encounter distribution of two random walkers on a finite one dimensional interval we analyse the first passage properties of two random walkers confined to a finite one dimensional domain for the case of absorbing boundaries at the endpoints of the interval we derive the probability that the two particles meet before either one of them becomes absorbed at one of the boundaries for the case of reflecting boundaries we obtain the mean first encounter time of the two particles our approach leads to closed form expressions that are more easily tractable than a previously derived solution in terms of the weierstrass elliptic function

dpoae group delays versus electrophysiological measures of cochlear delay in normal human ears group delays of 2 f1 f2 distortion product otoacoustic emissions dpoaes were determined using both f1 and f2 sweep paradigms in 24 normal hearing subjects these dpoae group delays were studied in comparison with cochlear delays estimated from derived band viiith nerve compound action potentials caps and auditory brainstem responses abrs in the same subjects the center frequencies of the derived bands in the electrophysiological experiment were matched with the f2 frequencies in the dpoae recording to ensure that dpoaes and derived caps and abrs were generated at the same places along the cochlear partition thus allowing for a direct comparison the degree to which dpoae group delays are larger in the f2 than in the f1 sweep paradigm is consistent with a theoretical analysis of the so called wave fixed model both dpoae group delays are highly correlated with cap and abr derived measures of cochlear delay the principal result of this study is that roundtrip dpoae group delay in the f1 sweep

discrete spline methods for solving two point fractional bagley torvik equation a new discrete spline method is developed to solve the two point fractional bagley torvik equation the method is based on discrete spline function and a nonstandard grunwald letnikov difference nsgd and the weighted and shifted grunwald letnikov difference wsgd operators to approximate the fractional derivative bounds for grunwald letnikov weights are considered convergence analysis is discussed and a class of second order and third order methods are obtained illustrative examples are presented to validate the practical usefulness of the methods

technical communique a note on fractional order derivatives of periodic functions in this paper it is shown that the fractional order derivatives of a periodic function with a specific period cannot be a periodic function with the same period the fractional order derivative considered here can be obtained based on each of the well known definitions grunwald letnikov definition riemann liouville definition and caputo definition this concluded point confirms the result of a recently published work proving the non existence of periodic solutions in a class of fractional order models also based on this point it can be easily proved the absence of periodic responses in a wider class of fractional order models finally some examples are presented to show the applicability of the paper achievements in the solution analysis of fractional order systems

otoacoustic emissions from normal hearing and hearing impaired subjects distortion product responses distortion product otoacoustic emissions dpoae were measured in normal hearing and hearing impaired human subjects analyses based on decision theory were used to evaluate dpoae test performance specifically relative operating characteristic roc curves were constructed and the areas under these curves were used to estimate the extent to which normal and impaired ears could be correctly identified by these measures dpoae amplitude and dpoae noise measurements were able to distinguish between normal and impaired subjects at 4000 8000 and to a lesser extent at 2000 hz the ability of these measures to distinguish between groups decreased however as frequency and audiometric criterion used to separate normal and hearing impaired ears decreased at 500 hz performance was no better than chance regardless of the audiometric criterion for normal hearing cumulative distributions of misses hearing impaired ears incorrectly identified as normal hearing and false alarms normal hearing ears identified as hearing impaired were constructed and used to evaluate test performance for a range of hit rates i e the percentage of correctly identified hearing impaired ears depending on the desired hit rate criterion values of 5 to 12 db spl for dpoae amplitudes and 8 to 15 db for dpoae noise accurately distinguished normal hearing ears from those with thresholds greater than 20 db hl for the two frequencies at which performance was best 4000 and 8000 hz it would appear that dpoae measurements can be used to accurately identify the presence of high frequency hearing loss but are not accurate predictors of hearing status at lower frequencies at least for the conditions of the present measurements

restart could optimize the probability of success in a bernoulli trial the recently noticed ability of restart to reduce the expected completion time of first passage processes allows appealing opportunities for performance improvement in a variety of settings however complex stochastic processes often exhibit several possible scenarios of completion which are not equally desirable in terms of efficiency here we show that restart may have profound consequences on the splitting probabilities of a bernoulli like first passage process i e of a process which can end with one of two outcomes particularly intriguing in this respect is the class of problems where a carefully adjusted restart mechanism maximizes the probability that the process will complete in a desired way we reveal the universal aspects of this kind of optimal behavior by applying the general approach recently proposed for the problem of first passage under restart

multicomponent acoustic distortion product otoacoustic emission phase in humans ii implications for distortion product otoacoustic emissions generation phase characteristics and latency of 2f1 f2 3f1 2f2 and 2f2 f1 acoustic distortion product otoacoustic emissions dpoaes recorded in normally hearing adults have been described in a companion paper moulin and kemp multicomponent acoustic distortion product otoacoustic emission phase in humans i general characteristics j acoust soc am 100 1617 1639 1996 phase versus frequency functions pff have been recorded using two methods depending whether f1 or f2 was swept in frequency defining respectively an f1 sweep and an f2 sweep method the present study compares 2f1 f2 3f1 2f2 4f1 3f2 and 2f2 f1 dpoaes phase characteristics and latencies obtained by these two methods for lower sideband dpoaes the f2 sweep gave consistently longer latencies than the f1 sweep method whereas no difference was obtained for the 2f2 f1 dpoae this suggests that the lower sideband dpoaes and the 2f2 f1 dpoae do not come from the same aspect of the traveling wave the longer delay obtained with an f2 sweep is suggested to be due to an additional delay added by the proximity of the peak of the f2 traveling wave the place fixed and the wave fixed models of dpoae generation are discussed and an intermediate model of dpoae generation is introduced to explain such additional delay and the existence of phase irregularities which were observed in the pff the ratio of the latencies obtained by the two sweep methods is frequency dependent and a relation to cochlear frequency selectivity is suggested finally analysis of the differences in latency of the different lower sideband dpoae components allowed an estimation of the return latency of dpoaes

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

analytic expression for the mean time to absorption for a random walker on the sierpinski gasket ii the eigenvalue spectrum we continue the study of a particle atom molecule undergoing an unbiased random walk on the sierpinski gasket and obtain for the gasket and tower the eigenvalue spectrum of the associated stochastic master equation analytic expressions for recurrence relations among the eigenvalues are derived the recurrence relations obtained are compared with those determined for two euclidean lattices the closed chain with an absorbing site and a finite chain with an absorbing site at one end we check and confirm the internal consistency between the smallest eigenvalue and the mean walklength in each of the cases studied attention is drawn to the relevance of the results obtained to a problem of electron transfer in proteins

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

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

evanescent continuous time random walks we study how an evanescence process affects the number of distinct sites visited by a continuous time random walker in one dimension we distinguish two very different cases namely when evanescence can only occur concurrently with a jump and when evanescence can occur at any time the first is characteristic of trapping processes on a lattice whereas the second is associated with spontaneous death processes such as radioactive decay in both of these situations we consider three different forms of the waiting time distribution between jumps namely exponential long tailed and ultraslow

a fractional differential equation for a mems viscometer used in the oil industry a mathematical model is developed for a micro electro mechanical system mems instrument that has been designed primarily to measure the viscosity of fluids that are encountered during oil well exploration it is shown that in one mode of operation the displacement of the device satisfies a fractional differential equation fde the theory of fdes is used to solve the governing equation in closed form and numerical solutions are also determined using a simple but efficient central difference scheme it is shown how knowledge of the exact and numerical solutions enables the design of the device to be optimised it is also shown that the numerical scheme may be extended to encompass the case of a nonlinear spring where the resulting fde is nonlinear

efficiency of trapping processes in regular and disordered networks we use a markov method to study the efficiency of trapping processes involving both a random walker and a deep trap in regular and disordered networks the efficiency is gauged by the mean absorption time average of the mean number of steps performed by the random walker before being absorbed by the trap we compute this quantity in terms of different control parameters namely the length of the walker jumps the mobility of the trap and the degree of spatial disorder of the network for a proper choice of the system size we find in all cases a nonmonotonic behavior of the efficiency in terms of the corresponding control parameter we thus arrive at the conclusion that despite the decrease of the effective system size underlying the increase of the control parameter the efficiency is reduced as a result of an increase of the escape probability of the walker once it finds itself in the interaction zone of the trap this somewhat anti intuitive effect is very robust in the sense that it is observed regardless of the specific choice of the control parameter for the case of a ring lattice results for the mean absorption time in systems of arbitrary size are given in terms of a two parameter scaling function for the case of a mobile trap we deal with both trapping via a single channel walker trap overlap and via two channels walker trap overlap and walker trap crossing thereby generalizing previous work as for the disordered case our analysis concerns small world networks for which we see several crossovers of the absorption time as a function of the control parameter and the system size the methodology used may be well suited to exploring characteristic time scales of encounter controlled phenomena in networks with a few interacting elements and the effect of geometric constraints in nanoscale systems with a very small number of particles

existence results for fractional order semilinear functional differential equations with nondense domain abstract in this paper we establish sufficient conditions for existence and uniqueness of solutions for some nondensely defined semilinear functional differential equations involving the riemann liouville derivative our approach is based on integrated semigroup theory the banach contraction principle and the nonlinear alternative of leray schauder type

approximate controllability of fractional order semilinear systems with bounded delay abstract in this paper sufficient conditions are established for the approximate controllability of a class of semilinear delay control systems of fractional order the existence and uniqueness of mild solution of the system is also proved the results are obtained by using contraction principle and the schauder fixed point theorem some examples are given to illustrate the theory

distortion product otoacoustic emissions cochlear source contributions and clinical test performance it has been proposed that the clinical accuracy of distortion product otoacoustic emissions dpoaes is affected by the interaction of distortion and reflection sources contributing to the response this study evaluated changes in dichotomous decision test performance and threshold prediction accuracy when dpoae source contribution was controlled data were obtained from 205 normal and impaired ears with l2 ranging from 0 to 80db spl and f2 2 and 4khz data were collected for control conditions no suppressor f3 and with f3 presented at three levels that previously had been shown to reduce the reflection source contribution the results indicated that controlling source contribution with a suppressor did not improve diagnostic accuracy as reflected by relative operating characteristic curve area and frequently resulted in poorer test performance compared to control conditions likewise correlations between dpoae and behavioral thresholds were not strengthened when using the suppressors to control sou

universality classes of first passage time distribution in confined media we study the first passage time fpt distribution to a target site for a random walker evolving in a bounded domain we show that in the limit of large volume of the confining domain this distribution falls into universality classes indexed by the walk dimension d w and the fractal dimension d f of the medium which have been recently identified previously benichou et al nat chem 2 472 2010 we present in this paper a complete derivation of these universal distributions discuss extensively the range of applicability of the results and extend the method to continuous time random walks this analysis puts forward the importance of the geometry and in particular the position of the starting point in first passage statistics analytical results are validated by numerical simulations applied to various models of transport in disordered media which illustrate the universality classes of the fpt distribution

exact calculations of first passage quantities on recursive networks we present general methods to exactly calculate mean first passage quantities on self similar networks defined recursively in particular we calculate the mean first passage time and the splitting probabilities associated to a source and one or several targets averaged quantities over a given set of sources e g same connectivity nodes are also derived the exact estimate of such quantities highlights the dependency of first passage processes with respect to the source target distance which has recently revealed to be a key parameter in characterizing transport in complex media we explicitly perform calculations for different classes of recursive networks finitely ramified fractals scale free trans fractals nonfractals mixtures between fractals and nonfractals nondecimable hierarchical graphs of arbitrary size our approach unifies and significantly extends the available results in the field

application of the collocation method for solving nonlinear fractional integro differential equations in this paper using the collocation method we solve the nonlinear fractional integro differential equations nfide of the form f t y t a cd t a 0y t a cd t a ry t email protected t y t a tk t s f s y s ds y k a d k k 0 1 m 0 1 we study the convergence and the stability analysis of this method for f t y t a cd t a 0y t a cd t a ry t y t email protected j 0 rb j a cd t a jy t g t some numerical examples are given to show the efficiency of the presented method

automated pure tone threshold estimations from extrapolated distortion product otoacoustic emission dpoae input output functions a promising approach to the prediction of pure tone thresholds through the estimation of dpoae thresholds by input output functions was recently published by boege and janssen j acoust soc am 111 1810 1818 2002 on the basis of their results a device that enables automated measurements of these thresholds was recently developed the purpose of the current study was to evaluate the reliability of this instrument for the objective assessment of hearing loss in 101 ears with either normal hearing or with cochlear hearing loss of up to 50 db hl the median difference between pure tone hearing and dpoae thresholds was approximately 2 db for individual subjects however dpoae thresholds differed from pure tone thresholds by up to 40 db we find therefore that the clinical benefits of this method are probably limited

locus of generation for the 2 f1 f2 vs 2 f2 f1 distortion product otoacoustic emissions in normal hearing humans revealed by suppression tuning onset latencies and amplitude correlations the present study used distortion product otoacoustic emission dpoae suppression tuning curves stcs dpoae onset latencies ols and dpoae amplitude correlations to investigate the locus of generation of the 2 f1 f2 dpoae versus the 2 f2 f1 dpoae in humans the results of the tuning study revealed that for the 2 f1 f2 dpoae the tips of the stcs tuned consistently below the geometric mean gm frequency of the primary tones in contrast for the 2 f2 f1 dpoae stcs tuned above the gm of the primaries with 50 of the tip frequencies at or above the 2 f2 f1 frequency place when the average ratio of the 2 f2 f1 to the 2 f1 f2 tip frequencies was computed a factor of 1 44 provided an estimate of the frequency shift needed to align the two dpoae generation sites other results showed that ols for the 2 f2 f1 dpoae were uniformly shorter than those for the 2 f1 f2 with differences at the low frequencies amounting to as much as 6 7 ms further for both dpoaes curves describing latency decreases as

determining mean first passage time on a class of treelike regular fractals relatively general techniques for computing mean first passage time mfpt of random walks on networks with a specific property are very useful since a universal method for calculating mfpt on general graphs is not available because of their complexity and diversity in this paper we present techniques for explicitly determining the partial mean first passage time pmfpt i e the average of mfpts to a given target averaged over all possible starting positions and the entire mean first passage time emfpt which is the average of mfpts over all pairs of nodes on regular treelike fractals we describe the processes with a family of regular fractals with treelike structure the proposed fractals include the t fractal and the peano basin fractal as their special cases we provide a formula for mfpt between two directly connected nodes in general trees on the basis of which we derive an exact expression for pmfpt to the central node in the fractals moreover we give a technique for calculating emfpt which is based on the relationship between characteristic polynomials of the fractals at different generations and avoids the computation of eigenvalues of the characteristic polynomials making use of the proposed methods we obtain analytically the closed form solutions to pmfpt and emfpt on the fractals and show how they scale with the number of nodes in addition to exhibit the generality of our methods we also apply them to the vicsek fractals and the iterative scale free fractal tree and recover the results previously obtained

synchronous vs asynchronous dynamics of diffusion controlled reactions abstract an analytical method based on the classical ruin problem is developed to compute the mean reaction time between two walkers undergoing a generalized random walk on a 1d lattice at each time step either both walkers diffuse simultaneously with probability p synchronous event or one of them diffuses while the other remains immobile with complementary probability asynchronous event reaction takes place through same site occupation or position exchange we study the influence of the degree of synchronicity p of the walkers and the lattice size n on the global reaction s efficiency for odd n the purely synchronous case p 1 is always the most effective one while for even n the encounter time is minimized by a combination of synchronous and asynchronous events this new parity effect is fully confirmed by monte carlo simulations on 1d lattices as well as for 2d and 3d lattices in contrast the 1d continuum approximation valid for sufficiently large lattices predicts a monotonic increase of the efficiency as a function of p the relevance of the model for several research areas is briefly discussed

first passage method for the study of the efficiency of a two channel reaction on a lattice we study the efficiency of a two channel reaction between two walkers on a finite one dimensional periodic lattice the walkers perform a combination of synchronous and asynchronous jumps on the lattice and react instantaneously when they meet at the same site first channel or upon position exchange second channel we develop a method based on a conditional first passage problem to obtain exact results for the mean number of time steps needed for the reaction to take place as well as for higher order moments previous results obtained in the framework of a difference equation approach are fully confirmed including the existence of a parity effect for even lattices the maximum efficiency corresponds to a mixture of synchronous events and a small amount of asynchronous events while for odd lattices the reaction time is minimized by a purely synchronous process we provide an intuitive explanation for this behavior in addition we give explicit expressions for the variance of the reaction time the latter displays a similar even odd behavior suggesting that the parity effect extends to higher order moments 2005 the american physical society

the use of distortion product otoacoustic emission suppression as an estimate of response growth distortion product otoacoustic emission dpoae levels in response to primary pairs f2 2 or 4 khz l2 ranging from 20 to 60 db spl l1 0 4l2 39 db were measured with and without suppressor tones f3 which varied from 1 octave below to 12 octave above f2 in normal hearing subjects suppressor level l3 varied from 5 to 85 db spl dpoae levels were converted into decrements by subtracting the level in the presence of the suppressor from the level in the absence of a suppressor dpoae decrement vs l3 functions showed steeper slopes when f3 f2 this pattern is similar to other measurements of response growth such as direct measures of basilar membrane motion single unit rate level functions suppression of basilar membrane motion and discharge rate suppression from lower animals as l2 increased the l3 necessary to maintain 3 db of suppression increased at a rate of about 1 db db when f3 was approximately equal to f2 but increased more slowly when f3 f2 functions r

approximate solution of nonlinear fractional integro differential equations using fractional alternative legendre functions abstract in this paper a new set of functions called fractional alternative legendre is defined for solving nonlinear fractional integro differential equations the concept of the fractional derivative in this problem is in the caputo sense to solve the problem first we obtain the operational matrix of the riemann liouville fractional integration of these functions for the first time then this matrix and collocation method are utilized to reduce the solution of the nonlinear fractional integro differential equations to a system of algebraic equations also the convergence analysis of the proposed method is investigated finally some examples are included to demonstrate the validity and applicability of the approach

pascal principle for diffusion controlled trapping reactions in this paper we analyze the long time behavior of the survival probability p a t of an a particle that performs lattice random walk in the presence of randomly moving traps b we show that for both perfect and imperfect trapping reactions for arbitrary spatial dimension d and for a rather general class of random walks p a t is less than or equal to the survival probability of an immobile target a in the presence of randomly moving traps

first passage properties of mortal random walks ballistic behavior effective reduction of dimensionality and scaling functions for hierarchical graphs we consider a mortal random walker on a family of hierarchical graphs in the presence of some trap sites the configuration comprising the graph the starting point of the walk and the locations of the trap sites is taken to be exactly self similar as one goes from one generation of the family to the next under these circumstances the total probability that the walker hits a trap is determined exactly as a function of the single step survival probability q of the mortal walker on the nth generation graph of the family this probability is shown to be given by the nth iterate of a certain scaling function or map q f q the properties of the map then determine in each case the behavior of the trapping probability the mean time to trapping the temporal scaling factor governing the random walk dimension on the graph and other related properties the formalism is illustrated for the cases of a linear hierarchical lattice and the sierpinski graphs in two and three euclidean dimensions we find an effective reduction of the random walk dimensionality due to the ballistic behavior of the surviving particles induced by the mortality constraint the relevance of this finding for experiments involving travel times of particles in diffusion decay systems is discussed

exploration and trapping of mortal random walkers exploration and trapping properties of random walkers that may evanesce at any time as they walk have seen very little treatment in the literature and yet a finite lifetime is a frequent occurrence and its effects on a number of random walk properties may be profound for instance whereas the average number of distinct sites visited by an immortal walker grows with time without bound that of a mortal walker may depending on dimensionality and rate of evanescence remain finite or keep growing with the passage of time this number can in turn be used to calculate other classic quantities such as the survival probability of a target surrounded by diffusing traps if the traps are immortal the survival probability will vanish with increasing time however if the traps are evanescent the target may be spared a certain death we analytically calculate a number of basic and broadly used quantities for evanescent random walkers

optimal search strategies of space time coupled random walkers with finite lifetimes we present a simple paradigm for detection of an immobile target by a space time coupled random walker with a finite lifetime the motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed duration interrupted by random changes in the direction of motion and resumption of motion in the new direction with the same speed we call these walkers mortal creepers a mortal creeper may die at any time during its motion according to an exponential decay law characterized by a finite mean death rate m while still alive the creeper has a finite mean frequency of change of the direction of motion in particular we consider the efficiency of the target search process characterized by the probability that the creeper will eventually detect the target analytic results confirmed by numerical results show that there is an m dependent optimal frequency opt that maximizes the probability of eventual target detection we work primarily in one dimensional d 1 domains and examine the role of initial conditions and of finite domain sizes numerical results in d 2 domains confirm the existence of an optimal frequency of change of direction thereby suggesting that the observed effects are robust to changes in dimensionality in the d 1 case explicit expressions for the probability of target detection in the long time limit are given in the case of an infinite domain we compute the detection probability for arbitrary times and study its early and late time behavior we further consider the survival probability of the target in the presence of many independent creepers beginning their motion at the same location and at the same time we also consider a version of the standard target problem in which many creepers start at random locations at the same time

lattice theory of trapping reactions with mobile species we present a stochastic lattice theory describing the kinetic behavior of trapping reactions a stackrel ensuremath rightarrow b b in which both the a and b particles perform an independent stochastic motion on a regular hypercubic lattice upon an encounter of an a particle with any of the b particles a is annihilated with a finite probability finite reaction rate is taken into account by introducing a set of two state random variables char22 gates imposed on each b particle such that an open closed gate corresponds to a reactive passive state we evaluate here a formal expression describing the time evolution of the a particle survival probability which generalizes our previous results we prove that for quite a general class of random motion of the species involved in the reaction process for infinite or finite number of traps and for any time t the a particle survival probability is always larger in the case when a stays immobile than in situations when it moves

semiparametric regression for the area under the receiver operating characteristic curve medical advances continue to provide new and potentially better means for detecting disease such is true in cancer for example where biomarkers are sought for early detection and where improvements in imaging methods may pick up the initial functional and molecular changes associated with cancer development in other binary classification tasks computational algorithms such as neural networks support vector machines and evolutionary algorithms have been applied to areas as diverse as credit scoring object recognition and peptide binding prediction before a classifier becomes an accepted technology it must undergo rigorous evaluation to determine its ability to discriminate between states characterization of factors influencing classifier performance is an important step in this process analysis of covariates may reveal subpopulations in which classifier performance is greatest or identify features of the classifier that improve accuracy we develop regression methods for the nonparametric area

territory covered by n random walkers on fractal media the sierpinski gasket and the percolation aggregate we address the problem of evaluating the number s n t of distinct sites visited up to time t by n noninteracting random walkers all starting from the same origin in fractal media for a wide class of fractals of which the percolation cluster at criticality and the sierpinski gasket are typical examples we propose for large n and after the short time compact regime an asymptotic series for s n t analogous to that found for euclidean media s n t approximately s n t 1 delta here s n t is the number of sites volume inside a hypersphere of radius l ln n c 1 v where l is the root mean square chemical displacement of a single random walker and v and c determine how fast 1 gamma t l the probability that a given site at chemical distance l from the origin is visited by a single random walker by time t decays for large values of l l 1 gamma t l approximately exp c l l v for the fractals considered in this paper v d l w d l w 1 d l w being the chemical diffusion exponent the corrective term delta is expressed as a series in ln n n ln m ln n with n or 1 and 0 or m or n which is given explicitly up to n 2 this corrective term contributes substantially to the final value of s n t even for relatively large values of n

efficiency of encounter controlled reaction between diffusing reactants in a finite lattice topology and boundary effects abstract the role of dimensionality euclidean vs fractal spatial extent boundary effects and system topology on the efficiency of diffusion reaction processes involving two simultaneously diffusing reactants is analyzed we present numerically exact values for the mean time to reaction as gauged by the mean walklength before reactive encounter obtained via application of the theory of finite markov processes and via monte carlo simulation as a general rule we conclude that for sufficiently large systems the efficiency of diffusion reaction processes involving two synchronously diffusing reactants two walker case relative to processes in which one reactant of a pair is anchored at some point in the reaction space one walker plus trap case is higher and is enhanced the lower the dimensionality of the system this differential efficiency becomes larger with increasing system size and for periodic systems its asymptotic value may depend on the parity of the lattice imposing confining boundaries on the system enhances the differential efficiency relative to the periodic case while decreasing the absolute efficiencies of both two walker and one walker plus trap processes analytic arguments are presented to provide a rationale for the results obtained the insights afforded by the analysis to the design of heterogeneous catalyst systems is also discussed

measuring human cochlear traveling wave delay using distortion product emission phase responses a method is presented here in which cochlear traveling wave delays are estimated through the measurement of distortion product emission phase dpe responses this method assumes that the site of generation of dpes is at the f2 place eighteen adult female and 18 adult male human ears all with normal hearing underwent dpe testing for each ear dpe phase responses were computed for eight values of f2 varying from 10 to 0 78 khz linear dpe phase versus dpe frequency relationships were found estimates of traveling wave delay from the ear canal to the f2 place varied from about 1 ms for the 10 khz place to 3 5 ms for the 0 78 khz place these estimates agree well with previous traveling wave delay estimates using electrocochleography test retest comparisons of delay estimates were generally within 0 25 ms in addition within subject interaural delay differences were smaller than between subject interaural differences within subject interaural delay differences were generally less than 0 5 ms male ear

stochastic theory of diffusion controlled reactions abstract we study the kinetics of diffusion controlled a b b reactions in which both species are moving randomly on a d dimensional lattice and react upon encounters provided that both species are in reactive states particles reactivity fluctuates randomly between active and passive forms we find that in low dimensions the a particle survival probability t is described by a stretched exponential function of time such that no reaction constant can be identified in three dimensions we recover the exponential decay law and evaluate the effective reaction constant in several particular cases in addition we derive some rigorous bounds on t

inverted regions induced by geometric constraints on a classical encounter controlled binary reaction abstract the efficiency of an encounter controlled reaction between two independently mobile reactants on a lattice is characterized by the mean number n of steps to reaction the two reactants are distinguished by their mass with the light walker performing a jump to a nearest neighbor site in each time step while the heavy walker hops only with a probability p we associate p with the temperature of the system to account for geometric exclusion effects in the reactive event two reaction channels are specified for the walkers irreversible reaction occurs either in a nearest neighbor collision or when the two reactants attempt to occupy the same site lattices subject to periodic and to confining boundary conditions are considered for periodic lattices depending on the initial state the reaction time either falls off monotonically with p or displays a local minimum with respect to p occurrence of the latter signals a regime where the efficiency of the reaction effectively decreases with increasing temperature such behavior can also occur when one averages over all initial conditions but it disappears if the jump probability of the light walker falls below a characteristic threshold value even more robust behavior can occur on lattices subject to confining boundary conditions depending on the initial conditions the reaction time as a function of p may increase monotonically decrease monotonically display a single maximum or even a maximum and minimum in the latter case one can identify distinct regimes where the above noted inversion in reaction efficiency can occur we document both numerically and theoretically that these inversion regions are a consequence of a strictly classical interplay between excluded volume effects implicit in the specification of the two reaction channels and the system s dimensionality and spatial extent our results highlight situations where the description of an encounter controlled reactive event cannot be described by a single effective diffusion coefficient we also distinguish between the inversion region identified here and the marcus inverted region which arises in electron transfer reactions

first passage times for random walks in bounded domains we present a novel computational method of first passage times between a starting site and a target site of regular bounded lattices we derive accurate expressions for all the moments of this first passage time validated by numerical simulations their range of validity is discussed we also consider the case of a starting site and two targets in addition we present the extension to continuous brownian motion these results are of great relevance to any system involving diffusion in confined media

role of depletion on the dynamics of a diffusing forager we study the dynamics of a starving random walk in general spatial dimension d this model represents an idealized description for the fate of an unaware forager whose motion is not affected by the presence or absence of resources the forager depletes its environment by consuming resources and dies if it wanders too long without finding food in the exactly solvable case of one dimension we explicitly derive the average lifetime of the walk and the distribution for the number of distinct sites visited by the walk at the instant of starvation we also give a heuristic derivation for the averages of these two quantities we tackle the complex but ecologically relevant case of two dimensions by an approximation in which the depleted zone is assumed to always be circular and which grows incrementally each time the walk reaches the edge of this zone within this framework we derive a lower bound for the scaling of the average lifetime and number of distinct sites visited at starvation we also determine the asymptotic distribution of the number of distinct sites visited at starvation finally we solve the case of high spatial dimensions within a mean field approach

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

short time regime propagator in fractals the propagator p r t for fractals in the short time regime i e the probability of finding at distance r at time t a particle that diffuses in a fractal substrate when ensuremath xi r sqrt 2d t 1 d w ensuremath gg 1 is studied in order to elucidate its full functional form for finitely ramified fractals it is shown and for any other self similar media conjectured that the short time propagator is given by p r t ensuremath approx p 0 t ensuremath d s 2 ensuremath xi ensuremath alpha mathrm exp ensuremath c ensuremath xi ensuremath nu where ensuremath nu d w d w ensuremath 1 and ensuremath alpha ensuremath nu 2 ensuremath d f d f and d w being the fractal and random walk dimension of the medium respectively the value for ensuremath nu agrees with that generally accepted however our result for the as yet not well established value of ensuremath alpha differs from other recent proposals we have checked these various short time propagator proposals by comparing them to the short time propagator calculated numerically for the sierpinsky gasket our numerical results are precise enough to clearly support the validity of the short time propagator proposed here in particular the validity of our relation for ensuremath alpha and to rule out the others

simultaneous latency estimations for distortion product otoacoustic emissions and envelope following responses the purpose of this research was to simultaneously estimate processing delays in the cochlea and brainstem using the same acoustic stimuli apparent latencies were estimated from ear canal measurements of 2f1 f2 distortion product otoacoustic emissions dpoaes and scalp recordings of the f2 f1 envelope following response efr the stimuli were equal level tone pairs 65db spl with the upper tone f2 set at either 900 or 1800hz to fix the initiation site of the dpoae and efr the frequency of f1 was swept continuously between frequency limits chosen to keep the efr response between 150 and 170hz the average dpoae latencies were 9 6 and 6 2ms for f2 900 and 1800hz and the corresponding efr latencies were 12 4 and 8 8ms in a control condition a third suppressor tone was added near the dpoae response frequency to evaluate whether the potential source at fdp was contributing significantly to the measured emission dpoae latency is the sum of both inward and outward cochlear delays the efr apparent la

group delays of distortion product otoacoustic emissions relating delays measured with f1 and f2 sweep paradigms a theoretical analysis is presented of group delays of distortion product otoacoustic emissions dpoaes measured with the phase gradient method the aim of the analysis is to clarify the differences in group delays d1 and d2 obtained using the f1 and the f2 sweep paradigms respectively and the dependence of group delays on the order of the dpoae two models are considered the place fixed and the wave fixed models while in the former model the generation place is assumed to be invariant with both f1 and f2 sweeps in the latter model the shift of generation place is fully accounted for by making a simple local approximation of the cochlear scale invariance a mathematical conversion from phase place to phase frequency gradients is incorporated in the wave fixed model under the assumption that the dpoae as recorded at the best f2 f1 ratio is dominated by the contribution from the generation site and not by e g reflection components the analysis leads to simple expressions for the ratio and difference between d1 and d2 validation of the models against experimental data indicates that lower sideband dpoaes 2f1 f2 3f1 2f2 4f1 3f2 are most consistent with the wave fixed model upper sideband components 2f2 f1 in contrast are not properly described by either the place fixed or the wave fixed model independent whether dpoae generation is assumed to originate at the f2 or at the more basally located f dp characteristic place

spectral shapes of forward and reverse transfer functions between ear canal and cochlea estimated using dpoae input output functions it is widely assumed that the distortion characteristics of the cochlea are uniform across its length or at least across some portion of its length for each distortion product otoacoustic emission dpoae input output i o function across frequency there is a corresponding cochlear i o function defined over the cochlear source region an assumption of distortion invariance is adopted such that these cochlear i o functions are identical across tonotopic place which is testable in the sense that a single nonlinear function should adequately describe the set of dpoae i o functions across frequency if so the differences in measured dpoae i o functions across frequency are produced by differences in the forward stimulus transmission to the generation site and reverse dp transmission back to the ear canal the absolute transfer function magnitude is not determined by this technique but the spectral shapes across frequency and between ears are determined the role of middle ear functioning is implicit in the i o functions because of its controlling influence on these transfer functions results have been obtained using the average dpoae i o functions measured in a population of healthy ears gorga et al j acoust soc am 107 2128 2135 2000 and support the hypothesis of cochlear distortion invariance the measured forward and reverse transfer functions have a general bandpass characteristic and a more narrow band structure with similarities to the behavioral threshold curve

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

distortion product otoacoustic emission delay measurement in human ears the measurement of distortion product otoacoustic emission dpoae delay using the phase gradient method is discussed a short f2 sweep paradigm is described its merits are discussed and comparisons made with other methods using sweeps of less than 4 consistent and reliable measurements were obtained from 12 normal ears except for a few isolated measurements investigation of these apparent anomalies indicated that the short f2 sweep method was sensitive to the localized effects of narrow distortion product intensity notches and spontaneous emissions it is possible that middle ear pressure instability or some local change in the cochlea sometimes compounded the situation the intersubject range 63 of the mean of dpoae delay values was greater than the range of values observed due to measurement variability 5 6 of the mean or intrasubject variability 8 5 of the mean demonstrating that the method can detect real differences between ears however comparison with previous work shows that caution is needed in interpreting these data as all dpoae phase methods provide only partial latency values the physical interpretation depends on both the stimulus sweep used and the origin of dpoaes our data shows that f1 sweep derived latency is lower than f2 sweep data by more than 20 caution also needs to be exercised when comparing cochlear traveling wave delay as inferred from electrophysiological data with that obtained from dpoae delay measurements

the use of cumulative distributions to determine critical values and levels of confidence for clinical distortion product otoacoustic emission measurements distortion product otoacoustic emission dpoae input output functions were measured at nine f2 frequencies ranging from 500 to 8000 hz in 210 normal hearing and hearing impaired subjects in a companion paper stover et al j acoust soc am 100 956 967 1996 l1 l2 was held constant at 10 db and l2 was varied from 65 to 10 db spl in 5 db steps based upon analyses using clinical decision theory it was demonstrated that dpoae amplitudes for 65 55 db spl primaries l1 l2 and dpoae thresholds resulted in the greatest separation between normal and impaired ears in this paper the data for these two conditions were recast as cumulative distributions which not only describe the extent of overlap between normal and impaired distributions but also provide the measured value i e the specific dpoae amplitude or threshold for any combination of hit and false alarm rates from these distributions confidence limits were constructed for both dpoae amplitude and threshold to determine the degree of ce

exact mean first passage time on the t graph we consider a simple random walk on the t fractal and we calculate the exact mean time taug to first reach the central node i0 the mean is performed over the set of possible walks from a given origin and over the set of starting points uniformly distributed throughout the sites of the graph except i0 by means of analytic techniques based on decimation procedures we find the explicit expression for taug as a function of the generation g and of the volume v of the underlying fractal our results agree with the asymptotic ones already known for diffusion on the t fractal and more generally they are consistent with the standard laws describing diffusion on low dimensional structures

trapping reactions with randomly moving traps exact asymptotic results for compact exploration trapping a1b b and recombination a1b 0 reactions tr and rr involving randomly moving a and b particles which react when they meet at a certain distance b are ubiquitous in nature a few stray examples include quenching of delocalized excitations coagulation recombination of radicals charge carriers or defects or biological processes related to population survival 1 in recent years there has been much interest in the longtime behavior of these processes following a remarkable discovery 2 10 of many particle effects which induce essential departures from the conventionally expected behavior 1 a pronounced deviation from the text book predictions was found for the diffusion controlled rr in case when initially the particles of the a and b species are all distributed at random with strictly equal mean densities n0 it has been first shown 2 and subsequently proven 3 4 that as t the mean density n t follows n t a d n 0 dt 2d 4 where d is the space dimensionality a d is a constant and d5d a 1db is the sum of particles diffusion coefficients this law contradicts the decay law obtained within the smoluchowski approach sa n t 1 f bd t 1 where as t

interrelations among distortion product phase gradient delays their connection to scaling symmetry and its breaking distortion product otoacoustic emission dpoae phase versus frequency functions and corresponding phase gradient delays have received considerable attention because of their potential for providing information about mechanisms of emission generation cochlear wave latencies and characteristics of cochlear tuning the three measurement paradigms in common use fixed f1 fixed f2 and fixed f2 f1 yield significantly different delays suggesting that they depend on qualitatively different aspects of cochlear mechanics in this paper theory and experiment are combined to demonstrate that simple phenomenological arguments which make no detailed mechanistic assumptions concerning the underlying cochlear mechanics predict relationships among the delays that are in good quantitative agreement with experimental data obtained in guinea pigs to understand deviations between the simple theory and experiment a general equation is found that relates the three delays for any deterministic model of dpoae generation both model independent and exact the general relation provides a powerful consistency check on the measurements and a useful tool for organizing and understanding the structure in dpoae phase data e g for interpreting the relative magnitudes and intensity dependencies of the three delays analysis of the general relation demonstrates that the success of the simple phenomenological approach can be understood as a consequence of the mechanisms of emission generation and the approximate local scaling symmetry of cochlear mechanics the general relation is used to quantify deviations from scaling manifest in the measured phase gradient delays the results indicate that deviations from scaling are typically small and that both linear and nonlinear mechanisms contribute significantly to these deviations intensity dependent mechanisms contributing to deviations from scaling include cochlear reflection and wave interference effects associated with the mixing of distortion and reflection source emissions as in dpoae fine structure finally the ratio of the fixed f1 and fixed f2 phase gradient delays is shown to follow from the choice of experimental paradigm and in the scaling limit contains no information about cochlear physiology whatsoever these results cast considerable doubt on the theoretical basis of recent attempts to use relative dpoae phase gradient delays to estimate the bandwidths of peripheral auditory filters

analytic expression for the mean time to absorption for a random walker on the sierpinski gasket the exact analytic expression for the mean time to absorption or mean walk length for a particle performing a random walk on a finite sierpinski gasket with a trap at one vertex is found to be t n 3 n 5 n 1 4 5 n ensuremath 3 n 3 n 1 1 where n denotes the generation index of the gasket and the mean is over a set of starting points of the walk distributed uniformly over all the other sites of the gasket in terms of the number n n of sites on the gasket and the spectral dimension stackrel ifmmode tilde else fi d of the gasket the precise asymptotic behavior for large n n is t n ensuremath rightarrow 1 3 2n n 2 stackrel ifmmode tilde else fi d ensuremath sim n 1 464 this serves as a partial check on our result as it is a intermediate between the known results t ensuremath sim n 2 d 1 and t ensuremath sim n mathrm ln n d 2 for random walks on d dimensional euclidean lattices and b consistent with the known result for the asymptotic behavior of the mean number of distinct sites visited in a random walk on a fractal lattice

toward optimizing the clinical utility of distortion product otoacoustic emission measurements this study examined the effect of primary stimulus level on the ability of distortion product otoacoustic emission dpoae measurements to separate normal hearing from hearing impaired ears complete i o functions were obtained for nine f2 frequencies on 210 people approximately evenly divided between normal hearing and hearing impaired clinical decision theory was used to assess both dpoae amplitudes and dpoae threshold as diagnostic indicators of hearing status moderate level primary stimuli elicited responses that separated normal from impaired better than either lower level or higher level stimuli the two populations were differentiated for all frequencies above 500 hz by dpoae amplitude given primary levels l1 and l2 of 65 and 55 db spl dpoae threshold performed equally well but threshold ambiguity in noise and longer testing times make it a less suitable dpoae measure to use diagnostically

group delays of distortion product otoacoustic emissions in the guinea pig this paper presents a comprehensive set of experimental data on group delays of distortion product otoacoustic emissions dpoaes in the guinea pig group delays of the dpoaes with frequencies 2f1 f2 3f1 2f2 4f1 3f2 and 2f2 f1 were measured with the phase gradient method both the f1 and the f2 sweep paradigm were used differences between the two sweep paradigms were investigated for the four dpoaes as well as the group delay differences between the dpoaes analysis revealed larger group delays with the f2 sweep paradigm but only for the lower sideband dpoaes with fdp f1 f2 for the lower sideband cubic distortion product 2f1 f2 the f2 sweep delays were a factor of 1 17 1 54 larger than the f1 sweep delays depending on frequency the upper sideband dpoae 2f2 f1 showed no significant difference between f1 and f2 sweep group delays except for the highest and lowest f2 frequencies comparing the group delays of the dpoaes for each sweep paradigm separately equal group delays were found for all four dpoaes measured with the f1 sweep with the f2 sweep paradigm on the other hand the group delays of the three lower sideband dpoaes occurred to be larger than the group delays of the upper sideband dpoae 2f2 f1 a tentative interpretation of the data in the context of proposed explanatory hypotheses on dpoae group delays is given

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

the exact solution of certain differential equations of fractional order by using operational calculus abstract in the present paper the authors first develop an operational calculus for the familiar riemann liouville fractional differential operator this operational calculus is then used here to solve a cauchy boundary value problem for a certain linear equation involving the riemann liouville fractional derivatives relevant connections are also indicated with the special cases of the equation which were solved earlier by using other methods

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

efficiency of encounter controlled reaction between diffusing reactants in a finite lattice non nearest neighbor effects abstract the influence of non nearest neighbor displacements on the efficiency of diffusion reaction processes involving one and two mobile diffusing reactants is studied an exact analytic result is given for dimension d 1 from which for large lattices one can recover the asymptotic estimate reported 30 years ago by lakatos lindenberg and shuler for dimensions d 2 3 we present numerically exact values for the mean time to reaction as gauged by the mean walklength before reactive encounter obtained via the theory of finite markov processes and supported by monte carlo simulations qualitatively different results are found between processes occurring on d 1 versus d 1 lattices and between results obtained assuming nearest neighbor only versus non nearest neighbor displacements

influence of primary frequencies ratio on distortion product otoacoustic emissions amplitude i intersubject variability and consequences on the dpoae gram distortion product otoacoustic emissions dpoaes are used widely in humans to assess cochlear function the standard procedure consists of recording the 2f1 f2 dpoae amplitude as a function of the f2 frequency using a fixed f2 f1 ratio dpoae gram close to 1 20 dpoae amplitude as recorded in the dpoae gram shows a wide range of values in normal hearing subjects which can impair the predictive value of the dpoae gram for hearing thresholds this study is aimed at comparing intersubject variability in 2f1 f2 dpoae amplitude according to three paradigms a fixed f2 f1 ratio such as the dpoae gram a variable ratio dpoae gram f2 f1 adapted to frequency and an optimum dpoae gram where the f2 f1 is adapted both to subject and frequency the 2f1 f2 dpoae amplitude has been investigated on 18 normally hearing subjects at ten different f2 frequencies from 0 75 to 6 khz using an f2 fixed f1 sweep paradigm and allowed to define for each frequency the f2 f1 ratio giving the greatest 2f1 f2 dpoae amplitude or optimum ratio results showed a large intersubject variability of the optimum ratio especially at frequencies below 1 5 khz and a significant decrease of the optimum ratio with frequency the optimum dpoae gram was underestimated by up to 5 8 db on average up to 14 9 db for an individual subject by the fixed ratio dpoae gram and by up to 3 db on average up to 10 6 db for an individual subject by the variable ratio dpoae gram intersubject variability was slightly but significantly reduced in the optimum dpoae gram versus the fixed ratio dpoae gram lastly correlations between tone burst evoked otoacoustic emission tboae amplitudes and maximum dpoae amplitudes were significantly greater than correlations between tboae amplitudes and fixed ratio dpoae amplitudes

further efforts to predict pure tone thresholds from distortion product otoacoustic emission input output functions recently boege and janssen j acoust soc am 111 1810 1818 2002 fit linear equations to distortion product otoacoustic emission dpoae input output i o functions after the dpoae level in db spl was converted into pressure in pa significant correlations were observed between these dpoae thresholds and audiometric thresholds the present study extends their work by 1 evaluating the effect of frequency 2 determining the behavioral thresholds in those conditions that did not meet inclusion criteria and 3 including a wider range of stimulus levels dpoae i o functions were measured in as many as 278 ears of subjects with normal and impaired hearing nine f2 frequencies 500 to 8000 hz in 12 octave steps were used l2 ranged from 10 to 85 db spl 5 db steps and l1 was set according to the equation l1 0 4l2 39 db kummer et al j acoust soc am 103 3431 3444 1998 for l2 levels up to 65 db spl beyond which l1 l2 for the same conditions as those used by boege and janssen we o

sources of dpoaes revealed by suppression experiments inverse fast fourier transforms and sfoaes in impaired ears dpoae sources are modeled by intermodulation distortion generated near the f2 place and a reflection of this distortion near the dp place in a previous paper inverse fast fourier transforms iffts of dpoae filter functions in normal ears were consistent with this model konrad martin et al j acoust soc am 109 2862 2879 2001 in the present article similar measurements were made in ears with specific hearing loss configurations it was hypothesized that hearing loss at f2 or dp frequencies would influence the relative contributions to the dpoae from the corresponding basilar membrane places and would affect the relative magnitudes of sfoaes at frequencies equal to f2 and fdp dpoaes were measured with f2 4 khz f1 varied and a suppressor near fdp l2 was 25 55 db spl l1 l2 10 db sfoaes were measured at f2 and at 2 7 khz the average fdp produced by the f1 sweep for stimulus levels of 20 60 db spl sfoae results supported predictions of the pattern of amplitude differences between sfoaes

effects of confinement on the statistics of encounter times exact analytical results for random walks in a partitioned lattice we study the effects of temporarily and permanently confining domains on the statistics of first passage times in finite lattices in one and two dimensions we present exact results for the mean and variance of the first passage time between arbitrary sites in the following 1 a finite one dimensional lattice partitioned into temporarily confining domains and 2 a finite two dimensional lattice with reflecting boundaries for a single random walker and an immobile target in the one dimensional case we also present the full first passage time distribution via numerical inversion of laplace transforms

random walks with spontaneous emission on lattices with periodically distributed imperfect traps abstract we study random walks on d dimensional lattices with periodically distributed traps in which the walker has a finite probability per step of disappearing from the lattice and a finite probability of escaping from a trap general expressions are derived for the total probability that the walk ends in a trap and for the moments of the number of steps made before this happens if it does happen the analysis is extended to lattices with more types of traps and to a model where the trapping occurs during special steps finally the green s function at the origin g 0 z for a finite lattice with periodic boundary conditions which enters into the main expressions is studied more closely a generalization of an expression for g 0 1 for the square lattice given by montroll to values of z different from but close to 1 is derived

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

on mittag leffler type functions in fractional evolution processes abstract we review a variety of fractional evolution processes so defined being governed by equations of fractional order whose solutions turn out to be related to mittag leffler type functions the chosen equations are the simplest of the fractional calculus and include the abel integral equations of the second kind which are relevant in typical inverse problems and the fractional differential equations which govern generalized relaxation and oscillation phenomena

periodogram based tests for distortion product otoacoustic emissions distortion product otoacoustic emissions dpoaes are an important nonbehavioral measure of cochlear function which provides a close analogue of the behavioral pure tone audiogram dpoaes are sinusoidal distortion products dps produced by nonlinearities in the healthy cochlea detection of dps is accomplished in the fourier domain with a periodogram based test the test compares the power in the dp periodogram bin to a noise estimate derived from a certain number of the surrounding bins statistical properties of this test to date have only been examined by constructing receiver operator characteristics curves derived from dpoae measurements in normal and hearing impaired individuals in this paper the null distribution of this order statistic based test is explicitly derived and via simulations intended to mimic the nonwhite features of real ear noise measurements the power of the test is demonstrated these simulations demonstrate that a local f test is more powerful than this dpoae test with critical values that are easier to calculate although the power of both tests increase with an increasing number of bins the improvement is negligible at around four bins since the power of both tests decrease at lower dp frequencies it is not recommended to use a large number of bins

distortion product otoacoustic emission test performance when both 2 f1 f2 and 2 f2 f1 are used to predict auditory status the objective of this study was to determine whether distortion product otoacoustic emission dpoae test performance defined as its ability to distinguish normal hearing ears from those with hearing loss can be improved by examining response and noise amplitudes at 2 f1 f2 and 2 f2 f1 simultaneously in addition there was interest in knowing whether measurements at both dps and for several primary frequency pairs can be used in a multivariate analysis to further optimize test performance dpoae and noise amplitudes were measured at 2 f1 f2 and 2 f2 f1 for 12 primary levels l2 from 10 to 65 db spl in 5 db steps and 9 pairs of primary frequencies 0 5 to 8 khz in 1 2 octave steps all data were collected in a sound treated room from 70 subjects with normal hearing and 80 subjects with hearing loss subjects had normal middle ear function at the time of the dpoae test based on standard tympanometric measurements measurement based stopping rules were used such that the test terminated when the noise