improving performance of fxlms algorithm for active noise control of impulsive noise this paper concerns active noise control anc of impulsive noise modeled using non gaussian stable processes the most famous filtered x least mean square fxlms algorithm for anc systems is based on minimization of variance of error signal for the impulse noise the fxlms algorithm becomes unstable as second order moments do not exist for non gaussian processes among the existing algorithms for anc of impulsive noise one is based on minimizing least mean p power lmp of the error signal resulting in fxlmp algorithm the other is based on modifying on the basis of statistical properties the reference signal in update of fxlms algorithm in this paper the proposed algorithm is an extension of the later approach extensive simulations are carried out which demonstrate the effectiveness of the proposed algorithm it achieves the best performance among the existing algorithms and at the same computational complexity as that of fxlms algorithm

invariants of 3 manifolds via link polynomials and quantum groups the aim of this paper is to construct new topological invariants of compact oriented 3 manifolds and of framed links in such manifolds our invariant of a link in a closed oriented 3 manifold is a sequence of complex numbers parametrized by complex roots of 1 for a framed link in s 3 the terms of the sequence are equale to the values of the suitably parametrized jones polynomial of the link in the corresponding roots of 1 in the case of manifolds with boundary our invariant is a sequence of finite dimensional complex linear operators this produces from each root of unity q a 3 dimensional topological quantum field theory

spectra and eigenvectors of scale free networks we study the spectra and eigenvectors of the adjacency matrices of scale free networks when bidirectional interaction is allowed so that the adjacency matrix is real and symmetric the spectral density shows an exponential decay around the center followed by power law long tails at both spectrum edges the largest eigenvalue ensuremath lambda 1 depends on system size n as ensuremath lambda 1 ensuremath sim n 1 4 for large n and the corresponding eigenfunction is strongly localized at the hub the vertex with largest degree the component of the normalized eigenfunction at the hub is of order unity we also find that the mass gap scales as n ensuremath 0 68

a tqft from quantum teichmuller theory by using quantum teichmuller theory we construct a one parameter family of tqfts on the categroid of admissible leveled shaped 3 manifolds

representations of the kauffman bracket skein algebra i invariants and miraculous cancellations we study finite dimensional representations of the kauffman bracket skein algebra of a surface s in particular we construct invariants of such irreducible representations when the underlying parameter q mathrm e 2 pi mathrm i hbar is a root of unity the main one of these invariants is a point in the character variety consisting of group homomorphisms from the fundamental group pi 1 s to mathrm sl 2 mathbb c or in a twisted version of this character variety the proof relies on certain miraculous cancellations that occur for the quantum trace homomorphism constructed by the authors these miraculous cancellations also play a fundamental role in subsequent work of the authors where novel examples of representations of the skein algebra are constructed

synchronizability of complex networks recent interest in the study of networks associated with complex systems has led to a better understanding of the factors and parameters relating the topology of the associated networks with the dynamics of the systems and in particular their synchronization in this paper by using known and new results from spectral graph theory we characterize relevant factors which affect the synchronization of complex networks

detecting outlying cells in two way contingency table via backwards stepping when fitting a model to a contingency table a significant lack of fit can sometimes be caused by a few outlier cells with the model fitting the remaining cells well these cells can be identified by using deleted residuals the residual from the expected count with the cell deleted and tested using the drop in likelihood ratio goodness of fit statistic from the model with the cell included to the model with the cell deleted with the cells being tested from least extreme to most extreme backwards stepping this article shows that using a bonferroni bound for the outlier test at each step results in a conservative test with good power to detect multiple outliers backwards stepping and the use of deleted residuals results in the limiting of both masking and swamping effects the procedure generalizes easily to complicated probability models

fine tuning some resistant rules for outlier labeling abstract a previous study examined the performance of a standard rule from exploratory data analysis which uses the sample fourths fl and fu and labels as outside any observations below fl k fu fl or above fu k fu fl customarily with k 1 5 in terms of the order statistics x 1 x 2 x n the standard definition of the fourths is fl x f and fu x n 1 f where f n 3 2 and denotes the greatest integer function the results of that study suggest that finer interpolation for the fourths might yield smoother behavior in the face of varying sample size in this article we show that using f i n 4 5 12 to define the fourths produces the desired smoothness corresponding to a common definition of quartiles fq n 4 1 4 leads to similar results instead of allowing the some outside rate per sample the probability that a sample contains one or more outside observations analogous to the experimentwise error rate in simultaneous inference to vary some us

patient specific detection of perfusion abnormalities combining within subject and between subject variances in arterial spin labeling in this paper patient specific perfusion abnormalities in arterial spin labeling asl were identified by comparing a single patient to a group of healthy controls using a mixed effect hierarchical general linear model glm two approaches are currently in use to solve hierarchical glms 1 the homoscedastic approach assumes homogeneous variances across subjects and 2 the heteroscedastic approach is theoretically more efficient in the presence of heterogeneous variances but algorithmically more demanding in practice in functional magnetic resonance imaging studies the superiority of the heteroscedastic approach is still under debate due to the low signal to noise ratio of asl sequences within subject variances have a significant impact on the estimated perfusion maps and the heteroscedastic model might be better suited in this context in this paper we studied how the homoscedastic and heteroscedastic approaches behave in terms of specificity and sensitivity in the detection of patient specific asl perfusion abnormalities validation was undertaken on a dataset of 25 patients diagnosed with brain tumors and 36 healthy volunteers we showed evidence of heterogeneous within subject variances in asl and pointed out an increased false positive rate of the homoscedastic model in the detection of patient specific brain perfusion abnormalities with asl modeling heterogeneous variances increases the sensitivity at the same specificity level

minimum vertex covers and the spectrum of the normalized laplacian on trees abstract we show that in the graph spectrum of the normalized graph laplacian on trees the eigenvalue 1 and eigenvalues near 1 are strongly related to minimum vertex covers in particular for the eigenvalue 1 its multiplicity is related to the size of a minimum vertex cover and zero entries of its eigenvectors correspond to vertices in minimum vertex covers while for eigenvalues near 1 their distance to 1 can be estimated from minimum vertex covers and for the largest eigenvalue smaller than 1 the sign graphs of its eigenvectors take vertices in a minimum vertex cover as representatives

on the use of an spsa based model free feedback controller in active noise control for periodic disturbances in a duct in this paper a feedback active noise control fanc system using a model free mf controller based on simultaneous perturbation stochastic approximation spsa algorithm is considered the structure of the fanc system is first described and the spsa algorithm is briefly reviewed subsequently the spsa based mf control algorithm employed in the fanc system is derived computer simulations are carried out to suggest that the spsa based mf control algorithm is effective for anc system and much more efficient than the finite difference stochastic approximation fdsa algorithm the controller based on the spsa based mf control algorithm is implemented on the texas instruments digital signal processor dsp tms320vc33 experimental results show that the proposed scheme is able to significantly reduce periodic disturbances without the need to model the secondary path at the same time the simulations and the experimental verification tests also show that the convergence rate of the spsa based mf control algorithm is acceptable and the spsa based mf control algorithm has better tracking ability under variable secondary path this observation implies that the spsa based mf controller eliminates the need of modeling of the secondary path for the fanc system

comparing classical and resistant outlier rules abstract in this article we compare rosner s 1983 extension of the outlier t test the generalized esd procedure to the boxplot rules tukey s 1977 resistant outlier labeling approach the underlying principles are contrasted and the behavior of the procedures is compared in a variety of sampling situations to facilitate power type comparisons of procedures that are based on different paradigms the conditional outside rate a performance criterion for assessing outlier labeling procedures is introduced this quantity represents the probability that an observation yi is labeled an outlier conditional on its distance from the center e yi e some exact expressions as well as simple approximations and a monte carlo swindle are developed the conditional outside rate together with the outside rate per observation and the some outside rate per sample are applied to compare performance of the classical and boxplot rules based on monte carlo simulation of samples of sizes n 10 30 and 50

graph identification by simulated annealing a new theoretical approach to graph processing based on the transformation of a topological graph into a time dependent periodic melody is proposed by using a self tuning oscillatory dynamical network graphs can be uniquely reconstructed from their melodies this opens a perspective for a content addressable memory invariant under large topology preserving distortions

resistant and test based outlier rejection effects on gaussian one and two sample inference resistant and sequential test based procedures for the detection of multiple outliers are compared in gaussian one and two sample problems subsequent to statistical rejection of putative outliers operating characteristics of hypothesis tests applied to samples that are outlier free may differ from their nominal values outlier rejection rules may be calibrated however to control the rate of erroneous outlier labeling in pure gaussian samples the small sample behavior of resistant location and scale estimators used in outlier detection is examined through simulation yielding new formulas for calibration of boxplot based and shorth based outlier rejection rules effects of different outlier criteria and calibration rubrics on postrejection hypothesis tests are compared in a variety of contamination settings and real world examples tests conducted subsequent to calibrated rejection have approximately nominal operating characteristics whether or not outliers are present the selection of an outlier cr

symplectic fermions and a quasi hopf algebra structure on bar u _i sl 2 abstract we consider the finite dimensional restricted quantum group u q s l 2 at q i we show that u i s l 2 does not allow for a universal r matrix even though u v v u holds for all finite dimensional representations u v of u i s l 2 we then give an explicit coassociator and a universal r matrix r such that u i s l 2 becomes a quasi triangular quasi hopf algebra our construction is motivated by the two dimensional chiral conformal field theory of symplectic fermions with central charge c 2 there a braided monoidal category sf has been computed from the factorisation and monodromy properties of conformal blocks and we prove that rep u i s l 2 r is braided monoidally equivalent to sf

nonlinear system identification in impulsive environments nonlinear system identification has been studied under the assumption that the noise has finite second and higher order statistics in many practical applications impulsive measurement noise severely weakens the effectiveness of conventional methods in this paper spl alpha stable noise is used as a noise model in such case the minimum mean square error mmse criterion is no longer an appropriate metric for estimation error due to the lack of finite second order statistics of the noise therefore we adopt minimum dispersion criterion which in turn leads to the adaptive least mean pth power lmp algorithm it is shown that the lmp algorithm under the spl alpha stable noise model converges as long as the step size satisfies certain conditions the effect of p on the performance is also investigated compared with conventional methods the proposed method is more robust to impulsive noise and has better performance

a new robust variable step size nlms algorithm a new framework for designing robust adaptive filters is introduced it is based on the optimization of a certain cost function subject to a time dependent constraint on the norm of the filter update particularly we present a robust variable step size nlms algorithm which optimizes the square of the a posteriori error we also show the link between the proposed algorithm and another one derived using a robust statistics approach in addition a theoretical model for predicting the transient and steady state behavior and a proof of almost sure filter convergence are provided the algorithm is then tested in different environments for system identification and acoustic echo cancelation applications

renormalized hennings invariants and 2 1 tqfts we construct non semisimple 2 1 tqfts yielding mapping class group representations in lyubashenko s spaces in order to do this we first generalize beliakova blanchet and geer s logarithmic hennings invariants based on quantum mathfrak sl 2 to the setting of finite dimensional non degenerate unimodular ribbon hopf algebras the tools used for this construction are a hennings augmented reshetikhin turaev functor and modified traces when the hopf algebra is factorizable we further show that the universal construction of blanchet habegger masbaum and vogel produces a 2 1 tqft on a not completely rigid monoidal subcategory of cobordisms

low complexity rls algorithms using dichotomous coordinate descent iterations in this paper we derive low complexity recursive least squares rls adaptive filtering algorithms we express the rls problem in terms of auxiliary normal equations with respect to increments of the filter weights and apply this approach to the exponentially weighted and sliding window cases to derive new rls techniques for solving the auxiliary equations line search methods are used we first consider conjugate gradient iterations with a complexity of operations per sample being the number of the filter weights to reduce the complexity and make the algorithms more suitable for finite precision implementation we propose a new dichotomous coordinate descent dcd algorithm and apply it to the auxiliary equations this results in a transversal rls adaptive filter with complexity as low as multiplications per sample which is only slightly higher than the complexity of the least mean squares lms algorithm multiplications simulations are used to compare the performance of the proposed algorithms against the classical rls and known advanced adaptive algorithms fixed point fpga implementation of the proposed dcd based rls algorithm is also discussed and results of such implementation are presented

spectral classes of regular random and empirical graphs abstract we define a pseudo distance between graphs based on the spectrum of the normalized laplacian since this quantity can be computed easily or at numerically estimated it is suitable for comparing in particular large graphs numerical experiments demonstrate that the spectral distance provides a practically useful measure of graph dissimilarity the asymptotic behavior of the laplacian spectrum furthermore yields a tool for classifying families of graphs in such a way that the distance of two graphs from the same family is bounded by o 1 n in terms of size n of their vertex sets

percentage points for a generalized esd many outlier procedure a generalized extreme studentized deviate esd many outlier procedure is given for detecting from 1 to k outliers in a data set this procedure has an advantage over the original esd many outlier procedure rosner 1975 in that it controls the type i error both under the hypothesis of no outliers and under the alternative hypotheses of 1 2 k l outliers a method is given for approximating percentiles for this procedure based on the t distribution this method is shown to be adequately accurate using monte carlo simulation for detecting up to 10 outliers in samples as small as 25 tables are given for implementing this method for n 25 1 50 10 100 50 500 k 10 05 ol 005

non markov stochastic dynamics of real epidemic process of respiratory infections abstract the study of social networks and especially of stochastic dynamics of diseases spread in human population has recently attracted considerable attention in statistical physics in this work we present a new statistical method of analyzing the spread of epidemic processes of grippe and acute respiratory track infections arti by means of the theory of discrete non markov stochastic processes we use the results of our last theory phys rev e 65 2002 046107 to study statistical memory effects long range correlation and discreteness in real data series describing the epidemic dynamics of human arti infections and grippe we have carried out the comparative analysis of the data of the two infections grippe and arti in one of the industrial districts of kazan one of the largest cities of russia the experimental data are analyzed by the power spectra of the initial time correlation function and the memory functions of junior orders the phase portraits of the four first dynamic variables the three first points of the statistical non markov parameter and the locally averaged kinetic and relaxation parameters the received results give an opportunity to provide a strict quantitative description of regular and stochastic components in epidemic dynamics of social networks taking into account their time discreteness and effects of statistical memory they also allow to reveal the degree of randomness and predictability of the real epidemic process in the specific social network

symmetry processing in neural network models the author proposes a simple way to preprocess symmetries based on the construction of invariant functions over the configuration space of the neural network

spectra of real world graphs beyond the semicircle law results on the spectra of adjacency matrices corresponding to models of real world graphs we find that when the number of links grows as the number of nodes the spectral density of uncorrelated random matrices does not converge to the semicircle law furthermore the spectra of real world graphs have specific features depending on the details of the corresponding models in particular scale free graphs develop a trianglelike spectral density with a power law tail while small world graphs have a complex spectral density consisting of several sharp peaks these and further results indicate that the spectra of correlated graphs represent a practical tool for graph classification and can provide useful insight into the relevant structural properties of real networks

outlier labeling with boxplot procedures in this article we focus on the detection of possible outliers based on the widely used boxplot procedures the outliers in a set of data are defined to be a subset of observations that appear to be inconsistent with the remaining observations we identify the outliers by constructing a boxplot with its lower fence lf and upper fence uf either a satisfying the requirement that if the given sample is outlier free then the probability that one or more of the sample data would fall outside the region lf uf is equal to a prescribed small value or b taken to be the tolerance limits derived from an outlier free random sample within which a specified large proportion of the sampled population would be asserted to fall with a given large probability exact expressions that can be routinely used to evaluate the constants needed in the construction of the boxplot s outlier region for samples taken from the family of location scale distributions are obtained for both procedures this article sh

adaptive volterra filter with continuous lp norm using a logarithmic cost for nonlinear active noise control abstract the filtered x least mean lp norm fxlmp algorithm is proven to be useful for nonlinear active noise control nanc systems however its performance deteriorates when the impulsive noises are presented in nanc systems to surmount this shortcoming a new nonlinear adaptive algorithm based on volterra expansion model vfxloglmp is developed in this paper which is derived by minimizing the lp norm of logarithmic cost it is found that the fxlmp and vfxloglmp require to select an appropriate value of p according to the prior information on noise characteristics which prohibit their practical applications based on vfxloglmp algorithm we proposed a continuous lp norm algorithm with logarithmic cost vfxlogclmp which does not need the parameter selection and thresholds estimation benefiting from the various error norms for 1 p 2 it remains the robustness of vfxloglmp moreover the convergence behavior of vfxlogclmp for moving average secondary paths and stochastic input signals is performed compared to the existing algorithms two versions of the proposed algorithms have much better convergence and stability in impulsive noise environments

modular group representations and fusion in logarithmic conformal field theories and in the quantum group center the sl 2 representation on the center of the restricted quantum group open image in new window at the primitive 2pth root of unity is shown to be equivalent to the sl 2 representation on the extended characters of the logarithmic 1 p conformal field theory model the multiplicative jordan decomposition of the open image in new window ribbon element determines the decomposition of into a pointwise product of two commuting sl 2 representations one of which restricts to the grothendieck ring this restriction is equivalent to the sl 2 representation on the 1 p characters related to the fusion algebra via a nonsemisimple verlinde formula the grothendieck ring of open image in new window at the primitive 2pth root of unity is shown to coincide with the fusion algebra of the 1 p logarithmic conformal field theory model as a by product we derive q binomial identities implied by the fusion algebra realized in the center of open image in new window

procedures for the identification of multiple outliers in linear models abstract we consider the problem of identifying and testing multiple outliers in linear models the available outlier identification methods often do not succeed in detecting multiple outliers because they are affected by the observations they are supposed to identify we introduce two test procedures for the detection of multiple outliers that appear to be less sensitive to this problem both procedures attempt to separate the data into a set of clean data points and a set of points that contain the potential outliers the potential outliers are then tested to see how extreme they are relative to the clean subset using an appropriately scaled version of the prediction error the procedures are illustrated and compared to various existing methods using several data sets known to contain multiple outliers also the performances of both procedures are investigated by a monte carlo study the data sets and the monte carlo indicate that both procedures are effective in the detection of multiple outliers

active noise control with on line estimation of non gaussian noise characteristics abstract active noise control anc is a methodology for attenuating noise based on adaptive signal processing algorithms anc is well assessed for the attenuation of gaussian noise but the rejection of non gaussian impulsive noise signals represents a much more critical task that may even impair algorithm convergence to overcome this problem the adaptive filter weight update process must be modified by discarding or discounting samples associated with impulsive noise this can be done either by modeling the impulsive noise with a non gaussian distribution such as the symmetric stable s s distribution or by applying an outlier detection method with both approaches the accuracy in the noise description appears to be crucial for effective noise reduction this paper proposes two novel approaches for the attenuation of impulsive noise both for invariant and time varying noise distributions the first one is based on the on line estimation of an s s model of the noise probabilistic description the second relies on a simple on line recursive procedure that reliably estimates amplitude thresholds for outlier detection both methods compare favorably with competitor approaches while maintaining a sufficiently low algorithm complexity several examples are shown to demonstrate the algorithms effectiveness

learning symmetry groups with hidden units beyond the perceptron learning to recognize mirror rotational and translational symmetries is a difficult problem for massively parallel network models these symmetries cannot be learned by first order perceptrons or hopfield networks which have no means for incorporating additional adaptive units that are hidden from the input and output layers we demonstrate that the boltzmann learning algorithm is capable of finding sets of weights which turn hidden units into useful higher order feature detectors capable of solving symmetry problems

the structure of the torelli group i a finite set of generators for j this is the first of three papers concerning the so called torelli group let m mg be a compact orientable surface of genus g having n boundary components and let 9 xg be its mapping class group that is the group of orientation preserving diffeomorphisms of m which are 1 on the boundary am modulo isotopies which fix 3m pointwise this group is also known to the complex analysts as the teichmuller group or modular group if n 0 or 1 let further 4 jg be the subgroup of d1 which acts trivially on h1 m z the topologists have no traditional name for a but the analysts tell me it was known classically and is called the torelli group several interesting problems and conjectures exist concerning f the principal one can be found in kirby s problem list k and asks if gg is finitely generated in this first paper we shall answer the question affirmatively for both gg 0 and fgg when g 3 and shall give a fairly simple set of generators two other conjectures were made by the author the first involves the subgroup j of f which is generated by twists on nulhomologous simple closed curves ji produces a surjective homomorphism t fgg 1 a3h1 m z which kills c and it is conjectured there that in fact 5y ker t the proof of this is the content of the second paper in the third paper we use the results of the second to compute the abelianization f f explicitly thereby verifying another conjecture in ji the first reasonably simple but infinite set of generators for fg0 was produced by powell in p his generators consist of two types a twists on bounding simple closed curves b opposite twists on a bounding pair of disjoint homologous simple closed curves each of which are nonbounding using his result the author showed in j2 that the maps of the second type which we call bp maps for bounding pair are actually sufficient to generate both kg 0 and fg 1 for g 3 and in fact that we need only those whose two curves bound a genus one subsurface of m note that for g 2 all bp maps are trivial and hence the result fails in this case in the finite set of generators produced in this paper only

evolutionary reconstruction of networks can a graph specifying the pattern of connections of a dynamical network be reconstructed from statistical properties of a signal generated by such a system in this model study we present a metropolis algorithm for reconstruction of graphs from their laplacian spectra through a stochastic process of mutations and selection evolving test networks converge to a reference graph applying the method to several examples of random graphs clustered graphs and small world networks we show that the proposed stochastic evolution allows exact reconstruction of relatively small networks and yields good approximations in the case of large sizes

adaptive nonlinear neuro controller with an integrated evaluation algorithm for nonlinear active noise systems an adaptive nonlinear neuro controller with an integrated evaluation algorithm for nonlinear active noise control systems is proposed to attenuate the nonlinear and non gaussian noises inspired by the structure of the hammerstein or wiener model the proposed controller is realized by the static nonlinear memory function mapping on the basis of a single neuron a generalized filtered x gradient descent algorithm based on an integrated evaluation criterion is developed to adaptively adjust the weights of the controller where the weighted sum of renyi s quadratic error entropy and the mean square error is applied as the integrated performance index which improves the performance of the adaptive algorithm by introducing the information entropy in addition the convergence of the proposed approach is analyzed and the computational complexity among different methods is investigated the proposed scheme can effectively attenuate the nonlinear and non gaussian noises and has a relative simple structure and less learning parameters the simulation results demonstrate the validity of the proposed method for attenuating the nonlinear and non gaussian noises

asymptotically independent scale free spacings with applications to discordancy testing de facon analogue a la construction des espacements independants et independants de l echelle pour la distribution exponentielle on definit des quantites pour une distribution arbitraire et on etudie leur comportement asymptotique conjoint

on the spectrum of the normalized graph laplacian we investigate how the spectrum of the normalized geometric graph laplacian is affected by operations like motif dougling graph splitting or joining the multiplicity of the eigenvalue 1 or equivalently the dimension of the kernel of the adjacency matrix of the graph is of particular interest this multiplicity can be increased for instance by motif doubling

improved convergence analysis of stochastic gradient adaptive filters using the sign algorithm convergence analysis of stochastic gradient adaptive filters using the sign algorithm is presented in this paper the methods of analysis currently available in literature assume that the input signals to the filter are white this restriction is removed for gaussian signals in our analysis expressions for the second moment of the coefficient vector and the steady state error power are also derived simulation results are presented and the theoretical and empirical curves show a very good match

spectral reconstruction of complex networks abstract in this paper we study the reconstruction of a network topology from the eigenvalues of its laplacian matrix we introduce a simple cost function and consider the tabu search combinatorial optimization method while comparing its performance when reconstructing different categories of networks random regular small world scale free and clustered from their eigenvalues we show that this combinatorial optimization method together with the information contained in the laplacian spectrum allows an exact reconstruction of small networks and leads to good approximations in the case of networks with larger orders we also show that the method can be used to generate a quasi optimal topology for a network associated to a dynamic process like in the case of metabolic or protein protein interaction networks of organisms

a generalized extreme studentized residual multiple outlier detection procedure in linear regression this article is concerned with procedures for detecting multiple y outhers in linear regression a generalized extreme studentized residual gesr procedure which controls type i error rate is developed an approximate formula to calculate the percentiles is given for large samples and more accurate percentiles for n 25 are tabulated the performance of this procedure is compared with others by monte carlo techniques and found to be superior the procedure however fails in detecting y outliers that are on high leverage cases for this a two phase procedure is suggested in phase 1 a set of suspect observations is identified by gesr and one of the diagnostics applied sequentially in phase 2 a backward testing is conducted using the gesr procedure to see which of the suspect cases are outlicrs several examples are analyzed

adaptive volterra filters for active control of nonlinear noise processes this paper presents a volterra filtered x least mean square lms algorithm for feedforward active noise control the research has demonstrated that linear active noise control anc systems can be successfully applied to reduce the broadband noise and narrowband noise specifically such linear anc systems are very efficient in reduction of low frequency noise however in some situations the noise that comes from a dynamic system may he a nonlinear and deterministic noise process rather than a stochastic white or tonal noise process and the primary noise at the canceling point may exhibit nonlinear distortion furthermore the secondary path estimate in the anc system which denotes the transfer function between the secondary source secondary speaker and the error microphone may have nonminimum phase and hence the causality constraint is violated if such situations exist the linear anc system will suffer performance degradation an implementation of a volterra filtered x lms vfxlms algorithm based on a multichannel structure is described for feedforward active noise control numerical simulation results show that the developed algorithm achieves performance improvement over the standard filtered x lms algorithm for the following two situations 1 the reference noise is a nonlinear noise process and at the same time the secondary path estimate is of nonminimum phase 2 the primary path exhibits the nonlinear behavior in addition the developed vfxlms algorithm can also be employed as an alternative in the case where the standard filtered x lms algorithm does not perform well

asymptotic faithfulness of the quantum su n representations of the mapping class groups we prove that the sequence of projective quantum su n representations of the mapping class group of a closed oriented surface obtained from the projective flat su n verlinde bundles over teichm uller space is asymptotically faithful that is the intersection over all levels of the kernels of these representations is trivial whenever the genus is at least 3 for the genus 2 case this intersection is exactly the order 2 subgroup generated by the hyper elliptic involution in the case of even degree and n 2 otherwise the intersection is also trivial in the genus 2 case

robust flood frequency analysis performance of ema with multiple grubbs beck outlier tests flood frequency analysis generally involves the use of simple parametric probability distributions to smooth and extrapolate the information provided by short flood records to estimate extreme flood flow quantiles parametric probability distributions can have difficulty simultaneously fitting both the largest and smallest floods a danger is that the smallest observations in a record can distort the exceedance probabilities assigned to the large floods of interest the identification and treatment of such potentially influential low floods pilfs frees a fitting algorithm to describe the distribution of the larger observations this can allow parametric flood frequency analysis to be both efficient and also robust to deviations from the proposed probability model s lower tail historically pilf identification involved subjective judgement we propose a new multiple grubbs beck outlier test mgbt for objective pilf identification mgbt pilf identification rates akin to type i errors are reported for the lognormal ln distribution and the log pearson type iii lp3 distribution with a variety of skew coefficients mgbt pilf identification generally matched subjective identification from a recent california flood frequency study monte carlo results show that censoring of pilfs identified by the mgbt algorithm improves the extreme quantile estimator efficiency of the expected moments algorithm ema for negatively skewed lp3 distributions and has little effect for zero or positive skews simultaneously it protects against deviations from the lp3 in the lower tail as illustrated by distorted ln examples thus mgbt generally makes flood frequency analysis based on the lp3 distribution with ema both more accurate and more robust

which graphs are determined by their spectrum for almost all graphs the answer to the question in the title is still unknown here we survey the cases for which the answer is known not only the adjacency matrix but also other types of matrices such as the laplacian matrix are considered

non semi simple tqfts reidemeister torsion and kashaev s invariants we construct and study a new family of tqfts based on nilpotent highest weight representations of quantum sl 2 at a root of unity indexed by generic complex numbers this extends to cobordisms the non semi simple invariants defined in arxiv 1202 3553 including the kashaev invariant of links here the modular category framework does not apply and we use the universal construction our tqft provides a monoidal functor from a category of surfaces and their cobordisms into the category of graded finite dimensional vector spaces and their degree 0 morphisms and depends on the choice of a root of unity of order 2r the functor is always symmetric monoidal but for even values of r the braiding on grvect has to be the super symmetric one thus our tqft may be considered as a super tqft in the special case r 2 our construction yields a tqft for a canonical normalization of reidemeister torsion and we re prove the classification of lens spaces via the non semi simple quantum invariants defined in arxiv 1202 3553 we prove that the representations of mapping class groups and torelli groups resulting from our constructions are potentially more sensitive than those obtained from the standard reshetikhin turaev functors in particular we prove that the action of the bounding pairs generators of the torelli group has always infinite order

a recursive least square algorithm for active control of mixed noise most currently available active control algorithms target noise sources with relatively singular characteristics such as tonal or wideband noise however noise in some practical environments is a mixture of different sounds generated by different sources where the existing algorithms designed for single noise sources may not be optimal this kind of noise is generally referred to as mixed noise and this paper develops a specific active control algorithm for mixed noise based on the recursive least square structure by minimizing the weighted summation of the logarithmic transformation of posterior errors and taking the commutation error into consideration the proposed algorithm not only reduces broadband narrowband and impulse noise successfully but also mixtures of them simulation results demonstrate the superiority of the proposed algorithm over existing algorithms such as the filtered x least mean square filtered x logarithmic least mean square filtered x normalized least mean square and filtered weight filtered x normalized least mean square algorithms in terms of convergence rate and noise reduction

the colored jones polynomials and the simplicial volume of a knot we show that the set of colored jones polynomials and the set of generalized alexander polynomials defined by akutsu deguchi and ohtsuki intersect non trivially moreover it is shown that the intersection is at least includes the set of kashaev s quantum dilogarithm invariants for links therefore kashaev s conjecture can be restated as follows the colored jones polynomials determine the hyperbolic volume for a hyperbolic knot modifying this we propose a stronger conjecture the colored jones polynomials determine the simplicial volume for any knot if our conjecture is true then we can prove that a knot is trivial if and only if all of its vassiliev invariants are trivial in 13 r m kashaev defined a family of complex valued link invariants indexed by integers n 2 using the quantum dilogarithm later he calculated the asymptotic behavior of his invariant and observed that for the three simplest hyperbolic knots it grows as exp vol k n 2 when n goes to the infinity where vol k is the hyperbolic volume of the complement of a knotk 14 this amazing result and his conjecture that the same also holds for any hyperbolic knot have been almost ignored by mathematicians since his definition of the invariant is too complicated though it uses only elementary tools the aim of this paper is to reveal his mysterious definition and to show that his invariant is nothing but a specialization of the colored jones polynomial the colored jones polynomial is defined for colored links each component is decorated with an irreducible representation of the lie algebra sl 2 c the original jones polynomial corresponds to the case that all the colors are identical to the 2 dimensional fundamental representation we show that kashaev s invariant with parameter n coincides with the colored jones polynomial in a certain normalization with every color the n dimensional representation evaluated at the primitive n th root of unity we have to normalize the colored jones polynomial so that the value for the trivial knot is one for otherwise it always vanishes on the other hand there are other colored polynomial invariants the generalized multivariable alexander polynomial defined by y akutsu t deguchi and t ohtsuki 1 they used the same lie algebra sl 2 c but a different hierarchy of representations their invariants are parameterized by c 1 parameters an integer date february 1 2008 1991 mathematics subject classification 57m25 57m50 17b37 81r50

the rank of a graph after vertex addition abstract let r g denote the rank of the adjacency matrix of a graph g when a vertex and its incident edges are deleted from g the rank of the resultant graph cannot exceed r g and can decrease by at most 2 the problem of determining the exact effect of adding a single vertex to a graph is more difficult since the number of edges that can be added with this vertex is variable the rank of the new graph cannot decrease and it can increase by at most 2 we obtain results examining several cases of vertex addition

determining amplitude limits for vibration spectra a method for determining vibration amplitude limits of a mechanical device the method comprises identifying a mechanical device and a frequency range for a spectrum to be analyzed retrieving vibration spectra comprising individual spectrum for the mechanical device and the frequency range calculating frequency for the individual spectrum and identifying the individual spectrum with the smallest number of frequency lines in addition the method comprises calculating noise bandwidths and a largest noise bandwidth removing outlier data calculating conditional kernel density and calculating vibration amplitude limits to detect faults in the mechanical device

the identification of multiple outliers abstract one approach to identifying outliers is to assume that the outliers have a different distribution from the remaining observations in this article we define outliers in terms of their position relative to the model for the good observations the outlier identification problem is then the problem of identifying those observations that lie in a so called outlier region methods based on robust statistics and outward testing are shown to have the highest possible breakdown points in a sense derived from donoho and huber but a more detailed analysis shows that methods based on robust statistics perform better with respect to worst case behavior a concrete outlier identifier based on a suggestion of hampel is given

braided groups and quantum fourier transform abstract we show that acting on every finite dimensional factorizable ribbon hopf algebra h there are invertible operators s t obeying the modular identities s t 3 s 2 where is a constant the class includes the finite dimensional quantum groups uq g associated to complex simple lie algebras we give the example of uq sl 2 at a root of unity in detail as well as an example relating to anyons the operator s plays the role of quantum fourier transform and acts naturally on h viewed by transmutation as a braided group h a braided cocommutative hopf algebra in a braided category it obeys s 2 s 1 where s is the antipode of h the results follow as an application of previous category theoretical constructions