pitch strength of regular interval click trains with different length runs of regular intervals click trains were generated with first and second order statistics following kaernbach and demany j acoust soc am 104 2298 2306 1998 first order intervals are between successive clicks while second order intervals are those between every other click click trains were generated with a repeating alternation of fixed and random intervals which produce a pitch at the reciprocal of the duration of the fixed interval the intervals were then randomly shuffled and compared to the unshuffled alternating click trains in pitch strength comparison experiments in almost all comparisons for the first order interval stimuli the shuffled interval click trains had a stronger pitch strength than the unshuffled interval click trains the shuffled interval click trains only produced stronger pitches for second order interval stimuli when the click trains were unfiltered several experimental conditions and an analysis of runs of regular and random intervals in these click trains suggest that the auditory system is sensitive to runs of regular intervals in a stimulus that contains a mix of regular and random intervals these results indicate that fine structure regularity plays a more important role in pitch perception than randomness and that the long term autocorrelation function or spectra of these click trains are not good predictors of pitch strength

single machine scheduling to minimize total weighted earliness subject to minimal number of tardy jobs abstract motivated by just in time manufacturing we consider a single machine scheduling problem with dual criteria i e the minimization of the total weighted earliness subject to minimum number of tardy jobs we discuss several dominance properties of optimal solutions we then develop a heuristic algorithm with time complexity o n 3 and a branch and bound algorithm to solve the problem the computational experiments show that the heuristic algorithm is effective in terms of solution quality in many instances while the branch and bound algorithm is efficient for medium size problems

the relationship between frequency selectivity and pitch discrimination sensorineural hearing loss this study tested the relationship between frequency selectivity and the minimum spacing between harmonics necessary for accurate fo discrimination fundamental frequency difference limens fo dls were measured for ten listeners with moderate sensorineural hearing loss snhl and three normal hearing listeners for sine and random phase harmonic complexes bandpass filtered between 1500 and 3500 hz with fo s ranging from 75 to 500 hz or higher all listeners showed a transition between small good fo dls at high fo s and large poor fo dls at low fo s although the fo at which this transition occurred fo tr varied across listeners three measures thought to reflect frequency selectivity were significantly correlated to both the fo tr and the minimum fo dl achieved at high fo s 1 the maximum fo for which fo dls were phase dependent 2 the maximum modulation frequency for which amplitude modulation and quasi frequency modulation were discriminable and 3 the equivalent rectangular bandwidth of the auditory filter estimated using the notched noise method these results provide evidence of a relationship between fo discrimination performance and frequency selectivity in listeners with snhl supporting spectral and spectro temporal theories of pitch perception that rely on sharp tuning in the auditory periphery to accurately extract fo information

embedding problem of fuzzy number space part ii abstract using a concrete structure into which we embed the fuzzy number space e1 several necessary and sufficient conditions of fuzzy set valued functions are given by means of abstract function theory

stochastic scheduling on parallel machines subject to random breakdowns to minimize expected costs for earliness and tardy jobs this paper addresses a stochastic scheduling problem in which a set of independent jobs are to be processed by a number of identical parallel machines under a common deadline each job has a processing time which is a random variable with an arbitrary distribution each machine is subject to stochastic breakdowns which are characterized by a poisson process the deadline is an exponentially distributed random variable the objective is to minimize the expected costs for earliness and tardiness where the cost for an early job is a general function of its earliness while the cost for a tardy job is a fixed charge optimal policies are derived for cases where there is only a single machine or are multiple machines the decision maker can take a static policy or a dynamic policy and job preemptions are allowed or forbidden in contrast to their deterministic counterparts which have been known to be np hard and are thus intractable from a computational point of view we find that optimal solutions for many cases of the stochastic problem can be constructed analytically

frequency resolution and discrimination of constant and dynamic tones in normal and hearing impaired listeners frequency resolution and three tasks of frequency discrimination were measured at 500 and 4000 hz in 12 normal and 12 hearing impaired listeners a three interval two alternative forced choice procedure was used frequency resolution was measured with an abbreviated psychoacoustical tuning curve frequency discrimination was measured for 1 a fixed frequency standard and target 2 a fixed frequency standard and a frequency transition target and 3 frequency transition standard and a frequency transition target the 50 ms frequency transitions had the same final frequency as the standards but the initial frequency was lowered to obtain about 79 discrimination performance there was a strong relationship between poor frequency resolution and elevated pure tone thresholds but only a very weak relationship between poor frequency discrimination and elevated pure tone thresholds several hearing impaired listeners had normal discrimination performance together with pure tone thresholds of 80 90 db hl a slight correlation was found between word recognition and frequency discrimination but a detailed comparison of the phonetic errors and either the frequency discrimination or frequency resolution tasks failed to suggest any consistent interdependencies these results are consistent with previous work that has suggested that frequency resolution and frequency discrimination are independent processes

sound quality characteristics of refrigerator noise in real living environments with relation to psychoacoustical and autocorrelation function parameters psychoacoustical and autocorrelation function acf parameters were employed to describe the temporal fluctuations of refrigerator noise during starting transition into from the stationary phase and termination of operation the temporal fluctuations of refrigerator noise include a click at start up followed by a rapid increase in volume a change of pitch and termination of the operation subjective evaluations of the noise of 24 different refrigerators were conducted in a real living environment the relationship between objective measures and perceived noisiness was examined by multiple regression analysis sound quality indices were developed based on psychoacoustical and acf parameters the psychoacoustical parameters found to be important for evaluating noisiness in the stationary phase were loudness and roughness the relationship between noisiness and acf parameters shows that sound energy and its fluctuations are important for evaluating noisiness also refrigerator sounds that had a fluctuat

numerical methods for fuzzy system of linear equations in this paper numerical algorithms for solving fuzzy system of linear equations fsle are considered schemes based on the iterative jacobi and gauss sidel methods in detail are discussed and there are followed by convergence theorems algorithms are illustrated by solving some numerical examples

robust controller design for stochastic nonlinear systems via convex optimization this paper presents a new nonlinear control design framework called convex optimization based stochastic steady state tracking error minimization cvstem for a class of ito stochastic nonlinear systems including stochastic lagrangian systems this state feedback controller design involves the use of multiple state dependent coefficient sdc models of a nonlinear system equation and computes its controller parameters by solving a convex optimization problem in order to minimize an upper bound of the steady state tracking error this problem is shown to be equivalent to the original nonlinear optimization problem of minimizing the upper bound the exponential stability and robustness properties due to the state dependent riccati inequality are proven using stochastic contraction analysis discrete time stochastic incremental contraction analysis with respect to a state and time dependent metric is also presented along with its explicit connection to continuous time contraction analysis a result of simulation is used to validate the superiority of the proposed controller compared to a known nonlinear controller a pid controller and an h infinity controller

finite element analysis with uncertain probabilities this paper presents a general method for the finite element analysis of linear mechanical systems by taking into account probability density functions whose parameters are affected by fuzziness within this framework the standard perturbation based stochastic finite element method is relaxed in order to incorporate uncertain probabilities in static dynamic and modal analyses general formulae are provided for assessing the fuzzy structural reliability and several typologies of optimization problems reliability based design robust design robust reliability based design are formalized in doing this the credibility theory is extensively used to extract qualified crisp data from the available set of fuzzy results so that standard optimizers can be adopted to solve the most important design problems it is shown that the proposed methodology is a general and versatile tool for finite element analyses because it is able to consider both probabilistic and non probabilistic sources of uncertainties such as randomness vagueness ambiguity and imprecision

duality in fuzzy linear systems according to fuzzy arithmetic dual fuzzy linear system can not be replaced by a fuzzy linear system in this paper we investigate the existence of a solution of duality fuzzy linear equation systems two necessary and sufficient conditions for the solution existence are given

rigorous sensitivity analysis for systems of linear and nonlinear equations methods are presented for performing a rigorous sensitivity analysis of numerical problems with independent noncorrelated data for general systems of linear and nonlinear equations the methods may serve for the following two purposes first to bound the dependency of the solution on changes in the input data in contrast to condition numbers a componentwise sensitivity analysis of the solution vector is performed second to estimate the true solution set for problems the input data of which are afflicted with tolerances the methods presented are very effective with the additional property that due to an automatic error control mechanism every computed result is guaranteed to be correct examples are given for linear systems demonstrating that the computed bounds are in general very sharp interesting comparisons to traditional condition numbers are given

iterated rippled noise discrimination at long durations iterated rippled noise irn was used to study discrimination of irn stimuli with a lower number of iterations from irn stimuli with a higher number of iterations as a function of stimulus duration 100 2000 ms such irn stimuli differ in the strength of the repetition pitch in some cases the gain used to generate irn stimuli was adjusted so that both irn stimuli in the discrimination task had the same height of the first peak in the autocorrelation function or autocorrelogram in previous work involving short duration irn stimuli 500 ms listeners were not able to discriminate between irn stimuli that had different numbers of iterations but the same height of the first peak in the autocorrelation function in the current study irn discrimination performance improved with increases in duration even in cases when the height of the first peak in the autocorrelation was the same for the two irn stimuli thus future studies involving discrimination of irn stimuli may need to use longer durations 1 s or greater than those that have been used in the past

vertex method for computing functions of fuzzy variables abstract this paper is to introduce a new approach the vertex method for computing functions of fuzzy variables the method is based on the cut concept and interval analysis the vertex method can avoid abnormality due to the discretization technique on the variables domain and the widening of the resulting function value set due to multi occurrence of variables in the functional expression by conventional interval analysis methods the algorithm is very easy to implement and can be applied to many practical problems some examples are given to illustrate the applications

model free control of nonlinear stochastic systems with discrete time measurements consider the problem of developing a controller for general nonlinear and stochastic systems where the equations governing the system are unknown using discrete time measurement this paper presents an approach for estimating a controller without building or assuming a model for the system such an approach has potential advantages in accommodating complex systems with possibly time varying dynamics the controller is constructed through use of a function approximator such as a neural network or polynomial this paper considers the use of the simultaneous perturbation stochastic approximation algorithm which requires only system measurements a convergence result for stochastic approximation algorithms with time varying objective functions and feedback is established it is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite difference gradient approximations

on the dichotic pitch of simultaneously presented interaurally delayed white noises implications for binaural theory a dichotic pitch known as fourcin pitch fp is perceived when two independent interaurally delayed white noises are presented simultaneously experiments in the past mainly dealt with stimulus situations where one interaural delay was smaller than 4 ms and the other was in the range 0 10 ms here experiments are reported showing a novel pitch percept that occurs when one noise is interaurally delayed at the left ear and the other noise is about equally delayed at the right ear for delays in the range of 4 10 ms it is shown that for both the previously reported fp and the novel pitch the central spectrum cs theory raatgever and bilsen j acoust soc am 80 429 441 1986 provides a correct prediction of both the pitch value and the lateral position of the pitch image where other current theories partly or completely fail further experiments indicate that the lateralized position of the pitch image is essentially not influenced by an interaural intensity difference iid this is also predicted by the cs model and leads to the generalized conclusion that interaural time and intensity differences are processed separately in the auditory system until at least the level where the dichotic pitch is generated

the frequency range applicable to pitch identification based upon the auto correlation function model abstract pitch identification experiments were conducted to determine the upper boundary of the frequency range within which the autocorrelation function acf model described by ando see reference 16 is applicable to the phenomenon of the missing fundamental of a complex tone pitch matching tests were conducted using 1 complex tones consisting of 2 f 3 f and 4 f where f denotes the fundamental frequencies of 0 5 1 0 1 2 1 6 2 0 or 3 0 khz and 2 complex tones consisting of 2 f and 3 f these tests showed that for both kinds of complex tones the acf model can account for the perception of pitch when the fundamental frequency is below 1200 hz

fuzzy linear systems of the form a1x b1 a2x b2 linear systems of equations with uncertainty on the parameters play a major role in several applications in various areas such as economics finance engineering and physics this paper investigates fuzzy linear systems of the form a 1x b 1 a 2x b 2 with a 1 a 2 square matrices of fuzzy coefficients and b 1 b 2 fuzzy number vectors the aim of this paper is twofold first we clarify the link between interval linear systems and fuzzy linear systems second a generalization of the vector solution of buckley and qu solving systems of linear fuzzy equations fuzzy sets and systems 43 1991 33 43 to the fuzzy system a 1x b 1 a 2x b 2 is provided in particular we give the conditions under which the system has a vector solution and we show that the linear systems ax b and a 1x b 1 a 2x b 2 with a a 1 a 2 and b b 2 b 1 have the same vector solutions moreover in order to find the vector solution a simple algorithm is proposed

proof of quasi adaptivity for the m measurement feedback class of stochastic control policies it is shown that the m measurement feedback mm policy for nonlinear stochastic control performs as well or better than the open loop optimal policy and hence becomes one of only a few suboptimal policies presently known to be quasi adaptive in the sense of witsenhausen

a forward method for optimal stochastic nonlinear and adaptive control a computational approach is taken to solve the optimal partially observed nonlinear stochastic control problem the approach is to systematically solve the stochastic dynamic programming equations forward in time using a nested stochastic approximation technique although computationally intensive this provides a straightforward numerical solution for this class of problems and provides an alternative to the usual curse of dimensionality associated with solving the dynamic programming equation backwards in time in particular the curse is seen to take a new form where the amount of computation depends on the amount of uncertainty in the problem and the length of the horizon as a matter of more practical interest it is shown that the cost degrades monotonically as the complexity of the algorithm is reduced this provides a strategy for suboptimal control with clear performance computation trade offs a numerical study focusing on a generic optimal stochastic adaptive control example is included to demonstrate the feasibility of the method

on using a cuts to evaluate fuzzy equations abstract consider an equation y f x1 xn where the extension principle is used to find y f x 1 x n when we subtitute fuzzy numbers x i for the xi 1 i n if x i denotes an cut of x i then we argue that for only certain simple equations will one obtain y equal to f x 1 x n where f is evaluated using interval arithmetic

receding horizon control of nonlinear systems the receding horizon control strategy provides a relatively simple method for determining feedback control for linear or nonlinear systems the method is especially useful for the control of slow nonlinear systems such as chemical batch processes where it is possible to solve sequentially open loop fixed horizon optimal control problems online the method has been shown to yield a stable closed loop system when applied to time invariant or time varying linear systems it is shown that the method also yields a stable closed loop system when applied to nonlinear systems

worst case scenario analysis for elliptic problems with uncertainty this work studies linear elliptic problems under uncertainty the major emphasis is on the deterministic treatment of such uncertainty in particular this work uses the worst scenario approach for the characterization of uncertainty on functional outputs quantities of physical interest assuming that the input data belong to a given functional set eventually infinitely dimensional this work proposes numerical methods to approximate the corresponding uncertainty intervals for the quantities of interest numerical experiments illustrate the performance of the proposed methodology

an autocorrelation model with place dependence to account for the effect of harmonic number on fundamental frequency discrimination fundamental frequency f0 difference limens dls were measured as a function of f0 for sine and random phase harmonic complexes bandpass filtered with 3 db cutoff frequencies of 2 5 and 3 5 khz low region or 5 and 7 khz high region and presented at an average 15 db sensation level approximately 48 db spl per component in a wideband background noise fundamental frequencies ranged from 50 to 300 hz and 100 to 600 hz in the low and high spectral regions respectively in each spectral region f0 dls improved dramatically with increasing f0 as approximately the tenth harmonic appeared in the passband generally f0 dls for complexes with similar harmonic numbers were similar in the two spectral regions the dependence of f0 discrimination on harmonic number presents a significant challenge to autocorrelation ac models of pitch in which predictions generally depend more on spectral region than harmonic number a modification involving a lag window is proposed and tested restricting the ac repr

detection of partially filled gaps in noise and the temporal modulation transfer function results of experiments on the detection of silent intervals or gaps in broadband noise are reported for normal hearing listeners in some preliminary experiments a gap threshold of about 2 ms was measured this value was independent of the duration of the noise burst variation of the noise level on each presentation or the temporal position of the gap within the noise burst in the main experiments the thresholds for partial decrements in the noise waveform as well as brief increments were determined as predicted by a model that assumes a single fixed peak to valley detection ratio thresholds for increments are slightly higher than thresholds for decrements when the signal is measured as the change in rms noise level a first order model describes the temporal properties of the auditory system as a low pass filter with a 7 to 8 ms time constant temporal modulation transfer functions were determined for the same subjects and the estimated temporal parameters agreed well with those estimated from the gap detection data more detailed modeling was carried out by simulating viemeister s three stage temporal model simulations using an initial stage bandwidth of 4000 hz and a 3 ms time constant for the low pass filter generate data that are very similar to those obtained from human subjects in both modulation and gap detection

stochastic scheduling with release dates and due dates we consider stochastic scheduling problems in which the processing times of jobs are independent exponentially distributed random variables the release dates are random variables with an arbitrary joint distribution and the due dates are random variables with a joint distribution that satisfies certain conditions our development establishes simple policies that minimize such criteria as the expected weighted sum of completion times and the expected weighted number of late jobs these results contrast markedly with the deterministic counterparts of these models for which no polynomial time algorithms are known

cancellation model of pitch perception a model of pitch perception is presented involving an array of delay lines and inhibitory gating neurons in response to a periodic sound a minimum appears in the pattern of outputs of the inhibitory neurons at a lag equal to the period of the sound the position of this minimum is the cue to pitch the model is similar to the autocorrelation model of pitch multiplication being replaced by an operation similar to subtraction and maxima by minima the two models account for a wide class of pitch phenomena in very much the same way the principal goal of this paper is to demonstrate this fact several features of the cancellation model may be to its advantage it is closely related to the operation of harmonic cancellation that can account for segregation of concurrent harmonic stimuli it can be generalized to explain the perception of multiple pitches and it shows a greater degree of sensitivity to phase than autocorrelation which may allow it to explain certain phenomena that autocorrelation cannot account for

v shape property for job sequences that minimize the expected completion time variance abstract we consider the problem of sequencing n jobs with random processing time on a single machine so as to minimize the expected variance of job completion times our main result is a new sufficient condition for an optimal sequence to be v shaped in terms of the mean processing times when n 3 we show that this condition is satisfied by a wide variety of problem instances including those in which the processing times follow different patterns of distributions this result relaxes a condition proposed before

solutions of algebraic equations involving generalized fuzzy numbers abstract this paper deals with algebraic equations involving generalized fuzzy numbers with continuous membership functions the generalized fuzzy number defined in this paper is a general name for fuzzy numbers fuzzy intervals crisp numbers and interval numbers three important properties of the generalized fuzzy numbers with continuous membership functions are introduced as the basis for deriving the solvability criterion the sufficient and necessary condition for solving a x c is derived the sufficient and necessary condition for solving a x c and a x c when a and c are nonzero generalized fuzzy numbers is also derived in this paper instead of the inverse operation method which fails for fuzzy sets inverse operations on the boundary points of level set intervals for continuous membership functions are used when the derived criteria of solvability are satisfied a unique solution rather than a solution set is obtained

psychophysical evidence against the autocorrelation theory of auditory temporal processing nowadays it is widely believed that the temporal structure of the auditory nerve fibers response to sound stimuli plays an important role in auditory perception an influential hypothesis is that information is extracted from this temporal structure by neural operations akin to an autocorrelation algorithm the goal of the present work was to test this hypothesis the stimuli consisted of sequences of unipolar clicks that were high pass filtered and mixed with low pass noise so as to exclude spectral cues in experiment 1 interfering clicks were inserted in an otherwise periodic isochronous click sequence each click belonging to the periodic sequence was followed after a random portion of the period by one interfering click this disrupted the detection of temporal regularity even when the interfering clicks were 5 db less intense than the periodic clicks experiments 2 4 used click sequences that showed a single peak in their autocorrelation functions for some sequences this peak originated from first order temporal regularities that is from the temporal relations between consecutive clicks for other sequences the peak originated instead from second order regularities relative to nonconsecutive clicks the detection of second order regularities appeared to be much more difficult than the detection of comparable first order regularities overall these results do not tally with the current autocorrelation models of temporal processing they suggest that the extraction of temporal information from a group of closely spaced spectral components makes no use of time intervals between nonconsecutive peaks of the amplitude envelope

primitive stream segregation of tone sequences without differences in fundamental frequency or passband peripheral channeling theorists argue that differences in excitation pattern between successive sounds are necessary for stream segregation to occur the component phases of complex tones comprising unresolved harmonics f0 100 hz were manipulated to change pitch and timbre without changing the power spectrum in experiment 1 listeners compared two alternating sequences of tones a and b one sequence was isochronous tone duration 60 ms intertone interval 40 ms the other began isochronously but the progressive delay of tone b made the rhythm irregular subjects had to identify the sequence with irregular rhythm stream segregation makes this task more difficult a and b could differ in passband 1250 2500 hz 1768 3536 hz 2500 5000 hz component phase cosine alternating random or both stimuli were presented at 70 db spl in pink noise dissimilarity in either passband or phase increased discrimination thresholds moreover phase differences raised threshold even when there was no passband difference in experiment 2 listeners judged moment by moment the grouping of long aba aba sequences the measure was the proportion of time a sequence was heard as segregated the factors that increased segregation were very similar to those that increased threshold in experiment 1 overall the findings indicate that substantial stream segregation can occur without differences in power spectrum it is concluded that differences in peripheral channeling are not a requirement for stream segregation

temporal gap detection measured with multiple sinusoidal markers effects of marker number frequency and temporal position detection thresholds were measured for silent temporal gaps within combinations of two three or four sinusoidal markers i e combinations of one or two pre gap markers with one or two post gap markers the markers were selected from the frequency range 2000 3100 hz sinusoidal frequencies f1 and f4 were used as pre gap markers while f2 and f3 served as post gap markers temporal gap detection tgd thresholds were measured from sets of three normal hearing adults who tracked 70 7 correct detection thresholds adaptively across blocks of 50 two interval two alternative forced choice trials for symmetric marker conditions where pre and post gap markers were equivalent in frequency e g f1 f2 or f1 f2 and f3 f4 tgd thresholds were 10 ms however for asymmetric marker frequency alignments across the silent gap including stimulus configurations where only three markers were presented on a trial e g f1 f2 f2 f3 no f4 performance was highly variable and was dramatically disrupted by the

age related changes in within and between channel gap detection using sinusoidal stimuli pure tone gap stimuli with identical within channel or dissimilar between channel marker frequencies of 1 and 2 khz were presented to young and old listeners in a two interval forced choice gap detection task to estimate the influence of extraneous duration cues on gap detection thresholds in the between channel conditions were obtained for two different sets of reference stimuli reference stimuli that were matched to the overall duration of the gap stimulus i e two markers plus the gap and reference stimuli that were fixed at the combined duration of the two markers excluding the gap results from within channel conditions were consistent with previous studies i e there were small but highly reliable age differences smaller gap thresholds at longer marker durations and an interaction between the two variables in between channel conditions however age differences were not as clear cut rather the effect of age varied as a function of duration cue and was more pronounced when stimuli were matched for overall duration than when the duration of the reference tone was fixed

gap detection in single and multiple channel stimuli by laura cochlear implantees gap detection thresholds were determined for different complex patterns of electrical stimulation in four postlingually deafened laura cochlear implantees to examine the nature of within and across channel auditory processes in more detail gap detectability was examined as a function of stimulus complexity one two or three channels channel distance within and across multichannel pre and post gap markers stimulus asymmetry and pulse rate all markers roved in duration from 200 to 500 ms to ensure that subjects were not using overall stimulus duration as a cue gap detection thresholds for all subjects were short 5 ms when the pre and post gap markers stimulated the same single or multiple channels even when the distance between simultaneously stimulated channels was large exp 1 for some subjects gap detectability was more difficult in the across channel condition when the pre and post gap markers each stimulated different channels although performance improved substantially in most subjects after extensive training exp 2 additional tests with random maskers also suggest that neural interaction only affects performance mildly and that the magnitude of the gap detection threshold probably depends more on the subject s cognitive in ability to attend to the temporal gap than on the temporal acuity of their auditory system other stimulus conditions showed a difference in performance related to the order of the markers gap thresholds were longer when the pre gap marker stimulated one channel and the post gap marker stimulated two or more channels than vice versa exp 3 in addition gap thresholds of three of the subjects increased with decreasing pulse rate from 1250 to 400 pps a finding which may be related to the rate of the speech processing strategies used by each individual implantee exp 4

the adomian decomposition method for fuzzy system of linear equations in this paper the application of the adomian method for solving fuzzy system of linear equations fsle is considered for a fsle has been shown that the adomian decomposition method is equivalent to the jacobi iterative method appl math comput in press the algorithm is illustrated by solving some numerical examples

the effect of cross channel synchrony on the perception of temporal regularity temporal models of pitch are based on the assumption that the auditory system measures the time intervals between neural events and that pitch corresponds to the most common time interval the current experiments were designed to test whether time intervals are analyzed independently in each peripheral channel or whether the time interval analysis in one channel is affected by synchronous activity in other channels regular and irregular click trains were filtered into narrow frequency bands to produce target and flanker stimuli the threshold for discriminating a regular target from an irregular distracter click train was measured in the presence of an irregular masker click train in the target band as a function of the frequency separation between the target band and a flanker band the flanker click train was either regular or irregular the threshold for detecting the regular target was 5 7 db lower when the flanker was regular the data indicate that the detection of temporal regularity and thus pitch involves cross channel processes that can operate over widely separated channels model simulations suggest that these cross channel processes occur after the time interval extraction stage and that they depend on the similarity or consistency of the time interval patterns in the relevant channels

fuzzy linear systems a general fuzzy linear system is investigated using the embedding approach conditions for the existence of a unique fuzzy solution to n n linear system are derived and a numerical procedure for calculating the solution is designed the applicability of the proposed model is illustrated with examples

systems of linear interval equations this paper presents theory and methods for computing the exact bounds on the solution of a system of n linear equations in n variables whose coefficients and right hand sides vary in some real intervals finite and iterative methods are given based on results from linear complementarity theory also regularity conditions regularity testing and computing the exact inverse of an interval matrix are dealt with

auditory stream segregation on the basis of amplitude modulation rate in this study auditory stream segregation based on differences in the rate of envelope fluctuations in the absence of spectral and temporal fine structure cues was tested the temporal sequences to segregate were composed of fully amplitude modulated am bursts of broadband noises a and b all sequences were built by the reiteration of a aba triplet where a modulation rate was fixed at 100 hz and b modulation rate was variable the first experiment was devoted to measuring the threshold difference in am rate leading subjects to perceive the sequence as two streams as opposed to just one the results of this first experiment revealed that subjects generally perceived the sequences as a single perceptual stream when the difference in am rate between the a and b noises was smaller than 0 75 oct and as two streams when the difference was larger than about 1 00 oct these streaming thresholds were found to be substantially larger than and not related to the subjects modulation rate discrimination thresholds the results of a second experiment demonstrated that am rate based streaming was adversely affected by decreases in am depth but that segregation remained possible as long as the am of either the a or b noises was above the subject s am detection threshold the results of a third experiment indicated that am rate based streaming effects were still observed when the modulations applied to the a and b noises were set individually either at a constant level in db above am detection threshold or at levels at which they were of the same perceived strength this finding suggests that am rate based streaming is not necessarily mediated by perceived differences in am depth altogether the results of this study indicate that sequential sounds can be segregated on the sole basis of differences in the rate of their temporal fluctuations in the absence of other temporal or spectral cues

evidence for an across frequency between channel process in asymptotic monaural temporal gap detection monaurally measured temporal gap detection tgd thresholds characteristically increase as the frequency difference is increased over a range of about half an octave to an octave between two sinusoids that mark the onset and offset of the silent gap for greater sinusoidal frequency separations the tgd thresholds often become asymptotic this pattern probably reflects two different processes the first process likely reflects within channel processing within a single auditory filter or channel the second process is less certain but may reflect between channel processing of the silent gap stimulus across two or more independent frequency channels to evaluate the hypothesis that asymptotic monaural gap detection can be explained by a simple between channel process tgd thresholds were measured as a function of frequency separation between a pregap sinusoid presented to the left ear channel 1 and a postgap sinusoid of higher frequency presented to the right ear channel 2 the rationale for dichotic presentation of the sinusoidal markers and gap signal followed from the fact that the gap detection task must be performed between two independent channels by combining the outputs from each channel ear and recovering the gap information centrally the resulting tgd thresholds for pregap sinusoids from 250 to 4000 hz were relatively invariant and increased only slightly with increasing marker frequency separation the average tgd thresholds for four listeners were in the range of 30 to 40 ms which corresponded closely with their asymptotic tgd thresholds for the same set of stimulus conditions measured monaurally this correspondence of the two data sets supports an across frequency between channel process for asymptotic monaural gap detection at marker frequency separations greater than about half an octave

solving systems of linear fuzzy equations abstract in this paper we wish to construct solutions for x to the fuzzy matrix equation ax b when the elements in a and b are triangular fuzzy numbers a is square and always non singular we argue that the previous method of solving for x based on the extension principle and regular fuzzy arithmetic should be abandoned since it too often fails to produce a solution we present six new solutions of which we show that five are identical we then adopt the common value x of these five new solutions as our solution to ax b we show that x is a fuzzy vector which is the generalization to rn of real fuzzy numbers we also show how these results pertain to and extend previous research on this problem within the area of interval analysis

the truncated second order nonlinear filter revisited by rederiving the truncated second order nonlinear filter it is shown that the original derivations of this filter contain errors or at least illogical approximations the so called modified truncated second order nonlinear filter is furthermore shown to be the correct form of this filter provided a small correction is made in the discrete time case

pitch strength and pitch dominance of iterated rippled noises in hearing impaired listeners reports using a variety of psychophysical tasks indicate that pitch perception by hearing impaired listeners may be abnormal contributing to difficulties in understanding speech and enjoying music pitches of complex sounds may be weaker and more indistinct in the presence of cochlear damage especially when frequency regions are affected that form the strongest basis for pitch perception in normal hearing listeners in this study the strength of the complex pitch generated by iterated rippled noise was assessed in normal hearing and hearing impaired listeners pitch strength was measured for broadband noises with spectral ripples generated by iteratively delaying a copy of a given noise and adding it back into the original octave band pass versions of these noises also were evaluated to assess frequency dominance regions for rippled noise pitch hearing impaired listeners demonstrated consistently weaker pitches in response to the rippled noises relative to pitch strength in normal hearing listeners

effect of masker level on overshoot overshoot refers to the phenomenon where signal detectability improves for a short duration signal as the onset of that signal is delayed relative to the onset of a longer duration masker a popular explanation for overshoot is that it reflects short term adaptation in auditory nerve fibers in this study overshoot was measured for a 10 ms 4 khz signal masked by a broadband noise in the first experiment masker duration was 400 ms and signal onset delay was 1 or 195 ms masker spectrum level ranged from 10 50 db spl overshoot was negligible at the lowest masker levels grew to about 10 15 db at the moderate masker levels but declined and approached 0 db at the highest masker levels in the second experiment the masker duration was reduced to 100 ms and the signal was presented with a delay of 1 or 70 ms masker spectrum level was 10 30 or 50 db spl overshoot was about 10 db for the two lower masker levels but about 0 db at the highest masker level the results from the second experiment suggest that the decline in overshoot at high masker levels is probably not due to auditory fatigue it is suggested instead that the decline may be attributable to the neural response at high levels being dominated by those auditory nerve fibers that do not exhibit short term adaptation i e those with low spontaneous rates and high thresholds

stochastic single machine scheduling with quadratic early tardy penalties we address the problem of scheduling n jobs on a single machine which is subject to random breakdowns to minimize an expected sum of nonregular penalty functions a simple recourse model is considered when the penalty function is the squared deviation of job completion times from a common due date and a deterministic equivalent objective function is developed characterizations of optimal schedules for this quadratic objective function are established both when the common due date is a decision variable and when it is given and fixed most importantly the v shaped nature of optimal schedules is investigated for a class of poisson processes n t t 0 describing the number of breakdowns in the interval 0 t in addition relationships to a class of bicriteria models are demonstrated

gap detection with sinusoids and noise in normal impaired and electrically stimulated ears thresholds for the detection of temporal gaps were measured using two types of signals to mark the gaps bandpass filtered noises and sinusoids the first experiment used seven subjects with relatively flat unilateral moderate cochlear hearing loss the normal ear of each subject was tested both at the same sound pressure level spl as the impaired ear and at the same sensation level sl background noise was used to mask spectral splatter associated with the gap for the noise markers gap thresholds tended to be larger for the impaired ears than for the normal ears when the comparison was made at equal spl the difference was reduced but not eliminated when the comparison was made at equal sl gap thresholds for both the normal and impaired ears decreased as the center frequency increased from 0 5 to 2 0 khz for the sinusoidal markers gap thresholds were often similar for the normal and impaired ears when tested at equal spl and were larger for the normal ears when tested at equal sl gap th

systems of fuzzy equations in structural mechanics systems of linear and nonlinear equations with fuzzy parameters are relevant to many practical problems arising in structure mechanics electrical engineering finance economics and physics in this paper three methods for solving such equations are discussed method for outer interval solution of systems of linear equations depending linearly on interval parameters fuzzy finite element method proposed by rama rao and sensitivity analysis method the performance and advantages of presented methods are described with illustrative examples extended version of the present paper can be downloaded from the web page of the utep i skalna m v rama rao a pownuk systems of fuzzy equations in structural mechanics the university of texas at el paso department of mathematical sciences research reports series texas research report no 2007 01 2007

the role of stimulus complexity spectral overlap and pitch for gap detection thresholds in young and old listeners thresholds for detecting a gap between two complex tones were determined for young listeners with normal hearing and old listeners with mild age related hearing loss the leading tonal marker was always a 20 ms 250 hz complex tone with energy at 250 500 750 and 1000 hz the lagging marker also tonal could differ from the leading marker with respect to fundamental frequency f0 the presence versus absence of energy at f0 and the degree to which it overlapped spectrally with the leading marker all stimuli were presented with steeper 1 ms and less steep 4 ms envelope rise and fall times f0 differences decreases in the degree of spectral overlap between the markers and shallower envelope shape all contributed to increases in gap detection thresholds age differences for gap detection of complex sounds were generally small and constant when gap detection thresholds were measured on a log scale when comparing the results for complex sounds to thresholds obtained for pure tones in a previous study by heinrich and schneider 2006 j acoust soc am 119 2316 2326 thresholds increased in an orderly fashion from markers with identical within channel pure tones to different between channel pure tones to complex sounds this pattern of results was true for listeners of both ages although younger listeners had smaller thresholds overall

neuronal periodicity detection as a basis for the perception of consonance a mathematical model of tonal fusion a mathematical model is presented here to explain the sensation of consonance and dissonance on the basis of neuronal coding and the properties of a neuronal periodicity detection mechanism this mathematical model makes use of physiological data from a neuronal model of periodicity analysis in the midbrain whose operation can be described mathematically by autocorrelation functions with regard to time windows musical intervals produce regular firing patterns in the auditory nerve that depend on the vibration ratio of the two tones the mathematical model makes it possible to define a measure for the degree of these regularities for each vibration ratio it turns out that this measure value is in line with the degree of tonal fusion as described by stumpf tonpsychologie psychology of tones knuf hilversum reprinted 1965 this finding makes it probable that tonal fusion is a consequence of certain properties of the neuronal periodicity detection mechanism together with strong roughness resulting from interval tones with fundamentals close together or close to the octave this neuronal mechanism may be regarded as the basis of consonance and dissonance

the effect of temporal placement on gap detectability the detectability of a masked sinusoid increases as its onset approaches the temporal center of a masker this study was designed to determine whether a similar change in detectability would occur for a silent gap as it was parametrically displaced from the onset of a noise burst gap thresholds were obtained for 13 subjects who completed five replications of each condition in 3 to 13 days six subjects were inexperienced listeners who ranged in age from 18 to 25 years seven subjects were highly experienced and ranged in age from 20 to 78 years the gaps were placed in 150 ms 6 khz low passed noise bursts presented at an overall level of 75 db spl the bursts were digitally shaped at onset and offset with 10 ms cosine squared rise fall envelopes the gated noise bursts were presented in a continuous unfiltered white noise floor attenuated to an overall level of 45 db spl gap onsets were parametrically delayed from the onset of the noise burst defined as the first nonzero point on the waveform envelope by 10 11 13 15 20 40 60 110 120 and 130 ms results of anovas indicated that the mean gap thresholds were longer when the gaps were proximal to signal onset or offset and shorter when the gaps approached the temporal center of the noise burst also the thresholds of the younger highly experienced subjects were significantly shorter than those of the younger inexperienced subjects especially at placements close to signal onset or offset the effect of replication short term practice was not significant nor was the interaction between gap placement and replication post hoc comparisons indicated that the effect of gap placement resulted from significant decreases in gap detectability when the gap was placed close to stimulus onset and offset

solution of the fully fuzzy linear systems using the decomposition procedure abstract this paper tries to extend the adomian decomposition method for solving fully fuzzy linear systems shown as ffls for finding a positive fuzzy vector x that satisfies a x b where a and b are respectively a fuzzy matrix and a fuzzy vector we employ dubois and prade s approximate arithmetic operators on lr fuzzy numbers we also transform the ffls and use the adomian decomposition method for solving an ffls then we compare this method with the jacobi iterative technique additionally we give some numerical examples

further evidence that fundamental frequency difference limens measure pitch discrimination difference limens for complex tones dlcs that differ in f0 are widely regarded as a measure of periodicity pitch discrimination however because f0 changes are inevitably accompanied by changes in the frequencies of the harmonics dlcs may actually reflect the discriminability of individual components to test this hypothesis dlcs were measured for complex tones the component frequencies of which were shifted coherently upward or downward by f 0 25 37 5 or 50 of the f0 yielding fully harmonic f 0 strongly inharmonic f 25 37 5 or odd harmonic f 50 tones if dlcs truly reflect periodicity pitch discriminability they should be larger worse for inharmonic tones than for harmonic and odd harmonic tones because inharmonic tones have a weaker pitch consistent with this prediction the results of two experiments showed a non monotonic dependence of dlcs on f with larger dlcs for f s of 25 or 37 5 than for f s of 0 or 50 of f0 these findings are consistent with

successive over relaxation iterative method for fuzzy system of linear equations in this paper the gauss sidel iterative method in allahviranloo appl math comput in press for solving fuzzy system of linear equations fsle is transformed to the successive over relaxation sor method this method is discussed in detail and followed by convergence theorem algorithm is compared with the gauss sidel method by solving a numerical example

detection of silent temporal gaps in sinusoidal markers gap detection thresholds were measured by forced choice procedure for conditions where the duration of a silent gap was varied adaptively between pairs of sinusoidal markers of the same or different frequency frequencies of the first sinusoid in a pair of markers ranged from f1 500 to 4000 hz second sinusoid marker frequencies f2 included f1 f2 and usually frequencies 2 5 24 and 50 higher than f1 in preliminary studies the role of presentation level e n0 on gap detection was considered preliminary data revealed confounding extraneous factors arising from gating transients and from overall stimulus i e markers gap and or masker duration cues in the main experiments the contributions of these extraneous cues were evaluated with experimental designs aimed at identifying and minimizing the confounding roles of these cues in gap detection for conditions where extraneous gating transient cues were minimized by presenting the sinusoidal markers in a continuous noise masker with random onset phase for the second sinusoid in every pair of markers and overall stimulus duration cues were diminished by randomizing the duration of each marker independently gap detection thresholds increased from 5 to 90 ms as the frequency separation between f1 and f2 was increased by half an octave when the gap detection thresholds were treated as filter attenuation values by normalizing and converting the data into decibels the data were closely fit by the roex filter model on average the listeners performances were modeled well by a constant percentage 7 bandwidth filter centered on f1

generalized hukuhara differentiability of interval valued functions and interval differential equations abstract in the present paper we use a recently proposed generalization of the hukuhara difference for compact convex sets to introduce and study a generalization of the hukuhara differentiability to the case of interval valued functions we also consider several possible definitions for the derivative of an interval valued function recently proposed in the literature and we study connections between them and their properties using these concepts we study interval differential equations local existence and uniqueness of two solutions is obtained together with characterizations of the solutions of an interval differential equation by ode systems several examples are also shown

perturbation analysis of fuzzy linear systems this paper deals with the perturbation analysis of fuzzy linear systems three cases of perturbation are considered a the right hand side is perturbed while the coefficient matrix remains unchanged b the coefficient matrix is perturbed while the right hand side remains unchanged and c both the coefficient matrix and the right hand side are perturbed for all of the three cases the respective relative error bounds for solutions of fuzzy linear system are derived the results are illustrated by numerical examples

deterministic and random single machine sequencing with variance minimization we discuss the problem of scheduling several jobs on a single machine so as to minimize the variance of the jobs completion times by exploiting the well known pooled variance formula we obtain a general formula for the change in variance due to the interchange of two specified jobs whose positions have not been fixed in the sequence this result permits us to obtain explicit optimal sequences for problems with 6 or 7 jobs and to show that schrage s conjecture on positioning the job with the third largest processing time is true for problems with up to 18 jobs we then develop a heuristic procedure based on a variance interchange formula and compare it with other known heuristic methods we also consider a problem never before examined namely the case when processing times are not known deterministically but are random variables we obtain some general results under certain assumptions on the parameters of the distributions of processing times and extend to the random situation many results applicable to the deterministic case finally we give some results for the exponential distribution of processing times

auditory stream segregation in cochlear implant listeners measures based on temporal discrimination and interleaved melody recognition the evidence that cochlear implant listeners routinely experience stream segregation is limited and equivocal streaming in these listeners was explored using tone sequences matched to the center frequencies of the implant s 22 electrodes experiment 1 measured temporal discrimination for short aba triplet and longer 12 ab cycles sequences tone silence durations 60 40 ms tone a stimulated electrode 11 tone b stimulated one of 14 electrodes on each trial one sequence remained isochronous and tone b was delayed in the other listeners had to identify the anisochronous interval the delay was introduced in the second half of the longer sequences prior build up of streaming should cause thresholds to rise more steeply with increasing electrode separation but no interaction with sequence length was found experiment 2 required listeners to identify which of two target sequences was present when interleaved with distractors tone silence durations 120 80 ms accuracy was high for isolated targets but most listeners performed near chance when loudness matched distractors were added even when remote from the target only a substantial reduction in distractor level improved performance and this effect did not interact with target distractor separation these results indicate that implantees often do not achieve stream segregation even in relatively unchallenging tasks

optimal stochastic allocation of machines under waiting time constraints the nonpreemptive scheduling of n geqslant 1 stochastic jobs is considered to minimize the expected number of parallel machines needed to meet given waiting time constraints the number of machines available is unlimited the running times of the jobs are denoted t 1 ldots t n and are taken to be independent samples of an exponentially distributed random variable t with mean 1 job waiting times are to be bounded stochastically by a nonnegative random variable w independent of t 1 ldots t n at time zero a timer is started with an initial value w and job scheduling begins when the timer expires all jobs still waiting for a machine are assigned to available machines only the distributions of w and the job durations t 1 ldots t n are known to the scheduler in advance a scheduling policy is defined which is proven to be optimal when w has an exponential distribution and is asymptotically optimal as n to infty when w is a constant hard deadline in the exponential case

listening experience with iterated rippled noise alters the perception of pitch strength of complex sounds in the chinchilla behavioral responses obtained from chinchillas trained to discriminate a cosine phase harmonic tone complex from wideband noise indicate that the perception of pitch strength in chinchillas is largely influenced by periodicity information in the stimulus envelope the perception of pitch strength was examined in chinchillas in a stimulus generalization paradigm after animals had been retrained to discriminate infinitely iterated rippled noise from wideband noise retrained chinchillas gave larger behavioral responses to test stimuli having strong fine structure periodicity but weak envelope periodicity that is chinchillas learn to use the information in the fine structure and consequently their perception of pitch strength is altered behavioral responses to rippled noises having similar periodicity strengths but large spectral differences were also tested responses to these rippled noises were similar suggesting a temporal analysis can be used to account for the behavior animals were then retested using the cosine phase harmonic tone complex as the expected signal stimulus generalization gradients returned to those obtained originally in the naive condition suggesting that chinchillas do not remain fine structure listeners but rather revert back to being envelope listeners when the periodicity strength in the envelope of the expected stimulus is high

gap detection and the precedence effect in young and old adults thresholds for detecting a gap between two gaussian enveloped standard deviation 0 5 ms 2 khz tones were determined in young and old listeners the gap detection thresholds of old adults were more variable and about twice as large as those obtained from young adults moreover gap detection thresholds were not correlated with audiometric thresholds in either group estimates of the width of the temporal window of young subjects based on the detection of a gap between two tone pips were smaller than those typically obtained when a relatively long duration pure tone is interrupted moore et al j acoust soc am 85 1266 1275 1989 because the amount of time it takes to recover from an adapting stimulus is likely to affect gap detection thresholds glasberg et al j acoust soc am 81 1546 1556 1987 smaller estimates of temporal window size would be expected in this paradigm if the amount of adaptation produced by the first tone pip was negligible the larger gap detection thresholds of o

the perceptual tone noise ratio of merged iterated rippled noises with octave harmonic and nonharmonic delay ratios the perceptual tone noise ratio was measured for merged iterated ripple noise stimuli irns in which one of the individual irns always had a delay of 16 ms the second irn was chosen to create merged irns with single octave delay ratios e g 16 ms 8 ms double octave delay ratios e g 16 ms 4 ms harmonic delay ratios e g 16 ms 12 ms and nonharmonic delay ratios e g 16 ms 3 9 ms all stimuli were high pass filtered at 800 hz the tone noise ratio was significantly enhanced for the octave ratios and there was a strong interaction between the single and double octave delay ratios and number of iterations but the perceptual tone noise ratio for nonoctave ratios was determined solely by the number of iterations the pattern of the results can be explained in terms of the height of the largest peak in the summary autocorrelogram meddis and hewitt j acoust soc am 89 2866 2882 1991 provided the model is modified to improve the simulation of the loss of phase locking

the perceptual tone noise ratio of merged iterated rippled noises iterated rippled noise irn is constructed by delaying a random noise by d ms adding it back to the same noise and repeating the process iteratively when two irns with the same power but slightly different delays are added together the perceptual tone noise ratio of the merged irn is markedly reduced with respect to that of either of the component irns in this paper the reduction in the perceptual tone noise ratio is measured for irns in which one of the delays is always 16 ms and the other is either 16 0 1 ms or 16 1 1 ms the component irns have the same number of iterations and the number varies across conditions from 4 to 256 the perceptual tone noise ratio is measured using a discrimination matching procedure developed for single irns each merged irn is compared with a range of standard stimuli having varying proportions of a complex tone and a broadband noise patterson et al j acoust soc am 100 3286 3294 1996 for single irns the function relating the signal to noise ratio of the matching standard to the number of iterations in the irn was found to be essentially straight this relationship was explained in terms of the height of the first peak in the autocorrelation of the stimulus wave or by the first peak in the summary autocorrelogram produced by a time domain auditory model for the merged irns in the current experiment the matching point functions are found to have pronounced downward curvature in addition to being well below the function for single irns to account for the reduction in the perceptual tone noise ratio of merged irns the autocorrelation model was extended to include a simple rule for combining adjacent peaks in the autocorrelation function of the wave and the autocorrelogram model was revised to improve the simulation of the loss of phase locking at higher frequencies in the autocorrelogram

perturbation analysis for a class of fuzzy linear systems in this paper the perturbation analysis is presented for a class of fuzzy linear systems which can be solved by an embedding method we deduce the nonlinear upper perturbation bounds for the solutions and discuss the normwise mixed and componentwise condition numbers the results show how the perturbations of the coefficient matrix and the right hand vector impact the solutions to fuzzy linear systems

searching for the time constant of neural pitch extraction multichannel auditory models have been repeatedly used to explain many aspects of human pitch perception among the most successful ones are models where pitch is estimated based on an analysis of periodicity in the simulated auditory nerve firing this periodicity analysis is typically implemented as a running autocorrelation i e the autocorrelation is calculated within a temporal window which is shifted along the time axis the window was suggested to have an exponential decay with time constant estimates between 1 5 and 100 ms the window length determines the minimal integration time of pitch extraction the present experiments are designed to quantify the temporal window of pitch extraction using regular interval noises rins rins were generated by concatenating equal duration noise samples which produce a pitch corresponding to the reciprocal of the sample duration when the samples are identical periodic noise when the samples are independent the stimulus is gaussian noise and produces no pitch using rin stimuli where periodic portions interchange with aperiodic portions it is shown that the temporal window of pitch extraction cannot be modeled using a single time constant but that the size of the temporal window depends on the pitch itself

solving fuzzy equations we start in the next section 10 2 with looking at possible solutions to the simple fuzzy linear equation overline a cdot overline x overline b overline c we discuss three different types of solution which we have studied before in solving fuzzy equations then we present a fourth type of solution based on our fuzzy monte carlo method in section 10 2 2 this new solution is based on random fuzzy numbers in section 10 3 we look at only classical solutions to the fuzzy quadratic equation and apply our fuzzy monte carlo method to obtain new solutions then in section 10 4 we consider the fuzzy matrix equation overline a cdot overline x overline b and a number of solution types for overline x and then another solution based on fuzzy monte carlo techniques the last section contains a brief summary and our conclusions

fuzzy finite element approach for the analysis of imprecisely defined systems many engineering systems are too complex to be defined in precise mathematical terms they often contain information and features that are vague imprecise qualitative linguistic or incomplete the traditional deterministic and probabilistic techniques are not adequate to analyze such systems this paper aims at developing a fuzzy finite element approach for the analysis of imprecisely defined systems the development of the methodology starts from the basic concepts of fuzzy numbers of fuzzy arithmetic and implements suitably defined fuzzy calculus concepts such as differentiation and integration for the derivation manipulation and solution of the finite element equations simple stress analysis problems involving vaguely defined geometry material properties external loads and boundary conditions are solved to establish and to illustrate the new procedure the approach developed is applicable to systems that are described in linguistic terms as well as those that are described by incomplete information if complete data are known the method handles the information similar to that of a probabilistic approach the present approach represents a unique methodology that enables us to handle certain types of imprecisely known data more realistically compared with the existing procedures

minimization of agreeably weighted variance in single machine systems abstract this paper considers the variance minimization problem with job dependent weights we show that an optimal job sequence must be v shaped in terms of weighted processing time when the problem is agreeably weighted in the sense that p i p j implies w i w j where p i and w i are the processing time and the weight of job i respectively an o nwp algorithm is proposed to find an optimal solution where n is the number of jobs w is the sum of weights and p is the sum of processing times furthermore an o np algorithm is derived to obtain a sub optimal solution the relative error of is guaranteed less than any pre specified amount and tends towards zero if w w min grows at a rate slower than n 3 as n increases where w min is the minimum weight particularly we show that in the special case where all weights are equal the o np algorithm can find a solution with relative error bounded above by 3 n 1 n 2 when n 2 numerical results are reported which indicate that the o np algorithm generated an optimal solution for almost every problem tested finally two fully polynomial approximation schemes are presented for problems in which the weights are bounded above by a polynomial in n the first one solves problems with p max 1 2 p while the second one solves problems with p max 1 2 p where p max is the maximum processing time

reduced complexity dynamic programming based on policy iteration abstract in this paper a forward method is introduced for solving the dynamic programming equations of bellman this is in contrast to most existing methods for dynamic programming which solve the problem backwards a key advantage is that the forward dynamic programming approach can be systematically simplified to provide computation optimality trade offs such trade offs are lacking in backwards iterative methods which tend to be all or nothing propositions a second advantage is that the computation is independent of the state dimension these properties together offer some promise for circumventing the curse of dimensionality on many problems of practical interest due to a strong connection with the work of bellman on policy iteration the method is denoted as the iteration in policy space ips algorithm several examples are given to demonstrate the general usefulness of the method

gap detection for similar and dissimilar gap markers detection thresholds for temporal gaps between markers of dissimilar frequency are usually elevated with respect to thresholds for gaps between markers of similar frequency because gaps between markers of dissimilar frequency represent both a spectrally based perceptual discontinuity as well as a temporal discontinuity it is not clear what factors underlie the threshold elevation this study sought to examine the effects of perceptual dissimilarities on gap detection the first experiment measured gap detection for configurations of narrow band gap markers comprised of pure tones frequency modulated tones and amplitude modulated tones the results showed that gap thresholds for frequency disparate pure tone markers were elevated with respect to isofrequency tonal markers but that perceptual discontinuities between markers restricted to the same frequency region did not uniformly elevate threshold the second experiment measured gap detection for configurations of markers where the leading and trailing markers could differ along the dimensions of bandwidth duration and pitch the results showed that in most cases gap detection deteriorated when the bandwidth of the two markers differed even when the spectral content of the narrower band marker was completely subsumed by the spectral content of the wider band marker this finding suggests that gap detection is sensitive to spectral dissimilarity between markers in addition to spectral discontinuity the effects of marker duration depended on the marker bandwidth pitch differences across spectrally similar markers had no effect

a time domain description for the pitch strength of iterated rippled noise two versions of a cascaded add attenuate and delay circuit were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose strength relative to the noise can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit listeners were asked to discriminate between various pairs of irn stimuli which differed in the type of network used to generate the sounds or the number of iterations n 1 2 3 4 7 and 9 performance was determined for irn stimuli generated with delays of 2 4 and 8 ms and for four bandpass filter conditions 0 2000 250 2000 500 2000 and 750 2000 hz some irn stimuli were extremely difficult to discriminate despite relatively large spectral differences while other irn stimuli produced readily discriminable changes in perception despite small spectral differences these contrasting results are inconsistent with simple spectral explanations for the perception of irn stimuli an explanation based on the first peak of the autocorrelation function of irn stimuli is consistent with the results simulations of the processing performed by the peripheral auditory system i e interval histograms and correlograms produce results which are consistent with the involvement of these temporal processes in the perception of irn stimuli

the role of the envelope in processing iterated rippled noise iterated rippled noise irn is generated by a cascade of delay and add the gain after the delay is 1 0 or delay and subtract the gain is 1 0 operations the delay and add subtract operations impart a spectral ripple and a temporal regularity to the noise the waveform fine structure is different in these two conditions but the envelope can be extremely similar four experiments were used to determine conditions in which the processing of irn stimuli might be mediated by the waveform fine structure or by the envelope in experiments 1 and 3 listeners discriminated among three stimuli in a single interval task irn stimuli generated with the delay and add operations g 1 0 irn stimuli generated using the delay and subtract operations g 1 0 and a flat spectrum noise stimulus in experiment 2 the listeners were presented two irn stimuli that differed in delay 4 vs 6 ms and a flat spectrum noise stimulus that was not an irn stimulus in experiments 1 and 2 both the envelope and waveform fine structure contained the spectral ripple and temporal regularity in experiment 3 only the envelope had this spectral and temporal structure in all experiments discrimination was determined as a function of high pass filtering the stimuli and listeners could discriminate between the two irn stimuli up to frequency regions as high as 4000 6000 hz listeners could discriminate the irn stimuli from the flat spectrum noise stimulus at even higher frequencies as high as 8000 hz but these discriminations did not appear to depend on the pitch of the irn stimuli a control experiment fourth experiment suggests that irn discriminations in high frequency regions are probably not due entirely to low frequency nonlinear distortion products the results of the paper imply that pitch processing of irn stimuli is based on the waveform fine structure