Towards a model-based integration of co-registered electroencephalography/functional magnetic resonance imaging data with realistic neural population meshes

Brain activity can be measured with several non-invasive neuroimaging modalities, but each modality has inherent limitations with respect to resolution, contrast and interpretability. It is hoped that multimodal integration will address these limitations by using the complementary features of already available data. However, purely statistical integration can prove problematic owing to the disparate signal sources. As an alternative, we propose here an advanced neural population model implemented on an anatomically sound cortical mesh with freely adjustable connectivity, which features proper signal expression through a realistic head model for the electroencephalogram (EEG), as well as a haemodynamic model for functional magnetic resonance imaging based on blood oxygen level dependent contrast (fMRI BOLD). It hence allows simultaneous and realistic predictions of EEG and fMRI BOLD from the same underlying model of neural activity. As proof of principle, we investigate here the influence on simulated brain activity of strengthening visual connectivity. In the future we plan to fit multimodal data with this neural population model. This promises novel, model-based insights into the brain's activity in sleep, rest and task conditions.

Scattering by infinite one-dimensional rough surfaces

We consider the Dirichlet boundary-value problem for the Helmholtz equation in a non-locally perturbed half-plane. This problem models time-harmonic electromagnetic scattering by a one-dimensional, infinite, rough, perfectly conducting surface; the same problem arises in acoustic scattering by a sound-soft surface. ChandlerWilde & Zhang have suggested a radiation condition for this problem, a generalization of the Rayleigh expansion condition for diffraction gratings, and uniqueness of solution has been established. Recently, an integral equation formulation of the problem has also been proposed and, in the special case when the whole boundary is both Lyapunov and a small perturbation of a flat boundary, the unique solvability of this integral equation has been shown by Chandler-Wilde & Ross by operator perturbation arguments. In this paper we study the general case, with no limit on surface amplitudes or slopes, and show that the same integral equation has exactly one solution in the space of bounded and continuous functions for all wavenumbers. As an important corollary we prove that, for a variety of incident fields including the incident plane wave, the Dirichlet boundary-value problem for the scattered field has a unique solution.

The middle atmosphere

The last 50 years have seen enormous advances in our knowledge and understanding of the stratosphere and mesosphere, which together comprise the middle atmosphere. Beginning from a phase of basic discovery, we have now reached the stage where most observed phenomena can be modelled from first principles with a reasonable degree of fidelity, and where there is an overall theoretical framework which can be tested against measurements and models. This review surveys a number of major surprises in middle atmosphere science over the past 50 years. A phenomenological and historical approach is adopted in each case, leading up to the current literature. Along the way, a common thread emerges: the central role of waves, of various types, in redistributing angular momentum within the atmosphere, and the global nature of the atmospheric response to such redistribution

On wave action and phase in the non-canonical Hamiltonian formulation

The long time–evolution of disturbances to slowly–varying solutions of partial differential equations is subject to the adiabatic invariance of the wave action. Generally, this approximate conservation law is obtained under the assumption that the partial differential equations are derived from a variational principle or have a canonical Hamiltonian structure. Here, the wave action conservation is examined for equations that possess a non–canonical (Poisson) Hamiltonian structure. The linear evolution of disturbances in the form of slowly varying wavetrains is studied using a WKB expansion. The properties of the original Hamiltonian system strongly constrain the linear equations that are derived, and this is shown to lead to the adiabatic invariance of a wave action. The connection between this (approximate) invariance and the (exact) conservation laws of pseudo–energy and pseudomomentum that exist when the basic solution is exactly time and space independent is discussed. An evolution equation for the slowly varying phase of the wavetrain is also derived and related to Berry's phase.

A Hamiltonian weak-wave model for shallow-water flow

A reduced dynamical model is derived which describes the interaction of weak inertia–gravity waves with nonlinear vortical motion in the context of rotating shallow–water flow. The formal scaling assumptions are (i) that there is a separation in timescales between the vortical motion and the inertia–gravity waves, and (ii) that the divergence is weak compared to the vorticity. The model is Hamiltonian, and possesses conservation laws analogous to those in the shallow–water equations. Unlike the shallow–water equations, the energy invariant is quadratic. Nonlinear stability theorems are derived for this system, and its linear eigenvalue properties are investigated in the context of some simple basic flows.

A synchrotron powder X-ray diffraction study of the skutterudite-related phases AB1.5Te1.5 (A=Co, Rh, Ir; B= Ge, Sn)

X-ray resonant scattering has been exploited to investigate the crystal structure of the AB1.5Te1.5 phases (A = Co, Rh, Ir; B = Ge, Sn). Analysis of the diffraction data reveals that CoGe1.5Te1.5 and ASn1.5Te1.5 adopt a rhombohedral skutterudite-related structure, containing diamond-shape B2Te2 rings, in which the B and Te atoms are ordered and trans to each other. Anion ordering is however incomplete, and with increasing the size of both cations and anions, the degree of anion ordering decreases. By contrast, the diffraction data of IrGe1.5Te1.5 are consistent with an almost statistical distribution of the anions over the available sites, although some ordered domains may be present. The thermoelectric properties of these materials are discussed in the light of these results.

Highly contrasting effects of different climate forcing agents on terrestrial ecosystem services

Many atmospheric constituents besides carbon dioxide (CO2) contribute to global warming, and it is common to compare their influence on climate in terms of radiative forcing, which measures their impact on the planetary energy budget. A number of recent studies have shown that many radiatively active constituents also have important impacts on the physiological functioning of ecosystems, and thus the ‘ecosystem services’ that humankind relies upon. CO2 increases have most probably increased river runoff and had generally positive impacts on plant growth where nutrients are non-limiting, whereas increases in near-surface ozone (O3) are very detrimental to plant productivity. Atmospheric aerosols increase the fraction of surface diffuse light, which is beneficial for plant growth. To illustrate these differences, we present the impact on net primary productivity and runoff of higher CO2, higher near-surface O3, and lower sulphate aerosols, and for equivalent changes in radiative forcing.We compare this with the impact of climate change alone, arising, for example, from a physiologically inactive gas such as methane (CH4). For equivalent levels of change in radiative forcing, we show that the combined climate and physiological impacts of these individual agents vary markedly and in some cases actually differ in sign. This study highlights the need to develop more informative metrics of the impact of changing atmospheric constituents that go beyond simple radiative forcing.

Granular flow in the marginal ice zone

The region of sea ice near the edge of the sea ice pack is known as the marginal ice zone (MIZ), and its dynamics are complicated by ocean wave interaction with the ice cover, strong gradients in the atmosphere and ocean and variations in sea ice rheology. This paper focuses on the role of sea ice rheology in determining the dynamics of the MIZ. Here, sea ice is treated as a granular material with a composite rheology describing collisional ice floe interaction and plastic interaction. The collisional component of sea ice rheology depends upon the granular temperature, a measure of the kinetic energy of flow fluctuations. A simplified model of the MIZ is introduced consisting of the along and across momentum balance of the sea ice and the balance equation of fluctuation kinetic energy. The steady solution of these equations is found to leading order using elementary methods. This reveals a concentrated region of rapid ice flow parallel to the ice edge, which is in accordance with field observations, and previously called the ice jet. Previous explanations of the ice jet relied upon the existence of ocean currents beneath the ice cover. We show that an ice jet results as a natural consequence of the granular nature of sea ice.

Cost effectiveness of mitigation measures for water security and water quality in the River Thames catchment: impacts of changing climate, land use and water scarcity

The catchment of the River Thames, the principal river system in southern England, provides the main water supply for London but is highly vulnerable to changes in climate, land use and population. The river is eutrophic with significant algal blooms with phosphorus assumed to be the primary chemical indicator of ecosystem health. In the Thames Basin, phosphorus is available from point sources such as wastewater treatment plants and from diffuse sources such as agriculture. In order to predict vulnerability to future change, the integrated catchments model for phosphorus (INCA-P) has been applied to the river basin and used to assess the cost-effectiveness of a range of mitigation and adaptation strategies. It is shown that scenarios of future climate and land-use change will exacerbate the water quality problems, but a range of mitigation measures can improve the situation. A cost-effectiveness study has been undertaken to compare the economic benefits of each mitigation measure and to assess the phosphorus reductions achieved. The most effective strategy is to reduce fertilizer use by 20% together with the treatment of effluent to a high standard. Such measures will reduce the instream phosphorus concentrations to close to the EU Water Framework Directive target for the Thames.

A continuum anisotropic model of sea-ice dynamics

We develop the essential ingredients of a new, continuum and anisotropic model of sea-ice dynamics designed for eventual use in climate simulation. These ingredients are a constitutive law for sea-ice stress, relating stress to the material properties of sea ice and to internal variables describing the sea-ice state, and equations describing the evolution of these variables. The sea-ice cover is treated as a densely flawed two-dimensional continuum consisting of a uniform field of thick ice that is uniformly permeated with narrow linear regions of thinner ice called leads. Lead orientation, thickness and width distributions are described by second-rank tensor internal variables: the structure, thickness and width tensors, whose dynamics are governed by corresponding evolution equations accounting for processes such as new lead generation and rotation as the ice cover deforms. These evolution equations contain contractions of higher-order tensor expressions that require closures. We develop a sea-ice stress constitutive law that relates sea-ice stress to the structure tensor, thickness tensor and strain rate. For the special case of empty leads (containing no ice), linear closures are adopted and we present calculations for simple shear, convergence and divergence.

New RGD-peptide amphiphile mixtures containing a negatively charged diluent

Here, we studied the self-assembly of two peptide amphiphiles, C16-Gly-Gly-Gly-Arg-Gly- Asp (PA 1: C16-GGG-RGD) and C16-Gly-Gly-Gly-Arg-Gly-Asp-Ser (PA 2: C16-GGG-RGDS).We showed that PA 1 and PA 2 self-assemble into nanotapes with an internal bilayer structure. C16 chains were highly interdigitated within the nanotape cores, while the peptide blocks formed water-exposed b-sheets too. PA 1 nanotapes were characterized by one spacing distribution, corresponding to a more regular internal structure than that of PA 2 nanotapes, which presented two different spacing distributions. We showed that it is possible to obtain homogeneous nanotapes in water by co-assembling PA 1 or PA 2 with the negatively charged diluent C16-Glu-Thr-Thr-Glu- Ser (PA 3: C16-ETTES). The homogeneous tapes formed by PA 1–PA 3 or PA 2–PA 3 mixtures presented a structure similar to that observed for the corresponding pure PA 1 or PA 2 nanotapes. The mixed nanotapes, which were able to form a stabilized matrix containing homogeneously distributed cell adhesive RGD groups, represent promising materials for designing new cell adhesion substrates.

Non-steady state heat conduction in composite walls

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux are prescribed there. Instead, the physical assumptions of their continuity at the interfaces are the only conditions imposed. The problem of two semi-infinite domains and that of two finite-sized domains are examined in detail. We indicate also how to extend the solution method to the setting of one finite-sized domain surrounded on both sides by semi-infinite domains, and on that of three finite-sized domains.