Multitemporal analysis of satellite imagery: implementation of a land evolution model in ALCS (ATSR LAND CLASSIFICATION SYSTEM)

In this report it was designed an innovative satellite-based monitoring approach applied on the Iraqi Marshlands to survey the extent and distribution of marshland re-flooding and assess the development of wetland vegetation cover. The study, conducted in collaboration with MEEO Srl , makes use of images collected from the sensor (A)ATSR onboard ESA ENVISAT Satellite to collect data at multi-temporal scales and an analysis was adopted to observe the evolution of marshland re-flooding. The methodology uses a multi-temporal pixel-based approach based on classification maps produced by the classification tool SOIL MAPPER ®. The catalogue of the classification maps is available as web service through the Service Support Environment Portal (SSE, supported by ESA). The inundation of the Iraqi marshlands, which has been continuous since April 2003, is characterized by a high degree of variability, ad-hoc interventions and uncertainty. Given the security constraints and vastness of the Iraqi marshlands, as well as cost-effectiveness considerations, satellite remote sensing was the only viable tool to observe the changes taking place on a continuous basis. The proposed system (ALCS – AATSR LAND CLASSIFICATION SYSTEM) avoids the direct use of the (A)ATSR images and foresees the application of LULCC evolution models directly to „stock‟ of classified maps. This approach is made possible by the availability of a 13 year classified image database, conceived and implemented in the CARD project (http://earth.esa.int/rtd/Projects/#CARD).The approach here presented evolves toward an innovative, efficient and fast method to exploit the potentiality of multi-temporal LULCC analysis of (A)ATSR images. The two main objectives of this work are both linked to a sort of assessment: the first is to assessing the ability of modeling with the web-application ALCS using image-based AATSR classified with SOIL MAPPER ® and the second is to evaluate the magnitude, the character and the extension of wetland rehabilitation.

Laplace operator on finite graphs and a network diffusion model for the progression of the Alzheimer disease

Nella tesi viene descritto il Network Diffusion Model, ovvero il modello di A. Ray, A. Kuceyeski, M. Weiner inerente i meccanismi di progressione della demenza senile. In tale modello si approssima l'encefalo sano con una rete cerebrale (ovvero un grafo pesato), si identifica un generale fattore di malattia e se ne analizza la propagazione che avviene secondo meccanismi analoghi a quelli di un'infezione da prioni. La progressione del fattore di malattia e le conseguenze macroscopiche di tale processo(tra cui principalmente l'atrofia corticale) vengono, poi, descritte mediante approccio matematico. I risultati teoretici vengono confrontati con quanto osservato sperimentalmente in pazienti affetti da demenza senile. Nella tesi, inoltre, si fornisce una panoramica sui recenti studi inerenti i processi neurodegenerativi e si costruisce il contesto matematico di riferimento del modello preso in esame. Si presenta una panoramica sui grafi finiti, si introduce l'operatore di Laplace sui grafi e si forniscono stime dall'alto e dal basso per gli autovalori. Al fine di costruire una cornice matematica completa si analizza la relazione tra caso discreto e continuo: viene descritto l'operatore di Laplace-Beltrami sulle varietà riemanniane compatte e vengono fornite stime dall'alto per gli autovalori dell'operatore di Laplace-Beltrami associato a tali varietà a partire dalle stime dall'alto per gli autovalori del laplaciano sui grafi finiti.

Keller-Segel system, chemotaxis and applications to a mathematical model for Alzheimer's disease

In questa tesi viene presentato il modello di Keller-Segel per la chemiotassi, un sistema di tipo parabolico-ellittico che appare nella descrizione di molti fenomeni in ambito biologico e medico. Viene mostrata l'esistenza globale della soluzione debole del modello, per dati iniziali sufficientemente piccoli in dimensione N>2. La scelta di dati iniziali abbastanza grandi invece può causare il blow-up della soluzione e viene mostrato sotto quali condizioni questo si verifica. Infine il modello della chemiotassi è stato applicato per descrivere una fase della malattia di Alzheimer ed è stata effettuata un'analisi di stabilità del sistema.

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.