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Structured matrices coming from PDE approximation theory: spectral analysis, spectral symbol and design of fast iterative solvers.
No full textPartial Differential Equations (PDE) are extensively used in Applied Sciences to model real-world problems. The solution u of a PDE is normally not available in closed form, and so it is necessary to approximate it by means of some numerical method.
Despite the differences among the various methods, the principle on which all of them are based is essentially the same: they first discretize the PDE by introducing a mesh, related to some discretization parameter n, and then they compute the corresponding numerical solution u_n, which will converge to u when n tends to infinity, i.e., when the mesh is progressively refined.
Now, if both the PDE and the numerical method are linear, the computation of u_n reduces to solving a certain linear system A_n * u_n = f_n whose size d_n tends to infinity with n. In addition, the sequence of discretization matrices A_n often enjoys an asymptotic spectral distribution described by a certain matrix-valued function f, which takes values in the space of Hermitian matrices of a certain size s. This means that, for large n, the eigenvalues of A_n are approximately given by a uniform sampling of the eigenvalue functions lambda_i(f), i=1,...,s, over the domain of f. In this situation, f is called the (spectral) symbol of the sequence of matrices A_n.
The identification and the study of the symbol are two interesting issues in themselves, because they provide an accurate information about the asymptotic global behavior of the eigenvalues of A_n. In particular, the number s coincides with the number of "branches" that compose the asymptotic spectrum of A_n.
However, the knowledge of the symbol f and of its properties is not only interesting in itself, but can also be used for practical purposes. In particular, it can be used to design effective preconditioned Krylov and multigrid solvers for the linear systems associated with A_n. The reason is clear: the convergence properties of preconditioned Krylov and multigrid methods strongly depend on the spectral features of the matrix to which they are applied. Hence, the spectral information provided by the symbol can be conveniently used for designing fast solvers of this kind.
The purpose of this thesis is to present some specific examples, of interest in practical applications, in which the above philosophical discussion comes to life. As our model PDE, we consider classical second-order elliptic differential equations. Concerning the numerical methods that we employ for their solution, we make three choices: the classical Qp Lagrangian Finite Element Method (FEM), the Galerkin B-spline Isogeometric Analysis (IgA) and the B-spline IgA Collocation Method. We first identify and study the symbol f that characterizes the asymptotic spectrum of the discretization matrices A_n arising from these approximation techniques. Then, by exploiting the properties of the symbol, we design fast iterative solvers for the matrices A_n associated with the two numerical methods based on IgA (the Galerkin B-spline IgA and the B-spline IgA Collocation Method)
The hidden complexity of stellar population properties in high-Redshift early-type galaxies.
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Degeneration of the larval midgut of Bombix Mori during metamorphosis: role and regulation of autophagy and apoptosis.
Get PDFThe midgut of the silkworm, Bombyx mori, is extensively remodeled during metamorphosis: in fact, while cell death processes lead to the degeneration of the larval epithelium, the adult midgut is formed by the proliferation and differentiation of stem cells. Our group previously described the intervention of apoptotic and autophagic events in larval midgut cells undergoing degeneration (Franzetti et al., 2012). The present study aims at investigating the molecular pathways of apoptosis and autophagy, the role of the two processes and their relationship in this tissue.
We first analyzed the expression pattern of autophagic and apoptotic genes, as well as used specific markers to assess the precise timing of autophagy and apoptosis during metamorphosis. The results obtained confirm that autophagy is activated at spinning stage, while apoptosis intervenes with a delay of 24-48 hours. The final demise of apoptotic cells occurs by secondary necrosis and their content is released in the lumen of the adult midgut.
To investigate the mechanisms that lead to the activation of autophagy and apoptosis we used 20-hydroxyecdysone (20E), one of the main regulators of metamorphosis in insects. The administration of a single dose of 20E induces the transcription of both autophagic and apoptotic genes, but fully activates only autophagy. In contrast, the activation of effector caspases needs a second injection of 20E. These data suggest that, during development, autophagy is induced at the end of the last larval stage by the 20E commitment peak, while the onset of apoptosis occurs concomitantly with 20E metamorphic peak. Moreover, our results demonstrate that 20E activates autophagy by inhibiting the Tor pathway. However, inactivation of Torc1 through rapamycin administration is not sufficient to trigger and maintain a full autophagic response, thus suggesting that the activation of autophagy by 20E is mediated by multiple downstream targets.
In order to study the role of autophagy and apoptosis in this setting we used specific inhibitors. The impairment of the autophagic flux, through administration of chloroquine, determines an increased degeneration of the larval midgut epithelium and higher levels of caspase activity compared to controls, while the inhibition of caspase activation, by using z.vad.fmk, leads to a severe delay in the degradation of the epithelium. These data demonstrate that, while autophagy has a pro-survival role in this setting, apoptosis is the major process that drives the demise of the larval midgut during metamorphosis
The benefits of biodiversity conservation through the Italian Marine Protected Areas: application of a Choice experiment in Portofino for the monetary valuation of three ecosystem services.
Get PDFThe biodiversity of the seas and oceans is gradually declining due to the exploitation of resources, habitat destruction, pollution, the introduction of alien species, and climate change and related perturbations of ocean biogeochemistry. In this context, it has been necessary over time to establish areas of protected sea in order to conserve marine biodiversity and ecosystem services that it provides.
In Italy have been established, to date, 27 Marine Protected Areas (MPAs) and 2 Underwater Parks, with the aim to preserve and conserve endangered species, critical habitats, fish stocks, the landscape features, cultural biodiversity, and historical and archeological heritage.
However, the funds allocated by the government to the Italian MPAs were progressively reduced from 2008 to 2015.
In this study, we aim to estimate the economic value of changes in ecosystem services from the political scenario in which the annual funding from the State for the conservation of marine biodiversity through the Italian MPAs remains current, to the political scenario in which the funds are increased to allow for more conservation. To meet this aim, we implemented a Choice experiment at the Portofino Marine Protected Area. In our research we accompanied the choice set by an additional questionnaire designed to obtain information to make supplementary considerations on ecosystem services. Questionnaires were put to a sample of 150 people, interviewed face-to-face at the commune of Portofino (a municipality included in the Marine Protected Area of Portofino, Liguria, Italy) during the summer of 2014.
We carried out the research at the Portofino MPA, which is one of the 27 Italian Marine Protected Areas, because the director gave us the availability to perform the study in the territory and provided us with information about the management of the MPA.
We have estimated the implicit prices of the three ecosystem services (Climate regulation, Aesthetic benefits, Food) on the basis of the coefficients obtained using a multinomial logit model where the dependent variable is represented by the choice of respondents (Option A, Option B or Status quo in the choice set), and the independent variables are the ecosystem services and the attribute Cost of Choice experiment; the willingness to pay was estimated by dividing the coefficients of the attributes of the services with the coefficient of the attribute Cost.
Implicit prices are interpreted as the incremental willingness to pay (WTP), through an increase in a national tax for Italian Marine Protected Areas per annum per household, for a change in any of the ecosystem services. Our results show that people is willing to pay € 9.77 per household per year for an increase of the ecosystem service Climate regulation, through greater protection of Posidonia oceanica meadows by the Italian Marine Protected Areas, in comparison to have a level of the ecosystem service that is maintained at the current level. For the ecosystem service Aesthetic benefits provided by the coralligenous, the WTP is € 10.06 per household per year. For the ecosystem service Food, the WTP is € 9.87 per household per year. The total WTP of each family for an increase in the flow of the three ecosystem services through the Italian MPAs is 29.7 euro per household per year. These values are related to changes in the flow of ecosystem services from the political scenario in which the annual funding from the State for the conservation of marine biodiversity through the Italian MPAs remains current, to the political scenario in which the funds are increased to allow for more conservation.
If we consider that from 2008 to present the budget of the Ministry of the Environment with regard to the MPAs has been reduced by 50% (source: Italian Ministry of the Environment, Land and Sea), our research indicates that it is beneficial and desirable a reversal of the trend towards an increase in public funding for Italian MPAs.
Additional applications of Choice experiment for the valuation of ecosystem services provided by Italian MPAs, which take the conclusions and considerations of our study into account, might extent the scope of the research. In particular, it is useful to apply the method to the other Italian MPAs and to a selected sample of the Italian population representative with regard to the socio-demographic
Black holes in galactic nuclei: seed formation from stellar mass black holes and massive black hole pairing in galaxy mergers.
Get PDFBlack holes (BHs) are a very important class of astrophysical objects. They are the most compact objects in the Universe, hence they represent the most extreme sources of gravity. BHs come in two flavours: the stellar mass BHs (SBHs) relic of young massive stars (1−20M⊙) and the massive BHs (MBHs), with masses of 106−109M⊙, dwelling in the nuclei of the most massive galaxies. While the formation mechanisms of SBHs are well understood, no clear consensus exists about MBH formation. According to the Soltan arguments (Soltan, 1982), MBHs gain the largest fraction of their mass via radiative efficient accretion of gas. As a consequence, we expect that MBH formed early in the Universe as smaller mass seeds. Recently, observations of high redshift quasars (e.g.; Mortlock et al., 2011; Fan et al., 2006) showed that MBHs with masses above 109M⊙ were already in place when the Universe was less than 1 Gyr old and posed tight constraints on the models for the formation and growth of MBHs. Two main scenarios have been developed for MBH seed formation: the light seed scenario, where seeds formed as relic of the first generation of stars with masses of up to few hundred solar masses (Madau & Rees, 2001), and the heavy seed scenarios, where seeds formed from the direct collapse of massive gas clouds in primordial haloes with masses of up to few 105M⊙ (Haehnelt & Rees, 1993). Despite the large number of studies about MBH formation models, each model still has its own caveats, which make the study of MBH formation worth of further investigations.
According to the -CDM cosmology, galaxies form when gas cools down within dark matter haloes, which assembly in a hierarchical fashion from small density perturbations. Galaxies grow via accretion and mergers, and the central MBHs evolve in the same way. So, when a galaxy merger occur, the MBHs hosted in the nucleus of the galaxy progenitors can sink towards the centre of the merger remnant, forming a MBH binary (MBHB). Despite galaxy mergers are usually observed, no clear detections of MBHBs exist to date. The formation and evolution of MBHBs is a complex process, since it occurs in a rapidly varying environment where gas, star formation and SNa feedback play a pivotal role. Several studies have been performed to date, but a clear understanding of the whole process is still far from being reached.
In this thesis I cover both aspects of MBH formation and evolution. In the first study I consider an alternative route for seed BH formation. Using two different codes, the AMR code RAMSES (Teyssier, 2002) and the meshfree code GIZMO (Hopkins, 2015), I studied the evolution of a single massive circum-nuclear gaseous disc embedding a population of SBHs. The disc was subject to radiative cooling, star formation and supernova feedback and becomes unstable to fragmentation, which led to the formation of clumps as massive as 104 − 105M⊙. My simulations showed that during the disc evolution, some SBHs can be gravitationally captured by a clump. Within the clumps, such BHs can experience episodes of super-critical accretion, which make them grow up to 103 − 104M⊙ in few Myr. Thanks to the very low radiative efficiency associated to the slim accretion disc (Abramowicz et al., 1988), the energy released to the surrounding gas is too small to halt the accretion flow, hence BHs can accrete almost unimpeded until one of these events occur: the clump is totally accreted by the BH, the clump is consumed by star formation or the clump is destroyed by supernova explosions.
In the second study, instead, I consider the intermediate stages of a galaxy merger, when the MBHs originally dwelling in the centre of their own progenitor galaxies reach few hundred separations in the nucleus of the merger remnant. I assumed that each MBH was embedded in a self-gravitating circumnuclear gaseous disc. With the code RAMSES I studied the evolution of the MBHs and their surrounding discs, including physical processes like radiative cooling, star formation and supernova feedback, which are implemented in the code as sub-grid recipes. First, I implemented a new refinement prescription aimed at improving the orbital evolution of massive particles, an already known major issue in AMR codes, like observed by Gabor & Bournaud (2013); Dubois et al. (2014). Secondly, I evolved the discs assuming different sub-grid recipes to study how the MBH and gas dynamics could be affected by the different choices. I found that the MBH dynamics is almost independent of the physical modelling, if one assumes that no previous star formation occurred in the discs, while the gas evolution and its final distribution can be significantly affected. On the other side, if one assumes that star formation was already ongoing, even the BH dynamics can be modified, if supernovae are powerful enough to disrupt gas clumps forming in the discs.
A general introduction to the work is reported in Chapter 1. In Chapter 3 I discuss the first study about an alternative model for seed BH formation. In Chapter 4, instead, I describe the second study concerning the evolution of the MBH pair in the intermediate stages of a galaxy merger. The reader interested in the main results of the work can directly move to Chapters 3 and 4. Finally, Chapter 5 reports my conclusions
Effect of hypercaloric and isocaloric diets different in fatty acid content on the endo cannabinoid system in pregnant dams and their offspring.
Get PDFLipid molecules are the building blocks of all cell membranes and provide essential secondary metabolites. The central nervous system is enriched in polyunsaturated fatty acids (PUFAs): arachidonic acid (AA) and docosahexaenoic acid (DHA). During brain development, PUFAs play a critical role in determining neuronal structure, particularly axonal outgrowth. In mammals, AA and DHA cannot be synthesized de novo and must be obtained largely from dietary sources. Moreover, during pregnancy and lactation, fetuses and infants rely on PUFAs from their mothers through the placenta and breast milk, respectively. Thus, the maternal diet needs to contain an appropriate omega-3/omega-6 PUFAs ratio to help child development. Based on these premises, we investigated the consequences of maternal malnutrition, defined as a shifted dietary ratio of omega-3 or omega-6 PUFAs on the brain of the offspring. In particular, we modeled human relevance by manipulating both the content and time of daily diets, with a keen focus on endocannabinoid (eCB) system given the critical roles of this AA-derived neuromodulator system during pre- and postnatal brain development.
In the first approach of this project we fed female mice with hypercaloric diets, rich in omega-3 or in omega-6 PUFA, for two (short-term diet) or nine weeks (long-term diet) before mating and during gestation. We found that, levels of endocannabinoids (AEA, 2-AG) and AEA-like mediators (PEA, OEA) did not change with short-term diet in pregnant dams. Moreover, only omega-3 diet induced a significant increase of 2-AG levels, after long-term protocol. In embryos, we found that the short-term exposure of two weeks of omega-3 and omega-6 diet feeding is already sufficient to allow alteration of endocannabinoid system, especially FAAH and CB1R. In fact, in female embryos, we found down-regulation of CB1R and increase of FAAH after treatment with both diets. Interestingly, both enzyme and receptor levels are normalized after high-fat diet administration for a long period, where AEA levels were found decreased. By contrast, in males the alterations found in CB1R after the shorter protocol persist also after the prolongation of the treatment. In line with this, these data suggest a relationship among AEA, CB1R and FAAH, and an important link between PUFAs and endocannabinoid system.
The second approach of this project was based on the administration of isocaloric diets, different in omega-3 levels but not in omega-6 PUFAs throughout gestation and until adulthood. We discovered that during gestation, not only the increase but also the decrease of omega-3 levels markedly affected the eCB system in the hippocampus of embryos. Furthermore, our in vivo results strongly suggest that omega-3 diets enriched and deficient affect the principal presynaptic marker in embryonic hippocampus but not in adult, where maternal malnutrition leads to long-term behavioral alterations in adult rats characterized by the presence of recognition memory deficits. As a whole, the second approach of this study supports our hypothesis about a relationship between PUFAs and the endocannabinoid system and provides further evidence on the importance of omega-3 PUFA on hippocampal development and functioning.
All together, our results suggest that changes in dietary omega-3/omega-6 PUFAs ratio during gestation affect the endocannabinoid system in the brain of the offspring and the major effects of diets are present at the beginning of the treatment (i.e during gestation). Moreover, these data suggest that not only lipids but also fat can have a role in these changes
Disturbo bipolare e asenapina: efficacia clinica e incidenza di effetti collaterali.
Get PDFThe study aims to evaluate the therapeutic response of Bipolar Disorder in the manic phase introduction FGA, SGA and mood stabilizer (1st Part) and the use of Asenapine in clinical practice in the treatment of Bipolar Disorder by detecting any side effects metabolic, endocrinological and elettrocardiographic (2nd Part).
In the 1st Part, in patients with Bipolar Disorder type I some psychometric scales (YMRS, CGI-BD, MADRS, FAST) were administered in five consecutive visits over three months.
In 2nd Part at baseline and 3 months of treatment with Asenapine it was recorded metabolic parameters, electrocardiograms, vital signs and clinical data of patients.
The study confirmed that in patients with Bipolar Disorder type I in the manic phase the manic symptoms (YMRS), depressive symptoms (MADRS), the clinical conditions (CGI-BP) and global functioning (FAST) improve within 12 weeks from the introduction of antipsychotics or mood stabilizers regardless of intrinsic and extrinsic factors.
These data are confirmed by both the experimental center of Varese and OSTER study (which ad respectively 8 and 192 patients that completed the protocol).
In 2nd Part there are 26 enrolled patients, 17 women and 9 men, mean age 44 ± 13,8 years, we obtained incomplete data for an in-depth statistical analysis but this sample allowed us to observe that only 26,9% of patients were affected by Bipolar Disorder type I. Most of the requirements was in fact off label, mostly in patients with personality disorder, but also schizoaffective disorder and psychosis, with variable dosages from 5 to 20 mg/die.
There were no statistically significant metabolic side effects
Studio prospettico multicentrico di efficacia della chirurgia laparoscopica colorettale per patologia neoplastica nel paziente grande anziano
Get PDFAim: to evaluate the effectiveness of laparoscopic surgery (LCS) for the treatment of colorectal cancer (CRC)
in the very elderly over 80 years of age
Methods: we performed a prospective multicentric analysis comparing patients over 80 yo and patients between 60 and 69 yo undergoing LCS for cancer from January 2008 to December 2013. We considered laparoscopic right colectomies, left colectomies, anterior rectal resections and other procedurel including segmental resections and Miles’ procedures. Colon and rectal cancers were analyzed separately. Preoperative workup, surgical techniques and instruments, peri-operative cares were standardized. Data on the patients’ demographics, disease features, operative details and short-term follow up were recorded and analyzed through an appropriate statistical comparison. Comorbidity and complications were classified using the Charlson Comorbidity index (CCI) and the Clavien Dindo classification system (CDCS) respectively.
Oncological parameters included tumor-free resection margins, number of lymph nodes harvested and circumferential resection margin.
Results: Group A included 96 and 33 patients, Group B 220 and 82 for colon and rectal cancers respectively.
Groups were similar except for ASA score and CCI, as expected.
We recorded a significant number of colonic in situ tumors Group B (0 vs 6.4%) and rectal T2 tumors (18.2 vs 39.0%) in Group B, a greater number of rectal T3 tumors (60.6 vs 26.8%) in Group A.
There was no significant difference in operative time [Colon; Rectum] (178,0 ± 42,0 vs 185,3 ± 43,2 min; NS - 190,3 ± 52,5 vs 201,4 ± 54,9 min; NS), estimated blood loss (59,9 ± 51,8 vs 63,3 ± 60,1 mL; NS - 78,3 ± 81,9 vs 61,0 ± 55,6 mL; NS) and conversion rate (2,1 vs 2,7%; NS – 3,0 vs 2,4%; NS). Timing of first stool (3,1 ± 1,3 vs 3,5 ± 1,8 gg; NS - 3,3 ± 1,2 vs 3,3 ± 1,7 gg; NS), length of hospital stay (7,4 ± 2,1 vs 7,2 ± 2,1 gg; NS - 8,5 ± 1,7 vs 8,5 ± 2,8 gg; NS) and 30 days readmission rate (1,0 vs 0,45%; NS – 6,1 vs 1,2%; NS) were similar.
Tumour-free margins were appropriate and positivity of CRM is poor (6.1 vs 4.9; NS). We didn’t record statistically significant differences in CDCS complications rate (47,9 vs 43,6%; NS – 63,6 vs 52,4%; NS).
Conclusions: Laparoscopic surgery is effective for the treatment of colorectal cancer even in the very elderly. Age is not a risk factor or a limitation for LCS
