loudness perception and frequency discrimination in subjects with steeply sloping hearing loss possible correlates of neural plasticity loudness functions and frequency difference limens dlfs were measured in five subjects with steeply sloping high frequency sensorineural hearing loss the stimuli were pulsed pure tones encompassing a range of frequencies loudness data were obtained using a 2afc matching procedure with a 500 hz reference presented at a number of levels dlfs were measured using a 3afc procedure with intensities randomized within 6 db around an equal loudness level results showed significantly shallower loudness functions near the cutoff frequency of the loss than at a lower frequency where hearing thresholds were near normal dlfs were elevated on average relative to dlfs measured using the same procedure in five normally hearing subjects but showed a local reduction near the cutoff frequency in most subjects with high frequency loss the loudness data are generally consistent with recent models that describe loudness perception in terms of peripheral excitation patterns that are presumably restricted by a steeply sloping hearing loss however the dlf data are interpreted with reference to animal experiments that have shown reorganization in the auditory cortex following the introduction of restricted cochlear lesions such reorganization results in an increase in the spatial representation of lesion edge frequencies and is comparable with the functional reorganization observed in animals following frequency discrimination training it is suggested that similar effects may occur in humans with steeply sloping high frequency hearing loss and therefore the local reduction in dlfs in our data may reflect neural plasticity

fixed point optimization algorithms for distributed optimization in networked systems this paper considers a networked system with a finite number of users and deals with the problem of minimizing the sum of all users objective functions over the intersection of all users constraint sets onto which the projection cannot be easily implemented the main objective of this paper is to devise distributed optimization algorithms which enable each user to find the solution of the problem without using other users objective functions and constraint sets to reach this goal we first introduce easily implementable nonexpansive mappings of which the intersection of the fixed point sets is equal to the constraint set in the problem we formulate the problem as a convex minimization problem over the intersection of the fixed point sets of the nonexpansive mappings we then present an iterative algorithm based on the conventional incremental subgradient methods which use the projection for solving the problem the algorithm can be implemented by using nonexpansive mappings other than the project

temporal integration of loudness measured using categorical loudness scaling and matching procedures temporal integration of loudness of 1 khz tones with 5 and 200 ms durations was assessed in four subjects using two loudness measurement procedures categorical loudness scaling cls and loudness matching cls provides a reliable and efficient procedure for collecting data on the temporal integration of loudness and previously reported nonmonotonic behavior observed at mid sound pressure level levels is replicated with this procedure stimuli that are assigned to the same category are effectively matched in loudness allowing the measurement of temporal integration with cls without curve fitting interpolation or assumptions concerning the form of the loudness growth function

convergence of approximate and incremental subgradient methods for convex optimization we present a unified convergence framework for approximate subgradient methods that covers various stepsize rules including both diminishing and nonvanishing stepsizes convergence in objective values and convergence to a neighborhood of the optimal set we discuss ways of ensuring the boundedness of the iterates and give efficiency estimates our results are extended to incremental subgradient methods for minimizing a sum of convex functions which have recently been shown to be promising for various large scale problems including those arising from lagrangian relaxation

distributed continuous time convex optimization on weight balanced digraphs this technical note studies the continuous time distributed optimization of a sum of convex functions over directed graphs contrary to what is known in the consensus literature where the same dynamics works for both undirected and directed scenarios we show that the consensus based dynamics that solves the continuous time distributed optimization problem for undirected graphs fails to converge when transcribed to the directed setting this study sets the basis for the design of an alternative distributed dynamics which we show is guaranteed to converge on any strongly connected weight balanced digraph to the set of minimizers of a sum of convex differentiable functions with globally lipschitz gradients our technical approach combines notions of invariance and cocoercivity with the positive definiteness properties of graph matrices to establish the results

cooperative convex optimization in networked systems augmented lagrangian algorithms with directed gossip communication we study distributed optimization in networked systems where nodes cooperate to find the optimal quantity of common interest x x the objective function of the corresponding optimization problem is the sum of private known only by a node convex nodes objectives and each node imposes a private convex constraint on the allowed values of x we solve this problem for generic connected network topologies with asymmetric random link failures with a novel distributed de centralized algorithm we refer to this algorithm as al g augmented lagrangian gossiping and to its variants as al mg augmented lagrangian multi neighbor gossiping and al bg augmented lagrangian broadcast gossiping the al g algorithm is based on the augmented lagrangian dual function dual variables are updated by the standard method of multipliers at a slow time scale to update the primal variables we propose a novel gauss seidel type randomized algorithm at a fast time scale al g uses unidirectional gossip communication only between immediate neighbors in the network and is resilient to random link failures for networks with reliable communication i e no failures the simplified al bg augmented lagrangian broadcast gossiping algorithm reduces communication computation and data storage cost we prove convergence for all proposed algorithms and demonstrate by simulations the effectiveness on two applications l1 regularized logistic regression for classification and cooperative spectrum sensing for cognitive radio networks

approximate projected consensus for convex intersection computation convergence analysis and critical error angle in this paper we study an approximate projected consensus algorithm for a network to cooperatively compute the intersection of convex sets where each set corresponds to one network node instead of assuming exact convex projection that each node can compute we allow each node to compute an approximate projection with respect to its own set after receiving the approximate projection information nodes update their states by weighted averaging with the neighbors over a directed and time varying communication graph the approximate projections are related to projection angle errors which introduces state dependent disturbance in the iterative algorithm projection accuracy conditions are presented for the considered algorithm to converge the results indicate how much projection accuracy is required to ensure global consensus to a point in the intersection set when the communication graph is uniformly jointly strongly connected in addition we show that pi 4 is a critical angle for the error of the projection approximation to ensure the boundedness finally the results are illustrated by simulations

loudness recalibration as a function of level recent research on loudness has focused on contextual effects on loudness both assimilation and recalibration the current experiments examined loudness recalibration marks j exp psychol 20 382 396 1994 in the first experiment an adaptive tracking procedure was used to measure loudness recalibration as a function of standard and recalibration tone level the standard tone frequencies were 500 and 2500 hz and the levels were 80 70 60 and 40 db spl and threshold seventeen db of loudness recalibration was obtained combined over both frequencies in the 60 db spl condition this amount of loudness recalibration while substantial is still less than that obtained by marks 22 db using the method of paired comparisons the second experiment sought to duplicate marks earlier experiment marks j exp psychol 20 382 396 1994 experiment 2 the results of this experiment 21 db were almost identical to those obtained by marks the results of experiment 1 indicate that loudness recalibration is maximum when the recalibration tone is moderately louder than the subsequent standard tones relatively little loudness recalibration is exhibited when the standard tone level equals the recalibration tone level in addition there is no loudness recalibration at threshold the tracking procedure also identified that the onset of loudness recalibration is very rapid the difference between the maximum loudness recalibration obtained at each frequency 11 db at 500 hz 6 db at 2500 hz suggests that loudness recalibration is dependent upon the frequency of the standard tone

randomized optimal consensus of multi agent systems in this paper we formulate and solve a randomized optimal consensus problem for multi agent systems with stochastically time varying interconnection topology the considered multi agent system with a simple randomized iterating rule achieves an almost sure consensus meanwhile solving the optimization problem min z r email protected i 1 nf i z in which the optimal solution set of objective function f i can only be observed by agent i itself at each time step simply determined by a bernoulli trial each agent independently and randomly chooses either taking an average among its neighbor set or projecting onto the optimal solution set of its own optimization component both directed and bidirectional communication graphs are studied connectivity conditions are proposed to guarantee an optimal consensus almost surely with proper convexity and intersection assumptions the convergence analysis is carried out using convex analysis we compare the randomized algorithm with the deterministic one via a numerical example the results illustrate that a group of autonomous agents can reach an optimal opinion by each node simply making a randomized trade off between following its neighbors or sticking to its own opinion at each time step

distributed convergence to nash equilibria in two network zero sum games this paper considers a class of strategic scenarios in which two networks of agents have opposing objectives with regard to the optimization of a common objective function in the resulting zero sum game individual agents collaborate with neighbors in their respective network and have only partial knowledge of the state of the agents in the other network for the case when the interaction topology of each network is undirected we synthesize a distributed saddle point strategy and establish its convergence to the nash equilibrium for the class of strictly concave convex and locally lipschitz objective functions we also show that this dynamics does not converge in general if the topologies are directed this justifies the introduction in the directed case of a generalization of this distributed dynamics which we show converges to the nash equilibrium for the class of strictly concave convex differentiable functions with globally lipschitz gradients the technical approach combines tools from algebraic graph theory nonsmooth analysis set valued dynamical systems and game theory

incremental subgradient methods for nondifferentiable optimization we consider a class of subgradient methods for minimizing a convex function that consists of the sum of a large number of component functions this type of minimization arises in a dual context from lagrangian relaxation of the coupling constraints of large scale separable problems the idea is to perform the subgradient iteration incrementally by sequentially taking steps along the subgradients of the component functions with intermediate adjustment of the variables after processing each component function this incremental approach has been very successful in solving large differentiable least squares problems such as those arising in the training of neural networks and it has resulted in a much better practical rate of convergence than the steepest descent method in this paper we establish the convergence properties of a number of variants of incremental subgradient methods including some that are stochastic based on the analysis and computational experiments the methods appear very promising and effective for important classes of large problems a particularly interesting discovery is that by randomizing the order of selection of component functions for iteration the convergence rate is substantially improved

loudness of tone pulses in a free field investigations of temporal loudness summation of tone pulses have been performed the investigations comprised equal loudness determinations between pairs of tone pulses with a duration ratio of 1 2 and threshold determinations of the same tone pulses pulse durations ranged from 5 to 640 ms the frequencies were 500 1000 and 4000 hz all pulses were shaped by means of 1 3 octave filters for 25 normal hearing observers the investigations were performed at the observer s threshold and at 35 and 55 db spl fitting of the experimental data to a single exponential function yields a time constant of about 200 ms near and at the threshold whereas is about 100 ms at levels well above threshold discrepancies exist nevertheless between this single time constant model and the experimental data obtained for the pulses of shortest duration to account for this a model is proposed comprising a combination of two exponential functions this yields a short time constant of 5 to 10 ms combined with the longer time constant mentioned above

a potential carry over effect in the measurement of induced loudness reduction the majority of studies on induced loudness reduction ilr use an experimental paradigm that results in an underestimation of the amount of ilr most of those studies utilize loudness matches between tones of two different frequencies a test tone and a comparison tone with experimental condition and without baseline condition an inducer tone at the test frequency the change in level of the comparison tone between the baseline and experimental conditions is the amount of ilr in those experiments the level of the comparison tone in the baseline condition tends to be substantially higher often about 10db than in the experimental condition because of this level difference exposure to the baseline condition immediately prior to the experimental condition causes unintended ilr for the comparison tone in this study the delay between the baseline and experimental conditions was varied and it was determined that the amount of ilr is underestimated by about 30 and the variability is increased when

acceleration method combining broadcast and incremental distributed optimization algorithms this paper considers a networked system consisting of an operator which manages the system and a finite number of subnetworks with all users and studies the problem of minimizing the sum of the operator s and all users objective functions over the intersection of the operator s and all users constraint sets when users in each subnetwork can communicate with each other they can implement an incremental subgradient method that uses the transmitted information from their neighbor users since the operator can communicate with users in the subnetworks it can implement a broadcast distributed algorithm that uses all available information in the subnetworks we present an iterative method combining broadcast and incremental distributed optimization algorithms our method has faster convergence and a wider range of application compared with conventional distributed algorithms we also prove that under certain assumptions our method converges to the solution to the problem in the sense of the strong topol

effect of adaptive psychophysical procedure on loudness matches large variability in equal loudness matches has been observed across studies the purpose of the present study was to gain insight into the extent to which this variability results from differences in psychophysical procedures and or differences among listeners four adaptive two interval two alternatives forced choice procedures were used to obtain equal loudness matches between 5 and 200 ms 1 khz tones as a function of level for each of six normal listeners the procedures differed primarily in the sequence in which the stimuli were presented the variations tested were the ordering of stimuli by amplitude across blocks of trials both increasing and decreasing amplitudes randomizing the order across those blocks and randomizing the order within blocks the random within block procedure which sought to randomize any intertrial information yielded a significantly greater amount of temporal integration than the other three procedures the results show significant differences in temporal integration

a randomized incremental subgradient method for distributed optimization in networked systems we present an algorithm that generalizes the randomized incremental subgradient method with fixed stepsize due to nedic and bertsekas siam j optim 12 2001 pp 109 138 our novel algorithm is particularly suitable for distributed implementation and execution and possible applications include distributed optimization e g parameter estimation in networks of tiny wireless sensors the stochastic component in the algorithm is described by a markov chain which can be constructed in a distributed fashion using only local information we provide a detailed convergence analysis of the proposed algorithm and compare it with existing both deterministic and randomized incremental subgradient methods

distributed algorithms for aggregative games on graphs we consider a class of nash games termed as aggregative games being played over a networked system in an aggregative game a player s objective is a function of the aggregate of all the players decisions every player maintains an estimate of this aggregate and the players exchange this information with their local neighbors over a connected network we study distributed synchronous and asynchronous algorithms for information exchange and equilibrium computation over such a network under standard conditions we establish the almost sure convergence of the obtained sequences to the equilibrium point we also consider extensions of our schemes to aggregative games where the players objectives are coupled through a more general form of aggregate function finally we present numerical results that demonstrate the performance of the proposed schemes

tracking the time to recovery after induced loudness reduction l in induced loudness reduction ilr a strong tone causes the loudness of a subsequently presented weak tone to decrease the aim of the experiment was to determine the time required for loudness to return to its initial level after ilr twenty four subjects were exposed to 5 10 20 or 40 brief bursts of 2500 hz pure tones at 80 db spl inducers and then tested in a series of paired comparison trials subjects compared the loudness of a weak target 2500 hz at 60 db spl to the loudness of a comparison tone at 500 hz previously judged to match the target the comparison task was repeated until the two tones were again judged equally loud the results showed that a recovery after ilr is a relatively long process with a time scale of minutes and b recovery time increased approximately 20 s with each doubling of the number of inducers

testing the concept of softness imperception loudness near threshold for hearing impaired ears buus and florentine j assoc res otolaryngol 3 120 139 2002 have proposed that loudness recruitment in cases of cochlear hearing loss is caused partly by an abnormally large loudness at absolute threshold this has been called softness imperception to evaluate this idea loudness matching functions were obtained using tones at very low sensation levels for subjects with asymmetrical hearing loss matches were obtained for a single frequency across ears for subjects with sloping hearing loss matches were obtained between tones at two frequencies one where the absolute threshold was nearly normal and one where there was a moderate hearing loss loudness matching was possible for sensation levels sls as low as 2 db when the fixed tone was presented at a very low sl in an ear or at a frequency where there was hearing impairment it was matched by a tone with approximately the same sl in an ear or at a frequency where hearing was normal e g 2 db sl matched 2 db sl this relationship held for sls up to 4 10 db depending on the subject these results are not consistent with the concept of softness imperception

on decentralized negotiation of optimal consensus a consensus problem consists of finding a distributed control strategy that brings the state or output of a group of agents to a common value a consensus point in this paper we propose a negotiation algorithm that computes an optimal consensus point for agents modeled as linear control systems subject to convex input constraints and linear state constraints by primal decomposition and incremental subgradient methods it is shown that the algorithm can be implemented such that each agent exchanges only a small amount of information per iteration with its neighbors

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

a convergent incremental gradient method with a constant step size an incremental aggregated gradient method for minimizing a sum of continuously differentiable functions is presented the method requires a single gradient evaluation per iteration and uses a constant step size for the case that the gradient is bounded and lipschitz continuous we show that the method visits infinitely often regions in which the gradient is small under certain unimodality assumptions global convergence is established in the quadratic case a global linear rate of convergence is shown the method is applied to distributed optimization problems arising in wireless sensor networks and numerical experiments compare the new method with other incremental gradient methods

distributed convex optimization via continuous time coordination algorithms with discrete time communication this paper proposes a novel class of distributed continuous time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents we establish the exponential convergence of the proposed algorithm under i strongly connected and weight balanced digraph topologies when the local costs are strongly convex with globally lipschitz gradients and ii connected graph topologies when the local costs are strongly convex with locally lipschitz gradients when the local cost functions are convex and the global cost function is strictly convex we establish asymptotic convergence under connected graph topologies we also characterize the algorithm s correctness under time varying interaction topologies and study its privacy preservation properties motivated by practical considerations we analyze the algorithm implementation with discrete time communication we provide an upper bound on the stepsize that guarantees exponential convergence over connected graphs for implementations with periodic communication building on this result we design a provably correct centralized event triggered communication scheme that is free of zeno behavior finally we develop a distributed asynchronous event triggered communication scheme that is also free of zeno with asymptotic convergence guarantees several simulations illustrate our results

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

an introduction to induced loudness reduction induced loudness reduction ilr is a phenomenon by which a preceding higher level tone an inducer tone reduces the loudness of a lower level tone a test tone the strength of this effect depends on a number of parameters reviewed here some of the implications of ilr on loudness data are presented via the analysis of several studies in which ilr likely resulted in otherwise unexplained biases in data sets these results serve as examples of the pervasiveness of ilr in loudness measurements and indicate that it is necessary to consider ilr when designing any psychoacoustical experiment in which level varies

image reducing words and subgroups of free groups a word w over a finite alphabet is said to be n collapsing if for an arbitrary finite automaton a q the inequality q w q n holds provided that q u q n for some word u depending on a we give an algorithm to test whether a word is 2 collapsing to this aim we associate to every word w a finite family of finitely generated subgroups in finitely generated free groups and prove that the property of being 2 collapsing reflects in the property that each of these subgroups has index at most 2 in the corresponding free group we also find a similar characterization for the closely related class of so called 2 synchronizing words

convergence analysis of iterative methods for nonsmooth convex optimization over fixed point sets of quasi nonexpansive mappings this paper considers a networked system with a finite number of users and supposes that each user tries to minimize its own private objective function over its own private constraint set it is assumed that each user s constraint set can be expressed as a fixed point set of a certain quasi nonexpansive mapping this enables us to consider the case in which the projection onto the constraint set cannot be computed efficiently this paper proposes two methods for solving the problem of minimizing the sum of their nondifferentiable convex objective functions over the intersection of their fixed point sets of quasi nonexpansive mappings in a real hilbert space one method is a parallel subgradient method that can be implemented under the assumption that each user can communicate with other users the other is an incremental subgradient method that can be implemented under the assumption that each user can communicate with its neighbors investigation of the two methods convergence properties for a constant step size reveals that with a small constant step size they approximate a solution to the problem consideration of the case in which the step size sequence is diminishing demonstrates that the sequence generated by each of the two methods strongly converges to the solution to the problem under certain assumptions convergence rate analysis of the two methods under certain situations is provided to illustrate the two methods efficiency this paper also discusses nonsmooth convex optimization over sublevel sets of convex functions and provides numerical comparisons that demonstrate the effectiveness of the proposed methods

convergence rate of distributed admm over networks we propose a new distributed algorithm based on alternating direction method of multipliers admm to minimize sum of locally known convex functions using communication over a network this optimization problem emerges in many applications in distributed machine learning and statistical estimation our algorithm allows for a general choice of the communication weight matrix which is used to combine the iterates at different nodes we show that when functions are convex both the objective function values and the feasibility violation converge with rate o 1 t where t is the number of iterations we then show that when functions are strongly convex and have lipschitz continuous gradients the sequence generated by our algorithm converges linearly to the optimal solution in particular an epsilon optimal solution can be computed with o left sqrt kappa f log 1 epsilon right iterations where kappa f is the condition number of the problem our analysis highlights the effect of network and communication weights on the convergence rate through degrees of the nodes the smallest nonzero eigenvalue and operator norm of the communication matrix

distributed adaptive convex optimization on directed graphs via continuous time algorithms this note considers the distributed optimization problem on directed graphs with nonconvex local objective functions and the unknown network connectivity a new adaptive algorithm is proposed to minimize a differentiable global objective function by introducing dynamic coupling gains and updating the coupling gains using relative information of system states the nonconvexity of local objective functions unknown network connectivity and the uncertain dynamics caused by locally lipschitz gradients are tackled concurrently consequently the global asymptotic convergence is established when the global objective function is strongly convex and the gradients of local objective functions are only locally lipschitz when the communication graph is strongly connected and weight balanced the algorithm is independent of any global information then the algorithm is naturally extended to unbalanced directed graphs by using the left eigenvector of the laplacian matrix associated with the zero eigenvalue several numerical simulations are presented to verify the results

incremental proximal methods for large scale convex optimization we consider the minimization of a sum sum i 1 mf i x consisting of a large number of convex component functions f i for this problem incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective we propose new incremental methods consisting of proximal iterations applied to single components as well as combinations of gradient subgradient and proximal iterations we provide a convergence and rate of convergence analysis of a variety of such methods including some that involve randomization in the selection of components we also discuss applications in a few contexts including signal processing and inference machine learning

reaching an optimal consensus dynamical systems that compute intersections of convex sets in this paper multi agent systems minimizing a sum of objective functions where each component is only known to a particular node is considered for continuous time dynamics with time varying interconnection topologies assuming that each node can observe a convex solution set of its optimization component and the intersection of all such sets is nonempty the considered optimization problem is converted to an intersection computation problem by a simple distributed control rule the considered multi agent system with continuous time dynamics achieves not only a consensus but also an optimal agreement within the optimal solution set of the overall optimization objective directed and bidirectional communications are studied respectively and connectivity conditions are given to ensure a global optimal consensus in this way the corresponding intersection computation problem is solved by the proposed decentralized continuous time algorithm we establish several important properties of the distance functions with respect to the global optimal solution set and a class of invariant sets with the help of convex and non smooth analysis

distributed optimal in network resource allocation algorithm design via a control theoretic approach abstract in this paper we consider an in network optimal resource allocation problem with multiple demand equations we propose a novel distributed continuous time algorithm that solves the problem over strongly connected and weight balanced digraph network topologies when the local cost functions are strongly convex we also discuss the extension of our convergence guarantees to dynamically changing topologies finally we show that if the network is an undirected connected graph we can guarantee stability and convergence of our algorithm for problems involving local convex functions this convergence guarantee is to a point in the set of minimizers of our optimal resource allocation problem the design and analysis of our algorithm are carried out using a control theoretic approach we demonstrate our results through a numerical example

temporal integration of loudness in listeners with hearing losses of primarily cochlear origin to investigate how hearing loss of primarily cochlear origin affects the loudness of brief tones loudness matches between 5 and 200 ms tones were obtained as a function of level for 15 listeners with cochlear impairments and for seven age matched controls three frequencies usually 0 5 1 and 4 khz were tested in each listener using a two interval two alternative forced choice 2i 2afc paradigm with a roving level up down adaptive procedure results for the normal listeners generally were consistent with published data e g j acoust soc am 99 1633 1644 1996 the amount of temporal integration defined as the level difference between equally loud short and long tones varied nonmonotonically with level and was largest at moderate levels no consistent effect of frequency was apparent the impaired listeners varied widely but most showed a clear effect of level on the amount of temporal integration overall their results appear consistent with expectations based on knowledge of the general properties of their loudness growth functions and the equal loudness ratio hypothesis which states that the loudness ratio between equal spl long and brief tones is the same at all spls the impaired listeners amounts of temporal integration at high spls often were larger than normal although it was reduced near threshold when evaluated at equal sls the amount of temporal integration well above threshold usually was in the low end of the normal range two listeners with abrupt high frequency hearing losses slopes 50 db octave showed larger than normal maximal amounts of temporal integration 40 to 50 db this finding is consistent with the shallow loudness functions predicted by our excitation pattern model for impaired listeners in modeling sensorineural hearing loss edited by w jesteadt erlbaum mahwah nj 1997 pp 187 198 loudness functions derived from impaired listeners temporal integration functions indicate that restoration of loudness in listeners with cochlear hearing loss usually will require the same gain whether the sound is short or long

the relation between loudness and intensity difference limens for tones in quiet and noise backgrounds recent studies of the relation between loudness and intensity difference limens dls suggest that if two tones of the same frequency are equally loud they will have equal relative dls r s schlauch and c c wier j speech hear res 30 13 20 1987 j j zwislocki and h n jordan j acoust soc am 79 772 780 1986 to test this hypothesis loudness matches and intensity dls for a 1000 hz pure tone in quiet and in a 40 db spl spectrum level broadband noise were obtained for four subjects with normal hearing the dls were obtained in both gated and continuous pedestal conditions contrary to previous reports equally loud tones do not yield equal relative dls at several midintensities in the gated condition and at many intensities in the continuous condition while the equal loudness equal relative dl hypothesis is not supported by the data the relation between loudness and intensity discrimination appears to be well described by a model reported by houtsma et al j acoust soc am 68 807 813 1980