on the minimal free resolution of n 1 general forms o roig abstract let r k x1 xn and let i be the ideal of n 1 generically chosen forms of degrees d1 dn 1 we give the precise graded betti numbers of r i in the following cases n 3 n 4 and p5 1 di is even n 4 p 5 1 di is odd and d2 d3 d4 d1 d5 4 n is even and all generators have the same degree a which is even pn 1 i 1 di i n is even and d2 dn d1 dn 1 n p n 1 i 1 di i n is odd n 6 is even d2 dn d1 dn 1 n and d1 dn i dn 1 i n 0 we give very good bounds on the graded betti numbers in many other cases we also extend a result of m boij by giving the graded betti numbers for a generic compressed gorenstein algebra i e one for which the hilbert function is maximal given n and the socle degree when n is even and the socle degree is large a recurring theme is to examine when and why the minimal free resolution may be forced to have redundant summands we conjecture that if the forms all have the same degree then there are no redundant summands and we present some evidence for this conjecture

ideals with stable betti numbers componentwise linear ideals were introduced earlier to generalize the result that the stanley reisner ideal i of a simplicial complex has a linear resolution if and only if its alexander dual is cohen macaulay it turns out that i is componentwise linear if and only if is sequentially cohen macaulay in this paper we discuss betti number properties of componentwise linear ideals let i be a graded ideal of a polynomial ring s and gin i the generic initial ideal of i with respect to the reverse lexicographic term order on s our main result is that i and gin i admit the same graded betti numbers if and only if i is componentwise linear for the proof of this fact we describe some properties of the betti diagram of a generic initial ideal combinatorial implications for shifted complexes will also be discussed

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

the absolutely koszul and backelin roos properties for spaces of quadrics of small codimension abstract let k be a field r a standard graded quadratic k algebra with dim k r 2 3 and let k denote an algebraic closure of k we construct a graded surjective golod homomorphism p r k k such that p is a complete intersection of codimension at most 3 furthermore we show that r is absolutely koszul that is every finitely generated r module has finite linearity defect if and only if r is koszul if and only if r is not a trivial fiber extension of a standard graded k algebra with hilbert series 1 2 t 2 t 3 1 t 1 in particular we recover earlier results on the koszul property of backelin 4 conca 7 and d ali 11

isomorphism classes of short gorenstein local rings via macaulay s inverse system in this paper we study the isomorphism classes of artinian gorenstein local rings with socle degree three by means of macaulay s inverse system we prove that their classification is equivalent to the projective classification of the hypersurfaces of p n of degree three this is an unexpected result because it reduces the study of this class of local rings to the homogeneous case the result has applications in problems concerning the punctual hilbert scheme hilbd p n and

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

minimal resolution of relatively compressed level algebras a relatively compressed algebra with given socle degrees is an artinian quotient a of a given graded algebra r c whose hilbert function is maximal among such quotients with the given socle degrees for us c is usually a general complete intersection and we usually require that a be level the precise value of the hilbert function of a relatively compressed algebra is open and we show that finding this value is equivalent to the froberg conjecture we then turn to the minimal free resolution of a level algebra relatively compressed with respect to a general complete intersection when the algebra is gorenstein of even socle degree we give the precise graded betti numbers when it is of odd socle degree we give good bounds on the graded betti numbers we also relate this case to the minimal resolution conjecture of musta for points on a projective variety finding the graded betti numbers is essentially equivalent to determining to what extent there can be redundant summands i e ghost terms in the minimal free resolution i e when copies of the same r t can occur in two consecutive free modules this is easy to arrange using koszul syzygies we show that it can also occur in more surprising situations that are not koszul using the equivalence to the froberg conjecture we show that in a polynomial ring where that conjecture holds e g in three variables the possible non koszul ghost terms are extremely limited finally we use the connection to the froberg conjecture as well as the calculation of the minimal free resolution for relatively compressed gorenstein algebras to find the minimal free resolution of general artinian almost complete intersections in many new cases this greatly extends previous work of the first two authors

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

speech perception localization and lateralization with bilateral cochlear implants five bilateral cochlear implant users were tested for their localization abilities and speech understanding in noise for both monaural and binaural listening conditions they also participated in lateralization tasks to assess the impact of variations in interaural time delays itds and interaural level differences ilds for electrical pulse trains under direct computer control the localization task used pink noise bursts presented from an eight loudspeaker array spanning an arc of approximately 108 in front of the listeners at ear level 0 degree elevation subjects showed large benefits from bilateral device use compared to either side alone typical root mean square rms averaged errors across all eight loudspeakers in the array were about 10 for bilateral device use and ranged from 20 to 60 using either ear alone speech reception thresholds srts were measured for sentences presented from directly in front of the listeners 0 in spectrally matching speech weighted noise at either 0 90 or 90 for four subjects out of five tested who could perform the task for noise to either side bilateral device use showed a substantial benefit over unilateral device use when noise was ipsilateral to the unilateral device this was primarily because of monaural head shadow effects which resulted in robust srt improvements p 0 001 of about 4 to 5 db when ipsilateral and contralateral noise positions were compared the additional benefit of using both ears compared to the shadowed ear i e binaural unmasking was only 1 or 2 db and less robust p 0 04 results from the lateralization studies showed consistently good sensitivity to ilds better than the smallest level adjustment available in the implants 0 17 db for some subjects sensitivity to itds was moderate on the other hand typically of the order of 100 s itd sensitivity deteriorated rapidly when stimulation rates for unmodulated pulse trains increased above a few hundred hz but at 800 pps showed sensitivity comparable to 50 pps pulse trains when a 50 hz modulation was applied in our opinion these results clearly demonstrate important benefits are available from bilateral implantation both for localizing sounds in quiet and for listening in noise when signal and noise sources are spatially separated the data do indicate however that effects of interaural timing cues are weaker than those from interaural level cues and according to our psychophysical findings rely on the availability of low rate information below a few hundred hz

poincare series of compressed local artinian rings with odd top socle degree abstract we define a notion of compressed local artinian ring that does not require the ring to contain a field let r m be a compressed local artinian ring with odd top socle degree s at least five and socle r m s 1 m s we prove that the poincare series of all finitely generated modules over r are rational sharing a common denominator and that there is a golod homomorphism from a complete intersection onto r

nonsense syllable recognition in noise using monaural and binaural listening strategies using a binaurally equipped kemar manikin syllables of the cuny nonsense syllable test were recorded in sound field at 0 degree azimuth against a background of cafeteria noise at 270 degrees azimuth at several signal to noise s n ratios the combination of inputs recorded at each ear was delivered to ten normal hearing nh and eight sensorineurally hearing impaired hi listeners through insert earphones to produce five experimental listening conditions 1 binaural head shadow hs in which ear presentation was analogous to the original stimulus recording 2 binaural favorable bf in which the noise shadowed right ear recording was presented to both ears 3 monaural favorable mf in which the noise shadowed recording was presented only to the right ear 4 monaural unfavorable mu in which the noise unshadowed left ear recording was presented only to the left ear and 5 simulated monaural aided sma in which the noise shadowed recording was presented to the right ear and the noise unshadowed recording attenuated by 20 db relative to the hs condition was presented to the left ear all main effects subject type listening condition and s n ratio were statistically significant normal listeners showed 3 3 and 3 2 db advantages respectively due to head shadow and binaural squelch over hearing impaired listeners some hearing impaired listeners performed better under the sma or bf conditions than under the hs condition potential digital signal processing strategies designed to optimize speech understanding under binaurally aided listening conditions are discussed

prediction of speech intelligibility in spatial noise and reverberation for normal hearing and hearing impaired listeners binaural speech intelligibility of individual listeners under realistic conditions was predicted using a model consisting of a gammatone filter bank an independent equalization cancellation ec process in each frequency band a gammatone resynthesis and the speech intelligibility index sii hearing loss was simulated by adding uncorrelated masking noises according to the pure tone audiogram to the ear channels speech intelligibility measurements were carried out with 8 normal hearing and 15 hearing impaired listeners collecting speech reception threshold srt data for three different room acoustic conditions anechoic office room cafeteria hall and eight directions of a single noise source speech in front artificial ec processing errors derived from binaural masking level difference data using pure tones were incorporated into the model except for an adjustment of the sii to intelligibility mapping function no model parameter was fitted to the srt data of this study the overall correlation coefficient between predicted and observed srts was 0 95 the dependence of the srt of an individual listener on the noise direction and on room acoustics was predicted with a median correlation coefficient of 0 91 the effect of individual hearing impairment was predicted with a median correlation coefficient of 0 95 however for mild hearing losses the release from masking was overestimated

the explicit minimal resolution constructed from a macaulay inverse system abstract let a be a standard graded artinian gorenstein algebra of embedding codimension three over a field k in the generic case the minimal homogeneous resolution g of a by free sym k a 1 modules is gorenstein linear fix a basis x y z for the k vector space a 1 if g is gorenstein linear then the socle degree of a is necessarily even and if n is the least index with dim k a n less than dim k sym n k a 1 then the socle degree of a is 2 n 2 let m m as m roams over the monomials in x y z of degree 2 n 2 with m k be an arbitrary homogeneous element of degree 2 n 2 in the divided power module d k a 1 the annihilator of denoted ann is the ideal of elements f in sym k a 1 with f 0 the element of d k a 1 is the macaulay inverse system for the ring sym k a 1 ann which is necessarily gorenstein and artinian consider the matrix m m as m and m roam over the monomials in x y z of degree n 1 the ring sym k a 1 ann has a gorenstein linear resolution if and only if det m m 0 if det m m 0 then we give explicit formulas for the minimal homogeneous resolution of sym k a 1 ann in terms the m s and x y z

predicting binaural speech intelligibility using the signal to noise ratio in the envelope power spectrum domain this study proposes a binaural extension to the multi resolution speech based envelope power spectrum model mr sepsm jorgensen ewert and dau 2013 j acoust soc am 134 436 446 it consists of a combination of better ear be and binaural unmasking processes implemented as two monaural realizations of the mr sepsm combined with a short term equalization cancellation process and uses the signal to noise ratio in the envelope domain snrenv as the decision metric the model requires only two parameters to be fitted per speech material and does not require an explicit frequency weighting the model was validated against three data sets from the literature which covered the following effects the number of maskers the masker types speech shaped noise ssn speech modulated ssn babble and reversed speech the masker s azimuths reverberation on the target and masker and the interaural time difference of the target and masker the pearson correlation coefficient between the simulated spee

proof of the gorenstein interval conjecture in low socle degree abstract roughly ten years ago the following gorenstein interval conjecture gic was proposed whenever 1 h 1 h i h e i h e 1 1 and 1 h 1 h i h e i h e 1 1 are both gorenstein hilbert functions for some 2 then 1 h 1 h i h e i h e 1 1 is also gorenstein for all 1 2 1 since an explicit characterization of which hilbert functions are gorenstein is widely believed to be hopeless the gic if true would at least provide the existence of a strong and very natural structural property for such basic functions in commutative algebra before now very little progress was made on the gic the main goal of this note is to prove the case e 5 in arbitrary codimension our arguments will be in part constructive and will combine several different tools of commutative algebra and classical algebraic geometry

the effect of spatial separation in distance on the intelligibility of speech in rooms the influence of spatial separation in source distance on speech reception thresholds srts is investigated in one scenario the target was presented at 0 5 m distance and the masker varied from 0 5 m distance up to 10 m in a second scenario the masker was presented at 0 5 m distance and the target distance varied the stimuli were synthesized using convolution with binaural room impulse responses brirs measured on a dummy head in a reverberant auditorium and were equalized to compensate for distance dependent spectral and intensity changes all sources were simulated directly in front of the listener srts decreased monotonically when the target was at 0 5 m and the speech masker was moved further away resulting in a srt improvement of up to 10 db when the speech masker was at 0 5 m and the target was moved away a large variation across subjects was observed neither short term signal to noise ratio snr improvements nor cross ear glimpsing could account for the observed improvement in intelligibility however the effect might be explained by an improvement in the snr in the modulation domain and a decrease in informational masking this study demonstrates that distance related cues can play a significant role when listening in complex environments

compressed algebras artin algebras having given socle degrees and maximal length j emsalem and the author showed in 18 that a general polynomialf of degree j in the ring sp k yl yr has jr rl 1 linearly independent partial derivates of order i for i 0 1 t j 2 here we generalize the proof to show that the various partial derivates of s polynomials of specified degrees are as independent as possible given the room available using this result we construct and describe the varieties g e and z e parametrizing the graded and nongraded compressed algebra quotients a r i of the power series ring r k xl sxr having given socle type e these algebras are artin algebras having maximal length dimk a possible given the embedding degree r and given the socle type sequence e els s es where ei is the number of generators of the dual module a of a having degree i the variety z e is locally closed irreducible and is a bundle over g e fibred by affine spaces an whose dimension is known we consider the compressed algebras a new class of interesting algebras and a source of examples many of them are nonsmoothable have no deformation to k k for dimension reasons for some choices of the sequence e d buchsbaum d eisenbud and the author have shown that the graded compressed algebras of socle type e have almost linear minimal resolutions over r with ranks and degrees determined by e other examples have given type e dimk socle a and are defined by an ideal i with certain given numbers of generators in r

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

expected total test time and bayesian estimation for generalized lindley distribution under progressively type ii censored sample where removals follow the beta binomial probability law in this paper we have proposed the progressive type ii censoring scheme which allows the removals of the live units from a life test with beta binomial probability law during the execution of the experiment to stablish the theory the generalized lindley distribution is considered for our proposed procedure the behaviour of the expected total test time has been investigated through the numerical study the classical as well as the bayesian procedures for the estimation of the unknown model parameters have also been developed under this censoring scheme further the discussion has been extended to the prediction of the future samples under bayesian paradigm finally a real data set has been analysed to illustrate the discussed methodology

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

the effect of better ear glimpsing on spatial release from masking the current experiment investigated whether better ear glimpsing can explain the spatial release achieved by normal hearing adults when situations are high in informational masking both modeling and behavioral methods were used the speech reception thresholds of 38 young adults were measured for co located spatially separated and two better ear glimpsed conditions in the better ear glimpsed conditions the binaural signals were processed so that in each time frequency segment the signal with the better snr left or right ear was presented diotically to investigate the effect of widening auditory filters on better ear glimpsing adjacent frequency bands were combined in one of the better ear glimpsing conditions twenty two participants were tested with maskers high in informational masking while 16 participants were tested with maskers lower in informational masking the mean speech reception thresholds achieved in the glimpsed conditions were significantly worse than in the spatially separated condition this suggests that better ear glimpsing can explain some but not all of the observed spatial release from masking the difference between performance in the spatially separated and glimpsed conditions was largest when informational masking was high suggesting better ear glimpsing may release energetic rather than informational masking reducing the number of frequency bands sampled had a small effect on performance

the structure of gorenstein linear resolutions of artinian algebras abstract let k be a field a a standard graded artinian gorenstein k algebra s the standard graded polynomial ring sym k a 1 i the kernel of the natural map d the vector space dimension dim k a 1 and n the least index with i n 0 assume that 3 d and 2 n in this paper we give the structure of the minimal homogeneous resolution b of a by free s modules provided b is gorenstein linear keep in mind that if a has even socle degree and is generic then a has a gorenstein linear minimal resolution our description of b depends on a fixed but arbitrary decomposition of a 1 of the form k x 1 v 0 for some non zero element x 1 and some d 1 dimensional subspace v 0 of a 1 much information about b is already contained in the complex b b x 1 b which we call the skeleton of b one striking feature of b is the fact that the skeleton of b is completely determined by the data d n no other information about a is used in the construction of b the skeleton b is the mapping cone of zero k l where l is a well known resolution of buchsbaum and eisenbud k is the dual of l and l and k are comprised of schur and weyl modules associated to hooks respectively the decomposition of b into schur and weyl modules lifts to a decomposition of b furthermore b inherits the natural self duality of b the differentials of b are explicitly given in a polynomial manner in terms of the coefficients of a macaulay inverse system for a in light of the properties of b the description of the differentials of b amounts to giving a minimal generating set of i and for the interior differentials giving the coefficients of x 1 as an application we observe that every non zero element of a 1 is a weak lefschetz element for a

reducible family of height three level algebras let r k x 1 x r be the polynomial ring in r variables over an infinite field k and let m be the maximal ideal of r here a level algebra will be a graded artinian quotient a of r having socle soc a 0 m in a single degree j the hilbert function h a h 0 h 1 h j gives the dimension h i dim k a i of each degree i graded piece of a for 0 i j the embedding dimension of a is h 1 and the type of a is dim k soc a here h j the family levalg h of level algebra quotients of r having hilbert function h forms an open subscheme of the family of graded algebras or via macaulay duality of a grassmannian we show that for each of the hilbert functions h 1 3 4 4 and h 2 1 3 6 8 9 3 the family levalg h has several irreducible components theorems 2 3 a 2 4 we show also that these examples each lift to points however in the first example an irreducible betti stratum for artinian algebras becomes reducible when lifted to points theorem 2 3 b we show that the second example is the first in an infinite sequence of examples of type three hilbert functions h c in which also the number of components gets arbitrarily large theorem 2 10 the first case where the phenomenon of multiple components can occur i e the lowest embedding dimension and then the lowest type is that of dimension three and type two examples of this first case have been obtained by the authors unpublished and also by j o kleppe

betti strata of height two ideals abstract let r k x y denote the polynomial ring in two variables over an infinite field k we study the betti strata of the family g h parametrizing graded artinian quotients of r k x y having given hilbert function h the betti stratum g h parametrizes all quotients a of having the graded betti numbers determined by h and the minimal relation degrees with i dim k tor 1 r i k i we recover that the betti strata are irreducible and we calculate their codimension in the family g h theorem the codimension of g h in g h satisfies letting i generators of degree i and i relations of degree i cod g h i i i here min i h i i 1 the initial degree of the ideals when k is algebraically closed we also show that the closure of a betti stratum is the union of more special strata and is cohen macaulay theorem 2 18 our method is to identify g h as a product of determinantal varieties ours is a more direct argument than that of a iarrobino v kanev power sums gorenstein algebras and determinantal loci lecture notes in math vol 1721 springer heidelberg 1999 345 xxvii pp theorem 5 63 which obtains the codimension of betti substrata of a postulation stratum for punctual subschemes of p 2 there we relied on a result of m boij determining the codimension of betti strata of height three gorenstein algebras m boij betti number strata of the space of codimension three gorenstein artin algebras preprint 2001 key tools throughout include properties of an invariant v the number of generators of the ancestor ideal v r and previous results concerning the projective variety g h in a iarrobino punctual hilbert schemes mem amer math soc 10 188 1977 we adapt a method of m boij that reduces the calculation of the codimension of the betti strata to showing that the most special stratum has the right codimension as applications we determine which hilbert functions are possible for artinian quotients of r given the socle type theorem 3 2 and we also determine the hilbert function of the intersection of t general enough level ideals in r each having a specified hilbert function theorem 3 6

inverse system of a symbolic power i abstract the authors determine macaulay s inverse system to a symbolic power of the graded ideal of functions vanishing at a union of irreducible varieties in projective space

hilbert functions and level algebras abstract the authors consider certain quotients a r i of the polynomial ring r k x1 xr over an arbitrary field k they first determine upper and lower bounds on the hilbert functions of any algebra having the form a r v where v is the largest ideal of r agreeing in degrees at least j with the ideal v generated by a vector subspace v rj of degree j forms these bounds extend the macaulay bounds theorem 1 4 a level artinian quotient of a r i has socle soc a 0 m m x1 xr in a single degree j the authors next determine the extremal hilbert functions hmax t j r and hmin t j r that occur for level graded artin algebra quotients of r having socle degree j and type t dimk soc a and they describe the extremal strata theorem 1 8 they next give a natural upper bound for the hilbert function of level algebra quotients of the coordinate ring o z of a punctual subscheme z p n n r 1 in terms of the hilbert function h z and j t this bound was known and known to be sharp in the case z is locally gorenstein and t 1 finally they show that there are no level algebras of hilbert function t 1 3 4 5 6 2 proposition 2 7 given that there are smooth punctual subschemes z of p 2 with hilbert function h z 1 3 4 5 6 6 this result shows that the sharpness of the natural upper bound in the case where z is gorenstein and t 1 does not extend to level algebra quotients of type 2 even when z is smooth the extremality results for the hilbert functions of level algebras and some counterexamples use the extremality theorem of f h s macaulay 1927 proc london math soc 26 531 555 and g gotzmann s 1978 math z 158 61 70 results on the hilbert scheme

binaural speech intelligibility in noise for hearing impaired listeners the effect of head induced interaural time delay itd and interaural level differences ild on binaural speech intelligibility in noise was studied for listeners with symmetrical and asymmetrical sensorineural hearing losses the material recorded with a kemar manikin in an anechoic room consisted of speech presented from the front 0 and noise presented at azimuths of 0 30 and 90 derived noise signals containing either only itd or only ild were generated using a computer for both groups of subjects speech reception thresholds srt for sentences in noise were determined as a function of 1 noise azimuth 2 binaural cue and 3 an interaural difference in overall presentation level simulating the effect of a monaural hearing aid comparison of the mean results with corresponding data obtained previously from normal hearing listeners shows that the hearing impaired have a 2 5 db higher srt in noise when both speech and noise are presented from the front and 2 6 5 1 db less binaural gain when the noise azimuth is changed from 0 to 90 the gain due to ild varies among the hearing impaired listeners between o db and normal values of 7 db or more it depends on the high frequency hearing loss at the side presented with the most favorable signal to noise s n ratio the gain due to itd is nearly normal for the symmetrically impaired 4 2 db compared with 4 7 db for the normal hearing but only 2 5 db in the case of asymmetrical impairment when itd is introduced in noise already containing ild the resulting gain is 2 2 5 db for all groups the only marked effect of the interaural difference in overall presentation level is a reduction of the gain due to ild when the level at the ear with the better s n ratio is decreased this implies that an optimal monaural hearing aid with a moderate gain will hardly interfere with unmasking through itd while it may increase the gain due to ild by preventing or diminishing threshold effects

free resolutions over short gorenstein local rings let r be a local ring with maximal ideal mathfrak m admitting a non zero element a in mathfrak m for which the ideal 0 a is isomorphic to r ar we study minimal free resolutions of finitely generated r modules m with particular attention to the case when mathfrak m 4 0 let e denote the minimal number of generators of mathfrak m if r is gorenstein with mathfrak m 4 0 and e 3 we show that rm p m r t is rational with denominator h r t 1 et et 2 t 3 for each finitely generated r module m in particular this conclusion applies to generic gorenstein algebras of socle degree 3

generic bounds for frobenius closure and tight closure we use geometric and cohomological methods to show that given a degree bound for membership in ideals of a fixed degree type in the polynomial ring p k x 0 ldots x d one obtains a good generic degree bound for membership in the tight closure of an ideal of that degree type in any standard graded k algebra r of dimension d 1 this indicates that the tight closure of an ideal behaves more uniformly than the ideal itself moreover if r is normal one obtains a generic bound for membership in the frobenius closure if d leq 2 then the bound for ideal membership in p can be computed from the known cases of the fr oberg conjecture and yields explicit generic tight closure bounds

hilbert function of local artinian level rings in codimension two abstract in this paper we characterize the possible hilbert functions of a local artinian level ring of given type and socle degree in the codimension two case in particular given an admissible numerical function h an effective method is given to produce a zero dimensional ideal i of r k x y such that r i is a local artinian level ring having h as hilbert function as a consequence we recover the well known result proved by briancon and iarrobino concerning the hilbert functions of a complete intersection of height two we extend notions of standard or grobner bases from the graded to the local algebra context the principal tools concern the concepts of enhanced standard basis and generic initial ideals which are defined for an ideal in the formal power series ring r k x 1 x n

inverse limits of macaulay s inverse systems abstract generalizing a result of masuti and the second author we describe inverse limits of macaulay s inverse systems for cohen macaulay factor algebras of formal power series or polynomial rings over an infinite field on the way we find a strictness result for filtrations defined by regular sequences it generalizes both a lemma of uli walther and the rees isomorphism

families of artinian and one dimensional algebras abstract the purpose of this paper is to study families of artinian or one dimensional quotients of a polynomial ring r with a special look to level algebras let gradalg h r be the scheme parametrizing graded quotients of r with hilbert function h let b a be any graded surjection of quotients of r with hilbert function h b 1 h 1 h j and h a respectively if dim a 0 respectively dim a depth a 1 and a is a truncation of b in the sense that h a 1 h 1 h j 1 0 0 respectively h a 1 h 1 h j 1 for some h j then we show there is a close relationship between gradalg h a r and gradalg h b r concerning e g smoothness and dimension at the points a and b respectively provided b is a complete intersection or provided the castelnuovo mumford regularity of a is at least 3 sometimes 2 larger than the regularity of b in the complete intersection case we generalize this relationship to non truncated artinian algebras a which are compressed or close to being compressed for more general artinian algebras we describe the dual of the tangent and obstruction space of graded deformations in a manageable form which we make rather explicit for level algebras of cohen macaulay type 2 this description and a linkage theorem for families allow us to prove a conjecture of iarrobino on the existence of at least two irreducible components of gradalg h r h 1 3 6 10 14 10 6 2 whose general elements are artinian level algebras of type 2

ancestor ideals of vector spaces of forms and level algebras let r k x1 xr denote the polynomial ring in r variables over a field k with maximal ideal m x1 xr and let v rj denote a vector subspace of the space rj of degree j homogeneous elements of r we study three related algebras determined by v the first is the ancestor algebra anc v r v whose defining ancestor ideal v is the largest graded ideal of r such that v mj v the ideal generated by v the second is the level algebra la v r l v whose defining ideal l v is the largest graded ideal of r such that the degree j component l v rj is v and third is the algebra r v we have that l v v mj 1 when r 2 we determine the possible hilbert functions h for each of these algebras and as well the dimension of each hilbert function stratum we characterize the graded betti numbers of these algebras in terms of certain partitions depending only on h and give the codimension of each stratum in terms of invariants of the partitions we show that when r 2 and k is algebraically closed the hilbert function strata for each of the three algebras attached to v satisfy a frontier property that the closure of a stratum is the union of more special strata in each case the family g h of all graded ideals of the given hilbert function is a natural desingularization of this closure we then solve a refinement of the simultaneous waring problem for sets of degree j binary forms key tools throughout include properties of an invariant v the number of generators of v k x1 x2 and previous results concerning the projective variety g h in mem amer math soc vol 10 188 1977

normal bundle of rational curves and waring decomposition abstract the problem of determining the splitting of the normal bundle of rational space curves has been considered in the 80s in a series of papers by ghione and sacchiero and by eisenbud and van de ven with our approach we are able to obtain results for curves embedded in p m for m 3 and we find an interesting interplay between the waring decomposition of binary forms and the splitting of the normal bundle

a non unimodal codimension 3 level h vector 1 3 6 10 15 21 28 27 27 28 is a level h vector this example answers negatively the open question as to whether all codimension 3 level h vectors are unimodal moreover using the same simple technique we are able to construct level algebras of codimension 3 whose h vectors have exactly n maxima for any positive integer n these non unimodal h vectors in particular provide examples of codimension 3 level algebras not enjoying the weak lefschetz property wlp their existence was also an open problem before in the second part of the paper we further investigate this fundamental property and show that there even exist codimension 3 level algebras of type 3 without the wlp

effect of spatial separation extended bandwidth and compression speed on intelligibility in a competing speech task the benefit for speech intelligibility of extending the bandwidth of hearing aids was assessed when the target speech sentences and background two talkers were co located or spatially separated also the relative benefits of slow and fast compression were assessed sixteen hearing impaired hi subjects with mild to moderate high frequency hearing loss and eight normal hearing nh subjects were tested the target and interfering sounds were recorded using a kemar manikin and were located at 60 azimuth either co located or spatially separated simulated binaural hearing aid processing using five channel slow or fast compression was performed offline with gains set individually for each hi subject upper cutoff frequencies were 5 7 5 or 10 khz processed stimuli were presented via headphones for both nh unaided and hi subjects there was no significant effect of cutoff frequency for the co located condition but a small but significant benefit from increasing the cutoff frequency from 5 to 7

algebraic geometric comparison of probability distributions we propose a novel algebraic algorithmic framework for dealing with probability distributions represented by their cumulants such as the mean and covariance matrix as an example we consider the unsupervised learning problem of finding the subspace on which several probability distributions agree instead of minimizing an objective function involving the estimated cumulants we show that by treating the cumulants as elements of the polynomial ring we can directly solve the problem at a lower computational cost and with higher accuracy moreover the algebraic viewpoint on probability distributions allows us to invoke the theory of algebraic geometry which we demonstrate in a compact proof for an identifiability criterion

on the hilbert function of one dimensional local complete intersections abstract the sequences that occur as hilbert functions of standard graded algebras a are well understood by macaulay s theorem those that occur for graded complete intersections are elementary and were known classically however much less is known in the local case once the dimension of a is greater than zero or the embedding dimension is three or more using an extension to the power series ring r of grobner bases with respect to local degree orderings we characterize the hilbert functions h of one dimensional quadratic complete intersections a r i i f g of type 2 2 that is that are quotients of the power series ring r in three variables by a regular sequence f g whose initial forms are linearly independent and of degree 2 we also give a structure theorem up to analytic isomorphism of a for the minimal system of generators of i given the hilbert function more generally when the type of i is 2 b we are able to give some restrictions on the hilbert function in this case we can also prove that the associated graded algebra of a is cohen macaulay if and only if the hilbert function of a is strictly increasing

on the number of channels needed to understand speech recent studies have shown that high levels of speech understanding could be achieved when the speech spectrum was divided into four channels and then reconstructed as a sum of four noise bands or sine waves with frequencies equal to the center frequencies of the channels in these studies speech understanding was assessed using sentences produced by a single male talker the aim of experiment 1 was to assess the number of channels necessary for a high level of speech understanding when sentences were produced by multiple talkers in experiment 1 sentences produced by 135 different talkers were processed through n 2 n 16 number of channels synthesized as a sum of n sine waves with frequencies equal to the center frequencies of the filters and presented to normal hearing listeners for identification a minimum of five channels was needed to achieve a high level 90 of speech understanding asymptotic performance was achieved with eight channels at least for the speech material used in this study the outcome of experiment 1 demonstrated that the number of channels needed to reach asymptotic performance varies as a function of the recognition task and or need for listeners to attend to fine phonetic detail in experiment 2 sentences were processed through 6 and 16 channels and quantized into a small number of steps the purpose of this experiment was to investigate whether listeners use across channel differences in amplitude to code frequency information particularly when speech is processed through a small number of channels for sentences processed through six channels there was a significant reduction in speech understanding when the spectral amplitudes were quantized into a small number 8 of steps high levels 92 of speech understanding were maintained for sentences processed through 16 channels and quantized into only 2 steps the findings of experiment 2 suggest an inverse relationship between the importance of spectral amplitude resolution number of steps and spectral resolution number of channels

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

interval estimation of parameters of life from progressively censored data a conditional method of inference is used to derive exact confidence intervals for several life characteristics such as location scale quantiles and reliability when the data are type ii progressively censored the method is shown to be feasible and practical although a computer program may be required for its implementation the method is applied for the purpose of illustration to the extreme value and the one and two parameter exponential models prediction limits for the lifelength of future units are also discussed an example consisting of data from an accelerated test on insulating fluid reported by nelson is used for illustration and comparison

mle and the estimated expected test time for the two parameter gompertz distribution under progressive censoring with binomial removals this study considers the estimation of two parameter gompertz distribution under type ii progressive censoring with random removals where the number of units removed at each failure time follows a binomial or a uniform distribution the maximum likelihood estimates of two parameters and their asymptotic distribution are derived the expected termination point to complete the censoring test is computed and analyzed for different censoring schemes for binomial removals the effect of various p on the expected termination point under progressive censoring and the relative expected termination point over the complete sample reet1 are investigated in this article for random removals pcr the expected termination point is computed and the relative expected termination point over the complete sample reet2 are also investigated

sentence reception in noise from one versus two sources effects of aging and hearing loss sentence reception thresholds srts and babble detection thresholds bdts were measured for signals presented from loudspeakers located at 0 deg and 90 deg azimuth in addition the s b ratios necessary to achieve srt in the presence of a 12 talker babble were determined under three conditions in which the speech and babble were presented from the same or spatially separated loudspeakers in the first experiment normal hearing subjects were tested on two occasions the results were highly reliable with standard errors of the test retest differences of less than 1db for all conditions in the second experiment srts bdts and s b ratios were measured for three normal hearing groups 39 40 54 and 55 years and for a fourth group with presbycusis 55 years presbycusics had higher srts and bdts than all other groups regardless of age and the oldest normals had higher thresholds than younger subjects presbycusics required higher s b ratios than any of the normal groups and the oldest normal group needed a higher s b ratio compared to the youngest group all groups demonstrated a significant advantage in s b ratio when the sentences and babble sources were spatially separated compared to when they were presented from the same loudspeaker there was no significant difference in the magnitude of advantage due to spatial separation of speech and noise between the normal groups regardless of age but the presbycusics had significantly smaller advantages than all normals these findings suggest that aging alone does not impair the ability to take advantage of the spatial separation of speech and noise and that the speech reception problems of aging individuals involve various components that depend upon the nature of the listening task

poincare series of modules over local rings of small embedding codepth or small linking number abstract let s n k be a commutative noetherian local ring and m be a finitely generated s module then the poincare series of m is rational if any of the following holds edim s depth s 3 edim s depth s 4 and s is gorenstein s is one link from a complete intersection s is two links from a complete intersection and s is gorenstein to prove this result we assume without loss of generality that s r i with r m regular local and the key to the argument is to produce a factorization of the canonical map r s as a composition of a complete intersection r c with a golod map c s this is accomplished by invoking a theorem of avramov and backelin once one has existence of a dg algebra structure on a minimal r free resolution of s together with detailed knowledge of the structure of the induced homology algebra tor r s k h k s linkage theory provides the main technical tool for this analysis

artinian level algebras of socle degree 4 abstract in this paper we study the o sequences of local or graded k algebras of socle degree 4 more precisely we prove that an o sequence h 1 3 h 2 h 3 h 4 where h 4 2 is the h vector of a local level k algebra if and only if h 3 3 h 4 a characterization is also presented for gorenstein o sequences in each of these cases we give an effective method to construct a local level k algebra with a given h vector moreover we refine a result of elias and rossi by showing that if h 1 h 1 h 2 h 3 1 is a unimodal gorenstein o sequence then h forces the corresponding gorenstein k algebra to be canonically graded if and only if h 1 h 3 and h 2 h 1 1 2 that is the h vector is maximal we discuss analogue problems for higher socle degrees

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

the influence of non spatial factors on measures of spatial release from masking this study tested the hypothesis that the reduction in spatial release from masking srm resulting from sensorineural hearing loss in competing speech mixtures is influenced by the characteristics of the interfering speech a frontal speech target was presented simultaneously with two intelligible or two time reversed unintelligible speech maskers that were either colocated with the target or were symmetrically separated from the target in the horizontal plane the difference in srm between listeners with hearing impairment and listeners with normal hearing was substantially larger for the forward maskers deficit of 5 8 db than for the reversed maskers deficit of 1 6 db this was driven by the fact that all listeners regardless of hearing abilities performed similarly and poorly in the colocated condition with intelligible maskers the same conditions were then tested in listeners with normal hearing using headphone stimuli that were degraded by noise vocoding reducing the number of available spectral channels systematically reduced the measured srm and again more so for forward reduction of 3 8 db than for reversed speech maskers reduction of 1 8 db the results suggest that non spatial factors can strongly influence both the magnitude of srm and the apparent deficit in srm for listeners with impaired hearing

decomposing gorenstein rings as connected sums in 2012 ananthnarayan avramov and moore gave a new construction of gorenstein rings they defined a connected sum of two gorenstein local rings as an appropriate quotient of their fibre product given a gorenstein ring one would like to know whether it can be decomposed as a connected sum and if so what are its components we answer these questions in the case of a gorenstein artin local algebra over a field

minimal free resolution of a finitely generated module over a regular local ring abstract numerical invariants of a minimal free resolution of a module m over a regular local ring r n can be studied by taking advantage of the rich literature on the graded case the key is to fix suitable n stable filtrations m of m and to compare the betti numbers of m with those of the associated graded module gr m m this approach has the advantage that the same module m can be detected by using different filtrations on it it provides interesting upper bounds for the betti numbers and we study the modules for which the extremal values are attained among others the koszul modules have this behavior as a consequence of the main result we extend some results by aramova conca herzog and hibi on the rigidity of the resolution of standard graded algebras to the local setting

homological properties of powers of the maximal ideal of a local ring abstract it is known that the powers m n of the maximal ideal of a local noetherian ring share certain homological properties for all sufficiently large integers n for example the natural homomorphisms r r m n are golod respectively small for all large n we give effective bounds on the smallest integers n for which such properties begin to hold

koszul homology and extremal properties of gin and lex for every homogeneous ideal i in a polynomial ring r and for every p dim r we consider the koszul homology h i p r i with respect to a sequence of p of generic linear forms the koszul betti number ijp r i is by definition the dimension of the degree j part of h i p r i in characteristic 0 we show that the koszul betti numbers of any ideal i are bounded above by those of the gin revlex gin i of i and also by those of the lex segment lex i of i we show that ijp r i ijp r gin i iff i is componentwise linear and that and ijp r i ijp r lex i iff i is gotzmann we also investigate the set gins i of all the gin of i and show that the koszul betti numbers of any ideal in gins i are bounded below by those of the gin revlex of i on the other hand we present examples showing that in general there is no j is gins i such that the koszul betti numbers of any ideal in gins i are bounded above by those of j

the effect of age on auditory spatial attention in conditions of real and simulated spatial separation the contributions of auditory and cognitive factors to age dependent differences in auditory spatial attention were investigated in conditions of real spatial separation the target sentence was presented from a central location and competing sentences were presented from left and right locations in conditions of simulated spatial separation different apparent spatial locations of the target and competitors were induced using the precedence effect the identity of the target was cued by a callsign presented either prior to or following each target sentence and the probability that the target would be presented at the three locations was specified at the beginning of each block younger and older adults with normal hearing sensitivity below 4khz completed all 16 conditions 2 spatial separation method 2 callsign conditions 4 probability conditions overall younger adults performed better than older adults for both age groups performance improved with target location certainty with a priori tar

the structure of the inverse system of gorenstein k algebras abstract macaulay s inverse system gives an effective method to construct artinian gorenstein k algebras to date a general structure for gorenstein k algebras of any dimension and codimension is not understood in this paper we extend macaulay s correspondence characterizing the submodules of the divided power ring in one to one correspondence with gorenstein d dimensional k algebras we discuss effective methods for constructing gorenstein graded rings several examples illustrating our results are given

the leading ideal of a complete intersection of height two abstract let s n be a noetherian local ring and let i f g be an ideal in s generated by a regular sequence f g of length two assume that the associated graded ring gr n s of s with respect to n is a ufd we examine generators of the leading form ideal i of i in gr n s and prove that i is a perfect ideal of gr n s if i is 3 generated thus in this case letting r s i and m n i if gr n s is cohen macaulay then gr m r gr n s i is cohen macaulay as an application we prove that if r m is a one dimensional gorenstein local ring of embedding dimension 3 then gr m r is cohen macaulay if the reduction number of m is at most 4

poincare series of modules over compressed gorenstein local rings abstract given two positive integers e and s we consider gorenstein artinian local rings r whose maximal ideal m satisfies m s 0 m s 1 and rank r m m m 2 e we say that r is a compressed gorenstein local ring when it has maximal length among such rings it is known that generic gorenstein artinian algebras are compressed if s 3 we prove that the poincare series of all finitely generated modules over a compressed gorenstein local ring are rational sharing a common denominator a formula for the denominator is given when s is even this formula depends only on the integers e and s note that for s 3 examples of compressed gorenstein local rings with transcendental poincare series exist due to bogvad

free resolutions of artinian compressed algebras abstract we construct free resolutions of compressed therefore generic artinian graded algebra quotients of polynomial rings and give a method to reduce them to a minimal resolutions this yields results on the form of the resolution and the degrees of the forms in the matrices of the differentials but not precise betti numbers in addition we discuss how this construction is related to a conjecture of boij last we treat the noncompressed case

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

schur functors and schur complexes the study of schur functors has a relatively long history its main impetus derived from representation theory originally in characteristic zero over the years however with the development of modular representations and algebraic geometry over fields of positive characteristic the need for a theory of universal polynomial functors increased and since the mid 1960s approaches to a characteristic free treatment of schur functors have been developing see for instance the recent book of green 1 l in which the treatments by carter and lusztig 6 higman 12 and towber 20 among others are discussed our own interest in such a treatment was awakened by the work of lascoux 141 on resolutions of determinantal ideals although his thesis treated only the characteristic zero case it suggested that a general and elementary theory of schur functors could be developed using only the rudiments of multilinear algebra involving the hopf algebra structures of the symmetric exterior and divided power algebras moreover this elementary development admitted of a natural generalization to the idea of schur complexes whose usefulness was demonstrated for instance in our construction of a universal minimal