multistate components assignment problem with optimal network reliability subject to assignment budget abstract the typical assignment problem for finding the optimal assignment of a set of components to a set of locations in a system has been widely studied in practical applications however this problem mainly focuses on maximizing the total profit or minimizing the total cost without considering component s failure in practice each component should be multistate due to failure partially failure or maintenance that is each component has several capacities with a probability distribution and may fail when a set of multistate components is assigned to a system the system can be treated as a stochastic flow network the network reliability is the probability that d units of homogenous commodity can be transmitted through the network successfully the multistate components assignment problem to maximize the network reliability is never discussed therefore this paper focuses on solving this problem under an assignment budget constraint in which each component has an assignment cost the network reliability under a components assignment can be evaluated in terms of minimal paths and state space decomposition subsequently an optimization method based on genetic algorithm is proposed the experimental results show that the proposed algorithm can be executed in a reasonable time

a brief biography and appreciation of calyampudi radhakrishna rao with a bibliography of his books and papers we present a brief biography and appreciation of calyampudi radhakrishna rao to whom this fifth special issue on linear algebra and statistics of linear algebra and its applications is dedicated in celebration of his 75th birthday a bibliography of his books and papers is also included

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

calculation of minimal capacity vectors through k minimal paths under budget and time constraints abstract reducing the transmission time is an important issue for a flow network to transmit a given amount of data from the source to the sink the quickest path problem thus arises to find a single path with minimum transmission time more specifically the capacity of each arc is assumed to be deterministic however in many real life networks such as computer networks and telecommunication networks the capacity of each arc is stochastic due to failure maintenance etc hence the minimum transmission time is not a fixed number such a network is named a stochastic flow network in order to reduce the transmission time the network allows the data to be transmitted through k minimal paths simultaneously including the cost attribute this paper evaluates the probability that d units of data can be transmitted under both time threshold t and budget b such a probability is called the system reliability an efficient algorithm is proposed to generate all of lower boundary points for d t b the minimal capacity vectors satisfying the demand time and budget requirements the system reliability can then be computed in terms of such points moreover the optimal combination of k minimal paths with highest system reliability can be obtained

auditory profile analysis frequency phase and weber s law this paper reports three separate experiments on different aspects of performance in auditory profile analysis the first experiment deals with the effects of the frequency and position of an increment in a single component of a multitonal complex the general results indicate that detection of the signal is easier for components in the mid frequency range around 1000 hz independent of signal position within the complex the second experiment investigates the effects of relative phase of the individual components of the complex regardless of the number of components our results indicate that phase has very little effect even when different phases are selected for each presentation the third experiment compares the detection of an increment in intensity of a single component the traditional weber fraction experiment and conditions where additional components are present a profile experiment the detection of the increment is measured as a function of the level of the standard the single tone condition shows the usual near miss to weber s law whereas the multitone condition does not in addition threshold for the increment is better for the multitone condition than for the single tone condition for levels of the standard up to 70 db spl this last result is investigated for ten observers five of whom were experienced in profile tasks and five of whom were not using a low level standard the five experienced observers replicate the results described above the inexperienced observers show the opposite result on average they are better able to detect the increment in the single component condition

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

further results on generalized and hypergeneralized projectors abstract the notions of generalized and hypergeneralized projectors introduced by gros and trenkler j gro s j trenkler generalized and hypergeneralized projectors linear algebra appl 264 1997 463 474 are revisited on the one hand the present paper provides several new characterizations of these sets and on the other the properties of generalized and hypergeneralized projectors related to various matrix partial orderings are considered moreover the paper demonstrates the usefulness in studying the properties of generalized and hypergeneralized projectors of the representation of complex matrices given in corollary 6 by hartwig and spindelbock r e hartwig k spindelbock matrices for which a and a commute linear and multilinear algebra 14 1984 241 256

the d variate vector hermite polynomial of order k abstract the multivariate hermite polynomials occur in edgeworth and saddle point approximations to the distributions of random vector variables explicit expressions in vector notation for the multivariate hermite polynomials of arbitrary order are given and shown to be a special case of a general addition property of hermite polynomials general properties of these polynomials are given in vector notation including an integral representation the orthogonality property differential properties and recurrence relations as well as inversion formulas various expansions of a multivariate normal density are given in terms of a multivariate normal density with different mean different covariance or both in special cases these results give mehler s formula

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

informational masking with small set sizes informational masking refers to interference in the detectability of a sound or discrimination of some property of a sound beyond that which can be attributed to interactions at the auditory periphery in the current experiments the signal to be detected was a tone added to a 6 tone masker and informational masking was introduced by randomly choosing the frequencies of the tones that comprise the masker the primary question was whether small numbers of maskers could replace randomly drawn maskers without sacrificing the underlying detection schemes adopted by observers similar to the method used by wright and saberi j acoust soc am 105 1765 1775 1999 detection thresholds were measured for different masker set sizes where set size refers to the number of 6 tone maskers from which any one masker was drawn set sizes of 3 6 12 and 24 were tested as well as conditions in which the maskers were chosen at random in addition observers memory for maskers was coarsely evaluated large differences in thresholds were found across observers and across different masker sets even for set sizes of 24 the memory test suggests some recognition of maskers for some observers post hoc analysis of the data included an evaluation of the relative contribution of different frequencies using a single linear model as a base for comparison a linear model fitted to each condition was also evaluated although the data were fitted better using many rather than one linear model the reduction in quality of fit was modest this result suggests substantial consistency in decision strategies regardless of masker set size

discrimination of stimulus variance in real world settings auditory signals such as speech are highly variable and differ across occurrences and sources the question addressed is our sensitivity to such differences in global stimulus variability in a variance discrimination task the stimuli were sequences of five 100 ms tone pulses separated by 30 ms the frequency of each tone was sampled independently from a probability distribution that was gaussian on logarithmic frequency in the non signal interval of the 2ifc task the sampled distribution had a mean frequency mf and variance vf in the signal interval the variance of the sequence was vf vf the task was to choose the interval with the larger variance feedback was provided to restrict the use of decision strategies mf was randomly chosen for each presentation m f 2 khz psychometric functions p c vs vf were obtained for various values of vf and overall performance was poorer than that of an ideal observer however like the ideal weber s law behavior was observed

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

study on the multicommodity reliability of a capacitated flow network abstract traditionally many researchers solved the multicommodity maximum flow problem by assuming that the arcs of the flow network are deterministic when the arcs are stochastic i e the capacity of each arc has several values this article studies how to calculate the probability that a capacitated flow network with a unique source mode satisfies a demand d 1 d 2 d p at the unique sink node where d k is the demand of commodity k such a probability is named the multicommodity reliability and is dependent on capacities of arcs one solution procedure is proposed to evaluate the multicommodity reliability which includes two parts an algorithm to generate all d 1 d 2 d p mps and a method to calculate the multicommodity reliability in terms of d 1 d 2 d p mps two illustrative examples are given

on semi orthogonality and a special class of matrices abstract the concept of semi orthogonality of two complex vectors is introduced as a consequence a generalization of the class of orthogonal projectors is investigated

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

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

psychometric functions for level discrimination to determine the form of psychometric functions for 2i 2afc level discrimination ten increment levels were presented in random order within blocks of 100 trials stimuli were chosen to encompass a wide range of conditions and difference limens eight 10 ms tones had frequencies of 0 25 1 8 or 14 khz and levels of 30 60 or 90 db spl two 500 ms stimuli also were tested a 1 khz tone at 90 db spl and a white noise at 63 db spl for each condition at least 20 blocks were presented in mixed order results for three normal listeners show that the sensitivity d is nearly proportional to l 20 log p p p where p is pressure over the entire range of difference limens when d is plotted against weber fractions for pressure p p or intensity i i exponents of the best fitting power functions decrease with increasing difference limens and are less than one for large difference limens these results indicate that the transformation from stimulus intensity to decision variable may be approximately lo

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

multiple observations and internal noise a multiple observation task was used to evaluate models of internal noise on each trial n tones n 1 2 3 4 6 8 10 or 12 within a block were independently sampled from one of two probability density functions on frequency each was normal in form with a standard deviation of 100 hz the two distributions had means of 1000 and 1100 hz respectively the sample was presented through headphones as n 50 ms tone bursts separated by 50 ms the subjects task was to decide from which of the two distributions the tones were sampled a model partitioning internal variance into peripheral variance added to each observation prior to formulating a decision statistic and central variance added to the decision statistic provided a good description of the data of all four subjects a subsequent study counterbalanced two levels of the difference between distribution means 100 or 150 hz with two levels of the standard deviation 100 or 150 hz increasing did not affect estimates of internal variance however increasing resulted in increased estimates of internal variance for both levels of one interpretation of this result is that external and internal variance are not independent work supported by afosr and nmrdc

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

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

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

effect of component relative entropy on the discrimination of simultaneous tone complexes results are reported from a number of experiments investigating the effects of stimulus uncertainty on the discrimination of simultaneous multitone complexes with few exceptions the data were well described by a model in which average threshold for the detection of a change in one or more components varies with the components relative entropy core in the complex r a lutfi j acoust soc am 94 748 758 1993 in different experiments thresholds for the detection of a change in target level were found to be linearly related to core for manipulations in the number of targets the number of context tones and the relative degree of level perturbation on tones from trial to trial the slopes of the functions did not change with measures taken at different points on the psychometric function and in most cases were close to the theoretical value of b 1 0 as predicted by strict application of the model also as predicted but for the exception of one listener increasing the level of the target beyond that of the context had little or no effect on threshold a correlational analysis of the trial by trial data revealed a tendency of listeners to give negative weight to frequencies immediately above the target and to adjust weights in response to changes in the relative degree of level perturbation though inconsistent with the basic premise of the model the variation in weights was not so great as to materially affect the predictions for mean thresholds

similarity uncertainty and masking in the identification of nonspeech auditory patterns this study examined whether increasing the similarity between informational maskers and signals would increase the amount of masking obtained in a nonspeech pattern identification task the signals were contiguous sequences of pure tone bursts arranged in six narrow band spectro temporal patterns the informational maskers were sequences of multitone bursts played synchronously with the signal tones the listener s task was to identify the patterns in a 1 interval 6 alternative forced choice procedure three types of multitone maskers were generated according to different randomization rules for the least signal like informational masker the components in each multitone burst were chosen at random within the frequency range of 200 6500 hz excluding a protected region around the signal frequencies for the intermediate masker the frequency components in the first burst were chosen quasirandomly but the components in successive bursts were constrained to fall in narrow frequency bands around the frequencies of the components in the initial burst within the narrow bands the frequencies were randomized this masker was considered to be more similar to the signal patterns because it consisted of a set of narrow band sequences any one of which might be mistaken for a signal pattern the most signal like masker was similar to the intermediate masker in that it consisted of a set of synchronously played narrow band sequences but the variation in frequency within each sequence was sinusoidal completing roughly one period in a sequence this masker consisted of discernible patterns but not patterns that were part of the set of signals in addition masking produced by gaussian noise bursts thought to produce primarily peripherally based energetic masking was measured and compared to the informational masking results for the three informational maskers more masking was produced by the maskers comprised of narrow band sequences than for the masker in which the frequencies were not constrained to narrow bands also the slopes of the performance level functions for the three informational maskers were much shallower than for the gaussian noise masker or for no masker the findings provided qualified support for the hypothesis that increasing the similarity between signals and maskers or parts of the maskers causes greater informational masking however it is also possible that the greater masking was a consequence of increasing the number of perceptual streams that had to be evaluated by the listener

perception of temporal patterns defined by tonal sequences this experiment tested how listeners discriminate between the temporal patterns defined by two sequences of tones two arrhythmic sequences of n tones were played successively n 8 12 or 16 tone duration 35 ms frequency 1000 hz and the listener reported whether the sequences had the same or different temporal patterns in the first sequence the durations of the intertone gaps were chosen at random in the second sequence the gaps were either a the same as the first sequence or b chosen at random discrimination performance increased with the variability of the gap sequences and decreased with the size of the correlation between the sequences a discrimination model based on computation of the sample correlation between the sequences of gaps but limited by an internal variability of approximately 15 ms described observer performance in a variety of conditions

different auditory filter bandwidth estimates based on profile analysis notched noise and hybrid tasks auditory filter bandwidths were estimated in three experiments the first experiment was a profile analysis experiment the stimuli were composed of sinusoidal components ranging in frequency from 200 to 5000 hz the standard stimulus was the sum of equal amplitude tones and the signal stimulus had a power spectrum that varied up down up down the number of components ranged from four to 60 interval by interval level randomization prevented the change in level of a single component from reliably indicating the change from standard to signal the second experiment was a notched noise experiment in which the 1000 hz tone to be detected was added to a noise with a notch arithmetically centered at 1000 hz detection thresholds were estimated both in the presence of and in the absence of level randomization in the third hybrid experiment a 1000 hz tone was to be detected and the masker was composed of equal amplitude sinusoidal components ranging in frequency from 200 to 5000 hz for this experiment thr

exponentiated beta distributions beta distributions are usually defined on the unit interval 0 1 for wider applicability we introduce six exponentiated beta distributions and derive several of their properties including the moment generating function expectation variance skewness kurtosis shannon entropy and the renyi entropy

effect of temporal position proportional variance and proportional duration on decision weights in temporal pattern discrimination two experiments investigated how listeners allocate their attention to different segments of a temporal pattern the experiments allowed a direct test of the predictions of the proportion of total duration ptd rule and the component relative entropy core model listeners had to decide whether two sequences of nine tones had the same or different temporal patterns tone duration 25 ms tone frequency 1000 hz a sequence s temporal pattern was determined by the time intervals between each tone s offset and the next tone s onset on same trials the time intervals at corresponding temporal positions in the two sequences were identical on different trials the corresponding time intervals were randomly varied listener attention to different temporal positions within a sequence was assessed by calculating the decision weights at each position the results supported the core model and were inconsistent with the ptd rule manipulating the mean of the time intervals within the sequence had no consistent ef

proceedings of the second international tampere conference in statistics keynote addresses anderson t w multivariate linear relations box g e p with r d meyer some aspects of statistical design in quality improvement hannan e j the statistical theory of linear systems rao c r estimation in linear models with mixed effects a unified theory invited papers atkinson a c robust regression and unmasking transformations baksalary j k algebraic characterizations and statistical implications ofthe commutativity of orthogonal projectors conradsen k with b k nielsen textural features useful in classification of digital images kariya t mtv model and its application to prediction of stock prices khatri c g quadratic forms and null robustness for elliptical distributions mustonen s editorial approach in statistical computing perlman m d with t w anderson consistency of invariant tests for the multivariate analysis of variance pratt j w dividing the indivisible using simple symmetry to partition variance explained pukelsheim f majorization orderings for linear regression designs pukkila t with a kalijnen on the order determination of time series models rissanen j complexity and information in contingency tables soctt a j generalized linear models with survey data sinha b k with r das robust optimum invariant unbiased tests for variance components speed t p generalized variance component models styan g p h with r e hartwig partially ordered idempotent matrices contributed papers anderson a j b fortran8x as a language forstatisticalcomputation baldessari b on regression analysisundertheintrinsicinference model for stratified dependent normal random variables brannas k control in the duration model framework danial e j and katti s k the asymptotic variances of the necessary and sufficient conditions for the infinite divisibility of discrete distributions through multivariate analysis danial e j and katti s k computing the maximum likelihood estimates of the hyper poisson parameters interactively through apl computer language diebold f x and nerlove m factor structure in a multivariate arch model of exchange ratefluctuations farebrother r w simultaneous confidence intervals when the regressor matrix is unbalanced feuerverger a some fourier procedures for time domain analysis of parametric and semi parametric time series models gelfand a e estimation of a restricted variance ratio de gooijer j g and heuts r m j higher order moments of bilinear time series processes with symmetrically distributed errors ignatov z g and kaishev v k on the computation of distributions of serial correlation coefficients through b splines jajuga k elliptically symmetric distributions and their application to classification and regression kollo t asymptotic distributions of functions of means and covariances konakov v d nonparametric density estimation l approach korhonen p and narula s c on subjectivity in statistics koukouvinos c and kounias s optimal designs in linear models and hadamard matrices latour d puntanen s and styan g p h equalities and inequalities for the canonical correlations associated with some partitioned generalized inverses of a covariance matrix liski e p identifying influential data in a growth curves model manly b f j and mcalevey l a randomization alternative to the bonferroni inequality with multiple f tests mejza s experiments in incomplete split plot designs merikoski j k underestimating the largest eigenvalue of a covariance matrix militkt j kvsmr k and cap j comparison of some influence measures in nonlinear regression nordstrom k and von rosen d algebra of subspaces with applications to problems in statistics ososkov g a robust regression for the heavy contaminated sample pynnonen s selection of variables in nonlinear discriminant analysis by information criteria salem a m and wahab s a on the determination of the amplitude of quasi stationary phenomena schaffrin b less sensitive tests by introducing stochastic linear hypotheses schall r and dunne t t on outliers and influence in the general multivariate normal linear model trenkler g stahlecker p schipp b and hering f iterative improvements of a partial minimax estimator in regression analysis wernecke k d kalb g and stdrzebecker e on classification strategies in medical functional diagnostics

generalizations of a property of orthogonal projectors abstract generalizing the result in lemma of baksalary and baksalary j k baksalary o m baksalary commutativity of projectors linear algebra appl 341 2002 129 142 baksalary et al j k baksalary o m baksalary t szulc linear algebra appl 354 2002 35 39 have shown that if p 1 and p 2 are orthogonal projectors then in all nontrivial situations a product of any length having p 1 and p 2 as its factors occurring alternately is equal to another such product if and only if p 1 and p 2 commute in which case all products involving p 1 and p 2 reduce to the orthogonal projector p 1 p 2 p 2 p 1 in the present paper further generalizations of this property are established they consist in replacing a product of the type specified above appearing on the left hand side say of the equality under considerations by an affine combination of two or three such products comments on the problem when the number of components in a combination exceeds three are also given

psychometric functions for pure tone intensity discrimination slope differences in school aged children and adults previous work on pure tone intensity discrimination in school aged children concluded that children might have higher levels of internal noise than adults for this task j acoust soc am 120 2777 2788 2006 if true this would imply that psychometric function slopes are shallower for children than adults a prediction that was tested in the present experiment normal hearing children 5 9 yr and adults were tested in a two stage protocol the first stage used a tracking procedure to estimate 71 correct for intensity discrimination with a gated 500 hz pure tone and a 65 db sound pressure level standard level the mean and standard deviation of these tracks were used to identify a set of five signal levels for each observer in the second stage of the experiment percent correct was estimated at these five levels psychometric functions fitted to these data were significantly shallower for children than adults as predicted by the internal noise hypothesis data from both stages of testing are consistent with a model wherein performance is based on a stable psychometric function with sensitivity limited by psychometric function slope across observers the relationship between slope and threshold conformed closely to predictions of a simple signal detection model

further properties of generalized and hypergeneralized projectors generalized and hypergeneralized projectors introduced by gros and trenkler linear algebra appl 264 1997 463 are revisited several properties of such matrices are established some of the results obtained extend and or generalize those given in the reference above and some others are solutions to new problems

on oblique projectors abstract oblique projectors are useful in many contexts especially in the instrumental variable estimation in regression models in econometrics where the disturbance term tends to be correlated with predictor variables this paper addresses two important questions regarding oblique projectors 1 products of two oblique projectors and 2 decompositions of oblique projectors in 1 we investigate what determines the onto and the along spaces of an oblique projector defined as a product of two oblique projectors under a variety of conditions in 2 we examine various decompositions of oblique projectors when both predictor variables and instrumental variables consist of two distinct sets of variables these decompositions are analogous to those of orthogonal projectors

an application of incomplete pairwise comparison matrices for ranking top tennis players pairwise comparison is an important tool in multi attribute decision making pairwise comparison matrices pcm have been applied for ranking criteria and for scoring alternatives according to a given criterion our paper presents a special application of incomplete pcms ranking of professional tennis players based on their results against each other the selected 25 players have been on the top of the atp rankings for a shorter or longer period in the last 40 years some of them have never met on the court one of the aims of the paper is to provide ranking of the selected players however the analysis of incomplete pairwise comparison matrices is also in the focus the eigenvector method and the logarithmic least squares method were used to calculate weights from incomplete pcms in our results the top three players of four decades were nadal federer and sampras some questions have been raised on the properties of incomplete pcms and remains open for further investigation

on a matrix decomposition of hartwig and spindelbock abstract the main task of the paper is to demonstrate that corollary 6 in r e hartwig k spindelbock matrices for which a and a commute linear and multilinear algebra 14 1984 241 256 provides a powerful tool to investigate square matrices with complex entries this aim is achieved on the one hand by obtaining several original results involving square matrices and on the other hand by reestablishing some of the facts already known in the literature often in extended and or generalized forms the particular attention is paid to the usefulness of the aforementioned corollary to characterize various classes of matrices and to explore matrix partial orderings

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

effect of variability in level on forward masking and on increment detection in the first of four experiments all with the same four subjects varying the level of a forward masker from interval to interval in a two interval forced choice 2ifc adaptive procedure had little effect on threshold in the second experiment the signal level was fixed and performance was measured in units of d varying the level of the forward masker again had little effect analyses of trial by trial data indicated that subjects did not vote for the interval with the higher level masker as would an energy detector performance was better on trials where the masker level in the interval with the signal was lower and was relatively independent of masker level in the nonsignal interval in the third experiment these results were replicated for a wider range of masker variability and with maskers lower in frequency than the signal in the fourth experiment the same range of variability from interval to interval was imposed on the level of the pedestal in an increment detection task results were sim

on a multicommodity stochastic flow network with unreliable nodes subject to budget constraint from the quality management and decision making view point reliability and unreliability are important indices to measure the quality level for a stochastic flow network in a multicommodity stochastic flow network with unreliable nodes the branches and nodes all have several possible capacities and may fail different types of the commodity which are transmitted through the same network simultaneously compete the capacities of branches and nodes in this paper we first define the system capacity as a vector for a multicommodity stochastic flow network with unreliable nodes then we design a performance index which is the probability that the upper bound of the system capacity is a given pattern subject to the budget constraint it can be applied to evaluate the quality level for such a network a simple approach based on minimal cuts is thus presented to evaluate the performance index

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

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

informational masking for simultaneous nonspeech stimuli psychometric functions for fixed and randomly mixed maskers sensitivity d and response bias were measured as a function of target level for the detection of a 1000 hz tone in multitone maskers using a one interval two alternative forced choice 1i 2afc paradigm ten such maskers each with eight randomly selected components in the region 200 5000 hz with 800 1250 hz excluded to form a protected zone were presented under two conditions the fixed condition in which the same eight component masker is used throughout an experimental run and the random condition in which an eight component masker is chosen randomly trial to trial from the given set of ten such maskers differences between the results obtained with these two conditions help characterize the listener s susceptibility to informational masking im the d results show great intersubject variability but can be reasonably well fit by simple energy detector models in which internal noise and filter bandwidth are used as fitting parameters in contrast the results are not well fit by these models in addition to presentation of new data and its relation to energy detector models this paper provides comments on a variety of issues problems and research needs in the im area 2005 acoustical society of america doi 10 1121 1 2032748

effects of a limited class of nonlinearities on estimates of relative weights perturbation analyses have been applied in recent years to determine the relative contribution of individual stimulus components in detection and discrimination tasks responses to stimulus samples are compared to stimulus parameters to determine the details of the decision rule often a linear model is assumed and it is of interest to determine the relative contribution of different stimulus elements to the decision here biases in estimated relative weights are considered for the case where the decision variable is given by d ixin k m and the stimulus components the xi are normally distributed of equal variance and mutually independent the i are the true combination weights and n k and m are positive reals the method used to estimate relative weights is the correlation coefficient between the xi and the observer s responses estimates of relative i do not depend on m but may depend on the mean values of the xi and the values of n and k a dependence on the variance i2 holds even fo

a gentle guide to the basics of two projections theory abstract this paper is a survey of the basics of the theory of two projections it contains in particular the theorem by halmos on two orthogonal projections and roch silbermann gohberg and krupnik s theorem on two idempotents in banach algebras these two theorems which deliver the desired results usually very quickly and comfortably are missing or wrongly cited in many recent publications on the topic the paper is intended as a gentle guide to the field the basic theorems are precisely stated some of them are accompanied by full proofs others not but precise references are given in each case and many examples illustrate how to work with the theorems

further properties of the star left star right star and minus partial orderings certain classes of matrices are indicated for which the star left star right star and minus partial orderings or some of them are equivalent characterizations of the left star and right star orderings similar to those devised by hartwig and styan linear algebra appl 82 1986 145 for the star and minus orderings are established along with other auxiliary results which are of independent interest as well some inheritance type properties of matrices are also given the class of ep matrices appears to be essential in several points of our considerations

stochastic flow networks via multiple paths under time threshold and budget constraint this paper extends the quickest path problem to a stochastic flow network in which the capacity of each arc is variable we mainly evaluate the system reliability that d units of data can be sent from the source to the sink under both time threshold t and budget b in particular the data are transmitted through multiple disjoint minimal paths simultaneously in order to reduce the transmission time a simple algorithm is proposed to generate all lower boundary points for d t b and the system reliability can then be computed in terms of such points by utilizing a union of subsets computational complexity in both worst case and average cases show that the proposed algorithm can be executed efficiently

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

detection of simple and complex changes of spectral shape in most of the previous studies see green 1987 concerning the detection of a change in spectral shape or profile analysis the listener s task was to detect an increment to a single component of an otherwise equal amplitude multicomponent background an important theoretical issue is whether listeners sensitivity to more complex spectral changes can be predicted from these results in the present investigation the sensitivity of a single group of listeners to a wide variety of simple and complex spectral changes was determined after collecting the data it was noted that almost all the thresholds could be predicted by a simple calculation scheme that assumed detection of a change in spectral shape occurs when the addition of the signal to the flat multicomponent background produces a sufficient difference in level between only two regions of the spectrum unfortunately this scheme while successful for our limited set of data fails to account for other profile data namely those obtain

the deterioration of hearing with age frequency selectivity the critical ratio the audiogram and speech threshold the frequency selectivity of the auditory system was measured by masking a sinusoidal signal 0 5 2 0 or 4 0 khz or a filtered speech signal with a wideband noise having a notch or stopband centered on the signal as the notch was widened performance improved for both types of signal but the rate of improvement decreased as the age of the 16 listeners increased from 23 to 75 years indicating a loss in frequency selectivity with age auditory filter shapes derived from the tone in noise data show a that the passband of the filter broadens progressively with age and b that the dynamic range of the filter ages like the audiogram that is the range changes little with age before 55 but beyond this point there is an accelerating rate of loss the speech experiment shows comparable but smaller effects the filter width measurements show that the critical ratio is a poor estimator of frequency selectivity because it confounds the tuning of the system with the efficiency of the signal detection and speech processing mechanisms that follow the filter an alternative one point measure of frequency selectivity which is both sensitive and reliable is developed via the filter shape model of masking

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

reliability evaluation of a revised stochastic flow network with uncertain minimum time abstract this paper constructs a revised stochastic flow network to model a realistic computer network in which each arc has a lead time and a stochastic capacity the minimum time to send a specified amount of data through the network is thus uncertain hence this paper mainly proposes an approach for evaluating the system reliability that d units of data can be transmitted through k minimal paths simultaneously within the time threshold t the idea of lower boundary points for d t the minimal system states satisfying the demand d within the time threshold t is proposed firstly all system states meeting the time and demand requirements can be represented as the union of subsets generated from all lower boundary points for d t and thus the system reliability is computed quickly

discrimination of random time varying spectra with statistical constraints in the present study a sample discrimination procedure is used to examine how various statistical constraints on random time varying spectra might aid listeners in discriminating among these signals time varying spectra were constructed by adding five sequences of tones five tones in each sequence centered at the octave frequencies from 250 to 4000 hz the levels frequencies and durations of the tones varied randomly from one presentation to the next the signal to be detected was an increment in the level of tones comprising the sequence centered at 1000 hz the target sequence three main conditions were examined in which the parameter values of tones varied independently of one another equal variance condition covaried across tone sequences cross channel covariance condition or covaried among themselves for each tone cross parameter covariance condition for the latter two conditions two special cases were examined in which the target sequence varied independently of nontarget sequence

revisitation of the product of two orthogonal projectors abstract several results involving a product of two orthogonal projectors i e hermitian idempotent matrices are established by exploring a representation of the product as a partitioned matrix these results concern for instance rank trace range null space generalized inverses and spectral properties of the product and its various functions particular attention is paid to the conditions equivalent to the requirement that the product of two orthogonal projectors is an orthogonal projector itself and these characterizations refer to such known classes of matrices as hermitian involutory normal star dagger unitary as well as partial isometries and semi orthogonal projectors moreover some results dealing with the notions of parallel sum and spectral norm are obtained the variety of problems considered shows that the approach utilized in the paper provides a powerful tool of wide applicability

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

time version of the shortest path problem in a stochastic flow network many studies on hardware framework and routing policy are devoted to reducing the transmission time for a flow network a time version of the shortest path problem thus arises to find a quickest path which sends a given amount of data from the unique source to the unique sink with minimum transmission time more specifically the capacity of each arc in the flow network is assumed to be deterministic however in many real life networks such as computer systems telecommunication systems etc the capacity of each arc should be stochastic due to failure maintenance etc such a network is named a stochastic flow network hence the minimum transmission time is not a fixed number we extend the quickest path problem to evaluating the probability that d units of data can be sent under the time constraint t such a probability is named the system reliability in particular the data are transmitted through two minimal paths simultaneously in order to reduce the transmission time a simple algorithm is proposed to generate all d t mps and the system reliability can then be computed in terms of d t mps moreover the optimal pair of minimal paths with highest system reliability could be obtained

signal frequency uncertainty in spectral shape discrimination psychometric functions psychometric functions were measured for spectral shape discrimination profile analysis with the signal frequency either fixed what we call the signal known condition or randomly varied what we call the signal unknown condition the functions were obtained using an adaptive up down procedure in the signal unknown condition independent tracks for each signal frequency were interleaved within the same block of trials the mean slope of the psychometric function k in log d k log delta l c where delta l 20 log 1 delta p p was 1 13 for the signal known conditions and 1 19 for the signal unknown condition the mean signal to standard ratio at threshold pc 79 4 obtained in the signal unknown condition was 3 to 4 db higher than that obtained in the signal known conditions the psychometric functions of the ideal observer were derived for both the signal known and signal unknown conditions a comparison of the measured and derived psychometric functions suggests that the internal noise component that is statistically independent across frequency channels contributes minimally to the total internal and external noise sources that are involved in the decision process

on semi star related matrices abstract in this note we introduce semi star related matrices investigate some of their properties and demonstrate how the usual definition of drazin s 1978 star partial ordering can be relaxed

spectral and temporal weights in spectral shape discrimination the coss analysis b g berg j acoust soc am 86 1743 1746 1989 was used to estimate spectral and temporal weights of a three component amplitude modulated stimulus in a spectral shape discrimination task in all experiments the task of the observer was to detect an increment in the level of the center component a spectral temporal weight quantifies the relative influence of a spectral component on the decisions of an observer during a specified segment of the total stimulus duration in the first two experiments the signal was added to all three temporal segments of the center component the ideal weights for each component should be the same across temporal segments spectral temporal weights were obtained for four conditions with different stimulus durations in general the estimated weights for each component were not equal at different temporal segments in the third experiment the signal was added to only one of three segments of the center component ideally weight patterns should have changed when the temporal position of the signal segment was altered two stimulus durations 300 and 15 ms were used for the 300 ms condition the signal was added to only the end segment and for all three observers the weight patterns are different from that obtained in experiment 1 with the signal added to all segments for the 15 ms conditions altering the signal position changed the estimated weights for only one observer

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 property of orthogonal projectors abstract it is shown that if p 1 and p 2 are orthogonal projectors then a product having p 1 and p 2 as its factors is equal to another such product if and only if p 1 and p 2 commute in which case all products involving p 1 and p 2 reduce to the orthogonal projector p 1 p 2 this is a generalization of a result by baksalary and baksalary linear algebra appl 341 2002 129 with the proof based on a simple property of powers of hermitian nonnegative definite matrices

reliability based assignment in stochastic flow freight network based on the reliability of transportation time a transportation assignment model of stochastic flow freight network is designed in this paper this transportation assignment model is built by mean of stochastic chance constraint programming and solved with a hybrid intelligent algorithm hia which integrates genetic algorithm ga stochastic simulation ss and neural network nn ga is employed to report the optimal solution as well as the optimal objective function values of the proposed model ss is used to simulate the value of uncertain system reliability function the uncertain function approximated via nn is embedded into ga to check the feasibility and to compute the fitness of the chromosomes these conclusions have been drawn after a test of numerical case using the proposed formulations system reliability total system cost and flow on each path would finally reach at their own convergence points increase of the system reliability causes increase of the total time cost the system reliability and the total time cost converge at a possible nash equilibrium point

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

generalized and hypergeneralized projectors abstract generalizations of the class of projectors are considered within the classes of normal and ep matrices some properties are derived and results on the sum difference and product of generalized and hypergeneralized projectors are given

models of auditory masking a molecular psychophysical approach gilkey et al j acoust soc am 78 1207 1219 1985 measured hit proportions and false alarm proportions for detecting a 500 hz tone at each of four starting phase angles in each of 25 reproducible noise samples in the present paper their results are modeled by fitting the general form of the electrical analog model of jeffress j acoust soc am 48 480 488 1967 to the diotic data the best fitting configurations of this model do not correspond to energy detectors or to envelope detectors a detector composed of a 50 hz wide single tuned filter followed by a half wave rectifier and an integrator with an integration time of 100 to 200 ms fits the data of all four subjects relatively well linear combinations of the outputs of several detectors that differ in center frequency or integration window provide even better fits to the data these linear combinations assign negative weights to some frequencies or to some time intervals suggesting that a subject s decision is based on a comparison of

two procedures for estimating internal noise internal noise was measured in two paradigms simultaneously in one method the listener s agreement in choosing the same masker as the one in a pair that sounds most signal like is used to estimate internal noise d m green psych rev 71 392 407 1964 in the other the increment in detection performance on those trials having identical as opposed to different maskers is used to estimate internal noise r a siegel unpublished master s thesis m i t 1979 most results place the estimate of additive internal noise as nearly equal to the external noise variability the estimates from the agreement method can be adversely affected by uncertainty regarding the observation interval and interval biases whereas the estimates obtained with the detection method are highly sensitive to measurement errors

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

a note on the rank subtractivity ordering abstract some well known matrix partial orderings can be created by supplementing the so called rank subtractivity partial ordering by an appropriate preordering in this note a new partial ordering with the same property is introduced this new ordering is seen to be weaker than the other orderings but still preserving some inheritance properties

the drazin invertibility of the difference and the sum of two idempotent operators in this note some equivalents are established of the drazin invertibility of differences and sums of idempotent operators on a hilbert space

frequency correlation functions for the detection of a tone added to modulated noise maskers psychophysical experiments using reproducible stimuli were completed for the detection of a 1000 hz tone added to a masker the noise masker was either sinusoidally amplitude modulated or not and masker bandwidths of 100 300 and 900 hz were tested the masker was centered at 1000 hz and the rate of amplitude modulation when present was 29 hz on average comodulation masking release values of 10 and 16 db were obtained for the 300 and 900 hz wide maskers respectively no release from masking was obtained for the 100 hz wide maskers data analysis consisted of computing the correlation coefficient between the level of each spectral component of each stimulus token and the observers responses to that token the resulting correlation functions estimate the relative contribution or weight of different frequency regions to the observers responses while the correlation functions for the modulated and unmodulated maskers share some features differences in both the pattern and quality of fit are apparent for wideband maskers for two of the observers however restricting the region of comparison to the region surrounding the signal frequency led to increased similarity of the correlation functions

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

commutativity of projectors abstract it is known that necessary and sufficient conditions for the sum p 1 p 2 and the difference p 1 p 2 of projectors p 1 and p 2 to be also projectors are p 1 p 2 0 p 2 p 1 and p 1 p 2 p 2 p 2 p 1 respectively independently of whether p 1 and p 2 are orthogonal or not the situation changes when considering the products of p 1 and p 2 in case of orthogonal projectors the condition p 1 p 2 p 2 p 1 is both necessary and sufficient for p 1 p 2 and thus for p 2 p 1 to be a projector but in the general case it discontinues to be necessary even if p 1 p 2 along with p 2 p 1 are required to be projectors the purpose of the present paper is to investigate similarities and dissimilarities of this kind between several results concerning orthogonal projectors and their counterparts corresponding to arbitrary projectors with special emphasis laid on the commutativity condition the investigations refer to matrix representations of projectors as well as to subspaces and generalized inverses connected with them

sensitivity to changes in overall level and spectral shape an evaluation of a channel model two experiments involving level and spectral shape discrimination which test an optimal channel model developed by durlach et al j acoust soc am 80 63 72 1986 are described the model specifies how the auditory system compares and or combines intensity information in different frequency channels in the first experiment psychometric functions were obtained for the discrimination of changes in level and discrimination of changes in spectral shape for an eight tone complex sound a variety of different base spectral shapes were tested in some conditions level randomization was introduced to reduce the reliability of across interval changes in level increasing the amount of level variation degraded performance for the level discrimination task but had no effect on the shape discrimination task in all conditions sensitivity to changes in spectral shape was superior to sensitivity to changes in level consequently two models of central noise are evaluated in an attempt to explain these results one in which central noise acts prior to the formation of the likelihood ratio and one in which central noise degrades the likelihood ratio the former model is more successful in accounting for the data in a second experiment the detectability of a level increment to one component of a multitone complex was measured the frequency content of the complex was varied by systematically removing six components from a 23 component complex thresholds were measured for increments at three different signal frequencies a common trend in the data was that when there was a spectral gap directly above the signal frequency thresholds were lowest this result differs from the predictions of a simple channel model and contrasts with results presented by green and berg q j exp psychol 43a 449 458 1991

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

expansion formulas for the inertias of hermitian matrix polynomials and matrix pencils of orthogonal projectors abstract this paper gives a group of expansion formulas for the inertias of hermitian matrix polynomials a a 2 i a 2 and a a 3 through some congruence transformations for block matrices where a is a hermitian matrix then the paper derives various expansion formulas for the ranks and inertias of some matrix pencils generated from two or three orthogonal projectors and hermitian unitary matrices as applications the paper establishes necessary and sufficient conditions for many matrix equalities to hold as well as many inequalities in the lowner partial ordering to hold

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

a phenomenological model for the responses of auditory nerve fibers i nonlinear tuning with compression and suppression a phenomenological model was developed to describe responses of high spontaneous rate auditory nerve an fibers including several nonlinear response properties level dependent gain compression bandwidth and phase properties were implemented with a control path that varied the gain and bandwidth of tuning in the signal path filter by making the bandwidth of the control path broad with respect to the signal path the wide frequency range of two tone suppression was included by making the control path filter level dependent and tuned to a frequency slightly higher than the signal path filter other properties of two tone suppression were also included these properties included the asymmetrical growth of suppression above and below the characteristic frequency and the frequency offset of the suppression tuning curve with respect to the excitatory tuning curve the implementation of this model represents a relatively simple phenomenological description of a single mechanism that underlies several important nonlinear response properties of an fibers the model provides a tool for studying the roles of these nonlinearities in the encoding of simple and complex sounds in the responses of populations of an fibers

idempotency of linear combinations of two idempotent matrices abstract a complete solution is established to the problem of characterizing all situations where a linear combination of two different idempotent matrices p 1 and p 2 is also an idempotent matrix including naturally three such situations known in the literature viz if the combination is either the sum p 1 p 2 or one of the differences p 1 p 2 p 2 p 1 and appropriate additional conditions are fulfilled the solution asserts that in the particular case where p 1 and p 2 are complex matrices such that p 1 p 2 is hermitian these three situations exhaust the list of all possibilities and that this list extends when the above assumption on p 1 and p 2 is violated a statistical interpretation of the idempotency problem considered in this note is also pointed out

system reliability for quickest path problems under time threshold and budget many studies on hardware framework and routing policy are devoted to reducing the transmission time for a computer network the quickest path problem thus arises to find a path which sends a given amount of data from the source to the sink such that the transmission time is minimized more specifically the capacity of each arc in the network is assumed to be deterministic however in many real life networks such as computer systems telecommunication systems etc the capacity of each arc is stochastic due to failure maintenance etc such a network is named stochastic flow network hence the minimum transmission time is not a fixed number we extend the quickest path problem to evaluating the probability that d units of data can be sent from the source to the sink under both time threshold t and budget b such a probability is named system reliability a simple algorithm is proposed to generate all lower boundary points for d t b and the system reliability can then be computed in terms of such points

perturbation analysis and optimization of stochastic flow networks we consider a stochastic fluid model of a network consisting of several single class nodes in tandem and perform perturbation analysis for the node queue contents and associated event times with respect to a threshold parameter at the first node we then derive infinitesimal perturbation analysis ipa derivative estimators for loss and buffer occupancy performance metrics with respect to this parameter and show that these estimators are unbiased we also show that the estimators depend only on data directly observable from a sample path of the actual underlying discrete event system without any knowledge of the stochastic characteristics of the random processes involved this renders them computable in online environments and easily implementable for network management and optimization this is illustrated by combining the ipa estimators with standard gradient based stochastic optimization methods and providing simulation examples

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

the decision process in forward masked intensity discrimination evidence from molecular analyses in a two interval forced choice intensity discrimination task presenting a fixed increment the level of the forward masker in interval 1 and interval 2 was sampled independently from the same normal distribution on each trial mean and standard deviation of the distribution were varied correlational analyses of the trial by trial data revealed different decision strategies depending on the relation between mean masker level and standard level if the two levels were identical listeners tended to select the interval containing the higher level masker behaving like an energy detector at the output of a temporal window of integration for mean masker level higher than the standard level most listeners showed a negative correlation between the masker level in a given interval and the probability of selecting this interval indicating a strategy of comparing the masker loudness and the target loudness in each of the two observation intervals and voting for the interval where the loudness difference was s