Methods for comparing and constraining models of dendritic spines

Physiological evidence using Infrared Video Microscopy during the uncaging of glutamate has proven the existence of excitable calcium ion channels in spine heads, highlighting the need for reliable models of spines. In this study we compare the three main methods of simulating excitable spines: Baer & Rinzel's Continuum (B&R) model, Coombes' Spike-Diffuse-Spike (SDS) model and paired cable and ion channel equations (Cable model). Tests are done to determine how well the models approximate each other in terms of speed and heights of travelling waves. Significant quantitative differences are found between the models: travelling waves in the SDS model in particular are found to travel at much lower speeds and sometimes much higher voltages than in the Cable or B&R models. Meanwhile qualitative differences are found between the B&R and SDS models over realistic parameter ranges. The cause of these differences is investigated and potential solutions proposed.

Singularities of optimal control problems on some 6-D lie groups

This paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices.

Prebiotics and probiotics: potential strategies for reducing travellers' diarrhoea in athletes competing abroad

Travellers’ diarrhoea (TD) is the most common gastrointestinal illness to affect athletes competing abroad. Consequences of this debilitating condition include difficulties with training and/or participating in competitions which the athlete may have spent several years preparing for. Currently, there are no targeted strategies to reduce TD incidence in athletes. General methods used to reduce TD risk, such as avoidance of contaminated foods, chemoprophylactics and immunoprophylactics, have disadvantages. Since most causative agents of TD are microbial, strategies to minimise TD risks may be better focused on the gut microbiota. Prebiotics and probiotics can fortify the gut microbial balance, thus potentially aiding the fight against TD-associated microorganisms. Specific probiotics have shown promising actions against TD-associated microorganisms through antimicrobial activities. Use of prebiotics has led to an improved intestinal microbial balance which may be better equipped to combat TD-associated microorganisms. Both approaches have shown promising results in general travelling populations; therefore, a targeted approach for athletes has the potential to provide a competitive advantage.

Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field

A unified view on the interfacial instability in a model of aluminium reduction cells in the presence of a uniform, vertical, background magnetic field is presented. The classification of instability modes is based on the asymptotic theory for high values of parameter β, which characterises the ratio of the Lorentz force based on the disturbance current, and gravity. It is shown that the spectrum of the travelling waves consists of two parts independent of the horizontal cross-section of the cell: highly unstable wall modes and stable or weakly unstable centre, or Sele’s modes. The wall modes with the disturbance of the interface being localised at the sidewalls of the cell dominate the dynamics of instability. Sele’s modes are characterised by a distributed disturbance over the whole horizontal extent of the cell. As β increases these modes are stabilized by the field.

Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth

We study weak solutions for a class of free-boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth. We show that such problems are equivalent to problems in fixed domains and study the regularity of their solutions. We also prove that in very general situations the free boundary is necessarily the graph of a function.

The elasticity of demand is about occupancy, not prices: building European demand curves based on occupancy elasticity

The peak congestion of the European grid may create significant impacts on system costs because of the need for higher marginal cost generation, higher cost system balancing and increasing grid reinforcement investment. The use of time of use rates, incentives, real time pricing and other programmes, usually defined as Demand Side Management (DSM), could bring about significant reductions in prices, limit carbon emissions from dirty power plants, and improve the integration of renewable sources of energy. Unlike previous studies on elasticity of residential electricity demand under flat tariffs, the aim of this study is not to investigate the known relatively inelastic relationship between demand and prices. Rather, the aim is to assess how occupancy levels vary in different European countries. This reflects the reality of demand loads, which are predominantly determined by the timing of human activities (e.g. travelling to work, taking children to school) rather than prices. To this end, two types of occupancy elasticity are estimated: baseline occupancy elasticity and peak occupancy elasticity. These represent the intrinsic elasticity associated with human activities of single residential end-users in 15 European countries. This study makes use of occupancy time-series data from the Harmonised European Time Use Survey database to build European occupancy curves; identify peak occupancy periods; draw time use demand curves for video and TV watching activity; and estimate national occupancy elasticity levels of single-occupant households. Findings on occupancy elasticities provide an indication of possible DSM strategies based on occupancy levels and not prices.

Root growth models: towards a new generation of continuous approaches

Models of root system growth emerged in the early 1970s, and were based on mathematical representations of root length distribution in soil. The last decade has seen the development of more complex architectural models and the use of computer-intensive approaches to study developmental and environmental processes in greater detail. There is a pressing need for predictive technologies that can integrate root system knowledge, scaling from molecular to ensembles of plants. This paper makes the case for more widespread use of simpler models of root systems based on continuous descriptions of their structure. A new theoretical framework is presented that describes the dynamics of root density distributions as a function of individual root developmental parameters such as rates of lateral root initiation, elongation, mortality, and gravitropsm. The simulations resulting from such equations can be performed most efficiently in discretized domains that deform as a result of growth, and that can be used to model the growth of many interacting root systems. The modelling principles described help to bridge the gap between continuum and architectural approaches, and enhance our understanding of the spatial development of root systems. Our simulations suggest that root systems develop in travelling wave patterns of meristems, revealing order in otherwise spatially complex and heterogeneous systems. Such knowledge should assist physiologists and geneticists to appreciate how meristem dynamics contribute to the pattern of growth and functioning of root systems in the field.

Effects of Thomson-scattering geometry on white-light imaging of an interplanetary shock: synthetic observations from forward magnetohydrodynamic modelling

Stereoscopic white-light imaging of a large portion of the inner heliosphere has been used to track interplanetary coronal mass ejections. At large elongations from the Sun, the white-light brightness depends on both the local electron density and the efficiency of the Thomson-scattering process. To quantify the effects of the Thomson-scattering geometry, we study an interplanetary shock using forward magnetohydrodynamic simulation and synthetic white-light imaging. Identifiable as an inclined streak of enhanced brightness in a time–elongation map, the travelling shock can be readily imaged by an observer located within a wide range of longitudes in the ecliptic. Different parts of the shock front contribute to the imaged brightness pattern viewed by observers at different longitudes. Moreover, even for an observer located at a fixed longitude, a different part of the shock front will contribute to the imaged brightness at any given time. The observed brightness within each imaging pixel results from a weighted integral along its corresponding ray-path. It is possible to infer the longitudinal location of the shock from the brightness pattern in an optical sky map, based on the east–west asymmetry in its brightness and degree of polarisation. Therefore, measurement of the interplanetary polarised brightness could significantly reduce the ambiguity in performing three-dimensional reconstruction of local electron density from white-light imaging.

‘These changes and accessions of knowledge’: translation, scientific travel writing and modernity - Alexander von Humboldt's Personal Narrative

A second English translation of Alexander von Humboldt's account of travel to South America, the Relation historique (1814–25), was published between 1852 and 1853. Appearing some 30 years after the first seven-volume translation (1814–29) by Helen Maria Williams, this second rendering of the Personal Narrative by Thomasina Ross was an abridged version that aimed to make Humboldt's travelogue more relevant to the mid-century reader. This translation has largely been overlooked by Humboldt scholars, despite it being a far more affordable, accessible and popular edition. I discuss here how Ross's revisions can be understood within a larger process of rereading and revision that responded to critics’ assessments of the first translation. Emphasising the status of the Personal Narrative as a text in flux, I assess how Ross modernised it to meet the demands of a new readership, recasting the image that Humboldt had constructed of himself as a travelling scientist, scientific writer and member of the international scientific community.

Axonal velocity distributions in neural feld equations

By modelling the average activity of large neuronal populations, continuum mean field models (MFMs) have become an increasingly important theoretical tool for understanding the emergent activity of cortical tissue. In order to be computationally tractable, long-range propagation of activity in MFMs is often approximated with partial differential equations (PDEs). However, PDE approximations in current use correspond to underlying axonal velocity distributions incompatible with experimental measurements. In order to rectify this deficiency, we here introduce novel propagation PDEs that give rise to smooth unimodal distributions of axonal conduction velocities. We also argue that velocities estimated from fibre diameters in slice and from latency measurements, respectively, relate quite differently to such distributions, a significant point for any phenomenological description. Our PDEs are then successfully fit to fibre diameter data from human corpus callosum and rat subcortical white matter. This allows for the first time to simulate long-range conduction in the mammalian brain with realistic, convenient PDEs. Furthermore, the obtained results suggest that the propagation of activity in rat and human differs significantly beyond mere scaling. The dynamical consequences of our new formulation are investigated in the context of a well known neural field model. On the basis of Turing instability analyses, we conclude that pattern formation is more easily initiated using our more realistic propagator. By increasing characteristic conduction velocities, a smooth transition can occur from self-sustaining bulk oscillations to travelling waves of various wavelengths, which may influence axonal growth during development. Our analytic results are also corroborated numerically using simulations on a large spatial grid. Thus we provide here a comprehensive analysis of empirically constrained activity propagation in the context of MFMs, which will allow more realistic studies of mammalian brain activity in the future.

Normal mode Rossby waves and their effects on chemical composition in the late summer stratosphere

During past MANTRA campaigns, ground-based measurements of several long-lived chemical species have revealed quasi-periodic fluctuations on time scales of several days. These fluctuations could confound efforts to detect long-term trends from MANTRA, and need to be understood and accounted for. Using the Canadian Middle Atmosphere Model, we investigate the role of dynamical variability in the late summer stratosphere due to normal mode Rossby waves and the impact of this variability on fluctuations in chemical species. Zonal wavenumber 1, westward travelling waves are considered with average periods of 5, 10 and 16 days. Time-lagged correlations between the temperature and nitrous oxide, methane and ozone fields are calculated in order to assess the possible impact of these waves on the chemical species. Using Fourier-wavelet decomposition and correlating the fluctuations between the temperature and chemical fields, we determine that variations in the chemical species are well-correlated with the 5- and 10-day waves between 30 and 60 km, although the nature of the correlations depend strongly on altitude. Interannual variability of the waves is also examined.

The distribution of interplanetary dust between 0.96 and 1.04 au as inferred from impacts on the STEREO spacecraft observed by the heliospheric imagers

The distribution of dust in the ecliptic plane between 0.96 and 1.04 au has been inferred from impacts on the two Solar Terrestrial Relations Observatory (STEREO) spacecraft through observation of secondary particle trails and unexpected off-points in the heliospheric imager (HI) cameras. This study made use of analysis carried out by members of a distributed web-based citizen science project Solar Stormwatch. A comparison between observations of the brightest particle trails and a survey of fainter trails shows consistent distributions. While there is no obvious correlation between this distribution and the occurrence of individual meteor streams at Earth, there are some broad longitudinal features in these distributions that are also observed in sources of the sporadic meteor population. The different position of the HI instrument on the two STEREO spacecraft leads to each sampling different populations of dust particles. The asymmetry in the number of trails seen by each spacecraft and the fact that there are many more unexpected off-points in the HI-B than in HI-A indicates that the majority of impacts are coming from the apex direction. For impacts causing off-points in the HI-B camera, these dust particles are estimated to have masses in excess of 10−17 kg with radii exceeding 0.1 μm. For off-points observed in the HI-A images, which can only have been caused by particles travelling from the anti-apex direction, the distribution is consistent with that of secondary ‘storm’ trails observed by HI-B, providing evidence that these trails also result from impacts with primary particles from an anti-apex source. Investigating the mass distribution for the off-points of both HI-A and HI-B, it is apparent that the differential mass index of particles from the apex direction (causing off-points in HI-B) is consistently above 2. This indicates that the majority of the mass is within the smaller particles of this population. In contrast, the differential mass index of particles from the anti-apex direction (causing off-points in HI-A) is consistently below 2, indicating that the majority of the mass is to be found in larger particles of this distribution.

Modelling the effects of gravity waves on stratocumulus clouds observed during VOCALS-UK

During the VOCALS campaign spaceborne satellite observations showed that travelling gravity wave packets, generated by geostrophic adjustment, resulted in perturbations to marine boundary layer (MBL) clouds over the south-east Pacific Ocean (SEP). Often, these perturbations were reversible in that passage of the wave resulted in the clouds becoming brighter (in the wave crest), then darker (in the wave trough) and subsequently recovering their properties after the passage of the wave. However, occasionally the wave packets triggered irreversible changes to the clouds, which transformed from closed mesoscale cellular convection to open form. In this paper we use large eddy simulation (LES) to examine the physical mechanisms that cause this transition. Specifically, we examine whether the clearing of the cloud is due to (i) the wave causing additional cloud-top entrainment of warm, dry air or (ii) whether the additional condensation of liquid water onto the existing drops and the subsequent formation of drizzle are the important mechanisms. We find that, although the wave does cause additional drizzle formation, this is not the reason for the persistent clearing of the cloud; rather it is the additional entrainment of warm, dry air into the cloud followed by a reduction in longwave cooling, although this only has a significant effect when the cloud is starting to decouple from the boundary layer. The result in this case is a change from a stratocumulus to a more patchy cloud regime. For the simulations presented here, cloud condensation nuclei (CCN) scavenging did not play an important role in the clearing of the cloud. The results have implications for understanding transitions between the different cellular regimes in marine boundary layer (MBL) clouds.

Optimal steady motions for oriented vehicles

Motivated by the motion planning problem for oriented vehicles travelling in a 3-Dimensional space; Euclidean space E3, the sphere S3 and Hyperboloid H3. For such problems the orientation of the vehicle is naturally represented by an orthonormal frame over a point in the underlying manifold. The orthonormal frame bundles of the space forms R3,S3 and H3 correspond with their isometry groups and are the Euclidean group of motion SE(3), the rotation group SO(4) and the Lorentzian group SO(1; 3) respectively. Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to left-invariant control systems defined on Lie groups. In this paper a method for integrating these systems is given where the controls are time-independent. For constant twist motions or helical motions, the corresponding curves g(t) 2 SE(3) are given in closed form by using the well known Rodrigues’ formula. However, this formula is only applicable to the Euclidean case. This paper gives a method for computing the non-Euclidean screw/helical motions in closed form. This involves decoupling the system into two lower dimensional systems using the double cover properties of Lie groups, then the lower dimensional systems are solved explicitly in closed form.

How do atmospheric rivers form?

Identifying the source of atmospheric rivers: Are they rivers of moisture exported from the subtropics or footprints left behind by poleward travelling storms? The term atmospheric river is used to describe corridors of strong water vapor transport in the troposphere. Filaments of enhanced water vapor, commonly observed in satellite imagery extending from the subtropics to the extratropics, are routinely used as a proxy for identifying these regions of strong water vapor transport. The precipitation associated with these filaments of enhanced water vapor can lead to high impact flooding events. However, there remains some debate as to how these filaments form. In this paper we analyse the transport of water vapor within a climatology of wintertime North Atlantic extratropical cyclones. Results show that atmospheric rivers are formed by the cold front which sweeps up water vapor in the warm sector as it catches up with the warm front. This causes a narrow band of high water vapor content to form ahead of the cold front at the base of the warm conveyor belt airflow. Thus, water vapor in the cyclone's warm sector, and not long-distance transport of water vapor from the subtropics, is responsible for the generation of filaments of high water vapor content. A continuous cycle of evaporation and moisture convergence within the cyclone replenishes water vapor lost via precipitation. Thus, rather than representing a direct and continuous feed of moist air from the subtropics into the centre of a cyclone (as suggested by the term atmospheric river), these filaments are, in-fact, the result of water vapor exported from the cyclone and thus they represent the footprints left behind as cyclones travel polewards from subtropics.