the existence of asymptotically unbiased nonnegative quadratic estimates of variance components in anova models abstract conditions for the existence of asymptotically unbiased nonnegative quadratic estimates of individual variance components in general anova models are investigated a simple necessary condition for general models is obtained necessary and sufficient conditions are obtained in the case of random balanced nested classification models and the random unbalanced one way model the investigation demonstrates the need for exercising caution when employing nonnegative quadratic estimates of individual variance components in practice

delta wye transformations and the efficient reduction of two terminal planar graphs a simple o v 2 time algorithm is presented that reduces a connected two terminal undirected planar graph to a single edge by way of series and parallel reductions and delta wye transformations the method is applied to a class of optimization equilibnum problems which includes max flow shortest path and electrical resistance problems

planar formulae and their uses we define the set of planar boolean formulae and then show that the set of true quantified planar formulae is polynomial space complete and that the set of satisfiable planar formulae is np complete using these results we are able to provide simple and nearly uniform proofs of np completeness for planar node cover planar hamiltonian circuit and line geometric connected dominating set and of polynomial space completeness for planar generalized geography the np completeness of planar node cover and planar hamiltonian circuit and line were first proved elsewhere m r garey and d s johnson the rectilinear steiner tree is np complete siam j appl math 32 1977 pp 826 834 and m r garey d s johnson and r e tarjan the planar hamilton circuit problem is np complete siam j comp 5 1976 pp 704 714

estimating loudness growth from tone burst evoked responses several studies have investigated the relationship between click evoked auditory brainstem responses abrs and loudness growth in human listeners while some of these studies have reported promising results showing a correlative relationship between click abr and loudness growth as a function of level additional studies are necessary to determine if similar results can be obtained with frequency specific stimuli and more specific details of the loudness function can be derived from abr recordings the aims of this study therefore were to 1 develop a fully objective procedure that segments specific features of evoked tone burst abr recordings 2 investigate the feasibility of using information derived from these recordings for estimating frequency specific loudness growth functions and 3 determine to what extent the loudness growth estimation performance through abr can be improved by controlling for residual noise levels and parametric fitting results from eight normal hearing listeners using 1 and 4 khz stimuli show that the average mean square error of the loudness growth estimation obtained through the procedure is comparable to that of standard psychoacoustical procedures used to estimate loudness growth the data set has been made publicly available at www physionet org

calculating k connectedness reliability using steiner bounds the k connectedness reliability problem considered in this paper has as input undirected graph g subset k of terminal vertices and common edge failure probability p and as output the probability rg k p that when edges fail independently each with probability p the set of operating edges connect every pair of vertices of k we show how the steiner property held by the underlying simplicial complex associated with this problem can lead to an extension of the ball provan shellability bounds to this more general problem we show in computational studies that this bound performs quite favorably in comparison with known approximation techniques

the computational complexity of tutte invariants for planar graphs for each pair of algebraic numbers x y the complexity of computing the tutte polynomial t g x y of a planar graph g is determined this computation is found to be overline rm p complete except when x 1 y 1 1 2 or when x y is one of 1 1 1 1 j j 2 or j 2 j where j e 2 pi i 3 in which case it is polynomial time computable a corollary gives the computational complexity of various enumeration problems for planar graphs

analysis of parameters for the estimation of loudness from tone burst otoacoustic emissions there is evidence that tone burst otoacoustic emissions tboaes might be useful for estimating loudness however within listener comparisons between loudness and tboae measurements are an essential prerequisite to determine appropriate analysis parameters for loudness estimation from tboae measurements the purpose of the present work was to collect tboae measurements and loudness estimates across a wide range of levels in the same listeners therefore tboaes were recorded for 1 and 4 khz stimuli and then analyzed using a wide range of parameters to determine which parameter set yielded the lowest mean square error estimation of loudness with respect to a psychoacoustical cross modality matching procedure and the inflected exponential inex loudness model the present results show strong agreement between 1 khz loudness estimates derived from tboaes and loudness estimated using cross modality matching cmm with tboae estimation accounting for almost 90 of the cmm variance additionally the results indicate that analysis parameters may vary within a reasonable range without compromising the results i e the estimates exhibit some parametric robustness the lack of adequate parametric optimization for tboaes at 4 khz suggests that measurements at this frequency are strongly contaminated by ear canal resonances meaning that deriving loudness estimates from tboaes at this frequency is significantly more challenging than at 1 khz

the effect of test signal type and bandwidth on the categorical scaling of loudness recently several methods for obtaining clinical measures of loudness growth through the use of categorical scaling cs have been proposed for the selection of hearing aids these methods use differing test signals or suggest frequency specific level corrections in an attempt to reflect the loudness perception of hearing aid processed speech while some decisions regarding the stimuli utilized for loudness perception procedures are based on measured relationships to speech signals the effect on loudness perception of changing signal type and bandwidth as measured by cs remains unclear the relationships between the cs loudness growth of signals of differing type pure tones noise bands filtered temporally inverted passband speech and bandwidth were examined for subjects with both normal and impaired hearing results suggest that when the bandwidth is similar e g pure tone and 1 3 oct signal type does not have significant bearing on loudness perception as expected increasing the bandwidth beyond the critical band affected loudness growth as wideband speech stimuli were judged to be significantly louder than narrow band speech at equivalent overall sound levels in this investigation similar loudness growth patterns were noted across category ratings for all test signal bandwidths in contrast loudness growth data obtained using an intelligible speech signal cox et al the american academy of audiology 1994a revealed loudness growth patterns for speech were fundamentally different than those obtained for tones implications for hearing aid fitting strategies are discussed recently several methods for obtaining clinical measures of loudness growth through the use of categorical scaling cs have been proposed for the selection of hearing aids these methods use differing test signals or suggest frequency specific level corrections in an attempt to reflect the loudness perception of hearing aid processed speech while some decisions regarding the stimuli utilized for loudness perception procedures are based on measured relationships to speech signals the effect on loudness perception of changing signal type and bandwidth as measured by cs remains unclear the relationships between the cs loudness growth of signals of differing type pure tones noise bands filtered temporally inverted passband speech and bandwidth were examined for subjects with both normal and impaired hearing results suggest that when the bandwidth is similar e g pure tone and 1 3 oct signal type does not have significant bearing on loudness perception as expected increasing the bandwidth bey

the complexity of reliability computations in planar and acyclic graphs we show that the problem of computing source sink reliability is np hard in fact p complete even for undirected and acyclic directed source sink planar graphs having vertex degree at most three thus the source sink reliability problem is unlikely to have an efficient algorithm even when the graph can be laid out on a rectilinear grid

the complexity of the residual node connectedness reliability problem this paper considers a probabilistic network in which the edges are perfectly reliable but the nodes fail with some known probabilities the network is in an operational state if the surviving nodes induce a connected graph the residual node connectedness reliability r g of a network g is the probability that the graph induced by the surviving nodes is connected this reliability measure is very different from the widely studied k terminal network reliability measure it is proven that the problem of computing the residual connectedness reliability is np hard by showing that the problem of counting the number of node induced connected subgraphs of a given graph is bf p complete the problem remains bf p complete for split graphs as well as planar and bipartite graphs

on the hardness of approximate reasoning abstract many ai problems when formalized reduce to evaluating the probability that a propositional expression is true in this paper we show that this problem is computationally intractable even in surprisingly restricted cases and even if we settle for an approximation to this probability we consider various methods used in approximate reasoning such as computing degree of belief and bayesian belief networks as well as reasoning techniques such as constraint satisfaction and knowledge compilation that use approximation to avoid computational difficulties and reduce them to model counting problems over a propositional domain we prove that counting satisfying assignments of propositional languages is intractable even for horn and monotone formulae and even when the size of clauses and number of occurrences of the variables are extremely limited this should be contrasted with the case of deductive reasoning where horn theories and theories with binary clauses are distinguished by the existence of linear time satisfiability algorithms what is even more surprising is that as we show even approximating the number of satisfying assignments i e approximating approximate reasoning is intractable for most of these restricted theories we also identify some restricted classes of propositional formulae for which efficient algorithms for counting satisfying assignments can be given

the complexity of counting self avoiding walks in subgraphs of two dimensional grids and hypercubes valiant siam j comput 8 1979 410 421 showed that the problem of computing the number of simple s t paths in graphs is p complete both in the case of directed graphs and in the case of undirected graphs welsh complexity knots colourings and counting cambridge university press cambridge 1993 p 17 asked whether the problem of computing the number of self avoiding walks of a given length in the complete two dimensional grid is complete for p1 the tally version of p this paper offers a partial answer to the question of welsh it is p complete to compute the number of self avoiding walks of a given length in a subgraph of a two dimensional grid several variations of the problem are also studied and shown to be p complete this paper also studies the problem of computing the number of self avoiding walks in a subgraph of a hypercube similar completeness results are shown for the problem by scaling the computation time to exponential it is shown that computing the number of self avoiding walks in hypercubes is a complete problem for exp in the case when a subgraph of a hypercube is specified by its dimension and a boolean circuit that accepts the nodes finally this paper studies the complexity of testing whether a given word over the four letter alphabet u d l r represents a self avoiding walk in a two dimensional grid a linear space lower bound is shown for nondeterministic turing machines with a 1 way input head to make this test

rate of loudness growth for pure tones in normal and impaired hearing the present article provides an analysis of loudness growth rates in normal and cochlear impaired hearing for diverse groups with respect to age and backgrounds slopes are obtained from absolute magnitude estimation and magnitude production of loudness measured values and from cross modality matching and absolute magnitude estimation of apparent length predicted values consistent with an earlier study r p hellman and c h meiselman j acoust soc am 88 2596 2606 1990 slopes calculated within the 15 30 db stimulus range above the elevated threshold increase in size with the degree of hearing loss the corresponding range of loudness values in normal hearing yields a slope near 0 60 independent of the threshold levels this pattern of loudness growth holds for individuals and groups but the intersubject variability of the slope is more labile being larger across than within groups and larger for the measured slopes than for the predicted values determined from the predicted slopes the coefficient of variation sigma m is approximately constant in normal and impaired hearing ranging from 20 27 in contrast sigma m obtained from the measured slopes increases with the degree of hearing loss to a value of almost 50 for a 75 db loss the overall stability and systematics of the observed effects further demonstrate that the loudness intensity relation can be specified with reasonable precision and accuracy from cross modality matching

jordan algebras and bayesian quadratic estimation of variance components the authors consider a linear model ey x cov y v where v is a quadratic subspace a jordan algebra using this property it is shown how multiplication computation of g inverses determination of a neutral element can be done more efficiently in v finally this technique is applied to obtain formulae for locally optimal estimators and bayesian estimators

the complexity of counting in sparse regular and planar graphs we show that a number of graph theoretic counting problems remain cal np hard indeed cal p complete in very restricted classes of graphs in particular we prove that the problems of counting matchings vertex covers independent sets and extremal variants of these all remain hard when restricted to planar bipartite graphs of bounded degree or regular graphs of constant degree we obtain corollaries about counting cliques in restricted classes of graphs and counting satisfying assignments to restricted classes of monotone 2 cnf formulae to achieve these results a new interpolation based reduction technique which preserves properties such as constant degree is introduced

the measurement of loudness in individual children and adults by absolute magnitude estimation and cross modality matching twelve adults and 11 children age range 4 7 years performed absolute magnitude estimation of the apparent lengths of lines and the loudnesses of 1000 hz tones as well as cross modality matching between loudness and apparent line length consistent with the notion that children and adults have similar impressions of loudness there were no major differences between the absolute magnitude estimation ame and cross modality matching cmm data of the adults and children a direct comparison between the exponents for loudness by ame and cmm was made when a correction factor was employed to eliminate the effects of idiosyncratic use of numbers from the ame exponents the results support the hypothesis that with proper instructions both children and adults can judge stimuli on an absolute scale specifically for 9 out of 12 adults and 9 out of 11 children lines and tones assigned the same number in absolute magnitude estimation were judged to be subjectively equal in cross modality matching

two dimensional monomer dimer systems are computationally intractable the classic problem of counting monomer dimer arrangements on a two dimensional lattice is analyzed using techniques from theoretical computer science under a certain assumption made precise in the text it can be shown that the general problem is computationally intractable this negative result contrasts with the special case of a system with monomer density zero for which efficient solutions have been known for some time a second much easier result obtained under the same assumption is that the partition function of a three dimensional ising system is computationally intractable again the negative result contrasts with known efficient techniques for evaluating the partition function of a two dimensional system

cross modality matching and the loudness growth function for click stimuli loudness intensity functions for click stimuli were obtained from 30 adult listeners having normal n 10 flat n 10 or sloping n 10 high frequency cochlear hearing loss configurations the procedure of cross modality matching cmm between loudness and perceived line length r p hellman and c h meiselman j speech hear res 31 605 615 1988 j acoust soc am 88 2596 2606 1990 j acoust soc am 93 966 975 1993 was used to validate their loudness growth functions mean group loudness exponents were similar to those reported in recent investigations that utilized pure tone stimuli further supporting the validity and reliability of the cmm task as an estimate of the loudness growth function the results also suggest that the mean loudness function for clicks is similar to the function obtained with tonal stimuli at least for listeners with moderately impaired hearing or better moreover cmm produced less variability than the more conventional psychophysical methods of magnitude estimation and production for the groups with cochlear hearing loss toward direct application of the cmm technique in lieu of absolute exponential slope values the individually determined loudness growth function over a range of intensities should be compared to the normal mean functions for calculations of deviations

note on a linear time algorithm for computing k terminal reliability in a series parallel network in an original and very interesting paper satyanarayana and wood 1 concerning polygon to chain reductions in a stochastic network a small inconsistency occurs in the proof of theorem 1 in particular this happens in cases where the whole set of bit k vertices lies in the remaining polygon such an example is the case of polygon type 5 where the appropriate note has been made by the authors for hbox bit k 2 analogous notes must also be made for polygon types 4 6 and 7 when bit k 2 3 and 4 respectively the correct transformations are given in table 1 note that dark vertices are bit k vertices

on unapproximable versions of np complete problems we prove that all of karp s 21 original np complete problems have a version that is hard to approximate these versions are obtained from the original problems by adding essentially the same simple constraint we further show that these problems are absurdly hard to approximate in fact no polynomial time algorithm can even approximate log k of the magnitude of these problems to within any constant factor where logk denotes the logarithm iterated k times unless np is recognized by slightly superpolynomial randomized machines we use the same technique to improve the constant epsilon such that max clique is hard to approximate to within a factor of n epsilon finally we show that it is even harder to approximate two counting problems counting the number of satisfying assignments to a monotone 2sat formula and computing the permanent of 1 0 1 matrices

the complexity of planar counting problems we prove the p hardness of the counting problems associated with various satisfiability graph and combinatorial problems when restricted to planar instances these problems include 3sat 1 3sat 1 ex3sat minimum vertex cover minimum dominating set minimum feedback vertex set x3c partition into triangles and clique cover we also prove the np completeness of the ambiguous satisfiability problems j b saxe two papers on graph embedding problems tech report cmu cs 80 102 dept of computer science carnegie mellon univ pittsburgh pa 1980 and the dp completeness with respect to random polynomial reducibility of the unique satisfiability problems l g valiant and v v vazirani np is as easy as detecting unique solutions in proc 17th acm symp on theory of computing 1985 pp 458 463 associated with several of the above problems when restricted to planar instances previously very few p hardness results no sf np hardness results and no dp completeness results were known for counting problems ambiguous satisfiability problems and unique satisfiability problems respectively when restricted to planar instances assuming sf p neq np one corollary of the above results is that there are no epsilon approximation algorithms for the problems of maximizing or minimizing a linear objective function subject to a planar system of linear inequality constraints over the integers

the delta wye approximation procedure for two terminal reliability the delta wye approximation procedure dwap is a procedure for estimating the two terminal reliability of an undirected planar network g v e by reducing the network to a single edge via a sequence of local graph transformations it combines the probability equations of lehman whose solutions provide bounds and approximations of two terminal reliability for the individual transformations with the delta wye reduction algorithm of the second two authors which performs the corresponding graph reduction in o v 2 time a computational study is made comparing the dwap to one of the best currently known methods for approximating two terminal reliability and it is shown that the dwap produces approximations that are between 10 and 80 times as accurate

loudness relations for individuals and groups in normal and impaired hearing individual and group loudness relations were obtained at a frequency in the region of impaired hearing for 100 people 98 with bilateral cochlear impairment slope distributions were determined from absolute magnitude estimation ame and absolute magnitude production amp of loudness they were also derived from cross modality matching cmm and ame of apparent length with respect to both the means and the individual slope values the two distributions closely agree more than half of the measured deviations are less than 20 with an overall average of 1 5 meaning that transitivity is preserved for bilaterally impaired individuals moreover over the stimulus range where cochlear impairment steepens the loudness function both the group means and the individual slope values are clearly larger than in normal hearing the results also show that for groups of people with approximately similar losses the standard deviation is a nearly constant proportion of the mean slope value giving a coefficient of variation of about 27 in normal and impaired hearing this indicates in accord with loudness matching that the size of the slopes depends directly on the degree of hearing loss the results disclose that loudness measurements obtained by magnitude scaling are able to reveal the operating characteristic of the ear for individuals