perturbation free measurement of the harmonics to noise ratio in voice signals using pitch synchronous harmonic analysis the measurement of the harmonics to noise ratio hnr in speech signals gives an indication of the aperiodicity of the speech waveform this may be due to the presence of jitter shimmer additive noise waveshape change or some unknown combination of these factors in order to estimate the hnr as a measure of the additive noise component only the contaminating effects of the other contributory components must first be removed a pitch synchronous harmonic analysis is proposed to overcome this problem the procedure takes advantage of the time scale compression frequency expansion property of the fourier series in order to eliminate jitter and shimmer successive spectra are added by harmonic number as opposed to frequency location and perturbation is removed due to the fact that the relative heights of the harmonic components remain the same for scaled signals the technique is examined on synthetically generated voice signals a discussion of the results is given in terms of human voice signals characterization of jitter vocal tract filtering effects perturbation mechanisms nonlinear dynamics and the possibility of developing the method for use with inverse filtering strategies

spectral characterization of jitter shimmer and additive noise in synthetically generated voice signals alteration of the harmonic structure in voice source spectra taken over at least two periods of the waveform may occur due to the presence of fundamental frequency f0 perturbation amplitude perturbation additive noise or changes within the glottal source signal itself in order to make accurate inferences regarding glottal flow dynamics or perceptual evaluations based on spectral measurements taken from the acoustic speech waveform investigation of the spectral features of each aperiodic component is required based on a heuristic development involving a consideration of the partial sum of the fourier series taken for two periods of a jittered shimmered and additive random noise contaminated signal the corresponding spectral characteristics are hypothesized subsequent to this the fourier series coefficients are calculated for the two periods in order to test the hypotheses definite spectral differences are found for each aperiodic component based on these findings differential quantitative spectral measurements are suggested further supportive evidence is obtained through use of fourier transform and periodogram averaged calculations the analysis is carried out on synthetically generated glottal pulse waveforms and on radiated speech waveforms a discussion of the results is given in terms of voice aperiodicity in general and in terms of their implication for future studies involving human voice signals

degenerations in a class of matrix varieties and prinjective modules abstract let k be an algebraically closed field and let i be a finite partially ordered set to any vector v n i we associate the irreducible variety mat v i with an action of the algebraic group g v i see section 6 the main aim of this paper is to give a description of degenerations of orbits of this action in terms of homomorphisms and extensions of prinjective ki modules

module varieties over canonical algebras abstract the main purpose of this paper is the study of module varieties over the class of canonical algebras providing a rich source of examples of varieties with interesting properties our main tool is a stratification of module varieties which was recently introduced by richmond this stratification does not require a precise knowledge of the module category if it is finite then it provides a method to classify irreducible components we determine the canonical algebras for which this stratification is finite in this case we describe the algorithm for calculating the dimension of the variety and the number of irreducible components of maximal dimension for an infinite family of examples we give easy combinatorial criteria for irreducibility cohen macaulay and normality

investigation of a glottal related harmonics to noise ratio and spectral tilt as indicators of glottal noise in synthesized and human voice signals the harmonics to noise ratio hnr of the voiced speech signal has implicitly been used to infer information regarding the turbulent noise level at the glottis however two problems exist for inferring glottal noise attributes from the hnr of the speech wave form i the measure is fundamental frequency f0 dependent for equal levels of glottal noise and ii any deviation from signal periodicity affects the ratio not just turbulent noise an alternative harmonics to noise ratio formulation glottal related hnr ghnr is proposed to overcome the former problem in ghnr a mean over the spectral range of interest of the hnrs at specific harmonic between harmonic frequencies expressed in linear scale is calculated for the latter issue ii two spectral tilt measures are shown using synthesis data to be sensitive to glottal noise while at the same time being comparatively insensitive to other glottal aperiodicities the theoretical development predicts that the spectral tilt measures reduce as noise levels increase a conventional hnr estimator ghnr and two spectral tilt measures are applied to a data set of 13 pathological and 12 normal voice samples one of the tilt measures and ghnr are shown to provide statistically significant differentiating power over a conventional hnr estimator

the complexity of minimal degenerations for representation finite selfinjective algebras abstract minimal degenerations of modules over all but one exceptional class of representation finite selfinjective algebras are given by extensions g zwara colloq math 75 1998 91 this means in terms of the complexity of degenerations that these minimal degenerations have complexity one the minimal degenerations of modules for the exceptional class of representation finite selfinjective algebras are studied by r aehle j london math soc 66 2002 73 in this paper it is shown that these degenerations have complexity less or equal to two

semi invariants for quivers with relations for a given quiver q and a dimension vector let si q be the ring of semi invariants for dimensional representations schofield defined in s for any dimensional representation v with 0 a semi invariant c si q we recall that we proved in dw that the ring of semi invariants si q is generated by such schofield semi invariants in this note we generalize the results of dw to quivers with relations in the case when the base field has characteristic zero we make this assumption throughout the paper let q be a quiver and let i be an ideal generated by admissible relations the variety rep q i of representations of q satisfying the relations from i does not have to be irreducible we are interested in the generators of rings of semiinvariants on the irreducible components of rep q i it is clear that the ring of semi invariants on such components will be generated by the restrictions of the semi invariants c where v is a representation of q however such description is not very useful we might have a case when the quiver q with relations i is of a finite or tame type but q is wild in such case one would still like to describe the semi invariants of q i explicitly but the description of indecomposable representations of q is impossible therefore it

on degenerations and extensions of finite dimensional modules abstract we derive a cancellation theorem for degenerations of modules that says in particular that projective or injective common direct summands can always be neglected combining the cancellation result with the existence of almost split sequences we characterize the orbit closure of a module living on preprojective components by the fact that the dimension of the homomorphism space to any other module does not decrease for representation directed algebras whence in particular for path algebras of dynkin quivers we provide an alternative proof which shows in addition that any minimal degenerationnofmcomes from an exact sequence with middle termmwhose end terms add up ton by a careful examination the same is true for degenerations of matrix pencils having used so far the existence of certain extensions to obtain degenerations we then turn the tables and use degenerations to produce a lot of interesting short exact sequences in particular we show that any non simple indecomposable over a tame quiver is an extension of an indecomposable and a simple

on the variety of complexes publisher summary this chapter focuses on the characteristic free study of the buchsbaum eisenbud varieties of complexes in detail with the use of young diagrams and young tableaux to give an explicit basis for buchsbaum and eisenbud have studied the varieties of complexes from the point of view of resolutions and have proven the results for the variety w k 1 a young tableau is a filling of the boxes of a young diagram with integers out of 1 2 and is called the shape of the young tableau the chapter presents a proposition that states that ach element in can be written as a linear combination of standard multitableaux

on minimal disjoint degenerations for preprojective representations of quivers we derive a root test for degenerations as described in the title in the case of dynkin quivers this leads to a conceptual proof of the fact that the codimension of a minimal disjoint degeneration is always one for euclidean quivers it enables us to show a periodic behaviour this reduces the classification of all these degenerations to a finite problem that we have solved with the aid of a computer it turns out that the codimensions are bounded by two somewhat surprisingly the regular and preinjective modules play an essential role in our proofs

relaxation of hypotheses in lasalle krasovskii type invariance results the usual invariance results for asymptotic stability for continuous autonomous finite dimensional dynamical systems involve a positive definite lyapunov function whose time derivative along the system motions is negative semidefinite along with certain invariance conditions this is equivalent to requiring that along the system motions the lyapunov function is nonincreasing at all times with increasing time in this paper we establish an invariance result for asymptotic stability for continuous and discontinuous nonautonomous finite dimensional dynamical systems which requires a positive definite lyapunov function which when evaluated along the system motions is nonincreasing only on certain unbounded discrete time sets e with increasing time this allows that between the time instants determined by e the lyapunov function may increase i e over some finite time intervals the system may exhibit unstable behavior we also show that the usual invariance theorem for asymptotic stability reduces to

on characters and formal degrees of discrete series of affine hecke algebras of classical types we address two fundamental questions in the representation theory of affine hecke algebras of classical types one is an inductive algorithm to compute characters of tempered modules and the other is the determination of the constants in the formal degrees of discrete series in the form conjectured by reeder j reine angew math 520 37 93 2000 the former is completely different from the lusztig shoji algorithm shoji in invent math 74 239 267 1983 lusztig in ann math 131 355 408 1990 and it is more effective in a number of cases the main idea in our proof is to introduce a new family of representations which behave like tempered modules but for which it is easier to analyze the effect of parameter specializations our proof also requires a comparison of the c theoretic results of opdam delorme slooten solleveld j inst math jussieu 3 531 648 2004 arxiv 0909 1227 int math res not 2008 adv math 220 1549 1601 2009 acta math 205 105 187 2010 and the geometric construction from kato duke math j 148 305 371 2009 am j math 133 518 553 2011 ciubotaru and kato adv math 226 1538 1590 2011

the resolution of the generic residual intersection of a complete intersection the concept of residual intersection introduced by artin and nagata l in 1972 is a fruitful generalization of linkage as the following two examples attest let i be a strongly cohen macaulay ideal in a cohenmacaulay local ring r if z satisfies the condition g then huneke 6 proposition 4 31 has proved that the extended rees algebra r it t 1 is defined by an ideal which is obtained from i by way of residual intersection since the extended rees algebra is a deformation of both the rees algebra r it and the associated graded algebra gz i it contains considerable information about the analytic properties of i the definitions of residual intersection strongly cohen macaulay and g may be found in section 4 huneke 6 theorem 4 11 has also shown that the ideal i generated by the maximal order minors of a generic n x m matrix is a residual intersection of a generic codimension two cohen macaulay ideal since j is rather poorly behaved with respect to linkage s it is promising that it is close to a well understood ideal once we weaken the tie from linkage to residual intersection

lyapunov based sufficient conditions for exponential stability in hybrid systems lyapunov based sufficient conditions for exponential stability in hybrid systems are presented the focus is on converting non strict lyapunov conditions having certain observability properties into strict lyapunov conditions for exponential stability both local and global results are considered the utility of the results is illustrated through an example

perception of aperiodicities in synthetically generated voices the purpose of this study was to investigate univariate relationships between perceived dysphonia and variation in pitch perturbation amplitude perturbation and additive noise a time domain pitch synchronous synthesis technique was used to generate sustained vowels varying in each of the three acoustic dimensions a panel of trained listeners provided direct magnitude estimates of roughness in the case of the stimuli varying in pitch and amplitude perturbation and breathiness in the case of the stimuli varying in additive noise very strong relationships were found between perceived roughness and either pitch or amplitude perturbation however unlike results reported previously for nonspeech stimuli the subjective quality associated with pitch perturbation was quite different from that associated with amplitude perturbation results also showed that perceived roughness was affected not only by the amount of perturbation but also by the degree of correlation between adjacent pitch or amplitude values a strong relationship was found between perceived breathiness and signal to noise ratio contrary to previous findings there was no interaction between signal to noise ratio and the amount of high frequency energy in the periodic component of the stimulus stimuli with similar signal to noise ratios received similar ratings regardless of differences in the spectral slope of the periodic component

relative beilinson monad and direct image for families of coherent sheaves the higher direct image complex of a coherent sheaf or finite complex of coherent sheaves under a projective morphism is a fundamental construction that can be defined via a cech complex or an injective resolution both inherently infinite constructions using exterior algebras and relative versions of theorems of beilinson and bernstein gel fand gel fand we give an alternate description in finite terms using this description we can characterize the generic complex over the variety of finite free complexes of a given shape as the direct image of an easily described vector bundle we can also give explicit descriptions of the loci in the base spaces of flat families of sheaves in which some cohomological conditions are satisfied for example the loci where vector bundles on projective space split in a certain way or the loci where a projective morphism has higher dimensional fibers our approach is so explicit that it yields an algorithm suited for computer algebra systems

generic modules for gentle algebras abstract in this article we construct the generic modules in each irreducible component of variety of dimensional modules of a triangular gentle algebra the construction is completely combinatorial and allows for determination of canonical decomposition of irreducible components as well as calculation of the dimension of the higher self extension spaces for generic modules

hodge dual operators and model algebras for rational representations of the general linear group abstract in this paper we construct a family of algebras each of whose members is a multiplicity free sum of irreducible rational representations of the general linear group gl n c we then use the properties of a generalized version of the hodge dual operator to determine an explicit basis for each of these algebras and by restriction we obtain an explicit basis for each of the irreducible rational representations of gl n c our results cleanly extends classical algebro combinatorial results on polynomial representations of gl n c to rational representations

codimension 1 orbits and semi invariants for the representations of an equioriented graph of type _ on considere le diagramme de dynkin d n equioriente et la variete hom v 1 v 3 i 2 n hom v i v i 1 v j un espace vectoriel sur k sur lequel agit le groupe g i 1 n gl v i on determine l orbite maximale et les orbites de codimension 1 de cette action

on the conormal bundle of the determinantal variety call w such variety if we choose bases b v a a b u v i b for each module we can identify w with the variety of pairs of matrices y x with entries in r x being an m x n matrix y an ii x m matrix such that x y omx y x onxm now let a be the coordinate ring of the affine space a of dimension 2 m x n i e the polynomial ring r x yji i l m j i n and

temporal and spectral estimations of harmonics to noise ratio in human voice signals the quantity harmonic to noise ratio hnr has been used to estimate the level of noise in human voice signals hnr estimation can be accomplished in two ways 1 on a time domain basis in which hnr is computed directly from the acoustic waveform and 2 on a frequency domain basis in which hnr is computed from a transformed representation of the waveform an algorithm for computing hnr in the frequency domain was modified and tested in the work described here the modifications were designed to reduce the influence of spectral leakage in the computation of harmonic energy and to remove the necessity of spectral baseline shifting prescribed in one existing algorithm g de krom j speech hear res 36 254 266 1993 frequency domain estimations of hnr based on this existing algorithm and our modified algorithm were compared to time domain estimations on synthetic signals and human pathological voice samples results indicated a highly significant linear correlation between frequency and time domain estimations of hnr for our modified approach

complexes which arise from a matrix and a vector resolutions of divisors on certain varieties of complexes abstract consider the polynomial ring r r0 x y where r0 is a normal domain and x1 g and yg f are matrices of indeterminates the r ideal j i1 xy imin f g y defines a variety of complexes over r0 the divisor class group of r j is isomorphic to cl r0 z i where i is an ideal of r j generated by appropriately chosen lower order minors of y we produce the minimal r free resolution of i i for all integers i 1 if f is greater than or equal to g then j is a generic residual intersection of the generic grade g complete intersection i1 x the resolutions that we produce in this case are in many ways analogous to resolutions of divisors on generic residual intersections of grade two perfect ideals or grade three gorenstein ideals

on first rahmonic amplitude in the analysis of synthesized aperiodic voice signals rahmonics comprise the prominent peaks in the cepstrum of voiced speech their locations correspond to the fundamental period and its multiples the amplitude of the first rahmonic r1 has previously been used to indicate voice quality although a correspondence between r1 and the richness of the harmonic spectrum for voiced speech is well recognized a formal description has remained absent a theoretical description of rahmonic analysis of voiced speech containing aspiration noise is provided leading to a characterization of r1 the theory suggests that r1 is directly proportional to the geometric mean harmonics to noise ratio gmhnr where the gmhnr is defined as the mean of the individual spectral i e at specific frequency locations harmonics to noise ratios in db this hypothesis is validated using synthetically generated voice signals r1 is shown to be directly proportional to gmhnr measured directly from the db spectrum it is shown that r1 estimated from speech is directly proportional to r1 taken from the glottal signal r1 and gmhnr measured spectrally underestimate the actual gmhnr when averaged noise levels exceed harmonic levels limiting the number of harmonics in the analysis window overcomes this problem and also alleviates the temporal window length f0 dependence of r1 when estimated period synchronously

on the minimal free resolution of the universal ring for resolutions of length two abstract hochster established the existence of a commutative noetherian ring c and a universal resolution u of the form 0 c e c f c g 0 such that for any commutative noetherian ring s and any resolution v equal to 0 s e s f s g 0 there exists a unique ring homomorphism c s with v u c s in the present paper we assume that f e g and we find the minimal resolution of c z q by free b modules where b is a polynomial ring over the field of rational numbers the modules of the resolution are described in terms of schur functors the graded strands of the differential are described in terms of pieri maps

on the invariant theory for acyclic gentle algebras in this paper we show that the fields of rational invariants over the irreducible components of the module varieties for an acyclic gentle algebra are purely transcendental extensions along the way we exhibit for such fields of rational invariants a transcendence basis in terms of schofield s determinantal semi invariants we also show that the moduli spaces of modules over regular irreducible component are just a products of projective spaces contents

on feedback passivity of discrete time nonlinear networked control systems with packet drops we analyze the feedback passivity of a networked control system in which the control packets may be dropped by the communication channel specifically we consider a discrete time switched nonlinear system with relative degree zero that switches between two modes at the instants when the communication link transmits the packet successfully the system evolves in closed loop and the increase in storage function is bounded below the energy supplied by the control input at the instants when a packet drop occurs the system evolves in open loop according to the free dynamics of the closed loop mode and the increase in storage function is not necessarily bounded by the supplied energy the literature on passivity of switched systems seems to consider only the case when all the modes are passive which is not the case here we prove that if the ratio of time steps for which the system evolves in closed loop versus in open loop is lower bounded by a critical number the system is locally feedback passive in a suitably defined sense this generalized definition of feedback passivity is useful since it preserves two important properties of classical passivity that feedback passivity implies asymptotic stabilizability for zero state detectable systems and that feedback passivity is preserved in parallel and negative feedback interconnections

arithmetic cohen macaulayness and arithmetic normality for schubert varieties let g be a semisimple simply connected chevalley group over a field k let t be a maximal torus b a borel subgroup d t and w the weyl group of g relative to t let p be a maximal parabolic subgroup of classical type cf 7 8 i e a maximal parabolic subgroup such that if w is the associated fundamental weight then i w av i 1 2 w c a is 2 for all roots ae being a w invariant scalar product on x t q where x t character group of t for t e w wp let x t denote the schubert variety in g p associated to t namely x t is the zariski closure btp mod p in g p of the bruhat cell endowed with the canonical reduced structure for the canonical projective embedding g p in p h g p l let rt denote the homogeneous co ordinate ring of x t then the main result of this paper is given by

geometric aspects of iterated matrix multiplication abstract this paper studies geometric properties of the iterated matrix multiplication polynomial and the hypersurface that it defines we focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the polynomial the dual variety and the jacobian loci of the hypersurface that are computed with the aid of representation theory of quivers

rigid ideals by deforming quadratic letterplace ideals abstract we compute the deformation space of quadratic letterplace ideals l 2 p of finite posets p when its hasse diagram is a rooted tree these deformations are unobstructed the deformed family has a polynomial ring as the base ring the ideal j 2 p defining the full family of deformations is a rigid ideal and we compute it explicitly in simple example cases j 2 p is the ideal of maximal minors of a generic matrix the pfaffians of a skew symmetric matrix and a ladder determinantal ideal

a pitch synchronous analysis of hoarseness in running speech a method of pitch synchronous acoustic analysis of hoarseness requiring a voice sample of only four fundamental periods is presented this method calculates a noise to signal n s ratio which indicates the depth of valleys between harmonic peaks in the power spectrum the spectrum is calculated pitch synchronously from a fourier transform of the signal windowed through a continuously variable hanning window spanning exactly four fundamental periods a two stage procedure is used to determine the exact duration of the four fundamental periods an initial estimate is obtained using autocorrelation in the time domain a more precise estimate is obtained in the frequency domain by minimizing the errors between the preliminary calculated power spectrum and the predicted spectrum spread of a windowed harmonic signal analysis of synthesized voices showed that the n s ratio is sensitive to additive noise jitter and shimmer and is insensitive to slow 8 hz modulation in fundamental frequency and amplitude an analysis of pre and postoperative voices of six patients with benign laryngeal disease showed that the n s ratio for vowel u in running speech consistently improved after surgery for all subjects in agreement with their successful therapeutic results