be a non singular skew form on v let f denote the reduction of v modulo 2 and let q be a hyperbolic i e arf invariant zero quadratic form on p with as associated bilinear form we let a v denote the set of oriented lagrangians i e free totally isotropic submodules of rank n in v and ao v ca v the subset of those l in a v whose reductions modulo 2 are totally isotropic for q we call such an l an oriented isotropic lagrangian we will study a certain function m on ao v x ao v with values in the group of fourth roots of unity the function m is skew symmetric m m l re l m t and is a 1 cocycle by this

transient field of a baffled planar piston having an arbitrary vibration amplitude distribution a theoretical model is presented for evaluating the transient velocity potential and pressure fields radiated by a pulsed planar piston set in an infinite rigid baffle and having an arbitrary spatial velocity distribution the method is based on the development of a generalized spatial impulse response function which describes the velocity potential either at a point or averaged over a finite receiving surface resulting from the velocity impulse excitation of a uniformly or nonuniformly vibrating piston source for the specific case of a circular source and receiver this function is plotted using several source distributions and receiver sizes then corresponding plots are presented for two piston velocity waveforms a gaussian pulse and a gaussian modulated sinusoidal burst these plots are compared and the effects of a nonuniformly vibrating source and finite receiver are discussed lastly a previous solution by schoch in which the field of a rigid piston is separated into geometrical and boundary d

self similar anisotropic texture analysis the hyperbolic wavelet transform contribution textures in images can often be well modeled using self similar processes while they may simultaneously display anisotropy the present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific classical class of gaussian anisotropic selfsimilar processes it will be first shown that accurate joint estimates of the anisotropy and selfsimilarity parameters are performed by replacing the standard 2d discrete wavelet transform with the hyperbolic wavelet transform which permits the use of different dilation factors along the horizontal and vertical axes defining anisotropy requires a reference direction that needs not a priori match the horizontal and vertical axes according to which the images are digitized this discrepancy defines a rotation angle second we show that this rotation angle can be jointly estimated third a nonparametric bootstrap based procedure is described which provides confidence intervals in addition to the estimates themselves and enables us to construct an isotropy test procedure which can be applied to a single texture image fourth the robustness and versatility of the proposed analysis are illustrated by being applied to a large variety of different isotropic and anisotropic self similar fields as an illustration we show that a true anisotropy built in self similarity can be disentangled from an isotropic self similarity to which an anisotropic trend has been superimposed

infinite loop spaces from operads with homological stability abstract motivated by the operad built from moduli spaces of riemann surfaces we consider a general class of operads in the category of spaces that satisfy certain homological stability conditions we prove that such operads are infinite loop space operads in the sense that the group completions of their algebras are infinite loop spaces the recent strong homological stability results of galatius and randal williams for moduli spaces of even dimensional manifolds can be used to construct examples of operads with homological stability as a consequence diffeomorphism groups and mapping class groups are shown to give rise to infinite loop spaces furthermore the map to k theory defined by the action of the diffeomorphisms on the middle dimensional homology is shown to be a map of infinite loop spaces

multifractality tests using bootstrapped wavelet leaders multifractal analysis which mostly consists of measuring scaling exponents is becoming a standard technique available in most empirical data analysis toolboxes making use of the most recent theoretical results it is based here on the estimation of the cumulants of the log of the wavelet leaders an elaboration on the wavelet coefficients these log cumulants theoretically enable discrimination between mono and multifractal processes as well as between simple log normal multifractal models and more advanced ones the goal of the present contribution is to design nonparametric bootstrap hypothesis tests aiming at testing the nature of the multifractal properties of stochastic processes and empirical data bootstrap issues together with six declinations of test designs are analyzed their statistical performance significances powers and p values are assessed and compared by means of monte carlo simulations performed on synthetic stochastic processes whose multifractal properties and log cumulants are known theoretically a priori we demonstrate that the joint use of wavelet leaders log cumulants and bootstrap procedures enable us to obtain a powerful tool for testing the multifractal properties of data this tool is practically effective and can be applied to a single observation of data with finite length

abelian quotients of mapping class groups of highly connected manifolds we compute the abelianisations of the mapping class groups of the manifolds w g 2n g s n times s n for n ge 3 and g ge 5 the answer is a direct sum of two parts the first part arises from the action of the mapping class group on the middle homology and takes values in the abelianisation of the automorphism group of the middle homology the second part arises from bordism classes of mapping tori and takes values in the quotient of the stable homotopy groups of spheres by a certain subgroup which in many cases agrees with the image of the stable j homomorphism we relate its calculation to a purely homotopy theoretic problem

on the jacobi group and the mapping class group of the paper contains a proof that the mapping class group of the manifold s 3 x s 3 is isomorphic to a central extension of the full jacobi group j by the group of 7 dimensional homotopy spheres using a presentation of the group j and the p invariant of the homotopy spheres we give a presentation of this mapping class group with generators and defining relations we also compute the cohomology of the group j and determine 2 cocycles that correspond to the mapping class group of s 3 s 3