numerical cubature using error correcting codes we present a construction for improving numerical cubature formulas with equal weights and a convolution structure in particular equal weight product formulas using linear error correcting codes the construction is most effective in low degree with extended bch codes using it we obtain several sequences of explicit positive interior cubature formulas with good asymptotics for each fixed degree t as the dimension n to infty using a special quadrature formula for the interval g kuperberg adv in appl math 34 2005 pp 853 870 arxiv math pr 0408360 we obtain an equal weight t cubature formula on the n cube with o n lfloor t 2 rfloor points which is within a constant of the stroud lower bound we also obtain t cubature formulas on the n sphere n ball and gaussian rn with o nt 2 points when t is odd when mu is spherically symmetric and t 5 we obtain o n2 points for each t ge 4 we also obtain explicit positive interior formulas for the n simplex with o nt 1 points for t 3 we obtain o n points these constructions asymptotically improve the nonconstructive tchakaloff bound some related results were recently found independently by victoir siam j numer anal 42 2004 pp 209 227 who also noted that the basic construction more directly uses orthogonal arrays

hardy s inequality and the l1 norm of exponential sums in this paper we generalize hardy s inequality 3 for measures of analytic type and obtain a proof of the littlewood conjecture 4 for the l norm of exponential sums as a simple consequence let t be the circle group z the additive group of integers and m t the customary convolution algebra of borel measures on t for pe e m t and n g z put m e ino dp o denote by h t the classical space of all measures e e m t such that j n 0 for all n 0 and let c denote the complex numbers we now state hardy s inequality for measures of analytic type theorem 1 if m c h t then

relative contributions of specific frequency bands to the loudness of broadband sounds listeners with normal hearing nh and sensorineural hearing loss snhl were asked to compare pairs of noise stimuli and choose the louder noise in each pair each noise was made up of 15 two erbn equivalent rectangular bandwidth wide frequency bands that varied independently over a 12 db range from one presentation to the next mean levels of the bands followed the long term average speech spectrum ltass or were set to 43 51 or 59 db sound pressure level spl the relative contribution of each band to the total loudness of the noise was determined by computing the correlation between the difference in levels for a given band on every trial and the listener s decision on that trial weights for snhl listeners were governed by audibility and the spectrum of the noise stimuli with bands near the spectral peak of the ltass noise receiving greatest weight nh listeners assigned greater weight to the lowest and highest bands an effect that increased with overall level but did not assign greater weight to bands near the ltass peak additional loudness matching and paired comparison studies using stimuli missing one of the 15 bands showed a significant contribution by the highest band but properties other than loudness may have contributed to the decisions

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

asymmetric cubature formulae with few points in high dimension for symmetric measures let mu be a positive measure on mathbb r d invariant under the group of reflections and permutations and let m be a natural number we describe a method to construct cubature formulae of degree m with respect to mu with n positive weights and n points in the support of mu and such that n grows at most like dm with the dimension d we apply this method to classical measures to explicitly construct cubature formulae of degree 5 with the number of points growing at most like d3

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

variation in spectral shape discrimination weighting functions at different stimulus levels and signal strengths this study evaluated whether weights for spectral shape discrimination depend on overall stimulus level and signal strength the degree of spectral shape change between two stimuli five listeners discriminated between standard stimuli that were the sum of six equal amplitude tones and signal stimuli created by decreasing the amplitudes of three low frequency components and increasing the amplitudes of three high frequency components weighting functions were influenced by stimulus level in that the relative contribution of the low frequency decremented components to the high frequency incremented components decreased with increasing stimulus level although individual variability was present a follow up experiment suggested that the level dependence was due to greater reliance on high frequency components rather than incremented components excitation pattern analyses indicated that the level dependence is primarily but not solely driven by cochlear factors in general different signal strengths had no effect on the weighting functions when normalized but two of the five listeners showed variability in the shape of the weighting function across signal strengths results suggest that the effects of stimulus level on weighting functions and individual variability in the shapes of the weighting functions should be considered when comparing weighting functions across conditions and groups that might require different stimulus levels and signal strengths

averaging sets a generalization of mean values and spherical designs 0 1 r one cannot of course expect there to be a single point x at which every one assumes its mean value but there is an easy generalization in terms of weighted averages there exist at most m points xi and positive weights oi summing to 1 so that aifj xi i fi dt for j 1 2 m

measuring decision weights in recognition experiments with multiple response alternatives comparing the correlation and multinomial logistic regression methods psychophysical reverse correlation methods allow researchers to gain insight into the perceptual representations and decision weighting strategies of individual subjects in perceptual tasks although these methods have gained momentum until recently their development was limited to experiments involving only two response categories recently two approaches for estimating decision weights in m alternative experiments have been put forward one approach extends the two category correlation method to m 2 alternatives the second uses multinomial logistic regression mlr in this article the relative merits of the two methods are discussed and the issues of convergence and statistical efficiency of the methods are evaluated quantitatively using monte carlo simulations the results indicate that for a range of values of the number of trials the estimated weighting patterns are closer to their asymptotic values for the correlation method than for the mlr method moreover for the mlr method weight estimates for different stimulus components can exhibit strong correlations making the analysis and interpretation of measured weighting patterns less straightforward than for the correlation method these and other advantages of the correlation method which include computational simplicity and a close relationship to other well established psychophysical reverse correlation methods make it an attractive tool to uncover decision strategies in m alternative experiments

on the weyl heisenberg frames generated by simple functions let x n 0 cn e x n with cn n 0 l1 and let a 1 0 a 1 be a weyl heisenberg system e2 imx x na m n z we show that if e 0 1 and some modulo extension of e then a 1 is a frame for each 0 a 1 for certain a respectively if and only if the analytic function h z n 0 cnzn has no zero on the unit circle z z 1 these results extend the case of casazza and kalton 2002 6 that x i 1k 0 1 x ni and a 1 which brought together the frame theory and the function theory on the closed unit disk our techniques of proofs are based on the zak transform and the distribution of fractional parts of na n z

the information divergence hypothesis of informational masking in recent years there has been growing interest in masking that cannot be attributed to interactions in the cochlea so called informational masking im similarity in the acoustic properties of target and masker and uncertainty regarding the masker are the two major factors identified with im these factors involve quite different manipulations of signals and are believed to entail fundamentally different processes resulting in im here however evidence is presented that these factors affect im through their mutual influence on a single factor the information divergence of target and masker given by simpson fitter s da lutfi et al 2012 j acoust soc am 132 el109 113 four experiments are described involving multitone pattern discrimination multi talker word recognition sound source identification and sound localization in each case standard manipulations of masker uncertainty and target masker similarity including the covariation of target masker frequencies are found to have the same effect on performance provided they produce the same change in da the function relating d performance to da moreover appears to be linear with constant slope across listeners the overriding dependence of im on da is taken to reflect a general principle of perception that exploits differences in the statistical structure of signals to separate figure from ground

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

gabor super frames with hermite functions we investigate vector valued gabor frames sometimes called gabor superframes based on hermite functions hn let h h0 h1 hn be the vector of the first n 1 hermite functions we give a complete characterization of all lattices lambda subseteq mathbb r 2 such that the gabor system rm e 2 pi i lambda 2 t bf h t lambda 1 lambda lambda 1 lambda 2 in lambda is a frame for l 2 mathbb r mathbb c n 1 as a corollary we obtain sufficient conditions for a single hermite function to generate a gabor frame and a new estimate for the lower frame bound the main tools are growth estimates for the weierstrass function a new type of interpolation problem for entire functions on the bargmann fock space and structural results about vector valued gabor frames

intensity discrimination in the presence of random frequency multicomponent maskers and broadband noise this study examined the effects of multicomponent random frequency maskers and broadband noise maskers on intensity discrimination at 1000 hz maskers and signals were 200 ms presented simultaneously in the first set of conditions thresholds were measured for the detection of a 1000 hz tone in the presence of 40 or 60 db spl random frequency or noise maskers with extensive training of listeners with the random frequency masker to assure stable effects of masker frequency uncertainty the random frequency maskers had two six or ten components chosen at random from a large frequency range 300 3000 hz excluding a 160 hz band around 1000 hz for these maskers performance across the four listeners was very similar showing large effects of masker frequency uncertainty for noise maskers performance matched predictions for energy based masking in the second and third sets of conditions intensity discrimination was measured at 1000 hz for pedestals ranging from 40 to 80 db spl first in isolation and then in the presence of the maskers the pattern of results for intensity discrimination in quiet showed the expected near miss to weber s law but poorer performance than typically observed the addition of broadband noise maskers had little effect on performance however random frequency maskers degraded performance in nearly all conditions with the size of the effect dependent on the level of the pedestal relative to the masker considering the pedestal as a tonal masker the data were fitted with various models of combined masking a simple power law model provided excellent fits with exponents ranging from 0 24 to 0 35 for the multicomponent maskers but 1 0 linear for the noise the results support models positing that the effects of individual maskers undergo nonlinear transformation before they are added independent of the mechanisms which produce these effects because random frequency maskers presumably produce informational uncertainty based masking the nonlinearity in this case appears central rather than peripheral

nonmonotonicity of informational masking neff and green percept psychophys 41 409 415 1987 report that the masking of single tones by random frequency multitone maskers varies nonmonotonically with number of masker components peaking at 10 50 components in this paper it is shown that such results are well predicted by a model the component relative entropy model core wherein thresholds increase linearly with the ensemble variance of masker spectra smoothed by peripheral auditory filters r a lutfi j acoust soc am 94 748 758 1993 three experiments were conducted in the first the nonmonotonic relation was replicated for 9 of 11 listeners in conditions similar to those of neff and green in the second the frequencies of masker components were fixed and the levels of components were varied randomly across presentations to simulate gaussian noise in this case the nonmonotonicity and the total amount of masking for these listeners were shown to be significantly reduced in the third experiment masked thresholds for the signal were found to vary monotonically with the frequency spacing of masker components for a fixed number of masker components large individual differences among listeners were obtained in some experimental conditions individual as well as mean thresholds were well predicted by the core model with an appropriate selection of the values of the two free parameters of the model for each listener

on a problem of byrnes concerning polynomials with restricted coefficients as in the earlier paper with this title we consider a question of byrnes concerning the minimal length n m of a polynomial with all coefficients in 1 1 which has a zero of a given order m at x 1 in that paper we showed that n m 2 m for all m 5 and showed that the extrernal polynomials for were those conjectured by byrnes but for m 6 that n 6 48 rather than 64 a polynomial with n 48 was exhibited for m 6 but it was not shown there that this extremal was unique here we show that the extremal is unique in the previous paper we showed that n 7 is one of the 7 values 48 56 64 72 80 88 or 96 here we prove that n 7 96 without determining all extremal polynomials we also make some progress toward determining n 8 as in the previous paper we use a combination of number theoretic ideas and combinatorial computation the main point is that if p is a primitive pth root of unity where p m 1 is a prime then the condition that all coefficients of p be in 1 1 together with the requirement that p x be divisible by x 1 m puts severe restrictions on the possible values for the cyclotomic integer p p

auditory discrimination of force of impact the auditory discrimination of force of impact was measured for three groups of listeners using sounds synthesized according to first order equations of motion for the homogenous isotropic bar morse and ingard 1968 theoretical acoustics pp 175 191 the three groups were professional percussionists nonmusicians and individuals recruited from the general population without regard to musical background in the two interval forced choice procedure listeners chose the sound corresponding to the greater force of impact as the length of the bar varied from one presentation to the next from the equations of motion a maximum likelihood test for the task was determined to be of the form log a log f 0 where a and f are the amplitude and frequency of any one partial and 0 5 relative decision weights on log f were obtained from the trial by trial responses of listeners and compared to percussionists generally outperformed the other groups however the obtained decision weights of all listeners deviated significantly from and showed variability within groups far in excess of the variability associated with replication providing correct feedback after each trial had little effect on the decision weights the variability in these measures was comparable to that seen in studies involving the auditory discrimination of other source attributes

counting zeros of cosine polynomials on a problem of littlewood abstract we show that if a is a finite set of non negative integers then the number of zeros of the function f a a a cos a in 0 2 is at least log log log a 1 2 e this gives the first unconditional lower bound on a problem of littlewood and solves a conjecture of borwein erdelyi ferguson and lockhart we also prove a result that applies to more general cosine polynomials with few distinct rational coefficients one of the main ingredients in the proof is perhaps of independent interest we show that if f is an exponential polynomial with few distinct integer coefficients and f correlates with a low degree exponential polynomial p then f has a very particular structure this result allows us to prove a structure theorem for trigonometric polynomials with few zeros in 0 2 and restricted coefficients

spectral weights for sample discrimination as a function of overall level doherty and lutfi 1996 spectral weights for overall level discrimination in listeners with sensorineural hearing loss j acoust soc am 99 1053 1058 examined the weights assigned to individual components of a six tone complex during a sample discrimination task and reported that hearing impaired subjects gave the most weight to components in the region of their high frequency hearing loss in contrast weighting patterns varied for normal hearing subjects in the current study the same six tone complex comprised of the octave frequencies from 0 25 to 8 khz was presented to three subjects with normal hearing in high pass noise in low pass noise and in quiet at two overall levels consistent with doherty and lutfi subjects assigned more weight to the 4 khz component in the high pass noise condition but roughly equal weight to all components in the lower level quiet condition weights in the low pass noise and higher level quiet conditions however were similar to those in the high pass no

individual differences in simultaneous masking with random frequency multicomponent maskers individual differences were examined for 49 listeners in a simultaneous masking task with random frequency multicomponent maskers and a 1000 hz signal across conditions the maskers were broadband noise or complexes of 2 100 sinusoids whose frequencies were randomly chosen with each presentation maskers were equal rms waveforms presented at 60 db spl thresholds for the multicomponent maskers spanned a range of up to 59 db across listeners within conditions without distinct groupings when divided into quartiles mean thresholds for listeners in the lowest quartile increased monotonically with the number of masker components and peaked below values produced by broadband noise listeners in the upper quartile had nonmonotonic functions with a broad peak around 10 20 components with values above those produced by broadband noise quiet thresholds and masked thresholds for the broadband noise masker did not distinguish high from low threshold groups lowering masker uncertainty frequencies randomized between but not within trials or introducing temporal differences by shortening the signal both improved performance by as much as 40 db dependent on the masking produced with maximum uncertainty training effects within experiment excluding an initial training period were examined for all listeners and for five listeners across two consecutive experiments eleven of forty nine listeners 22 showed systematic improvement averaging 12 db within experiment independent of high or low original thresholds for the five tested longer four improved by 5 db or more in at least one condition but the change in performance occurred primarily during initial training for the second experiment the large individual differences documented present a challenge to the development of models for masking produced by masker frequency uncertainty

forward masking as a function of frequency masker level and signal delay the forward masking of a sinusoidal signal by a sinusoid of the same frequency was investigated for frequencies ranging from 125 to 4000 hz forward masking in db is proportional to both masker level and log signal delay at each frequency more forward masking occurs at very low frequencies than at high frequencies given equal sensation level maskers and masked thresholds are greater at low frequencies than at high frequencies given equal spl maskers the data can be described equally well by assuming that the difference in forward masking as a function of frequency is due to a change in the time course of recovery from masking or to a change in the growth of masking at each signal delay the frequency effect is not large enough to change the interpretation of forward masking data in studies of suppression or psychophysical tuning curves

the z sub 4 linearity of kerdock preparata goethals and related codes certain notorious nonlinear binary codes contain more codewords than any known linear code these include the codes constructed by nordstrom robinson 1967 kerdock 1972 preparata 1968 goethals 1974 and delsarte goethals 1975 it is shown here that all these codes can be very simply constructed as binary images under the gray map of linear codes over z sub 4 the integers mod 4 although this requires a slight modification of the preparata and goethals codes the construction implies that all these binary codes are distance invariant duality in the z sub 4 domain implies that the binary images have dual weight distributions the kerdock and preparata codes are duals over z sub 4 and the nordstrom robinson code is self dual which explains why their weight distributions are dual to each other the kerdock and preparata codes are z sub 4 analogues of first order reed muller and extended hamming codes respectively all these codes are extended cyclic codes over z sub 4 which greatly simplifies encoding and decoding an algebraic hard decision decoding algorithm is given for the preparata code and a hadamard transform soft decision decoding algorithm for the i kerdock code binary first and second order reed muller codes are also linear over z sub 4 but extended hamming codes of length n spl ges 32 and the golay code are not using z sub 4 linearity a new family of distance regular graphs are constructed on the cosets of the preparata code

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

on minimal cubature formulae of small degree for spherically symmetric integrals the aim of this paper is to develop the existence and nonexistence problem of a cubature formula of degree 4k 1 for a spherically symmetric integral which attains the moller lower bound for this purpose we bring together the theory of euclidean design in combinatorics and that of reproducing kernels in numerical analysis we show that if there exists a minimal formula of degree 4k 1 then the nodes are distributed into k 1 concentric spheres including the origin and the weights in the formula are a constant on each concentric sphere we particularly focus on the cases of degrees 5 and 9 we show the equivalence between a minimal formula of degrees 5 and 4 and a spherical tight 5 and 4 design we also prove that there exists no minimal formula of degree 9 for some classical weights such as the gaussian weight on mathbb r d the radial exponential weight on mathbb r d and the jacobi weight on b d

estimates of internal templates for the detection of sequential tonal patterns in this experiment listeners detected sequential tonal patterns embedded in multitone multiburst random maskers the maskers consisted of eight 30ms bursts of random frequency tones the signal when present occupied the central six bursts and was centered at 1000hz the six sequential signal tones formed several spectro temporal patterns an equal frequency pattern three ascending patterns with frequency ranges spanning 0 5 1 and 2 equivalent rectangular bandwidths erbs and a random pattern with frequencies drawn at random from the range of 925 1075hz the total number of tones in each burst m was varied to determine detection threshold the detectability of the signal pattern declined as the frequency range of the signal pattern increased and when the signal was random relative weights as a function of time and frequency interpreted as listeners internal templates depended systematically on the properties of the signal pattern tested the templates indicated that when sensitivity was po

numerical cubature from archimedes hat box theorem archimedes hat box theorem states that uniform measure on a sphere projects to uniform measure on an interval this fact can be used to derive simpson s rule we present various constructions of and lower bounds for numerical cubature formulas using moment maps as a generalization of archimedes theorem we realize some well known cubature formulas on simplices as projections of spherical designs we combine cubature formulas on simplices and tori to make new formulas on spheres in particular sn admits a 7 cubature formula and sometimes a 7 design with o n4 points we establish a local lower bound on the density of a positive interior cubature formula on a simplex using the moment map along the way we establish other quadrature and cubature results of independent interest for each t we construct a lattice trigonometric 2t 1 cubature formula in n dimensions with o nt points we derive a variant of the moller lower bound using vector bundles and we show that gaussian quadrature is very sharply locally optimal among positive quadrature formulas

a model of auditory pattern analysis based on component relative entropy recently results from detection and information theory have been used to predict performance of human observers in experiments involving the discriminability of changes in individual components of unfamiliar or uncertain tone patterns r a lutfi j acoust soc am 91 3391 3401 1992 in this paper the theoretical analysis is expanded to yield a general rule of pattern analysis that accounts for nearly all of the major results of such experiments conducted over the last 18 years the rule can be stated as follows component discriminability in an unfamiliar tone pattern profile or sequence is a linearly increasing function of the component s relative entropy core in the pattern ancillary the threshold for detection of a change decreases by one order of magnitude factor of 10 for each one bit increase in core this precise relation of threshold to core is demonstrated repeatedly in a review of past studies and is shown to account for the relative effects of a variety of important variables and their interactions such variables include the total duration of the pattern the number of tones in the pattern the number of tones subject to change the relative level and duration of individual tones in the pattern the relative variability and the physical dimension of the tones parameters that are subject to change the number and position of targets in the pattern the psychophysical procedure used method of adjustment versus same different the type of discrimination task frequency versus intensity discrimination and the manner of presentation of the tones simultaneous or sequential the core rule seems to reflect a general property of auditory analysis wherein the perception of patterns in an ensemble is dominated by those features that dominate the variance of the ensemble

oversampling in the gabor scheme a method for calculating the coefficients of the gabor expansion in the case of oversampling is presented the method is based on the concept of frames and utilizes the zak transform as such the zak transform highlights the meaning and importance of frames in the context of oversampling and other aspects of signal representation by means of nonorthogonal bases

temporal limits of level dominance in a sample discrimination task level dominance refers to the effect where attention is automatically directed to the loudest part of an auditory display in a sample discrimination task the frequencies of five 50ms tones were sampled from normal distributions with means of 1000 and 1100hz and presented sequentially with the tones alternating in intensity observers decide from which distribution the sample was drawn the informativeness of the even numbered tones d 2 was greater than the informativeness of the odd numbered tones d 1 estimates of decision weights and performance levels d show that when the more informative tones were less intense observers attended to the louder tones rather than the more informative tones this effect extends well beyond the temporal limits expected from forward masking studies

density theorems for sampling and interpolation in the bargmann fock space we give a complete description of sampling and interpolation in the bargmann fock space based on a density concept of beurling roughly speaking a discrete set is a set of sampling if and only if its density in every part of the plane is strictly larger than that of the von neumann lattice and similarly a discrete set is a set of interpolation if and only if its density in every part of the plane is strictly smaller than that of the von neumann lattice

level dominance in sound source identification impact sounds were synthesized according to standard textbook equations given for the motion of simply supported metal plates in a two interval forced choice procedure highly practiced listeners identified from these sounds a predefined class of target plates based on their particular material and geometric properties the effects of two factors on identification were examined the relative level of partials comprising the sounds and the relative amount of information given as the difference in d each partial provided for identification in different conditions one factor was fixed while the other either increased or decreased with frequency the effect on listener identification in each case was determined from a logistic discriminant analysis of trial by trial responses yielding a vector of listener decision weights on the frequency and decay of individual partials the weights increased proportionally with relative level but were largely uninfluenced by relative information content a result exactly opposite to that expected from a maximum likelihood observer the dominant effect of relative level was replicated for other sound sources clamped bars and stretched membranes and was not diminished by randomizing the relative level of partials across trials the results are taken to underscore the importance of relative level in the identification of rudimentary sound sources

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

level dominance for the detection of changes in level distribution in sound streams sound streams were generated by randomly choosing the levels of tone pips from two different distributions a and b of the 18 tone pips the first nine were drawn from distribution a and the second nine from distribution b or the opposite the listeners task was to indicate order a b or b a in two conditions the a and b distributions differed in mean condition 1 or variance condition 2 in contrast to an ideal observer listeners strategies were consistent across the two conditions analyses suggest that listeners relied primarily on the more intense tone pips in making their decisions

relative dominance of individual partials in determining the pitch of complex tones these experiments were conducted to determine the dominance of each partial in determining the residue pitch of a complex tone subjects were required to make pitch matches to a complex tone which had one partial slightly mistuned from its correct harmonic value the shift in residue pitch was measured as a function of the frequency shift of the harmonic for each harmonic in turn for mistunings up to 2 3 the shift in residue pitch was approximately a linear function of the shift in the harmonic but for greater mistunings the shift in residue pitch was reduced the degree to which a given harmonic can influence residue pitch gives a measure of the dominance of that harmonic the dominant harmonics were always contained within the lowest six harmonics for fundamental frequencies of 100 200 and 400 hz but there were marked individual differences in the exact distribution of dominance across harmonics the level of a harmonic relative to adjacent harmonics can have a significant effect on its dominance the implications of the results for theories of pitch perception are discussed

perceptual weights for loudness judgments of six tone complexes subjects with normal hearing nh and with sensorineural hearing loss snhl judged the overall loudness of six tone complexes comprised of octave frequencies from 0 25 to 8 khz the level of each tone was selected from a normal distribution with a standard deviation of 5 db and subjects judged which of two complexes was louder overall level varied across conditions in the loudness task there was no difference in mean level across the two stimuli in the sample discrimination task the two complexes differed by an average of 5 db for both tasks perceptual weights were derived by correlating the differences in level between matched frequency tones in the complexes and the loudness decision on each trial weights obtained in the two tasks showed similar shifts from low to high frequency components with increasing overall level simulation of these experiments using a model of loudness perception moore and glasberg 2004 hear res 188 70 88 yielded predicted weights for these stimuli that were highly correlated with predicted specific loudness but not with the observed weights

observer weighting strategies in interaural time difference discrimination and monaural level discrimination for a multi tone complex two experiments measured listeners abilities to weight information from different components in a complex of 553 753 and 953 hz the goal was to determine whether or not the ability to adjust perceptual weights generalized across tasks weights were measured by binary logistic regression between stimulus values that were sampled from gaussian distributions and listeners responses the first task was interaural time discrimination in which listeners judged the laterality of the target component the second task was monaural level discrimination in which listeners indicated whether the level of the target component decreased or increased across two intervals for both experiments each of the three components served as the target ten listeners participated in both experiments the results showed that those individuals who adjusted perceptual weights in the interaural time experiment could also do so in the monaural level discrimination task the fact that the same individuals appeared to be analytic in both tasks is an indication that the weights measure the ability to attend to a particular region of the spectrum while ignoring other spectral regions

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

on the zeros of cosine polynomials solution to a problem of littlewood littlewood in his 1968 monograph some problems in real and complex analysis 12 problem 22 poses the following research problem which appears to be still open problem if the nj are integral and all different what is the lower bound

frames in the bargmann space of entire functions we look at the decomposition of arbitrary f in l2 r in terms of the family of functions cp x w exp iimnab iman i x nb 2 with a b 0 we derive bounds and explicit formulas for the minimal expansion coefficients in the case where ab 2w n n an integer 2 2 transported to the hilbert space f of entire functions introduced by v bargmann these results are expressed as inequalities of the form

cubature formulas for symmetric measures in higher dimensions with few points we study cubature formulas for d dimensional integrals with an arbitrary symmetric weight function of product form we present a construction that yields a high polynomial exactness for fixed degree l 5 or l 7 and large dimension d the number of knots is only slightly larger than the lower bound

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

polynomials with coefficients from a finite set in 1945 duffin and schaeffer proved that a power series that is bounded in a sector and has coefficients from a finite subset of c is already a rational function their proof is relatively indirect it is one purpose of this paper to give a shorter direct proof of this beautiful and surprising theorem this will allow us to give an easy proof of a recent result of two of the authors stating that a sequence of polynomials with coefficients from a finite subset of c cannot tend to zero uniformly on an arc of the unit circle another main result of this paper gives explicit estimates for the number and location of zeros of polynomials with bounded coefficients let n be so large that v satisfies n 1 we show that any polynomial in has at least zeros in any disk with center on the unit circle and radius n

relative weights for frequency glide detection using narrowband noise narrowband noise stimuli were used to derive relative weights for detecting frequency glides in a yes no procedure one stimulus set was restricted to the duration of the glide for the second stimulus set there were fringe noise bands preceding and following the glide for both sets the center frequency of the linear glide was either fixed at 1000hz or randomly chosen on each trial from the range of 800 1200hz relative weights as a function of time were derived using a linear model and the linear classification method a ahumada j vis 2 121 131 2002 sensitivity was better for the fixed than random frequency conditions and weight patterns from the random frequency conditions were less reliable than those obtained from the fixed frequency conditions the magnitudes of the relative weights tended to be larger for the second half of the stimulus suggesting that subjects paid more attention to the later than the earlier parts of stimuli in the random frequency conditions the linear model failed to account for subjects performance unless the stimuli were expressed in terms of relative changes in frequency rather than absolute frequency

auditory discrimination of material changes in a struck clamped bar the principles of theoretical acoustics were applied to approximately reconstruct the sound pressure waveform at the ear as would be generated by an idealized struck clamped bar the result is an inharmonic sum of damped sinusoids whose individual acoustic parameters frequency intensity and decay modulus are for a fixed geometry and fixed driving force uniquely determined by the material composition of the bar in the standard 2ifc procedure listeners were asked to discriminate changes in material composition based on their perception of the acoustic waveform listener strategies for discriminating such changes were estimated by perturbing slightly the individual acoustic parameters from trial to trial and computing correlations with the listener s response cf r a lutfi and e oh j acoust soc am 95 2963 a 1994 in general the correlations reveal that listeners fail to make optimal use of the information in the acoustic waveform by tending to give undue weight for a given material change to changes in component frequency in some case the accompanying reduction in performance efficiency amounted to 80

performance of cubature formulae in probabilistic model analysis and optimization in probabilistic model analysis and optimization expected values of a model output f x in face of continuous random inputs x are estimated through n dimensional integrals where n d i m x cubature formulae are approximations of these integrals by a weighted sum of function evaluations at carefully chosen points when each function evaluation corresponds to a heavy computational simulation and particularly in optimization problems one needs very efficient formulae with few integration points even though only having modest accuracy in this paper we evaluate the performance of several cubature formulae with few points including smolyak type formulae also known as sparse grid integration and recently proposed thinned cubatures constructed using orthogonal arrays tests are made for a wide family of smooth and non oscillatory functions f x possibly with significant anisotropy and covering both normal and uniform input probability distributions two practical case studies are also presented one of analysis of a large scale mass transfer model with uncertain parameters and a second one of optimal production planning under uncertain market conditions results clearly indicate that cubatures with large negative weights including smolyak type formulae are not reliable contrary to positive thinned cubatures that produce very reasonable estimates up to dimension 24 these thinned cubatures may also surpass quasi monte carlo methods also up to dimension 24

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

the effect of onset asynchrony on relative weights in profile analysis decision weights were estimated in a profile analysis task to determine whether onset asynchronies between the signal component and the nonsignal components encourage the segregation of the signal relative to the other components the signal component onset was either synchronous or asynchronous with respect to the nonsignal components in the asynchronous conditions thresholds were higher and the decision weights were less efficient than in the synchronous conditions these data are largely consistent with a segregation hypothesis onset asynchrony encourages subjects to shift strategies from one of spectral shape discrimination toward one of intensity discrimination

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

sensory constraints on auditory identification of the material and geometric properties of struck bars a computational formula is derived for estimating the constraints limited auditory sensitivity imposes on auditory identification of the material and geometric properties of struck bars the formula combines a model of the transverse motion of the bar with empirical psychometric functions to map out null regions in the bar s physical parameter space where changes in the frequency amplitude and decay of partials are likely below threshold for detection parameters of the physical space include bar density young s modulus fluid and viscoelastic damping factors bar length and bar cross sectional area as related to bar shape and hollowness the formula is used to estimate the possible effect of limited sensitivity in past studies on the auditory identification of bar attributes the results suggest that sensitivity may indeed have played a role in some studies and that apparent discrepancies in results may be understood based on whether the predominant source of damping was internal or external to the bar the formula identifies conditions representing an expected bound on identification performance and thereby may be used to aid in the design of future studies for which the struck bar is the sound source of choice