the determinant of a tree s neighborhood matrix abstract let n be an n n neighborhood matrix for a tree or forest we show that det n is bounded by the nth fibonacci number we obtain a simple elegant algorithm to compute det n that operates directly on the forest and uses o n space and o n arithmetic operations

the influence of age and high frequency hearing loss on sensitivity to temporal fine structure at low frequencies l sensitivity to temporal fine structure tfs at low frequencies may be adversely affected by hearing loss at high frequencies even when absolute thresholds at low frequencies are within the normal range however in several studies suggesting this the effects of hearing loss and age were confounded here interaural phase discrimination ipd thresholds for pure tones at 500 and 750 hz were measured for 39 subjects with ages from 61 to 83 yr all subjects had near normal audiometric thresholds at low frequencies but thresholds varied across subjects at high frequencies ipd thresholds were correlated with age ipd thresholds for the test frequency of 750 hz were weakly correlated with absolute thresholds at high frequencies but these correlations became non significant when the effect of age was partialed out the results do not confirm that sensitivity to tfs at low frequencies is influenced by hearing loss at high frequencies independently of age

trees with minimal laplacian coefficients let g be a simple undirected graph with the characteristic polynomial of its laplacian matrix l g p g m email protected k 0 n 1 kc email protected n k it is well known that for trees the laplacian coefficient c n 2 is equal to the wiener index of g while c n 3 is equal to the modified hyper wiener index of the graph in this paper we characterize n vertex trees with given matching number m which simultaneously minimize all laplacian coefficients the extremal tree a n m is a spur obtained from the star graph s n m 1 with n m 1 vertices by attaching a pendant edge to each of certain m 1 non central vertices of s n m 1 in particular a n m minimizes the wiener index the modified hyper wiener index and the recently introduced incidence energy of trees defined as ie g email protected k 0 email protected k where m k are the eigenvalues of signless laplacian matrix q g d g a g we introduced a general r transformation which decreases all laplacian coefficients simultaneously in conclusion we illustrate on examples of wiener index and incidence energy that the opposite problem of simultaneously maximizing all laplacian coefficients has no solution

analyzing lattice networks through substructures abstract analyzing the topology of network structures is an important topic studied from many different aspects of science and mathematics the wiener polarity index number of unordered pairs of vertices at distance 3 from each other is one of the representative descriptors of graph structures it was computed for several lattice networks by chen et al 11 in an effort to understand the properties of these networks the wiener polarity index is a variation of the classic distance based graph invariant the wiener index sum of distances between all pairs of vertices which is known to be closely related to the number of substructures in this paper we examine the numbers of various subgraphs of order 4 for these lattice networks in addition to confirming their symmetric nature comparing the numbers of various substructures leads to insights on other less trivial characteristics of these network structures of common interest

the effect of tone vocoding on spatial release from masking for old hearing impaired listeners old hearing impaired listeners generally benefit little from lateral separation of multiple talkers when listening to one of them this study aimed to determine how spatial release from masking srm in such listeners is affected when the interaural time differences itds in the temporal fine structure tfs are manipulated by tone vocoding tvc at the ears by a master hearing aid system word recall was compared with and without tvc when target and masker sentences from a closed set were played simultaneously from the front loudspeaker co located and when the maskers were played 45 to the left and right of the listener separated for 20 hearing impaired listeners aged 64 to 86 srm was 3 7 db smaller with tvc than without tvc this difference in srm correlated with mean audiometric thresholds below 1 5 khz even when monaural tfs sensitivity discrimination of frequency shifts in identically filtered complexes was partialed out suggesting that low frequency audiometric thresholds may be a good indicator of candidacy for hearing aids that preserve itds the tvc difference in srm was not correlated with age pure tone itd thresholds nor fundamental frequency difference limens and only with monaural tfs sensitivity before control for low frequency audiometric thresholds

an explicit formula for eigenvalues of bethe trees and upper bounds on the largest eigenvalue of any tree a bethe tree bd k is a rooted unweighted of k levels in which the root vertex has degree equal to d the vertices at level j 2 j k 1 have degree equal to d 1 and the vertices at level k are the pendant vertices in this paper we first derive an explicit formula for the eigenvalues of the adjacency matrix of bd k moreover we give the corresponding multiplicities next we derive an explicit formula for the simple nonzero eigenvalues among them the largest eigenvalue of the laplacian matrix of bd k finally we obtain upper bounds on the largest eigenvalue of the adjacency matrix and of the laplacian matrix of any tree t these upper bounds are given in terms of the largest vertex degree and the radius of t and they are attained if and only if t is a bethe tree

on the laplacian coefficients of tricyclic graphs abstract let g d e t i n l g k 0 n 1 k c k n k be the characteristic polynomial of the laplacian matrix of a graph g of order n in this paper we show that among all connected tricyclic graphs of order n the k th coefficient c k is smallest when the graph is b n 7 1 3 3 3 obtained from the complete graph k 4 by adding n 4 pendent vertices attached to the vertex of degree 3 and for some lemmas in c x he h y shan on the laplacian coefficients of bicyclic graphs discrete math 310 2010 3404 3412 we present a new method to prove them

abnormal processing of temporal fine structure in speech for frequencies where absolute thresholds are normal the identification of nonsense syllables that were lowpass filtered at 1 5khz was compared for subjects with normal hearing and subjects with mild to severe hearing loss at high frequencies but with normal or near normal hearing at low frequencies absolute thresholds were mostly within the normal range 20db hearing level for both groups for frequencies below 1 5khz performance was assessed with intact speech speech that had been processed to preserve only temporal envelope cues in a few frequency bands e speech and speech that had been processed to remove envelope cues as far as possible while preserving temporal fine structure cues again in a few frequency bands tfs speech for the intact speech and e speech the hearing impaired subjects performed slightly more poorly than the normal hearing subjects but this effect was significant only for the intact speech for the tfs speech the hearing impaired subjects performed significantly more poorly than the normal hearing subjects with 12 out o

the laplacian incidence energy of graphs abstract the laplacian incidence energy of a graph is defined as the sum of the singular values of its normalized oriented incidence matrix in this paper we give sharp upper and lower bounds as well as the coulson integral formula for the laplacian incidence energy moreover we show a close relation of the laplacian incidence energy normalized incidence energy and randic energy

applications of recurrence relations for the characteristic polynomials of bethe trees a bethe tree of k levels b k d is a rooted tree such that the root vertex has degree d the vertices from level 2 to k 1 have degree d 1 and the vertices at level k are leaves in this paper we obtain a recurrence relation for the characteristic polynomial and the laplacian characteristic polynomial of bethe trees as an application we prove that there are no integral bethe trees except for the star b 2 n 2 and we obtain a recurrence relation for the laplacian energy like invariant of bethe trees

relations between frequency selectivity temporal fine structure processing and speech reception in impaired hearing frequency selectivity temporal fine structure tfs processing and speech reception were assessed for six normal hearing nh listeners ten sensorineurally hearing impaired hi listeners with similar high frequency losses and two listeners with an obscure dysfunction od tfs processing was investigated at low frequencies in regions of normal hearing through measurements of binaural masked detection tone lateralization and monaural frequency modulation fm detection lateralization and fm detection thresholds were measured in quiet and in background noise speech reception thresholds were obtained for full spectrum and lowpass filtered sentences with different interferers both the hi listeners and the od listeners showed poorer performance than the nh listeners in terms of frequency selectivity tfs processing and speech reception while a correlation was observed between the monaural and binaural tfs processing deficits in the hi listeners no relation was found between tfs processing and frequency selectivity the effect of noise on tfs processing was not larger for the hi listeners than for the nh listeners finally tfs processing performance was correlated with speech reception in a two talker background and lateralized noise but not in amplitude modulated noise the results provide constraints for future models of impaired auditory signal processing

asymptotic energy of lattices abstract the energy of a simple graph g arising in chemical physics denoted by e g is defined as the sum of the absolute values of eigenvalues of g as the dimer problem and spanning trees problem in statistical physics in this paper we propose the energy per vertex problem for lattice systems in general for a type of lattice in statistical physics to compute the entropy constant with toroidal cylindrical mobius band klein bottle and free boundary conditions are different tasks with different hardness and may have different solutions we show that the energy per vertex of plane lattices is independent of the toroidal cylindrical mobius band klein bottle and free boundary conditions in particular the asymptotic formulae of energies of the triangular 3 3 4 2 and hexagonal lattices with toroidal cylindrical mobius band klein bottle and free boundary conditions are obtained explicitly

the effect of interaural delay of the masker on masking level differences in young and old adults diotic sono thresholds and dichotic s pi n pi tau thresholds were measured for young and old adults using a 500 hz pure tone signal and broadband burst masking noise at 37 db spl hz in the dichotic condition both the signal and the masker were phase reversed and the masker was presented with an interaural delay of 0 25 0 5 0 75 1 1 25 1 5 1 75 2 3 or 5 ms masking level differences mlds were determined by subtracting dichotic thresholds from diotic thresholds the sono thresholds for the old subjects did not differ significantly from those for the young subjects however when mlds were plotted as a function of delay the pattern of results differed significantly between young and old subjects this difference in pattern was completely accounted for in terms of a delay line version of durlach s equalization and cancellation ec model n i durlach in foundations of modern auditory theory edited by j v tobias academic new york 1972 b a schneider and p m zurek j acoust soc am 86 1756 1763 1989 by assuming that temporal jitter increases with internal delay in young subjects but that it does not vary with the amount of internal delay in old subjects

adaptive approximation bounds for vertex based contour encoding when approximating the shape of a region a fixed bound on the tolerable distortion is set for approximating its contour points an adaptive approximation bound for lossy coding of the contour points is proposed a function representing the relative significance of the contour points is defined to adjust the distortion bound along the region contour allowing an adaptive approximation of the region shape the effectiveness of the adaptive contour coding approach for a region based coding system is verified through experiments

on the energy of some circulant graphs we give an explicit construction of circulant graphs of very high energy this construction is based on gauss sums we also show the littlewood conjecture can be used to establish new result for a certain class of circulant graphs

the spectra of the adjacency matrix and laplacian matrix for some balanced trees abstract let t be an unweighted rooted tree of k levels such that in each level the vertices have equal degree let dk j 1 denotes the degree of the vertices in the level j we find the eigenvalues of the adjacency matrix and of the laplacian matrix of t they are the eigenvalues of principal submatrices of two nonnegative symmetric tridiagonal matrices of order k k the codiagonal entries for both matrices are d j 1 2 j k 1 and d k while the diagonal entries are zeros in the case of the adjacency matrix and dj 1 j k in the case of the laplacian matrix moreover we give some results concerning to the multiplicity of the above mentioned eigenvalues

discrimination of interaural temporal disparities by normal hearing listeners and listeners with high frequency sensorineural hearing loss thresholds of ongoing interaural time difference itd were obtained from normal hearing and hearing impaired listeners who had high frequency sensorineural hearing loss several stimuli a 500 hz sinusoid a narrow band noise centered at 500 hz a sinusoidally amplitude modulated 4000 hz tone and a narrow band noise centered at 4000 hz and two criteria equal sound pressure level eq spl and equal sensation level eq sl for determining the level of stimuli presented to each listener were employed the itd thresholds and slopes of the psychometric functions were elevated for hearing impaired listeners for the two high frequency stimuli in comparison to a the listener s own low frequency thresholds and b data obtained from normal hearing listeners for stimuli presented with eq spl interaurally the two groups of listeners required similar itds to reach threshold when stimuli were presented at eq sls to each ear for low frequency stimuli the itd thresholds of the hearing impaired listener were

energy matching number and odd cycles of graphs abstract the energy e g of a graph g is the sum of the absolute values of the eigenvalues of the adjacency matrix of g wong et al 2018 11 proved that e g 2 g where g denotes the matching number of g we settle the equality case that was left open from that paper we also show that for connected graphs without perfect matching e g 2 g 1 except for complete bipartite graphs of the form k r r 1 further for graphs with vertex disjoint cycles we prove that e g 2 g c o g where c o g denotes the number of odd cycles of g with length at least 5 this improves another result of wong et al

the importance of temporal fine structure information in speech at different spectral regions for normal hearing and hearing impaired subjects speech reception thresholds srts were measured for target and competing speech signals processed to contain variable amounts of temporal fine structure tfs information signals were filtered into 30 1 erb n wide channels where erb n refers to the bandwidth of normal auditory filters which were either tone vocoded preserving temporal envelope information extracted using the hilbert transform or left unprocessed containing both tfs and envelope information improvements in srt were compared when tfs was progressively introduced starting with the high or low frequency channels the results suggest some redundancy in the tfs information across frequency regions in a second experiment the signal was divided into five 6 erb n wide spectral regions four of which were tone vocoded the remaining region was either absent creating a spectral notch or was present and unprocessed srts were measured for normal hearing and hearing impaired subjects conditions where all channels were vocoded or unprocessed were also included normal hearing subjects benefited similarly when tfs information was added to each region suggesting that tfs information is important over a wide frequency range hearing impaired subjects benefited less although the benefit varied across subjects benefit from tfs information in speech was correlated with a psychophysical measure of tfs sensitivity obtained at two center frequencies

estimating three dimensional motion parameters of a rigid planar patch we present a new direct method of estimating the three dimensional motion parameters of a rigid planar patch from two time sequential perspective views image frames first a set of eight pure parameters are defined these parameters can be determined uniquely from the two given image frames by solving a set of linear equations then the actual motion parameters are determined from these pure parameters by a method which requires the solution of a sixth order polynomial of one variable only and there exists a certain efficient algorithm for solving a sixth order polynomial aside from a scale factor for the translation parameters the number of real solutions never exceeds two in the special case of three dimensional translation the motion parameters can be expressed directly as some simple functions of the eight pure parameters thus only a few arithmetic operations are needed

the energy of a graph abstract the energy e g of a simple graph g is defined to be the sum of the absolute values of the eigen values of g if g is a k regular graph on n vertices then e g k k n 1 n k b 2 and this bound is sharp it is shown that for each 0 there exist infinitely many n for each of which there exists a k regular graph g of order n with k e g b 2 two graphs with the same number of vertices are equienergetic if they have the same energy we show that for any positive integer n 3 there exist two equienergetic graphs of order 4n that are not cospectral

graphs and matrices with maximal energy abstract given a complex m n matrix a we index its singular values as 1 a 2 a and call the value e a 1 a 2 a the energy of a thereby extending the concept of graph energy introduced by gutman koolen and moulton proved that e g n 2 1 n for any graph g of order n and exhibited an infinite family of graphs with e g v g 2 1 v g we prove that for all sufficiently large n there exists a graph g g n with e g n 3 2 2 n 11 10 this implies a conjecture of koolen and moulton we also characterize all square nonnegative matrices and all graphs with energy close to the maximal one in particular such graphs are quasi random

on the laplacian coefficients of unicyclic graphs abstract let g be a graph of order n and let p g k 0 n 1 k c k n k be the characteristic polynomial of its laplacian matrix generalizing an approach of mohar on graph transformations we show that among all connected unicyclic graphs of order n the k th coefficient c k is largest when the graph is a cycle c n and smallest when the graph is the a s n with an additional edge between two of its pendent vertices a relation to the recently established laplacian like energy of a graph is discussed

the effects of age and cochlear hearing loss on temporal fine structure sensitivity frequency selectivity and speech reception in noise temporal fine structure tfs sensitivity frequency selectivity and speech reception in noise were measured for young normal hearing nhy old normal hearing nho and hearing impaired hi subjects two measures of tfs sensitivity were used the tfs lf test interaural phase difference discrimination and the tfs2 test discrimination of harmonic and frequency shifted tones these measures were not significantly correlated with frequency selectivity after partialing out the effect of audiometric threshold suggesting that insensitivity to tfs cannot be wholly explained by a broadening of auditory filters the results of the two tests of tfs sensitivity were significantly but modestly correlated suggesting that performance of the tests may be partly influenced by different factors the nho group performed significantly more poorly than the nhy group for both measures of tfs sensitivity but not frequency selectivity suggesting that tfs sensitivity declines with age in the absence of elevated audiometric thresholds or broadened auditory filters when the effect of mean audiometric threshold was partialed out speech reception thresholds in modulated noise were correlated with tfs2 scores but not measures of frequency selectivity or tfs lf test scores suggesting that a reduction in sensitivity to tfs can partly account for the speech perception difficulties experienced by hearing impaired subjects

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

remarks on hyperenergetic circulant graphs we first settle an open problem of balakrishnan from linear algebra appl 387 2004 287 295 further if ci n k1 k2 km n n k1 k2 km n 2 ki n for i 1 2 m denotes a circulant graph with the vertex set v 0 1 n 1 such that a vertex u is adjacent to all vertices of v u except u ki mod n i 1 2 m w e show that for any given k1 k2 km almost all circulant graphs ci n k1 k2 km are hyperenergetic

lower bounds of nikiforov s energy over digraphs abstract the energy of a graph g is defined as e g i 1 n i where 1 2 n are the eigenvalues of the adjacency matrix of g this concept was extended by nikiforov 8 to digraphs as n d i 1 n i where d is a digraph with n vertices and singular values 1 n upper bounds of n were found by kharaghani and tayfeh rezaie 4 in this work we find lower bounds of n over the set of digraphs

the energy of graphs and matrices abstract given a complex m n matrix a we index its singular values as 1 a 2 a and call the value e a 1 a 2 a the energy of a thereby extending the concept of graph energy introduced by gutman let 2 m n a be an m n nonnegative matrix with maximum entry and a 1 n extending previous results of koolen and moulton for graphs we prove that e a a 1 m n m 1 a 2 2 a 1 2 m n n m m 2 furthermore if a is any nonconstant matrix then e a 1 a a 2 2 1 2 a 2 a finally we note that wigner s semicircle law implies that e g 4 3 o 1 n 3 2 for almost all graphs g

remarks on the energy of regular graphs abstract the energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix this note is about the energy of regular graphs it is shown that graphs that are close to regular can be made regular with a negligible change of the energy also a k regular graph can be extended to a k regular graph of a slightly larger order with almost the same energy as an application it is shown that for every sufficiently large n there exists a regular graph g of order n whose energy g satisfies g 1 2 n 3 2 n 13 10 several infinite families of graphs with maximal or submaximal energy are given and the energy of almost all regular graphs is determined

generalized interframe vertex based shape encoding scheme for video sequences the efficiency of shape coding is an important problem concerning content based image manipulations and object based coding of the video sequences in order to encode the shape information of an object the boundary is approximated by a polygon which can be encoded with the smallest number of bits for maximum allowable distortion the conventional boundary coding schemes however does not successfully remove the temporal redundancy of the video sequences this paper proposes a new boundary encoding scheme by which the temporal redundancy between two successive frames is efficiently removed resulting in lower bit rate than the conventional algorithms the interframe vertex selection problem is solved by finding the path with the minimum cost in the directed acyclic graph dag and its fast version using a simplified graph is introduced to reduce the computational load the vertices were selected from both the current frame to be encoded and the previous frame already encoded and thus the temporal redundancy was effectively removed

moderate cochlear hearing loss leads to a reduced ability to use temporal fine structure information the ability of normally hearing and hearing impaired subjects to use temporal fine structure information in complex tones was measured subjects were required to discriminate a harmonic complex tone from a tone in which all components were shifted upwards by the same amount in hz in a three alternative forced choice task the tones either contained five equal amplitude components non shaped stimuli or contained many components but were passed through a fixed bandpass filter to reduce excitation pattern changes shaped stimuli components were centered at nominal harmonic numbers n 7 11 and 18 for the shaped stimuli hearing impaired subjects performed much more poorly than normally hearing subjects with most of the former scoring no better than chance when n 11 or 18 suggesting that they could not access the temporal fine structure information performance for the hearing impaired subjects was significantly improved for the non shaped stimuli presumably because they could benefit from spectral cues it is proposed that normal hearing subjects can use temporal fine structure information provided the spacing between fine structure peaks is not too small relative to the envelope period but subjects with moderate cochlear hearing loss make little use of temporal fine structure information for unresolved components

evaluation of a method for enhancing interaural level differences at low frequencies a method called binaural enhancement for enhancing interaural level differences at low frequencies based on estimates of interaural time differences was developed and evaluated five conditions were compared all using simulated hearing aid processing 1 linear amplification with frequency response shaping 2 binaural enhancement combined with linear amplification and frequency response shaping 3 slow acting four channel amplitude compression with independent compression at the two ears agc4ch 4 binaural enhancement combined with four channel compression be agc4ch and 5 four channel compression but with the compression gains synchronized across ears ten hearing impaired listeners were tested and gains and compression ratios for each listener were set to match targets prescribed by the cam2 fitting method stimuli were presented via headphones using virtualization methods to simulate listening in a moderately reverberant room the intelligibility of speech at 60 azimuth in the presence of competing speech on the opposite side of the head at 60 azimuth was not affected by the binaural enhancement processing sound localization was significantly better for condition be agc4ch than for condition agc4ch for a sentence but not for broadband noise lowpass noise or lowpass amplitude modulated noise the results suggest that the binaural enhancement processing can improve localization for sounds with distinct envelope fluctuations

use of high rate envelope speech cues and their perceptually relevant dynamic range for the hearing impaired the ability of hearing impaired hi listeners to use high rate envelope information in a competing talker situation was assessed in experiment 1 signals were tone vocoded and the cutoff frequency fc of the envelope extraction filter was either 50 hz e filter or 200 hz p filter the channels for which the p or e filter was used were varied intelligibility was higher with the p filter regardless of whether it was used for low or high center frequencies performance was best when the p filter was used for all channels experiment 2 explored the dynamic range over which hi listeners made use of high rate cues in each channel of a vocoder the envelope extracted using fc 16 hz was replaced by the envelope extracted using fc 300 hz either at the peaks or valleys with a parametrically varied switching threshold for a target to background ratio of 5 db changes in speech intelligibility occurred mainly when the switching threshold was between 8 and 8 db relative to the channel root mean square level this range is similar in width to but about 3 db higher in absolute level than that found for normal hearing listeners despite the reduced dynamic range of the hi listeners