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

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’

Incomplete approach to homoclinicity in a model with bent-slow manifold geometry

The dynamics of a model, originally proposed for a type of instability in plastic flow, has been investigated in detail. The bifurcation portrait of the system in two physically relevant parameters exhibits a rich variety of dynamical behaviour, including period bubbling and period adding or Farey sequences. The complex bifurcation sequences, characterized by Mixed Mode Oscillations, exhibit partial features of Shilnikov and Gavrilov-Shilnikov scenario. Utilizing the fact that the model has disparate time scales of dynamics, we explain the origin of the relaxation oscillations using the geometrical structure of the bent-slow manifold. Based on a local analysis, we calculate the maximum number of small amplitude oscillations, $s$, in the periodic orbit of $L^s$ type, for a given value of the control parameter. This further leads to a scaling relation for the small amplitude oscillations. The incomplete approach to homoclinicity is shown to be a result of the finite rate of `softening' of the eigen values of the saddle focus fixed point. The latter is a consequence of the physically relevant constraint of the system which translates into the occurrence of back-to-back Hopf bifurcation.Comment: 14 Figures(Postscript); To Appear in Physica D : Nonlinear Phenomen

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.

Design and synthesis of new quinazolin-4-one derivatives with negative mGlu7mGlu_7 receptor modulation activity and antipsychotic-like properties

Following the glutamatergic theory of schizophrenia and based on our previous study regarding the antipsychotic-like activity of mGlu7 NAMs, we synthesized a new compound library containing 103 members, which were examined for NAM mGlu7 activity in the T-REx 293 cell line expressing a recombinant human mGlu7 receptor. Out of the twenty-two scaffolds examined, active compounds were found only within the quinazolinone chemotype. 2-(2-Chlorophenyl)-6-(2,3-dimethoxyphenyl)-3-methylquinazolin-4(3H)-one (A9-7, ALX-171, mGlu7 IC50 = 6.14 µM) was selective over other group III mGlu receptors (mGlu4 and mGlu8), exhibited satisfactory drug-like properties in preliminary DMPK profiling, and was further tested in animal models of antipsychotic-like activity, assessing the positive, negative, and cognitive symptoms. ALX-171 reversed DOI-induced head twitches and MK-801-induced disruptions of social interactions or cognition in the novel object recognition test and spatial delayed alternation test. On the other hand, the efficacy of the compound was not observed in the MK-801-induced hyperactivity test or prepulse inhibition. In summary, the observed antipsychotic activity profile of ALX-171 justifies the further development of the group of quinazolin-4-one derivatives in the search for a new drug candidate for schizophrenia treatment

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

Surmounting the resistance against EGFR inhibitors through the development of thieno[2,3-d]pyrimidine-based dual EGFR/HER2 inhibitors

In light of the emergence of resistance against the currently available EGFR inhibitors, our study focuses on tackling this problem through the development of dual EGFR/HER2 inhibitors with improved enzymatic affinities. Guided by the binding mode of the marketed dual EGFR/HER2 inhibitor, Lapatinib, we proposed the design of dual EGFR/HER2 inhibitors based on the 6-phenylthieno[2,3-d]pyrimidine as a core scaffold and hinge binder. After two cycles of screening aiming to identify the optimum aniline headgroup and solubilizing group, we eventually identified 27b as a dual EGFR/HER2 inhibitor with IC50 values of 91.7 nM and 1.2 μM, respectively. Notably, 27b dramatically reduced the viability of various patient-derived cancer cells preferentially overexpressing EGFR/HER2 (A431, MDA-MBA-361 and SKBr3 with IC50 values of 1.45, 3.5 and 4.83 μM, respectively). Additionally, 27b efficiently thwarted the proliferation of lapatinib-resistant human non-small lung carcinoma (NCI-H1975) cells, harboring T790 M mutation, with IC50 of 4.2 μM. Consistently, 27b significantly blocked EGF-induced EGFR activation and inactivated its downstream AKT/mTOR/S6 signalling pathway triggering apoptotic cell death in NCI-H1975 cells. The present study presents a promising candidate for further design and development of novel EGFR/HER2 inhibitors capable of overcoming EGFR TKIs resistance

Synthesis and Implementation of Reconfigurable PLC on FPGA Platform

The paper presents a set of algorithms dedicated for synthesis of reconfigurable logic controllers implemented on FPGA platform and programmed according to IEC1131 and EN61131. The program is compiled to hardware structure with a massive parallel processing. The developed method automatically allocates resources and operations. It controls resource usage and operation timing. Using mixed concept of operation allocation that considers operation timing and forms combinatorial chains of operations number of execution cycles can be reduced. An example of logic functions, PID controller and mixed arithmetic and logic programming examples are considered. Introducing the automatic implementation method allows flexible implementing the control algorithms. The maximal possible parallelism (limited only by the algorithm dependencies and available resources) is introduced