Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

La moltiplicazione relazionale dei non imparentati. Un'etnografia delle attese di genitorialità e filiazione intorno alla categoria giuridica di "minore straniero non accompagnato" in Italia.

Sulla spinta dell’approvazione della legge italiana 47/2017 “Disposizioni in materia di misure di protezione dei minori stranieri non accompagnati”, questo lavoro è teso ad affrontare le complesse aspettative genitoriali e parentali sviluppatesi intorno al processo di categorizzazione MSNA di cui questa legge è diventata approdo giuridico. Le controverse aspettative di accompagnamento legatesi alla denominazione di “non accompagnato”, prese come aspetto scontato e assiomatico in molta parte della letteratura scientifica che utilizza l’acronimo, sono state qui intese come un nodo ambiguo e questionabile. Attraverso una ricerca e una metodologia antropologico-etnografica queste rappresentazioni contradditorie sono esplorate a partire da un “crocevia di campi” da queste interessati in un territorio amministrativo dell’Italia Settentrionale variamente frequentato tra 2018 e 2021. Insieme ad ambienti, metodi e sfide della ricerca locale, una prima sezione situa storicamente e contestualmente la categoria MSNA come fenomeno in sé piuttosto che come efficace espressione descrittiva di soggetti. Le due sezioni successive, dedicate rispettivamente alla neo-realtà di tutela volontaria e a quella di una comunità socio-educativa/di tipo familiare rivolta a persone di minore età, interrogano invece questi ambienti come spazi e tempi di elaborazione prima e negoziazione poi di rappresentazioni e pratiche relazionali e parentali molteplici.

User scheduling for low earth orbit multi-user multiple-input-multiple-output non-terrestrial network systems

In rural and isolated areas without cellular coverage, Satellite Communication (SatCom) is the best candidate to complement terrestrial coverage. However, the main challenge for future generations of wireless networks will be to meet the growing demand for new services while dealing with the scarcity of frequency spectrum. As a result, it is critical to investigate more efficient methods of utilizing the limited bandwidth; and resource sharing is likely the only choice. The research community’s focus has recently shifted towards the interference management and exploitation paradigm to meet the increasing data traffic demands. In the Downlink (DL) and Feedspace (FS), LEO satellites with an on-board antenna array can offer service to numerous User Terminals (UTs) (VSAT or Handhelds) on-ground in FFR schemes by using cutting-edge digital beamforming techniques. Considering this setup, the adoption of an effective user scheduling approach is a critical aspect given the unusually high density of User terminals on the ground as compared to the on-board available satellite antennas. In this context, one possibility is that of exploiting clustering algorithms for scheduling in LEO MU-MIMO systems in which several users within the same group are simultaneously served by the satellite via Space Division Multiplexing (SDM), and then these different user groups are served in different time slots via Time Division Multiplexing (TDM). This thesis addresses this problem by defining a user scheduling problem as an optimization problem and discusses several algorithms to solve it. In particular, focusing on the FS and user service link (i.e., DL) of a single MB-LEO satellite operating below 6 GHz, the user scheduling problem in the Frequency Division Duplex (FDD) mode is addressed. The proposed State-of-the-Art scheduling approaches are based on graph theory. The proposed solution offers high performance in terms of per-user capacity, Sum-rate capacity, SINR, and Spectral Efficiency.

Non-invasive detection of acute cell-mediated graft rejection in paediatric heart transplant recipients: the role of cardiovascular magnetic resonance

Background and Aim: Acute cardiac rejection is currently diagnosed by endomyocardial biopsy (EMB), but multiparametric cardiac magnetic resonance (CMR) may be a non-invasive alternative by its capacity for myocardial structure and function characterization. Our primary aim was to determine the utility of multiparametric CMR in identifying acute graft rejection in paediatric heart transplant recipients. The second aim was to compare textural features of parametric maps in cases of rejection versus those without rejection. Methods: Fifteen patients were prospectively enrolled for contrast-enhanced CMR followed by EMB and right heart catheterization. Images were acquired on a 1,5 Tesla scanner including T1 mapping (modified Look-Locker inversion recovery sequence – MOLLI) and T2 mapping (modified GraSE sequence). The extracellular volume (ECV) was calculated using pre- and post-gadolinium T1 times of blood and myocardium and the patient’s hematocrit. Markers of graft dysfunction including hemodynamic measurements from echocardiography, catheterization and CMR were collated. Patients were divided into two groups based on degree of rejection at EMB: no rejection with no change in treatment (Group A) and acute rejection requiring new therapy (Group B). Statistical analysis included student’t t test and Pearson correlation. Results: Acute rejection was diagnosed in five patients. Mean T1 values were significantly associated with acute rejection. A monotonic, increasing trend was noted in both mean and peak T1 values, with increasing degree of rejection. ECV was significantly higher in Group B. There was no difference in T2 signal between two groups. Conclusion: Multiparametric CMR serves as a noninvasive screening tool during surveillance encounters and may be used to identify those patients that may be at higher risk of rejection and therefore require further evaluation. Future and multicenter studies are necessary to confirm these results and explore whether multiparametric CMR can decrease the number of surveillance EMBs in paediatric heart transplant recipients.