self dual instantons and holomorphic curves a gradient flow of a morse function on a compact riemannian manifold is said to be of morse smale type if the stable and unstable manifolds of any two critical points intersect transversally for such a morse smale gradient flow there is a chain complex generated by the critical points and graded by the morse index the boundary operator has as its x y entry the number of gradient flow lines running from x to y counted with appropriate signs whenever the difference of the morse indices is 1 the homology of this chain complex agrees with the homology of the underlying manifold m and this can be used to prove the morse inequalities cf 33 26 around 1986 floer generalized this idea to infinite dimensional variational problems in which every critical point has infinite morse index but the moduli spaces of connecting orbits form finite dimensional manifolds for every pair of critical points the dimensions of these spaces give rise to a relative morse index and the boundary operator is defined by counting connecting

quantum cohomology of flag manifolds and toda lattices we discuss relations of vafa s quantum cohomology with floer s homology theory introduce equivariant quantum cohomology formulate some conjectures about its general properties and on the basis of these conjectures compute quantum cohomology algebras of the flag manifolds the answer turns out to coincide with the algebra of regular functions on an invariant lagrangian variety of a toda lattice

on the maslov index in this paper we give four definitions of maslov index and show that they all satisfy the same system of axioms and hence are equivalent to each other moreover relationships of several symplectic and differential geometric analytic and topological invariants including triple maslov indices eta invariants spectral flow and signatures of quadratic forms to the maslov index are developed and formulae relating them are given the broad presentation is designed with a view to applications both in geometry and in analysis 1994 john wiley sons inc

correction of bias due to heterogeneous capture probability in capture recapture studies of open populations heterogeneity of individual capture probabilities pi is a commonly acknowledged cause of bias in capture recapture studies of open populations we propose and evaluate an extension of the indirect method of carothers 1979 journal of animal ecology 48 863 869 carothers method identifies by simulation and inverse prediction the parametric survival rate the mean capture probability e p and cv p that could have given rise to an observed set of capture histories and biased capture recapture estimates we also extend carothers approach to estimate population size and evaluate it in relation to field data from a study of brushtail possums in new zealand if heterogeneity is the only source of bias and it is adequately modelled by a beta distribution the method provides unbiased estimates of average population size average survival rate e p and cv p under the cormack jolly seber model although the method assumes a constant population size our results suggest that it is robust to temporal variation

removal of boundary singularities of pseudo holomorphic curves with lagrangian boundary conditions we give a proof of the theorem of removing isolated singularities of pseudo holomorphic curves with lagrangian boundary conditions and bounded symplectic area the proof is a combination of some lp type estimates standard techniques of geometric p d e and some ideas from symplectic geometry and calibration theory

a symplectic fixed point theorem for cpn two symplectic diffeomorphisms 0 1 of a symplectic manifold x are said to be homologous if there exists a smooth homotopy 1 t 0 1 of symplectic diffeomorphisms between them such that the timedependent vector field t defined byd dt t t o t is a globally hamiltonian vector field for allt i e there exists a smooth real valued timedependent hamiltonian functionh x t onx x 0 1 such that t dh t whereht h x t

on the obstructed lagrangian floer theory abstract lagrangian floer homology in a general case has been constructed by fukaya oh ohta and ono where they construct an a algebra or an a bimodule from lagrangian submanifolds they developed obstruction and deformation theories of the lagrangian floer homology theory but for obstructed lagrangian submanifolds the standard lagrangian floer homology cannot be defined we explore several well known homology theories on these a objects which are hochschild and cyclic homology for an a objects and chevalley eilenberg or cyclic chevalley eilenberg homology for their underlying l objects we show that these homology theories are well defined and invariant even in the obstructed cases due to the existence of m 0 the standard homological algebra does not work and we develop analogous homological algebra over novikov fields we provide computations of these homology theories in some cases we show that for an obstructed a algebra with a non trivial primary obstruction chevalley eilenberg floer homology vanishes whose proof is inspired by the comparison with cluster homology theory of lagrangian submanifolds by cornea and lalonde in contrast we also provide an example of an obstructed case whose cyclic floer homology is non vanishing

oscillation threshold of a clarinet model a numerical continuation approach this paper focuses on the oscillation threshold of single reed instruments several characteristics such as blowing pressure at threshold regime selection and playing frequency are known to change radically when taking into account the reed dynamics and the flow induced by the reed motion previous works have shown interesting tendencies using analytical expressions with simplified models in the present study a more elaborated physical model is considered the influence of several parameters depending on the reed properties the design of the instrument or the control operated by the player are studied previous results on the influence of the reed resonance frequency are confirmed new results concerning the simultaneous influence of two model parameters on oscillation threshold regime selection and playing frequency are presented and discussed the authors use a numerical continuation approach numerical continuation consists in following a given solution of a set of equations when a parameter varies considering the instrument as a dynamical system the oscillation threshold problem is formulated as a path following of hopf bifurcations generalizing the usual approach of the characteristic equation as used in previous works the proposed numerical approach proves to be useful for the study of musical instruments it is complementary to analytical analysis and direct time domain or frequency domain simulations since it allows to derive information that is hardly reachable through simulation without the approximations needed for analytical approach

estimating the size of a closed population from a single mark recapture regime by using a diffusion probability of marked individuals a population estimate model was developed to account for the unequal recapture probability of marked animals when their diffusion into the released population has yet to reach the equilibrium we assumed a spatial bias for marked individuals within the finite area of the animals territory and used a correction parameter to account for the bias mark recapture data previously collected for field colonies of the formosan subterranean termite coptotermes formosanus shiraki were applied to the new model and the results were compared with the peterson and weighted mean models

symplectic topology and hamiltonian dynamics on etudie des applications symplectiques non lineaires capacites symplectiques construction d une capacite symplectique problemes de plongement problemes de rigidite

multiplicity of lagrangian orbits on symmetric star shaped hypersurfaces abstract in this paper the multiplicity of lagrangian orbits on c 2 smooth compact symmetric star shaped hypersurfaces with respect to the origin in r 2 n is studied we prove an infinitely many existence result via z 2 index theory this is a multiplicity result about the arnold chord in some sense

lagrangian floer theory on compact toric manifolds i we introduced the notion of weakly unobstructed lagrangian submanifolds and constructed their potential function po purely in terms of a model data in fooo3 in this article we carry out explicit calculations involving po on toric manifolds and study the relationship between this class of lagrangian submanifolds with the earlier work of givental g1 which advocates that the quantum cohomology ring is isomorphic to the jacobian ring of a certain function called the landau ginzburg superpotential combining this study with the results from fooo3 we also apply the study to various examples to illustrate its implications to symplectic topology of lagrangian fibers of toric manifolds in particular we relate it to the hamiltonian displacement property of lagrangian fibers and to entov polterovich s symplectic quasi states

stability conditions on an singularities we study the spaces of locally finite stability conditions on the derived categories of coherent sheaves on the minimal resolutions of a n singularities supported at the exceptional sets our main theorem is that they are connected and simply connected the proof is based on the study of spherical objects in a ishii and h uehara autoequivalences of derived categories on the minimal resolutions of a n singularities on surfaces j differential geom 71 3 385 435 2005 and the homological mirror symmetry for a n singularities

homotopy equivalence of nearby lagrangians and the serre spectral sequence we construct using relatively basic techniques a spectral sequence for exact lagrangians in cotangent bundles similar to the one constructed by fukaya seidel and smith that spectral sequence was used to prove that exact relative spin lagrangians in simply connected cotangent bundles with vanishing maslov class are homology equivalent to the base a similar result was also obtained by nadler the ideas in that paper were extended by abouzaid who proved that vanishing maslov class alone implies homotopy equivalence in this paper we present a short proof of the fact that any exact lagrangian with vanishing maslov class is homology equivalent to the base and that the induced map on fundamental groups is an isomorphism when the fundamental group of the base is pro finite this implies homotopy equivalence

finite energy foliations of tight three spheres and hamiltonian dynamics surfaces of sections are a classical tool in the study of 3 dimensional dynamical systems their use goes back to the work of poincare and birkhoff in the present paper we give a natural generalization of this concept by constructing a system of transversal sections in the complement of finitely many distinguished periodic solutions such a system is established for nondegenerate reeb flows on the tight 3 sphere by means of pseudoholomorphic curves the applications cover the nondegenerate geodesic flows on t1s2 rp3 via its double covering s3 and also nondegenerate hamiltonian systems in ir4 restricted to sphere like energy surfaces of contact type

the unregularized gradient flow of the symplectic action the symplectic action can be defined on the space of smooth paths in a symplectic manifold p which join two lagrangian submanifolds of p to pursue a new approach to the variational theory of this function we define on a subset of the path space the flow whose trajectories are given by the solutions of the cauchy riemann equation with respect to a suitable almost complex structure on p in particular we prove compactness and transversality results for the set of bounded trajectories

an iterated graph construction and periodic orbits of hamiltonian delay equations abstract according to the arnold conjectures and floer s proofs there are non trivial lower bounds for the number of periodic solutions of hamiltonian differential equations on a closed symplectic manifold whose symplectic form vanishes on spheres we use an iterated graph construction and lagrangian floer homology to show that these lower bounds also hold for certain hamiltonian delay equations

logistic regression in capture recapture models the effect of population heterogeneity in capture recapture or dual registration models is discussed an estimator of the unknown population size based on a logistic regression model is introduced the model allows different capture probabilities across individuals and across capture times the probabilities are estimated from the observed data using conditional maximum likelihood the resulting population estimator is shown to be consistent and asymptotically normal a variance estimator under population heterogeneity is derived the finite sample properties of the estimators are studied via simulation an application to finnish occupational disease registration data is presented

flute like musical instruments a toy model investigated through numerical continuation abstract self sustained musical instruments bowed string woodwind and brass instruments can be modelled by nonlinear lumped dynamical systems among these instruments flutes and flue organ pipes present the particularity to be modelled as a delay dynamical system in this paper such a system a toy model of flute like instruments is studied using numerical continuation equilibrium and periodic solutions are explored with respect to the blowing pressure with focus on amplitude and frequency evolutions along the different solution branches as well as jumps between periodic solution branches the influence of a second model parameter namely the inharmonicity on the behaviour of the system is addressed it is shown that harmonicity plays a key role in the presence of hysteresis or quasiperiodic regime throughout the paper experimental results on a real instrument are presented to illustrate various phenomena and allow some qualitative comparisons with numerical results

morse theory for lagrangian intersections soit p une variete symplectique compacte et soit l p une sous variete lagrangienne avec 2 p l 0 pour un diffeomorphisme exact de p avec la propriete que l coupe l transversalement on demontre une inegalite de morse reliant l ensemble l l a la cohomologie de l

link homology theories from symplectic geometry for each positive integer n khovanov and rozansky constructed an invariant of links in the form of a doubly graded cohomology theory whose euler characteristic is the link polynomial we use lagrangian floer cohomology on some suitable affine varieties to build a similar series of link invariants and we conjecture them to be equal to those of khovanov and rozansky after a collapse of the bigrading our work is a generalization of that of seidel and smith who treated the case n 2

the birkhoff lewis fixed point theorem and a conjecture of v i arnold abstract the following conjecture of v i arnold is proved every measure preserving diffeomorphism of the torus t2 which is homologeous to the identity and which leaves the center of mass invariant possesses at least 3 fixed points the proof of this global fixed point theorem does not make use of the generating function technique the theorem is a consequence of the statement that a hamiltonian vector field on a torus t2n which depends periodically on time possesses at least 2n 1 forced oscillations these periodic solutions are are found using the classical variational principle by means of two qualitative statements for general flows a second conjecture of v i arnold proved concerns a birkhoff lewis type fixed point theorem for symplectic maps additional keywords periodic functions variational principles equations reprints author

morse theory for lagrange multipliers and adiabatic limits abstract given two morse functions f on a compact manifold m we study the morse homology for the lagrange multiplier function on m r which sends x to f x x take a product metric on m r and rescale its r component by a factor 2 we show that generically for large the morse smale witten chain complex is isomorphic to the one for f and the metric restricted to 1 0 with grading shifted by one on the other hand in the limit 0 we obtain another chain complex which is geometrically quite different but has the same homology as the singular homology of 1 0 the isomorphism between the chain complexes is provided by the homotopy obtained by varying our proofs use both the implicit function theorem on banach manifolds and geometric singular perturbation theory

a morse complex for infinite dimensional manifolds part i abstract in this paper and in the forthcoming part ii we introduce a morse complex for a class of functions f defined on an infinite dimensional hilbert manifold m possibly having critical points of infinite morse index and co index the idea is to consider an infinite dimensional subbundle or more generally an essential subbundle of the tangent bundle of m suitably related with the gradient flow of f this part i deals with the following questions about the intersection w of the unstable manifold of a critical point x and the stable manifold of another critical point y finite dimensionality of w possibility that different components of w have different dimension orientability of w and coherence in the choice of an orientation compactness of the closure of w classification up to topological conjugacy of the gradient flow on the closure of w in the case dim w 2

a combinatorial description of knot floer homology given a grid presentation of a knot or link k in the three sphere we describe a heegaard diagram for the knot complement in which the heegaard surface is a torus and all elementary domains are squares using this diagram we obtain a purely combinatorial description of the knot floer homology of k

mixture models for estimating the size of a closed population when capture rates vary among individuals nous developpons une parametrisation du melange de lois beta et binomiale qui fournit un cadre inferentiel approprie pour estimer l effectif d une population fermee lorsque les probabilites de capture ou de detection varient entre individus nous ajustons trois classes de modeles de melange beta binomiale logistique normale et modele a classes latentes d une part a des donnees de recapture de lievres d amerique pour en estimer l abondance et d autre part a des comptages d especes d oiseaux pour estimer la richesse specifique dans les deux jeux de donnees les taux de detection varient davantage entre individus lievres ou especes qu entre occasions ou lieux de capture les estimateurs de l effectif de la population et de la richesse specifique sont sensibles aux hypotheses faites sur la distribution sous jacente des probabilites individuelles de detection nous montrons par simulations que les outils habituels d evaluation de la qualite du modele comme la deviance ne sont pas fiables pour choisir entre des modeles de melanges celui qui fournit une inference correcte de l effectif de la population lorsqu elles existent des connaissances a priori sur les causes d heterogeneite des taux de detection doivent etre utilisees pour aider a choisir quelle classe de modeles de melanges utiliser pour l inference

cup length estimate for lagrangian intersections abstract in this paper we consider the arnold conjecture on the lagrangian intersections of some closed lagrangian submanifold of a closed symplectic manifold with its image of a hamiltonian diffeomorphism we prove that if the hofer s symplectic energy of the hamiltonian diffeomorphism is less than a topology number defined by the lagrangian submanifold then the arnold conjecture is true in the degenerated nontransversal case

explicit mapping of acoustic regimes for wind instruments this paper proposes a methodology to map the various acoustic regimes of wind instruments the maps can be generated in a multidimensional space consisting of design control parameters and initial conditions the boundaries of the maps are obtained explicitly in terms of the parameters using a support vector machine svm classifier as well as a dedicated adaptive sampling scheme the approach is demonstrated on a simplified clarinet model for which several maps are generated based on different criteria examples of computation of the probability of occurrence of a specific acoustic regime are also provided in addition the approach is demonstrated on a design optimization example for optimal intonation

a high order purely frequency based harmonic balance formulation for continuation of periodic solutions combining the harmonic balance method hbm and a continuation method is a well known technique to follow the periodic solutions of dynamical systems when a control parameter is varied however since deriving the algebraic system containing the fourier coefficients can be a highly cumbersome procedure the classical hbm is often limited to polynomial quadratic and cubic nonlinearities and or a few harmonics several variations on the classical hbm such as the incremental hbm or the alternating frequency time domain hbm have been presented in the literature to overcome this shortcoming here we present an alternative approach that can be applied to a very large class of dynamical systems autonomous or forced with smooth equations the main idea is to systematically recast the dynamical system in quadratic polynomial form before applying the hbm once the equations have been rendered quadratic it becomes obvious to derive the algebraic system and solve it by the so called asymptotic numerical method anm continuation technique several classical examples are presented to illustrate the use of this numerical approach

differential algebra of legendrian links let the space r q p u be equipped with the standard contact form du pdq a link l r3 is called legendrian if the restriction of to l vanishes two legendrian links are said to be legendrian isotopic if they can be connected by a path in the space of legendrian embeddings consider the map r3 r2 q p u q p since the kernel of d is everywhere transverse to the kernel of the projection l of a legendrian link l is an immersed curve we say that a link l r3 is generic with respect to or generic if all self intersections of l are transverse double points given a generic legendrian link l its diagram is the curve l r2 at every crossing of which the overpassing branch the one with the larger value of u is marked it is well known that every smooth link type can be realized by a legendrian link it is shown in sect 11 that such a realization can be chosen to have a diagram with relatively few crossings the so called classical invariants of an oriented legendrian link l are defined as follows first of them is just the smooth isotopy type of l let l1 lk be the components of l the maslov number m li of li is twice the rotation number of li the thurston bennequin number li of li is the linking number between li and s li where s is a small shift along the u direction the orientation on r3 involved in the definition of the linking number is given by the form d dq dp du in terms of the diagram li is the number of double points of li counted with signs shown in fig 1 the thurston bennequin number does not depend on the orientation of li while the maslov number changes its sign when the orientation changes

exact lagrangian immersions with one double point revisited we study exact lagrangian immersions with one double point of a closed orientable manifold k into mathbb c n we prove that if the maslov grading of the double point does not equal 1 then k is homotopy equivalent to the sphere and if in addition the lagrangian gauss map of the immersion is stably homotopic to that of the whitney immersion then k bounds a parallelizable n 1 manifold the hypothesis on the gauss map always holds when n 2k or when n 8k 1 the argument studies a filling of k obtained from solutions to perturbed cauchy riemann equations with boundary on the image f k of the immersion this leads to a new and simplified proof of some of the main results of ekholm and smith exact lagrangian immersions with a single double point 2011 which treated lagrangian immersions in the case n 2k by applying similar techniques to a lagrange surgery of the immersion as well as to an extension of these results to the odd dimensional case

propagation in hamiltonian dynamics and relative symplectic homology the main result asserts the existence of noncontractible periodic orbits for compactly supported time dependent hamiltonian systems on the unit cotangent bundle of the torus or of a negatively curved manifold whenever the generating hamiltonian is sufficiently large over the zero section the proof is based on floer homology and on the notion of a relative symplectic capacity applications include results about propagation properties of sequential hamiltonian systems periodic orbits on hypersurfaces hamiltonian circle actions and smooth lagrangian skeletons in stein manifolds

a sampling based approach for probabilistic design with random fields an original technique to incorporate random fields non intrusively in probabilistic design is presented the approach is based on the extraction of the main features of a random field using a limited number of experimental observations snapshots an approximation of the random field is obtained using proper orthogonal decomposition pod for a given failure criterion an explicit limit state function lsf in terms of the coefficients of the pod expansion is obtained using a support vector machine svm an adaptive sampling technique is used to generate samples and update the approximated lsf the coefficients of the orthogonal decomposition are considered as random variables with distributions determined from the snapshots based on these distributions and the explicit lsf the approach allows for an efficient assessment of the probabilities of failure in addition the construction of explicit lsf has the advantage of handling discontinuous responses two test problems are used to demonstrate the proposed methodology used for the calculation of probabilities of failure the first example involves the linear buckling of an arch structure for which the thickness is a random field the second problem concerns the impact of a tube on a rigid wall the planarity of the walls of the tube is considered as a random field

floer cohomology and pencils of quadrics there is a classical relationship in algebraic geometry between a hyperelliptic curve and an associated pencil of quadric hypersurfaces we investigate symplectic aspects of this relationship with a view to applications in low dimensional topology

hamiltonian delay equations examples and a lower bound for the number of periodic solutions abstract we describe a variational approach to a notion of hamiltonian delay equations our delay hamiltonians are of product form we consider several examples for closed symplectically aspherical symplectic manifolds m we prove that for generic delay hamiltonians the number of 1 periodic solutions of the hamiltonian delay equation is at least the sum of the betti numbers of m extending the proof of the arnold conjecture to the case with delay

generating the fukaya categories of hamiltonian g manifolds abstract let g be a compact lie group and let k be a field of characteristic p geq 0 such that h g has no p torsion if p 0 we show that a free lagrangian orbit of a hamiltonian g action on a compact monotone symplectic manifold x split generates an idempotent summand of the monotone fukaya category mathcal f x k if and only if it represents a nonzero object of that summand slightly more general results are also provided our result is based on an explicit understanding of the wrapped fukaya category mathcal w t g k through koszul twisted complexes involving the zero section and a cotangent fibre and on a functor d b mathcal w t g k to d b mathcal f x times x k canonically associated to the hamiltonian g action on x we explore several examples which can be studied in a uniform manner including toric fano varieties and certain grassmannians

addendum to floer cohomology of lagrangian intersections and pseudo holomorphic discs i this is an addendum to the author s earlier paper floer cohomology of lagrangian intersection and pseudo holomorphic discs i comm pure appl math 46 1993 pp 949 993 the main result of this addendum extends the definition of the floer cohomology of lagrangian intersection to the case where the minimal maslov number is equal to 2 1996 john wiley sons inc

morse bott homology we give a new proof of the morse homology theorem by constructing a chain complex associated to a morse bott smale function that reduces to the morse smale witten chain complex when the function is morse smale and to the chain complex of smooth singular n cube chains when the function is constant we show that the homology of the chain complex is independent of the morse bott smale function by using compactified moduli spaces of time dependent gradient flow lines to prove a floer type continuation theorem

symplectic fixed points and holomorphic spheres letp be a symplectic manifold whose symplectic form integrated over the spheres inp is proportional to its first chern class on the loop space ofp we consider the variational theory of the symplectic action function perturbed by a hamiltonian term in particular we associate to each isolated invariant set of its gradient flow an abelian group with a cyclic grading it is shown to have properties similar to the homology of the conley index in locally compact spaces as an application we show that if the fixed point set of an exact diffeomorphism onp is nondegenerate then it satisfies the morse inequalities onp we also discuss fixed point estimates for general exact diffeomorphisms

statistical inference procedure for a hypergeometric model for capture recapture experiments abstract we use martingale theory and a method of moments technique to derive a class of estimators for a multihypergeometric model for a capture recapture experiment certain choices of weight function lead to some standard estimators explicit expression for the estimators and their associated standard errors of the parameter population size is obtained optimal estimator among the class of estimators is derived which gives the tightest confidence interval for the population size three examples are given a simulation study is given to assess the performance of the proposed estimators with other existing ones

a high order purely frequency based harmonic balance formulation for continuation of periodic solutions the case of non polynomial nonlinearities abstract in this paper we extend the method proposed by cochelin and vergez a high order purely frequency based harmonic balance formulation for continuation of periodic solutions journal of sound and vibration 324 2009 243 262 to the case of non polynomial nonlinearities this extension allows for the computation of branches of periodic solutions of a broader class of nonlinear dynamical systems the principle remains to transform the original ode system into an extended polynomial quadratic system for an easy application of the harmonic balance method hbm the transformation of non polynomial terms is based on the differentiation of state variables with respect to the time variable shifting the nonlinear non polynomial nonlinearity to a time independent initial condition equation not concerned with the hbm the continuation of the resulting algebraic system is here performed by the asymptotic numerical method high order taylor series representation of the solution branch using a further differentiation of the non polynomial algebraic equation with respect to the path parameter a one dof vibro impact system is used to illustrate how an exponential nonlinearity is handled showing that the method works at very high order 1000 in that case various kinds of nonlinear functions are also treated and finally the nonlinear free pendulum is addressed showing that very accurate periodic solutions can be computed with the proposed method

some practical aspects of a conditional likelihood approach to capture experiments the use of conditional likelihood methods in the analysis of capture data allows the modeling of capture probabilities in terms of observable characteristics of the captured individuals and the trapping occasions the resulting models may then be used to estimate the size of the population here the use of conditional likelihood procedures to construct models for capture probabilities is discussed and illustrated by an example