Multi-learner based recursive supervised training

In this paper, we propose the Multi-Learner Based Recursive Supervised Training (MLRT) algorithm which uses the existing framework of recursive task decomposition, by training the entire dataset, picking out the best learnt patterns, and then repeating the process with the remaining patterns. Instead of having a single learner to classify all datasets during each recursion, an appropriate learner is chosen from a set of three learners, based on the subset of data being trained, thereby avoiding the time overhead associated with the genetic algorithm learner utilized in previous approaches. In this way MLRT seeks to identify the inherent characteristics of the dataset, and utilize it to train the data accurately and efficiently. We observed that empirically, MLRT performs considerably well as compared to RPHP and other systems on benchmark data with 11% improvement in accuracy on the SPAM dataset and comparable performances on the VOWEL and the TWO-SPIRAL problems. In addition, for most datasets, the time taken by MLRT is considerably lower than the other systems with comparable accuracy. Two heuristic versions, MLRT-2 and MLRT-3 are also introduced to improve the efficiency in the system, and to make it more scalable for future updates. The performance in these versions is similar to the original MLRT system

Observability for two dimensional systems

Sufficient conditions that a two-dimensional system with output is locally observable are presented. Known results depend on time derivatives of the output and the inverse function theorem. In some cases, no informaton is provided by these theories, and one must study observability by other methods. The observability problem is dualized to the controllability problem, and the deep results of Hermes on local controllability are applied to prove a theorem concerning local observability

A canonical form for nonlinear systems

The conceptions of transformation and canonical form have been much used to analyze the structure of linear systems. A coordinate system and a corresponding canonical form are developed for general nonlinear control systems. Their usefulness is demonstrated by showing that every feedback linearizable system becomes a system with only feedback paths in the canonical form

Two-player envy-free multi-cake division

We introduce a generalized cake-cutting problem in which we seek to divide multiple cakes so that two players may get their most-preferred piece selections: a choice of one piece from each cake, allowing for the possibility of linked preferences over the cakes. For two players, we show that disjoint envy-free piece selections may not exist for two cakes cut into two pieces each, and they may not exist for three cakes cut into three pieces each. However, there do exist such divisions for two cakes cut into three pieces each, and for three cakes cut into four pieces each. The resulting allocations of pieces to players are Pareto-optimal with respect to the division. We use a generalization of Sperner's lemma on the polytope of divisions to locate solutions to our generalized cake-cutting problem.Comment: 15 pages, 7 figures, see related work at http://www.math.hmc.edu/~su/papers.htm

SuperWIMP Gravitino Dark Matter from Slepton and Sneutrino Decays

Dark matter may be composed of superWIMPs, superweakly-interacting massive particles produced in the late decays of other particles. We focus on the case of gravitinos produced in the late decays of sleptons or sneutrinos and assume they are produced in sufficient numbers to constitute all of non-baryonic dark matter. At leading order, these late decays are two-body and the accompanying energy is electromagnetic. For natural weak-scale parameters, these decays have been shown to satisfy bounds from Big Bang nucleosynthesis and the cosmic microwave background. However, sleptons and sneutrinos may also decay to three-body final states, producing hadronic energy, which is subject to even more stringent nucleosynthesis bounds. We determine the three-body branching fractions and the resulting hadronic energy release. We find that superWIMP gravitino dark matter is viable and determine the gravitino and slepton/sneutrino masses preferred by this solution to the dark matter problem. In passing, we note that hadronic constraints disfavor the possibility of superWIMPs produced by neutralino decays unless the neutralino is photino-like.Comment: 22 pages, updated figures and minor changes, version to appear in Phys. Rev.

On length spectrum metrics and weak metrics on Teichmüller spaces of surfaces with boundary

We define and study metrics and weak metrics on the Teichmüller space of a surface of topologically finite type with boundary. These metrics and weak metrics are associated to the hyperbolic length spectrum of simple closed curves and of properly embedded arcs in the surface. We give a comparison between the defined metrics on regions of Teichmüller space which we call $\varepsilon_0$-relative $\epsilon$-thick parts} for $\epsilon >0$ and $\varepsilon_0\geq \epsilon>0$

On local comparison between various metrics on Teichmüller spaces

International audienceThere are several Teichmüller spaces associated to a surface of infinite topological type, after the choice of a particular basepoint ( a complex or a hyperbolic structure on the surface). These spaces include the quasiconformal Teichmüller space, the length spectrum Teichmüller space, the Fenchel-Nielsen Teichmüller space, and there are others. In general, these spaces are set-theoretically different. An important question is therefore to understand relations between these spaces. Each of these spaces is equipped with its own metric, and under some hypotheses, there are inclusions between these spaces. In this paper, we obtain local metric comparison results on these inclusions, namely, we show that the inclusions are locally bi-Lipschitz under certain hypotheses. To obtain these results, we use some hyperbolic geometry estimates that give new results also for surfaces of finite type. We recall that in the case of a surface of finite type, all these Teichmüller spaces coincide setwise. In the case of a surface of finite type with no boundary components (and possibly with punctures), we show that the restriction of the identity map to any thick part of Teichmüller space is globally bi-Lipschitz with respect to the length spectrum metric and the classical Teichmüller metric on the domain and on the range respectively. In the case of a surface of finite type with punctures and boundary components, there is a metric on the Teichmüller space which we call the arc metric, whose definition is analogous to the length spectrum metric, but which uses lengths of geodesic arcs instead of lengths of closed geodesics. We show that the restriction of the identity map restricted to any ``relative thick" part of Teichmüller space is globally bi-Lipschitz, with respect to any of the three metrics: the length spectrum metric, the Teichmüller metric and the arc metric on the domain and on the range

Perceived Family Life Quality in Junior Secondary School Students in Hong Kong

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The present longitudinal study examined perceived family functioning and related socio-demographic correlates from the perspective of adolescents in Hong Kong. Results showed that adolescent perceptions of family functioning based on different indicators gradually deteriorated over time. Regarding the socio-demographic correlates, (a) boys had more favourable perceived family functioning than did girls; (b) adolescents from non-intact families had poorer perceived family functioning than those from intact families; and (c) economically disadvantaged adolescents had poorer perceived family functioning than non-economically disadvantaged adolescents. Results also revealed that adolescents’ perceived family functioning was positively related to positive youth devel- opment. Analyses further indicated that perceived family functioning and positive youth development were concurrently and longitudinally related