a new technique for measuring spectral shape discrimination a new technique is described for studying the ability of listeners to discriminate between sounds on the basis of spectral shape a process called auditory profile analysis the advantage of the technique is that it reduces the range of the random rove in level necessary to provide a specified limit on the performance which listeners could achieve by level detection that is by employing a detection strategy based solely on comparisons of stimulus level thresholds were measured for the just discriminable ripple a pattern of alternating intensity increments and decrements in an equal amplitude multitone reference spectrum for a group of normal hearing listeners broadband high pass and low pass filtered conditions were tested the results indicated that the thresholds obtained using the new technique were well below the lowest level achievable by level detection referred to as the level detection limit in all conditions using a 20 db random within trial rove in overall level the lowest threshold occurred for the broadband stimulus while the highest threshold was observed for the most extreme high pass filtered condition the new technique appears to be well suited for study of profile analysis in hearing impaired listeners where stimulus bandwidth and rove range are limited

fast recursion formula for weight multiplicities the purpose of this note is to describe and prove a fast recursion formula for computing multiplicities of weights of finite dimensional representations of simple lie algebras over c until now information about weight multiplicities for all but some special cases 1 2 has had to be found from the recursion formulas of freudenthal 3 or racah 4 typically these formulas become too laborious to use for hand computations for ranks 5 and dimensions 1 0 0 and for ranks 10 and dimensions 10 on a large computer 5 6 with the proposed method the multiplicities can routinely be calculated even by hand for dimensions far exceeding these as an example we present a summary of calculations 7 of all multiplicities in the first sixteen irreducible representations of es let be a semisimple lie algebra over c with root system a and weyl group w relative to a cartan subalgebra let a be the positive roots with respect to some ordering and ii at a the set of simple roots let q and p be the root and weight lattices respectively spanning the real vector space f c if x c p we denote by x the set of dominant elements of x relative to n let m be an irreducible module with highest weight a and weight system 2 an important feature of the approach is the direct determination of 2 without computing outside the dominant chamber since every w orbit is represented by one weight x 2 of the same multiplicity it suffices to compute such x s the recursion formula for computing the multiplicities is a modification proposition 4 of the freudenthal formula in which the weyl group has been exploited to collapse it as much as possible after describing the procedure we present the e example finally the necessary proofs are given

refinement equations and distributional fixed points abstract connections between l 1 solutions of the refinement equation of the form f x l f lx m dp and distributional fixed points of a special random affine map are investigated using results on convergence of perpetuities the direct form of the fourier transform of l 1 solutions of the above refinement equation is obtained

spectral shape discrimination by hearing impaired and normal hearing listeners the ability to discriminate between sounds with different spectral shapes was evaluated for normal hearing and hearing impaired listeners listeners discriminated between a standard stimulus and a signal stimulus in which half of the standard components were decreased in level and half were increased in level in one condition the standard stimulus was the sum of six equal amplitude tones equal spl and in another the standard stimulus was the sum of six tones at equal sensation levels re audiometric thresholds for individual subjects equal sl spectral weights were estimated in conditions where the amplitudes of the individual tones were perturbed slightly on every presentation sensitivity was similar in all conditions for normal hearing and hearing impaired listeners the presence of perturbation and equal sl components increased thresholds for both groups but only small differences in weighting strategy were measured between the groups depending on whether the equal spl or equal sl condition was tested the average data suggest that normal hearing listeners may rely more on the central components of the spectrum whereas hearing impaired listeners may have been more likely to use the edges however individual weighting functions were quite variable especially for the hi listeners perhaps reflecting difficulty in processing changes in spectral shape due to hearing loss differences in weighting strategy without changes in sensitivity suggest that factors other than spectral weights such as internal noise or difficulty encoding a reference stimulus also may dominate performance

refinement type equations and grincevicjus series abstract we consider l 1 solutions of the following refinement type equations f x n z c n 1 f k x n n z c n 1 f k x n where k 2 is an integer and for all n z reals c n 1 c n 1 are non negative with n z c n 1 c n 1 k and n z log n c n 1 c n 1 necessary and sufficient conditions for the existence of non trivial l 1 solutions in several special cases are given

the effects of amplitude perturbation and increasing numbers of components in profile analysis in a profile analysis task the effect of randomly perturbing the amplitudes of the components of multi tone stimuli was studied in two experiments in the first experiment thresholds for a signal added in phase to the central component of a standard were measured for different numbers of components in two conditions in one condition thresholds were measured in blocks for six different jagged standards and in another thresholds were measured when one of the six standards was chosen randomly on a presentation by presentation basis regardless of condition thresholds did not depend on the numbers of components and increased magnitude of perturbation increased thresholds moreover the slope relating thresholds to number of components did not increase with increasing magnitude of perturbation in the second experiment the signal consisted of an increase in amplitude of the central components and a decrease in amplitude of the outer components of the standard a stimulus type which has been shown to maximize the change in threshold with increasing number of components the amplitudes of component tones were selected randomly on a presentation by presentation basis thresholds fell with increases in the number of components but the slope relating thresholds to numbers of components did not change as the magnitude of perturbation increased the latter result contrasts with that reported by kidd et al j acoust soc am 90 1340 1354 1991

informational processing of complex sound normal hearing listeners discriminated among complex nonspeech sounds in which the difference to be discriminated was randomly varied from trial to trial all other physical parameters of the sounds were fixed within a block of trials on each trial the listener heard two sounds e g tone complexes the values of the variable parameter e g tone frequencies were drawn from two normal distributions differing only in mean the listener s task was to identify the sound having the higher mean value of the variable parameter discrimination performance was found to be largely independent of the particular physical dimensions along which the sounds varied rather performance appeared to depend primarily on information content of the sounds information content was defined in terms of a stimulus equivocation factor that was derived from the data based on this model transmitted information was estimated to be between 1 0 3 0 bits work supported by afosr

psychometric functions for level discrimination in cochlearly impaired and normal listeners with equivalent threshold masking the purpose of this study was to determine whether the form of the psychometric functions for level discrimination also known as intensity discrimination measured in a two interval two alternative forced choice paradigm changes with hearing impairment measurements of sensitivity d as a function of delta l 20 log p delta p lp where p is pressure were obtained in six listeners with cochlear impairments five normal listeners tested in the quiet and two masked normal listeners stimuli were chosen to encompass a wide range of conditions and difference limens results show that the d is nearly proportional to delta l over the entire range of stimuli this simple relationship is not changed by cochlear impairments or masking noise these findings indicate that if the transformation from stimulus intensity to decision variable is affected by hearing impairment or masking the change affects both the mean and the standard deviation in the same manner i e the standard deviation may be proportional to the derivative of the transformation as was suggested by zwislocki and jordan j acoust soc am 79 772 780 1986 the results also lend support to the notion that delta l plotted on a logarithmic scale is an appropriate representation of level discrimination performance

on l1 solutions of a two direction refinement equation abstract in this paper we examine l 1 solutions of the following two direction refinement equation f x n n n c n 1 f k x n n n n c n 1 f k x n we prove that the vector space of all l 1 solutions of the above equation is at most one dimensional and consists of compactly supported functions of constant sign we also show that in many interesting cases any l 1 solution of the two direction refinement equation is either positive or negative on its support next we present sufficient conditions easy for verification for the existence of nontrivial l 1 solutions of the two direction refinement equation as well as for the nonexistence of such solutions

spectral weights for overall level discrimination in listeners with sensorineural hearing loss a conditional on a single stimulus coss analysis procedure b g berg j acoust soc am 86 1743 1746 1989 was used to measure the weight or relative reliance that normal hearing and hearing impaired listeners give to different frequencies in the discrimination of the overall level of a multitone complex on each trial two multitone tone complexes comprised of six octave frequencies from 250 to 8000 hz were presented to subjects the levels of the frequencies for each complex were randomly varied the listeners task was to identify the complex with the higher overall intensity level normal hearing listeners used a variety of listening strategies to perform the task showing no general preference to weight one component over another hearing impaired listeners however showed a general tendency to give greatest weight to the spectral information in the region of their hearing loss thirteen of the 14 hearing impaired listeners all of whom had a high frequency sensorineural hearing loss weighted one or more of the high frequency components in the complex the greatest

auditory intensity perception successive versus simultaneous across channel discriminations this study measures the ability of observers to compare the intensities of two stimuli occupying different frequency regions it includes three experiments each experiment having two conditions in one condition the two stimuli to be compared were presented simultaneously within each interval this condition has been called profile analysis in the other condition the two stimuli were presented successively within each interval because the overall level of the stimuli was randomized between intervals the observers were encouraged to compare the intensities of the two stimuli within each observation interval rather than between intervals the stimuli were two simple tones in experiment 1 and two tonal complexes in both experiments 2 and 3 the stimuli used in experiments 2 and 3 differed in frequency the results show that simultaneous comparisons are superior to successive comparisons for simple tones the difference in threshold is about 8 db for complexes with 10 to 11 components the difference

observer efficiency and weights in a multiple observation task a sequence of seven tones sampled from one of two distributions differing in mean frequency is presented to observers who try to report which distribution was sampled estimates are obtained of the weight or importance given to each tone as a function of its temporal position in five experiments the reliability of the information is varied by changing the variance of the distributions tones with high reliability are sampled from distributions with relatively small variance whereas tones with low reliability are sampled from distributions with relatively large variance results show that the observations are weighted more efficiently when the tones have equal rather than unequal reliability and when the most reliable tones have the greater intensity additional results show that the most intense tones often receive the greatest weight even when those tones have the least reliability

informational processing of complex sound ii cross dimensional analysis a series of experiments investigated listeners ability simultaneously to process information across different acoustic dimensions on each trial the listener heard a pair of brief n tone sequences n 1 to 12 the frequency intensity and duration of each tone in the sequence varied randomly from trial to trial on average the values of these three parameters were greater for one sequence the target than the other the nontarget the listener s task was to identify the target on each trial for an ideal observer in this task d performance grows as the square root n obtained d grew at a rate slightly less than the square root of n close to cube root of n growth was observed when the average difference occurred in only one of the three tone parameter values within a block of trials although performance fell short of ideal optimum weights were consistently given to each tone and each parameter the results are consistent with a model in which performance depends predominantly on the information content of the sounds regardless of how the information is packaged in the stimulus transmitted information is estimated to be 0 9 2 0 bits within a single acoustic dimension 2 1 3 0 bits when distributed across dimensions

individual differences in the improvement in spectral shape discrimination due to increasing number of nonsignal tones the effect of the number of nonsignal tones on the just discriminable difference in spectral shape was evaluated for 12 naive subjects the signal was an intensity increment to the center tone of a multitone complex the tones were spaced at equal frequency ratios and except for the signal increment were equal in level the number of nonsignal tones ranged from 2 to 20 consistent with previous studies using equally spaced components group mean thresholds improved monotonically with increasing number of tones group mean thresholds improved about 8 db over the range of reference spectra employed large differences were found across subjects in overall performance and in the magnitude of the improvement with increasing number of nonsignal tones the greatest intersubject variability was observed for the stimuli composed of the fewest components it was concluded that the differences reported in the literature concerning the presence and magnitude of the improvement are due both to differences in the pr

construction of biorthogonal two direction refinable function and two direction wavelet with dilation factor m an algorithm for constructing a pair of biorthogonal two direction refinable function and the corresponding biorthogonal two direction wavelet is presented in particular the algorithm can also be used to construct two direction orthogonal refinable function finally we give an example illustrating how to use our method to construct biorthogonal two direction scaling function with dilation factor 3

on compactly supported spline wavelets and a duality principle let v 1 v 0 v 1 be a multiresolution analysis of l 2 generated by the mth order b spline n m x we exhibit a compactly supported basic wavelet m x that generates the corresponding orthogonal complementary wavelet subspaces w 1 w 0 w 1 consequently the two finite sequences that describe the two scale relations of n m x and m x in terms of n m 2x j j z yield an efficient reconstruction algorithm to give an efficient wavelet decomposition algorithm based on these two finite sequences we derive a duality principle which also happens to yield the dual bases n m x j and 59 m x j relative to n m x j and m x j respectively

evaluation of simple models of auditory profile analysis using random reference spectra this article describes further study of the finding reported by green et al j acoust soc am 73 639 643 1983 and others that in certain conditions the threshold of detectability for an intensity increment to the center tone of a multitone reference spectrum decreased as the number of nonsignal tones increased that result was considered remarkable since critical band theory would predict that these nonsignal tones spaced outside the critical band containing the signal would have no effect on or at most slightly decrease within band detectability and certainly could not account for the result of improved detectability found in the study cited above recently henn and turner j acoust soc am 88 126 131 1990 were unable to replicate the result described above concluding that the phenomenon exists only in limited conditions and that it is highly individual in nature further they speculated that the most likely reason for the discrepancy between their study and previous s

dilation equations and markov operators abstract using the theory of markov operators we give a new proof of the known fact saying that for every positive integers n and k 1 and for every nonnegative reals c 0 c n satisfying the first sum rule the dilation equation f x n 0 n c n f k x n has a nontrivial l 1 solution

informational processing of complex sound iii interference in this study theoretical results from information theory and detection theory are applied to provide a formal analysis of the interaction of target and context uncertainty on the discrimination of brief multitone sequences the experiments employ a sample discrimination task in which the performance of an ideal observer is held constant while the relative variability of the target t and context c is varied listener performance in these experiments was less than ideal but increased monotonically with t c whether the task was to discriminate the frequency or the intensity of the target performance was also constant for a constant t c regardless of the target s position in the sequence the results are consistent with a class of models in which the decision variable is a weighted sum of the tone values comprising the sequence weighting functions computed from the trial by trial data suggest that limits in performance result from trial by trial variability in the weights the decision variable also

matrix refinement type equations abstract taking advantage of perpetuities and the asymptotic behavior of products of random matrices we obtain the direct form of the fourier transform of an l 1 solution of the following random matrix refinement type equation f x det l c f l x m p d where m r p is a random vector and l r p p c r q q are random matrices moreover the dimension of the space of all l 1 solutions of this refinement type equation is examined

a molecular description of profile analysis decision weights and internal noise systematic inefficiencies and internal noise in a spectral profile discrimination task were investigated listeners detected a 1000 hz sinusoid added in phase to the central component of a complex consisting of 11 equal intensity sinusoids parameters for a channel model that employs decision weights and internal noise were estimated with molecular psychophysical techniques maximum likelihood predictions of the model were generally within a few decibels of observed thresholds the degree to which an assumption of ideal weights leads to overestimation of internal noise was also assessed

relative weights for three different psychophysical tasks relative weights for two profile analysis and one detection task were estimated for the profile analysis bump task the standard was the sum of n equal amplitude sinusoidal components ranging in frequency from 200 to 5000 hz the signal for this task was an increment in level to the 1000 hz component of the standard the number of components n ranged from 4 to 50 for the profile analysis down up task the standard was composed of n equal amplitude tones ranging in frequency from 200 to 5000 hz the signal to be detected led to a spectrum that varied down up down up the detection task used the same standard as the profile analysis down up task but the signal to be detected was an added 1000 hz tone comparisons of the relative weights revealed that profile analysis bump and the detection of a tone added to a notched masker rely on similar processing strategies by contrast it was apparent that auditory processing in the profile analysis down up task depended on a different strategy than the other two tasks finally rough estimates of the auditory filter bandwidths suggest invariance with regard to task work supported by nih

uniform refinement of curves abstract we propose and analyze a class of algorithms for the generation of curves and surfaces these algorithms encompass some well known methods of subdivision for bernstein bezier curves de casteljau s algorithm and b spline curves lane and riesenfeld s algorithm several results concerning properties of the limiting curves as well as related questions are discussed

two direction refinable functions and two direction wavelets with dilation factor m abstract motivated by cardinal b spline scaling functions we introduce the concept of two direction refinable functions and two direction wavelets with dilation factor m we investigate the following two direction refinement equation x k p k mx k k p k k mx where m 2 is an integer here two sequences p k k and p k k are called the positive mask and negative mask respectively based on the positive mask and negative mask the conditions that the above equation has compactly distributional solutions are established the conditions that the above equation has l2 stable solutions are also presented the support of x is discussed amply an algorithm for constructing orthogonal two direction refinable functions and their two direction wavelets is presented based on orthogonal two direction scaling functions and two direction wavelets orthogonal and symmetric multiscaling functions and their multiwavelets can be constructed easily in the end a construction example is given

black brane solution for c2 algebra black p brane solutions for a wide class of intersection rules and ricci flat internal spaces are considered they are defined up to moduli functions hs obeying nonlinear differential equations with certain boundary conditions imposed a new solution with intersections corresponding to the lie algebra c2 is obtained the functions h1 and h2 for this solution are polynomials of degree 3 and 4

multiplicity formulas for fundamental strings of representations of classical lie algebras we call the p fundamental string of a complex simple lie algebra to the sequence of irreducible representations having highest weights of the form k 1 p for k 0 where j denotes the jth fundamental weight of the associated root system for a classical complex lie algebra we establish a closed explicit formula for the weight multiplicities of any representation in any p fundamental string

two direction multiwavelet moments abstract two direction multiscaling functions and two direction multiwavelets associated with are a more general and more flexible setting than one direction multiscaling functions and multiwavelets in this paper we derive two methods for computing continuous moments of orthogonal two direction multiscaling functions and multiwavelets the first method is by doubling and the second method is by separation examples for both methods are given

level discrimination of single tones in a multitone complex by normal hearing and hearing impaired listeners a conditional on a single stimulus coss analysis procedure j acoust soc am 86 1743 1746 1989 was used to estimate how well normal hearing and hearing impaired listeners selectively attend to individual spectral components of a broadband signal in a level discrimination task on each trial two multitone complexes consisting of six octave frequencies from 250 to 8000 hz were presented to listeners the levels of the individual tones were chosen independently and at random on each presentation the target tone was selected within a block of trials as the 250 1000 or 4000 hz component on each trial listeners were asked to indicate which of the two complex sounds contained the higher level target as a group normal hearing listeners exhibited greater selectivity than hearing impaired listeners to the 250 hz target while hearing impaired listeners showed greater selectivity than normal hearing listeners to the 4000 hz target which is in the region of their hearing loss both groups of listeners displayed large variability in their ability to selectively weight the 1000 hz target trial by trial analysis showed a decrease in weighting efficiency with increasing frequency for normal hearing listeners but a relatively constant weighting efficiency across frequency for hearing impaired listeners interestingly hearing impaired listeners selectively weighted the 4000 hz target which was in the region of their hearing loss more efficiently than did the normal hearing listeners

spectral weights in profile listening the coss analysis suggested by berg b g berg j acoust soc am 86 1743 1746 1989 is applied to a profile listening task the listener s task is to detect an increment in the level of the middle component of an n component spectrum the overall level of the components is randomly selected from a 20 db range on each presentation thus the detection task is essentially one of detecting a change in spectral shape to implement the coss analysis a small perturbation in level is added to each component of the complex coss functions are generated from these perturbations and the spectral weight that the listener assigns to each component is estimated data are reported for n 3 5 and 11 components and for perturbations with standard deviations of 0 5 1 and 2 db the estimated weights are similar to those derived for an optimum detector namely the level at the signal component is compared with the average level of the nonsignal components this result supports the view that profile analysis invol

decision strategies of hearing impaired listeners in spectral shape discrimination the ability to discriminate between sounds with different spectral shapes was evaluated for normal hearing and hearing impaired listeners listeners detected a 920 hz tone added in phase to a single component of a standard consisting of the sum of five tones spaced equally on a logarithmic frequency scale ranging from 200 to 4200 hz an overall level randomization of 10 db was either present or absent in one subset of conditions the no perturbation conditions the standard stimulus was the sum of equal amplitude tones in the perturbation conditions the amplitudes of the components within a stimulus were randomly altered on every presentation for both perturbation and no perturbation conditions thresholds for the detection of the 920 hz tone were measured to compare sensitivity to changes in spectral shape between normal hearing and hearing impaired listeners to assess whether hearing impaired listeners relied on different regions of the spectrum to discriminate between sounds spectral weights were estimated from the perturbed standards by correlating the listener s responses with the level differences per component across two intervals of a two alternative forced choice task results showed that hearing impaired and normal hearing listeners had similar sensitivity to changes in spectral shape on average across frequency correlation functions also were similar for both groups of listeners suggesting that as long as all components are audible and well separated in frequency hearing impaired listeners can use information across frequency as well as normal hearing listeners analysis of the individual data revealed however that normal hearing listeners may be better able to adopt optimal weighting schemes this conclusion is only tentative as differences in internal noise may need to be considered to interpret the results obtained from weighting studies between normal hearing and hearing impaired listeners

biorthogonal two direction refinable function and two direction wavelet the concept of two direction refinable function and two direction wavelet is generalized to the biorthogonal setting the definition of biorthogonal two direction refinable function is introduced and the biorthogonality criteria for two direction refinable function is established we present an algorithm for constructing a pair of biorthogonal two direction refinable function and the corresponding biorthogonal two direction wavelet finally we give two examples illustrating how to use our method to construct a pair of biorthogonal refinable function and its corresponding biorthogonal two direction wavelet pair

auditory streaming of tones of uncertain frequency level and duration stimulus uncertainty is known to critically affect auditory masking but its influence on auditory streaming has been largely ignored standard aba aba tone sequences were made increasingly uncertain by increasing the sigma of normal distributions from which the frequency level or duration of tones were randomly drawn consistent with predictions based on a model of masking by lutfi gilbertson chang and stamas j acoust soc am 134 2160 2170 2013 the frequency difference for which a and b tones formed separate streams increased as a linear function of sigma in tone frequency but was much less affected by sigma in tone level or duration

correlation coefficients and correlation ratios as estimates of observer weights in multiple observation tasks advantages of correlational methods are described for estimating the relative reliance or weight observers give to different elements of a complex display when performing auditory or visual discriminations correlational methods differ from other such methods by providing a least squares estimate of weights rather than a maximum likelihood estimate based on a presumed model the main benefit is that these methods can be generally applied in cases where the statistical properties of elements are unknown where correlations exist between elements or where it is necessary to evaluate decision models that are inherently nonlinear

relative estimates of combination weights decision criteria and internal noise based on correlation coefficients a means by which relative combination weights may be determined is described for a signal detection model in which the decision variable is a weighted linear combination of several independent normally distributed random variables xi s the first theorem presents the correlation between the binary response variables signal versus no signal and the component xi the second theorem presents a parallel result for the case that additive internal noise is present thus in psychophysical experiments the relative combination weights may be obtained by correlating the observers responses and the input random variables third three numerical methods which allow the evaluation of the relative magnitude of the decision criterion and the variance of a hypothetical additive internal noise are considered

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

discrimination of frequency variance for tonal sequences real world auditory stimuli are highly variable across occurrences and sources the present study examined the sensitivity of human listeners to differences in global stimulus variability in a two interval forced choice task variance discrimination was measured using sequences of five 100 ms tone pulses the frequency of each pulse was sampled randomly from a distribution that was gaussian in logarithmic frequency in the non signal interval the sampled distribution had a variance of stan2 while in the signal interval the variance of the sequence was sig2 with sig2 stan2 the listener s task was to choose the interval with the larger variance to constrain possible decision strategies the mean frequency of the sampling distribution of each interval was randomly chosen for each presentation psychometric functions were measured for various values of stan2 although the performance was remarkably similar across listeners overall performance was poorer than that of an ideal observer io which perfectly compares interval variances however like the io weber s law behavior was observed with a constant ratio of sig2 stan2 to stan2 yielding similar performance a model which degraded the io with a frequency resolution noise and a computational noise provided a reasonable fit to the real data

molecular analysis of the effect of relative tone level on multitone pattern discrimination molecular psychophysics attempts to model the observer s response to stimuli as they vary from trial to trial the approach has gained popularity in multitone pattern discrimination studies as a means of estimating the relative reliance or decision weight listeners give to different tones in the pattern various factors affecting decision weights have been examined but one largely ignored is the relative level of tones in the pattern in the present study listeners detected a level increment in a sequence of 5 100 ms 2 0 khz tone bursts alternating in level between 40 and 80db spl the level increment was made largest on the 40 db tones yet despite this all four highly practiced listeners gave near exclusive weight to the 80 db tones the effect was the same when the tones were replaced by bursts of broadband gaussian noise alternating in level it was reduced only when the level differences were made 10db and it was entirely reversed only when the low level tones alternated with louder bursts of ga

successive versus simultaneous comparison in auditory intensity discrimination the ability to discriminate between two brief sounds having identical frequency components but differing in the intensity of one or more of the components is studied the stimulus manipulations include randomizing the overall intensity of the sounds varying the number and spacing of the components and varying the interval of time between the sounds the results from the experiment in which interstimulus interval is manipulated clearly support a profile analysis mechanism that computes two rough spectral analyses stores a classification of these spectra in memory and compares the two stores this profile mechanism involves a simultaneous comparison of different components of the complex some remote from the signal frequency rather than a successive comparison of the difference in intensity at the signal frequency the simultaneous comparison process is more sensitive when the profile is composed of many components spaced over a wide frequency range

psychometric functions for the discrimination of spectral variance an experiment was conducted to measure the shape of the psychometric function for the discrimination of spectral variance the stimuli were simultaneous tone complexes comprised of the six octave frequencies from 250 to 8000 hz on each presentation the levels of components in db were drawn independently and at random from one of two normal distributions having identical means but different variances n 1 db s 2 10 db in the standard two interval forced choice procedure the listeners task was to indicate which complex had the greater variance in component level the shape of the psychometric function for all five listeners was markedly different from that of an observer limited only by additive internal noise it was consistent with an observer that gives weight to only one or two components in the complex however this result was inconsistent with the weighting functions computed from the trial by trial data from these listeners both measures can be reconciled if it is assumed that listener wei

construction of nonseparable dual ω wavelet frames in l2 rs suppose j 1 a 1 j 1 a 1 and j 1 2 a 2 1 j 1 2 a 2 1 are two pairs of dual m wavelet frames and n wavelet frames in l 2 r s 1 and l 2 r s 2 respectively where m and n are s 1xs 1 and s 2xs 2 dilation matrices with a 1 det m 1 and 2a 2 1 det n 1 moreover their mask symbols both satisfy mixed extension principle mep based on the mask symbols a family of nonseparable dual w wavelet frames in l 2 r s are constructed where s s 1 s 2 and w m qon with q and m 1 q both being integer matrices then a convolution scheme for improving regularity of wavelet frames is given from the nonseparable dual w wavelet frames nonseparable w wavelet frames with high regularity can be constructed easily we give an algorithm for constructing nonseparable dual symmetric or antisymmetric wavelet frames in l 2 r s from the dual w wavelet frames nonseparable dual w wavelet frames with symmetry can be obtained easily in the end two examples are given

on character generators for simple lie algebras we study character generating functions character generators of simple lie algebras the expression due to patera and sharp derived from the weyl character formula is first reviewed a new general formula is then found it makes clear the distinct roles of outside and inside elements of the integrity basis and helps determine their quadratic incompatibilities we review analyse and extend the results obtained by gaskell using the demazure character formulae we find that the fundamental generalized poset graphs underlying the character generators can be deduced from such calculations these graphs introduced by baclawski and towber can be simplified for the purposes of constructing the character generator the generating functions can be written easily using the simplified graphs and associated demazure expressions the rank two algebras are treated in detail but we believe our results are indicative of those for general simple lie algebras

informational processing of complex sound i intensity discrimination this paper reports on some initial experiments using the sample discrimination paradigm to investigate normal hearing listeners ability to process information in complex nonspeech sounds an important feature of the sample discrimination experiment is that the value of the d i f f e r e n c e to be discriminated randomly varies from trial to trial it is this variation that yields potential information in the present study listeners heard a pair of multitone complexes or sequences on each trial the individual levels of the tones were drawn from two normal distributions differing only in mean the listener s task was to identify the sound having the higher mean tone level for an ideal observer in these experiments performance in d grows as the square root n where n is the number of tones obtained d grew more nearly as the cube root of n regardless of whether the tones were played sequentially or simultaneously or whether they were increased in number from high frequencies to low or from low frequencies to high a preliminary model is proposed in which discrimination performance depends predominantly on the information content of the sounds and is largely independent of the physical dimensions along which the sounds vary information content is defined in terms of the variance of the underlying stimulus distributions and a stimulus equivocation factor that is derived from the data based on this model transmitted information is estimated to be between 1 0 and 2 6 bits

generating functions and multiplicity formulas the case of rank two simple lie algebras a procedure is described that makes use of the generating function of characters to obtain a new generating function h giving the multiplicities of each weight in all the representations of a simple lie algebra the way to extract from h explicit multiplicity formulas for particular weights is explained and the results corresponding to rank two simple lie algebras are shown

probability distribution functions of the grincevicjus series abstract given a sequence n n of independent identically distributed vectors of random variables we consider the grincevicjus series n 1 n k 1 n 1 k and a functional integral equation connected with it we prove that the equation characterizes all probability distribution functions of the grincevicjus series moreover some application of this characterization to a continuous refinement equation is presented

sample discrimination of frequency differences with distracters this study examined the effect of the type and frequency range of remote frequency distracters on sample discrimination of frequency differences sd f for baseline sd f conditions normal hearing listeners judged frequency differences between pairs of target tones drawn from gaussian frequency distributions near 2000 hz in experiment 1 the distracters were pairs of random frequency tones fixed frequency tones or noise bands with one distracter above and one below the target region three frequency separations of targets and distracters were tested none overlapping the target region effects of fixed frequency or noise band distracters were small compared to that of random frequency distracters which drove performance to near chance in experiment 2 dominance of the low frequency distracter was supported by the effects of changing distracter level by presenting only the higher or lower frequency distracter and by the pattern of weights derived from trial by trial responses performance recovered only when the lower frequency distracter was attenuated 40 50 db relative to the targets in experiment 3 all stimulus distributions were shifted 2 octaves higher in frequency the stronger influence of the distracter frequency below the target remained the results demonstrate the importance of both stimulus variability and frequency relationships in the interaction of targets and distracters for sd f

a measure of internal noise based on sample discrimination internal noise is often inferred from the difference between observed performance and optimum performance in detection and discrimination tasks it can be measured directly in some cases by observing the extent to which a change in external variability impacts performance in the studies reported here external variability was added to an intensity discrimination task by adding a gaussian random variable with zero mean to the overall level presented in each interval of a two interval forced choice task the standard deviation of the random variable was set to half the mean difference between the levels in the two intervals resulting in d ideal 2 as the mean difference and the corresponding standard deviation of the random variable decreased in size performance was increasingly limited by internal noise permitting a reliable estimate of internal noise to be obtained this can be viewed as a sample discrimination task with one component per sample in the first study performance was measured using 2 khz tones presented at an average level of 70 db spl with mean differences between distributions ranging from 0 1 to 2 2 db in steps of 0 3 db the distributions were either gaussian in level or in power conditions with no external variability were used to obtain a psychometric function in the second study performance was measured using 2 khz tones presented at average levels of 50 and 90 db spl with mean differences ranging from 0 4 to 2 2 db in steps of 0 6 db in both studies the measure of internal noise was highly reliable and in good agreement with the intensity difference limen dl estimated from the psychometric function analyses suggest that this measure could be used to estimate the mean difference between the decision distributions as well as the amount of internal noise in cases where the mean difference between the distributions is unknown

decision rules of listeners in spectral shape discrimination with or without signal frequency uncertainty a correlation technique was used to assess the decision rules of three listeners in two cases of spectral shape discrimination tasks in one case the signal frequency was fixed and in the other it was randomly varied within each block of trials in order to estimate the decision rule of the listeners the experimenter superimposed random level perturbations on each frequency component upon each stimulus presentation over many trials correlation coefficients were computed between the random perturbations and the binary responses of the listeners and were expressed as a function of signal level for both the fixed and random signal cases the measured correlation functions were in reasonably good agreement with those predicted based on the likelihood ratio decision rules thus the listeners appeared to use information nearly optimally in discriminating spectral shapes this investigation demonstrated that the correlation technique can be used to reveal the decision rules for cases where the decision statistics are nonlinear functions of the observations

sample discrimination of frequency by hearing impaired and normal hearing listeners in a multiple observation sample discrimination experiment normal hearing nh and hearing impaired hi listeners heard two multitone complexes each consisting of six simultaneous tones with nominal frequencies spaced evenly on an erbn logarithmic scale between 257 and 6930hz on every trial the frequency of each tone was sampled from a normal distribution centered near its nominal frequency in one interval of a 2ifc task all tones were sampled from distributions lower in mean frequency and in the other interval from distributions higher in mean frequency listeners had to identify the latter interval decision weights were obtained from multiple regression analysis of the between interval frequency differences for each tone and listeners responses frequency difference limens an index of sensorineural resolution and decision weights for each tone were used to predict the sensitivity of different decision theoretic models results indicate that low frequency tones were given much greater perceptu

on the generating function of weight multiplicities for the representations of the lie algebra c2 we use the generating function of the characters of c2 to obtain a generating function for the multiplicities of the weights entering in the irreducible representations of that simple lie algebra from this generating function we derive some recurrence relations among the multiplicities and a simple graphical recipe to compute them

on an approach for computing the generating functions of the characters of simple lie algebras we describe a general approach to obtain the generating functions of the characters of simple lie algebras which is based on the theory of the quantum trigonometric calogero sutherland model we show how the method works in practice by means of a few examples involving some low rank classical algebras