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Function spaces in the Grothendieck completion of Lawvereâ's hyperdoctrines
No full textThis thesis deals with topics in the field of mathematical logic called categorical logic in order to produce models of deductive logical systems by employing tools of category theory. Our aim is to study su cient conditions to ensure the existence of function spaces for free categorical constructions applied to models of many sorted fi rst order intuitionistic predicative logic represented by Lawver's hyperdoctrines.
Given a Lawver's hyperdoctrine we consider three free constructions:
1. the Grothendieck completion which freely adds comprehensions
2. the quotient completion which freely adds quotients of equivalence relations
3. the composition of the rst two which freely adds quotients of partial equivalence relations We show that the composition of the extensional collapse with the Grothendieck completion of an hyperdoctrine produces an hyperdoctrine whose base category, called category of predicates, is not only closed under functional spaces but it is also locally cartesian closed , namely its slice categories are closed under function spaces.
The application of the constructions above to the yperdoctrine of the power set functor over the category of Sets will provide not only a relevant example but also a sort of inspiration for guiding our categorical proofs
Cohomological field theories e varietà di Frobenius.
No full textL'argomento centrale di questa tesi saranno le Cohomological Field Theories
(CohFTs, al singolare CohFT) e le varietà di Frobenius. Si daranno tutti gli
strumenti necessari per definire questi argomenti e comprendere il teorema di
Teleman, teorema di fondamentale importanza per chiunque si approcci allo
studio delle CohFTs. Nello specifico il risultato che porteremo in questa tesi è
mostrare la corrispondenza univoca, sotto certe ipotesi, tra CohFTs e varietà
di Frobenius
Cosmic Microwave Background Spectral Distortions and Primordial Gravitational Waves
Get PDFDistortions of the Cosmic Microwave Background (CMB) spectrum in the frequency domain provides a new
window onto a variety of cosmological phenomena, including the physics of the early Universe. These
distortions are tiny departures of the CMB frequency spectrum from a pure blackbody which are created
whenever the energy or the number density of the CMB photons is changed and therefore encode
information about the thermal history of the Universe. They can be produced by a number of processes
occurring at the early stages of cosmic history and therefore allow us to probe the standard picture of
cosmology.
Spectral distortions are created by processes that drive matter and radiation out of equilibrium. This could be
related to early energy injection. Depending on the moment of injection, this causes a distortion which can be
of two main types, namely the so called µ and y-type distortions. The standard cosmological model
predicts the production of CMB spectral distortions, thanks to various effects, one of which is the dissipation
of acoustic waves of the photon-baryon plasma through the Silk damping effect. Such distortions can be
used to constrain the power of the primordial density perturbations arising from inflation in the range .
Moreover, this work will include an original part focused on the possibility of generating statistically
anisotropic features in the CMB spectral distortions and on sources of these anisotropic features. Within
many candidates, there are the so called inflationary fossils, models in which the scalar field driving
inflation couples to a new primordial degree of freedom. In particular, tensor fossils refer to
long wavelength relic gravitational waves from inflation that produce a quadrupolar modulation of
curvature perturbations. The tensor fossils no longer interact, or interact very weakly, during late time
cosmic evolution. Therefore, the unique observational effect due to the coupling with the inflaton field would
be to give rise to local departures from statistical isotropy in the primordial curvature perturbation field.
The original contribution of this Thesis will consist in the study of how this new tensor degree of freedom
can distort the primordial scalar curvature two point correlation function. In order to evaluate this, the
mixed bispectrum involving tensor scalar scalar fluctuations will be computed in the so called squeezed
limit configuration, which gives rise to an anisotropic power spectrum of curvature (density) perturbations.
Hence, in this work, we delve into CMB spectral distortions, pointing out the main features and their
importance. We derive the cross correlation between CMB anisotropies and CMB spectral distortions,
which is a useful observable to constrain primordial non Gaussianity. We then focus on the study of the
imprints of the tensor fossils on cosmic structures. We will see how tensor fossils can leave a signature in the
CMB spectral distortions, by evaluating the ensemble average of the µ distortion modulated by the
long wavelength tensor mode. Then, we will also compute the corresponding cross correlation between
CMB anisotropies and µ distortions, computing the tensor scalar scalar and the scalar tensor tensor
bispectra, both in the case of modulation
Teoria della formazione di strutture regolari sulle reti
Get PDFNel 1952 Alan Turing propose un modello matematico in grado di spiegare la formazione di strutture spaziali regolari grazie a un meccanismo di instabilità che poi prese il suo nome. In alcune reazioni chimiche, per esempio, dove sono presenti un elemento attivatore e uno inibitore, tale instabilità si manifesta con il meccanismo di attivazione e inibizione, in cui uno stato stazionario e omogeneo stabile, risulta instabile a piccole perturbazioni. Quando l'elemento inibitore diffonde molto più velocemente di quello attivatore, lo stato stazionario omogeneo diventa instabile e si formano strutture che alternano regioni ad alta e bassa densità di attivatori. Il meccanismo di Turing è stato utilizzato in contesti molto diversi (chimica, biologia, ecologia) per spiegare la formazione di strutture spaziali regolari. Più recentemente, si è capito che tale meccanismo può spiegare l'emergere di strutture anche nelle reti con topologie eterogenee. In questo caso le specie diffondono attraverso i link per poi interagire nei vari nodi della rete. Queste classi di modelli offrono la possibilità di studiare l'emergere di strutture regolari in condizioni molto più generali. Questa tesi si propone di spiegare in dettaglio la formulazione matematica del meccanismo proposto da Turing e generalizzarlo alle reti sulla base della letteratura corrente
Simple and mixed poisson processes: theory and examples
No full textInsurance policies have gained a central role in our daily routine,
therefore we move our first steps on the underlying models and processes
involved in non-life insurance: the Number of Claim Arrivals, the Times of
Arrival and the Total Claim Amount. Our main goal is the development of a
consistent theory of Simple, Mixed, and Compound Poisson Processes in order
to find the distribution that fits better reality over time. After highlighting the fundamental properties of the Poisson Processes, we make appeal to the Strong law for a first glance approximation of the Total Claim Amount. Only at the end, we will revive a recursive algorithm for determining its distribution
Oscillatory behavior in ising type spin systems with dissipation
No full textIn this thesis we study the appearance of self-sustained periodic behavior in the macroscopic dynamics of two one-dimensional interacting systems. In particular, we focus on a Curie-Weiss model and a short-range interaction Ising model both with dissipation. In a regime obtained by letting inverse of temperature and volume go to infinite, the magnetization of both the spin systems presents an oscillating behaviour
Climate-growth relationships of Norway spruce beyond its natural distribution range
No full textThe aim of this thesis is to study, using dendrochronological techniques, the growth response to climate of Norway spruce (Picea abies) beyond its natural distribution. The work has been conducted in Iceland, to see how the species is behaving beyond its current northern natural range; moreover, further Norway spruce samples have been collected in two plantations in Marche and Emilia Romagna Regions, Central Italy, to study species’ growth trends in correspondence of the southern distribution limit and beyond it. In order to better understand growth dynamics within the Icelandic sites, we also collected more samples from two other tree species, Picea sitchensis (Sitka spruce) and Pinus contorta (lodgepole pine).
The analysis of the radial increment of the trees showed an overall high fluctuation in the tree ring width, beginning in the 1990s both in Italian and Icelandic sites. This pattern is maybe related to climate, testifying an increase of hot and dry summers in the last thirty years. Moreover, the climate-growth correlation profiles highlighted a diverse action of climate on tree growth, which seems to vary according to latitude: at northern latitudes, within the Icelandic sites, Norway spruce growth is mainly affected by temperatures, especially mean summer temperature (June July and August), whereas, towards southern latitudes, within the Italian sites, precipitation regime plays a major role on the species’ growth, especially during July of the current year and June of the previous year. The Emilia Romagna site showed an overall low correlation with climate, probably due to the shortness of available data. Sitka spruce and lodgepole pine climate-growth relationships proved useful to better understand growth patterns in Iceland, supporting the growth trend showed by Norway spruce.
Considering the present warming climate scenario and the general uncertainties on tree migration and growth patterns, these results can contribute for a better understanding on the growth of the species outside its distribution and therefore on how spruce might behave in the future. Moreover, these results can be useful in further developing strategies such as assisted migration: knowing the future trees requirements can facilitate the movement of species to improve natural population dynamics and range expansion in a climate change scenario
Caratterizzazione Microstrutturale e Meccanica di un Bimateriale - Lega di Alluminio/Acciaio
Get PDFCon questo elaborato si sono analizzate due leghe appartenenti alla famiglia Al-Si con l'aggiunta in fase di colata una rete metallica in acciaio INOX. In questa tesi si è cercato di definire due aspetti principali di questa tipologia di materiali ibridi ovvero, cosa accade all'interfaccia fra i due materiali e se l'inserimento del rinforzo aiuta in termini di resistenza meccanica