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Black hole critical collapse in infinite dimensions : continuous self-similar solutions
Full text linkWe investigate the dynamics of black hole critical collapse in the limit of a large number of spacetime dimensions, D. In particular, we study the spherical gravitational collapse of a massless, scale-invariant scalar field with continuous self-similarity (CSS). The large number of dimensions provides a natural separation of scales, simplifying the equations of motion at each scale where different effects dominate. With this approximation scheme, we construct matched asymptotic solutions for this family, including the critical solution. We then compute the mass critical exponent of the black hole for linear perturbations that break CSS, finding that it asymptotes to a constant value in infinite dimensions. Additionally, we present a link between these solutions and closed Friedmann-Lema & icirc;tre-Robertson-Walker (FLRW) cosmologies with a dimension-dependent equation of state and cosmological constant. The critical solution corresponds to an unstable Einstein-like universe, while subcritical and supercritical solutions correspond to bouncing and crunching cosmologies respectively. Our results provide a proof of concept for the large-D expansion as a powerful analytic tool in gravitational collapse and suggest potential extensions to other self-similar systems
Complexity of quantum tomography from genuine non-Gaussian entanglement
No full textQuantum state tomography typically requires exponentially many copies of a quantum state, due to the complex correlations present in large systems. We show that, for bosonic systems, the scaling is completely determined by the nature of these correlations. Motivated by the Hong-Ou-Mandel effect and boson sampling, we define Gaussian-entanglable (GE) states, produced by generalized interference between separable bosonic modes. GE states greatly extend the Gaussian family, encompassing separable states, multi-mode Gottesman-Kitaev-Preskill codes, entangled cat states, and boson-sampling outputs—resources for error correction and quantum advantage. We prove
that any pure GE state of m modes can be learned efficiently, requiring only poly(m) copies, via a protocol based on Gaussian unitaries, local tomography, and classical post-processing; for boson-sampling states, no Gaussian unitaries are needed. For states outside GE, we define an operational monotone—the minimal number of ancillary modes needed to make them GE—which exactly
characterizes the exponential tomography overhead. We also show that deterministic generation of NOON states with N ≥ 3 via two-mode interference is impossible
Nonlocal phase transitions in codimension-one: diffuse approximation, stability, and asymptotics
Full text linkThis thesis explores the theory of the fractional perimeter on closed Riemannian manifolds, with a focus on codimension-one phenomena and their approximation through diffuse interface models. A central theme is the existence and regularity of nonlocal minimal surfaces, which arise as critical points of the fractional perimeter, on closed manifolds. Despite their intrinsic nonlocality, which is an anomalous feature compared with the classical theory of minimal surfaces, these surfaces share many structural elements with classical minimal hypersurfaces. In several respects, particularly in the context of stability and finite Morse index, we aim to show that they exhibit improved compactness and regularity properties. These properties make nonlocal minimal surfaces highly suitable for min-max constructions since Morse theory for nonlocal minimal surfaces is, in some sense, as flawless as finite-dimensional Morse theory.
At the core of our existence result is the use of the fractional Allen-Cahn equation as a diffuse approximation of nonlocal minimal surfaces. This method has proved to be particularly effective in the context of min-max constructions, as it allows for the existence of many critical points with precise index and energy bounds.
Addressing the regularity theory of nonlocal minimal surfaces on manifolds requires several key ingredients: precise local estimates on the heat kernel of complete manifolds, rigidity results for stationary cones stable in , and the development of the Caffarelli-Silvestre extension theory on closed manifolds. In this work, we develop (some of) these ingredients and utilize these technical tools to address different problems. For example, the local estimates for the heat kernel will be used both to deduce regularity, via a blow-up procedure, of finite Morse index nonlocal minimal surfaces arising as limits of the fractional Allen-Cahn equation and to characterize the asymptotics of the fractional Laplacian on noncompact manifolds as
Evidence for B- -> D∗∗0 tau- \bar{nu}_{τ} Decays
No full textThe first evidence for the decay B- -> D**(0)tau(-)(nu) over bar (tau) is obtained using proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of 9 fb(-1), at centre-of-mass energies of 7, 8, and 13 TeV. Here, the D**0 meson represents any of the three excited charm mesons D-1(2420)(0), D*(2)(2460)(0), and D'(1)(2400)(0). The B- -> D**(0)tau(-)(nu) over bar (tau) signal is measured with a significance of 3.5 sigma, including systematic uncertainties. The combined branching fraction B(B- -> D**(0)(1,2) tau(-)(nu) over bar (tau)) x B(D**(0)(1,2) -> D*(+) pi(-)), where D**(0)(1,2) denotes both D-1(2420)(0) and D*(2)(2460)(0) contributions, is measured to be [0.051 +/- 0.013(stat) +/- 0.006(syst) +/- 0.009(ext)]%, where the last uncertainty reflects that of the branching fraction of the normalization channel B- -> D**D-0(1,2)-(*())(s). The ratio between the tauonic and muonic semileptonic B decays, with the latter taken from world average values, is also determined and found to be R(D**(0)(1,2)) = 0.13 +/- 0.03(stat) +/- 0.01(syst) +/- 0.02(ext)
Immagini, spazi e pratiche delle confraternite di devozione a Siena nel tardo Medioevo
Full text linkImages, Spaces, and Practices of Devotional Confraternities in Late Medieval SienaThis thesis explores the artistic patronage dynamics of devotional confraternities in Siena from the late 13th to 15th centuries, focusing on the role played by the images in the different religious and communal practices. Siena, rich in historical sources, offers an exemplary framework despite the scarcity of surviving material evidence: the introduction highlights the complexity of Siena’s confraternal landscape and the dispersal of artistic heritage due to renovations and the late 18th-century Suppressions. It also outlines the historical evolution of confraternities, from the 13th century foundation to the late 15th century, identifying key moments like the early 14th-century rise of the disciplinati and the impact of the Observant reform and the preaching of Bernardino of Siena at the beginning of the Quattrocento. The second chapter, “Images, Spaces, and Practices”, examines how confraternity members engaged with art in various rituals, including flagellation, processions and funerals, revealing the “multimedia” connection between the images viewed by the socii and the texts read or sung during ceremonies. The chapter also analyses how spaces evolved, particularly highlighting the shift to independent oratories and the architectural features of confraternal buildings, such as “double chapels” with separate spaces for members and outsiders. This section also delves into the role of confraternal murals and the iconography, functions, and techniques used in these artworks. Additionally, the chapter investigates the furnishings of confraternities, such as altarpieces, processional banners, and funerary artifacts. It highlights their central role in devotional practices and examines their modifications over time, including restorations and repurposing. A final section focuses on the recruitment of artists, the confraternities’ economic capacities, and fluctuating expenditures. The second section of the thesis offers an ‘atlas’ formed by analytical entries dedicated to particularly significant confraternities or related groups, categorized by centre of aggregation, detailing their foundation, development, devotional customs, headquarters, furnishings, and a complete edition of their oldest inventories
A Modular Proof of Semantic Completeness for Normal Systems beyond the Modal Cube, Formalised in HOLMS
Full text linkWe communicate here the most recent extension of HOLMS, our library for modal logics aimed at introducing automated modal reasoning within the HOL Light proof assistant. Based on a uniform proof strategy, we present a more refined formal proof of completeness for systems within and beyond the S5-normal modal cube, notably Gödel-Löb logic. We report on our development by adopting a measure of its modularity based on Strachey’s distinction between parametric and ad hoc polymorphic code
A World Not of this World : The Reality of Images and Imagination
No full textWhat do we mean by imagination? Is the image, as a long tradition has insisted, the faint copy of the thing? If not, and images can be of different kinds, how can we distinguish among them? What is the relation between image and word?
Can imagination be simply the faculty for images? Is imagination fiction or escape from reality, or can we ascribe a cognitive function to it? Must we call into question the widespread reduction of imagination to a solely theoretical faculty of a pure ego, i.e., a mental and private space, at the expense of its practical, intersubjective, affective aspects?
This book seeks a systematic and comprehensive answer to these questions. It begins by disputing several commonplaces on images and imagination, both in everyday language and in many traditional scholarly approaches. It continues by examining the power of fascination images have on us. After these indispensable premises aimed at narrowing down the field of inquiry, this volume seeks an analysis of the twofold nature of every image (the image is something in itself, and yet refers to what it is an image of) and specifies the criteria by which we distinguish natural, artificial, mental and memory images. It then proceeds to probe the heuristic and cognitive functions of imagination, as well as the notions of fiction, play, and literary creation. Finally, the book shows the necessity of broadening the understanding of imagination, from the suspension of the world to the manifold ways in which it works to transform it
Structural properties in the diffusion of the solar photovoltaic in Italy: individual people/householder vs firms
No full textThis paper develops two mathematical models to understand subjects’ behavior in response to the urgency of a change and inputs from governments e.g., (subsides) in the context of the diffusion of the solar photovoltaic in Italy. The first model is a Markov model of interacting particle systems. The second one, instead, is a Mean-Field Game model. In both cases, we derive the scaling limit deterministic dynamics, and we compare the latter to the Italian solar photovoltaic data. We identify periods where the first model describes the behavior of domestic data well and a period where the second model captures a particular feature of data corresponding to companies. The comprehensive analysis, integrated with a philosophical inquiry focusing on the conceptual vocabulary and correlative implications, leads to the formulation of hypotheses about the efficacy of different forms of governmental subsidies