deriving loudness growth functions from categorical loudness scaling data the goal of this study was to reconcile the differences between measures of loudness obtained with continuous unbounded scaling procedures such as magnitude estimation and production and those obtained using a limited number of discrete categories such as categorical loudness scaling cls the former procedures yield data with ratio properties but some listeners find it difficult to generate numbers proportional to loudness and the numbers cannot be compared across listeners to explore individual differences cls where listeners rate loudness on a verbal scale is an easier task but the numerical values or categorical units cus assigned to the points on the scale are not proportional to loudness sufficient cls data are now available to assign values in sones a scale proportional to loudness to the loudness categories as a demonstration of this approach data from heeren hohmann appell and verhey j acoust soc am 133 el314 el319 2013 were used to develop a cusone metric whose valu

complex earthquakes and teichmuller theory it is known that any two points in teichmuller space are joined by an earthquake path in this paper we show any earthquake path r t s extends to a proper holomorphic mapping of a simplyconnected domain d into teichmuller space where r d c these complex earthquakes relate weil petersson geometry projective structures pleated surfaces and quasifuchsian groups using complex earthquakes we prove grafting is a homeomorphism for all 1 dimensional teichmuller spaces and we construct bending coordinates on bers slices and their generalizations in the appendix we use projective surfaces to show the closure of quasifuchsian space is not a topological manifold

iterative validation of eigensolvers a scheme for improving the reliability of hermitian eigenvalue solvers iterative eigenvalue solvers for large sparse matrices may miss some of the required eigenvalues that are of high algebraic multiplicity or tightly clustered block methods locking a posteriori validation or simply increasing the required accuracy are often used to avoid missing or to detect a missed eigenvalue but each has its own shortcomings in robustness or performance to resolve these shortcomings we have developed a postprocessing algorithm iterative validation of eigensolvers ive that combines the advantages of each technique ive detects numerically multiple eigenvalues among the approximate eigenvalues returned by a given solver adjusts the block size accordingly then calls the given solver using locking to compute a new approximation in the subspace orthogonal to the current approximate eigenvectors this process is repeated until no additional missed eigenvalues can be identified ive is general and can be applied as a wrapper to any rayleigh ritz based hermitian eigensolver our experiments show that ive is very effective in computing missed eigenvalues even with eigensolvers that lack locking or block capabilities although such capabilities may further enhance robustness by focusing on robustness in a postprocessing stage ive allows the user to decouple the notion of robustness from that of performance when choosing the block size or the convergence tolerance

relative contributions of specific frequency bands to the loudness of broadband sounds listeners with normal hearing nh and sensorineural hearing loss snhl were asked to compare pairs of noise stimuli and choose the louder noise in each pair each noise was made up of 15 two erbn equivalent rectangular bandwidth wide frequency bands that varied independently over a 12 db range from one presentation to the next mean levels of the bands followed the long term average speech spectrum ltass or were set to 43 51 or 59 db sound pressure level spl the relative contribution of each band to the total loudness of the noise was determined by computing the correlation between the difference in levels for a given band on every trial and the listener s decision on that trial weights for snhl listeners were governed by audibility and the spectrum of the noise stimuli with bands near the spectral peak of the ltass noise receiving greatest weight nh listeners assigned greater weight to the lowest and highest bands an effect that increased with overall level but did not assign greater weight to bands near the ltass peak additional loudness matching and paired comparison studies using stimuli missing one of the 15 bands showed a significant contribution by the highest band but properties other than loudness may have contributed to the decisions

regenerating singular hyperbolic structures from sol let m be a torus bundle over s 1 with an orientation preserving anosov monodromy the manifold m admits a geometric structure modeled on sol we prove that the sol structure can be deformed into singular hyperbolic cone structures whose singular locus m is the mapping torus of the fixed point of the monodromy the hyperbolic cone metrics are parametred by the cone angle in the interval 0 2 when 2 the cone manifolds collapse to the basis of the fibration s 1 and they can be rescaled in the direction of the fibers to converge to the sol manifold

a low cost goal oriented compact proper orthogonal decomposition basis for model reduction of static systems a novel model reduction technique for static systems is presented the method is developed using a goal oriented framework and it extends the concept of snapshots for proper orthogonal decomposition pod to include sensitivity derivatives of the state with respect to system input parameters the resulting reduced order model generates accurate approximations due to its goal oriented construction and the explicit training of the model for parameter changes the model is less computationally expensive to construct than typical pod approaches since efficient multiple right hand side solvers can be used to compute the sensitivity derivatives the effectiveness of the method is demonstrated on a parameterized aerospace structure problem

relation of distortion product otoacoustic emission input output functions to loudness the aim of this study is to further explore the relationship between distortion product otoacoustic emission dpoae measurements and categorical loudness scaling cls measurements using multiple linear regression mlr analysis recently thorson et al j acoust soc am 131 1282 1295 2012 obtained predictions of cls loudness ratings from dpoae input output i o functions using mlr analysis the present study extends that work by 1 considering two different and potentially improved mlr models one for predicting loudness rating at specified input level and the other for predicting the input level for each loudness category and 2 validating the new models predictions using an independent set of data strong correlations were obtained between predicted and measured data during the validation process with overall root mean square errors in the range 10 43 16 78 db for the prediction of cls input level supporting the view that dpoae i o measurements can predict cls loudness ratings and input levels and thus may be useful for fitting hearing aids

reliability of distortion product otoacoustic emissions and their relation to loudness the reliability of distortion product otoacoustic emission dpoae measurements and their relation to loudness measurements was examined in 16 normal hearing subjects and 58 subjects with hearing loss the level of the distortion product l d was compared across two sessions and resulted in correlations that exceeded 0 90 the reliability of dpoaes was less when parameters from nonlinear fits to the input output i o functions were compared across visits next the relationship between dpoae i o parameters and the slope of the low level portion of the categorical loudness scaling cls function soft slope was assessed correlations of 0 65 0 74 and 0 81 at 1 2 and 4 khz were observed between cls soft slope and combined dpoae parameters behavioral threshold had correlations of 0 82 0 83 and 0 88 at 1 2 and 4 khz with cls soft slope combining dpoaes and behavioral threshold provided little additional information lastly a multivariate approach utilizing the entire dpoae i o function was used to predict the cls rating for each input level db spl standard error of the estimate when using this method ranged from 2 4 to 3 0 categorical units cu suggesting that dpoae i o functions can predict cls measures within the cu step size used in this study 5

distortion product otoacoustic emission suppression tuning curves in hearing impaired humans distortion product otoacoustic emission dpoae suppression tuning curves stcs were measured in 65 hearing impaired hi subjects at f2 frequencies of 2 0 2 8 4 0 and 5 6 khz and l2 levels relative to sensation level sl from 10 db to as much as 50 db best frequency cochlear amplifier gain tip to tail difference t t and tuning qerb were estimated from stcs as with normal hearing nh subjects t t differences and qerb decreased as l2 increased t t differences and qerb were reduced in hi ears compared to normal for conditions in which l2 was fixed relative to behavioral threshold db sl when stcs were compared with l2 at constant sound pressure levels db spl differences between nh and hi subjects were reduced the large effect of level and small effect of hearing loss were both confirmed by statistical analyses therefore the magnitude of the differences in dpoae stcs between nh and hi subjects is mainly dependent on the manner in which level l2 is specified although this conclusion may appear to be at odds with previous invasive measures of cochlear response gain and tuning the apparent inconsistency may be resolved when the manner of specifying stimulus level is taken into account

laminations mesurees de plissage des varietes hyperboliques de dimension 3 for a hyperbolic metric on a 3 dimensional manifold the boundary of its convex core is a surface which is almost everywhere totally geodesic but which is bent along a family of disjoint geodesics the locus and intensity of this bending is described by a measured geodesic lamination which is a topological object we consider two problems the topological characterization of those measured geodesic laminations which can occur as bending measured laminations of hyperbolic metrics and the uniqueness problem which asks whether a hyperbolic metric is uniquely determined by its bending measured lamination

a pade based factorization free algorithm for identifying the eigenvalues missed by a generalized symmetric eigensolver when computing the solution of a generalized symmetric eigenvalue problem of the form ku mu the sturm sequence check also known as the inertia check is the most popular method for reporting the number of missed eigenvalues within a range l r this method requires the factorization of the matrices k l m and k r m when the size of the problem is reasonable and the matrices k and m are assembled these factorizations are possible when the eigensolver is equipped with an iterative solver which is nowadays the preferred choice for large scale problems the factorization of k m is not desired or feasible and therefore the inertia check cannot be performed to this effect the purpose of this paper is to present a factorization free algorithm for detecting and identifying the eigenvalues that were missed by an eigensolver equipped with an iterative linear equation solver within an interval of interest l r this algorithm constructs a scalar rational transfer function whose poles are exactly the eigenvalues of the symmetric pencil k m approximates it by a pade expansion and computes the poles of this approximation to detect and identify the missed eigenvalues the proposed algorithm is illustrated with an academic numerical example its potential for real engineering applications is also demonstrated with a large scale structural vibrations problem

projective structures with degenerate holonomy and the bers density conjecture we prove the bers density conjecture for singly degenerate kleinian surface groups without parabolics

pinching constants for hyperbolic manifolds we show in this paper that for everyn 4 there exists a closedn dimensional manifoldv which carries a riemannian metric with negative sectional curvaturek but which admits no metric with constant curvaturek 1 we also estimate the pinching constantsh for which our manifoldsv admit metrics with 1 k h

a behavioral measure of basilar membrane nonlinearity in listeners with normal and impaired hearing this paper examines the possibility of estimating basilar membrane bm nonlinearity using a psychophysical technique the level of a forward masker required to mask a brief signal was measured for conditions where the masker was either at or one octave below the signal frequency the level of the forward masker at masked threshold provided an indirect measure of the bm response to the signal as follows consistent with physiological studies it was assumed that the bm responds linearly to frequencies well below the characteristic frequency cf thus the ratio of the slopes of the masking functions between a masker at the signal frequency and a masker well below the signal frequency should provide an estimate of bm compression at cf results obtained from normally hearing listeners were in quantitative agreement with physiological estimates of bm compression furthermore differences between normally hearing listeners and listeners with cochlear hearing impairment were consistent with the physiological effects of damage to the cochlea the results support the hypothesis that bm nonlinearity governs the nonlinear growth of the upward spread of masking and suggest that this technique provides a straightforward method for estimating bm nonlinearity in humans

fast frequency sweep computations using a multi point pade based reconstruction method and an efficient iterative solver problems of the form z u f where z is a given matrix f is a given vector and is a circular frequency or circular frequency related parameter arise in many applications including computational structural and fluid dynamics and computational acoustics and electromagnetics the straightforward solution of such problems for fine increments of is computationally prohibitive particularly when z is a large scale matrix this paper discusses an alternative solution approach based on the efficient computation of u and its successive derivatives with respect to at a few sample values of this parameter and the reconstruction of the solution u in the frequency band of interest using multi point pade approximants this computational methodology is illustrated with applications from structural dynamics and underwater acoustic scattering in each case it is shown to reduce the cpu time required by the straightforward approach to frequency sweep computations by two orders of magnitude copyright 2006 john wiley sons ltd

a feti dp method for the parallel iterative solution of indefinite and complex valued solid and shell vibration problems the dual primal finite element tearing and interconnecting feti dp domain decomposition method ddm is extended to address the iterative solution of a class of indefinite problems of the form k 2 m u f and a class of complex problems of the form k 2 m i d u f where k m and d are three real symmetric matrices arising from the finite element discretization of solid and shell dynamic problems i is the imaginary complex number and a is a real positive number a key component of this extension is a new coarse problem based on the free space solutions of navier s equations of motion these solutions are waves and therefore the resulting ddm is reminiscent of the feti h method for this reason it is named here the feti dph method for a practically large a range feti dph is shown numerically to be scalable with respect to all of the problem size substructure size and number of substructures the cpu performance of this iterative solver is illustrated on a 40 processor computing system with the parallel solution for various a ranges of several large scale indefinite or complex valued systems of equations associated with shifted eigenvalue and forced frequency response structural dynamics problems

loudness growth in 1 2 octave bands lgob a procedure for the assessment of loudness in this paper a method that has been developed for the assessment and quantification of loudness perception in normal hearing and hearing impaired persons is described the method has been named lgob which stands for loudness growth in 1 2 octave bands the method uses 1 2 octave bands of noise centered at 0 25 0 5 1 0 2 0 and 4 0 khz with subjective levels between a subject s threshold of hearing and the too loud level the noise bands are presented to the subject randomized over frequency and level and the subject is asked to respond with a loudness rating one of very soft soft ok loud very loud too loud subject responses normal and hearing impaired are then compared to the average responses of a group of normal hearing subjects this procedure allows one to estimate the subject s loudness growth relative to normals as a function of frequency and level the results may be displayed either as isoloudness contours or as recruitment curves in its present form the measurements take less than 30 min the signal presentation and analysis is done using a pc and a pc plug in board having a digital to analog converter

the effect of test signal type and bandwidth on the categorical scaling of loudness recently several methods for obtaining clinical measures of loudness growth through the use of categorical scaling cs have been proposed for the selection of hearing aids these methods use differing test signals or suggest frequency specific level corrections in an attempt to reflect the loudness perception of hearing aid processed speech while some decisions regarding the stimuli utilized for loudness perception procedures are based on measured relationships to speech signals the effect on loudness perception of changing signal type and bandwidth as measured by cs remains unclear the relationships between the cs loudness growth of signals of differing type pure tones noise bands filtered temporally inverted passband speech and bandwidth were examined for subjects with both normal and impaired hearing results suggest that when the bandwidth is similar e g pure tone and 1 3 oct signal type does not have significant bearing on loudness perception as expected increasing the bandwidth beyond the critical band affected loudness growth as wideband speech stimuli were judged to be significantly louder than narrow band speech at equivalent overall sound levels in this investigation similar loudness growth patterns were noted across category ratings for all test signal bandwidths in contrast loudness growth data obtained using an intelligible speech signal cox et al the american academy of audiology 1994a revealed loudness growth patterns for speech were fundamentally different than those obtained for tones implications for hearing aid fitting strategies are discussed recently several methods for obtaining clinical measures of loudness growth through the use of categorical scaling cs have been proposed for the selection of hearing aids these methods use differing test signals or suggest frequency specific level corrections in an attempt to reflect the loudness perception of hearing aid processed speech while some decisions regarding the stimuli utilized for loudness perception procedures are based on measured relationships to speech signals the effect on loudness perception of changing signal type and bandwidth as measured by cs remains unclear the relationships between the cs loudness growth of signals of differing type pure tones noise bands filtered temporally inverted passband speech and bandwidth were examined for subjects with both normal and impaired hearing results suggest that when the bandwidth is similar e g pure tone and 1 3 oct signal type does not have significant bearing on loudness perception as expected increasing the bandwidth bey

the grafting map of teichmuller space one of the underlying principles in the study of kleinian groups is that aspects of the complex projective geometry of quotients of by these groups reflect properties of the three dimensional hyperbolic geometry of the quotients ofh by these groups yet even though it has been over thirty five years since lipman bers exhibited a holomorphic embedding of the teichmuller space of riemann surfaces in terms of the projective geometry of a teichmuller space of quasi fuchsian manifolds no corresponding embedding in terms of the three dimensional hyperbolic geometry has been presented one of the goals of this paper is to give such an embedding this embedding is straightforward and has been expected for some time ta97 mc98 to each member of a bers slice of the space qf of quasi fuchsian 3manifolds we associate the bending measured lamination of the convex hull facing the fixed conformal end the geometric relationship between a boundary component of a convex hull and the projective surface at infinity for its end is given by a process known as grafting an operation on projective structures on surfaces that traces its roots back at least to klein kl33 p 230 50 with a modern history developed by many authors ma69 he75 fa83 st83 go87 gkm00 ta97 mc98 the main technical tool in our proof that bending measures give coordinates for bers slices and the second major goal of this paper is the completion of the proof of the grafting conjecture this conjecture states that for a fixed measured lamination the self map of teichmuller space induced by grafting a surface along is a homeomorphism of teichmuller space our contribution to this argument is a proof of the injectivity of the grafting map while the principal application of this result that we give is to geometric coordinates on the bers slice of qf one expects that the grafting homeomorphism might lead to other systems of geometric coordinates for other families of kleinian groups see 5 2 thus we feel that this result is of interest in its own right we now state our results and methods more precisely throughout s will denote a fixed differentiable surface which is closed orientable and of genus g 2 let tg be the corresponding teichmuller space of marked conformal structures on s and let pg denote the deformation space of complex projective structures on s see 2 for definitions

rate of loudness growth for pure tones in normal and impaired hearing the present article provides an analysis of loudness growth rates in normal and cochlear impaired hearing for diverse groups with respect to age and backgrounds slopes are obtained from absolute magnitude estimation and magnitude production of loudness measured values and from cross modality matching and absolute magnitude estimation of apparent length predicted values consistent with an earlier study r p hellman and c h meiselman j acoust soc am 88 2596 2606 1990 slopes calculated within the 15 30 db stimulus range above the elevated threshold increase in size with the degree of hearing loss the corresponding range of loudness values in normal hearing yields a slope near 0 60 independent of the threshold levels this pattern of loudness growth holds for individuals and groups but the intersubject variability of the slope is more labile being larger across than within groups and larger for the measured slopes than for the predicted values determined from the predicted slopes the coefficient of variation sigma m is approximately constant in normal and impaired hearing ranging from 20 27 in contrast sigma m obtained from the measured slopes increases with the degree of hearing loss to a value of almost 50 for a 75 db loss the overall stability and systematics of the observed effects further demonstrate that the loudness intensity relation can be specified with reasonable precision and accuracy from cross modality matching

a fast method for solving acoustic scattering problems in frequency bands abstract we present a methodology for computing efficiently scattered fields in a frequency band the main feature of this methodology is the construction of a series of discrete problems that differ only by their right hand sides rather than by both their left and right hand sides its key steps are a the reformulation of the acoustic scattering problem in a bounded domain using any preferred absorbing boundary condition b the characterization of the repeated derivatives with respect to the frequency of the scattered field as solutions of scattering type problems with different source terms and boundary conditions and c the reconstruction of a scattered field by either the pade approximants or wynn s algorithm we report on several multifrequency acoustic scattering examples that illustrate the accuracy and computational efficiency of the proposed solution methodology

spectral loudness summation for short and long signals as a function of level the equal loudness ratio hypothesis elrh assumes that the loudness ratio between equal level long and short signals with the same spectrum is independent of level and spectrum thus it predicts the same amount of spectral loudness summation for equal level short and long signals to investigate how duration and level affect spectral loudness summation loudness functions for 10 and 1000 ms bandpass filtered noise centered at 2khz were obtained for normal hearing listeners using categorical loudness scaling the bandwidth was varied from 200 to 6400hz from the loudness functions the level difference between the 3200 hz wide reference signal and the equally loud test signals was determined for reference levels in the range from 25 to 105db spl in addition for two reference levels 45 and 65db spl this level difference was measured using a loudness matching procedure both procedures showed similar results for the two reference levels over a wide level range spectral loudness summation is larger fo

feti dp a dual primal unified feti method part i a faster alternative to the two level feti method the feti method and its two level extension feti 2 are two numerically scalable domain decomposition methods with lagrange multipliers for the iterative solution of second order solid mechanics and fourth order beam plate and shell structural problems respectively the feti 2 method distinguishes itself from the basic or one level feti method by a second set of lagrange multipliers that are introduced at the subdomain cross points to enforce at each iteration the exact continuity of a subset of the displacement field at these specific locations in this paper we present a dual primal formulation of the feti 2 concept that eliminates the need for that second set of lagrange multipliers and unifies all previously developed one level and two level feti algorithms into a single dual primal feti dp method we show that this new feti dp method is numerically scalable for both second order and fourth order problems we also show that it is more robust and more computationally efficient than existing feti solvers particularly when the number of subdomains and or processors is very large copyright 2001 john wiley sons ltd

on the density of geometrically finite kleinian groups the density conjecture of bers sullivan and thurston predicts that each complete hyperbolic 3 manifold m with finitely generated fundamental group is an algebraic limit of geometrically finite hyperbolic 3 manifolds we prove that the conjecture obtains for each complete hyperbolic 3manifold with no cusps and incompressible ends

relation between loudness in categorical units and loudness in phons and sones data are presented on the relation between loudness measured in categorical units cus using a standardized loudness scaling method iso 16832 2006 and loudness expressed as the classical standardized measures phon and sone based on loudness scaling of narrowband noise signals by 31 normal hearing subjects sound pressure levels eliciting the same categorical loudness were derived for various center frequencies the results were comparable to the standardized equal loudness level contours a comparison between the loudness function in cus at 1000 hz and the standardized loudness function in sones indicates a cubic relation between the two loudness measures

categorical loudness scaling and equal loudness contours in listeners with normal hearing and hearing loss this study describes procedures for constructing equal loudness contours elcs in units of phons from categorical loudness scaling cls data and characterizes the impact of hearing loss on these estimates of loudness additionally this study developed a metric level dependent loudness loss which uses cls data to specify the deviation from normal loudness perception at various loudness levels and as function of frequency for an individual listener with hearing loss cls measurements were made in 87 participants with hearing loss and 61 participants with normal hearing an assessment of the reliability of cls measurements was conducted on a subset of the data cls measurements were reliable there was a systematic increase in the slope of the low level segment of the cls functions with increase in the degree of hearing loss elcs derived from cls measurements were similar to standardized elcs international organization for standardization iso 226 2003 the presence of hearing loss decreased the vertical spacing of the elcs reflecting loudness recruitment and reduced cochlear compression representing cls data in phons may lead to wider acceptance of cls measurements like the audiogram that specifies hearing loss at threshold level dependent loudness loss describes deficit for suprathreshold sounds such information may have implications for the fitting of hearing aids

collisions of particles in locally ads spacetimes i local description and global examples we investigate 3 dimensional globally hyperbolic ads manifolds or more generally constant curvature lorentz manifolds containing particles i e cone singularities along a graph we impose physically relevant conditions on the cone singularities e g positivity of mass angle less than 2 on time like singular segments we construct examples of such manifolds describe the cone singularities that can arise and the way they can interact the local geometry near the vertices of we then adapt to this setting some notions like global hyperbolicity which are natural for lorentz manifolds and construct some examples of globally hyperbolic ads manifolds with interacting particles

an adaptive scheme for a class of interpolatory model reduction methods for frequency response problems frequency sweep problems arise in many structural dynamic acoustic and structural acoustic applications in each case they incur the evaluation of a frequency response function for a typically large number of frequencies because each function evaluation requires the solution of an often large scale system of equations frequency sweep problems are computationally intensive interpolatory model order reduction is a powerful tool for reducing their cost however the performance of this tool depends on the location and number of the interpolation frequency points it also depends on the number of consecutive frequency derivatives of the response function that are matched at each frequency point so far these two choices have been made in the literature in a heuristic manner in contrast this paper proposes an automatic adaptive strategy based on monitoring the euclidean norm of the relative residual associated with the function to be evaluated over the frequency band of interest more specifically the number of interpolation points and the number of matched frequency derivatives are adaptively increased until the global euclidean norm of the relative residual is reduced below a user specified tolerance the robustness accuracy and computational efficiency of this adaptive strategy are highlighted with the solution of several frequency sweep problems associated with large scale structural dynamic acoustic and structural acoustic finite element models copyright 2012 john wiley sons ltd

equal loudness level contours for pure tones equal loudness level contours provide the foundation for theoretical and practical analyses of intensity frequency characteristics of auditory systems since 1956 equal loudness level contours based on the free field measurements of robinson and dadson br j appl phys 7 166 181 1956 have been widely accepted however in 1987 some questions about the general applicability of these contours were published h fastl and e zwicker fortschritte der akustik daga 87 pp 189 193 1987 as a result a new international effort to measure equal loudness level contours was undertaken the present paper brings together the results of 12 studies starting in the mid 1980s to arrive at a new set of contours the new contours estimated in this study are compared with four sets of classic contours taken from the available literature the contours described by fletcher and munson j acoust soc am 5 82 108 1933 exhibit some overall similarity to our proposed estimated contours in the mid frequency range up to 60 phons the contours described by robinson and dadson exhibit clear differences from the new contours these differences are most pronounced below 500 hz and the discrepancy is often as large as 14 db

quasi fuchsian manifolds with particles we consider 3 dimensional hyperbolic cone manifolds which are convex cocompact in a natural sense with cone singularities along infinite lines such singularities are sometimes used by physicists as models for massive spinless point particles we prove an infinitesimal rigidity statement when the angles around the singular lines are less than any infinitesimal deformation changes either these angles or the conformal structure at infinity with marked points corresponding to the endpoints of the singular lines moreover any small variation of the conformal structure at infinity and of the singular angles can be achieved by a unique small deformation of the cone manifold structure these results hold also when the singularities are along a graph i e for interacting particles

three dimensional manifolds kleinian groups and hyperbolic geometry 1 a conjectural picture of 3 manifolds a major thrust of mathematics in the late 19th century in which poincare had a large role was the uniformization theory for riemann surfaces that every conformai structure on a closed oriented surface is represented by a riemannian metric of constant curvature for the typical case of negative euler characteristic genus greater than 1 such a metric gives a hyperbolic structure any small neighborhood in the surface is isometric to a neighborhood in the hyperbolic plane and the surface itself is the quotient of the hyperbolic plane by a discrete group of motions the exceptional cases the sphere and the torus have spherical and euclidean structures three manifolds are greatly more complicated than surfaces and i think it is fair to say that until recently there was little reason to expect any analogous theory for manifolds of dimension 3 or more except perhaps for the fact that so many 3 manifolds are beautiful the situation has changed so that i feel fairly confident in proposing the

contributions of individual components to the overall loudness of a multitone complex the contributions of individual components to the overall loudness of a multitone complex were examined in a two interval loudness judgment task stimuli were five tone complexes centered on 1000hz with six different logarithmic frequency spacings corresponding to bandwidths from 46 to 2119hz stimuli were presented for 300ms 10ms rise fall the overall level of the standard complex was fixed at 60db spl 53db component levels of the individual components of the comparison complex were selected at random from a rectangular distribution with a range of 20db perceptual weights were computed by calculating the point biserial correlation between the difference in the level of each component across the two intervals and the subject s response when all components fell within the same critical band weights varied little across components in contrast the range of weights increased with increasing frequency separation with more weight given to the lowest and highest frequency components a relation be

limits of geometries author s cooper d danciger j wienhard a abstract 2018 american mathematical society a geometric transition is a continuous path of geometric structures that changes type meaning that the model geometry i e the homogeneous space on which the structures are modeled abruptly changes in order to rigorously study transitions one must define a notion of geometric limit at the level of homogeneous spaces describing the basic process by which one homogeneous geometry may transform into another we develop a general framework to describe transitions in the context that both geometries involved are represented as sub geometries of a larger ambient geometry specializing to the setting of real projective geometry we classify the geometric limits of any sub geometry whose structure group is a symmetric subgroup of the projective general linear group as an application we classify all limits of three dimensional hyperbolic geometry inside of projective geometry finding euclidean nil and sol geometry among the limits we prove however that the other thurston geometries in particular 2 and sl2 do not embed in any limit of hyperbolic geometry in this sense

examples of relative deformation spaces that are not locally connected we provide an infinite family of pared manifolds with the property that the relative deformation spaces of hyperbolic structures on these manifolds are not locally connected this is a natural extension of the recent result of bromberg that shows the space of kleinian punctured torus groups is not locally connected