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

algebraic shifting and graded betti numbers let s k x 1 x n denote the polynomial ring in n variables over a field k with each deg x i 1 let be a simplicial complex on n 1 n and i c s its stanley reisner ideal we write e for the exterior algebraic shifted complex of a and c for a combinatorial shifted complex of a let ii j i dim k tor i k i i j denote the graded betti numbers of i in the present paper it will be proved that i ii j i e ii j i c for all i and j where the base field is infinite and ii ii j i ii j i c for all i and j where the base field is arbitrary thus in particular one has ii j i ii j i lex for all i and j where lex is the unique lexsegment simplicial complex with the same f vector as a and where the base field is arbitrary

cayley bacharach schemes and their canonical modules a set of s points in p d is called a cayley bacharach scheme cb scheme if every subset of s 1 points has the same hilbert function we investigate the consequences of this weak uniformity the main result characterizes cb schemes in terms of the structure of the canonical module of their projective coordinate ring from this we get that the hilbert function of a cb scheme x has to satisfy growth conditions which are only slightly weaker than the ones given by harris and eisenbud for points with the uniform position property we also characterize cb schemes in terms of the conductor of the projective coordinate ring in its integral closure and in terms of the forms of minimal degree passing through a linked set of points

bounded disturbance adaptive control with exponential and selective data weightings a method of combination of selective and exponential data weighting algorithms for parameter identification is proposed bounded disturbances in systems with unknown statistical properties are considered the proposed method ensures a stable control system in addition it does not need the condition of persistent excitation when the predicted output error is small

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

estimates of effective frequency selectivity based on the detection of a tone added to complex maskers in experiment 1 the validity of parameters associated with the roex p r auditory filter shape was examined for three different types of maskers a a noise masker b a random 12 tone masker whose frequencies varied on a burst by burst basis multiple burst different mbd and c a random 12 tone masker whose frequencies were the same across bursts multiple burst same mbs first the power spectrum model of masking was used to estimate auditory filter shapes for four observers second the resulting auditory filter shapes were used in a computer simulation that provided an estimate of internal noise for each observer third relative weights across frequency were estimated for each observer and each masker type for the noise masker these analyses provided predictions and relative weights that were consistent across the three analyses for the mbd and mbs maskers there was little consistency neither the estimated internal noise nor the estimated relative weights reliably supported a single f

the effect of spatial separation on informational and energetic masking of speech the effect of spatial separation of sources on the masking of a speech signal was investigated for three types of maskers ranging from energetic to informational normal hearing listeners performed a closed set speech identification task in the presence of a masker at various signal to noise ratios stimuli were presented in a quiet sound field the signal was played from 0 azimuth and a masker was played either from the same location or from 90 to the right signals and maskers were derived from sentences that were preprocessed by a modified cochlear implant simulation program that filtered each sentence into 15 frequency bands extracted the envelopes from each band and used these envelopes to modulate pure tones at the center frequencies of the bands in each trial the signal was generated by summing together eight randomly selected frequency bands from the preprocessed signal sentence three maskers were derived from the preprocessed masker sentences 1 different band sentence which was generated by summing together six randomly selected frequency bands out of the seven bands not present in the signal resulting in primarily informational masking 2 different band noise which was generated by convolving the different band sentence with gaussian noise and 3 same band noise which was generated by summing the same eight bands from the preprocessed masker sentence that were used in the signal sentence and convolving the result with gaussian noise resulting in primarily energetic masking results revealed that in the different band sentence masker the effect of spatial separation averaged 18 db at 51 correct while in the different band and same band noise maskers the effect was less than 10 db these results suggest that in these conditions the advantage due to spatial separation of sources is greater for informational masking than for energetic masking

maximal minimal resolutions that is exact everywhere except at f0 where the cokernel is m such a resolution always exists if r is a noetherian n graded ring with r0 a field and m is a finitely generated z graded r module then a resolution may be constructed in a minimal way in which each fi is graded and each differential is homogeneous of degree 0 the rank of the ith free module in a minimal free resolution of m is an invariant of m called the ith betti number of m and denoted i m likewise r ij m the number of elements of degree j in a minimal set of homogeneous generators of fi is also an invariant of m called the i j th graded betti number of m in this paper we study modules with maximal graded betti numbers more precisely consider a set consisting of pairs r m where r is a noetherian n graded ring with r0 a field and m is a finitely generated graded r module is there some r m such that ij m ij m for every i and j and every r m there are trivial examples in which the answer is yes e g has only one element or no e g consists of all such pairs theorems 1 and 2 below give affirmative answers for certain sets defined by conditions on the hilbert series and the depths of r and m theorem 3 allows one to compute the maximal graded betti numbers for the pairs in the sets considered in theorems 1 and 2 throughout this paper k denotes a field and q the polynomial ring k x1 xn with the usual n grading given by degxi 1 the hilbert series of a finitely generated graded q module m is hm s dimk mis we define d lexicographic ideals and submodules in section 2 the poincare series of an r module m is p m s t ij m s t we write 4 for coefficient wise inequality of laurent series with coefficients in z

non extremal sextic moment problems abstract positive semidefiniteness recursiveness and the variety condition of a moment matrix are necessary and sufficient conditions to solve the quadratic and quartic moment problems also positive semidefiniteness combined with another necessary condition consistency is a sufficient condition in the case of extremal moment problems i e when the rank of the moment matrix denoted by r and the cardinality of the associated algebraic variety denoted by v are equal however these conditions are not sufficient for non extremal sextic or higher order truncated moment problems in this paper we settle three key instances of the non extremal i e r v sextic moment problem as follows when r 7 positive semidefiniteness consistency and the variety condition guarantee the existence of a 7 atomic representing measure when r 8 we construct two determining algorithms corresponding to the cases v 9 and v to accomplish this we generalize the rank reduction technique developed in previous work where we solved the nonsingular quartic moment problem and found an explicit way to build a representing measure

poset embeddings of hilbert functions for a standard graded algebra r we consider embeddings of the poset of hilbert functions of r ideals into the poset of r ideals as a way of classification of hilbert functions there are examples of rings for which such embeddings do not exist we describe how the embedding can be lifted to certain ring extensions which is then used in the case of polarization and distraction a version of a theorem of clements lindstrom is proved we exhibit a condition on the embedding that ensures that the classification of hilbert functions is obtained with images of lexicographic segment ideals

distractions of shakin rings abstract we study by means of embeddings of hilbert functions a class of rings which we call shakin rings i e quotients k x 1 x n a of a polynomial ring over a field k by ideals a l p which are the sum of a piecewise lex segment ideal l as defined by shakin and a pure powers ideal p our main results extend abedelfatah s recent work on the eisenbud green harris conjecture shakin s generalization of macaulay and bigatti hulett pardue theorems on betti numbers and when char k 0 mermin murai theorem on the lex plus power inequality from monomial regular sequences to a larger class of ideals we also prove an extremality property of embeddings induced by distractions in terms of hilbert functions of local cohomology modules

sums of squares on the hypercube let x be a finite set of points in mathbb r n a polynomial p nonnegative on x can be written as a sum of squares of rational functions modulo the vanishing ideal i x from the point of view of applications such as polynomial optimization we are interested in rational function representations of small degree we derive a general upper bound in terms of the hilbert function of x and we show that this upper bound is tight for the case of quadratic functions on the hypercube c 0 1 n a very well studied case in combinatorial optimization using the lower bounds for c we construct a family of globally nonnegative quartic polynomials which are not sums of squares of rational functions of small degree to our knowledge this is the first construction for hilbert s 17th problem of a family of polynomials of bounded degree which need increasing degrees in rational function representations as the number of variables n goes to infinity we note that representation theory of the symmetric group s n plays a crucial role in our proofs of the lower bounds

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

on the cohomology of galois groups determined by witt rings let f denote a field of characteristic different from two in this paper we describe the mod 2 cohomology of a galois group gf called the w group of f which is known to essentially characterize the witt ring wf of anisotropic quadratic modules over f we show that h gf f2 contains the mod 2 galois cohomology of f and that its structure will reflect important properties of the field we construct a space xf endowed with an action of an elementary abelian group e such that the computation of the cohomology of gf reduces to calculating the equivariant cohomology h e xf f2 for the case of a field which is not formally real this amounts to computing the cohomology of an explicit euclidean space form an object which is interesting in its own right we provide a number of examples and a substantial combinatorial computation for the cohomology of the universal w groups

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

cayley bacharach theorems and conjectures a theorem of pappus of alexandria proved in the fourth century a d began a long development in algebraic geometry in its changing expressions one can see reflected the changing concerns of the field from synthetic geometry to projective plane curves to riemann surfaces to the modern development of schemes and duality we survey this development historically and use it to motivate a brief treatment of a part of duality theory we then explain one of the modern developments arising from it a series of conjectures about the linear conditions imposed by a set of points in projective space on the forms that vanish on them we give a proof of the conjectures in a new

suggested formulae for calculating auditory filter bandwidths and excitation patterns recent estimates of auditory filter shape are used to derive a simple formula relating the equivalent rectangular bandwidth erb of the auditory filter to center frequency the value of the auditory filter bandwidth continues to decrease as center frequency decreases below 500 hz a formula is also given relating erb rate to frequency finally a method is described for calculating excitation patterns from filter shapes

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

determination of error values for algebraic geometry codes and the forney formula in the decoding of one point algebraic geometry codes with one defining equation in two variables we generalize the forney formula for the bose chaudhuri hocqungham bch codes

discrete multivariable adaptive control abstract an extension of a monovariable adaptive control algorithm is given for the multi variable case a linear constant feedforward controller and a non linear feedback one are used for the design four control schemes are analysed which allow independent specification of the objectives of regulation and tracking of a given model under not very strong conditions the global convergence of the given schemes is ensured

applications of mapping cones over clements lindstrom rings abstract we prove that gotzmann s persistence theorem holds over every clements lindstrom ring we also construct the infinite minimal free resolution of a square free borel ideal over such a ring

informational processing of complex sound ii cross dimensional analysis a series of experiments investigated listeners ability simultaneously to process information across different acoustic dimensions on each trial the listener heard a pair of brief n tone sequences n 1 to 12 the frequency intensity and duration of each tone in the sequence varied randomly from trial to trial on average the values of these three parameters were greater for one sequence the target than the other the nontarget the listener s task was to identify the target on each trial for an ideal observer in this task d performance grows as the square root n obtained d grew at a rate slightly less than the square root of n close to cube root of n growth was observed when the average difference occurred in only one of the three tone parameter values within a block of trials although performance fell short of ideal optimum weights were consistently given to each tone and each parameter the results are consistent with a model in which performance depends predominantly on the information content of the sounds regardless of how the information is packaged in the stimulus transmitted information is estimated to be 0 9 2 0 bits within a single acoustic dimension 2 1 3 0 bits when distributed across dimensions

ideals containing the squares of the variables we study the betti numbers of graded ideals containing the squares of the variables in a polynomial ring we prove the lex plus powers conjecture for such ideals

the lex plus powers inequality for local cohomology modules we prove an inequality between hilbert functions of local cohomology modules supported in the homogeneous maximal ideal of standard graded algebras over a field within the framework of embeddings of posets of hilbert functions as a main application we prove an analogue for local cohomology of evans lex plus powers conjecture for betti numbers this results implies some cases of the classical lex plus powers conjecture namely an inequality between extremal betti numbers in particular for the classes of ideals for which the eisenbud green harris conjecture is currently known the projective dimension and the castelnuovo mumford regularity of a graded ideal do not decrease by passing to the corresponding lex plus powers ideal

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

extremal betti numbers and applications to monomial ideals recall that the mumford castelnuovo regularity of m is the least integer such that for each i all free generators of fi lie in degree i that is i j 0 for j i in terms of macaulay mac regularity is the number of rows in the diagram produced by the betti command a betti number i j 0 will be called extremal if l r 0 for all l i r j 1 and r l j i that is if i j is the nonzero top left corner in a block of zeroes in the macaulay betti diagram in other words extremal betti numbers account for notches in the shape of the minimal free resolution and one of them computes the regularity in this sense extremal betti numbers can be seen as a refinement of the notion of mumford castelnuovo regularity in the first part of this note we connect the extremal betti numbers of an arbitrary submodule of a free s module with those of its generic initial module in the second part which can be read independently of the first we relate extremal multigraded betti numbers in the minimal resolution of a square free monomial ideal with those of the monomial ideal corresponding to the alexander dual simplicial complex our techniques give also a simple geometric proof of a more precise version of a recent result of terai te97 see also ft97 for a homological reformulation and related results generalizing eagon and reiner s theorem er96 that a stanleyreisner ring is cohen macaulay if and only if the homogeneous ideal corresponding to the alexander dual simplicial complex has a linear resolution we are grateful to david eisenbud for useful discussions

on the uniformity of zero dimensional complete intersections abstract after showing that the general cayley bacharach conjecture formulated by d eisenbud m green and j harris 1996 6 is equivalent to a conjecture about the region of uniformity of a zero dimensional complete intersection we prove this conjecture in a number of special cases in particular after splitting the conjecture into several intervals we prove it for the first the last and part of the penultimate interval moreover we generalize the uniformity results of j hansen 2003 12 and l gold j little and h schenck 2005 9 to level schemes and apply them to obtain bounds for the minimal distance of generalized reed muller codes

paper adaptive controllers for discrete time systems with arbitrary zeros an overview the paper presents a comprehensive review of the problem of designing discrete time adaptive controllers for systems with arbitrary zeros minimum or non minimum phase systems being particular cases the authors have attempted to give a unified presentation of the various existing schemes by stripping away the technical details and highlighting their close interrelation through the use of a common framework both algorithmic and theoretical aspects are discussed with particular emphasis on the stability of the schemes

cayley bacharach theorem of piecewise algebraic curves the piecewise algebraic curve determined by a bivariate spline function is a generalization of the classical algebraic curve in this paper by using bezout s theorem and nother type theorem of piecewise algebraic curves the cayley bacharach theorem and hilbert function of c0 piecewise algebraic curves are presented

rational plane curves parameterizable by conics abstract we introduce the class of rational plane curves parameterizable by conics as an extension of the family of curves parameterizable by lines also known as monoid curves we show that they are the image of monoid curves via suitable quadratic transformations in projective plane we also describe all the possible proper parameterizations of them and a set of minimal generators of the rees algebra associated to these parameterizations extending well known results for curves parameterizable by lines

the extent to which a position based explanation accounts for binaural release from informational masking detection was measured for a 500hz tone masked by noise an energetic masker or sets of ten randomly drawn tones an informational masker presenting the maskers diotically and the target tone with a variety of interaural differences interaural amplitude ratios and or interaural time delays resulted in reduced detection thresholds relative to when the target was presented diotically binaural release from masking thresholds observed when time and amplitude differences applied to the target were reinforcing favored the same ear resulting in a lateralized position for the target were not significantly different from thresholds obtained when differences were opposing favored opposite ears resulting in a centered position for the target this irrelevance of differences in the perceived location of the target is a classic result for energetic maskers but had not previously been shown for informational maskers however this parallellism between the patterns of binaural release for energet

a novel approach to the explicit pole assignment self tuning controller design a recursive algorithm for the controller design phase of the adaptive pole assignment controller is presented compared to other pole assignment adaptive controllers the computation time to get the controller parameters is drastically reduced and the numerical stability of the controller parameters is increased if persistent excitation is imposed the system poles will be located at the desired position in the steady state and the global stability of the system can be easily obtained

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

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

free resolutions of lex ideals over a koszul toric ring in this paper we study the minimal free resolution of lex ideals over a koszul toric ring in particular we study in which toric ring r all lex ideals are componentwise linear we give a certain necessity and sufficiency condition for this property and show that lex ideals in a strongly koszul toric ring are componentwise linear in addition it is shown that in the toric ring arising from the segre product p p every hilbert function of a graded ideal is attained by a lex ideal and that lex ideals have the greatest graded betti numbers among all ideals having the same hilbert function

the gonality of complete intersection curves abstract the purpose of this paper is to show that for a complete intersection curve c in projective space other than a few exceptions stated below any morphism f c p r satisfying deg f o p r 1 deg c is obtained by projection from a linear space in particular we obtain bounds on the gonality of such curves and compute the gonality of general complete intersection curves we also prove a special case of one of the well known cayley bacharach conjectures posed by eisenbud green and harris

listening to every other word examining the strength of linkage variables in forming streams of speech in a variation on a procedure originally developed by broadbent 1952 failures of attention in selective listening j exp psychol 44 428 433 listeners were presented with two sentences spoken in a sequential interleaved word format sentence one target comprised the odd numbered words in the sequence and sentence two masker comprised the even numbered words in the sequence the task was to report the words in sentence one the goal was to determine the effectiveness of cues linking the words of the target or masker over time three such linkage variables were examined 1 fixed talker 2 fixed perceived interaural location and 3 correct syntactic structure all of the linkage variables provided a significant advantage when applied to the target compared to the baseline condition in which the linkage variables were randomized however these linkage variables were not effective when applied to the masker word position effects were found such that performance in the baseline condition declined and the advantages of the linkage variables increased for the words near the end of the sentence overall this approach appears to be useful for examining interference in speech recognition that has little or no peripheral component the results suggest that variables that link target words together improve their resiliency to interference and or their recall

hilbert schemes and maximal betti numbers over veronese rings macaulay s theorem macaulay in proc lond math soc 26 531 555 1927 characterizes the hilbert functions of graded ideals in a polynomial ring over a field we characterize the hilbert functions of graded ideals in a veronese ring r the coordinate ring of a veronese embedding of pr 1 we also prove that the hilbert scheme which parametrizes all graded ideals in r with a fixed hilbert function is connected this is an analogue of hartshorne s theorem hartshorne in math ihes 29 5 48 1966 that hilbert schemes over a polynomial ring are connected furthermore we prove that each lex ideal in r has the greatest betti numbers among all graded ideals with the same hilbert function

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

globally convergent adaptive pole assignment for a class of non minimum phase stochastic systems a key difficulty of the explicit approach to self tuning control both theoretically and computationally is the need to solve a polynomial identity to generate the required controller coefficients for systems with uncorrelated output noise however the identity has a simple solution and in this paper the implications of this phenomenon are discussed in relation to self tuning regulation a suitable explicit algorithm is introduced and it is shown that under certain conditions global stability and system identifiability can be established without recourse to sophisticated estimator management techniques

superposition interpolation process in cn in this paper we deeply research lagrange interpolation by polynomial in several variables and give an application of cayley bacharach theorem for it particularly on the sufficiently intersected algebraic manifold or siam for short we introduce a general method of constructing properly posed set of nodes or ppsn for short for lagrange interpolation namely the superposition interpolation process then we give an equivalent condition about a ppsn along a siam further we introduce a relation between the sufficiently intersected algebraic hypersurfaces and h basis at the end of this paper we use the extended cayley bacharach theorem to resolve some problems of lagrange interpolation along the zero dimensional and one dimensional algebraic manifolds

recent researches on multivariate spline and piecewise algebraic variety the multivariate splines as piecewise polynomials have become useful tools for dealing with computational geometry computer graphics computer aided geometrical design and image processing it is well known that the classical algebraic variety in algebraic geometry is to study geometrical properties of the common intersection of surfaces represented by multivariate polynomials recently the surfaces are mainly represented by multivariate piecewise polynomials i e multivariate splines so the piecewise algebraic variety defined as the common intersection of surfaces represented by multivariate splines is a new topic in algebraic geometry moreover the piecewise algebraic variety will be also important in computational geometry computer graphics computer aided geometrical design and image processing the purpose of this paper is to introduce some recent researches on multivariate spline piecewise algebraic variety curve and their applications

an application of liaison theory to the eisenbud green harris conjecture abstract in this paper we apply liaison theory to the eisenbud green harris conjecture and prove that the conjecture holds for a certain subclass of homogeneous ideals in the linkage class of a complete intersection ideal in the case of three variables we prove that the conjecture holds for gorenstein ideals

the projective geometry of the gale transform abstract the gale transform an involution on sets of points in projective space appears in a multitude of guises and in subjects as diverse as optimization coding theory theta functions and recently in our proof that certain general sets of points fail to satisfy the minimal free resolution conjecture see eisenbud and popescu 1999 invent math 136 419 449 in this paper we reexamine the gale transform in the light of modern algebraic geometry we give a more general definition in the context of finite locally gorenstein subschemes we put in modern form a number of the more remarkable examples discovered in the past and we add new constructions and connections to other areas of algebraic geometry we generalize goppa s theorem in coding theory and we give new applications to castelnuovo theory we also give references to classical and modern sources

resolutions of a stable ideals abstract let a a 1 a 2 a n be a sequence of integers or we introduce a stable ideals in a polynomial ring and study their homological properties our results generalize results on square free monomial ideals by aramova avramov herzog hibi and srinivasan

brief paper variable forgetting factors in parameter estimation this paper is concerned with the influence of forgetting factors on the consistency of prediction error methods of identification based on ljung s analysis of the off line case it is shown that the use of forgetting factors can give rise to identifiability problems unless the behaviour of these factors over time satisfied certain conditions the main theorem covers the cases when the factors are deterministic functions of time or calculated via an adaptive mechanism

auditory streaming of tones of uncertain frequency level and duration stimulus uncertainty is known to critically affect auditory masking but its influence on auditory streaming has been largely ignored standard aba aba tone sequences were made increasingly uncertain by increasing the sigma of normal distributions from which the frequency level or duration of tones were randomly drawn consistent with predictions based on a model of masking by lutfi gilbertson chang and stamas j acoust soc am 134 2160 2170 2013 the frequency difference for which a and b tones formed separate streams increased as a linear function of sigma in tone frequency but was much less affected by sigma in tone level or duration

algebraic integrability of foliations of the plane we give an algorithm to decide whether an algebraic plane foliation f has a rational first integral and to compute it in the affirmative case the algorithm runs whenever we assume the polyhedrality of the cone of curves of the surface obtained after blowing up the set bf of infinitely near points needed to get the dicritical exceptional divisors of a minimal resolution of the singularities of f this condition can be detected in several ways one of them from the proximity relations in bf and as a particular case it holds when the cardinality of bf is less than 9

the abel map for surface singularities i generalities and examples let x o be a complex normal surface singularity we fix one of its good resolutions widetilde x rightarrow x an effective cycle z supported on the reduced exceptional curve and any possible first chern class l in h 2 widetilde x mathbb z with these data we define the variety mathrm eca l z of those effective cartier divisors d supported on z which determine a line bundles mathcal o z d with first chern class l furthermore we consider the affine space mathrm pic l z subset h 1 mathcal o z of isomorphism classes of holomorphic line bundles with chern class l and the abel map c l z mathrm eca l z rightarrow mathrm pic l z the present manuscript develops the major properties of this map and links them with the determination of the cohomology groups h 1 z mathcal l where we might vary the analytic structure x o supported on a fixed topological type resolution graph and we also vary the possible line bundles mathcal l in mathrm pic l z the case of generic line bundles of mathrm pic l z and generic line bundles of the image of the abel map will have priority roles rewriting the abel map via laufer duality based on integration of forms on divisors we can make explicit the abel map and its tangent map the case of superisolated and weighted homogeneous singularities are exemplified with several details the theory has similar goals but rather different techniques as the theory of abel map or brill noether theory of reduced smooth projective curves

interaural fluctuations and the detection of interaural incoherence iii narrowband experiments and binaural models in the first two articles of this series reproducible noises with a fixed value of interaural coherence 0 992 were used to study the human ability to detect interaural incoherence it was found that incoherence detection is strongly correlated with fluctuations in interaural differences especially for narrow noise bandwidths but it remained unclear what function of the fluctuations best agrees with detection data in the present article ten different binaural models were tested against detection data for 14 and 108 hz bandwidths these models included different types of binaural processing independent interaural phase difference interaural level difference lateral position and short term cross correlation several preprocessing transformations of the interaural differences were incorporated compression of binaural cues temporal averaging and envelope weighting for the 14 hz bandwidth data the most successful model postulated that incoherence is detected via fluctuations of interaural phase and interaural level processed by independent centers that model correlated with detectability at r 0 87 that model proved to be more successful than short term cross correlation models incorporating standard physiologically based model features r 0 78 for the 108 hz bandwidth data detection performance varied much less among different waveforms and the data were less able to distinguish between models

almost complete intersections and the lex plus powers conjecture abstract we prove the almost complete intersection case of the lex plus powers conjecture on graded betti numbers we show that the resolution of a lex plus powers almost complete intersection provides an upper bound for the graded betti numbers of any other ideal with regular sequence in the same degrees and the same hilbert function a key ingredient is finding an explicit comparison map between two koszul complexes finally we obtain bounds on the hilbert function of an almost complete intersection including a special case of a conjecture of eisenbud green harris

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

on the asymptotic distribution of exponentially weighted prediction error estimators the authors establish the distribution of the exponentially weighted prediction error estimators for a class of general possibly nonlinear discrete time systems an explicit formula for the covariance matrix of the estimation errors is provided the distributional results presented hold for a large number n of data points and a weighting or forgetting factor lambda close to one

the dual minimum distance of arbitrary dimensional algebraic geometric codes abstract in this article the minimum distance of the dual c of a functional code c on an arbitrary dimensional variety x over a finite field f q is studied the approach is based on problems a la cayley bacharach and consists in describing the minimal configurations of points on x which fail to impose independent conditions on forms of some degree m if x is a curve the result improves in some situations the well known goppa designed distance

psychometric functions for the discrimination of spectral variance an experiment was conducted to measure the shape of the psychometric function for the discrimination of spectral variance the stimuli were simultaneous tone complexes comprised of the six octave frequencies from 250 to 8000 hz on each presentation the levels of components in db were drawn independently and at random from one of two normal distributions having identical means but different variances n 1 db s 2 10 db in the standard two interval forced choice procedure the listeners task was to indicate which complex had the greater variance in component level the shape of the psychometric function for all five listeners was markedly different from that of an observer limited only by additive internal noise it was consistent with an observer that gives weight to only one or two components in the complex however this result was inconsistent with the weighting functions computed from the trial by trial data from these listeners both measures can be reconciled if it is assumed that listener wei

extended self tuning algorithm this article concerns the practical implications of an extended self tuning property the extension represents a refinement of existing asymptotic self tuning properties in the sense that it allows the designer to make arbitrary assumptions concerning the disturbance dynamics the important practical consequence of this is that a simple pole assignment self tuner may now be designed which combines servo tracking and regulatory closed loop criteria in the pure regulation case a priori parametrization of the noise dynamics can be used to aid convergence of the self tuning algorithm in addition an implicit pole assignment regulator is easily formulated from the extended self tuner

informational masking by everyday sounds tone in noise detection is severely degraded when only a few spectral components of the noise are presented at random on each trial neff and green percept psychophys 41 409 415 1987 the elevations in threshold are attributed to uncertainty regarding the noise caused by sparse sampling of noise components informational masking is the term used to describe the result the present experiment was undertaken to determine how informational masking is affected when sparse sampling is from a set of common everyday sounds instead of noise on each presentation a different masker waveform of constant total power was synthesized from the magnitude and phase of a fixed number m of spectral components m 2 921 across blocks of trials the components were selected at random from 1 of 50 common environmental sounds e g baby crying door slamming phone ringing or 1 of 50 samples of gaussian noise masked thresholds for a 1 0 khz signal in the presence of both types of maskers were obtained using an adaptive two interval forced choice procedure results with noise replicated earlier results showing largest elevations in threshold for 10 20 sampled components results with everyday sounds showed a similar pattern with thresholds elevated above those for noise by as much as 10 db at the larger values of m the differences in masked thresholds were systematically related to differences in the ensemble variance of masker spectra as predicted by a model previously applied to noise lutfi j acoust soc am 94 748 758 1993 not predicted was the result of a subsequent trial by trial analysis in which 9 11 db less masking was observed for samples from everyday sounds rated as easily recognized by listeners the results suggest that listeners fail to exploit lawful dependencies among spectral components of everyday sounds to aid detection unless enough information is available for the sound to be easily recognized

sum of squares length of real forms for n d ge 1 let p n 2d denote the smallest number p such that every sum of squares of degree d forms in mathbb r x 1 ldots x n is a sum of p squares we establish lower bounds for p n 2d that are considerably stronger than the bounds known so far combined with known upper bounds they give p 3 2d in d 1 d 2 in the ternary case assuming a conjecture of iarrobino kanev on dimensions of tangent spaces to catalecticant varieties we show that p n 2d sim const cdot d n 1 2 for d rightarrow infty and all n ge 3 for ternary sextics and quaternary quartics we determine the exact value of the invariant showing p 3 6 4 and p 4 4 5

informational processing of complex sound i intensity discrimination this paper reports on some initial experiments using the sample discrimination paradigm to investigate normal hearing listeners ability to process information in complex nonspeech sounds an important feature of the sample discrimination experiment is that the value of the d i f f e r e n c e to be discriminated randomly varies from trial to trial it is this variation that yields potential information in the present study listeners heard a pair of multitone complexes or sequences on each trial the individual levels of the tones were drawn from two normal distributions differing only in mean the listener s task was to identify the sound having the higher mean tone level for an ideal observer in these experiments performance in d grows as the square root n where n is the number of tones obtained d grew more nearly as the cube root of n regardless of whether the tones were played sequentially or simultaneously or whether they were increased in number from high frequencies to low or from low frequencies to high a preliminary model is proposed in which discrimination performance depends predominantly on the information content of the sounds and is largely independent of the physical dimensions along which the sounds vary information content is defined in terms of the variance of the underlying stimulus distributions and a stimulus equivocation factor that is derived from the data based on this model transmitted information is estimated to be between 1 0 and 2 6 bits

release from speech on speech masking by adding a delayed masker at a different location the amount of masking exerted by one speech sound on another can be reduced by presenting the masker twice from two different locations in the horizontal plane with one of the presentations delayed to simulate an acoustical reflection three experiments were conducted on various aspects of this phenomenon experiment 1 varied the number of masking talkers from one to three and the signal to noise s n ratio from 12to 4db evidence of masking release was found for every combination of these variables tested for the most difficult conditions multiple maskers and negative s n the amount of release was approximately 10db experiment 2 varied the timing of leading and lagging masker presentations over a broad range to include shorter delay times where room reflections of speech are rarely noticed by listeners and longer delays where reflections can become disruptive substantial masking release was found for all of the shorter delay times tested and negligible release was found at the longer delays f

spatial release from speech on speech masking in the median sagittal plane several studies have described a release from speech on speech masking associated with separation of target and masker sources in the median sagittal plane some have excluded the possibility that small differences between target and masker interaural time disparities can fully account for this release this study explored the mechanisms underlying the spatial release from speech on speech masking that can be obtained in the absence of such differences in one condition interaural time disparities were removed from the nominal median sagittal plane head related impulse responses used to generate the virtual auditory space within which competing sentences were presented in other conditions interaural level and spectral disparities also were manipulated by presenting competing sentences monaurally or diotically after convolution with one ear s head related impulse responses it was found that substantial spatial release from masking can be obtained in the absence of any interaural disparities and that such disparities probably make a relatively minor contribution to spatial release from speech on speech masking in the median sagittal plane it is argued that this release from masking is driven primarily by a reduction in informational masking that occurs when monaural information at one or both of the listener s ears facilitates differentiation of competing sentences that emanate from spatially separated sources

estimation technique for tracking rapid parameter changes this paper describes a relatively simple technique that enables a recursive least squares algorithm to track both abrupt and smooth parameter changes without being unduly affected by varying noise levels the technique differs from methods based on a scalar forgetting factor by its use of vectors to detect parameter variation and adjust the parameter updating gain it also incorporates a test to determine when parameter updating should be suspended so as to avoid divergence when little new information about the parameters is arriving

on the lex plus powers conjecture abstract let s be a polynomial ring over a field and i s a homogeneous ideal containing a regular sequence of forms of degrees d 1 d c in this paper we prove the lex plus powers conjecture when the field has characteristic 0 for all regular sequences such that d i j 1 i 1 d j 1 1 for each i that is we show that the betti table of i is bounded above by the betti table of the lex plus powers ideal of i

bias compensating least squares method for identification of continuous time systems from sampled data abstract least squares ls techniques are applied to the identification problem of continuous time systems from sampled data of input output measurements the linear integral filter which solves the intial condition problem is employed for handling time derivatives the asymptotic bias in the ls estimator is derived and is compensated in a modified ls algorithm called a bias compensating ls method to obtain consistent estimates of the unknown parameters when it is unknown the variance of the noise can be estimated recursively together with the system parameters the bias compensating ls method not only has all merits of the ls method but also possesses good consistency properties it is applicable to both time invariant and time varying continuous time systems in the time varying case an adaptive ls algorithm with a variable forgetting factor is chosen to make the estimates track the changing parameters quickly and the bias is compensated as is done in the time invariant case representative nu

a recursive least squares based control algorithm for the suppression of tonal disturbances mitigation of the effects of tonal noise and vibration has importance across a wide range of application domains for low frequency disturbances active control methodologies have proven to be highly effective when coupled with harmonic algorithms that target specific problematic frequencies in this paper a novel harmonic control approach is presented that combines a classical exponential forgetting recursive least squares exf rls estimator with an optimal gradient descent update law the paper provides a rigorous proof that with a sinusoidal reference the exf rls estimator can be approximated by a fixed parameter filter and that the accuracy of the approximation is dependent upon the values of both the forgetting factor and the sampling frequency with this approximation it is also proven that the complete iterative frequency domain harmonic control algorithm when used with an instantaneous update can be accurately represented by a linear time invariant lti feedback compensator such representations have clear importance since the stability performance convergence and robustness properties of the adaptive system can thereby be examined using well established lti analysis tools the algorithm and the analytical results described above are illustrated in the paper using an experimental active vibration isolation mount that has been developed for marine systems application

poset embeddings of hilbert functions and betti numbers abstract we study inequalities between graded betti numbers of ideals in a standard graded algebra over a field and their images under embedding maps defined earlier by us in caviglia and kummini 2013 5 we show that if graded betti numbers do not decrease when we replace ideals in an algebra by their embedded versions then the same behaviour is carried over to ring extensions as a corollary we give alternative inductive proofs of earlier results of bigatti hulett pardue mermin peeva stillman and murai we extend a hypersurface restriction theorem of herzog and popescu to the situation of embeddings we show that we can obtain the betti table of an ideal in the extension ring from the betti table of its embedded version by a sequence of consecutive cancellations we further show that the lex plus powers conjecture of evans reduces to the artinian situation