semi supervised metric learning via topology preserving multiple semi supervised assumptions learning an appropriate distance metric is a critical problem in pattern recognition this paper addresses the problem of semi supervised metric learning we propose a new regularized semi supervised metric learning rssml method using local topology and triplet constraints our regularizer is designed and developed based on local topology which is represented by local neighbors from the local smoothness cluster low density and manifold information point of view the regularizer is then combined with the large margin hinge loss on the triplet constraints in other words we keep a large margin between different labeled samples and in the meanwhile we use the unlabeled samples to regularize it then the semi supervised metric learning method is developed we have performed experiments on classification using publicly available databases to evaluate the proposed method to our best knowledge this is the only method satisfying all the three semi supervised assumptions namely smoothness cluster low density and manifold experimental results have shown that the proposed method outperforms state of the art semi supervised distance metric learning algorithms

generalized conformal pseudo galilean algebras and their casimir operators a generalization of the conformal galilei algebra with levi subalgebra isomorphic to is introduced and a virtual copy of the latter in the enveloping algebra of the extension is constructed explicit expressions for the casimir operators are obtained from the determinant of polynomial matrices for the central factor algebra an exact formula giving the number of invariants is obtained and a procedure to compute invariant functions that do not depend on the variables of the levi subalgebra is developed it is further shown that such solutions determine complete sets of invariants provided that the relation is satisfied

n dimensional superintegrable systems from symplectic realizations of lie coalgebras the construction of n dimensional nd integrable systems from coalgebras is reviewed in the case of poisson coalgebras a necessary condition for the integrability of the nd coalgebra hamiltonian coming from a given coalgebra is obtained in terms of the dimension of the symplectic realization and the number of nonlinear casimir functions from this viewpoint the full set of three four and five dimensional lie poisson coalgebras is analysed and many new families of multiparametric nd integrable systems coming from the cases that fulfil the integrability condition are obtained including the explicit form of the integrals of the motion the superintegrability of these hamiltonians is also emphasized and the generalization of the whole construction to the quantum mechanical case is straightforward

an algorithm to calculate the invariants of any lie algebra an analytical method to calculate invariants is developed based on the theory of complete systems of simultaneous linear first order partial differential equations the application of this algorithm to the general case in which the invariants are not polynomials is included for the case of lie algebras with one invariant the procedure of finding the invariant can be computerized as an example of this procedure the algorithm is applied in the calculation of the invariants of the group sa n r the explicit construction of its invariants for n 2 3 4 is given a theorem determining the order of a polynomial invariant of a lie group is proven allowing us to show that the invariant of sa n r is a homogeneous polynomial of order 1 2n n 1 in the generators from this fact an immediate consequence is that the order in the generators of translations is n the method is also applied in the calculation of invariants of the dimension six solvable lie algebras and dimension seven nilpotent

a second order cone programming approach for semi supervised learning semi supervised learning ssl involves the training of a decision rule from both labeled and unlabeled data in this paper we propose a novel ssl algorithm based on the multiple clusters per class assumption the proposed algorithm consists of two stages in the first stage we aim to capture the local cluster structure of the training data by using the k nearest neighbor knn algorithm to split the data into a number of disjoint subsets in the second stage a maximal margin classifier based on the second order cone programming socp is introduced to learn an inductive decision function from the obtained subsets globally for linear classification problems once the knn algorithm has been performed the proposed algorithm trains a classifier using only the first and second order moments of the subsets without considering individual data points since the number of subsets is usually much smaller than the number of training points the proposed algorithm is efficient for handling big data sets with a large amount of unlabeled data despite its simplicity the classification performance of the proposed algorithm is guaranteed by the maximal margin classifier we demonstrate the efficiency and effectiveness of the proposed algorithm on both synthetic and real world data sets

stability and bifurcation for a delayed predator prey model and the effect of diffusion abstract we consider a predator prey system with one or two delays and a unique positive equilibrium e its dynamics are studied in terms of the local stability of e and of the description of the hopf bifurcation that is proven to exist as one of the delays taken as a parameter crosses some critical values we also consider a reaction diffusion system with neumann conditions resulting from adding one spatial variable and diffusion terms in the previous model the spectral and bifurcation analysis in the neighborhood of e now as a stationary point of this latter system is addressed and the results obtained for the case without diffusion are applied

manifold regularization a geometric framework for learning from labeled and unlabeled examples we propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution we focus on a semi supervised framework that incorporates labeled and unlabeled data in a general purpose learner some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases we use properties of reproducing kernel hilbert spaces to prove new representer theorems that provide theoretical basis for the algorithms as a result in contrast to purely graph based approaches we obtain a natural out of sample extension to novel examples and so are able to handle both transductive and truly semi supervised settings we present experimental evidence suggesting that our semi supervised algorithms are able to use unlabeled data effectively finally we have a brief discussion of unsupervised and fully supervised learning within our general framework

non solvable contractions of semisimple lie algebras in low dimension the problem of non solvable contractions of lie algebras is analysed by means of a stability theorem the problem is shown to be deeply related to the embeddings among semisimple lie algebras and the resulting branching rules for representations with this procedure we determine all deformations of indecomposable lie algebras having a nontrivial levi decomposition onto semisimple lie algebras of dimension n 8 and obtain the non solvable contractions of the latter class of algebras

a view of margin losses as regularizers of probability estimates regularization is commonly used in classifier design to assure good generalization classical regularization enforces a cost on classifier complexity by constraining parameters this is usually combined with a margin loss which favors large margin decision rules a novel and unified view of this architecture is proposed by showing that margin losses act as regularizers of posterior class probabilities in a way that amplifies classical parameter regularization the problem of controlling the regularization strength of a margin loss is considered using a decomposition of the loss in terms of a link and a binding function the link function is shown to be responsible for the regularization strength of the loss while the binding function determines its outlier robustness a large class of losses is then categorized into equivalence classes of identical regularization strength or outlier robustness it is shown that losses in the same regularization class can be parameterized so as to have tunable regularization strength this parameterization is finally used to derive boosting algorithms with loss regularization boostlr three classes of tunable regularization losses are considered in detail canonical losses can implement all regularization behaviors but have no flexibility in terms of outlier modeling shrinkage losses support equally parameterized link and binding functions leading to boosting algorithms that implement the popular shrinkage procedure this offers a new explanation for shrinkage as a special case of loss based regularization finally tunable losses enable the independent parameterization of link and binding functions leading to boosting algorithms of great exibility this is illustrated by the derivation of an algorithm that generalizes both adaboost and logitboost behaving as either one when that best suits the data to classify various experiments provide evidence of the benefits of probability regularization for both classification and estimation of posterior class probabilities

determinantal formulae for the casimir operators of inhomogeneous lie algebras the author would like to correct some inaccuracy in formula 6 please see pdf for details

semi supervised learning via regularized boosting working on multiple semi supervised assumptions semi supervised learning concerns the problem of learning in the presence of labeled and unlabeled data several boosting algorithms have been extended to semi supervised learning with various strategies to our knowledge however none of them takes all three semi supervised assumptions i e smoothness cluster and manifold assumptions together into account during boosting learning in this paper we propose a novel cost functional consisting of the margin cost on labeled data and the regularization penalty on unlabeled data based on three fundamental semi supervised assumptions thus minimizing our proposed cost functional with a greedy yet stagewise functional optimization procedure leads to a generic boosting framework for semi supervised learning extensive experiments demonstrate that our algorithm yields favorite results for benchmark and real world classification tasks in comparison to state of the art semi supervised learning algorithms including newly developed boosting algorithms finally we discuss relevant issues and relate our algorithm to the previous work

the casimir operators of inhomogeneous groups we have found the number of invariant operators for the inhomogeneous groups igl n r isl n r iso p q iu p q isu p q isp 2n i e the inhomogeneous groups with the classical homogeneous subgroups and also for the weyl group w p q for some special cases explicit forms of the invariant operators are obtained we also discuss the methods applied together with problems in some cases possible further developments and relevance for the supersymmetric theories

all solvable extensions of a class of nilpotent lie algebras of dimension n and degree of nilpotency n 1 we construct all solvable lie algebras with a specific n dimensional nilradical of degree of nilpotency n 1 and with an n 2 dimensional maximal abelian ideal we find that for given n such a solvable algebra is unique up to isomorphisms using the method of moving frames we construct a basis for the casimir invariants of the nilradical we also construct a basis for the generalized casimir invariants of its solvable extension consisting entirely of rational functions of the chosen invariants of the nilradical

semisupervised classification with cluster regularization semisupervised classification ssc learns from cheap unlabeled data and labeled data to predict the labels of test instances in order to make use of the information from unlabeled data there should be an assumed relationship between the true class structure and the data distribution one assumption is that data points clustered together are likely to have the same class label in this paper we propose a new algorithm namely cluster based regularization clusterreg for ssc that takes the partition given by a clustering algorithm as a regularization term in the loss function of an ssc classifier clusterreg makes predictions according to the cluster structure together with limited labeled data the experiments confirmed that clusterreg has a good generalization ability for real world problems its performance is excellent when data follows this cluster assumption even when these clusters have misleading overlaps it still outperforms other state of the art algorithms

stability and bifurcation for a kind of nonlinear delayed differential equations abstract in this paper a kind of nonlinear delayed differential equations which can describe a two species predator prey system with stage structure is discussed the stability of the equilibria of the system and the existence of hopf bifurcations are given and the stability and the direction of the hopf bifurcation are determined by applying the normal form theory and the center manifold theorem

a reaction diffusion model for a single species with age structure i travelling wavefronts on unbounded domains in this paper we derive the equation for a single species population with two age classes and a fixed maturation period living in a spatially unbounded environment we show that if the mature deat

contractions of invariants of lie algebras with applications to classical inhomogeneous lie algebras we study in full generality the contraction of invariants of finite dimensional lie algebras and give some illustrative examples our applications show that the contraction method is not only quite flexible but also has the advantage over other methods that independent invariants can be contracted into independent ones and that they appear in compact tensorial form for our applications of physical interest we can restrict ourselves to polynomial invariants casimir operators and generalized inonu wigner contractions we show how to get all invariants of the inhomogeneous lie algebras iso p q iu p q isl n r and isp 2n r from those of the homogeneous lie algebras these invariants are all known but our results for isl n r and isp 2n r appear in a much more desirable form

virtual copies of semisimple lie algebras in enveloping algebras of semidirect products and casimir operators given a semidirect product g s r of semisimple lie algebras s and solvable algebras r we construct polynomial operators in the enveloping algebra u g of g that commute with r and transform like the generators of s up to a functional factor that turns out to be a casimir operator of r such operators are said to generate a virtual copy of s in u g and allow to compute the casimir operators of g in closed form using the classical formulae for the invariants of s the behavior of virtual copies with respect to contractions of lie algebras is analyzed applications to the class of hamilton algebras and their inhomogeneous extensions are given

non semisimple lie algebras with levi factor fraktur so 3 fraktur sfraktur l 2 bbb r and their invariants we analyse the number of functionally independent generalized casimir invariants for non semisimple lie algebras r with levi factors isomorphic to 3 and 2 in dependence of the pair r formed by a representation r of and a solvable lie algebra we show that for any dimension n 6 there exist lie algebras r with non trivial levi decomposition such that r 0

internal labelling operators and contractions of lie algebras we analyse under which conditions the missing label problem associated with a reduction chain of simple lie algebras can be completely solved by means of an inonu wigner contraction naturally related to the embedding this provides a new interpretation of the missing label operators in terms of the casimir operators of the contracted algebra and shows that the available labelling operators are not completely equivalent further the procedure is used to obtain upper bounds for the number of invariants of affine lie algebras arising as contractions of semi simple algebras

dynamic cluster formation using level set methods density based clustering has the advantages for 1 allowing arbitrary shape of cluster and 2 not requiring the number of clusters as input however when clusters touch each other both the cluster centers and cluster boundaries as the peaks and valleys of the density distribution become fuzzy and difficult to determine we introduce the notion of cluster intensity function cif which captures the important characteristics of clusters when clusters are well separated cifs are similar to density functions but when clusters become closed to each other cifs still clearly reveal cluster centers cluster boundaries and degree of membership of each data point to the cluster that it belongs clustering through bump hunting and valley seeking based on these functions are more robust than that based on density functions obtained by kernel density estimation which are often oscillatory or oversmoothed these problems of kernel density estimation are resolved using level set methods and related techniques comparisons with two existing density based methods valley seeking and dbscan are presented which illustrate the advantages of our approach

multi label image categorization with sparse factor representation the goal of multilabel classification is to reveal the underlying label correlations to boost the accuracy of classification tasks most of the existing multilabel classifiers attempt to exhaustively explore dependency between correlated labels it increases the risk of involving unnecessary label dependencies which are detrimental to classification performance actually not all the label correlations are indispensable to multilabel model negligible or fragile label correlations cannot be generalized well to the testing data especially if there exists label correlation discrepancy between training and testing sets to minimize such negative effect in the multilabel model we propose to learn a sparse structure of label dependency the underlying philosophy is that as long as the multilabel dependency cannot be well explained the principle of parsimony should be applied to the modeling process of the label correlations the obtained sparse label dependency structure discards the outlying correlations between labels which makes the learned model more generalizable to future samples experiments on real world data sets show the competitive results compared with existing algorithms

analysis of a model representing stage structured population growth with state dependent time delay a stage structured model of population growth is proposed where the time to ma turity is itself state dependent it is shown that under appropriate assumptions all solutions are positive and bounded criteria for the existence of positive equilibria and further conditions for the uniqueness of the equilibria are given the stability of the equilibria are also discussed in addition an attracting region is determined for solutions such that this region collapses to the unique positive equilibrium in the state independent case

stability and traveling fronts in lotka volterra competition models with stage structure this paper is concerned with a delay differential equation model for the interaction between two species the adult members of which are in competition the competitive effects are of the lotka volterra kind and in the absence of competition it is assumed that each species evolves according to the predictions of a simple age structured model which reduces to a single equation for the total adult population for each of the two species the model incorporates a time delay which represents the time from birth to maturity of that species thus the time delays appear in the adult recruitment terms the dynamics of the model are determined and global stability results are established for each equilibrium the equilibria of the model involve the maturation delays the criteria for global convergence to each equilibrium are sharp and involve these delays a reaction diffusion extension of the model is also studied for the case when only the adult members of each species can diffuse we prove the existence of a

semi supervised classification method through oversampling and common hidden space semi supervised classification methods attempt to improve classification performance based on a small amount of labeled data through full use of abundant unlabeled data although existing semi supervised classification methods have exhibited promising results in many applications they still have drawbacks including performance degeneration due to the introduction of unlabeled data and partially false labels in a small amount of labeled data to circumvent such drawbacks a new semi supervised classification method ochs ssc through oversampling and a common hidden space is proposed in the paper the primary characteristics of the proposed method include two aspects one is that unlabeled data are only used to generate new synthetic data to extend the minimal amount of labeled data the other is that the final classifier is learned in the extended feature space which is composed of the original feature space and the common hidden space found between labeled data and the synthetic data instead of the original feature space extensive experiments on 23 datasets indicate the effectiveness of the proposed method

central extensions of the families of quasi unitary lie algebras the most general possible central extensions of two whole families of lie algebras which can be obtained by contracting the special pseudo unitary algebras of the cartan series and the pseudo unitary algebras are completely determined and classified for arbitrary p and q in addition to the and algebras whose second cohomology group is well known to be trivial each family includes many non semisimple algebras their central extensions which are explicitly given can be classified into three types as far as their properties under contraction are involved a closed expression for the dimension of the second cohomology group of any member of these families of algebras is given

casimir invariants for the complete family of quasisimple orthogonal algebras a complete choice of generators of the centre of the enveloping algebras of real quasisimple lie algebras of orthogonal type for arbitrary dimension is obtained in a unified setting the results simultaneously include the well known polynomial invariants of the pseudo orthogonal algebras as well as the casimirs for many non simple algebras such as the inhomogeneous the newton hooke and galilei type etc which are obtained by contraction s starting from the simple algebras the dimension of the centre of the enveloping algebra of a quasisimple orthogonal algebra turns out to be the same as for the simple algebras from which they come by contraction the structure of the higher order invariants is given in a convenient pyramidal manner in terms of certain sets of pauli lubanski elements in the enveloping algebras as an example showing this approach at work the scheme is applied to recovering the casimirs for the 3 1 kinematical algebras some prospects on the relevance of these results for the study of expansions are also given

hopf bifurcation analysis and amplitude control of the modified lorenz system this paper is concerned with the hopf bifurcation analysis and amplitude control of the modified lorenz system the hopf bifurcation of system is investigated by utilizing the hopf bifurcation theory and the center manifold theorem firstly then the direction and stability of limit cycle emerging from hopf bifurcation are determined by the designed controller moreover the amplitude of limit cycle emerging from hopf bifurcation is controlled by a nonlinear feedback controller finally numerical simulations are given to verify theoretical analysis