birkhoff normal form for some nonlinear pdes we consider the problem of extending to pdes birkhoff normal form theorem on hamiltonian systems close to nonresonant elliptic equilibria as a model problem we take the nonlinear wave equation with dirichlet boundary conditions on 0 g is an analytic skewsymmetric function which vanishes for u 0 and is periodic with period 2 in the x variable we prove under a nonresonance condition which is fulfilled for most g s that for any integer m there exists a canonical transformation that puts the hamiltonian in birkhoff normal form up to a reminder of order m the canonical transformation is well defined in a neighbourhood of the origin of a sobolev type phase space of sufficiently high order some dynamical consequences are obtained the technique of proof is applicable to quite general semilinear equations in one space dimension

normal forms and quadratic nonlinear klein gordon equations on construit une transformation qui change l equation a non linearite cubique que l on sait resoudre a 3 1 dimensions on demontre que la solution du probleme original a le meme comportement asymptotique que l equation de klein gordon non lineaire

a sub graph isomorphism algorithm for matching large graphs we present an algorithm for graph isomorphism and subgraph isomorphism suited for dealing with large graphs a first version of the algorithm has been presented in a previous paper where we examined its performance for the isomorphism of small and medium size graphs the algorithm is improved here to reduce its spatial complexity and to achieve a better performance on large graphs its features are analyzed in detail with special reference to time and memory requirements the results of a testing performed on a publicly available database of synthetically generated graphs and on graphs relative to a real application dealing with technical drawings are presented confirming the effectiveness of the approach especially when working with large graphs

bayesian graph edit distance this paper describes a novel framework for comparing and matching corrupted relational graphs the paper develops the idea of edit distance originally introduced for graph matching by sanfeliu and fu 1983 we show how the levenshtein distance 1966 can be used to model the probability distribution for structural errors in the graph matching problem this probability distribution is used to locate matches using map label updates we compare the resulting graph matching algorithm with that recently reported by wilson and hancock the use of edit distance offers an elegant alternative to the exhaustive compilation of label dictionaries moreover the method is polynomial rather than exponential in its worst case complexity we support our approach with an experimental study on synthetic data and illustrate its effectiveness on an uncalibrated stereo correspondence problem this demonstrates experimentally that the gain in efficiency is not at the expense of quality of match

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

an isoperimetric problem for point interactions we consider a hamiltonian with n point interactions in all with the same coupling constant placed at vertices of an equilateral polygon it is shown that the ground state energy is locally maximized by a regular polygon the question whether the maximum is global is reduced to an interesting geometric problem

on the complexity of submap isomorphism and maximum common submap problems generalized maps describe the subdivision of objects in cells and are widely used to model 2d and 3d images in this context several pattern recognition tasks involve solving submap isomorphism problems to decide if a map is included in another map or more generally computing maximum common submaps to measure the distance between two maps recently we have described a polynomial time algorithm for solving the submap isomorphism problem when the pattern map is connected in this paper we show that submap isomorphism is np complete when the pattern map is not connected then we characterize the inherent difficulty of submap isomorphism with respect to the number of connected components we show that it is fixed parameter tractable fpt and we give an fpt algorithm for submap isomorphism we experimentally compare this algorithm with a state of the art subgraph isomorphism algorithm for searching for patterns in an image and we show that it is both more accurate and more efficient finally we study the complexity of the maximum common submap problem and we show that it is np hard even though we restrict the problem to the search of common connected submaps highlightswe show that submap isomorphism is np complete we give a fixed parameter tractable algorithm for submap isomorphism we experimentally evaluate it to search for patterns in segmented images we show that maximum common connected submap is np hard

temps d existence pour l equation de klein gordon semi lineaire a donnees petites periodiques we study lower bounds for the maximal time of existence t of a smooth solution to a semi linear klein gordon equation u u f u u with periodic cauchy data of small size if f vanishes at order r at 0 we prove that t c 2 if r 2 t c r 1 log r 3 if r 3 we construct examples showing the optimality of these results for convenient values of r

the stability of full dimensional kam tori for nonlinear schrodinger equation abstract in this paper it is proved that the full dimensional invariant tori obtained by bourgain j funct anal 229 2005 no 1 62 94 is stable in a very long time for 1d nonlinear schrodinger equation with periodic boundary conditions

an isoperimetric problem for leaky loops and related mean chord inequalities we consider a class of hamiltonians in l2 r2 with attractive interaction supported by piecewise c2 smooth loops of a fixed length l formally given by x with 0 it is shown that the ground state of this operator is locally maximized by a circular we also conjecture that this property holds globally and show that the problem is related to an interesting family of geometric inequalities concerning mean values of chords of

planar formulae and their uses we define the set of planar boolean formulae and then show that the set of true quantified planar formulae is polynomial space complete and that the set of satisfiable planar formulae is np complete using these results we are able to provide simple and nearly uniform proofs of np completeness for planar node cover planar hamiltonian circuit and line geometric connected dominating set and of polynomial space completeness for planar generalized geography the np completeness of planar node cover and planar hamiltonian circuit and line were first proved elsewhere m r garey and d s johnson the rectilinear steiner tree is np complete siam j appl math 32 1977 pp 826 834 and m r garey d s johnson and r e tarjan the planar hamilton circuit problem is np complete siam j comp 5 1976 pp 704 714

structural matching by discrete relaxation this paper describes a bayesian framework for performing relational graph matching by discrete relaxation our basic aim is to draw on this framework to provide a comparative evaluation of a number of contrasting approaches to relational matching broadly speaking there are two main aspects to this study firstly we focus on the issue of how relational inexactness may be quantified we illustrate that several popular relational distance measures can be recovered as specific limiting cases of the bayesian consistency measure the second aspect of our comparison concerns the way in which structural inexactness is controlled we investigate three different realizations of the matching process which draw on contrasting control models the main conclusion of our study is that the active process of graph editing outperforms the alternatives in terms of its ability to effectively control a large population of contaminating clutter

a nekhoroshev type theorem for the derivative nonlinear schrodinger equation abstract it is proved a nekhoroshev type theorem for the derivative nonlinear schrodinger equation in a gevrey space more precisely we prove that if the norm of initial datum is equal to e 2 then if e is small enough the norm of the solution of the nonlinear schrodinger equation above is bounded by 2e over a very long time interval of order e ln e 1 where 0 1 2 is arbitrary

a validity measure for fuzzy clustering the authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c partitions without assumptions as to the number of substructures inherent in the data this function depends on the data set geometric distance measure distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used the function is mathematically justified via its relationship to a well defined hard clustering validity function the separation index for which the condition of uniqueness has already been established the performance of this validity function compares favorably to that of several others the application of this validity function to color image segmentation in a computer color vision system for recognition of ic wafer defects which are otherwise impossible to detect using gray scale image processing is discussed

almost global existence for the semi linear klein gordon equation on the circle abstract we show that the solution to the semi linear klein gordon equation on the circle with a nonlinearity satisfying a convenient condition exists almost globally for almost every positive mass provided that it is either even or odd as a function of the space variable we also show that if the nonlinearity is independent of the space derivative of the unknown and if it is also even as a function of the time derivative then the solution exists almost globally for almost every positive mass the results are based on the method of normal forms the difficulty is to find a structure of the nonlinearity so that the process of normal forms can be performed up to any order

structural pattern recognition using genetic algorithms this paper presents a genetic algorithm ga based optimization procedure for the solution of structural pattern recognition problem using the attributed relational graph representation and matching technique in this study candidate solutions are represented by integer strings and the population is randomly initialized the ga is employed to generate a monomorphic mapping as all the mapping constraints are not enforced during the search phase in order to speedup the search an efficient pose clustering algorithm is used to eliminate spurious matches and to determine the presence of the model in the scene the performance of the proposed approach to pattern recognition by subgraph isomorphism is demonstrated using line patterns and silhouette images

long time existence for semi linear klein gordon equations with small cauchy data on zoll manifolds we prove a long time existence result for semi linear klein gordon equations with small cauchy data on zoll manifolds this generalizes a preceding result concerning the case of spheres obtained in an earlier paper by the authors the proof relies on almost orthogonality properties of products of eigenfunctions of positive elliptic selfadjoint operators on a compact manifold and on the specific distribution of eigenvalues of the laplacian perturbed by a potential on zoll manifolds

an eigendecomposition approach to weighted graph matching problems an approximate solution to the weighted graph matching problem is discussed for both undirected and directed graphs the weighted graph matching problem is that of finding the optimum matching between two weighted graphs which are graphs with weights at each arc the proposed method uses an analytic instead of a combinatorial or iterative approach to the optimum matching problem using the eigendecompositions of the adjacency matrices in the case of the undirected graph matching problem or hermitian matrices derived from the adjacency matrices in the case of the directed graph matching problem a matching close to the optimum can be found efficiently when the graphs are sufficiently close to each other simulation results are given to evaluate the performance of the proposed method

polynomial algorithms for open plane graph and subgraph isomorphisms graphs are used as models in a variety of situations in some cases e g to model images or maps the graphs will be drawn in the plane and this feature can be used to obtain new algorithmic results in this work we introduce a special class of graphs called open plane graphs which can be used to represent images or maps for robots they are planar graphs embedded in the plane in which certain faces can be removed are absent or unreachable we give a normal form for such graphs and prove that one can check in polynomial time if two normalised graphs are isomorphic or if two open plane graphs are equivalent their normal forms are isomorphic then we consider a new kind of subgraphs built from subsets of faces and called patterns we show that searching for a pattern in an open plane graph is tractable if and only if the faces are contiguous that is we prove that the problem is np complete otherwise

improving bipartite graph edit distance approximation using various search strategies recently the authors of the present paper introduced an approximation framework for the graph edit distance problem the basic idea of this approximation is to first build a square cost matrix c c ij where each entry cij reflects the cost of a node substitution deletion or insertion plus the matching cost arising from the local edge structure based on c an optimal assignment of the nodes and their local structure can be established in polynomial time since this approach considers local rather than the global structural properties of the graphs only the graph edit distance derived from the optimal node assignment generally overestimates the true edit distance the present paper pursues the idea of applying additional search strategies that build upon the initial assignment in order to reduce this overestimation to this end six different search strategies are investigated in this paper in an exhaustive experimental evaluation on five real world graph data sets we empirically verify a substantial gain of distance accuracy by means of all search methods while run time remains remarkably low highlightswe show how the well known bipartite graph edit distance approximation can substantially be improved with respect to distance accuracy to this end we introduce and compare six different methodologies for extending the graph matching framework we empirically verify a substantial gain of distance accuracy by means of all methods while run time remains remarkably low the benefit of improved distance quality is also verified in a clustering application

a local start search algorithm to compute exact hausdorff distance for arbitrary point sets this paper discovers the spatial locality feature of point sets and proposes a novel search algorithm called local start search lss to compute the exact hausdorff distance the lss algorithm can greatly reduce the running time when dealing with large scale of point set in which the spatial continuity and distance continuity are very common lss maintains high performance in both overlap and non overlap situations of a pair of regular point sets while earlybreak experiences degraded performance in overlap situations furthermore for general point sets in overlap situations the preprocess of excluding the intersection in earlybreak will fail however lss can still process the general point sets with different point sizes after ordering the sets our algorithm outperforms the state of the art algorithm experiments demonstrate the efficiency and accuracy of the proposed method the hausdorff distance hd is a very important similarity measurement in pattern recognition shape matching and artificial intelligence because of its inherent computational complexity computing the hd using the naivehd brute force algorithm is difficult especially for comparing the similarity between large scale point sets in the time of big data to overcome this problem we propose a novel efficient and general algorithm for computing the exact hd for arbitrary point sets which takes advantage of the spatial locality of point sets namely local start search lss different from the state of the art algorithm earlybreak in pami 2015 our idea comes from the observation and fact that the neighbor points of a break position in the current loop have higher probability to break the next loop than other points therefore in our algorithm we add a new mechanism to record the current break position as a start position which is initialized as search center of the next loop then lss executes the next loop by scanning the neighbor points around the center in this way lss maintains high performance in both overlap and non overlap situations furthermore the lss algorithm can process arbitrary data by adopting the morton curve to establish the order of scattered point sets while the earlybreak is mainly applied to regular data which require the same grid size such as medical images or voxel data in the non overlapping situation when comparing pairs of arbitrary point sets lss achieves performance as good as earlybreak algorithm while in the overlapping situation when comparing pairs of arbitrary point sets lss is faster than earlybreak by three orders of magnitude thus as a whole lss outperforms earlybreak in addition lss compared against the increment hausdorff distance calculation algorithm inc and significantly outperforms it by an order of magnitude faster experiments demonstrate the efficiency and accuracy of the proposed method

approximation of graph edit distance based on hausdorff matching graph edit distance is a powerful and flexible method for error tolerant graph matching yet it can only be calculated for small graphs in practice due to its exponential time complexity when considering unconstrained graphs in this paper we propose a quadratic time approximation of graph edit distance based on hausdorff matching in a series of experiments we analyze the performance of the proposed hausdorff edit distance in the context of graph classification and compare it with a cubic time algorithm based on the assignment problem investigated applications include nearest neighbor classification of graphs representing letter drawings fingerprints and molecular compounds as well as hidden markov model classification of vector space embedded graphs representing handwriting in many cases a substantial speedup is achieved with only a minor loss in accuracy or in one case even with a gain in accuracy overall the proposed hausdorff edit distance shows a promising potential in terms of flexibility efficiency and accuracy highlightsquadratic time approximation of graph edit distance based on hausdorff matching error tolerant graph matching method without constraints on node and edge labels experimental evaluation for classification of graphs representing letter drawings fingerprints and molecules experimental evaluation for hidden markov model recognition of vector space embedded graphs representing handwriting promising potential in terms of flexibility efficiency and accuracy

optimal quadratic time isomorphism of ordered graphs in this paper we introduce the concept of ordered graph and ordered graph isomorphism that provides a natural representation of many objects in applications such as computer vision and pattern recognition while no efficient polynomial bound isomorphism algorithm for general graphs exists today we show that the ordered graph isomorphism problem can be optimally solved in quadratic time an experimental evaluation demonstrates the superior performance of the new method our ordered graph isomorphism algorithm is simple and can be easily implemented it is therefore expected to be practically useful in many applications

symbol recognition by error tolerant subgraph matching between region adjacency graphs we propose an error tolerant subgraph isomorphism algorithm formulated in terms of region adjacency graphs rag a set of edit operations to transform one rag into another one are defined as regions are represented by polylines and string matching techniques are used to measure their similarity the algorithm follows a branch and bound approach driven by the rag edit operations this formulation allows matching computing under distorted inputs and also reaching a solution in a near polynomial time the algorithm has been used for recognizing symbols in hand drawn diagrams

leaky quantum graphs approximations by point interaction hamiltonians we prove an approximation result showing how operators of the type x in where is a graph can be modelled in the strong resolvent sense by point interaction hamiltonians with an appropriate arrangement of the potentials the result is illustrated on finding the spectral properties in cases when is a ring or a star furthermore we use this method to indicate that scattering on an infinite curve which is locally close to a loop shape or has multiple bends may exhibit resonances due to quantum tunnelling or repeated reflections

enumerating all connected maximal common subgraphs in two graphs we represent a new method for finding all connected maximal common subgraphs in two graphs which is based on the transformation of the problem into the clique problem we have developed new algorithms for enumerating all cliques that represent connected maximal common subgraphs these algorithms are based on variants of the bron kerbosch algorithm in this paper we explain the transformation of the maximal common subgraph problem into the clique problem we give a short summary of the variants of the bron kerbosch algorithm in order to explain the modification of that algorithm such that the detected cliques represent connected maximal common subgraphs after introducing and proving several variants of the modified algorithm we discuss the runtimes for all variants by means of random graphs the results show the drastical reduction of the runtimes for the new algorithms

polynomial time metrics for attributed trees we address the problem of comparing attributed trees and propose four novel distance measures centered around the notion of a maximal similarity common subtree the proposed measures are general and defined on trees endowed with either symbolic or continuous valued attributes and can be applied to rooted as well as unrooted trees we prove that our measures satisfy the metric constraints and provide a polynomial time algorithm to compute them this is a remarkable and attractive property since the computation of traditional edit distance based metrics is in general np complete at least in the unordered case we experimentally validate the usefulness of our metrics on shape matching tasks and compare them with an approximation of edit distance

a sharp bound for the ratio of the first two eigenvalues of dirichlet laplacians and extensions the first author s work was partially supported by fondecyt chile project 0132 88 and by a summer research fellowship provided by the research council of the university of missouri columbia he would like to thank the physics department and others at the universidad de chile for their hospitality during his visit in april 1990 when much of this research was completed the second author was supported in part by fondecyt chile projects 0132 88 and 1238 90 both authors also thank fritz gesztesy for general comments and encouragement

automatic learning of cost functions for graph edit distance abstract graph matching and graph edit distance have become important tools in structural pattern recognition the graph edit distance concept allows us to measure the structural similarity of attributed graphs in an error tolerant way the key idea is to model graph variations by structural distortion operations as one of its main constraints however the edit distance requires the adequate definition of edit cost functions which eventually determine which graphs are considered similar in the past these cost functions were usually defined in a manual fashion which is highly prone to errors the present paper proposes a method to automatically learn cost functions from a labeled sample set of graphs to this end we formulate the graph edit process in a stochastic context and perform a maximum likelihood parameter estimation of the distribution of edit operations the underlying distortion model is learned using an expectation maximization algorithm from this model we finally derive the desired cost functions in a series of experiments we demonstrate the learning effect of the proposed method and provide a performance comparison to other models

pattern vectors from algebraic graph theory graph structures have proven computationally cumbersome for pattern analysis the reason for this is that before graphs can be converted to pattern vectors correspondences must be established between the nodes of structures which are potentially of different size to overcome this problem in this paper we turn to the spectral decomposition of the laplacian matrix we show how the elements of the spectral matrix for the laplacian can be used to construct symmetric polynomials that are permutation invariants the coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner we extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a hermitian property matrix that can be viewed as a complex analogue of the laplacian to embed the graphs in a pattern space we explore whether the vectors of invariants can be embedded in a low dimensional space using a number of alternative strategies including principal components analysis pca multidimensional scaling mds and locality preserving projection lpp experimentally we demonstrate that the embeddings result in well defined graph clusters our experiments with the spectral representation involve both synthetic and real world data the experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure the real world experiments show that the method can be used to locate clusters of graphs

an algorithm for weighted sub graph matching based on gradient flows an algorithm for matching the weighted sub graphs based on gradient flows is proposed in this paper first the smaller and larger graphs for matching are represented by means of their weighted adjacency matrices then an objective function is introduced to measure the differences between two weighted adjacency matrices because the permutation matrix for graph matching is usually relaxed to an orthogonal matrix with non negative elements an optimization based approach is adopted to navigate the solution toward an appropriate permutation matrix to accomplish this goal two gradient flows in the space of orthogonal matrices are defined in such a way that they minimize the objective functions one minimizes the objective function in the space of orthogonal matrices and the other minimizes the distance of an orthogonal matrix from the set of permutations in addition two cost functions are introduced to force satisfaction approximately of the constraint that a translation matrix must have integer entries of different values the experimental results show that the proposed sub graph matching is feasible

new binary linear programming formulation to compute the graph edit distance graph edit distance ged is a powerful and flexible graph matching paradigm that can be used to address different tasks in structural pattern recognition machine learning and data mining in this paper some new binary linear programming formulations for computing the exact ged between two graphs are proposed a major strength of the formulations lies in their genericity since the ged can be computed between directed or undirected fully attributed graphs i e with attributes on both vertices and edges moreover a relaxation of the domain constraints in the formulations provides efficient lower bound approximations of the ged a complete experimental study comparing the proposed formulations with 4 state of the art algorithms for exact and approximate graph edit distances is provided by considering both the quality of the proposed solution and the efficiency of the algorithms as performance criteria the results show that none of the compared methods dominates the others in the pareto sense as a consequence faced to a given real world problem a trade off between quality and efficiency has to be chosen w r t the application constraints in this context this paper provides a guide that can be used to choose the appropriate method

almost global existence for hamiltonian semilinear klein gordon equations with small cauchy data on zoll manifolds this paper is devoted to the proof of almost global existence results for klein gordon equations on zoll manifolds e g spheres of arbitrary dimension with hamiltonian nonlinearities when the cauchy data are smooth and small the proof relies on birkhoff normal form methods and on the specific distribution of eigenvalues of the laplacian perturbed by a potential on zoll manifolds 2007 wiley periodicals inc

hierarchical attributed graph representation and recognition of handwritten chinese characters abstract this paper presents a new method of recognizing handwritten chinese characters a structural representation called hierarchical attributed graph representation hagr is introduced to describe handwritten chinese characters the hagr provides a simple and direct representation of handwritten chinese characters with hagr the recognition process becomes a simple task of graph matching a cost function mapping a candidate to a model graph is introduced this approach can tolerate the variations of hagr which reflect the instabilities or variabilities of handwritten chinese characters resulting from different writing styles several rules have been introduced to rearrange the order of the vertices of the graphs in order to avoid the combinatorial explosion in graph matching in addition the database of the character models is organized in a search tree structure for a candidate character the search process to find a corresponding model character has been divided into a number of simple and local decisions at different levels of the tree this considerably improves the efficiency and accuracy of the matching process

inexact graph matching using genetic search this paper describes a framework for performing relational graph matching using genetic search there are three novel ingredients to the work firstly we cast the optimisation process into a bayesian framework by exploiting the recently reported global consistency measure of wilson and hancock as a fitness measure the second novel idea is to realise the crossover process at the level of subgraphs rather than employing string based or random crossover finally we accelerate convergence by employing a deterministic hill climbing process prior to selection since we adopt the bayesian consistency measure as a fitness function the basic measure of relational distance underpinning the technique is hamming distance our standpoint is that genetic search provides a more attractive means of performing stochastic discrete optimisation on the global consistency measure than alternatives such as simulated annealing moreover the action of the optimisation process is easily understood in terms of its action in the hamming distance domain we demonstrate empirically not only that the method possesses polynomial convergence time but also that the convergence rate is more rapid than simulated annealing we provide some experimental evaluation of the method in the matching of aerial stereograms and evaluate its sensitivity on synthetically generated graphs

the scaling network simplex algorithm in this paper we present a new primal simplex pivot rule and analyze the worst case complexity of the resulting simplex algorithm for the minimum cost flow the assignment and the shortest path problems we consider networks with n nodes m arcs integral arc capacities bounded by an integer number u and integral arc costs whose magnitudes are bounded by an integer number c our pivot rule may be regarded as a scaling version of dantzig s pivot rule our pivot rule defines a threshold value which is initially at most 2c and the rule permits any arc with a violation of at least 2 to be the editing variable we select the leaving arc so that strong feasibility of the basis is maintained when there is no arc satisfying this rule then we replace by 2 and repeat the process the algorithm terminates when 1 we show that the simplex algorithm using this rule performs o nmu log c pivots and can be implemented to run in o m2u log c time specializing these results for the assignment and short

long time sobolev stability for small solutions of quasi linear klein gordon equations on the circle we prove that higher sobolev norms of solutions of quasi linear klein gordon equations with small cauchy data on s 1 remain small over intervals of time longer than the ones given by local existence theory this result extends previous ones obtained by several authors in the semi linear case the main new difficulty one has to cope with is the loss of one derivative coming from the quasi linear character of the problem the main tool used to overcome it is a global paradifferential calculus adapted to the sturm liouville operator with periodic boundary conditions

birkhoff normal form for partial differential equations with tame modulus we prove an abstract birkhoff normal form theorem for hamiltonian partial differential equations pdes the theorem applies to semilinear equations with nonlinearity satisfying a property that we call tame modulus such a property is related to the classical tame inequality by moser in the nonresonant case we deduce that any small amplitude solution remains very close to a torus for very long times we also develop a general scheme to apply the abstract theory to pdes in one space dimensions and we use it to study some concrete equations nonlinear wave nlw equation nonlinear schrodinger nls equation with different boundary conditions an application to an nls equation on the d dimensional torus is also given in all cases we deduce bounds on the growth of high sobolev norms in particular we get lower bounds on the existence time of solutions