lateralization of complex binaural stimuli a weighted image model this article describes a new model that predicts the subjective lateral position of bandpass stimuli it is assumed as in other models that stimuli are bandpass filtered and rectified and that the rectified outputs of filters with matching center frequencies undergo interaural cross correlation the model specifies and utilizes the shape and location of assumed patterns of neural activity that describe the cross correlation function individual modes of this function receive greater weighting if they are straighter describing consistent interaural delay over frequency and or more central describing interaural delays of smaller magnitude this weighting of straightness and centrality is used by the model to predict the perceived laterality of several types of low frequency bandpass stimuli with interaural time delays and or phase shifts including bandpass noise amplitude modulated stimuli with time delayed envelopes and bandpass filtered clicks this model is compared to other theories that describe lateralization in terms of the relative contributions of information in the envelopes and fine structures of binaural stimuli

markov chain sensitivity measured by mean first passage times abstract the purpose of this article is to present results concerning the sensitivity of the stationary probabilities for an n state time homogeneous irreducible markov chain in terms of the mean first passage times in the chain

on single and double soules matrices abstract until now the concept of a soules basis matrix of sign pattern n consisted of an orthogonal matrix r r n n generated in a certain way from a positive n vector which has the property that for any diagonal matrix diag 1 n with 1 n 0 the symmetric matrix a r r t has nonnegative entries only in the present paper we introduce the notion of a pair of double soules basis matrices of sign pattern n which is a pair of matrices p q each in r n n which are not necessarily orthogonal and which are generated in a certain way from two positive vectors but such that pq t i and such that for any of the aforementioned diagonal matrices the matrix a p q t also has nonnegative entries only we investigate the interesting properties which such matrices a have as a preamble to the above investigation we show that the iterates a k r k r k t generated in the course of the qr algorithm when it is applied to a r r t where r is a soules basis matrix of sign pattern n are again symmetric matrices generated by the soules basis matrices r k of sign pattern n which are themselves modified as the algorithm progresses our work here extends earlier works by soules and elsner et al

on clifford algebras and conjugate splittings in 1921 in a paper entitled on division algebras j h m wedderburn proved that every division algebra of degree 3 over a field of characteristic not 3 is cyclic in the process he proved two other remarkable results first he showed that if d is a division algebra over a field f and q e d f then the minimal polynomial g l of 0 over f factors over d into linear factors that is in the polynomial ring d lr where 1 commutes with the elements of d we have g 1 2 0 l l3 1 2 0 for some tii e d where b 8 each ei is a root of g a and hence a conjugate in d of 8 wedderburn then proceeded to prove that if d has degree 3 then one can do better in that case there is an element 4 in d such that g a a t 28t2 a p et l q in d a it follows that t3 e f and using this he quickly derived his main result the cyclicity of division algebras of degree 3 in this paper we introduce the notion of a conjugate splitting for a polynomial with coefficients in some field f over an f algebra a it is precisely the kind of decomposition wedderburn proved for division algebras of degree 3 we then prove that the clifford algebra of the homogenization of the polynomial is universal for these conjugate splittings see theorem 1 2 the rest of the paper consists of consequences and interpretations of this result along with a number of examples in the first section we present examples of conjugate splittings including examples for polynomials of degree greater than 3 in addition we show among other things that wedderburn s theorem extends to m f the split central simple f algebra of degree 3 in the second section we restrict attention to cubic polynomials and use the known structure of the clifford

on explicit forms for ergodicity coefficients abstract explicit forms for ergodicity coefficients are known only when the l1 norm or the l norm is used 11 15 the purpose of this paper is to give a new approach to ergodicity coefficients and their functional forms realizations of this general procedure provide further ergodicity coefficients their explicit forms and new eigenvalue bounds which are compared with the deutsch zenger numerical radius 2 8

sensitivity of the stationary distribution vector for an ergodic markov chain stationary distribution vectors p sup infinity for markov chains with associated transition matrices t are important in the analysis of many models in the mathematical sciences such as queuing networks input output economic models and compartmental tracer analysis models the purpose of this paper is to provide insight into the sensitivity of p sup infinity to perturbations in the transition probabilities of t and to understand some of the difficulties in computing an accurate p sup infinity the group inverse a sup number of i t is shown to be of fundamental importance in understanding sensitivity or conditioning of p sup infinity the main result shows that if there is a state that is accessible from every other state and the corresponding column of t has no small off diagonal elements then p sup infinity cannot be sensitive to small perturbations in t ecological examples are given a new stable algorithm for calculating a sup number is described

explicit forms for ergodicity coefficients and spectrum localization explicit forms for orgodicity coefficients which bound the non unit eigenvalues of finite stochastic matrices are known in the cases p 1 when the lp norm is used 3 6 7 the purpose of this report is to generalize these results to arbitrary real matrices in particular square matrices with a real valued eigenvalue by giving a generalized and to some extent simplified synthesis of methods used hitherto alternative procedures are mentioned in the light of the framework established the results are of particular relevance for a primitive nonnegative matrix for which a bound results for the non perron frobenius eigenvalues

lateralization predictions for high frequency binaural stimuli the position variable model r m stern jr and h s colburn j acoust soc am 64 127 140 1978 g d shear and r m stern j acoust soc am suppl 1 81 s27 1987 is extended to describe the subjective lateral position of amplitude modulated tones and bandpass noise as well as other complex stimuli that are presented within spectral regions at which the binaural system appears to be unable to make use of cycle by cycle interaural temporal differences predictions of the model are based on the centroid of the cross correlation of the hypothetical auditory nerve response to the stimuli which is either calculated using analytical techniques or simulated numerically the model of auditory nerve activity which is typically used to describe the response to stimuli at lower frequencies also extracts envelopes of higher frequency stimuli as discussed previously by colburn and esquissaud this information appears to be useful in predicting the lateral position of such high frequency stimuli p

upper bounds on the maximum modulus of subdominant eigenvalues of nonnegative matrices abstract upper bounds for the maximum modulus of the subdominant roots of square nonnegative matrices are obtained we provide a unified approach that yields or improves upon most of the bounds that have been obtained so far

a central spectrum theory of binaural processing evidence from dichotic pitch a theory is presented that describes the binaural processing of interaural time or phase differences it is an elaboration of the central spectrum concept for the explanation of dichotic pitch phenomena f a bilsen pitch of noise signals evidence for a central spectrum j acoust soc am 61 150 161 1977 the generation is postulated for central activity patterns cap due to binaural interaction from these caps the central processor selects specific spectral information that constitutes the information for lateralization dichotic pitch binaural masking etc here a strategy is assumed to be based on central spectra cs rather than on interaural cross correlation for the calculation of the central activity patterns a number of assumptions have been introduced the peripheral filters are supposed to be infinitesimally narrow the analog filter outputs from corresponding filters at both ears are thought to interact by means of a linear delay and add mechanism the squared output power

clifford algebras of binary homogeneous forms abstract we study the generalized clifford algebras associated to homogeneous binary forms of prime degree p focusing on exponentiation forms of p central spaces in division algebra for a two dimensional p central space we make the simplifying assumption that one basis element is a sum of two eigenvectors with respect to conjugation by the other if the product of the eigenvalues is 1 then the clifford algebra is a symbol azumaya algebra of degree p generalizing the theory developed for p 3 furthermore when p 5 and the product is not 1 we show that any quotient division algebra of the clifford algebra is a cyclic algebra or a tensor product of two cyclic algebras and every product of two cyclic algebras can be obtained as a quotient explicit presentation is given to the clifford algebra when the form is diagonal

on the generalized clifford algebra of a monic polynomial abstract in this paper we study the generalized clifford algebra defined by pappacena of a monic with respect to the first variable homogeneous polynomial z x 1 x n z d k 1 d f k x 1 x n z d k of degree d in n 1 variables over some field f we completely determine its structure in the following cases n 2 and d 3 and either char f 3 f 1 0 and f 2 x 1 x 2 e x 1 x 2 for some e f or char f 3 f 1 x 1 x 2 r x 2 and f 2 x 1 x 2 e x 1 x 2 t x 2 2 for some r t e f excluding a few exceptions this algebra is an azumaya algebra of rank nine whose center is the coordinate ring of an affine elliptic curve we also discuss representations of arbitrary generalized clifford algebras assuming the base field f is algebraically closed of characteristic zero

on the first and second order derivatives of the perron vector abstract in a previous work 5 the authors developed formulas for the second order partial derivatives of the perron root as a function of the matrix entries at an essentially nonnegative and irreducible matrix these formulas which involve the group generalized inverse of an associated m matrix were used to investigate the concavity and convexity of the perron root as a function of the entries the authors now combine the above results together with an approach taken in an earlier joint paper 6 of the second author with l elsner and c johnson and they develop formulas for the second order derivatives of an appropriately normalized perron vector with respect to the matrix entries which again are given in terms the group generalized inverse of an associated m matrix convexity properties of the perron vector as a function of the entries of the matrix are then examined in addition formulas for the first derivative of the perron vector resulting from different normalizations of this eigenvector are also given a by product of one of these formulas yields that the group generalized inverse of a singular and irreducible m matrix can be diagonally scaled to a matrix which is entrywise column diagonally dominant

down up algebras and their representations abstract the down up algebras were introduced in g benkart and t roby 1998 j algebra209 305 344 and g benkart 1998 contemp math 224 29 45 their representations were studied via category o and verma modules here we prove that when 0 they are hyperbolic rings and we study their representations via their left spectrum as defined in a l rosenberg 1995 noncommutative algebraic geometry and representations of quantized algebras kluwer academic dordrecht the center of these algebras is computed using results from hyperbolic rings which are also proved here the case when the down up algebra is a finite module over its center is considered in detail and its relation to the clifford algebra of a binary form of arbitrary degree is established

improved bounds for a condition number for markov chains abstract let p be the transition matrix for an n state homogeneous ergodic markov chain set q i p and let q q i j be the group generalized inverse of q a well known condition number due to funderlic and meyer which is used in the error analysis for the computation of the stationary distribution vector 1 n t of the chain is 4 max 1 i j n q i j in this paper we refine two upper estimates on 4 due to meyer in the course of proving one of our results we show that q i j j 1 i q 1 j where q j is the n 1 n 1 principal submatrix of q obtained from deleting its j th row and column and we characterize the case of equality the fact that we have a tight upper bound on the individual entries of the group inverse allows us to apply it in other contexts in which the group inverse arises for an irreducible nonnegative matrix such applications include for instance bounds on the second order partial derivative of the perron root with respect to any entry of the matrix and on the elasticity of the perron root with respect to any entry of the matrix

applications of paz s inequality to perturbation bounds for markov chains abstract in several papers meyer singly and with coauthors established the usefulness of the group generalized inverse in the study and computations of various aspects of markov chains here we are interested in those results which concern bounds on the condition number of the chain and on the error in the computation of the stationary distribution vector we show that a lemma due to paz can be used to improve sometimes by a factor of 2 some of the constants in the bounds obtained in the aforementioned papers

additive versus multiplicative combination of differences of interaural time and intensity predictions of the position variable model r m stern jr and h s colburn j acoust soc am 64 127 140 1978 are compared to the observed lateralization of bandpass noise as a joint function of differences of interaural time intensity and phase itd iid and ipd respectively t n buell and c trahiotis j acoust soc am 90 2266 a 1991 this presentation is primarily concerned with the effect of iids on the lateralization of bandpass noise it is shown that the multiplicative intensity weighting function that had been a feature of all previous implementations of the position variable model is fundamentally unable to describe the data of buell and trahiotis it is argued that the form of these data suggests that the effects of iid must be introduced in an additive fashion at a more central level after image position is estimated on the basis of timing information alone such a model provides a very good description of the buell and trahiotis data as well as the results of severa

representations of a clifford algebra that are azumaya algebras and generate the brauer group abstract clifford algebras of forms of degree d 2 are infinite dimensional see theorem 3 p 272 of l childs j lin mul alg 5 1978 267 278 and corollary 2 p 273 of m orzech and l small lecture notes in pure and applied mathematics vol 11 dekker new york 1975 in the case of a non singular binary cubic form over field f d haile amer math j 106 no 6 1984 1269 1280 demonstrated an injective representation of the clifford algebra in m 3 k where k is a transcendental extension of f he showed that the clifford algebra is thus an azumaya algebra over the coordinate ring of an elliptic curve and that for any algebraic extension f of f the group of f points on the curve map homomorphically into the brauer group of f

derivatives of the perron root at an essentially nonnegative matrix and the group inverse of an m matrix abstract the results of the work in this paper can be divided into two major parts in the first part we develop formulae using group inverses of irreducible m matrices for the second order partial derivatives with respect to the entries of the perron root r at an essentially nonnegative and irreducible matrix a we use these formulae to obtain explicit expressions for the matrices 2 r a ij 2 and 2 r a ii jj and examine these expressions at some special cases when for example in addition to a being essentially nonnegative and irreducible a is row stochastic or a is of rank 1 and so on in the second major part of this paper we investigate for a singular and irreducible m matrix q a certain matrix g which is a positive diagonal scaling of the group inverse q of q we show for instance that z gz 0 for all real vectors z and use this result and some of the formulae obtained in the first part of the paper to provide a matrix theoretic proof of a theorem due to j e cohen math proc cambridge philos soc 86 1979 343 350 which states that for an essentially nonnegative and irreducible matrix a the perron root is a convex function of the main diagonal of a

on azumaya algebras arising from clifford algebras in this paper we continue the investigation begun in haile 4 and tesser 12 into the structure of the clifford algebra of a form if f is a form of degree d in n variables over a field f then the clifford algebra off is the f algebra c r t where r fix x is the free associative f algebra in n variables and t is the ideal generated by a x x y f 1 cx jcxl cl f if d 2 this is the classical clifford algebra of a quadratic form if d 2 then this is also called the generalized clifford algebra and has been studied by various authors see roby 111 revoy lo childs 2 in haile 4 it was shown that if d 3 and n 2 i e iffis a binary cubic form and the characteristic of the field f is not 2 or 3 then the clifford algebra c of the form is azymaya with center the affine coordinate ring of an explicitly given elliptic curve over f the center was also determined by heerema in 6 moreover the algebra c can be extended to an azumaya algebra over the projective closure of the elliptic curve applying the pairing investigated by lichtenbaum 4 and manin 9 one obtains then for each field extension k f a homomorphism from the group of k rational points on the elliptic curve to the brauer group of k given by specialization in lo revoy using results of roby 111 exhibited an explicit f basis for the clifford algebra of an arbitrary form using this basis it is easy to

stationary distributions and mean first passage times of perturbed markov chains stationary distributions of perturbed finite irreducible discrete time markov chains are intimately connected with the behaviour of associated mean first passage times this interconnection is explored through the use of generalized matrix inverses some interesting qualitative results regarding the nature of the relative and absolute changes to the stationary probabilities are obtained together with some improved bounds ams classification 15a51 60j10 60j20 65f20 65f35

representing clifford algebras as crossed products soit d un entier positif plus grand que 2 soit f un corps de caracteristique ne divisant pas d et soit f une forme binaire diagonale de degre d on note par cf l algebre de clifford associee a f on considere des images homomorphes de cf et on montre qu elles peuvent etre vues comme des produits croises sur l anneau des coordonnees d une courbe plane de degre d sur f par un groupe fini cyclique d ordre d

comparison of perturbation bounds for the stationary distribution of a markov chain abstract the purpose of this paper is to review and compare the existing perturbation bounds for the stationary distribution of a finite irreducible homogeneous markov chain

lateral position based models of interaural discrimination this letter investigates the hypothesis that lateral position is the only cue available for interaural discrimination experiments using 500 hz stimuli the discussion of this hypothesis is in the context of comparisons of the experimental data to predictions of the position variable model of binaural interaction the model predicts the mean and variance of the subjective lateral position of stimuli used in the discrimination experiments assuming that discrimination performance is based on optimal processing of this subjective position to the extent that the laterality predictions of the model are accurate data that are inconsistent with its predictions would also be problematical for any model based on the subjective laterality of a single binaural image the predictions at least qualitatively describe much of the observed experimental data including a number of results that have not been addressed by any previous theory nevertheless the observed performance is significantly better than the corresponding predictions for three types of experiments in which the utility of the position cue has been eliminated by experimental design we believe that our results indicate that changes in lateral position are the primary cue in most interaural discrimination experiments but that secondary attributes of the perceptual images can be useful when performance based on position alone would be poor

on the clifford algebra of a binary form the clifford algebra cj of a binary form f of degree d is the k algebra k x y i where i is the ideal generated by ax y d f e k c f has a natural homomorphic image a f that is a rank d 2 azumaya algebra over its center we prove that the center is isomorphic to the coordinate ring of the complement of an explicit divisor in pic d g 1 c where c is the curve w d f u v and g is the genus of c