The problem of determining the neuronal current inside the brain from measurements of the induced magnetic field outside the head is discussed under the assumption that the space occupied by the brain is approximately spherical. By inverting the Geselowitz equation, the part of the current which can be reconstructed from the measurements is precisely determined. This actually consists of only certain moments of one of the two functions specifying the tangential part of the current. The other function specifying the tangential part of the current as well as the radial part of the current are completely arbitrary. However, it is also shown that with the assumption of energy minimization, the current can be reconstructed uniquely. A numerical implementation of this unique reconstruction is also presented.

The energy sector is closely interconnected with the building sector and integrated Information and Communication Technologies (ICT) solutions for effective energy management supporting decision-making at building, district and city level are key fundamental elements for making a city Smart. The available systems are designed and intended exclusively for a predefined number of cases and systems without allowing for expansion and interoperability with other applications that is partially due to the lack of semantics. This paper presents an advanced Internet of Things (IoT) based system for intelligent energy management in buildings. A semantic framework is introduced aiming at the unified and standardised modelling of the entities that constitute the building environment. Suitable rules are formed, aiming at the intelligent energy management and the general modus operandi of Smart Building. In this context, an IoT-based system was implemented, which enhances the interactivity of the buildings’ energy management systems. The results from its pilot application are presented and discussed. The proposed system extends existing approaches and integrates cross-domain data, such as the building’s data (e.g., energy management systems), energy production, energy prices, weather data and end-users’ behaviour, in order to produce daily and weekly action plans for the energy end-users with actionable personalised information.

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In this work we study second and third order approximations of water wave equations of the Korteweg–de Vries (KdV) type. First we derive analytical expressions for solitary wave solutions for some special sets of parameters of the equations. Remarkably enough, in all these approximations, the form of the solitary wave and its amplitude-velocity dependence are identical to the sech2 formula of the one-soliton solution of the KdV. Next we carry out a detailed numerical study of these solutions using a Fourier pseudospectral method combined with a finite-difference scheme, in parameter regions where soliton-like behavior is observed. In these regions, we find solitary waves which are stable and behave like solitons in the sense that they remain virtually unchanged under time evolution and mutual interaction. In general, these solutions sustain small oscillations in the form of radiation waves (trailing the solitary wave) and may still be regarded as stable, provided these radiation waves do not exceed a numerical stability threshold. Instability occurs at high enough wave speeds, when these oscillations exceed the stability threshold already at the outset, and manifests itself as a sudden increase of these oscillations followed by a blowup of the wave after relatively short time intervals.