An optimal control approach to cell tracking

Cell tracking is of vital importance in many biological studies, hence robust cell tracking algorithms are needed for inference of dynamic features from (static) in vivo and in vitro experimental imaging data of cells migrating. In recent years much attention has been focused on the modelling of cell motility from physical principles and the development of state-of-the art numerical methods for the simulation of the model equations. Despite this, the vast majority of cell tracking algorithms proposed to date focus solely on the imaging data itself and do not attempt to incorporate any physical knowledge on cell migration into the tracking procedure. In this study, we present a mathematical approach for cell tracking, in which we formulate the cell tracking problem as an inverse problem for fitting a mathematical model for cell motility to experimental imaging data. The novelty of this approach is that the physics underlying the model for cell migration is encoded in the tracking algorithm. To illustrate this we focus on an example of Zebrafish (Danio rerio's larvae) Neutrophil migration and contrast an ad-hoc approach to cell tracking based on interpolation with the model fitting approach we propose in this study

Lessons learnt from mining meter data of residential consumers

Tracking end-users' usage patterns can enable more accurate demand forecasting and the automation of demand response execution. Accordingly, more advanced applications, such as electricity market design, integration of distributed generation and theft detection can be developed. By employing data mining techniques on smart meter recordings, the suppliers can efficiently investigate the load patterns of consumers. This paper presents applications where data mining of energy usage can derive useful information. Higher demands, on one side, and the energy price increase on the other side, have caused serious issues with regards to electricity theft, especially among developing countries. This phenomenon leads to considerable operational losses within the electrical network. In order to identify illegal residential consumers, a new method of analysing and identifying electricity consumption patterns of consumers is proposed in this paper. Moreover, the importance of data mining for analysing the consumer's usage curves was investigated. This helps to determine the behaviour of end-users for demand response purposes and improve the reliability and security of the electricity network. Clustering load profiles for large scale energy datasets are discussed in detail

Optimal control for a phase field system with a possibly singular potential

In this paper we study a distributed control problem for a phase field system of Caginalp type with logarithmic potential. The main aim of this work would be to force the location of the diffuse interface to be as close as possible to a prescribed set. However, due to the discontinuous character of the cost functional, we have to approximate it by a regular one and, in this case, we solve the associated control problem and derive the related first order necessary optimality conditions

Leaf area estimation by considering leaf dimensions in olive tree

Area (LA) estimation, based on individual leaf dimensions [length (L) and width (W)], was addressed in olive tree. Ten cultivars exposed to two watering regimes (irrigated versus rainfed) under field conditions were examined. Petiole length, leaf L, W, perimeter, base and apex angles, four shape indicators, together with LA were digitally assessed in fully-expanded leaves (480 leaves per treatment; 9.600 leaves in total). Large cultivar differences mainly in leaf size and secondarily in leaf shape were apparent. All parameters were affected by water deficit, but to a cultivar dependent extent. Leaf size was generally reduced by lack of irrigation in most cultivars. LA was estimated with higher accuracy by employing L alone, as compared to W alone, in eight cultivars. LA estimation was always improved by considering both L and W simultaneously, as compared to a single dimension. By studying each cultivar individually, LA estimation was within accepted limits (0.71 ≤ R2 ≤ 0.92) in nine cultivars, whereas in the tenth one a moderate R2 (0.63) was obtained. The accuracy of this estimation was not improved by pooling the data of all cultivars. Watering did not significantly affect the relation between estimated and measured LA. The obtained data indicate that a universal LA estimation model for olive tree carries the pitfall of moderate accuracy, owing only to cultivar differences, since environmental effects were trivial