Dynamical systems analysis of spike-adding mechanisms in transient bursts

The electronic version of this article is the complete one and can be found online at: doi:10.1186/2190-8567-2-7Open Access ArticleTransient bursting behaviour of excitable cells, such as neurons, is a common feature observed experimentally, but theoretically, it is not well understood. We analyse a five-dimensional simplified model of after-depolarisation that exhibits transient bursting behaviour when perturbed with a short current injection. Using one-parameter continuation of the perturbed orbit segment formulated as a well-posed boundary value problem, we show that the spike-adding mechanism is a canard-like transition that has a different character from known mechanisms for periodic burst solutions. The biophysical basis of the model gives a natural time-scale separation, which allows us to explain the spike-adding mechanism using geometric singular perturbation theory, but it does not involve actual bifurcations as for periodic bursts. We show that unstable sheets of the critical manifold, formed by saddle equilibria of the system that only exist in a singular limit, are responsible for the spike-adding transition; the transition is organised by the slow flow on the critical manifold near folds of this manifold. Our analysis shows that the orbit segment during the spike-adding transition includes a fast transition between two unstable sheets of the slow manifold that are of saddle type. We also discuss a different parameter regime where the presence of additional saddle equilibria of the full system alters the spike-adding mechanism.Engineering and Physical Sciences Research Council (EPSRC

Deep inelastic scattering from A=3 nuclei and the neutron structure function

We present a comprehensive analysis of deep inelastic scattering from He-3 and H-3, focusing in particular on the extraction of the free neutron structure function, F_2^n. Nuclear corrections are shown to cancel to within 1-2% for the isospin-weighted ratio of He-3 to H-3 structure functions, which leads to more than an order of magnitude improvement in the current uncertainty on the neutron to proton ratio F_2^n/F_2^p at large x. Theoretical uncertainties originating from the nuclear wave function, including possible non-nucleonic components, are evaluated. Measurement of the He-3 and H-3 structure functions will, in addition, determine the magnitude of the EMC effect in all A < 4 nuclei.Comment: 40 pages, 12 figures, to appear in Phys. Rev.

The future of spaceborne altimetry. Oceans and climate change: A long-term strategy

The ocean circulation and polar ice sheet volumes provide important memory and control functions in the global climate. Their long term variations are unknown and need to be understood before meaningful appraisals of climate change can be made. Satellite altimetry is the only method for providing global information on the ocean circulation and ice sheet volume. A robust altimeter measurement program is planned which will initiate global observations of the ocean circulation and polar ice sheets. In order to provide useful data about the climate, these measurements must be continued with unbroken coverage into the next century. Herein, past results of the role of the ocean in the climate system is summarized, near term goals are outlined, and requirements and options are presented for future altimeter missions. There are three basic scientific objectives for the program: ocean circulation; polar ice sheets; and mean sea level change. The greatest scientific benefit will be achieved with a series of dedicated high precision altimeter spacecraft, for which the choice of orbit parameters and system accuracy are unencumbered by requirements of companion instruments

Ontology patterns for the representation of quality changes of cells in time

Background: Cell tracking experiments, based on time-lapse microscopy, have become an important tool in biomedical research. The goal is the reconstruction of cell migration patterns, shape and state changes, and, comprehensive genealogical information from these data. This information can be used to develop process models of cellular dynamics. However, so far there has been no structured, standardized way of annotating and storing the tracking results, which is critical for comparative analysis and data integration. The key requirement to be satisfied by an ontology is the representation of a cell’s change over time. Unfortunately, popular ontology languages, such as Web Ontology Language (OWL), have limitations for the representation of temporal information. The current paper addresses the fundamental problem of modeling changes of qualities over time in biomedical ontologies specified in OWL. Results: The presented analysis is a result of the lessons learned during the development of an ontology, intended for the annotation of cell tracking experiments. We present, discuss and evaluate various representation patterns for specifying cell changes in time. In particular, we discuss two patterns of temporally changing information: n-ary relation reification and 4d fluents.These representation schemes are formalized within the ontology language OWL and are aimed at the support for annotation of cell tracking experiments. We analyze the performance of each pattern with respect to standard criteria used in software engineering and data modeling, i.e. simplicity, scalability, extensibility and adequacy. We further discuss benefits, drawbacks, and the underlying design choices of each approach. Conclusions: We demonstrate that patterns perform differently depending on the temporal distribution of modeled information. The optimal model can be constructed by combining two competitive approaches. Thus, we demonstrate that both reification and 4d fluents patterns can work hand in hand in a single ontology. Additionally, we have found that 4d fluents can be reconstructed by two patterns well known in the computer science community, i.e. state modeling and actor-role pattern

Comparison of sea-ice freeboard distributions from aircraft data and cryosat-2

The only remote sensing technique capable of obtain- ing sea-ice thickness on basin-scale are satellite altime- ter missions, such as the 2010 launched CryoSat-2. It is equipped with a Ku-Band radar altimeter, which mea- sures the height of the ice surface above the sea level. This method requires highly accurate range measure- ments. During the CryoSat Validation Experiment (Cry- oVEx) 2011 in the Lincoln Sea, Cryosat-2 underpasses were accomplished with two aircraft, which carried an airborne laser-scanner, a radar altimeter and an electro- magnetic induction device for direct sea-ice thickness re- trieval. Both aircraft flew in close formation at the same time of a CryoSat-2 overpass. This is a study about the comparison of the sea-ice freeboard and thickness dis- tribution of airborne validation and CryoSat-2 measure- ments within the multi-year sea-ice region of the Lincoln Sea in spring, with respect to the penetration of the Ku- Band signal into the snow