intersection forms of non spin four manifolds 1 introductionit remains a central question in four manifold topology which quadratic formoccurs as the intersection form of an orientable four manifold in the topologicalcategory there is a beautiful answer the celebrated result of freedman assertsthat all the quadratic forms can be realized however in the smooth category wehave a rather different picture by the surprising result of donaldson d fs a among the de nite quadratic forms only the diagonalizable ones can berealized thereisalsoalongstanding11

an identification algorithm for polynomial narx models based on simulation error minimization classical prediction error approaches for the identification of non linear polynomial narx narmax models often yield unsatisfactory results for long range prediction or simulation purposes mainly due to incorrect or redundant model structure selection the paper discusses some limitations of the standard approach and suggests two modifications namely a new index based on the simulation error is employed as the regressor selection criterion and a pruning mechanism is introduced in the model selection algorithm the resulting algorithm is shown to be effective in the identification of compact and robust models generally yielding model structures closer to the correct ones computational issues are also discussed finally the identification algorithm is tested on a long range prediction benchmark application

factorization homology i higher categories abstract we construct a pairing which we call factorization homology between framed manifolds and higher categories the essential geometric notion is that of a vari framing of a stratified manifold which is a framing on each stratum together with a coherent system of compatibilities of framings along links between strata our main result constructs labeling systems on disk stratified vari framed n manifolds from n categories these n categories in contrast with the literature to date are not required to have adjoints this allows the following conceptual definition the factorization homology m c of a framed n manifold m with coefficients in an n category c is the classifying space of c labeled disk stratifications over m the core calculation underlying our main result is the following for any disk stratified manifold the space of conically smooth diffeomorphisms which preserve a vari framing is discrete

instanton approximation periodic asd connections and mean dimension abstract we study a moduli space of asd connections over s 3 r we consider not only finite energy asd connections but also infinite energy ones so the moduli space is infinite dimensional in general we study the local mean dimension of this infinite dimensional moduli space we show the upper bound on the mean dimension by using a runge approximation for asd connections and we prove its lower bound by constructing an infinite dimensional deformation theory of periodic asd connections

a vanishing result for a casson type instanton invariant casson type invariants emerging from donaldson theory over certain negative definite 4 manifolds were recently suggested by andrei teleman these are defined by a count of a zero dimensional moduli space of flat instantons motivated by the cobordism program of proving witten s conjecture we use a moduli space of pu 2 seiberg witten monopoles to exhibit an oriented one dimensional cobordism of the instanton moduli space to the empty space the casson type invariant must therefore vanish

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

dirac operators coupled to instantons on positive definite four manifolds we study the moduli space of instantons on a simply connected positive definite closed four manifold by analyzing the classifying map of the index bundle of a family of dirac operators parameterized by the moduli space as an application we compute the cohomology rings for the charge 1 and 2 moduli spaces in the rank stable limit

the geography problem for irreducible spin four manifolds we study the geography problem for smooth irreducible simplyconnected spin four manifolds for a large class of hoinotopy types we exhibit both symplectic and non symplectic representatives we also compute the seiberg witten invariants of all the four manifolds we construct

a conformally invariant gap theorem in yang mills theory we show a sharp conformally invariant gap theorem for yang mills connections in dimension 4 by exploiting an associated yamabe type problem

text pin 2 monopole equations and intersection forms with local coefficients of four manifolds we introduce a variant of the seiberg witten equations text pin 2 monopole equations and give its applications to intersection forms with local coefficients of four manifolds the first application is an analogue of froyshov s results on four manifolds with definite intersection forms with local coefficients the second is a local coefficient version of furuta s 10 8 inequality as a corollary we construct nonsmoothable spin four manifolds satisfying rohlin s theorem and the 10 8 inequality

on slicing invariants of knots the slicing number of a knot u s k is the minimum number of crossing changes required to convert k to a slice knot this invariant is bounded above by the unknotting number and below by the slice genus g s k we show that for many knots previous bounds on the unknotting number obtained by ozsvath and szabo and by the author in fact give bounds on the slicing number livingston defined another invariant u s k which takes into account signs of crossings changed to get a slice knot and which is bounded above by the slicing number and below by the slice genus we exhibit an infinite family of knots k n with slice genus n and livingston invariant greater than n our bounds are based on restrictions using donaldson s diagonalisation theorem or heegaard floer homology on the intersection forms of four manifolds bounded by the double branched cover of a knot

a fast nonlinear model identification method the identification of nonlinear dynamic systems using linear in the parameters models is studied a fast recursive algorithm fra is proposed to select both the model structure and to estimate the model parameters unlike orthogonal least squares ols method fra solves the least squares problem recursively over the model order without requiring matrix decomposition the computational complexity of both algorithms is analyzed along with their numerical stability the new method is shown to require much less computational effort and is also numerically more stable than ols

nonorientable 4 manifolds with fundamental group of order 2 in this paper we classify nonorientable topological closed 4 manifolds with fundamental group z 2 up to homeomorphism our results give a complete list of such manifolds and show how they can be distinguished by explicit invariants including characteristic numbers and the ti invariant associated to a normal pinc structure by the spectral asymmetry of a certain dirac operator in contrast to the oriented case there exist homotopy equivalent nonorientable topological 4 manifolds which are stably homeomorphic after connected sum with s2 x s2 but not homeomorphic

the conjecture and equivariant e c invariants let x be a smooth closed oriented non spin 4 manifold with even intersection form ke8 nh n 1 the conjecture states that n is greater than or equal to k in this paper we give a proof of the conjecture the strategy of this paper is to use the finite dimensional approximation of the map induced from the seiberg witten equations and equivariant ec invariants as in the paper of m furuta and y kametani

eigenvalue asymptotics of the neumann laplacian of regions and manifolds with cusps abstract we study the eigenvalue asymptotics of a neumann laplacian n in unbounded regions of r2 with cusps at infinity a typical example is x y r 2 x 1 y x 2 and prove that n e n n e h v e 2 vol where hv is the canonical one dimensional schrodinger operator associated to the problem we establish a similar formula for manifolds with cusps and derive the eigenvalue asymptotics of a dirichlet laplacian d for a class of cusp type regions of infinite volume

4 manifold topology i subexponential groups the technical lemma underlying the 5 dimensional topologicals cobordism conjecture and the 4 dimensional topological surgery conjecture is a purely smooth category statement about locating 1 null immersions of disks these conjectures are theorems precisely for those fundamental groups good groups where the 1 null disk lemma ndl holds we expand the class of known good groups to all groups of subexponential growth and those that can be formed from these by a finite number of application of two operations 1 extension and 2 direct limit the finitely generated groups in this class are amenable and no amenable group is known to lie outside this class

blinking eigenvalues of the steklov problem generate the continuous spectrum in a cuspidal domain abstract we study the steklov spectral problem for the laplace operator in a bounded domain r d d 2 with a cusp such that the continuous spectrum of the problem is non empty and also in the family of bounded domains e e 0 obtained from by blunting the cusp at the distance of e from the cusp tip while the spectrum in the blunted domain e consists for a fixed e of an unbounded positive sequence j e j 1 of eigenvalues we single out different types of behavior of some eigenvalues as e 0 in particular stable blinking and gliding families of eigenvalues are found we also describe a mechanism which transforms the family of the eigenvalue sequences into the continuous spectrum of the problem in when e 0

dynamical effects of overparametrization in nonlinear models abstract this paper is concemed with dynamical reconstruction for nonlinear systems the effects of the driving function and of the complexity of a given representation on the bifurcation patter are investigated it is shown that the use of different driving functions to excite the system may yield models with different bifurcation patterns the complexity of the reconstructions considered is quantified by the embedding dimension and the number of estimated parameters in this respect it appears that models which reproduce the original bifurcation behaviour are of limited complexity and that excessively complex models tend to induce ghost bifurcations and spurious dynamical regimes moreover some results suggest that the effects of overparametrization on the global dynamical behaviour of a nonlinear model may be more deleterious than the presence of moderate noise levels in order to precisely quantify the complexity of the reconstructions global polynomials are used although the results are believed to apply to a much wider class of representations including neural networks

the geometry of the yang mills moduli space for definite manifolds on etudie la geometrie riemannienne de l espace des modules des connexions auto duales su 2 k 1 sur une classe tres generale de 4 varietes des 4 varietes compactes orientees simplement connexe m a forme d intersection definie positive

theory of ordered spaces this is the first of a planned series of investigations on the theory of ordered spaces based upon four axioms two of these the order i 1 1 and the local structure ii 5 1 axioms provide the structure of the theory and the other two the identification i 1 11 and cone i 2 7 axioms eliminate pathologies or excessive generality in the present paper the axioms are supplemented by the nontriviality conditions i 1 9 and a regularity property ii 4 2

regularized orthogonal least squares algorithm for constructing radial basis function networks the paper presents a regularized orthogonal least squares learning algorithm for radial basis function networks the proposed algorithm combines the advantages of both the orthogonal forward regression and regularization methods to provide an efficient and powerful procedure for constructing parsimonious network models that generalize well examples of nonlinear modelling and prediction are used to demonstrate better generalization performance of this regularized orthogonal least squares algorithm over the unregularized one

input output parametric models for non linear systems part ii stochastic non linear systems recursive input output models for non linear multivariate discrete time systems are derived and sufficient conditions for their existence are defined the paper is divided into two parts the first part introduces and defines concepts such as nerode realization multistructural forms and results from differential geometry which are then used to derive a recursive input output model for multivariable deterministic non linear systems the second part introduces several examples compares the derived model with other representations and extends the results to create prediction error or innovation input output models for non linear stochastic systems these latter models are the generalization of the multivariable arm ax models for linear systems and are referred to as narmax or non linear autoregressive moving average models with exogenous inputs

group actions corks and exotic smoothings of mathbb r 4 r 4 we provide the first information on diffeotopy groups of exotic smoothings of mathbb r 4 for each of uncountably many smoothings there are uncountably many isotopy classes of self diffeomorphisms we realize these by various explicit group actions there are also actions at infinity by nonfinitely generated groups for which no nontrivial element extends over the whole manifold in contrast every diffeomorphism of the end of the universal mathbb r 4 extends our techniques apply to many other open 4 manifolds and are related to cork theory we show that under broad hypotheses cork twisting is equivalent up to blowups to twisting on an exotic mathbb r 4 and give applications

gauge theory on asymptotically periodic 4 manifolds il existe une famille non denombrable de classes de diffeomorphismes des 4 varietes orientees homeomorphes a r 4

orientability for gauge theories on calabi yau manifolds abstract we study orientability issues of moduli spaces from gauge theories on calabi yau manifolds our results generalize and strengthen those for donaldson thomas theory on calabi yau manifolds of dimensions 3 and 4 we also prove a corresponding result in the relative situation which is relevant to the gluing formula in dt theory

smooth group actions on definite 4 manifolds and moduli spaces in this paper we give an application of equivariant moduli spaces to the study of smooth group actions on certain 4 manifolds a rich source of examples for such actions is the collection of algebraic surfaces compact and nonsingular together with their groups of algebraic automorphisms from this collection further examples of smooth but generally nonalgebraic actions can be constructed by an equivariant connected sum along an orbit of isolated points given a smooth oriented 4 manifold x which is diffeomorphic to a connected sum of algebraic surfaces we can ask i which finite groups can act smoothly on x preserving the orientation and ii how closely does a smooth action on x resemble some equivariant connected sum of algebraic actions on the algebraic surface factors of x for the purposes of this paper we will restrict our attention to the simplest case namely x p2 c p2 c a connected sum of n copies of the complex projective plane arranged so thatx is simply connected furthermore assumption all actions will be assumed to induce the identity on h x z

instanton homology of seifert fibred homology three spheres for an oriented integral homology 3 sphere 2 a casson has introduced an integer invariant a 2 that is defined by using the space 2 of conjugacy classes of irreducible representations of 2 into su 2 see 1 this invariant a 2 can be computed from a surgery or heegard description of 2 and satisfies a 2 ju 2 mod 2 where i 2 is the kervaire milnor rochlin invariant of 2 this powerful new invariant was used to settle an outstanding problem in 3 manifold topology namely showing that if 2 is a homotopy 3 sphere then ju 2 o c taubes 17 utilizing gauge theoretic considerations has reinterpreted casson s invariant in terms of flat connections refining this approach a floer 13 has recently defined another invariant of 2 its instanton homology which takes the form of an abelian group 2 with a natural z8 grading that is an enhancement of a 2 in that

on the intersection forms of spin four manifolds with boundary we prove furuta type bounds for the intersection forms of spin cobordisms between homology 3 spheres the bounds are in terms of a new numerical invariant of homology spheres obtained from mathrm pin 2 equivariant seiberg witten floer k theory in the process we introduce the notion of a floer k g split homology sphere this concept may be useful in an approach to the 11 8 conjecture

configurations of surfaces in 4 manifolds we consider collections of surfaces f smoothly embedded except for a finite number of isolated singularities self intersections and mutual intersections in a 4 manifold m a small 3 sphere about each exceptional point will intersect these surfaces in a link if fi e h2 m are linearly dependent modulo a prime power we find lower bounds for i genus fi in terms of the f and invariants of the links that describe the exceptional points 0 introduction the following special case of our main theorem is easy to state theorem 0 1 let m be a closed smooth 4 manifold and fi a collection of n smoothly embedded surfaces in general position let xi fi e h2 m suppose u fi is connected and e aixi p r where p is a prime 0 2y xiy x x sign m 1 b 0 and a b 1 let be the total number of intersection points of f1 and f2 then we have

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

the geometry of the moduli space of cp2 instantons the moduli space of self dual connections instantons of instanton numberk 1 overcp2 is topologically a cone oncp2 the complement of the vertex of this cone carries a natural riemannian metric the l2 metric we find an explicit formula for this metric and deduce certain consequences in particular i the boundary is a totally geodesic submanifold of the completion ii is positively curved at and iii is negatively curved in certain directions near the vertex of the cone

on the signature of four manifolds with universal covering spin in this note we study closed oriented 4 manifolds whose universal covering is spin and ask whether there are restrictions on the divisibility of the signature since any natural number appears as the signature of a connected sum of r 2 s without the assumption on the universal covering there cannot exist any restrictions certainly the most famous such restriction was proved by rohlin in 10 where he showed that the signature a of a smooth 4 dimensional spin manifold is divisible by 16 compare part 2 of our main theorem for a new proof the kummer surface k shows that this is the best possible general result dividing by a certain free holomorphic involution on k one obtains the enriques surface compare 1 which by construction has signature 8 and fundamental group 7 2 furthermore hitchin showed in 5 that there exists an antiholomorphic free involution on the enriques surface we will refer to the quotient as the hitchin manifold which then has signature 4 and fundamental group 7 2 x 7 2 rohlin s theorem admits a nice generalization to nonspin 4 manifolds compare 4 theorem 6 3

negatively curved metrics on kodaira surfaces it has been known that kodaira surfaces of general type have negative holomorphic tangent bundles cf 1 this definition of negativity is algebraic geometric in nature i e negative in the sense of grauert 5 griffiths 7 discussed the relations between various notions of negativity in algebraic geometry and those in differential geometry and raised the question of whether a grauert negative holomorphic vector bundle also admits a hermitian metric of negative holomorphic bisectional curvature if it does we would say that this metric is negatively curved and the vector bundle is negative in griffiths sense the aim of this work is to show that the tangent bundles of certain type of surfaces considered in 11 by schneider including kodaira surfaces of general type are negative in griffiths sense we also remark here that cheung 2 constructed on kodaira surfaces of general type a k ihler metric of negative holomorphic sectional curvature

locally flat 2 knots in with the same fundamental group we consider a locally flat 2 sphere in s x s2 representing a primitive homology class 4 which is referred to as a 2 knot in s x s2 representing 4 then for any given primitive class there exists a 2 knot in s2 x s2 representing 4 with simply connected complement in this paper we consider the classification of 2 knots in s2 x s2 whose complements have a fixed fundamental group we show that if the complement of a 2 knot s in s2 x s2 is simply connected then the ambient isotopy type of s is determined in the case of nontrivial 7r1 however we show that the ambient isotopy type of a 2 knot in s2 x s2 with nontrivial 71 is not always determined by 71

differentiable classification of 4 manifolds with singular riemannian foliations in this paper we first prove that any closed simply connected 4 manifold that admits a decomposition into two disk bundles of rank greater than 1 is diffeomorphic to one of the standard elliptic 4 manifolds mathbb s 4 mathbb cp 2 mathbb s 2 times mathbb s 2 or mathbb cp 2 pm mathbb cp 2 as an application we prove that any closed simply connected 4 manifold admitting a nontrivial singular riemannian foliation is diffeomorphic to a connected sum of copies of standard mathbb s 4 pm mathbb cp 2 and mathbb s 2 times mathbb s 2 a classification of singular riemannian foliations of codimension 1 on all closed simply connected 4 manifolds is obtained as a byproduct in particular there are exactly 3 non homogeneous singular riemannian foliations of codimension 1 complementing the list of cohomogeneity one 4 manifolds

magnetic monopoles on three manifolds on etudie des monopoles magnetiques sur une 3 variete de riemann complete orientee m on associe a m une collection d espaces de modules de solutions des equations des monopoles pourvu que m soit non compacte et que la metrique de riemann sur m soit bonne pres de l infini

new topological field theories in two dimensions it is shown that two 1 1 dimensional 2d free abelian and self interacting non abelian gauge theories without any interaction with matter fields belong to a new class of topological field theories tfts these new theories capture together some of the key features of witten and schwarz types of tft because they are endowed with symmetries that are reminiscent of the schwarz type theories but their lagrangian density has the appearance of the witten type theories the topological invariants for these theories are computed on a 2d compact manifold and their recursion relations are obtained these new theories are shown to provide a class of tractable field theoretical models for the hodge theory in two dimensions of flat minkowski spacetime where there are no propagating degrees of freedom associated with the 2d gauge boson

multivariate stochastic approximation using a simultaneous perturbation gradient approximation the problem of finding a root of the multivariate gradient equation that arises in function minimization is considered when only noisy measurements of the function are available a stochastic approximation sa algorithm for the general kiefer wolfowitz type is appropriate for estimating the root the paper presents an sa algorithm that is based on a simultaneous perturbation gradient approximation instead of the standard finite difference approximation of keifer wolfowitz type procedures theory and numerical experience indicate that the algorithm can be significantly more efficient than the standard algorithms in large dimensional problems

orthogonal parameter estimation algorithm for non linear stochastic systems an orthogonal parameter estimation algorithm is derived which allows each parameter in a linear in the parameters non linear difference equation model to be estimated sequentially and quite independently of the other parameters in the model the algorithm can be applied for any persistently exciting input and provides both unbiased estimates in the presence of correlated noise and an indication of which terms to include in the model several simulated examples are included to demonstrate the effectiveness of the algorithm

plummeting and blinking eigenvalues of the robin laplacian in a cuspidal domain we consider the robin laplacian in the domains and e e 0 with sharp and blunted cusps respectively assuming that the robin coefficient a is large enough the spectrum of the problem in is known to be residual and to cover the whole complex plane but on the contrary the spectrum in the lipschitz domain e is discrete however our results reveal the strange behaviour of the discrete spectrum as the blunting parameter e tends to 0 we construct asymptotic forms of the eigenvalues and detect families of hardly movable and plummeting ones the first type of the eigenvalues do not leave a small neighbourhood of a point for any small e 0 while the second ones move at a high rate o ln e downwards along the real axis to at the same time any point is a blinking eigenvalue i e it belongs to the spectrum of the problem in e almost periodically in the ln e scale besides standard spectral theory we use the techniques of dimension reduction and self adjoint extensions to obtain these results

holomorphic triangles and invariants for smooth four manifolds abstract in earlier articles the authors introduced invariants for closed oriented three manifolds defined using a variant of lagrangian floer homology in the symmetric products of riemann surfaces the aim of this article is to introduce invariants of oriented smooth four manifolds built using these floer homology groups this four dimensional theory also endows the corresponding three dimensional theories with additional structure an absolute grading of certain of its floer homology groups

anti self dual yang mills connections over complex algebraic surfaces and stable vector bundles on presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels soit une surface algebrique projective x qui a un plongement donne x cp n et soit une metrique de kahler sur x dont la classe de cohomologie associee est duale a la classe de section d hyperplan h un fibre sur x est stable par rapport au plongement projectif si et seulement si il admet une connexion irreductible d hermite einstein par rapport a la metrique cette connexion est alors unique

real rational surfaces are quasi simple we show that real rational over c surfaces are quasi simple i e that such a surface is determined up to deformation in the class of real surfaces by the topological type of its real structure

a gradient free adaptation method for nonlinear active noise control abstract active noise control anc problems are often affected by nonlinear effects such as saturation and distortion of microphones and loudspeakers nonlinear models and specific adaptation algorithms must be employed to properly account for these effects the nonlinear structure of the problem complicates the application of gradient based least mean squares lms algorithms due to the fact that exact gradient calculation requires executing nonlinear recursive filtering operations which pose computational and stability issues one favored solution to this problem consists in neglecting recursive terms in the gradient calculation an approximation which is not always without consequences on the convergence performance besides an efficient application of nonlinear models cannot avoid some form of model structure selection to avoid the well known effects of overparametrization and to reduce the computational load on line unfortunately the standard anc setting configures an indirect identification problem due to the presence of the secondary path in the control loop in the nonlinear case this destroys the linear regression structure of the problem even if the control filter is linear in the parameters thereby making it impossible to apply the many existing model selection methods for linear regression problems a simple and computationally wise low demanding approach is here proposed for parameter estimation and model structure selection that provides an answer to the mentioned issues the proposed method avoids altogether the use of the error gradient and relies on direct cost function evaluations a virtualization scheme is used to assess the accuracy improvements when the model is subject to parametric or structural modifications without directly affecting the control performance several simulation examples are discussed to show the effectiveness of the proposed algorithms

an application of gauge theory to four dimensional topology soit x une u variete compacte reguliere simplement connexe orientee avec la propriete que la forme associee q est definie positive alors cette forme est equivalente sur les entiers a la forme diagonale standard soit dans une base q u 1 u 2 u 2 u 2 1 u 2 2 u 2 2