Generalized external indexes for comparing data partitions with overlapping categories

There is a family of well-known external clustering validity indexes to measure the degree of compatibility or similarity between two hard partitions of a given data set, including partitions with different numbers of categories. A unified, fully equivalent set-theoretic formulation for an important class of such indexes was derived and extended to the fuzzy domain in a previous work by the author [Campello, R.J.G.B., 2007. A fuzzy extension of the Rand index and other related indexes for clustering and classification assessment. Pattern Recognition Lett., 28, 833-841]. However, the proposed fuzzy set-theoretic formulation is not valid as a general approach for comparing two fuzzy partitions of data. Instead, it is an approach for comparing a fuzzy partition against a hard referential partition of the data into mutually disjoint categories. In this paper, generalized external indexes for comparing two data partitions with overlapping categories are introduced. These indexes can be used as general measures for comparing two partitions of the same data set into overlapping categories. An important issue that is seldom touched in the literature is also addressed in the paper, namely, how to compare two partitions of different subsamples of data. A number of pedagogical examples and three simulation experiments are presented and analyzed in details. A review of recent related work compiled from the literature is also provided. (c) 2010 Elsevier B.V. All rights reserved.

A GRADIENT-LIKE NONAUTONOMOUS EVOLUTION PROCESS

In this paper we consider a dissipative damped wave equation with nonautonomous damping of the form u(tt) + beta(t)u(t) - Delta u + f(u) (1) in a bounded smooth domain Omega subset of R(n) with Dirichlet boundary conditions, where f is a dissipative smooth nonlinearity and the damping beta : R -> (0, infinity) is a suitable function. We prove, if (1) has finitely many equilibria, that all global bounded solutions of (1) are backwards and forwards asymptotic to equilibria. Thus, we give a class of examples of nonautonomous evolution processes for which the structure of the pullback attractors is well understood. That complements the results of [Carvalho & Langa, 2009] on characterization of attractors, where it was shown that a small nonautonomous perturbation of an autonomous gradient-like evolution process is also gradient-like. Note that the evolution process associated to (1) is not a small nonautonomous perturbation of any autonomous gradient-like evolution processes. Moreover, we are also able to prove that the pullback attractor for (1) is also a forwards attractor and that the rate of attraction is exponential.

An extension of the concept of gradient semigroups which is stable under perturbation

In this article we introduce the concept of a gradient-like nonlinear semigroup as an intermediate concept between a gradient nonlinear semigroup (those possessing a Lyapunov function, see [J.K. Hale, Asymptotic Behavior of Dissipative Systems, Math. Surveys Monogr., vol. 25, Amer. Math. Soc., 1989]) and a nonlinear semigroup possessing a gradient-like attractor. We prove that a perturbation of a gradient-like nonlinear semigroup remains a gradient-like nonlinear semigroup. Moreover, for non-autonomous dynamical systems we introduce the concept of a gradient-like evolution process and prove that a non-autonomous perturbation of a gradient-like nonlinear semigroup is a gradient-like evolution process. For gradient-like nonlinear semigroups and evolution processes, we prove continuity, characterization and (pullback and forwards) exponential attraction of their attractors under perturbation extending the results of [A.N. Carvalho, J.A. Langa, J.C. Robinson, A. Suarez, Characterization of non-autonomous attractors of a perturbed gradient system, J. Differential Equations 236 (2007) 570-603] on characterization and of [A.V. Babin, M.I. Vishik, Attractors in Evolutionary Equations, Stud. Math. Appl.. vol. 25, North-Holland, Amsterdam, 1992] on exponential attraction. (C) 2009 Elsevier Inc. All rights reserved.

Stability of gradient semigroups under perturbations

In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space).

Reduced gradient method combined with augmented Lagrangian and barrier for the optimal power flow problem

A new approach for solving the optimal power flow (OPF) problem is established by combining the reduced gradient method and the augmented Lagrangian method with barriers and exploring specific characteristics of the relations between the variables of the OPF problem. Computer simulations on IEEE 14-bus and IEEE 30-bus test systems illustrate the method. (c) 2007 Elsevier Inc. All rights reserved.

A new family of generalized distributions

Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79-88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix `Kw`) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with an application to real data.

Partial spectral projected gradient method with active-set strategy for linearly constrained optimization

A method for linearly constrained optimization which modifies and generalizes recent box-constraint optimization algorithms is introduced. The new algorithm is based on a relaxed form of Spectral Projected Gradient iterations. Intercalated with these projected steps, internal iterations restricted to faces of the polytope are performed, which enhance the efficiency of the algorithm. Convergence proofs are given and numerical experiments are included and commented. Software supporting this paper is available through the Tango Project web page: http://www.ime.usp.br/similar to egbirgin/tango/.

Transformed generalized linear models

The estimation of data transformation is very useful to yield response variables satisfying closely a normal linear model, Generalized linear models enable the fitting of models to a wide range of data types. These models are based on exponential dispersion models. We propose a new class of transformed generalized linear models to extend the Box and Cox models and the generalized linear models. We use the generalized linear model framework to fit these models and discuss maximum likelihood estimation and inference. We give a simple formula to estimate the parameter that index the transformation of the response variable for a subclass of models. We also give a simple formula to estimate the rth moment of the original dependent variable. We explore the possibility of using these models to time series data to extend the generalized autoregressive moving average models discussed by Benjamin er al. [Generalized autoregressive moving average models. J. Amer. Statist. Assoc. 98, 214-223]. The usefulness of these models is illustrated in a Simulation study and in applications to three real data sets. (C) 2009 Elsevier B.V. All rights reserved.

Generalized log-gamma regression models with cure fraction

In this paper, the generalized log-gamma regression model is modified to allow the possibility that long-term survivors may be present in the data. This modification leads to a generalized log-gamma regression model with a cure rate, encompassing, as special cases, the log-exponential, log-Weibull and log-normal regression models with a cure rate typically used to model such data. The models attempt to simultaneously estimate the effects of explanatory variables on the timing acceleration/deceleration of a given event and the surviving fraction, that is, the proportion of the population for which the event never occurs. The normal curvatures of local influence are derived under some usual perturbation schemes and two martingale-type residuals are proposed to assess departures from the generalized log-gamma error assumption as well as to detect outlying observations. Finally, a data set from the medical area is analyzed.

Power series generalized nonlinear models

We introduce in this paper a new class of discrete generalized nonlinear models to extend the binomial, Poisson and negative binomial models to cope with count data. This class of models includes some important models such as log-nonlinear models, logit, probit and negative binomial nonlinear models, generalized Poisson and generalized negative binomial regression models, among other models, which enables the fitting of a wide range of models to count data. We derive an iterative process for fitting these models by maximum likelihood and discuss inference on the parameters. The usefulness of the new class of models is illustrated with an application to a real data set. (C) 2008 Elsevier B.V. All rights reserved.

Patterns of water and heat flux across a biome gradient from tropical forest to savanna in Brazil

We investigated the seasonal patterns of water vapor and sensible heat flux along a tropical biome gradient from forest to savanna. We analyzed data from a network of flux towers in Brazil that were operated within the Large-Scale Biosphere-Atmosphere Experiment in Amazonia (LBA). These tower sites included tropical humid and semideciduous forest, transitional forest, floodplain (with physiognomies of cerrado), and cerrado sensu stricto. The mean annual sensible heat flux at all sites ranged from 20 to 38 Wm(-2), and was generally reduced in the wet season and increased in the late dry season, coincident with seasonal variations of net radiation and soil moisture. The sites were easily divisible into two functional groups based on the seasonality of evaporation: tropical forest and savanna. At sites with an annual precipitation above 1900 mm and a dry season length less than 4 months (Manaus, Santarem and Rondonia), evaporation rates increased in the dry season, coincident with increased radiation. Evaporation rates were as high as 4.0 mm d(-1) in these evergreen or semidecidous forests. In contrast, ecosystems with precipitation less than 1700 mm and a longer dry season (Mato Grosso, Tocantins and Sao Paulo) showed clear evidence of reduced evaporation in the dry season. Evaporation rates were as low as 2.5 mm d(-1) in the transitional forests and 1 mm d(-1) in the cerrado. The controls on evapotranspiration seasonality changed along the biome gradient, with evaporative demand (especially net radiation) playing a more important role in the wetter forests, and soil moisture playing a more important role in the drier savannah sites.

Numerical test of Born-Oppenheimer approximation in chaotic systems

We study the validity of the Born-Oppenheimer approximation in chaotic dynamics. Using numerical solutions of autonomous Fermi accelerators. we show that the general adiabatic conditions can be interpreted as the narrowness of the chaotic region in phase space. (C) 2009 Elsevier B.V. All rights reserved.

First-principles calculation of the AlAs/GaAs interface band structure using a self-energy-corrected local density approximation

We apply a self-energy-corrected local density approximation (LDA) to obtain corrected bulk band gaps and to study the band offsets of AlAs grown on GaAs (AlAs/GaAs). We also investigate the Al(x)Ga(1-x)As/GaAs alloy interface, commonly employed in band gap engineering. The calculations are fully ab initio, with no adjustable parameters or experimental input, and at a computational cost comparable to traditional LDA. Our results are in good agreement with experimental values and other theoretical studies. Copyright (C) EPLA, 2011

Role of Surfactants in Carbon Nanotubes Density Gradient Separation

Several strategies aimed at sorting single-walled carbon nanotubes (SWNT) by diameter and/or electronic structure have been developed in recent years. A nondestructive sorting method was recently proposed in which nanotube bundles are dispersed in water-surfactant solutions and submitted to ultracentrifugation in a density gradient. By this method, SWNTs of different diameters are distributed according to their densities along the centrifuge tube. A mixture of two anionic amphiphiles, namely sodium dodecylsulfate (SIDS) and sodium cholate (SC), presented the best performance in discriminating nanotubes by diameter. We present molecular dynamics studies of the water-surfactant-SWNT system. The simulations revealed one aspect of the discriminating power of surfactants: they can actually be attracted toward the interior of the nanotube cage. The binding energies of SDS and SC on the outer nanotube surface are very similar and depend weakly on diameter. The binding inside the tubes, on the contrary, is strongly diameter dependent: SDS fits best inside tubes with diameters ranging from 8 to 9 angstrom, while SC is best accommodated in larger tubes, with diameters in the range 10.5-12 angstrom. The dynamics at room temperature showed that, as the amphiphile moves to the hollow cage, water molecules are dragged together, thereby promoting the nanotube filling. The resulting densities of filled SWNT are in agreement with measured densities.

Self-adjoint extensions and spectral analysis in the generalized Kratzer problem

We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional non-relativistic motion of a particle in the potential field V(x) = g(1)x(-1) + g(2)x(-2), x is an element of R(+) = [0, infinity). For g(2) > 0 and g(1) < 0, the potential is known as the Kratzer potential V(K)(x) and is usually used to describe molecular energy and structure, interactions between different molecules and interactions between non-bonded atoms. We construct all self-adjoint Schrodinger operators with the potential V(x) and represent rigorous solutions of the corresponding spectral problems. Solving the first part of the problem, we use a method of specifying self-adjoint extensions by (asymptotic) self-adjoint boundary conditions. Solving spectral problems, we follow Krein`s method of guiding functionals. This work is a continuation of our previous works devoted to the Coulomb, Calogero and Aharonov-Bohm potentials.