Hero's journey in bifurcation diagram

The hero's journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure. In a simplified version, this journey is divided into three acts separated by two crucial moments. Here we propose a discrete-time dynamical system for representing the protagonist's evolution. The suffering along the journey is taken as the control parameter of this system. The bifurcation diagram exhibits stationary, periodic and chaotic behaviors. In this diagram, there are transition from fixed point to chaos and transition from limit cycle to fixed point. We found that the values of the control parameter corresponding to these two transitions are in quantitative agreement with the two critical moments of the three-act hero's journey identified in 10 movies appearing in the list of the 200 worldwide highest-grossing films. (C) 2011 Elsevier B.V. All rights reserved.

Generation of self-similar Gaussian time series by means of the DWT and DWPT variance maps

Due to the several kinds of services that use the Internet and data networks infra-structures, the present networks are characterized by the diversity of types of traffic that have statistical properties as complex temporal correlation and non-gaussian distribution. The networks complex temporal correlation may be characterized by the Short Range Dependence (SRD) and the Long Range Dependence - (LRD). Models as the fGN (Fractional Gaussian Noise) may capture the LRD but not the SRD. This work presents two methods for traffic generation that synthesize approximate realizations of the self-similar fGN with SRD random process. The first one employs the IDWT (Inverse Discrete Wavelet Transform) and the second the IDWPT (Inverse Discrete Wavelet Packet Transform). It has been developed the variance map concept that allows to associate the LRD and SRD behaviors directly to the wavelet transform coefficients. The developed methods are extremely flexible and allow the generation of Gaussian time series with complex statistical behaviors.

A novel MAP-MRF approach for multispectral image contextual classification using combination of suboptimal iterative algorithms

In this paper we present a novel approach for multispectral image contextual classification by combining iterative combinatorial optimization algorithms. The pixel-wise decision rule is defined using a Bayesian approach to combine two MRF models: a Gaussian Markov Random Field (GMRF) for the observations (likelihood) and a Potts model for the a priori knowledge, to regularize the solution in the presence of noisy data. Hence, the classification problem is stated according to a Maximum a Posteriori (MAP) framework. In order to approximate the MAP solution we apply several combinatorial optimization methods using multiple simultaneous initializations, making the solution less sensitive to the initial conditions and reducing both computational cost and time in comparison to Simulated Annealing, often unfeasible in many real image processing applications. Markov Random Field model parameters are estimated by Maximum Pseudo-Likelihood (MPL) approach, avoiding manual adjustments in the choice of the regularization parameters. Asymptotic evaluations assess the accuracy of the proposed parameter estimation procedure. To test and evaluate the proposed classification method, we adopt metrics for quantitative performance assessment (Cohen`s Kappa coefficient), allowing a robust and accurate statistical analysis. The obtained results clearly show that combining sub-optimal contextual algorithms significantly improves the classification performance, indicating the effectiveness of the proposed methodology. (C) 2010 Elsevier B.V. All rights reserved.

Probability inundation map for a scenario combining storm surge and sea-level rise

Coastal managers require reliable spatial data on the extent and timing of potential coastal inundation, particularly in a changing climate. Most sea level rise (SLR) vulnerability assessments are undertaken using the easily implemented bathtub approach, where areas adjacent to the sea and below a given elevation are mapped using a deterministic line dividing potentially inundated from dry areas. This method only requires elevation data usually in the form of a digital elevation model (DEM). However, inherent errors in the DEM and spatial analysis of the bathtub model propagate into the inundation mapping. The aim of this study was to assess the impacts of spatially variable and spatially correlated elevation errors in high-spatial resolution DEMs for mapping coastal inundation. Elevation errors were best modelled using regression-kriging. This geostatistical model takes the spatial correlation in elevation errors into account, which has a significant impact on analyses that include spatial interactions, such as inundation modelling. The spatial variability of elevation errors was partially explained by land cover and terrain variables. Elevation errors were simulated using sequential Gaussian simulation, a Monte Carlo probabilistic approach. 1,000 error simulations were added to the original DEM and reclassified using a hydrologically correct bathtub method. The probability of inundation to a scenario combining a 1 in 100 year storm event over a 1 m SLR was calculated by counting the proportion of times from the 1,000 simulations that a location was inundated. This probabilistic approach can be used in a risk-aversive decision making process by planning for scenarios with different probabilities of occurrence. For example, results showed that when considering a 1% probability exceedance, the inundated area was approximately 11% larger than mapped using the deterministic bathtub approach. The probabilistic approach provides visually intuitive maps that convey uncertainties inherent to spatial data and analysis.

Noise-induced attractor annihilation in the delayed feedback logistic map

We study dynamics of the bistable logistic map with delayed feedback, under the influence of white Gaussian noise and periodic modulation applied to the variable. This system may serve as a model to describe population dynamics under finite resources in noisy environment with seasonal fluctuations. While a very small amount of noise has no effect on the global structure of the coexisting attractors in phase space, an intermediate noise totally eliminates one of the attractors. Slow periodic modulation enhances the attractor annihilation.

Gaussian phase-space representations for fermions

We introduce a positive phase-space representation for fermions, using the most general possible multimode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive equivalences between quantum and stochastic moments, as well as operator correspondences that map quantum operator evolution onto stochastic processes in phase space. The representation thus enables first-principles quantum dynamical or equilibrium calculations in many-body Fermi systems. Potential applications are to strongly interacting and correlated Fermi gases, including coherent behavior in open systems and nanostructures described by master equations. Examples of an ideal gas and the Hubbard model are given, as well as a generic open system, in order to illustrate these ideas.

General gaussian priors for improved generalisation

We explore the dependence of performance measures, such as the generalization error and generalization consistency, on the structure and the parameterization of the prior on `rules', instanced here by the noisy linear perceptron. Using a statistical mechanics framework, we show how one may assign values to the parameters of a model for a `rule' on the basis of data instancing the rule. Information about the data, such as input distribution, noise distribution and other `rule' characteristics may be embedded in the form of general gaussian priors for improving net performance. We examine explicitly two types of general gaussian priors which are useful in some simple cases. We calculate the optimal values for the parameters of these priors and show their effect in modifying the most probable, MAP, values for the rules.

Semi-supervised Gaussian process latent variable model with pairwise constraints

In machine learning, Gaussian process latent variable model (GP-LVM) has been extensively applied in the field of unsupervised dimensionality reduction. When some supervised information, e.g., pairwise constraints or labels of the data, is available, the traditional GP-LVM cannot directly utilize such supervised information to improve the performance of dimensionality reduction. In this case, it is necessary to modify the traditional GP-LVM to make it capable of handing the supervised or semi-supervised learning tasks. For this purpose, we propose a new semi-supervised GP-LVM framework under the pairwise constraints. Through transferring the pairwise constraints in the observed space to the latent space, the constrained priori information on the latent variables can be obtained. Under this constrained priori, the latent variables are optimized by the maximum a posteriori (MAP) algorithm. The effectiveness of the proposed algorithm is demonstrated with experiments on a variety of data sets. © 2010 Elsevier B.V.

Simple approximate MAP inference for Dirichlet processes mixtures

The Dirichlet process mixture model (DPMM) is a ubiquitous, flexible Bayesian nonparametric statistical model. However, full probabilistic inference in this model is analytically intractable, so that computationally intensive techniques such as Gibbs sampling are required. As a result, DPMM-based methods, which have considerable potential, are restricted to applications in which computational resources and time for inference is plentiful. For example, they would not be practical for digital signal processing on embedded hardware, where computational resources are at a serious premium. Here, we develop a simplified yet statistically rigorous approximate maximum a-posteriori (MAP) inference algorithm for DPMMs. This algorithm is as simple as DP-means clustering, solves the MAP problem as well as Gibbs sampling, while requiring only a fraction of the computational effort. (For freely available code that implements the MAP-DP algorithm for Gaussian mixtures see http://www.maxlittle.net/.) Unlike related small variance asymptotics (SVA), our method is non-degenerate and so inherits the “rich get richer” property of the Dirichlet process. It also retains a non-degenerate closed-form likelihood which enables out-of-sample calculations and the use of standard tools such as cross-validation. We illustrate the benefits of our algorithm on a range of examples and contrast it to variational, SVA and sampling approaches from both a computational complexity perspective as well as in terms of clustering performance. We demonstrate the wide applicabiity of our approach by presenting an approximate MAP inference method for the infinite hidden Markov model whose performance contrasts favorably with a recently proposed hybrid SVA approach. Similarly, we show how our algorithm can applied to a semiparametric mixed-effects regression model where the random effects distribution is modelled using an infinite mixture model, as used in longitudinal progression modelling in population health science. Finally, we propose directions for future research on approximate MAP inference in Bayesian nonparametrics.

Non-gaussian Spatial Correlations Dramatically Weaken Localization.

We perform variational studies of the interaction-localization problem to describe the interaction-induced renormalizations of the effective (screened) random potential seen by quasiparticles. Here we present results of careful finite-size scaling studies for the conductance of disordered Hubbard chains at half-filling and zero temperature. While our results indicate that quasiparticle wave functions remain exponentially localized even in the presence of moderate to strong repulsive interactions, we show that interactions produce a strong decrease of the characteristic conductance scale g^{*} signaling the crossover to strong localization. This effect, which cannot be captured by a simple renormalization of the disorder strength, instead reflects a peculiar non-Gaussian form of the spatial correlations of the screened disordered potential, a hitherto neglected mechanism to dramatically reduce the impact of Anderson localization (interference) effects.

Deformed Gaussian-orthogonal-ensemble description of small-world networks

The study of spectral behavior of networks has gained enthusiasm over the last few years. In particular, random matrix theory (RMT) concepts have proven to be useful. In discussing transition from regular behavior to fully chaotic behavior it has been found that an extrapolation formula of the Brody type can be used. In the present paper we analyze the regular to chaotic behavior of small world (SW) networks using an extension of the Gaussian orthogonal ensemble. This RMT ensemble, coined the deformed Gaussian orthogonal ensemble (DGOE), supplies a natural foundation of the Brody formula. SW networks follow GOE statistics until a certain range of eigenvalue correlations depending upon the strength of random connections. We show that for these regimes of SW networks where spectral correlations do not follow GOE beyond a certain range, DGOE statistics models the correlations very well. The analysis performed in this paper proves the utility of the DGOE in network physics, as much as it has been useful in other physical systems.

INFERENCE FOR EIGENVALUES AND EIGENVECTORS OF GAUSSIAN SYMMETRIC MATRICES

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic background radiation data, where the observations are, respectively, 3 x 3 and 2 x 2 symmetric positive definite matrices. The parameter sets involved in the inference problems for eigenvalues and eigenvectors are subsets of Euclidean space that are either affine subspaces, embedded submanifolds that are invariant under orthogonal transformations or polyhedral convex cones. We show that for a class of sets that includes the ones considered in this paper, the MLEs of the mean parameter do not depend on the covariance parameters if and only if the covariance structure is orthogonally invariant. Closed-form expressions for the MLEs and the associated LLRs are derived for this covariance structure.

Low dimensional behavior in three-dimensional coupled map lattices

The analysis of one-, two-, and three-dimensional coupled map lattices is here developed under a statistical and dynamical perspective. We show that the three-dimensional CML exhibits low dimensional behavior with long range correlation and the power spectrum follows 1/f noise. This approach leads to an integrated understanding of the most important properties of these universal models of spatiotemporal chaos. We perform a complete time series analysis of the model and investigate the dependence of the signal properties by change of dimension. (c) 2008 Elsevier Ltd. All rights reserved.

Tick saliva induces regulatory dendritic cells: MAP-kinases and Toll-like receptor-2 expression as potential targets

Ticks (Acari: Ixodidae) are bloodsucking ectoparasitic arthropods of human and veterinary medical importance. Tick saliva has been shown to contain a wide range of bioactive molecules with vasodilatory, antihemostatic, and immunomodulatory activities. We have previously demonstrated that saliva from Rhipicephalus sanguineus ticks inhibits the maturation of dendritic cells (DCs) stimulated with LPS. Here we examined the mechanism of this immune subversion, evaluating the effect of tick saliva on Toll-like receptor (TLR)-4 signalling pathway in bone marrow-derived DCs. We demonstrated that R. sanguineus tick saliva impairs maturation of DCs stimulated with LIPS, a TLR-4 ligand, leading to increased production of interleukin (IL)-10 and reduced synthesis of IL-12p70 and TNF-alpha. The immunomodulatory effect of the tick saliva on the production of pro-inflammatory cytokines by DCs stimulated with LPS was associated with the observation that tick saliva inhibits the activation of the ERK 1/2 and p38 MAP kinases. These effects were independent of the expression of TLR-4 on the surface of DCs. Additionally, saliva-treated DCs also presented a similar pattern of cytokine modulation in response to other TLR ligands. Since the recent literature reports that several parasites evade immune responses through TLR-2-mediated production of IL-10, we evaluated the effect of tick saliva on the percentage of TLR-2(+) DCs stimulated with the TLR-2 ligand lipoteicoic acid (LTA). The data showed that the population of DCs expressing TLR-2 was significantly increased in DCs treated with LTA plus saliva. In addition, tick saliva alone increased the expression of TLR-2 in a dose- and time-dependent manner. Our data suggest that tick saliva induces regulatory DCs, which secrete IL-10 and low levels of IL-12 and TNF-alpha when stimulated by TLR ligands. Such regulatory DCs are associated with expression of TLR-2 and inhibition of ERK and p38, which promotes the production of IL-10 and thus down-modulates the host`s immune response, possibly favouring susceptibility to tick infestations. (C) 2009 Elsevier B.V. All rights reserved.

New prediction methods for CO2 evaporation inside tubes: Part I - A two-phase flow pattern map and a flow pattern based phenomenological model for two-phase flow frictional pressure drops

An updated flow pattern map was developed for CO2 on the basis of the previous Cheng-Ribatski-Wojtan-Thome CO2 flow pattern map [1,2] to extend the flow pattern map to a wider range of conditions. A new annular flow to dryout transition (A-D) and a new dryout to mist flow transition (D-M) were proposed here. In addition, a bubbly flow region which generally occurs at high mass velocities and low vapor qualities was added to the updated flow pattern map. The updated flow pattern map is applicable to a much wider range of conditions: tube diameters from 0.6 to 10 mm, mass velocities from 50 to 1500 kg/m(2) s, heat fluxes from 1.8 to 46 kW/m(2) and saturation temperatures from -28 to +25 degrees C (reduced pressures from 0.21 to 0.87). The updated flow pattern map was compared to independent experimental data of flow patterns for CO2 in the literature and it predicts the flow patterns well. Then, a database of CO2 two-phase flow pressure drop results from the literature was set up and the database was compared to the leading empirical pressure drop models: the correlations by Chisholm [3], Friedel [4], Gronnerud [5] and Muller-Steinhagen and Heck [6], a modified Chisholm correlation by Yoon et al. [7] and the flow pattern based model of Moreno Quiben and Thome [8-10]. None of these models was able to predict the CO2 pressure drop data well. Therefore, a new flow pattern based phenomenological model of two-phase flow frictional pressure drop for CO2 was developed by modifying the model of Moreno Quiben and Thome using the updated flow pattern map in this study and it predicts the CO2 pressure drop database quite well overall. (C) 2007 Elsevier Ltd. All rights reserved.