hopf bifurcation for equivariant conservative and time reversible systems we study the bifurcation of small periodic solutions at a non semi simple 1 1 resonance in equivariant conservative or equivariant time reversible systems by using an equivariant liapunov schmidt method and restricting to solutions with an appropriate isotropy we reduce the problem to a scalar bifurcation equation the analysis of this equation shows a bifurcation behaviour similar to that found for the hamiltonian hopf bifurcation

fine structure of the 2f1 f2 acoustic distortion product changes with primary level the fine frequency structure of the 2f1 f2 acoustic distortion product adp fine structure was examined in ten human subjects with normal hearing primary frequencies f1 and f2 were incremented in steps of 1 32 octave with an f2 f1 ratio of 1 2 the primary levels were kept equal to each other and varied from 45 to 65 db spl in 2 5 db steps the results show that the adp fine structure is characterized by a series of peaks and valleys across frequency with a peak to peak frequency spacing of about 3 32 octave and a peak to valley amplitude ratio of up to 20 db at frequencies below 4000 hz as primary level increases the sharpness of the adp fine structure is not significantly reduced and the pattern gradually shifts to lower frequencies at frequencies above 4000 hz a flattening of the pattern is sometimes observed at high levels a consequence of the underlying process responsible for the fine structure is that adp input output i o functions can be highly variable in shape dramatic shape change

robust nonparametric inference for the median we consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination we propose a modification of the sign test and its associated confidence interval which attains the nominal significance level probability coverage for any distribution in the contamination neighborhood of a continuous distribution we also define some measures of robustness and efficiency under contamination for confidence intervals and tests these measures are computed for the proposed procedures

distortion product otoacoustic emission input output characteristics in normal hearing and hearing impaired human ears dpoae input output i o functions were measured at 7f2 frequencies 1 to 8 khz f2 f1 1 22 over a range of levels 5 to 95 db spl in normal hearing and hearing impaired human ears l1 l2 was level dependent in order to produce the largest 2f1 f2 responses in normal ears system distortion was determined by collecting dp data in six different acoustic cavities these data were used to derive a multiple linear regression model to predict system distortion levels the model was tested on cochlear implant users and used to estimate system distortion in all other ears at most but not all f2 s measurements in cochlear implant ears were consistent with model predictions at all f2 frequencies the ears with normal auditory thresholds produced i o functions characterized by compressive nonlinear regions at moderate levels with more rapid growth at low and high stimulus levels as auditory threshold increased dpoae threshold increased accompanied by dpoae amplitude reductions notably over the range of levels where normal ears showed compression the slope of the i o function was steeper in impaired ears the data from normal hearing ears resembled direct measurements of basilar membrane displacement in lower animals data from ears with hearing loss showed that the compressive region was affected by cochlear damage however responses at high levels of stimulation resembled those observed in normal ears

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

low frequency and high frequency cochlear nonlinearity in humans low and high frequency cochlear nonlinearity was studied by measuring distortion product otoacoustic emission input output dpoae i o functions at 0 5 and 4khz in 103 normal hearing subjects behavioral thresholds at both f2 s were used to set l2 in db sl for each subject primary levels were optimized by determining the l1 resulting in the largest ldp for each l2 for each subject and both f2 s dpoae i o functions were measured using l2 inputs from 10db sl 0 5khz or 20db sl 4khz to 65db sl both frequencies mean dpoae i o functions averaged across subjects differed between the two frequencies even when threshold was taken into account the slopes of the i o functions were similar at 0 5 and 4khz for high level inputs with maximum compression ratios of about 4 1 at both frequencies the maximum slope near dpoae threshold was approximately 1 which occurred at lower levels at 4khz compared to 0 5khz these results suggest that there is a wider dynamic range and perhaps greater cochlear ampl

correspondence between behavioral and individually optimized otoacoustic emission estimates of human cochlear input output curves previous studies have shown a high within subject correspondence between distortion product otoacoustic emission dpoae input output i o curves and behaviorally inferred basilar membrane bm i o curves for frequencies above 2 khz for lower frequencies dpoae i o curves contained notches and plateaus that did not have a counterpart in corresponding behavioral curves it was hypothesized that this might improve by using individualized optimal dpoae primary levels here data from previous studies are re analyzed to test this hypothesis by comparing behaviorally inferred bm i o curves and dpoae i o curves measured with well established group average primary levels and two individualized primary level rules one optimized to maximize dpoae levels and one intended for primaries to evoke comparable bm responses at the f2 cochlear region test frequencies were 0 5 1 and 4 khz behavioral i o curves were obtained from temporal forward masking curves results showed high within subject correspondence between behavioral and dpoae i o curves at 4 khz only regardless of the primary level rule plateaus and notches were equally common in low frequency dpoae i o curves for individualized and group average dpoae primary levels at 0 5 and 1 khz results are discussed in terms of the adequacy of dpoae i o curves for inferring individual cochlear nonlinearity characteristics

breakdown robustness of tests abstract power and level breakdown functions of a test statistic are introduced to obtain a unified analysis of local stability as typified by the influence function and global stability as illustrated by the breakdown point the power breakdown function gives the amount of contamination of each alternative distribution that can carry the test statistic to a null value the level breakdown function gives the amount of contamination of a null distribution that can carry the test statistic to each value in the alternative space in many cases the breakdown function bears an inverse relationship to the maximum bias as a function of the contamination as the maximum bias is not invariant to one to one transformations however equivalent test statistics can have different scales for bias a distinct advantage of the inverse scale is the invariance of the breakdown functions to such transformations the resulting stability curves depend on the parameters in a way analogous to the power curve the slopes o

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

perturbed homoclinic solutions in reversible 1 1 resonance vector fields we consider a smooth reversible vector field in r 4 such that the origin is a fixed point the differential at the origin has two double pure imaginary eigenvalues iq for the critical value 0 of the parameter we show by a normal form analysis that the vector field can be approximated by an integrable field in r 4 for which we know all solutions specially interesting ones are the homoclinics to 0 and homoclinics to periodic solutions depending on the sign of a leading nonlinear coefficient we prove in particular the persistence of these homoclinics for the full vector field

effects of ear canal standing waves on measurements of distortion product otoacoustic emissions at frequencies above 3 khz standing waves in the ear canal complicate calibration of stimulus sound pressure levels spls for measurements of distortion product otoacoustic emissions dpoaes in the literature two stimulus presentation strategies have been used for dpoae measurements in the in the ear adjustment strategy the voltage command to the speakers is adjusted to maintain a constant stimulus spl across frequency at the dpoae measurement microphone in the iso voltage strategy the voltage presented to the speakers is held constant across frequency on the basis of the assumption that the frequency response of the speakers is approximately flat at the eardrum in the average human ear canal because of standing wave effects there are large systematic but idiosyncratic differences of stimulus spl between the two strategies dpoae versus frequency functions dpoae audiograms obtained using both stimulus presentation strategies in the same ears are presented the differences of sti

estimating loudness growth from tone burst evoked responses several studies have investigated the relationship between click evoked auditory brainstem responses abrs and loudness growth in human listeners while some of these studies have reported promising results showing a correlative relationship between click abr and loudness growth as a function of level additional studies are necessary to determine if similar results can be obtained with frequency specific stimuli and more specific details of the loudness function can be derived from abr recordings the aims of this study therefore were to 1 develop a fully objective procedure that segments specific features of evoked tone burst abr recordings 2 investigate the feasibility of using information derived from these recordings for estimating frequency specific loudness growth functions and 3 determine to what extent the loudness growth estimation performance through abr can be improved by controlling for residual noise levels and parametric fitting results from eight normal hearing listeners using 1 and 4 khz stimuli show that the average mean square error of the loudness growth estimation obtained through the procedure is comparable to that of standard psychoacoustical procedures used to estimate loudness growth the data set has been made publicly available at www physionet org

the behavior of the acoustic distortion product 2f1 f2 from the human ear and its relation to auditory sensitivity the acoustic intermodulation distortion product 2f1 f2 adp was measured in human subjects to investigate 1 the dependence of adp level on stimulus parameters and 2 the relationship between adp level and auditory sensitivity the frequency ratio f2 f1 at which adp level is maximal varies only slightly across frequency and subjects the average optimal ratio is 1 225 beyond the maximum the adp level declines with increasing f2 f1 ratio at rates of up to 250 db oct as the level of one stimulus is increased relative to the other the adp grows saturates and in most cases shows a bendover maximum distortion is generated when l 1 exceeds l 2 growth rate and saturation point are dependent on which stimulus is incremented and on the level of the stationary stimulus with optimal stimulus parameters levels below 60 db spl l 1 greater than l 2 by 15 db f2 f1 1 225 adp levels are commonly 30 db below l 2 patterns of adp level across frequency vary between subjects but are repeatable within each subject as the frequency of one or both of the stimuli is varied changes in adp level exhibit a broadly featured pattern with a fine structure superimposed upon it this fine structure was compared with the features in the stimulus frequency emission spectrum in one subject with appropriate stimulus parameters half of our subjects show a statistically significant correlation across frequency between adp level and auditory sensitivity at the corresponding f1 frequency our results suggest that with low levels of stimulation adp measurements could form the basis of an objective measure of cochlear function in human subjects

analysis of parameters for the estimation of loudness from tone burst otoacoustic emissions there is evidence that tone burst otoacoustic emissions tboaes might be useful for estimating loudness however within listener comparisons between loudness and tboae measurements are an essential prerequisite to determine appropriate analysis parameters for loudness estimation from tboae measurements the purpose of the present work was to collect tboae measurements and loudness estimates across a wide range of levels in the same listeners therefore tboaes were recorded for 1 and 4 khz stimuli and then analyzed using a wide range of parameters to determine which parameter set yielded the lowest mean square error estimation of loudness with respect to a psychoacoustical cross modality matching procedure and the inflected exponential inex loudness model the present results show strong agreement between 1 khz loudness estimates derived from tboaes and loudness estimated using cross modality matching cmm with tboae estimation accounting for almost 90 of the cmm variance additionally the results indicate that analysis parameters may vary within a reasonable range without compromising the results i e the estimates exhibit some parametric robustness the lack of adequate parametric optimization for tboaes at 4 khz suggests that measurements at this frequency are strongly contaminated by ear canal resonances meaning that deriving loudness estimates from tboaes at this frequency is significantly more challenging than at 1 khz

loudness of brief tones measured by magnitude estimation and loudness matching mcfadden j acoust soc am 57 702 704 1975 questioned the accuracy and reliability of magnitude estimation for measuring loudness of tones that vary both in duration and level whereas stevens and hall percept psychophys 1 319 327 1966 reported reasonable group data to gain insight into this discrepancy the present study compares loudness measures for 5 and 200 ms tones using magnitude estimation and equal loudness matches from the same listeners results indicate that both procedures provide rapid and accurate assessments of group loudness functions for brief tones but may not be reliable enough to reveal specific characteristics of loudness in individual listeners

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

strong selection or rejection of spatially periodic patterns in degenerate bifurcations abstract when studying bifurcating space periodic solutions one often has a situation common in many problems of fluid dynamics in which in the r k plane r a control parameter such as reynolds number k wave number the passage from linear stability to instability is characterized by a parabola like curve having a minimum at r c k c we analyse classes of problems in which the coefficients of nonlinear terms in the amplitude equation go through zero near k c various examples of such degenerate problems can be found in the literature but have not been studied yet we give an extensive classification of bifurcation pictures which display rather unusual behaviour we further study the stability of these periodic solutions subject to quite general perturbation we find as a general result that all bifurcating solutions are unstable except for a small neighbourhood of a curve in the r k plane there is hence a strong selection mechanism of periodic patterns which fixes for each value of r with a very small uncertainty the wave number of the stable bifurcating periodic solution for one class of problems the curve continues to exist for all values of r for which our theory is consistent for another class the curve stops at a value r r c for r r all bifurcating periodic solutions are unstable in this case instability provides a mechanism of rejection of all periodic patterns in the last section we analyse the particular case of the blasius boundary layer flow

a test of the equal loudness ratio hypothesis using cross modality matching functions this study tests the equal loudness ratio hypothesis florentine et al j acoust soc am 99 1633 1644 1996 which states that the loudness ratio between equal spl long and short tones is independent of spl the amount of temporal integration i e the level difference between equally loud short and long sounds is maximal at moderate levels therefore the equal loudness ratio hypothesis predicts that the loudness function is shallower at moderate levels than at low and high levels equal loudness matches and cross modality string length matches were used to assess the form of the loudness function for 5 and 200 ms tones at 1 khz and the loudness ratio between them results from nine normal listeners show that 1 the amount of temporal integration is largest at moderate levels in agreement with previous studies and 2 the loudness functions are shallowest at moderate levels for eight of the nine listeners the loudness ratio between the 200 and 5 ms tones is approximately constant except at

cochlear nonlinearity in normal hearing subjects as inferred psychophysically and from distortion product otoacoustic emissions the aim was to investigate the correlation between estimates of compression ratio compression threshold and cochlear gain for normal hearing subjects inferred from temporal masking curves tmc and distortion product otoacoustic emission dpoaes input output i o curves special care was given to reduce the influence of dpoae fine structure on the i o curves data were collected for 10 subjects and for cochlear places with characteristic frequencies cfs of 0 5 1 2 and 4 khz except at 4 khz little correlation was found between ratio estimates obtained with the two methods one reason is that the dpoae i o curves show plateaus or dips which result in unexpectedly high compression estimates moderately high correlation was found between the compression threshold estimates obtained with the two methods although dpoae based values were systematically lower than those based on the tmcs both methods confirmed that compression ratio and threshold are approximately constant across the cf range considered cochlear gain could be estimated from tmcs only and it was found to increase slightly with increasing cf it is discussed that dpoae i o curves may be inappropriate to infer precise individual nonlinear cochlear characteristics in normal hearing listeners particularly at low cfs work supported by imserso 131 06 profit cit 390000 2005 4 mec bfu 2006 07536 and the oticon foundation

poisson structure of the reversible 1 1 resonance abstract vector fields that are reversible but non hamiltonian are considered in the neighborhood of a 1 1 resonance it is found that the normalized vector field has a hidden poisson structure on the orbit space that is reminiscent of the equations governing the rigid body in mechanics the theory is used to give a geometric characterization of the phase space in the neighborhood of a reversible 1 1 resonance certain similarities and also essential differences with the hamiltonian 1 1 resonance are found

similarity in loudness and distortion product otoacoustic emission input output functions implications for an objective hearing aid adjustment the aim of the present study was to compare distortion product otoacoustic emissions dpoaes to loudness with regard to the potentiality of dpoaes to determine characteristic quantities of the cochlear impaired ear and to derive objective hearing aid parameters recently neely et al j acoust soc am 114 1499 1507 2003 compared dpoae input output functions to the fletcher and munson j acoust soc am 5 82 108 1933 loudness function finding a close resemblance in the slope characteristics of both measures the present study extended their work by performing both loudness and dpoae measurements in the same subject sample and by developing a method for the estimation of gain needed to compensate for loss of cochlear sensitivity and compression dpoaes and loudness exhibited similar behavior when plotted on a logarithmic scale and slope increased with increasing hearing loss confirming the findings of neely et al to compensate for undesired nonpathological impacts on the magnitude of dpoae level normalization of dpoae data was implemented a close resemblance between gain functions based on loudness and normalized dpoae data was achieved these findings suggest that dpoaes are able to quantify the loss of cochlear sensitivity and compression and thus might provide parameters for a noncooperative hearing aid adjustment

basilar membrane nonlinearity and loudness loudness matching functions for tones for persons with one shifted threshold ear hearing loss and noise shifted thresholds and one ear within normal limits were used to derive the presumed basilar membrane bm input output i o function in a normal ear the comparison was made by assuming that the bm i o function for the ear with the cochlear threshold shift has a slope of one a linearized cochlea the function for the normal ear was derived from the loudness matching function based on this assumption comparisons were made for archival basilar membrane data m a ruggero n c rich a recio s s narayan and l robles j acoust soc am 101 2151 2163 1997 for chinchilla and archival loudness matches for long duration tones for persons with various degrees of cochlear hearing loss f miskolczy fodor j acoust soc am 32 486 492 1960 comparisons were made also between bm i o functions and ones derived from loudness matches for persons with unilateral hearing loss simulated by broa

distortion product otoacoustic emission measured with continuously varying stimulus level distortion product otoacoustic emissions dpoae are measured by stimulating the ear with two simultaneous tones a novel method for measuring dpoaes has been developed in which the tone levels vary continuously instead of in discrete steps varying the tone levels continuously may offer advantages for characterizing dpoae level as a function of stimulus level for equivalent primary levels dpoae levels measured with the continuous level method were the same as levels obtained with the discrete level method thus validating the new method continuous level measurements were used to determine the optimal l1 for each l2 in individual subjects n 20 at f2 1 2 4 and 8 khz by using a lissajous path that covered a wide range of stimulus levels the optimal l1 defined as the l1 that resulted in the largest dpoae for each l2 varied across subjects and across frequency the optimal difference between l1 and l2 decreased with increasing l2 at all frequencies and increased with frequency when l2 was low whe

qualitative robustness of rank tests an asymptotic notion of robust tests is studied which is based on the requirement of equicontinuous error probabilities if the test statistics are consistent their robustness in hampel s sense and robustness of the associated tests turn out to be equivalent uniform extensions are considered moreover test breakdown points are defined the main applications are on rank statistics they are generally robust under a slight condition even uniformly so their points of final breakdown coincide with the breakdown points of the corresponding r estimators

comparing different estimates of cochlear compression in listeners with normal and impaired hearing a loss of cochlear compression may underlie many of the difficulties experienced by hearing impaired listeners two behavioral forward masking paradigms that have been used to estimate the magnitude of cochlear compression are growth of masking gom and temporal masking tm the aim of this study was to determine whether these two measures produce within subjects results that are consistent across a range of signal frequencies and if so to compare them in terms of reliability or efficiency gom and tm functions were measured in a group of five normal hearing and five hearing impaired listeners at signal frequencies of 1000 2000 and 4000 hz compression values were derived from the masking data and confidence intervals were constructed around these estimates both measures produced comparable estimates of compression but both measures have distinct advantages and disadvantages so that the more appropriate measure depends on factors such as the frequency region of interest and the degree of hearing loss because of the long testing times needed neither measure is suitable for clinical use in its current form

capillary gravity solitary waves with damped oscillations abstract capillary gravity solitary waves with damped oscillations are studied analytically the analysis follows the work of iooss and kirchgassner who proved that these waves exist for all values of the froude number smaller than one the water wave problem is reduced to a system of ordinary differential equations by using the center manifold theorem the normal form of this reduced system can be obtained and a good approximation to these waves for small amplitude is constructed the limit as the water depth becomes infinite is considered as a special case a comparison with existing numerical results is made for small amplitude waves

cochlear compression estimates from measurements of distortion product otoacoustic emissions evidence of the compressive growth of basilar membrane displacement can be seen in distortion product otoacoustic emission dpoae levels measured as a function of stimulus level when the levels of the two stimulus tones f1 and f2 are related by the formula l1 39 db 0 4 l2 kummer et al j acoust soc am 103 3431 3444 1998 the shape of the function relating dpoae level to l2 is similar up to an l2 of 70 db spl to the classic fletcher and munson j acoust soc am 9 1 10 1933 loudness function when plotted on a logarithmic scale explicit estimates of compression have been derived based on recent dpoae measurements from the laboratory if dpoae growth rate is defined as the slope of the dpoae i o function in db db then a cogent definition of compression is the reciprocal of the growth rate in humans with normal hearing compression varies from about 1 at threshold to about 4 at 70 db spl with hearing loss compression is still about 1 at threshold but grows more slowly above thresh

loudness functions for long and short tones this study tests the equal loudness ratio hypothesis florentine et al j acoust soc am 99 1633 1644 1996 which states that the loudness ratio between equal spl long and short tones is independent of spl the amount of temporal integration i e the level difference between equally loud long and short sounds is maximal at moderate levels therefore the equal loudness ratio hypothesis predicts that the loudness function is shallower at moderate levels than at low and high levels equal loudness matches and cross modality string length matches were used to assess the form of the loudness function for 200 and 5 ms tones at 1 khz results from nine normal listeners show that 1 the amount of temporal integration is largest at moderate levels in agreement with previous studies and 2 the loudness function is shallowest at moderate levels for eight of the nine listeners the loudness ratio between the 200 and 5 ms tones is approximately constant except at low levels where it tends to increas

cross modality matching and the loudness growth function for click stimuli loudness intensity functions for click stimuli were obtained from 30 adult listeners having normal n 10 flat n 10 or sloping n 10 high frequency cochlear hearing loss configurations the procedure of cross modality matching cmm between loudness and perceived line length r p hellman and c h meiselman j speech hear res 31 605 615 1988 j acoust soc am 88 2596 2606 1990 j acoust soc am 93 966 975 1993 was used to validate their loudness growth functions mean group loudness exponents were similar to those reported in recent investigations that utilized pure tone stimuli further supporting the validity and reliability of the cmm task as an estimate of the loudness growth function the results also suggest that the mean loudness function for clicks is similar to the function obtained with tonal stimuli at least for listeners with moderately impaired hearing or better moreover cmm produced less variability than the more conventional psychophysical methods of magnitude estimation and production for the groups with cochlear hearing loss toward direct application of the cmm technique in lieu of absolute exponential slope values the individually determined loudness growth function over a range of intensities should be compared to the normal mean functions for calculations of deviations

evidence for the distortion product frequency place as a source of distortion product otoacoustic emission dpoae fine structure in humans ii fine structure for different shapes of cochlear hearing loss distortion product otoacoustic emissions dpoae were recorded from eight human subjects with mild to moderate cochlear hearing loss using a frequency spacing of 48 primary pairs per octave and at a level l1 l2 60 dbspl and with a fixed ratio f2 f1 subjects with different shapes of hearing thresholds were selected they included subjects with near normal hearing within only a limited frequency range subjects with a notch in the audiogram and subjects with a mild to moderate high frequency loss if the primaries were located in a region of normal or near normal hearing but dp frequencies were located in a region of raised thresholds the distortion product 2 f1 f2 was still observable but the dp fine structure disappeared if the dp frequencies fell into a region of normal thresholds fine structure was preserved as long as dpoae were generated even in cases of mild hearing loss in the region of the primaries these experimental results give further strong evidence that in addition to the initial s

influence of primary level and primary frequency ratios on human distortion product otoacoustic emissions the combined influence of primary level differences l1 l2 and primary frequency ratio f2 f1 on distortion product otoacoustic emission dpoae level was investigated in 20 normal hearing subjects dpoaes were recorded with continuously varying stimulus levels neely et al j acoust soc am 117 1248 1259 2005 for the following stimulus conditions f2 1 2 4 and 8 khz and f2 f1 1 05 to 1 4 various l1 l2 including one individually optimized to produce the largest dpoae for broadly spaced primary frequencies at low l2 levels the largest dpoaes were recorded when l1 was much higher than l2 with l1 remaining relatively constant as l2 increased as f2 fl decreased the largest dpoaes were observed when l1 was closer to l2 and increased as l2 increased optimal values for l1 l2 and f2 f1 were derived from these data in general average dpoae levels for the new l1 l2 and f2 f1 were equivalent to or larger than those observed for other stimulus combinations including the l1 l2 described by kummer et al j acoust soc am 103 3431 3444 1998 and those defined by neely et al in which l1 l2 was evaluated but f2 f1 was fixed at 1 2

critical states and minima for an energy with second order gradients coleman marcus mizel studied the thermodynamical equilibrium of second order materials i e materials for which the free energy density depends not only on the concentration but also on its first and second gradients they showed that in certain regimes such materials must exhibit equilibrium states that are non uniform by proving that space periodic solutions can have lower energy than space uniform solutions a dynamical systems approach is used here and it is shown that there is a critical value of the mean concentration when the mean concentration crosses this critical value the uniform state can lose its minimizing character and periodic or quasi periodic states can have lower energy mathematically speaking the presence of that critical value corresponds to a 1 1 resonance the reversible 1 1 resonance has been studied extensively by iooss peroueme who showed that a reversible system having a 1 1 resonance singularity can be approximated as closely as desired by an integrable vector field on this integrable field all bounded solutions can be easily found and they are described by two integrals however in the present application a zero eigenvalue is present in addition to the double imaginary eigenvalues bounded solutions are then described by three integrals moreover since the average concentration must remain constant a non local constraint is added which changes the results significantly finally a selection principle for second order materials stemming from energy considerations is introduced the energy of all bounded solutions is compared with the energy of the uniform state in some cases non uniform solutions have a lower energy and lead to non uniform equilibrium states more precisely it is shown that space periodic or space quasi periodic states are minima quite surprisingly it may occur that non uniform states appear by dilution i e by decreasing the concentration

time reversal symmetry in dynamical systems a survey abstract in this paper we survey the topic of time reversal symmetry in dynamical systems we begin with a brief discussion of the position of time reversal symmetry in physics after defining time reversal symmetry as it applies to dynamical systems we then introduce a major theme of our survey namely the relation of time reversible dynamical sytems to equivariant and hamiltonian dynamical systems we follow with a survey of the state of the art on the theory of reversible dynamical systems including results on symmetric periodic orbits local bifurcation theory homoclinic orbits and renormalization and scaling some areas of physics and mathematics in which reversible dynamical systems arise are discussed in an appendix we provide an extensive bibliography on the topic of time reversal symmetry in dynamical systems

objective estimation of loudness growth in hearing impaired listeners a methodology for the estimation of individual loudness growth functions using tone burst otoacoustic emissions tboaes and tone burst auditory brainstem responses tbabrs was proposed by silva and epstein j acoust soc am 127 3629 3642 2010 this work attempted to investigate the application of such technique to the more challenging cases of hearing impaired listeners the specific aims of this study were to 1 verify the accuracy of this technique with eight hearing impaired listeners for 1 and 4 khz tone burst stimuli 2 investigate the effect of residual noise levels from the tbabrs on the quality of the loudness growth estimation and 3 provide a public dataset of physiological and psychoacoustical responses to a wide range of stimuli intensity the results show that some of the physiological loudness growth estimates were within the mean square error range for standard psychoacoustical procedures with closer agreement at 1 khz the median residual noise in the tbabrs was found to be related to the performance of the estimation with some listeners showing strong improvements in the estimated loudness growth function when controlling for noise levels this suggests that future studies using evoked potentials to estimate loudness growth should control for the estimated averaged residual noise levels of the tbabrs

interpretation of distortion product otoacoustic emission measurements i two stimulus tones the interpretation of common but poorly understood observed characteristics of distortion product emissions is assisted by the development of a simple model this model essentially includes only saturation of the cochlear amplifier with emissions arising naturally from the same nonlinear processes which cause the saturation the model provides useful physical explanations of emission behavior particularly considered as a function of the stimulus intensities of the two primaries i e behavior with fixed stimulus frequencies it is assumed that emission generation consists of two main components which are always present in the total emission but which most often have approximately opposite i e canceling phases one component arises in a small region centered about the peak of the emission generation function while the other arises from the region basal to this peak at low stimulus levels with normal cochlear amplifier operation the peak of the emission generation function is sharp so the emission from the peak region dominates the total emission this peak emission has typically been characterized as the active emission at high stimulus levels where saturation is important or at all levels when the gain of the cochlear amplifier is reduced the summed basal component dominates the total emission the characteristics of this basal emission are similar to and continuous with the characteristics of the truly passive emission i e the emission observed when the cochlear amplifier gain is identically zero under circumstances when the emissions from the peak and basal components are approximately equal there is seen a sharp notch characteristic of phase cancellation the simple model produces emission distributions as a function of independent variation of the two stimulus amplitudes which are in good agreement with observation it is shown that the furosemide assay provides a good estimate of cochlear amplifier gain when a correction factor of about 10 db is added however when using two stimulus tones neither absolute emission amplitudes or emission input output functions or the furosemide assay can adequately distinguish between cases of moderate versus poor cochlear amplifier dysfunction when the cochlear amplifier gains are in the range from about half normal to zero

intensity resolution and loudness in broadband noise intensity resolution and loudness matching behavior for pure tones was studied in quiet and in two levels of noise 15 and 40 db spectrum level to test the predictions of several models for relating these phenomena five normally hearing listeners participated the weber functions in noise were elevated compared to the ones in quiet when comparisons were made at equal sound pressure levels spls loudness matching functions db spl in quiet versus db spl in noise showed a slope greater than unity modified power functions with threshold corrections were fitted to the matching data to estimate the loudness function exponent the best fitting loudness exponent for individual and group data range 0 24 0 35 was in the range of values typically found using magnitude estimation procedures for the loudness equation yielding the best fit three models for predicting weber functions from loudness were evaluated with this loudness representation one of these models the subjective analog to weber s law yield

normal linear stability of quasi periodic tori abstract we consider families of dynamical systems having invariant tori that carry quasi periodic motions our interest is the persistence of such tori under small nearly integrable perturbations this persistence problem is studied in the dissipative the hamiltonian and the reversible setting as part of a more general kam theory for classes of structure preserving dynamical systems this concerns the parametrized kam theory as initiated by moser j k moser on the theory of quasiperiodic motions siam rev 8 2 1966 145 172 j k moser convergent series expansions for quasi periodic motions math ann 169 1967 136 176 and further developed in g b huitema unfoldings of quasi periodic tori phd thesis university of groningen 1988 h w broer g b huitema f takens unfoldings of quasi periodic tori mem amer math soc 83 421 1990 1 82 h w broer g b huitema unfoldings of quasi periodic tori in reversible systems j dynam differential equations 7 1 1995 191 212 the corresponding nondegeneracy condition involves certain trans versality conditions on the normal linear leading part at the invariant tori we show that as a consequence a cantor family of diophantine tori with positive hausdorff measure is persistent under nearly integrable perturbations this result extends the above references since presently the case of multiple floquet exponents is included our leading example is the normal 1 1 resonance which occurs a lot in applications both hamiltonian and reversible as an illustration of this we briefly describe the lagrange top coupled to an oscillator

loudness relations for individuals and groups in normal and impaired hearing individual and group loudness relations were obtained at a frequency in the region of impaired hearing for 100 people 98 with bilateral cochlear impairment slope distributions were determined from absolute magnitude estimation ame and absolute magnitude production amp of loudness they were also derived from cross modality matching cmm and ame of apparent length with respect to both the means and the individual slope values the two distributions closely agree more than half of the measured deviations are less than 20 with an overall average of 1 5 meaning that transitivity is preserved for bilaterally impaired individuals moreover over the stimulus range where cochlear impairment steepens the loudness function both the group means and the individual slope values are clearly larger than in normal hearing the results also show that for groups of people with approximately similar losses the standard deviation is a nearly constant proportion of the mean slope value giving a coefficient of variation of about 27 in normal and impaired hearing this indicates in accord with loudness matching that the size of the slopes depends directly on the degree of hearing loss the results disclose that loudness measurements obtained by magnitude scaling are able to reveal the operating characteristic of the ear for individuals

relation between the growth of loudness and high frequency excitation to test the conjecture that cochlear impairment and a masking noise in normal ears produce analogous effects on the growth of loudness loudness was measured for 21 listeners all with bilateral symmetrical high frequency cochlear losses beyond the normal hearing region thresholds increased by 30 49 db octave for 10 listeners in group i and by 51 71 db octave for 11 listeners in group ii measured by absolute magnitude estimation and production at two frequencies where thresholds were normal the dynamic range over which loudness grows was not altered by the adjacent hearing loss this was not true however for the slope whereas the overall shape and slope of the loudness functions were essentially the same for group i the mid to high level slope for group ii was noticeably flatter for a tone at the cutoff frequency than for a lower frequency tone in contrast markedly steeper loudness functions characteristic of loudness recruitment were obtained for both groups at a frequency in the region of impaired hearing the reduced rate of loudness growth observed in the region of normal hearing for listeners with steep low pass losses like the reduction usually found for a tone masked by an adjacent high frequency noise is ascribed to the tone s restricted excitation pattern these results indicate that high frequency auditory cues are effectively eliminated by a steeply sloping high frequency hearing loss just as they are eliminated by the addition of an external noise to test the conjecture that cochlear impairment and a masking noise in normal ears produce analogous effects on the growth of loudness loudness was measured for 21 listeners all with bilateral symmetrical high frequency cochlear losses beyond the normal hearing region thresholds increased by 30 49 db octave for 10 listeners in group i and by 51 71 db octave for 11 listeners in group ii measured by absolute magnitude estimation and production at two frequencies where thresholds were normal the dynamic range over which loudness grows was not altered by the adjacent hearing loss this was not true however for the slope whereas the overall shape and slope of the loudness functions were essentially the same for group i the mid to high level slope for group ii was noticeably flatter for a tone at the cutoff frequency than for a lower frequency tone in contrast markedly steeper loudness functions characteristic of loudness recruitment were obtained for both groups at a frequency in the region of im