brief paper convergence of the iterative algorithm for a general hammerstein system identification the convergence of the iterative identification algorithm for a general hammerstein system has been an open problem for a long time in this paper it is shown that the convergence can be achieved by incorporating a regularization procedure on the nonlinearity in addition to a normalization step on the parameters

roots in the mapping class groups the purpose of this paper is the study of the roots in the mapping class groups letbe a compact oriented surface possibly with boundary let p be a finite set of punctures in the interior of and let m p denote the mapping class group of p we prove that if is of genus 0 then each f m has at most one m root for all m 1 we prove that if is of genus 1 and has non empty boundary then each f m has at most one m root up to conjugation for all m 1 we prove that however ifis of genus 2 then there exist f g m p such that f 2 g 2 f is not conjugate to g and none of the conjugates of f commutes with g afterwards we focus our study on the roots of the pseudo anosov elements we prove that if 6 then each pseudo anosov element f m p has at most one m root for all m 1 we prove that however if and the genus of is 2 then there exist two pseudo anosov elements f g m explicitely constructed such that f m g m for some m 2 f is not conjugate to g and none of the conjugates of f commutes with g furthermore if the genus ofis 0 mod4 then we can take m 2 finally we show that if is a pure subgroup of m p and f then f has at most one m root in for all m 1 note that there are finite index pure subgroups in m p

the lower central series and pseudo anosov dilatations the theme of this paper is that algebraic complexity implies dynamical complexity for pseudo anosov homeomorphisms of a closed surface s g of genus g penner proved that the logarithm of the minimal dilatation for a pseudo anosov homeomorphism of s g tends to zero at the rate 1 g we consider here the smallest dilatation of any pseudo anosov homeomorphism of s g acting trivially on gamma gamma k the quotient of gamma pi 1 s g by the k rm th term of its lower central series k geq 1 in contrast to penner s asymptotics we prove that this minimal dilatation is bounded above and below independently of g with bounds tending to infinity with k for example in the case of the torelli group cal i s g we prove that l cal i s g the logarithm of the minimal dilatation in cal i s g satisfies 197 l cal i s g 4 127 in contrast we find pseudo anosov mapping classes acting trivially on gamma gamma k whose asymptotic translation lengths on the complex of curves tend to 0 as g to infty

positive configurations of flags in a building and limits of positive representations parreau compactified the hitchin component of a closed surface s of negative euler characteristic in such a way that a boundary point corresponds to the projectivized length spectrum of an action of pi 1 s on an mathbb r euclidean building in this paper we use the positivity properties of hitchin representations introduced by fock and goncharov to explicitly describe the geometry of a preferred collection of apartments in the limiting building

behavior of geodesic length functions on teichmuller space let t be the teichmuller space of marked genus g n punctured riemann surfaces with its bordification t the augmented teichmuller space of marked riemann surfaces with nodes abi77 ber74 pro vided with the wp metric t is a complete cat 0 metric space dw03 wol03 yam04 an invariant of a marked hyperbolic struc ture is the lengthof the geodesic in a free homotopy class a basic feature of teichmuller theory is the interplay of two dimensional hyperbolic geometry weil petersson wp geometry and the behavior of geodesic length functions our goal is to develop the understanding of the intrinsic local wp geometry through a study of the gradient and hessian of geodesic length functions considerations include ex pansions for the wp pairing of gradients expansions for the hessian and covariant derivative comparability models for the wp metric as well as the behavior of wp geodesics including a description of the alexandrov tangent cone at the augmentation approximations and applications for geodesics close to the augmentation are developed an application for fixed points of group actions is described bound ing configurations and functions on the hyperbolic plane is basic to our approach considerations include analyzing the orbit of a dis crete group of isometries and bounding sums of the inverse square exponential distance

determining thurston classes using nielsen types in previous work 3 we showed how the thurston or bers classifications of diffeomorphisms of surfaces could be obtained using the nielsen types of the lifts of the diffeomorphism to the unit disc in this paper we find improved conditions on the nielsen types for the thurston and bers classes we use them to verify that an example studied by nielsen is a pseudo anosov diffeomorphism with stretching factor of degree 4 this example is of interest in its own right but it also serves to illustrate exactly how the nielsen types are used for verifying examples we discuss the general usefulness of this method

dehn twists and pseudo anosov diffeomorphisms we show that it is possible to obtain many pseudo anosov diffeomorphisms from dehn twists in particular we generalize a theorem of long and morton to obtain that iff is a pseudo anosov diffeomorphism of an oriented surface andt is the dehn twist around the simple closed curve then the isotopy class oft n f contains a pseudo anosov diffeomorphism except for at most 7 consecutive values ofn

new proofs of some results of nielsen given a compact oriented surface m with negative euler characteristic and a homeomorphism z m2 m2 what is the best representative cp m2 m2 in the isotopy class of s thurston s answered this question by defining pseudo anosov homeomorphisms a generalization of anosov diffeomorphisms on t2 which may be characterized as follows the homeomorphism rp is pseudo anosov iff there is a pair of transverse measured geodesic laminations i and au which intersect each closed nonperipheral geodesic in h4 which are topologically preserved by cp and which have their respective transverse measures multiplied under the action of cp by l n and d for some l 1 thurston showed that cp m m2 can be pieced together from homeomorphisms of subsurfaces which are either periodic or pseudoanosov more precisely thurston proved theorem 0 1 the preprint s provides an introduction to this theorem describing many of the useful properties of pseudo anosov diffeomorphisms the proof outlined in s is contained in 111

sparse signal approximation via nonseparable regularization the calculation of a sparse approximate solution to a linear system of equations is often performed using either l1 norm regularization and convex optimization or nonconvex regularization and nonconvex optimization combining these principles this paper describes a type of nonconvex regularization that maintains the convexity of the objective function thereby allowing the calculation of a sparse approximate solution via convex optimization the preservation of convexity is viable in the proposed approach because it uses a regularizer that is nonseparable the proposed method is motivated and demonstrated by the calculation of sparse signal approximation using tight frames examples of denoising demonstrate improvement relative to l1 norm regularization

adaptive tracking and recursive identification for hammerstein systems a weighted least squares wls based adaptive tracker is designed for a class of hammerstein systems it is proved that the tracking error is asymptotically minimized incorporating with the diminishing excitation technique the minimality of the tracking error and strong consistency of the estimates for parameters of the system are simultaneously achieved numerical examples are given and the simulation results are consistent with the theoretical analysis

totally geodesic seifert surfaces in hyperbolic knot and link complements ii the first examples of totally geodesic seifert surfaces are constructed for hyperbolic knots and links including both free and totally knotted surfaces then it is proved that two bridge knot complements cannot contain totally geodesic orientable surfaces

brief paper making parametric hammerstein system identification a linear problem in this paper we study the identification of parametric hammerstein systems with fir linear parts by a proper normalization and a clever characterization it is shown that the average squared error cost function for identification can be expressed in terms of the inner product between the true but unknown parameter vector and its estimate further the cost function is concave in the inner product and linear in the inner product square therefore the identification of parametric hammerstein systems with fir linear parts is a globally convergent problem and has one and only one local and global minimum this implies that the identification of such systems is a linear problem in terms of the inner product square and any local search based identification algorithm converges globally

fixed points of pseudo anosov diffeomorphisms of surfaces this article supplements richard miller s paper 6 by establishing a result on the minimum number of fixed points in the homotopy class of a pseudo anosov surface transformation we thus verify one of the many farreaching results that william thurston announced in 1977 in a preprint s dealing with the classification up to homotopy of diffeomorphisms of compact surfaces thurston stated his theorems without proofs but with many hints at techniques fathi laudenbach poenaru and other workers at an intensive seminar at the university of orsay gave detailed proofs of some but not all of thurston s assertions and published their findings in a monograph 7 more recently miller 6 and gilman 2 have verified thurston s claim that his theorem 4 s p 81 follows from the classical investigations of jakob nielsen 4 using miller s exposition of the nielsenthurston theory we establish

nonconvex splitting for regularized low rank sparse decomposition we develop new nonconvex approaches for matrix optimization problems involving sparsity the heart of the methods is a new nonconvex penalty function that is designed for efficient minimization by means of a generalized shrinkage operation we apply this approach to the decomposition of video into low rank and sparse components which is able to separate moving objects from the stationary background better than in the convex case in the case of noisy data we add a nonconvex regularization and apply a splitting approach to decompose the optimization problem into simple parallelizable components the nonconvex regularization ameliorates contrast loss thereby allowing stronger denoising without losing more signal to the residual

strong consistency of recursive identification for hammerstein systems with discontinuous piecewise linear memoryless block this note deals with identification of hammerstein systems with discontinuous piecewise linear memoryless block followed by a linear subsystem recursive algorithms are proposed for estimating coefficients of the linear subsystem and six unknown parameters contained in the nonlinear static block by taking a sequence of iid random variables with uniform distribution to serve as the system input strong consistency is proved for all estimates given in the note the theoretical results are verified by computer simulation

identifying mimo hammerstein systems in the context of subspace model identification methods in this paper we outline the extension of the moesp family of subspace model identification schemes to the hammerstein type of nonlinear system two types of identification problem are considered the first type assumes the polynomial structure of the static nonlinearity to be given and the task is to identify both the linear system dynamics and the unknown proportional constants in the para metrization of the static nonlinearity the second type addresses the identification of both the linear dynamic part and the static nonlinearity where only limited a priori information regarding the structure of the nonlinearity is available the improved robustness properties of the algorithms developed for this second type of hammerstein identification problem over existing correlation based schemes is illustrated by a numerical example

on the nielsen type and the classification for the mapping class group let s be a compact surface of genus g with n boundary components with 2g 2 n 0 and let m s be its mapping class group also known as the teichmiiller modular group using measurd foliations thurston 15 has shown that m s contains three different types of elements bers has shown this decomposition can be obtained using teichmiiller distance 3 subdividing one of the classes further he obtains four classes nielsen has a series of papers 7 8 parts i iii in which he develops an elaborate theory of fixed points of mapping classes if t is any homeomorphism of s and h a lift of t or of a power of 1 to the upper half plane nielsen s theory involves the assignment of a pair of integers to h called the nielsen type of h the purpose of this paper is to show how the thurston classes and the bers classes can be defined in terms of the nielsen types of the lifts of

stochastic approximation in nonparametric identification of hammerstein systems derived from the idea of stochastic approximation recursive algorithms to identify a hammerstein system are presented two of them recover the characteristic of the nonlinear memoryless subsystem while the third one estimates the impulse response of the linear dynamic part the a priori information about both subsystems is nonparametric consistency in quadratic mean is shown and the convergence rate is examined results of numerical simulation are also presented

nonparametric identification of hammerstein systems a discrete time nonlinear hammerstein system is identified and the correlation and frequency domain methods for identification of its linear subsystem are presented the main results concern the estimation of the nonlinear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a nonparametric kernel estimate of the regression function calculated from dependent data it is shown that the algorithm converges to the characteristic of the subsystem regardless of the probability distribution of the input variable pointwise as well as global consistencies are established for lipschitz characteristics the rate of the convergence in probability is o n sup 1 3

completely periodic directions and orbit closures of many pseudo anosov teichmueller discs in q 1 1 1 1 in this paper we investigate the closure of a large class of teichmuller discs in the stratum mathcal q 1 1 1 1 or equivalently in a rm gl 2 mathbb r invariant locus mathcal l of translation surfaces of genus three we describe a systematic way to prove that the rm gl 2 mathbb r orbit closure of a translation surface in mathcal l is the whole locus mathcal l the strategy of the proof is an analysis of completely periodic directions on such a surface and an iterated application of ratner s theorem to unipotent subgroups acting on an adequate splitting this analysis applies for example to all teichmuller discs obtained by the thurston veech s construction with a trace field of degree three which are moreover obviously not veech we produce an infinite series of such examples and show moreover that the favourable splitting situation does not arise everywhere on mathcal l contrary to the situation in genus two we also study completely periodic directions on translation surfaces in mathcal l for instance we prove that completely periodic directions are dense on surfaces obtained by the thurston veech s construction

pathwise convergence of recursive identification algorithms for hammerstein systems this paper gives estimates for 1 coefficients contained in the linear part of the hammerstein system 2 the value of the nonlinear function f u in the hammerstein system at any u 3 ef u sub k and eu sub k f u sub k with u sub k denoting the system input no assumption is made on structure of f spl middot the estimates given by the stochastic approximation algorithms with expanding truncations are recursive and convergent to the true values with probability one two numerical examples are given

variational depth from focus reconstruction this paper deals with the problem of reconstructing a depth map from a sequence of differently focused images also known as depth from focus dff or shape from focus we propose to state the dff problem as a variational problem including a smooth but nonconvex data fidelity term and a convex nonsmooth regularization which makes the method robust to noise and leads to more realistic depth maps in addition we propose to solve the nonconvex minimization problem with a linearized alternating directions method of multipliers allowing to minimize the energy very efficiently a numerical comparison to classical methods on simulated as well as on real data is presented

an efficient nonconvex regularization for wavelet frame and total variation based image restoration in order to improve the quality of the image many works impose explicit priors on the solution to regularize the ill posed inverse problem in this paper we propose a hybrid variational model which takes advantages of the wavelet tight frame model and the total variation model for image restoration the core of the method is a new nonconvex penalty function that is designed for efficient minimization by means of the firm thresholding and soft shrinkage operations we address the proposed optimization problem by converting it to a constrained problem with variable splitting and using the alternating direction method of multipliers numerical examples for image restoration are given to show that the proposed method outperforms some existing methods in terms of the peak signal to noise ratio and structural similarity index

sparse view spectral ct reconstruction using spectral patch based low rank penalty spectral computed tomography ct is a promising technique with the potential for improving lesion detection tissue characterization and material decomposition in this paper we are interested in kvp switching based spectral ct that alternates distinct kvp x ray transmissions during gantry rotation this system can acquire multiple x ray energy transmissions without additional radiation dose however only sparse views are generated for each spectral measurement and the spectra themselves are limited in number to address these limitations we propose a penalized maximum likelihood method using spectral patch based low rank penalty which exploits the self similarity of patches that are collected at the same position in spectral images the main advantage is that the relatively small number of materials within each patch allows us to employ the low rank penalty that is less sensitive to intensity changes while preserving edge directions in our optimization formulation the cost function consists of the poisson log likelihood for x ray transmission and the nonconvex patch based low rank penalty since the original cost function is difficult to minimize directly we propose an optimization method using separable quadratic surrogate and concave convex procedure algorithms for the log likelihood and penalty terms which results in an alternating minimization that provides a computational advantage because each subproblem can be solved independently we performed computer simulations and a real experiment using a kvp switching based spectral ct with sparse view measurements and compared the proposed method with conventional algorithms we confirmed that the proposed method improves spectral images both qualitatively and quantitatively furthermore our gpu implementation significantly reduces the computational cost

stability of the homology of the mapping class groups of orientable surfaces the mapping class group of f fgs r is f rgs wo a where a is the topological group of orientation preserving diffeomorphisms of f which are the identity on df and fix the s punctures when r 0 and 2g s 3 an important feature of f is that it acts properly discontinuously on the teichmiller space us the quotient is the moduli space f of isometry classes of complete hyperbolic metrics of finite area on f since us is homeomorphic to euclidean space and f is virtually torsion free we have

recursive identification of multi input multi output errors in variables hammerstein systems the note considers the identification of multi input multi output errors in variables hammerstein systems in which both the input and output can be observed but with additive noises being arma processes with unknown coefficients with the help of stochastic approximation combined with the deconvolution kernel function the recursive algorithms are proposed for estimating coefficients of the linear subsystem and for the values of the nonlinear function under some reasonable conditions all the estimates are proved to converge to the true values with probability one these results include identification of the errors in variables linear systems as a special case a simulation example is given justifying the theoretical analysis

a new frequency estimation method for equally and unequally spaced data spectral estimation is an important classical problem that has received considerable attention in the signal processing literature in this contribution we propose a novel method for estimating the parameters of sums of complex exponentials embedded in additive noise from regularly or irregularly spaced samples the method relies on kronecker s theorem for hankel operators which enables us to formulate the nonlinear least squares problem associated with the spectral estimation problem in terms of a rank constraint on an appropriate hankel matrix this matrix is generated by sequences approximating the underlying sum of complex exponentials unequally spaced sampling is accounted for through a proper choice of interpolation matrices the resulting optimization problem is then cast in a form that is suitable for using the alternating direction method of multipliers admm the method can easily include either a nuclear norm or a finite rank constraint for limiting the number of complex exponentials the usage of a finite rank constraint makes in contrast to the nuclear norm constraint the method heuristic in the sense that the problem is non convex and convergence to a global minimum can not be guaranteed however we provide a large set of numerical experiments that indicate that usage of the finite rank constraint nevertheless makes the method converge to minima close to the global minimum for reasonably high signal to noise ratios hence essentially yielding maximum likelihood parameter estimates moreover the method does not seem to be particularly sensitive to initialization and performs substantially better than standard subspace based methods

convergence analysis for recursive hammerstein identification this paper derives a recursive prediction error identification method based on the hammerstein model structure the convergence properties of the algorithm are analysed by application of ljung s associated differential equation method it is proved that the algorithm can only converge to stable stationary points of the associated ordinary differential equation general conditions for local convergence to the true parameter vector are given and the cases with piecewise linear and polynomial nonlinearities are treated in detail the derived identification method is illustrated in a numerical study that treats identification of a subsystem of a cement mill

sparsity aware data selective adaptive filters we propose two adaptive filtering algorithms that combine sparsity promoting schemes with data selection mechanisms sparsity is promoted via some well known nonconvex approximations to the l 0 norm in order to increase convergence speed of the algorithms when dealing with sparse compressible signals these approximations circumvent some difficulties of working with the l 0 norm thus allowing the development of online data selective algorithms data selection is implemented based on set membership filtering which yields robustness against noise and reduced computational burden the proposed algorithms are analyzed in order to set properly their parameters to guarantee stability in addition we characterize their updating processes from a geometrical viewpoint simulation results show that the proposed algorithms outperform the state of the art algorithms designed to exploit sparsity

a weakly mixing tiling dynamical system with a smooth model we describe a weakly mixing one dimensional tiling dynamical system in which the tiling space is modeled by a surface m of genus 2 the tiling system satisfies an inflation and the inflation map is modeled by a pseudo anosov diffeomorphism d on m the expansion coefficient for d is a non pisot number in particular the leaves of the expanding foliation for d are tiled by their visits to the elements of a markov partition for d the tiling dynamical system is an almost 1 1 extension of the unit speed flow along these leaves

deviation of ergodic averages for substitution dynamical systems with eigenvalues of modulus 1 deviation of ergodic sums is studied for substitution dynamical systems with a matrix that admits eigenvalues of mod ulus 1 the functions we consider are the corresponding eigen functions in theorem 1 1 we prove that the limit inferior of the ergodic sums n x 0 x n 1 n n is bounded for every point x in the phase space in theorem 1 2 we prove existence of limit distributions along certain exponential subsequences of times for substitutions of constant length under additional assumptions we prove that ergodic integrals satisfy the central limit theorem theorem 1 3 theorem 1 9

robust pca via ell _ 0 ell _ 1 regularization we study the problem of low rank and sparse decomposition from possibly noisy observations known as robust pca where the sparse component can be seen as outliers we first propose a modified objective function where the nuclear norm captures the low rank term ell 0 norm addresses the sparse outlier term and an ell 1 norm to deal with the additive noise term the associated algorithm termed sparsity regularized principal component pursuit srpcp is shown to converge under certain model and algorithm parameter settings it is shown that srpcp can recover the low rank component and sparse component exactly in the noiseless case in the noisy case we first prove that the widely used principal component pursuit pcp method which was designed for the noiseless case is actually stable to dense noise then we show that srpcp has smaller estimation error bound and can identify outlier entries without any false alarm another important byproduct of our analysis is the result that pcp with missing entries is also stable to dense noise we further propose another objective function which replaces the above nuclear norm by the log determinant the proposed algorithm termed iterative reweighted sparsity regularized principal component pursuit is also shown to converge in each iteration it solves a weighted nuclear norm regularized robust matrix completion problem we propose an alternating direction method of multipliers algorithm to solve this nonconvex subproblem which also converges empirical studies demonstrate the efficacy of the proposed ell 0 ell 1 regularization framework to deal with the outliers as well as its advantage over the existing state of the art methods

degenerations of hyperbolic structures ii measured laminations in 3 manifolds that paper concerned the general theory of groups acting on r trees and the relationship of these actions to representations into sl2 c the purpose of the present paper is to develop the foundations of a general theory of measured laminations in 3 manifolds in the third paper 8 the results of this paper will be applied to study actions of 3 manifold groups on trees the starting point of 8 is the idea that dual to an action of qg m on an r tree is a codimension 1 measured lamination in m combining the latter results with 7 gives information about how hyperbolic structures on 3 manifolds can degenerate we view measured laminations in 3 manifolds as generalizations of both geodesic laminations on surfaces and surfaces in 3 manifolds most of this paper consists in extending thurston s theory of geodesic laminations and the hakenstallings waldhausen theory of incompressible surfaces to our context the paper is organized along the following lines in chapter i we develop the basic notions of codimension 1 measured laminations we prove one new and quite useful result theorem i 3 2 concerning a decomposition of these objects we also give a definition of the euler characteristic of a measured lamination and show that it has all the usual properties in chapter ii we introduce the branched surfaces of williams 16 and hatcher thurston we establish analogues for measured laminations carried by branched surfaces of some results of thurston s for train tracks and geodesic laminations by imitating an argument of plante s 10 we show that the leaves of a measured lamination have polynomial growth this is used to show that if a branched surface n carries some lamination all of whose leaves have virtually abelian fundamental groups and carries no disks or spheres then all laminations carried by n have zero euler characteristic we express the latter property by saying that n is flat in chapter iii generalizing haken s notion of normal surfaces we develop the theory of normal measured laminations and of normal branched surfaces in a

computing boundary slopes of 2 bridge links we describe an algorithm for computing boundary slopes of 2bridge links as an example we work out the slopes of the links obtained by 1 k surgery on one component of the borromean rings a table of all boundary slopes of all 2 bridge links with 10 or less crossings is also included

ideal triangle groups dented tori and numerical analysis we prove the goldman parker conjecture a complex hyperbolic ideal triangle group is discretely embedded in pu 2 1 if and only if the product of its three standard generators is not elliptic we also prove that such a group is indiscrete if the product of its three standard generators is elliptic a novel feature of this paper is that it uses a rigorous computer assisted proof to deal with difficult geometric estimates

identification of wiener hammerstein and narx systems as markov chains with improved estimates for their nonlinearities abstract the wiener hammerstein and nonlinear arx systems are identified not only for their linear subsystems if they exist but also for the nonlinearities with their first derivatives it is assumed that the input signals and noises are mutually independent and both are sequences of independent and identically distributed iid random variables the estimates based on the stochastic approximation algorithms with expanding truncations saawet are proved to be strongly consistent with the help of the markov properties possessed by these systems the estimates of the first derivatives improve the accuracy of interpolating the nonlinearity curves as validated by simulation examples

infinitely many hyperbolic 3 manifolds which contain no reebless foliation calegari ca has shown that if m is also atoroidal then or1 m is gromov negatively curved furthermore thurston has proposed an approach to demonstrating geometrization for such m many 3 manifolds contain reebless foliations and it has often been conjectured that all closed hyperbolic 3 manifolds do it is our impression that for many years hatcher provided the sole voice of dissent in this paper we give the first examples of closed hyperbolic 3 manifolds which contain no reebless foliation

recursive identification of hammerstein systems convergence rate and asymptotic normality in this work recursive identification algorithms are developed for hammerstein systems under the conditions considerably weaker than those in the existing literature for example orders of linear subsystems may be unknown and no specific conditions are imposed on their moving average part the recursive algorithms for estimating both linear and nonlinear parts are based on stochastic approximation and kernel functions almost sure convergence and strong convergence rates are derived for all estimates in addition the asymptotic normality of the estimates for the nonlinear part is also established the nonlinearity considered in the paper is more general than those discussed in the previous papers a numerical example verifies the theoretical analysis with simulation results

parametric identification of hammerstein systems with consistency results using stochastic inputs the extended least squares algorithm is applied to identify the hammerstein system where the nonlinear static function f is expressed as a linear combination of basic functions with unknown coefficients strong consistency of the estimates is established and their convergent rates are obtained as well

on the series expansion approach to the identification of hammerstein systems a polynomial identification algorithm for recovering a nonlinearity in the hammerstein system is proposed the estimate employs the legendre orthogonal system with adaptively selected number of terms the global consistency along with rates of convergence are established no assumptions concerning continuity of the nonlinearity or its functional form are made a data driven method using the cross validation technique for selecting the number of terms in the estimate is presented

ergodicity of billiard flows and quadratic differentials on considere un systeme billard de 2 objets de masses m 1 et m 2 on montre que pour un ensemble dense de paires m 1 m 2 ce systeme est ergodique

hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics we prove that the stable holonomies of a proper codimension 1 attractor lambda for a c r diffeomorphism f of a surface are not c1 theta for theta greater than the hausdorff dimension of the stable leaves of f intersected with lambda to prove this result we show that there are no diffeomorphisms of surfaces with a proper codimension 1 attractor that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor

weighted nuclear norm minimization and its applications to low level vision as a convex relaxation of the rank minimization model the nuclear norm minimization nnm problem has been attracting significant research interest in recent years the standard nnm regularizes each singular value equally composing an easily calculated convex norm however this restricts its capability and flexibility in dealing with many practical problems where the singular values have clear physical meanings and should be treated differently in this paper we study the weighted nuclear norm minimization wnnm problem which adaptively assigns weights on different singular values as the key step of solving general wnnm models the theoretical properties of the weighted nuclear norm proximal wnnp operator are investigated albeit nonconvex we prove that wnnp is equivalent to a standard quadratic programming problem with linear constrains which facilitates solving the original problem with off the shelf convex optimization solvers in particular when the weights are sorted in a non descending order its optimal solution can be easily obtained in closed form with wnnp the solving strategies for multiple extensions of wnnm including robust pca and matrix completion can be readily constructed under the alternating direction method of multipliers paradigm furthermore inspired by the reweighted sparse coding scheme we present an automatic weight setting method which greatly facilitates the practical implementation of wnnm the proposed wnnm methods achieve state of the art performance in typical low level vision tasks including image denoising background subtraction and image inpainting

dual garside structure and reducibility of braids abstract benardete gutierrez and nitecki showed an important result which relates the geometrical properties of a braid as a homeomorphism of the punctured disk to its algebraic garside theoretical properties namely they showed that if a braid sends a standard curve to another standard curve then the image of this curve under the action of each factor of the left normal form of the braid with the classical garside structure is also standard we provide a new simple geometric proof of the result by benardete gutierrez nitecki which can be easily adapted to the case of the dual garside structure of braid groups with the appropriate definition of standard curves in the dual setting this yields a new algorithm for determining the nielsen thurston type of braids

quantum representations and monodromies of fibered links abstract andersen masbaum and ueno conjectured that certain quantum representations of surface mapping class groups should send pseudo anosov mapping classes to elements of infinite order for large enough level r in this paper we relate the amu conjecture to a question about the growth of the turaev viro invariants t v r of hyperbolic 3 manifolds we show that if the r growth of t v r m for a hyperbolic 3 manifold m that fibers over the circle is exponential then the monodromy of the fibration of m satisfies the amu conjecture building on earlier work 11 we give broad constructions of oriented hyperbolic fibered links of arbitrarily high genus whose s o 3 turaev viro invariants have exponential r growth as a result for any g n 2 we obtain infinite families of non conjugate pseudo anosov mapping classes acting on surfaces of genus g and n boundary components that satisfy the amu conjecture we also discuss integrality properties of the traces of quantum representations and we answer a question of chen and yang about turaev viro invariants of torus links

ergodic properties of infinite extensions of area preserving flows we consider volume preserving flows phi f t t in mathbb r on s times mathbb r where s is a compact connected surface of genus g 2 and phi f t t in mathbb r has the form phi f t x y phi t x y int 0 t f phi s x ds where phi t t in mathbb r is a locally hamiltonian flow of hyperbolic periodic type on s and f is a smooth real valued function on s we investigate ergodic properties of these infinite measure preserving flows and prove that if f belongs to a space of finite codimension in fancyscript c 2 epsilon s then the following dynamical dichotomy holds if there is a fixed point of phi t t in mathbb r on which f does not vanish then phi f t t in mathbb r is ergodic otherwise if f vanishes on all fixed points it is reducible i e isomorphic to the trivial extension phi 0 t t in mathbb r the proof of this result exploits the reduction of phi f t t in mathbb r to a skew product automorphism over an interval exchange transformation of periodic type if there is a fixed point of phi t t in mathbb r on which f does not vanish the reduction yields cocycles with symmetric logarithmic singularities for which we prove ergodicity

enhanced sparsity by non separable regularization this paper develops a convex approach for sparse one dimensional deconvolution that improves upon l1 norm regularization the standard convex approach we propose a sparsity inducing non separable non convex bivariate penalty function for this purpose it is designed to enable the convex formulation of ill conditioned linear inverse problems with quadratic data fidelity terms the new penalty overcomes limitations of separable regularization we show how the penalty parameters should be set to ensure that the objective function is convex and provide an explicit condition to verify the optimality of a prospective solution we present an algorithm an instance of forward backward splitting for sparse deconvolution using the new penalty

the space of incompressible surfaces in a 2 bridge link complement projective lamination spaces for 2 bridge link complements are computed explicitly in this paper we construct a polyhedron p s3 lp q whose rational points correspond bijectively in a natural way with the projective isotopy classes of incompressible surfaces in the exterior of a 2 bridge link lp q c s3 here projective means that we factor out by scalar multiplication taking any number of parallel copies of a surface surfaces are not assumed to be connected we expect that p s3 lp q will turn out to be the projective lamination space of s3 lp q33 as defined and studied for general compact irreducible 3 manifolds in 5 and 12 an unexpected complication not present in thurston s theory of projective lamination spaces for surfaces is the fact that p s3 lp q is frequently noncompact for example for the whitehead link l3 8 see figure 5 4 upper left hand corner however as in the general theory p s3 lp q has a natural compactification p7 53 lp q which is a finite polyhedron to construct p s3 lp q 3 we first find a fairly natural finite collection of branched surfaces bi c s3 lp q which carry all the incompressible surfaces in s3lp q to each bi is associated a convex cell ci whose rational points parametrize the projective classes of surfaces carried by bi diserent rational points of ci can determine isotopic surfaces however due to the possibility of pushing parts of surfaces across product regions in the complement of bi the analogue of digon regions in the complement of a train track on a surface this leads to a linear projection pi ci ci f ci onto another convex polyhedral cell ci such that over the interior of ci projective isotopy classes of surfaces coincide with fibers of pi however these isotopy relations may not persist over the boundary of ci namely passing to a face of ci corresponds to passing to a branched subsurface of bi and a nonproduct complementary region of this branched subsurface may be decomposed by bi into product complementary regions of bi in this case rational points of this face of ci correspond not to projective isotopy classes of incompressible surfaces but to incompressible surfaces with these limiting phantom isotopy relations the space p7 53 lp q is foed from the cells ci by identifying their faces in the most natural way distinguishing different phantom isotopies between the same sets of surfaces pz s3 lp q consists of the open cells of ps s3 lp q for which the phantom isotopies are actual isotopies received by the editors april 12 1986 1980 mathematics subject classification 1985 revtaion primary 57m25

cantor exchange systems and renormalization we prove a one to one correspondence between i c1 conjugacy classes of c1 h cantor exchange systems that are c1 h fixed points of renormalization and ii c1 conjugacy classes of c1 h diffeomorphisms f with a codimension 1 hyperbolic attractor lambda that admit an invariant measure absolutely continuous with respect to the hausdorff measure on lambda however we prove that there is no c1 alpha cantor exchange system with bounded geometry that is a c1 alpha fixed point of renormalization with regularity alpha greater than the hausdorff dimension of its invariant cantor set

motion adaptive patch based low rank approach for compressed sensing cardiac cine mri one of the technical challenges in cine magnetic resonance imaging mri is to reduce the acquisition time to enable the high spatio temporal resolution imaging of a cardiac volume within a short scan time recently compressed sensing approaches have been investigated extensively for highly accelerated cine mri by exploiting transform domain sparsity using linear transforms such as wavelets and fourier however in cardiac cine imaging the cardiac volume changes significantly between frames and there often exist abrupt pixel value changes along time in order to effectively sparsify such temporal variations it is necessary to exploit temporal redundancy along motion trajectories this paper introduces a novel patch based reconstruction method to exploit geometric similarities in the spatio temporal domain in particular we use a low rank constraint for similar patches along motion based on the observation that rank structures are relatively less sensitive to global intensity changes but make it easier to capture moving edges a nash equilibrium formulation with relaxation is employed to guarantee convergence experimental results show that the proposed algorithm clearly reconstructs important anatomical structures in cardiac cine image and provides improved image quality compared to existing state of the art methods such as k t focuss k t slr and master

multi stage convex relaxation method for low rank and sparse matrix separation problem the low rank and sparse matrix separation problem recovering a low rank matrix and a sparse matrix from a small number of linear observations has arisen in a broad set of applications the desire for efficiency motivated the research on it however most of them focus on the nuclear norm plus 1 norm minimization problem which is a single convex relaxation of the low rank and sparse matrix separation problem this paper is devoted to investigate a multi stage convex relaxation method to recover the low rank and sparse components via solving a sequence of convex relaxations while the first stage of the method includes the nuclear norm plus 1 norm minimization problem numerical studies indicate that the multi stage convex relaxation outperforms the one stage convex relaxation especially when observations are incomplete and noisy we have also verified the efficiency of the proposed method by applying it to the static background extraction from surveillance video

brief paper parameter identification of hammerstein systems containing backlash operators with arbitrary shape parametric borders a two stage parameter identification method is developed for hammerstein systems containing backlash nonlinearities bordered by parametric arbitrary shape lines in the first stage a persistently exciting input is designed so that the linear subsystem can be made decoupled from the nonlinear element therefore linear subsystem identification is coped with using a least squares estimator enjoying consistency due to input persistent excitation then the backlash parameters are estimated using appropriate periodic exciting signals and consistent parameter estimators

a recipe for short word pseudo anosovs given any generating set of any subgroup g of the mapping class group of a surface we find an element f with word length bounded by a constant k depending only on the surface and with the property that the minimal subsurface supporting a power of f is as large as possible for elements of g in particular if g contains a pseudo anosov map we find one of word length at most k we also find new examples of convex cocompact free subgroups of the mapping class group

recursive identification for hammerstein system with arx subsystem identification is considered for the hammerstein system consisting of a static nonlinear block f middot followed by an arx subsystem when the system output is observed with noise no assumption is made on the structure of f middot recursive estimates are given for coefficients of the arx subsystem and for the value of f u at any u all estimates are proved to converge to the true values with probability one numerical examples are provided justifying the theoretical analysis

identification scheme for hammerstein output error models with bounded noise this technical note presents a method for the identification of hammerstein output error hoe models corrupted by bounded noise the method is based on an iterative scheme using two optimal bounding ellipsoid obe type algorithms the proposed approach allows the joint estimation of the linear part and of the nonlinear part with a low computational burden a numerical example is given so as to show the efficiency of the method