Hierarchical Reconstruction Method for Solving Ill-posed Linear Inverse Problems

We present a detailed analysis of the application of a multi-scale Hierarchical Reconstruction method for solving a family of ill-posed linear inverse problems. When the observations on the unknown quantity of interest and the observation operators are known, these inverse problems are concerned with the recovery of the unknown from its observations. Although the observation operators we consider are linear, they are inevitably ill-posed in various ways. We recall in this context the classical Tikhonov regularization method with a stabilizing function which targets the specific ill-posedness from the observation operators and preserves desired features of the unknown. Having studied the mechanism of the Tikhonov regularization, we propose a multi-scale generalization to the Tikhonov regularization method, so-called the Hierarchical Reconstruction (HR) method. First introduction of the HR method can be traced back to the Hierarchical Decomposition method in Image Processing. The HR method successively extracts information from the previous hierarchical residual to the current hierarchical term at a finer hierarchical scale. As the sum of all the hierarchical terms, the hierarchical sum from the HR method provides an reasonable approximate solution to the unknown, when the observation matrix satisfies certain conditions with specific stabilizing functions. When compared to the Tikhonov regularization method on solving the same inverse problems, the HR method is shown to be able to decrease the total number of iterations, reduce the approximation error, and offer self control of the approximation distance between the hierarchical sum and the unknown, thanks to using a ladder of finitely many hierarchical scales. We report numerical experiments supporting our claims on these advantages the HR method has over the Tikhonov regularization method.

Guiding Monte Carlo tree searches with neural networks in the game of go

A dissertation submitted in fulfillment of the requirements to the degree of Master in Computer Science and Computer Engineering

A contribution to semantic description of images and videos: an application of soft biometrics

Humans have a high ability to extract visual data information acquired by sight. Trought a learning process, which starts at birth and continues throughout life, image interpretation becomes almost instinctively. At a glance, one can easily describe a scene with reasonable precision, naming its main components. Usually, this is done by extracting low-level features such as edges, shapes and textures, and associanting them to high level meanings. In this way, a semantic description of the scene is done. An example of this, is the human capacity to recognize and describe other people physical and behavioral characteristics, or biometrics. Soft-biometrics also represents inherent characteristics of human body and behaviour, but do not allow unique person identification. Computer vision area aims to develop methods capable of performing visual interpretation with performance similar to humans. This thesis aims to propose computer vison methods which allows high level information extraction from images in the form of soft biometrics. This problem is approached in two ways, unsupervised and supervised learning methods. The first seeks to group images via an automatic feature extraction learning , using both convolution techniques, evolutionary computing and clustering. In this approach employed images contains faces and people. Second approach employs convolutional neural networks, which have the ability to operate on raw images, learning both feature extraction and classification processes. Here, images are classified according to gender and clothes, divided into upper and lower parts of human body. First approach, when tested with different image datasets obtained an accuracy of approximately 80% for faces and non-faces and 70% for people and non-person. The second tested using images and videos, obtained an accuracy of about 70% for gender, 80% to the upper clothes and 90% to lower clothes. The results of these case studies, show that proposed methods are promising, allowing the realization of automatic high level information image annotation. This opens possibilities for development of applications in diverse areas such as content-based image and video search and automatica video survaillance, reducing human effort in the task of manual annotation and monitoring.

Coupled wellbore-reservoir simulation of thermal effects during multiphase CO2 injection

T2Well-ECO2M is a coupled wellbore reservoir simulator still under development at Lawrence Berkeley National Laboratory (USA) with the ability to deal with a mixture of H2O-CO2-NaCl and includes the simulation of CO2 phase transition and multiphase flow. The code was originally developed for the simulation of CO2 injection into deep saline aquifers and the modelling of enhanced geothermal systems; however, the focus of this research was to modify and test T2Well-ECO2M to simulate CO2 injection into depleted gas reservoirs. To this end, the original code was properly changed in a few parts and a dedicated injection case was developed to study CO2 phase transition inside of a wellbore and the corresponding thermal effects. In the first scenario, the injection case was run applying the fully numerical approach of wellbore to formation heat exchange calculation. Results were analysed in terms of wellbore pressure and temperature vertical profiles, wellhead and bottomhole conditions, and characteristic reservoir displacement fronts. Special attention was given to the thorough analysis of bottomhole temperature as the critical parameter for hydrate formation. Besides the expected direct effect of wellbore temperature changes on reservoir conditions, the simulation results indicated also the effect of CO2 phase change in the near wellbore zone on BH pressure distribution. To test the implemented software changes, in a second scenario, the same injection case was reproduced using the improved semi-analytical time-convolution approach for wellbore to formation heat exchange calculation. The comparison of the two scenarios showed that the simulation of wellbore and reservoir parameters after one year of continuous CO2 injection are in good agreement with the computation time to solve the time-convolution semi-analytical reduced. The new updated T2Well-ECO2M version has shown to be a robust and performing wellbore-reservoir simulator that can be also used to simulate the CO2 injection into depleted gas reservoirs.

Preharvest factors affecting quality and antioxidant levels on Abate Fétel pears: study of superficial scald with a multivariate statistical approach and neural networks

There are only a few insights concerning the influence that agronomic and management variability may have on superficial scald (SS) in pears. Abate Fétel pears were picked during three seasons (2018, 2019 and 2020) from thirty commercial orchards in the Emilia Romagna region, Italy. Using a multivariate statistical approach, high heterogeneity between farms for SS development after cold storage with regular atmosphere was demonstrated. Indeed, some factors seem to affect SS in all growing seasons: high yields, soil texture, improper irrigation and Nitrogen management, use of plant growth regulators, late harvest, precipitations, Calcium and cow manure, presence of nets, orchard age, training system and rootstock. Afterwards, we explored the spatio/temporal variability of fruit attributes in two pear orchards. Environmental and physiological spatial variables were recorded by a portable RTK GPS. High spatial variability of the SS index was observed. Through a geostatistical approach, some characteristics, including soil electrical conductivity and fruit size, have been shown to be negatively correlated with SS. Moreover, regression tree analyses were applied suggesting the presence of threshold values of antioxidant capacity, total phenolic content, and acidity against SS. High pulp firmness and IAD values before storage, denoting a more immature fruit, appeared to be correlated with low SS. Finally, a convolution neural networks (CNN) was tested to detect SS and the starch pattern index (SPI) in pears for portable device applications. Preliminary statistics showed that the model for SS had low accuracy but good precision, and the CNN for SPI denoted good performances compared to the Ctifl and Laimburg scales. The major conclusion is that Abate Fétel pears can potentially be stored in different cold rooms, according to their origin and quality features, ensuring the best fruit quality for the final consumers. These results might lead to a substantial improvement in the Italian pear industry.

Local and nonlocal integro-differential reaction-diffusion models for protein dynamics in Alzheimer's disease

In this work, integro-differential reaction-diffusion models are presented for the description of the temporal and spatial evolution of the concentrations of Abeta and tau proteins involved in Alzheimer's disease. Initially, a local model is analysed: this is obtained by coupling with an interaction term two heterodimer models, modified by adding diffusion and Holling functional terms of the second type. We then move on to the presentation of three nonlocal models, which differ according to the type of the growth (exponential, logistic or Gompertzian) considered for healthy proteins. In these models integral terms are introduced to consider the interaction between proteins that are located at different spatial points possibly far apart. For each of the models introduced, the determination of equilibrium points with their stability and a study of the clearance inequalities are carried out. In addition, since the integrals introduced imply a spatial nonlocality in the models exhibited, some general features of nonlocal models are presented. Afterwards, with the aim of developing simulations, it is decided to transfer the nonlocal models to a brain graph called connectome. Therefore, after setting out the construction of such a graph, we move on to the description of Laplacian and convolution operations on a graph. Taking advantage of all these elements, we finally move on to the translation of the continuous models described above into discrete models on the connectome. To conclude, the results of some simulations concerning the discrete models just derived are presented.