Non-integrability of the mixmaster universe

We comment on an analysis by Contopoulos et al. which demonstrates that the governing six-dimensional Einstein equations for the mixmaster space-time metric pass the ARS or reduced Painlev\'{e} test. We note that this is the case irrespective of the value, $I$, of the generating Hamiltonian which is a constant of motion. For $I < 0$ we find numerous closed orbits with two unstable eigenvalues strongly indicating that there cannot exist two additional first integrals apart from the Hamiltonian and thus that the system, at least for this case, is very likely not integrable. In addition, we present numerical evidence that the average Lyapunov exponent nevertheless vanishes. The model is thus a very interesting example of a Hamiltonian dynamical system, which is likely non-integrable yet passes the reduced Painlev\'{e} test.Comment: 11 pages LaTeX in J.Phys.A style (ioplppt.sty) + 6 PostScript figures compressed and uuencoded with uufiles. Revised version to appear in J Phys.

Homoclinic chaos in the dynamics of a general Bianchi IX model

The dynamics of a general Bianchi IX model with three scale factors is examined. The matter content of the model is assumed to be comoving dust plus a positive cosmological constant. The model presents a critical point of saddle-center-center type in the finite region of phase space. This critical point engenders in the phase space dynamics the topology of stable and unstable four dimensional tubes $R \times S^3$, where $R$ is a saddle direction and $S^3$ is the manifold of unstable periodic orbits in the center-center sector. A general characteristic of the dynamical flow is an oscillatory mode about orbits of an invariant plane of the dynamics which contains the critical point and a Friedmann-Robertson-Walker (FRW) singularity. We show that a pair of tubes (one stable, one unstable) emerging from the neighborhood of the critical point towards the FRW singularity have homoclinic transversal crossings. The homoclinic intersection manifold has topology $R \times S^2$ and is constituted of homoclinic orbits which are bi-asymptotic to the $S^3$ center-center manifold. This is an invariant signature of chaos in the model, and produces chaotic sets in phase space. The model also presents an asymptotic DeSitter attractor at infinity and initial conditions sets are shown to have fractal basin boundaries connected to the escape into the DeSitter configuration (escape into inflation), characterizing the critical point as a chaotic scatterer.Comment: 11 pages, 6 ps figures. Accepted for publication in Phys. Rev.

A Comparative Study between Two Regression Methods on LiDAR Data: A Case Study

Airborne LiDAR (Light Detection and Ranging) has become an excellent tool for accurately assessing vegetation characteristics in forest environments. Previous studies showed empirical relationships between LiDAR and field-measured biophysical variables. Multiple linear regression (MLR) with stepwise feature selection is the most common method for building estimation models. Although this technique has provided very interesting results, many other data mining techniques may be applied. The overall goal of this study is to compare different methodologies for assessing biomass fractions at stand level using airborne Li- DAR data in forest settings. In order to choose the best methodology, a comparison between two different feature selection techniques (stepwise selection vs. genetic-based selection) is presented. In addition, classical MLR is also compared with regression trees (M5P). The results when each methodology is applied to estimate stand biomass fractions from an area of northern Spain show that genetically-selected M5P obtains the best results

Lubricating Bacteria Model for Branching growth of Bacterial Colonies

Various bacterial strains (e.g. strains belonging to the genera Bacillus, Paenibacillus, Serratia and Salmonella) exhibit colonial branching patterns during growth on poor semi-solid substrates. These patterns reflect the bacterial cooperative self-organization. Central part of the cooperation is the collective formation of lubricant on top of the agar which enables the bacteria to swim. Hence it provides the colony means to advance towards the food. One method of modeling the colonial development is via coupled reaction-diffusion equations which describe the time evolution of the bacterial density and the concentrations of the relevant chemical fields. This idea has been pursued by a number of groups. Here we present an additional model which specifically includes an evolution equation for the lubricant excreted by the bacteria. We show that when the diffusion of the fluid is governed by nonlinear diffusion coefficient branching patterns evolves. We study the effect of the rates of emission and decomposition of the lubricant fluid on the observed patterns. The results are compared with experimental observations. We also include fields of chemotactic agents and food chemotaxis and conclude that these features are needed in order to explain the observations.Comment: 1 latex file, 16 jpeg files, submitted to Phys. Rev.

Antimicrobials: A Global Alliance for Optimizing Their Rational Use in Intra-Abdominal Infections (AGORA)

Intra-abdominal infections (IAI) are an important cause of morbidity and are frequently associated with poor prognosis, particularly in high-risk patients. The cornerstones in the management of complicated IAIs are timely effective source control with appropriate antimicrobial therapy. Empiric antimicrobial therapy is important in the management of intra-abdominal infections and must be broad enough to cover all likely organisms because inappropriate initial antimicrobial therapy is associated with poor patient outcomes and the development of bacterial resistance. The overuse of antimicrobials is widely accepted as a major driver of some emerging infections (such as C. difficile), the selection of resistant pathogens in individual patients, and for the continued development of antimicrobial resistance globally. The growing emergence of multi-drug resistant organisms and the limited development of new agents available to counteract them have caused an impending crisis with alarming implications, especially with regards to Gram-negative bacteria. An international task force from 79 different countries has joined this project by sharing a document on the rational use of antimicrobials for patients with IAIs. The project has been termed AGORA (Antimicrobials: A Global Alliance for Optimizing their Rational Use in Intra-Abdominal Infections). The authors hope that AGORA, involving many of the world\u27s leading experts, can actively raise awareness in health workers and can improve prescribing behavior in treating IAIs

A Comparative Study of Machine Learning Regression Methods on LiDAR Data: A Case Study

Light Detection and Ranging (LiDAR) is a remote sensor able to extract vertical information from sensed objects. LiDAR-derived information is nowadays used to develop environmental models for describing fire behaviour or quantifying biomass stocks in forest areas. A multiple linear regression (MLR) with previous stepwise feature selection is the most common method in the literature to develop LiDAR-derived models. MLR defines the relation between the set of field measurements and the statistics extracted from a LiDAR flight. Machine learning has recently been paid an increasing attention to improve classic MLR results. Unfortunately, few studies have been proposed to compare the quality of the multiple machine learning approaches. This paper presents a comparison between the classic MLR-based methodology and common regression techniques in machine learning (neural networks, regression trees, support vector machines, nearest neighbour, and ensembles such as random forests). The selected techniques are applied to real LiDAR data from two areas in the province of Lugo (Galizia, Spain). The results show that support vector regression statistically outperforms the rest of techniques when feature selection is applied. However, its performance cannot be said statistically different from that of Random Forests when previous feature selection is skipped

The mixmaster universe: A chaotic Farey tale

When gravitational fields are at their strongest, the evolution of spacetime is thought to be highly erratic. Over the past decade debate has raged over whether this evolution can be classified as chaotic. The debate has centered on the homogeneous but anisotropic mixmaster universe. A definite resolution has been lacking as the techniques used to study the mixmaster dynamics yield observer dependent answers. Here we resolve the conflict by using observer independent, fractal methods. We prove the mixmaster universe is chaotic by exposing the fractal strange repellor that characterizes the dynamics. The repellor is laid bare in both the 6-dimensional minisuperspace of the full Einstein equations, and in a 2-dimensional discretisation of the dynamics. The chaos is encoded in a special set of numbers that form the irrational Farey tree. We quantify the chaos by calculating the strange repellor's Lyapunov dimension, topological entropy and multifractal dimensions. As all of these quantities are coordinate, or gauge independent, there is no longer any ambiguity--the mixmaster universe is indeed chaotic.Comment: 45 pages, RevTeX, 19 Figures included, submitted to PR

Do spinal cord-injured individuals with stronger sense of coherence use different psychological defense styles?

Objectives: Although the importance of sense of coherence (SOC) and psychological defense mechanisms (PDMs) in the process of coping has been demonstrated, it has not yet been clarified whether individuals with stronger SOC use specific PDMs.Study design: Cross-sectional. Setting: Iran. Methods: Demographic and injury-related variables including injury level, time since injury, American Spinal Cord Association (ASIA) Scale and Spinal cord independence measure-III were collected among individuals with spinal cord injury (SCI). SOC was assessed by the Short-form Sense of Coherence Scale. PDMs were identified using 40-version of the Defense Style Questionnaire. Results: Neurotic defense style was the most commonly used style especially. The overall most commonly used PDM was 'rationalization', which was used by 95. Individuals with stronger SOC used more mature style (P=0.001, r=0.52), particularly 'humor' and 'suppression' mechanisms (P<0.0001 and 0.024, respectively). There was a negative correlation between stronger SOC and the use of immature defenses including passive aggression (P=0.001, r=-0.51), acting out (P=0.001, r=-0.48), isolation (P=0.009, r=-0.50), autistic fantasy (P=0.010, r=-0.30) and somatization (P<0.0001, r=-0.62). Married individuals had significantly stronger SOC (P=0.01). Age, gender, age at the time of injury incidence, time since injury, ASIA score and cause of injury were not determinants of SOC. Conclusion: In this study, PDMs, which are more probable to be used by individuals with stronger SOC, have been identified. Mature defenses including 'humor' and 'suppression' are used by stronger SOC more often, whereas immature mechanisms are less likely to be used. © 2016 International Spinal Cord Society

Adiabatic invariants and Mixmaster catastrophes

We present a rigorous analysis of the role and uses of the adiabatic invariant in the Mixmaster dynamical system. We propose a new invariant for the global dynamics which in some respects has an improved behaviour over the commonly used one. We illustrate its behaviour in a number of numerical results. We also present a new formulation of the dynamics via Catastrophe Theory. We find that the change from one era to the next corresponds to a fold catastrophe, during the Kasner shifts the potential is an Implicit Function Form whereas, as the anisotropy dissipates, the Mixmaster potential must become a Morse 0--saddle. We compare and contrast our results to many known works on the Mixmaster problem and indicate how extensions could be achieved. Further exploitation of this formulation may lead to a clearer understanding of the global Mixmaster dynamics.Comment: 24 pages, LaTeX, 5 figures (which can be obtained by sending a message to the first author), submitted to Phys.Rev.