tunnelling in multidimensional systems tunnelling is examined from the point of view of analytic continuation of lagrangian manifolds this enables an intrinsically multidimensional approach to many problems we illustrate the ideas by computing energy splittings between congruent tori in a number of integrable systems the examples include an integrable but non separable system which cannot be solved by reduction to one dimensional systems the calculations can all be viewed in a geometrical way that does not make explicit use of separation of coordinates

scaling up cosine interesting pattern discovery a depth first method this paper presents an efficient algorithm called cosminer t for interesting pattern discovery the widely used cosine similarity found to possess the null invariance property and the anti cross support pattern property is adopted as the interestingness measure in cosminer t cosminer t is generally an fp growth like depth first traversal algorithm that rests on an important property of the cosine similarity the conditional anti monotone property camp the combined use of camp and the depth first support ascending traversal strategy enables the pre pruning of uninteresting patterns during the mining process of cosminer t extensive experiments demonstrate the high efficiency of cosminer t in interesting pattern discovery in comparison to the breath first strategy and the post evaluation strategy in particular cosminer t shows its capability in suppressing the generation of cross support patterns and discovering rare but truly interesting patterns finally an interesting case of landmark recognition is presented to illustrate the value of cosine interesting patterns found by cosminer t in real world applications

the lax pairs for the holt system by using the known relation between the holt system and the henon heiles system the lax pairs for all the integrable cases of the holt system are constructed from the known lax representations for the henon heiles system

configurational invariants of hamiltonian systems in this paper we explore the general conditions in order that a two dimensional natural hamiltonian system possess a second invariant which is a polynomial in the momenta and is therefore liouville integrable we examine the possibility that the invariant is preserved by the hamiltonian flow on a given energy hypersurface only weak integrability and derive the additional requirement necessary to have conservation at arbitrary energy strong integrability using null complex coordinates we show that the leading order coefficient of the polynomial is an arbitrary holomorphic function in the case of weak integrability and a polynomial in the coordinates in the strongly integrable one we review the results obtained so far with strong invariants up to degree four and provide some new examples of weakly integrable systems with linear and quadratic invariants

separation of variables for the generalized henon heiles system and system with quartic potential we consider two well known integrable systems on the plane using the concept of natural poisson bivectors on riemannian manifolds a geometric approach to construction of variables of separation and separated relations for the generalized henon heiles system and the generalized system with quartic potential is discussed in detail

a theory of exact and approximate configurational invariants abstract a theory of integrable hamiltonian systems in two dimensions is formulated and applied the four dimensional phase space problem that is the vanishing of the poisson bracket between another invariant and the hamiltonian is here reduced to the solution of a series of two dimensional configuration space equations the theory is also applicable to more than two dimensions the constraints are found which admit to integrability of the orbits for magnetic or coriolis forces as well as for forces derivable from a potential when a system admits a given invariant the invariant is found for example by quadrature a number of examples including known and apparently previously unknown invariants are given the theory of exact integrals of the motion also can be extended to the derivation of approximate invariants the orbital structure of integrable or approximately integrable systems correlates with the degree maximum power of the velocity of a standardized invariant the theory admits a variational principle among other approximation techniques for the computation of a best approximate invariant the problem of the general cubic potential with one symmetric coordinate v 1 2 ax 2 1 2 by 2 cx 2 y 1 3 dy 3 of which the well studied henon heiles potential is the special case for a b and c d is examined in detail

a generalized henon heiles system and related integrable newton equations a detailed description is given of integrable cases of the generalized henon heiles systems which differs from the standard h h ones by the term q22 their connection with fifth order one component soliton equations is discussed lax representations are constructed and the bi hamiltonian formulation of dynamics is given it is also shown that the gh h system can be mapped onto another system of newton equations with a nonstandard hamiltonian structure

topology and bifurcations of the invariant level sets of a fokker planck hamiltonian through two coupled anisotropic quartic anharmonic oscillators integrable hamiltonians with velocity dependent potentials including those of fokker planck hamiltonians h px2 py2 kxpx kypy are constructed from integrable hamiltonians of type h px2 py2 v x y in order to carry out the analytical investigations we convert the problem into that of two coupled anisotropic quartic anharmonic oscillators using certain canonical transformations afterwards we give a complete description of the real phase space topology of the system we give also an explicit periodic solution for singular common level sets of the first integrals all generic bifurcations of liouville tori were determined analytically and numerically

cubic theta functions abstract the theory of the cubic theta function q m 2 m n n 2 z 1 m z 2 n is developed analogously to the theory of the classical jacobian theta functions many inversion formulas addition formulas and modular equations are derived and these results extend previous work on cubic theta functions

looking for a structural characterization of the sparseness measure of frequent closed itemset contexts it is widely recognized that the performances of frequent pattern mining algorithms are closely dependent on data being handled i e sparse or dense the same situation applies to the efficiency of concise representations of frequently occurring patterns with respect to the extraction task and the obtained compactness rates as well as for other data mining techniques such as clustering and for the mining algorithms of different pattern classes such as hypergraphs in this paper we raise a fundamental question how can we formally define the sparseness of an arbitrary context and assess its value as an answer based on the framework of the succinct system of minimal generators we present an innovative characterization of context sparseness as well as a new sparseness measure which results from the aggregation of two complementary measures namely the succinctness and compactness measures of each equivalence class induced by the galois closure operator experiments carried out mainly attain a finer classification of benchmark contexts and then confirm our viewpoint that the dense and sparse labels are not absolute

quasi point separation of variables for the henon heiles system and a system with a quartic potential we examine the problem of integrability of two dimensional hamiltonian systems by means of separation of variables a systematic approach to the construction of the special non pure coordinate separation of variables for certain natural two dimensional hamiltonians is proposed

fiut a new method for mining frequent itemsets this paper proposes an efficient method the frequent items ultrametric trees fiut for mining frequent itemsets in a database fiut uses a special frequent items ultrametric tree fiu tree structure to enhance its efficiency in obtaining frequent itemsets compared to related work fiut has four major advantages first it minimizes i o overhead by scanning the database only twice second the fiu tree is an improved way to partition a database which results from clustering transactions and significantly reduces the search space third only frequent items in each transaction are inserted as nodes into the fiu tree for compressed storage finally all frequent itemsets are generated by checking the leaves of each fiu tree without traversing the tree recursively which significantly reduces computing time fiut was compared with fp growth a well known and widely used algorithm and the simulation results showed that the fiut outperforms the fp growth in addition further extensions of this approach and their implications are discussed

efficient mining of weighted interesting patterns with a strong weight and or support affinity most algorithms for frequent pattern mining use a support constraint to prune the combinatorial search space but support based pruning is not enough after mining datasets to obtain frequent patterns the resulting patterns can have weak affinity although the minimum support can be increased it is not effective for finding correlated patterns with increased weight and or support affinity interesting measures have been proposed to detect correlated patterns but any approach does not consider both support and weight in this paper we present a new strategy weighted interesting pattern mining wip in which a new measure weight confidence is suggested to mine correlated patterns with the weight affinity a weight range is used to decide weight boundaries and an h confidence serves to identify support affinity patterns in wip without additional computation cost original h confidence is used instead of the upper bound of h confidence for performance improvement wip not only gives a balance between the two measures of weight and support but also considers weight affinity and or support affinity between items within patterns so more correlated patterns can be detected to our knowledge ours is the first work specifically to consider weight affinity between items of patterns a comprehensive performance study shows that wip is efficient and scalable for finding affinity patterns moreover it generates fewer but more valuable patterns with the correlation to decrease the number of thresholds w confidence h confidence and weighted support can be used selectively according to requirement of applications

investigation of painleve property under time singularities transformations in this paper the relation between the painleve property for ordinary differential equations and some coordinate transformations in the complex plane is investigated two sets of transformations are introduced for which the transformations of singularities structure in the complex plane are explicitly computed the first set acts only on the dependent variables while the second one acts also on the independent variables it allows for defining an extended painleve test which is coordinates invariant our results are applied on various problems arising in the singularity analysis such as the problem of negative resonances and the weak painleve conjecture the method for finding new first integrals for dynamical systems is also shown

the master integrable two dimensional system with a quartic second integral in this paper we construct a new integrable natural conservative mechanical system admitting a second invariant of the fourth degree in velocities this system is quite general and involves 21 parameters we also show that all systems with a quartic integral known up to date can be obtained from it as special cases by a relevant choice of the values of parameters the results are applied to problems of particle and rigid body dynamics new integrable cases are obtained as special versions of the new system these cases include motions in a plane lobachevsky plane sphere and surfaces of variable curvature they also include generalizations of the classical cases of kovalevskaya chaplygin and goriatchev with the addition of certain singular terms to the potential

indecomposable quadratic spaces over the affine plane let k be a field of characteristic f2 it is by now a well known theorem of harder 4 p 1861 that any quadratic space over the polynomial ring k x in one variable is extended from k and hence is decomposable it is also known that quadratic spaces of ranks 62 and isotropic quadratic spaces of all ranks over k x a are extended from k for any rn and hence are again decomposable 8 proposition 1 1 5 111 however if k admits of a quaternion division algebra then there do exist indecomposable anisotropic quadratic spaces of ranks 3 and 4 over k x y 3 sect 63 recently indecomposable positive definite quadratic spaces of rank 4n over rw x y were constructed for each n 3 1 6 using a classification of these spaces in terms of linear algebraic data these results motivate the following question let k be a field of characteristic 22 which admits of an anisotropic quadratic space q of rank 3 3 does there exist an indecomposable quadratic space over k x y whose reduction modulo the variables is isometric to q the aim of this paper is to answer this question in the affirmative we in fact prove that if a1 a is an anisotropic quadratic space of rank 3 3 over k then there exist infinitely many inequivalent indecomposable quadratic spaces over k x y whose reductions modulo a y are isometric to i r i the idea of the proof is to start with rank 3 indecomposable quadratic spaces and to build inductively higher rank spaces by the process of glueing for a construction of a rank 6 indecomposable quadratic space over lr x y using a glueing technique see 2 sect 31 the indecomposability is achieved thanks to the rigidity properties of isometries of anisotropic spaces

on the hbar2 correction terms in quantum integrability the authors study the question of quantum integrability for two dimensional hamiltonian systems with special attention on the 2 correction terms in the potential a class of hamiltonians of type h 1 2 px2 py2 v4y4 y2 f2 x 6 f0 x with a second invariant of type i px4 a x y px2 b x y pxpy c x y py2 d x y is considered the general solution for f2 involves elliptic integrals for quantum integrability the potential must be modified with 2 dependent terms they construct a point transformation which after coupling constant metamorphosis takes the hamiltonian to a new quantum integrable hamiltonian for which no correction terms are necessary the new system does not in general have a flat space kinetic part

a local global principle for quadratic forms over polynomial rings if further k has no real completion i e k is either a totally imaginary number field or a function field then every quadratic space over k of rank 5 is isotropic and in view of a theorem of ojanguren 5 it follows that any quadratic space of rank 5 over k x x is extended from k so that theorem 1 in this case holds for all quadratic spaces without restriction on the rank our proof of theorem 1 uses the following result which seems to be of some independent interest

on the connection between hyperelliptic separability and painleve integrability we consider systems of odes which are associated with some physically significant examples shallow water equilibrium solutions travelling waves of the harry dym equation a lotka volterra system of competing species and the geodesic flow on the triaxial ellipsoid the first three are shown to share the following properties i they are hyperelliptically separable systems hss and after a suitable nonlinear time transformation become algebraically completely integrable aci and ii they are of the weak painleve type and become full painleve after the application of this transformation the geodesic flow on the other hand although it passes the usual painleve test does not possess a full set of free constants and thus one may not conclude whether it has the painleve property or not this system is also hss and becomes aci after the application of a suitable nonlinear time transformation we also combine our geometric analytical investigation with a numerical analysis of the system in the complex plane and show that there is perfect correspondence between the results of the two approaches this correspondence strengthens the reliability of such numerical studies and helps us better understand their implication in cases where such nonlinear transformations to complete integrability are not available

a new class of integrable systems we present a family of dynamical systems associated with the motion of a particle in two space dimensions these systems possess a second integral of motion quadratic in velocities apart from the hamiltonian and are thus completely integrable they were found through the derivation and subsequent resolution of the integrability condition in the form of a partial differential equation pde for the potential a most important point is that the same pde was derived through considerations on the analytic structure of the singularities of the solutions weak painleve property

an algorithm to mine general association rules from tabular data most methods for mining association rules from tabular data mine simple rules which only use the equality operator in their items for quantitative attributes approaches tend to discretize domain values by partitioning them into intervals limiting the operator only to results in many interesting frequent patterns that may not be identified it is obvious that where there is an order between objects operators such as greater than or less than a given value are as important as the equality operator this motivates us to extend association rules from the simple equality operator to a more general set of operators we address the problem of mining general association rules in tabular data where rules can have all operators in their antecedent part the proposed algorithm mining general rules mgr is applicable to datasets with discrete ordered attributes and on quantitative discretized attributes the proposed algorithm stores candidate general itemsets in a tree structure in such a way that supports of complex itemsets can be recursively computed from supports of simpler itemsets the algorithm is shown to have benefits in terms of time complexity memory management and has good potential for parallelization

canonical transformation between integrable henon heiles systems a canonical transformation between two known integrable cases of the h enon heiles systems is given and the separation of variables for the corresponding hamilton jacobi equations is discussed

higher order superintegrability of a holt related potential in a recent paper post and winternitz 2011 j phys a math theor 44 162001 studied the properties of two dimensional euclidean potentials that are linear in one of the two cartesian variables in particular they proved the existence of a potential endowed with an integral of third order and an integral of fourth order in this paper we show that these results can be obtained in a more simple and direct way by noting that this potential is directly related to the holt potential it is proved that the existence of a potential with higher order superintegrability is a direct consequence of the integrability of the family of holt type potentials

high utility pattern mining using the maximal itemset property and lexicographic tree structures the problem of high utility mining is discovering all of the high utility itemsets in a transactional database most algorithms find high utility itemsets in two steps the first step identifies all of the potential itemsets the second step then determines the high utility itemsets from the set of potential itemsets the large number of potential itemsets in the first step is generally the mining bottleneck if we can reduce the number of potential itemsets the mining performance can be improved significantly in this paper we use a maximal itemset property and propose an algorithm called ummi high utility mining using the maximal itemset property to significantly reduce the number of potential itemsets in the first step in the second step ummi uses an effective lexicographic tree structure to determine all of the high utility itemsets in general ummi outperforms all three of the previously used algorithms including ctu pro an optimized twu mining algorithm and two phase in our experiments using synthetic datasets on average ummi is 5 3 and 7 times faster than ctu pro twu mining and two phase respectively in a real data experiment ummi is 6 times faster than two phase the other two algorithms are not capable of completing the mining step in a reasonable amount of time ummi uses an approximately fixed amount of memory which is generally less than the other algorithms for each mining the experimental results show that the proposed algorithm can mine the high utility itemsets efficiently in addition ummi is linearly scalable with respect to the number of transactions

cluster ensembles a knowledge reuse framework for combining multiple partitions this paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings we first identify several application scenarios for the resultant knowledge reuse framework that we call cluster ensembles the cluster ensemble problem is then formalized as a combinatorial optimization problem in terms of shared mutual information in addition to a direct maximization approach we propose three effective and efficient techniques for obtaining high quality combiners consensus functions the first combiner induces a similarity measure from the partitionings and then reclusters the objects the second combiner is based on hypergraph partitioning the third one collapses groups of clusters into meta clusters which then compete for each object to determine the combined clustering due to the low computational costs of our techniques it is quite feasible to use a supra consensus function that evaluates all three approaches against the objective function and picks the best solution for a given situation we evaluate the effectiveness of cluster ensembles in three qualitatively different application scenarios i where the original clusters were formed based on non identical sets of features ii where the original clustering algorithms worked on non identical sets of objects and iii where a common data set is used and the main purpose of combining multiple clusterings is to improve the quality and robustness of the solution promising results are obtained in all three situations for synthetic as well as real data sets

a unified treatment of quartic invariants at fixed and arbitrary energy two dimensional hamiltonian systems admitting second invariants which are quartic in the momenta are investigated using the jacobi geometrization of the dynamics this approach allows for a unified treatment of invariants at both arbitrary and fixed energy in the differential geometric picture the quartic invariant corresponds to the existence of a fourth rank killing tensor expressing the jacobi metric in terms of a kahler potential the integrability condition for the existence of the killing tensor at fixed energy is a nonlinear equation involving the kahler potential at arbitrary energy further conditions must be imposed which lead to an overdetermined system with isolated solutions we obtain several new integrable and superintegrable systems in addition to all previously known examples

hamiltonians with high order integrals and the weak painleve concept we examine the singularity structure of the equations of motion associated to integrable two dimensional hamiltonians with second integrals of order higher than 2 we show in these specific examples that the integrability is associated to a singularity expansion of the weak painleve type new cases of integrability are discovered with still higher order integrals which are explicitly computed

linearization on a submanifold of integrable hamiltonians with polynomials potentials abstract following a method proposed by j weiss we linearize the integrable hamiltonians with quartic potentials as well as the remaining integrable cubic potentials a non generic solution is obtained in each case we explain this phenomenon in terms of a constraint submanifold over which the solution of the system is in fact linearizable we show that the linearization approach can depending on the particular case lead to generic solutions non generic ones or even to no solutions at all

integrability of hamiltonians with third and fourth degree polynomial potentials the weak painleve property as a criterion of integrability is applied to the case of simple hamiltonians describing the motion of a particle in two dimensional polynomial potentials of degree three and four this allows a complete identification of all the integrable cases of cubic potentials in the case of quartic potentials although our results are not exhaustive some new integrable cases are discovered in both cases the integrability is explicited by a direct calculation of the second integral of motion of the system

symmetries of hamiltonian systems with two degrees of freedom we classify the lie point symmetry groups for an autonomous hamiltonian system with two degrees of freedom with the exception of the harmonic oscillator or a free particle where the dimension is 15 we obtain all dimensions between 1 and 7 for each system in the classification we examine integrability

symmetries separability and volume forms in order to clarify certain misconceptions in the literature we discuss the details of the way determining equations for general symmetries of a lagrangian system differ from determining equations for noether symmetries and establish the minimal set of extra conditions which have to be imposed in practical situations for the former to reduce to the latter we further derive properties by which in situations where the system is integrable through quadratic integrals in involution the components of the corresponding noether symmetries themselves can be used to compute the separation variables if they exist for the hamilton jacobi equation

explicit integrability for hamiltonian systems and the painleve conjecture we analyze a class of hamiltonian systems in two dimensions for which we proved that a second constant of motion exists it is shown that using the two first integrals the equations of motion can be written in a form which allows their integration by quadratures an analysis of the equations of motion in this reduced form establishes the behavior of the solutions in the complex time plane it is shown explicitly that the systems belonging to this class possess the weak painleve property i e their solutions in complex time can present singularities of a specific algebraic type

integrability of toda lattice by generalized variational symmetry approach a systematic method of finding nontrivial generalized variational symmetries are presented herein and the corresponding first integrals for nonlinear dynamical system with two degrees of freedom are derived then a method is applied to a toda lattice given by the potential v ex y c1e2y c2ey c3e 2x c4 e x where c1 c2 c3 and c4 are parameters the symmetries and constants of motion are presented explicitly

quasi periodic and periodic solutions for coupled nonlinear schrodinger equations of manakov type we consider travelling periodic and quasi periodic wave solutions in coupled nonlinear schrodinger equations in fibre optics these equations can be used to model single mode fibres with strong birefringence and two mode optical fibres recently these equations appear as a model describing pulse pulse interactions in wavelength division multiplexed channels of optical fibre transmission systems in some cases this model reduces to the integrable manakov system ims two phase quasi periodic solutions for the ims are given in terms of two dimensional kleinian functions the reduction of quasi periodic solutions to elliptic functions is discussed new solutions are found in terms of generalized hermite polynomials which are associated with two gap treibich verdier potentials

lax representation for two particle dynamics splitting on two tori the lax representation in terms of matrices is constructed for separable multiply periodic systems splitting on two tori hyperelliptic kleinian functions and their reduction to elliptic functions are used

a note on integrable two degrees of freedom hamiltonian systems with a second integral quartic in the momenta two of the simplest integrable hamiltonians h x y px py px2 py2 2 v x y with a second integral quartic in the momenta are those with potentials v3 x y by 3x2 16y2 d x2 16y2 eta y and v4 x y a x4 6x2y2 8y4 c x2 4y2 vy 2 we show how v3 can be obtained from v4 in the process we obtain a new potential of the class vn that includes both v3 and v4 as particular cases for this potential we give the second integral of motion separating variables a lax representation and a bi hamiltonian structure thus synthesizing the corresponding results for potentials v3 and v4 the integrable extension vn mu x 2 is also discussed

exact solutions to a nonlinear reaction diffusion equation and hyperelliptic integrals inversion an approach is proposed to obtain some exact explicit stationary solutions in terms of elliptic functions to a nonlinear reaction diffusion equation the method is based on the reduction of the hyperelliptic integral to the elliptic one and its inversion via the weierstrass and jacobi elliptic functions the solutions for both polynomial reaction and diffusion functions include bounded periodic and localized in space functions such solutions seem to be the best candidates to describe periodic nanostructures observed in experiments on formation of thin films by means of molecular epitaxy the so called quantum wires generalization of the approach is discussed for reaction and diffusion functions distinctive from polynomials in particular explicit stationary solutions are found in terms of elliptic functions for arbitrary diffusion and relevant reaction terms

the he non heiles system revisited abstract the known integrable cases of the henon heiles system are shown to be closely related to the stationary flows of the known and only integrable fifth order single component and polynomial nonlinear evolution equations this is further evidence that these are the only integrable cases of the henon heiles system lax pairs are deduced for each of the integrable cases and used to construct the constants of motion a curious lax operator recently found by the painleve method is explained

completely integrable 2d lagrangian systems and related integrable geodesic flows on various manifolds in this study we have formulated a theorem that generates deformations of the natural integrable conservative systems in the plane into integrable systems on riemannian and other manifolds by introducing additional parameters into their structures the relation of explicit solutions of the new and the original dynamics to the corresponding jacobi maupertuis geodesic flow is clarified for illustration we apply the result to three concrete examples of the many available integrable systems in the literature complementary integrals in those systems are polynomial in velocity with degrees 3 4 and 6 respectively as a special case of the first deformed system a new several parameter family of integrable mechanical systems and geodesic flows on s2 is constructed

integration of a generalized henon heiles hamiltonian the generalized henon heiles hamiltonian h 1 2 px2 py2 c1x2 c2y2 axy2 bx3 3 with an additional nonpolynomial term y 2 is known to be liouville integrable for three sets of values of b a c1 c2 it has been previously integrated by genus two theta functions only in one of these cases defining the separating variables of the hamilton jacobi equations we succeed here in the two other cases to integrate the equations of motion with hyperelliptic functions

adaptive estimated maximum entropy distribution model the estimation of distribution algorithm eda model is an optimization procedure through learning and sampling a conditional probabilistic function the use of conditional density function permits multivariate dependency modelling which is not captured in a population based representation like the classical genetic algorithms the gaussian model is a simple and widely used model for density estimation however an assumption of normality is not realistic for many real life problems alternatively the maximum entropy model can be used which makes no assumption of a normal distribution one disadvantage of the maximum entropy model is the learning cost of its parameters this paper proposes an adaptive estimated maximum entropy distribution adaptive meed model which aims to reduce learning complexity of building a model adaptive meed exploits the fact that samples have a low average fitness in the early stage but they gradually converge to an optima towards the end of the search hence it is not necessary to inference the model with a full account of observed constraints in the early stage of the search the proposed model attempts to estimate the density function with a dynamic set of samples and active constraints in addition the proposed model includes a global sampling function to address the issue of a missing mutation operator the ergodic convergence properties of the proposed model are discussed with the markov chain analysis the preliminary experimental evaluation shows that the proposed model performs well against genetic algorithms on several clustering problems

adjoint symmetries separability and volume forms two results of a preceding paper are generalized the first is about characterizing to what extent preservation of the energy function of a lagrangian of mechanical type turns dynamical symmetries into noether symmetries the generalization here is twofold polynomial integrals of arbitrary degree are considered and the kinetic energy can have an arbitrary metric the second result here again for arbitrary metrics is about the way separation variables for the hamilton jacobi equation when they are ensured to exist by eisenhart s theorem can be computed in principle from a factorization property of a certain volume form the main novelty in the way the generalizations are discussed is that the emphasis is shifted from symmetries to the dual concept of adjoint symmetries

the singularity analysis for nearly integrable systems homoclinic intersections and local multivaluedness abstract in this study a new perturbative scheme for nonintegrable ordinary differential equations is proposed these perturbative expansions are based on the singularity analysis of the unperturbed system and is performed in the neighborhood of its singularities under suitable conditions on the homoclinic structure of the unperturbed system the melnikov vector can be computed based on the knowledge of the laurent expansions of the solutions the existence of transverse homoclinic intersections is therefore explicitly related to the existence of critical points for the solutions in the complex plane of the independent variable

cosine interesting pattern discovery recent years have witnessed an increasing interest in computing cosine similarity between high dimensional documents transactions and gene sequences etc most previous studies limited their scope to the pairs of items which cannot be adapted to the multi itemset cases therefore from a frequent pattern mining perspective there exists still a critical need for discovering interesting patterns whose cosine similarity values are above some given thresholds however the knottiest point of this problem is the cosine similarity has no anti monotone property to meet this challenge we propose the notions of conditional anti monotone property and support ascending set enumeration tree sa set we prove that the cosine similarity has the conditional anti monotone property and therefore can be used for the interesting pattern mining if the itemset traversal sequence is defined by the sa set we also identify the anti monotone property of an upper bound of the cosine similarity which can be used in further pruning the candidate itemsets an apriori like algorithm called cosminer is then put forward to mine the cosine interesting patterns from large scale multi item databases experimental results show that cosminer can efficiently identify interesting patterns using the conditional anti monotone property of the cosine similarity and the anti monotone property of its upper bound even at extremely low levels of support

when is a hamiltonian system separable the hamiltonian system given by h 1 2 p2 v q with v c rn is considered a method for integrating such a system is that of separating the variables in the hamilton jacobi equation it is known that if such a separation is possible then it can take place only when the equation is expressed in terms of generalized elliptic coordinates or in a degeneration of these a criterion is proposed for deciding if separation is possible and if it is in which degeneration of elliptic coordinates it takes place

itemset generalization with cardinality based constraints abstract generalized itemset mining is an established data mining technique that focuses on discovering high level correlations among large databases by exploiting a taxonomy built over the data items items are aggregated into higher level concepts and thus data correlations at different abstraction levels can be discovered however since a large number of patterns can be extracted the result of the mining process is often not easily manageable by domain experts we propose a novel approach to discovering a compact subset of generalized itemsets from structured data to guarantee model conciseness and readability a set of itemsets that has a common generalization is generated only when its cardinality is so small that its manual inspection is practically feasible furthermore generalizations are generated only when their knowledge is covered by a large number of low level descendant itemsets and the generalizations are worth considering in place of their many low level descendants only in these cases experiments performed on synthetic benchmark and real data taken from a mobile application scenario demonstrate the effectiveness and efficiency of the proposed approach

how to construct integrable fokker planck and electromagnetic hamiltonians from ordinary integrable hamiltonians integrable hamiltonians with velocity dependent potentials including those of fokker planck type h 1 2 p2x p2y kxpx kypy are constructed from integrable hamiltonians of type h 1 2 p2x p2y v x y using certain canonical and noncanonical transformations some of the hamiltonians obtained this way are integrable only for zero energy candidates for the potential which is of interest for fokker planck models are constructed in several cases

new bi hamiltonian systems on the plane we discuss several new bi hamiltonian integrable systems on the plane with integrals of motion of third fourth and sixth orders in momenta the corresponding variables of separation separated relations compatible poisson brackets and recursion operators are also presented in the framework of the jacobi method

lie symmetries of the lorenz model abstract we study the generalized symmetries of the lorenz model to find the parameter values at which one or more time dependent integrals of motion exist in these cases the integrals are found trivially from the symmetries themselves a complete study of the one completely algebraically integrable case shows a the dynamics can be integrated exactly by reducing it first to a lower dimensional system b the symmetry vector field is hamiltonian these facts hold for other dissipative completely integrable dynamical systems as well the analytic study of a natural two form reveals that it is an entire function of time the foliation of phase space induced by the two form for the partially integrable cases has a simple description in terms of the coefficients occurring in the laurent series expansions of the dependent variables

indecomposable quadratic bundles of rank 4n over the real affine plane keywords real affine plane quadratic space extended from subring hermitian bundle non extended quadratic spaces indecomposable quadratic bundles indecomposable quadratic spaces reference cma article 1983 001doi 10 1007 bf02095998 record created on 2008 12 16 modified on 2016 08 08

quadratic spaces over laurent extensions of dedekind domains let abea dedekind domain in which 2 is invertible we show in this paper that any isotropic quadratic space over r t 7 1 is isometric to n ii q q hip with rank p n where if p denotes the hyperbolic space 1 some preliminary results in this section we prove some lemmas which will be used in the later sections we assume throughout the paper that in all the rings considered 2 is invertible if a q2 are quadratic spaces over r a j tq2 denotes the quadratic space a r r t t x l t a2 r r t t x over r t t x

image categorization graph edit distance edge direction histogram this paper presents a novel algorithm for computing graph edit distance ged in image categorization this algorithm is purely structural i e it needs only connectivity structure of the graph and does not draw on node or edge attributes there are two major contributions 1 introducing edge direction histogram edh to characterize shape features of images it is shown that ged can be employed as distance of edhs this algorithm is completely independent on cost function which is difficult to be defined exactly 2 computing distance of edhs with earth mover distance emd which takes neighborhood bins into account so as to compute distance of edhs correctly a set of experiments demonstrate that the newly presented algorithm is available for classifying and clustering images and is immune to the planar rotation of images compared with ged from spectral seriation our algorithm can capture the structure change of graphs better and consume 12 79 time used by the former one the average classification rate is 5 and average clustering rate is 25 higher than the spectral seriation method

construction of new integrable hamiltonians in two degrees of freedom a new procedure for deriving integrable hamiltonians and their constants of the motion is introduced we term this procedure the truncation program integrable hamiltonians occurring in the truncation program possess constants of the motion which are polynomials in a perturbation parameter e the relationship between this program and the whittaker program in two degrees of freedom is discussed integrable hamiltonians occurring in the whittaker program a generalization of whittaker s work possess constants of the motion which are polynomials in the momentum coordinates many previously known integrable hamiltonians are derived a new family of integrable double resonance hamiltonians and a new family of integrable hamiltonians of the form p21 p22 2 v q1 q2 are derived

an order clique based approach for mining maximal co locations most algorithms for mining spatial co locations adopt an apriori like approach to generate size k prevalence co locations after size k 1 prevalence co locations however generating and storing the co locations and table instances is costly a novel order clique based approach for mining maximal co locations is proposed in this paper the efficiency of the approach is achieved by two techniques 1 the spatial neighbor relationships and the size 2 prevalence co locations are compressed into extended prefix tree structures which allows the order clique based approach to mine candidate maximal co locations and co location instances and 2 the co location instances do not need to be stored after computing some characteristics of the corresponding co location which significantly reduces the execution time and space required for mining maximal co locations the performance study shows that the new method is efficient for mining both long and short co location patterns and is faster than some other methods in particular the join based method and the join less method

separability and lax pairs for henon heiles system the hamiltonian system corresponding to the generalized henon heiles hamiltonian h 1 2 px2 py2 1 2ax2 1 2by2 x2y ey3 is known to be integrable in the following three cases a b e 1 3 e 2 b 16a e 16 3 in the first two the system has been integrated by making use of genus one and genus two theta functions we show that in the third case the system can also be integrated by making use of elliptic functions finally using the fairbanks theorem we find lax pairs for each of the three integrable systems under consideration

painleve conjecture revisited the discovery of new integrable two dimensional hamiltonian systems is reported the analytic structure of the solutions makes necessary the generalization of the painlev e conjecture a widely used integrability criterion such a generalization is presented which the authors believe should replace the usual conjecture for two dimensional hamiltonian systems it is indeed compatible with all the systems already found and in addition leads to still new integrable cases

mining maximal hyperclique pattern a hybrid search strategy a hyperclique pattern is a new type of association pattern that contains items which are highly affiliated with each other specifically the presence of an item in one transaction strongly implies the presence of every other item that belongs to the same hyperclique pattern in this paper we present an algorithm for mining maximal hyperclique patterns which specifies a more compact representation of hyperclique patterns and are desirable for many applications such as pattern based clustering our algorithm exploits key advantages of both the depth first search dfs strategy and the breadth first search bfs strategy indeed we adapt the equivalence pruning method one of the most efficient pruning methods of the dfs strategy into the process of the bfs strategy our experimental results show that the performance of our algorithm can be orders of magnitude faster than standard maximal frequent pattern mining algorithms particularly at low levels of support

on the structure of picard fuchs type equations for liouville arnold integrable hamiltonian system on cotangent phase spaces there are studied in detail the structure properties of integral submanifold imbedding mapping for a class of algebraically liouville integrable hamiltonian systems on cotangent phase spaces and related with it so called picard fuchs type equations it is shown that these equations can be in general regularly constructed making use of a given a priori system of involutive invariants and proved that their solutions in the hamolton jacobi separable variable case give rise exactly to the integral submanifold imbedding mapping being as known a main ingredient for liouville arnold integrability by quadratures of the hamiltonian system under regard

the stackel systems and algebraic curves we show how the abel jacobi map provides all the principal properties of an ample family of integrable mechanical systems associated to hyperelliptic curves we prove that derivative of the abel jacobi map is just the stackel matrix which determines n orthogonal curvilinear coordinate systems in a flat space the lax pairs r matrix algebras and explicit form of the flat coordinates are constructed an application of the weierstrass reduction theory allows us to construct several flat coordinate systems on a common hyperelliptic curve and to connect among themselves different integrable systems on a single phase space

treibich verdier potentials and the stationary m kdv hierarchy here x x col co3 denotes the elliptic weierstrass function with fundamental periods f p 2a l 2co3 im co3 wl 5 0 see 1 ch 18 in the special case where col is real and co3 is purely imaginary the potential q is real valued and ince s striking result 31 in modern spectral theoretic terminology yields the fact that the self adjoint operator l associated with the differential expression d 2 q in l2 ir has a finite gap spectrum of the type