pure tone threshold estimation from extrapolated distortion product otoacoustic emission i o functions in normal and cochlear hearing loss ears a new method for direct pure tone threshold estimation from input output functions of distortion product otoacoustic emissions dpoaes in humans is presented previous methods use statistical models relating dpoae level to hearing threshold including additional parameters e g age or slope of dpoae i o function here we derive a dpoae threshold from extrapolated dpoae i o functions directly cubic 2 f1 f2 distortion products and pure tone threshold at f2 were measured at 51 frequencies between f2 500 hz and 8 khz at up to ten primary tone levels between l2 65 and 20 db spl in 30 normally hearing and 119 sensorineural hearing loss ears using an optimized primary tone level setting l1 0 4l2 39 db that accounts for the nonlinear interaction of the two primaries at the dpoae generation site at f2 the pressure of the 2 f1 f2 distortion product pdp is a linear function of the primary tone level l2 linear regression yields correlation coefficients higher than 0 8 in the majority of the dpoae i o functions

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

reducing reflected contributions to ear canal distortion product otoacoustic emissions in humans distortion product otoacoustic emission dpoae fine structure has been attributed to the interaction of two cochlear source mechanisms distortion and reflection sources a suppressor presented near the 2f1 f2 frequency reduces the reflection source contribution and therefore dpoae fine structure optimal relationships between stimulus and suppressor conditions however have not been described in this study the relationship between suppressor level l3 and stimulus level l2 was evaluated to determine the l3 that was most effective at reducing fine structure subjects were initially screened to find individuals who produced dpoae fine structure a difference in the prevalence of fine structure in two frequency intervals was observed at 2 khz 11 of 12 subjects exhibited fine structure as compared to 5 of 22 subjects at 4 khz only subjects demonstrating fine structure participated in subsequent measurements dpoae responses were evaluated in 1 3 octave intervals centered at 2 or 4 khz with 4 subjects contributing data at each interval multiple l3 s were evaluated for each l2 which ranged from 20 to 80 db spl the results indicated that one or more l3 s at each l2 were roughly equally effective at reducing dpoae fine structure however no single l3 was effective at all l2 s in every subject

measuring distortion product otoacoustic emissions using continuously sweeping primaries distortion product otoacoustic emission dpoae level from normal hearing individuals can vary by as much as 30db with small frequency changes a phenomenon known as dpoae fine structure this fine structure is hypothesized to stem from the interaction of components from two different regions of the cochlea the nonlinear generator region and the reflection component from the dp region an efficient procedure to separate these two components would improve the clinical and research utility of dpoae by permitting separate evaluation of different cochlea regions in this paper two procedures for evaluating dpoae fine structure are compared dpoae generated by fixed frequency primaries versus continuously sweeping primaries the sweep dpoae data are analyzed with a least squares fit filter sweep rates of greater than 8s per octave permit rapid evaluation of the cochlear fine structure a higher sweep rate of 2s per octave provided dpoae without fine structure under these conditions the longer latency reflection component falls outside the range of the filter consequently dpoae obtained with sweeping tones can be used either to get more rapid estimates of dpoae fine structure or to obtain estimates of dpoae from the generator region uncontaminated by energy from the reflection region

the regularized chapman enskog expansion for scalar conservation laws rosenao r has recently proposed a regularized version of the chapmanenskog expansion of hydrodynamics this regularized expansion resembles the usual navier stokes viscosity terms at low wave numbers but unlike the latter it has the advantage of being a bounded macroscopic approximation to the linearized collision operator in this paper we study the behavior of the rosenau regularization of the chapman enskog expansion r c e in the context of scalar conservation laws we show that this r c e model retains the essential properties of the usual viscosity approximation e g existence of travelling waves monotonicity upper lipschitz continuity etc and at the same time it sharpens the standard viscous shock layers we prove that the regularized r c e approximation converges to the underlying inviscid entropy solution as its mean free path e 0 and we estimate the convergence rate

existence of weak solutions for a nonlocal pseudo parabolic model for brinkman two phase flow in asymptotically flat porous media abstract we study a nonlocal evolution equation that involves a pseudo parabolic third order term the equation models almost uni directional two phase flow in brinkman regimes we prove the existence of weak solutions for this equation we also give a series of numerical examples that demonstrate the ability of the equation to support overshooting like in 26 and explore the behavior of solutions in various limit regimes

singular limits for a parabolic elliptic regularization of scalar conservation laws abstract we consider scalar hyperbolic conservation laws with a nonconvex flux in one space dimension then weak solutions of the associated initial value problems can contain undercompressive shock waves we regularize the hyperbolic equation by a parabolic elliptic system that produces undercompressive waves in the hyperbolic limit regime moreover we show that in another limit regime called capillarity limit we recover solutions of a diffusive dispersive regularization which is the standard regularization used to approximate undercompressive waves in fact the new parabolic elliptic system can be understood as a low order approximation of the third order diffusive dispersive regularization thus sharing some similarities with the relaxation approximations a study of the traveling waves for the parabolic elliptic system completes the paper

singular limit problem of the camassa holm type equation abstract we consider a shallow water equation of camassa holm type containing nonlinear dispersive effects as well as fourth order dissipative effects we prove the strong convergence and establish the condition under which as diffusion and dispersion parameters tend to zero smooth solutions of the shallow water equation converge to the entropy solution of a scalar conservation law using methodology developed by hwang and tzavaras s hwang a e tzavaras kinetic decomposition of approximate solutions to conservation laws applications to relaxation and diffusion dispersion approximations comm partial differential equations 27 2002 1229 1254 the proof relies on the kinetic formulation of conservation laws and the averaging lemma

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

distortion product otoacoustic emission reflection component delays and cochlear tuning estimates from across the human lifespan a consistent relationship between reflection emission delay and cochlear tuning has been demonstrated in a variety of mammalian species as predicted by filter theory and models of otoacoustic emission oae generation as a step toward the goal of studying cochlear tuning throughout the human lifespan this paper exploits the relationship and explores two strategies for estimating delay trends energy weighting and peak picking both of which emphasize data at the peaks of the magnitude fine structure distortion product otoacoustic emissions dpoaes at 2f1 f2 were recorded and their reflection components were extracted in 184 subjects ranging in age from prematurely born neonates to elderly adults dpoaes were measured from 0 5 4 khz in all age groups and extended to 8 khz in young adults delay trends were effectively estimated using either energy weighting or peak picking with the former method yielding slightly shorter delays and the latter somewhat smaller confidence intervals delay and tuning est

the influence of systematic primary tone level variation l2 l1 on the acoustic distortion product emission 2f1 f2 in normal human ears the purpose of the present study was to determine the effect of primary tone level variation l2 l1 on the amplitude of distortion product otoacoustic emissions dpoaes the dpoae at the frequency 2f1 f2 f2 f1 was measured in 20 ears of ten normally hearing subjects acoustic distortion products were generated by primaries f1 and f2 with geometric mean frequencies of 1 2 and 4 khz the f2 f1 ratios were 1 25 1 khz 1 23 2 khz and 1 21 4 khz the primary tone level l1 was kept constant at either 65 or 75 db spl while the second primary tone level l2 was varied between 20 and 90 db spl in 5 db steps the level differences l2 l1 generating maximal dpoae amplitudes depended on l1 and on the geometric mean frequency of f1 and f2 there were large interindividual differences overall the l2 l1 evoking maximal mean dpoae amplitudes was 10 db for geometric mean frequencies of 1 and 2 khz with both l1 65 db spl and l1 75 db spl for 4 khz l2 l1 was 5 db with l1 65 db spl and 0 db with l1 75 db sp

parabolic approximations of diffusive dispersive equations abstract we consider a lower order approximation for a third order diffusive dispersive conservation law with nonlinear flux it consists of a system of two second order parabolic equations a coupling parameter is also added if the flux has an inflection point it is well known on the one hand that the diffusive dispersive law admits traveling wave solutions whose end states are also connected by undercompressive shock waves of the underlying hyperbolic conservation law on the other hand if the diffusive dispersive regularization vanishes the solutions of the corresponding initial value problem converge to a weak solution of the hyperbolic conservation law we show that both of these properties also hold for the lower order approximation furthermore when the coupling parameter tends to infinity we prove that solutions of initial value problems for the approximation converge to a weak solution of the diffusive dispersive law the proofs rely on new a priori energy estimates for higher order derivatives and the technique of compensated compactness

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

sources of distortion product otoacoustic emissions revealed by suppression experiments and inverse fast fourier transforms in normal ears primary and secondary sources combine to produce the 2f1 f2 distortion product otoacoustic emission dpoae measured in the ear canals of humans dpoaes were obtained in nine normal hearing subjects using a fixed f2 paradigm in which f1 was varied the f2 was 2 or 4 khz and absolute and relative primary levels were varied data were obtained with and without a third tone f3 placed 15 6 hz below 2f1 f2 the level of f3 was varied in order to suppress the stimulus frequency otoacoustic emission sfoae coming from the 2f1 f2 place these data were converted from the complex frequency domain into an equivalent time representation using an inverse fast fourier transform ifft iffts of unsuppressed dpoae data were characterized by two or more peaks relative amplitudes of these peaks depended on overall primary level and on primary level differences the suppressor eliminated later peaks but early peaks remained relatively unaltered results are interpreted to mean that the dpoae measured in humans includes components from the f2 place intermodulation distortion and dp place in the form of a sfoae these findings build on previous work by providing evidence that multiple peaks in the ifft are due to a secondary source at the dp place

comparing the optimal signal conditions for recording cubic and quadratic distortion product otoacoustic emissions odd and even order distortion products dps evoked by two primary tones f1 f2 f1 f2 represent different aspects of cochlear nonlinearity the cubic and quadratic difference tones cdt 2f1 f2 and qdt f2 f1 are prominent representatives of the odd and even dps distortion product otoacoustic emissions dpoaes were measured within a primary level l1 l2 space over a wide range of f2 f1 ratios to compare the optimal signal conditions for these dps for cdt the primary level difference decreased as l1 increased with a rate proportional to the f2 f1 ratio moreover the optimal ratio increased with l1 a set of two formulas is proposed to describe the optimal signal conditions however for a given level of a primary increasing the other tone level could maximize the qdt amplitude the frequency ratio at the maximal qdt was about 1 3 and quite constant across different primary levels a notch was found in the qdt amplitude at the f2 f1 ratio of about 1 22 1 25 these opposite behaviors suggest that the optimal recording conditions are different for cdt and qdt due to the different aspects in the cochlear nonlinearity optimizing the dpoae recordings could improve the reliability in clinical or research practices

level dependence of the nonlinear distortion component of distortion product otoacoustic emissions in humans distortion product otoacoustic emissions dpoaes emerge when presenting two primary tones with different frequencies f1 and f2 to the cochlea and are commonly used in diagnosis and research to evaluate the functional state of the cochlea optimal primary tone stimulus levels accounting for the different level dependencies of the traveling wave amplitudes of the two primary tones near the f2 tonotopic place on the basilar membrane are often used to maximize dpoae amplitudes however parameters defining the optimal levels can be affected by wave interference between the nonlinear distortion and coherent reflection components of the dpoae here the components were separated in the time domain using a pulsed stimulus paradigm and optimal levels determined based on the amplitude dependence of the nonlinear distortion components on primary tone stimulus levels level parameters yielding maximum dpoae amplitudes were derived for six normal hearing adults and compared to data recorded with continuous two tone stimulation the level parameters resulting from analysis of the nonlinear distortion components show dependence on stimulus frequency and small standard deviations dpoae input output functions derived for optimal levels exhibit larger slopes wider dynamic range and less variability across subjects than those derived for conventional stimulus and analysis conditions potentially increasing their reliability and sensitivity for assessing cochlea function

dependence of distortion product otoacoustic emissions on primary levels in normal and impaired ears i effects of decreasing l2 below l1 the 2f1 f2 distortion product otoacoustic emission dpoae is evoked by two primary tones of frequencies f1 f2 and levels l1 and l2 previous reports indicate that decreasing l2 below l1 l2 can 1 increase dpoae amplitude in normal ears and 2 increase the degree to which dpoae amplitudes are reduced by cochlear trauma although both of these factors could be advantageous for clinical applications of dpoaes neither has been explored in detail in the present study 2f1 f2 dpoae amplitude frequency functions were collected from normal and impaired ears of rabbits and humans with l1 l2 and with l2 l1 at each of three values of l1 in rabbits controlled tonal or noise overexposures were used to produce permanent reductions of dpoae amplitudes comparison of pre and postexposure dpoae amplitude frequency functions demonstrated that the frequency specific reductions of dpoaes were enhanced by decreasing l2 below l1 in humans dpoae amplitude frequency functions obtained with the various l1 and l2 c

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

visualization of the onset of distortion product otoacoustic emissions and measurement of their latency this paper describes a method for visualization of the onset of distortion product otoacoustic emission dpoae waveforms in the time domain the dpoae waveforms are obtained using ensemble averaging of samples of microphone output a rectangular sample window is used and the primary tones are turned on within the sample window the phases of the primary tones f1 and f2 are varied systematically between samples in such a way that the primary tones and all dpoaes e g 2f2 f1 3f1 2f2 2f1 except the dpoae of interest e g 2f1 f2 are cancelled in the ensemble average visualization of the dpoae onset allows measurement of the onset latency osl of the dpoae these direct measurements of osl are compared to phase gradient latencies pgls in the same ears determined by measuring the phase change of the dpoae as a function of dpoae frequency the direct measures of osl vary from 10 to 1 ms decrease with increasing frequency and increasing stimulus level and are shorter in rabbits than humans the direct measures of osl are in general quantitatively similar to pgl estimates but there are exceptions visualization of dpoae onset also allows quantification of dpoae rise times and reveals phase and amplitude changes of the dpoae that occur several milliseconds after onset in rabbits and humans it is proposed that the phase and amplitude changes result from vector summation of multiple components of the dpoae signal each with a different latency

input output functions of the nonlinear distortion component of distortion product otoacoustic emissions in normal and hearing impaired human ears distortion product otoacoustic emissions dpoaes arise in the cochlea in response to two tones with frequencies f1 and f2 and mainly consist of two components a nonlinear distortion and a coherent reflection component wave interference between these components limits the accuracy of dpoaes when evaluating the function of the cochlea with conventional continuous stimulus tones here dpoae components are separated in the time domain from dpoae signals elicited with short stimulus pulses the extracted nonlinear distortion components are used to derive estimated distortion product thresholds edpts from semi logarithmic input output i o functions for 20 normal hearing and 21 hearing impaired subjects i o functions were measured with frequency specific stimulus levels at eight frequencies f2 1 8 khz f2 f1 1 2 for comparison dpoaes were also elicited with continuous primary tones both acquisition paradigms yielded edpts which significantly correlated with behavioral thresholds p 0 001

global well posedness and relaxation limits of a model for radiating gas abstract we study the initial value problem for a hyperbolic elliptic coupled system with arbitrary large discontinuous initial data we prove existence and uniqueness for that model by means of l1 contraction and comparison properties moreover after suitable scalings we study both the hyperbolic parabolic and the hyperbolic hyperbolic relaxation limits for that system

time domain demonstration of distributed distortion product otoacoustic emission components distortion product otoacoustic emissions dpoaes were measured in rabbits as time waveforms by employing a phase rotation technique to cancel all components in the final average except the 2f1 f2 dpoae subsequent filtering allowed the dpoae waveform to be clearly visualized in the time domain in most conditions f2 was turned off for 6 ms which produced a gap so that the dpoae was no longer generated these procedures allowed the dpoae onset as well as the decay during the gap to be observed in the time domain dpoaes were collected with l1 l2 65 db sound pressure level primary tone levels for f2 f1 ratios from 1 25 to 1 01 in 0 02 steps findings included the appearance of complex onsets and decays for the dpoae time waveforms as the f2 f1 ratio was decreased and the dpoae level was reduced these complexities were unaffected by interference tones its near the dpoae frequency place fdp but could be removed by its presented above f2 which also increased dpoae levels similar outcomes were o

non classical shocks and kinetic relations scalar conservation laws this paper analyzes the non classical shock waves which arise as limits of certain diffusive dispersive approximations to hyperbolic conservation laws such shocks occur for non convex fluxes and connect regions of different convexity they have negative entropy dissipation for a single convex entropy function but not all convex entropies and do not obey the classical oleinik entropy criterion we derive necessary conditions for the existence of non classical shock waves and construct them as limits of traveling wave solutions for several diffusive dispersive approximations

canonical form of three fermion pure states with six single particle states we construct a canonical form for pure states in 3 c6 the three fermion system with six single particle states under local unitary lu transformations i e the unitary group u 6 we also construct a minimal set of generators of the algebra of polynomial u 6 invariants on 3 c6 it turns out that this algebra is isomorphic to the algebra of polynomial lu invariants of three qubits which are additionally invariant under qubit permutations as a consequence of this surprising fact we deduce that there is a one to one correspondence between the u 6 orbits of pure three fermion states in 3 c6 and the lu orbits of pure three qubit states when qubit permutations are allowed as an important byproduct we obtain a new canonical form for pure three qubit states under lu transformations u 2 u 2 u 2 no qubit permutations allowed

time frequency domain filtering of evoked otoacoustic emissions time domain filtering is a standard analysis technique which is used to disentangle the two main vector components of the distortion product otoacoustic emission response exploiting their different phase frequency relation in this study a time frequency filtering technique based on the continuous wavelet transform is proposed to overcome the intrinsic limitations of the time domain filtering technique and to extend it also to the analysis of stimulus frequency and transient evoked otoacoustic emissions the advantages of the proposed technique are first discussed on a theoretical basis then practically demonstrated by applying it to the analysis of synthesized and real otoacoustic data the results show that the time frequency approach can be empirically optimized to get effective separation of the components of the otoacoustic response associated with either different generation mechanisms or different generation places focusing on a single component of the otoacoustic response with a given time frequency signature may also improve significantly the signal to noise ratio because the random noise contribution tends to be uniformly distributed on the time frequency plane