Chaos at the border of criticality

The present paper points out to a novel scenario for formation of chaotic attractors in a class of models of excitable cell membranes near an Andronov-Hopf bifurcation (AHB). The mechanism underlying chaotic dynamics admits a simple and visual description in terms of the families of one-dimensional first-return maps, which are constructed using the combination of asymptotic and numerical techniques. The bifurcation structure of the continuous system (specifically, the proximity to a degenerate AHB) endows the Poincare map with distinct qualitative features such as unimodality and the presence of the boundary layer, where the map is strongly expanding. This structure of the map in turn explains the bifurcation scenarios in the continuous system including chaotic mixed-mode oscillations near the border between the regions of sub- and supercritical AHB. The proposed mechanism yields the statistical properties of the mixed-mode oscillations in this regime. The statistics predicted by the analysis of the Poincare map and those observed in the numerical experiments of the continuous system show a very good agreement.Comment: Chaos: An Interdisciplinary Journal of Nonlinear Science (tentatively, Sept 2008

Persistent Unstable Equilibria in Wonderland

Models of the interactions between population, economy, and environment often contain nonlinear functional relationships and variables that vary at different speeds. These properties foster apparent unpredictabilities in system behavior. Using a simple deterministic model of demographic, economic and environmental interactions, we illustrate the usefulness of geometric singular perturbation theory and local bifurcation theory. In particular we show how it is possible to obtain analytic expressions for: (1) the level of emissions above which environmental deterioration begins, (2) the time it takes from reaching the critical level of emissions to the beginning of rapid environmental deterioration, and (3) the level of emissions at the time that rapid deterioration begins. Because our results are analytic, they make the outcomes of demographic, economic, and environmental interactions more predictable, and, therefore, potentially more manageable

Endogenous Growth of Population and Income Depending on Resource and Knowledge

We consider a three sector demoeconomic model and its interdependence with the accumulation of human capital and resources. The primary sector harvests a renewable resource (fish, corn or wood) which constitutes the input into industrial production, the secondary sector of our economy. Both sectors are always affected by the stock of knowledge. The tertiary sector (schooling, teaching, training, research) is responsible for the accumulation of this stock that represents a public good for all three sectors. Labor is divided up between the three sectors under the assumption of competitive labor markets. A crucial feature of this economy is the importance of public goods--stock of knowledge and the common--which requires collective actions. Absence of collective actions describes the limiting case of hunters and gatherers. The central focus of this study is whether and what kind of interactions between the economy, the population and the environment foster sustainability and, if possible, continuous growth

Slow-fast Dynamics in Wonderland

Taking Wonderland -- a simple model of demographic, economic, and environmental interactions -- as our artificial world, we illustrate the use of geometric singular perturbation theory in environmental demoeconomics. The theory of slow-fast dynamics helps us to gain new insights into the systems behavior and allows us one to reduce the inherent unpredictability of a "natural catastrophe" in Wonderland. Though we cannot predict the exact date of such an "environmental crash," we can state the specific demographic, economic and environmental constellations of our artificial world at which the sustainability of nature becomes endangered

Deciphering the folding kinetics of transmembrane helical proteins

Nearly a quarter of genomic sequences and almost half of all receptors that are likely to be targets for drug design are integral membrane proteins. Understanding the detailed mechanisms of the folding of membrane proteins is a largely unsolved, key problem in structural biology. Here, we introduce a general model and use computer simulations to study the equilibrium properties and the folding kinetics of a $C_{\alpha}$-based two helix bundle fragment (comprised of 66 amino-acids) of Bacteriorhodopsin. Various intermediates are identified and their free energy are calculated toghether with the free energy barrier between them. In 40% of folding trajectories, the folding rate is considerably increased by the presence of non-obligatory intermediates acting as traps. In all cases, a substantial portion of the helices is rapidly formed. This initial stage is followed by a long period of consolidation of the helices accompanied by their correct packing within the membrane. Our results provide the framework for understanding the variety of folding pathways of helical transmembrane proteins

Developing mathematical thinking in the primary classroom: liberating students and teachers as learners of mathematics

This paper reports on a research study conducted with a group of practising primary school teachers (n = 24) in North East Scotland during 2011–2012. The teachers were all participants in a newly developed Masters course that had been designed with the aim of promoting the development of mathematical thinking in the primary classroom as part of project supported by the Scottish Government. The paper presents the background for this initiative within the context of the Scottish Curriculum for Excellence reform. Particular attention is given to the epistemological positioning of the researchers as this influenced both the curriculum design process and also the theoretical framing of the research study which are both described. The project was set up within a design research framework, which aimed to promote classroom-based action research on the part of participants through the course and also research by the university researchers into the process of curriculum development. The research questions focused on the teachers’ confidence, competence, attitudes and beliefs in relation to mathematics and their expectations and experiences of the impact on pupil learning arising from this course. Empirical data were drawn from pre- and post-course surveys, interviews and observations of the discussion forums in the online environment. Findings from this study highlight the way the course had a transformational and emancipatory impact on these teachers. They also highlight ways in which the ‘framing’ of particular aspects of the curriculum had an oppressive impact on learners in the ways that suppressed creativity and limited the exercise of learner autonomy. Furthermore, they highlight the ways in which a number of these teachers had experienced mathematics as a school subject in very negative ways, involving high levels of ‘symbolic violence’ and of being ‘labelled’

Relaxation oscillations and negative strain rate sensitivity in the Portevin - Le Chatelier effect

A characteristic feature of the Portevin - Le Chatelier effect or the jerky flow is the stick-slip nature of stress-strain curves which is believed to result from the negative strain rate dependence of the flow stress. The latter is assumed to result from the competition of a few relevant time scales controlling the dynamics of jerky flow. We address the issue of time scales and its connection to the negative strain rate sensitivity of the flow stress within the framework of a model for the jerky flow which is known to reproduce several experimentally observed features including the negative strain rate sensitivity of the flow stress. We attempt to understand the above issues by analyzing the geometry of the slow manifold underlying the relaxational oscillations in the model. We show that the nature of the relaxational oscillations is a result of the atypical bent geometry of the slow manifold. The analysis of the slow manifold structure helps us to understand the time scales operating in different regions of the slow manifold. Using this information we are able to establish connection with the strain rate sensitivity of the flow stress. The analysis also helps us to provide a proper dynamical interpretation for the negative branch of the strain rate sensitivity.Comment: 7 figures, To appear in Phys. Rev.

A genetic approach for building different alphabets for peptide and protein classification

<p>Abstract</p> <p>Background</p> <p>In this paper, it is proposed an optimization approach for producing reduced alphabets for peptide classification, using a Genetic Algorithm. The classification task is performed by a multi-classifier system where each classifier (Linear or Radial Basis function Support Vector Machines) is trained using features extracted by different reduced alphabets. Each alphabet is constructed by a Genetic Algorithm whose objective function is the maximization of the area under the ROC-curve obtained in several classification problems.</p> <p>Results</p> <p>The new approach has been tested in three peptide classification problems: HIV-protease, recognition of T-cell epitopes and prediction of peptides that bind human leukocyte antigens. The tests demonstrate that the idea of training a pool classifiers by reduced alphabets, created using a Genetic Algorithm, allows an improvement over other state-of-the-art feature extraction methods.</p> <p>Conclusion</p> <p>The validity of the novel strategy for creating reduced alphabets is demonstrated by the performance improvement obtained by the proposed approach with respect to other reduced alphabets-based methods in the tested problems.</p

The Feasibility and Impact of Delivering a Mind-Body Intervention in a Virtual World

Introduction: Mind-body medical approaches may ameliorate chronic disease. Stress reduction is particularly helpful, but face-to-face delivery systems cannot reach all those who might benefit. An online, 3-dimensional virtual world may be able to support the rich interpersonal interactions required of this approach. In this pilot study, we explore the feasibility of translating a face-to-face stress reduction program into an online virtual setting and estimate the effect size of the intervention. Methods and Findings: Domain experts in virtual world technology joined with mind body practitioners to translate an existing 8 week relaxation response-based resiliency program into an 8-week virtual world-based program in Second Life™ (SL). Twenty-four healthy volunteers with at least one month's experience in SL completed the program. Each subject filled out the Perceived Stress Scale (PSS) and the Symptom Checklist 90- Revised (SCL-90-R) before and after taking part. Participants took part in one of 3 groups of about 10 subjects. The participants found the program to be helpful and enjoyable. Many reported that the virtual environment was an excellent substitute for the preferred face-to-face approach. On quantitative measures, there was a general trend toward decreased perceived stress, (15.7 to 15.0), symptoms of depression, (57.6 to 57.0) and anxiety (56.8 to 54.8). There was a significant decrease of 2.8 points on the SCL-90-R Global Severity Index (p<0.05). Conclusions: This pilot project showed that it is feasible to deliver a typical mind-body medical intervention through a virtual environment and that it is well received. Moreover, the small reduction in psychological distress suggests further research is warranted. Based on the data collected for this project, a randomized trial with less than 50 subjects would be appropriately powered if perceived stress is the primary outcome