Weighted geometric mean of large-scale matrices: numerical analysis and algorithms

Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

Outdoor production of Isochrysis galbana (T-iso) in industrial scale photobioreactors and modelling of its photosynthesis and respiration rate

Isochrysis galbana is a widely-used strain in aquaculture in spite of its low productivity. To maximize the productivity of processes based on this microalgae strain, a model was developed considering the influence of irradiance, temperature, pH and dissolved oxygen concentration on the photosynthesis and respiration rate. Results demonstrate that this strain tolerates temperatures up to 35ºC but it is highly sensitive to irradiances higher than 500 µE·m-2·s-1 and dissolved oxygen concentrations higher than 11 mg·l-1. With the researcher group of the “Universidad de Almeria”, the developed model was validated using data from an industrial-scale outdoor tubular photobioreactor demonstrating that inadequate temperature and dissolved oxygen concentrations reduce productivity to half that which is maximal, according to light availability under real outdoor conditions. The developed model is a useful tool for managing working processes, especially in the development of new processes based on this strain and to take decisions regarding optimal control strategies. Also the outdoor production of Isochrysis galbana T-iso in industrial size tubular photobioreactors (3.0 m3) has been studied. Experiments were performed modifying the dilution rate and evaluating the biomass productivity and quality, in addition to the overall performance of the system. Results confirmed that T-iso can be produced outdoor at commercial scale in continuous mode, productivities up to 20 g·m-2·day-1 of biomass rich in proteins (45%) and lipids (25%) being obtained. The utilization of this type of photobioreactors allows controlling the contamination and pH of the cultures, but daily variation of solar radiation imposes the existence of inadequate dissolved oxygen concentration and temperature at which the cells are exposed to inside the reactor. Excessive dissolved oxygen reduced the biomass productivity to 68% of maximal, whereas inadequate temperature reduces to 63% of maximal. Thus, optimally controlling these parameters the biomass productivity can be duplicated. These results confirm the potential to produce this valuable strain at commercial scale in optimally designed/operated tubular photobioreactors as a biotechnological industry.

Analysis and Evaluation of Tiny Machine Learning applications

The aim of TinyML is to bring the capability of Machine Learning to ultra-low-power devices, typically under a milliwatt, and with this it breaks the traditional power barrier that prevents the widely distributed machine intelligence. TinyML allows greater reactivity and privacy by conducting inference on the computer and near-sensor while avoiding the energy cost associated with wireless communication, which is far higher at this scale than that of computing. In addition, TinyML’s efficiency makes a class of smart, battery-powered, always-on applications that can revolutionize the collection and processing of data in real time. This emerging field, which is the end of a lot of innovation, is ready to speed up its growth in the coming years. In this thesis, we deploy three model on a microcontroller. For the model, datasets are retrieved from an online repository and are preprocessed as per our requirement. The model is then trained on the split of preprocessed data at its best to get the most accuracy out of it. Later the trained model is converted to C language to make it possible to deploy on the microcontroller. Finally, we take step towards incorporating the model into the microcontroller by implementing and evaluating an interface for the user to utilize the microcontroller’s sensors. In our thesis, we will have 4 chapters. The first will give us an introduction of TinyML. The second chapter will help setup the TinyML Environment. The third chapter will be about a major use of TinyML in Wake Word Detection. The final chapter will deal with Gesture Recognition in TinyML.

Collection and real-time analysis of images from aircraft to support civil protection operational activities

This report describes the realization of a system, in which an object detection model will be implemented, whose aim is to detect the presence of people in images. This system could be used for several applications: for example, it could be carried on board an aircraft or a drone. In this case, the system is designed in such a way that it can be mounted on light/medium weight helicopters, helping the operator to find people in emergency situations. In the first chapter the use of helicopters for civil protection is analysed and applications similar to this case study are listed. The second chapter describes the choice of the hardware devices that have been used to implement a prototype of a system to collect, analyse and display images. At first, the PC necessary to process the images was chosen, based on the characteristics of the algorithms that are necessary to run the analysis. In the further, a camera that could be compatible with the PC was selected. Finally, the battery pack was chosen taking into account the electrical consumption of the devices. The third chapter illustrates the algorithms used for image analysis. In the fourth, some of the requirements listed in the regulations that must be taken into account for carrying on board all the devices have been briefly analysed. In the fifth chapter the activity of design and modelling, with the CAD Solidworks, the devices and a prototype of a case that will house them is described. The sixth chapter discusses the additive manufacturing, since the case was printed exploiting this technology. In the seventh chapter, part of the tests that must be carried out on the equipment to certificate it have been analysed, and some simulations have been carried out. In the eighth chapter the results obtained once loaded the object detection model on a hardware for image analyses were showed. In the ninth chapter, conclusions and future applications were discussed.