High-dimensional Bayesian optimization with intrinsically low-dimensional response surfaces

Bayesian optimization is a powerful technique for the optimization of expensive black-box functions. It is used in a wide range of applications such as in drug and material design and training of machine learning models, e.g. large deep networks. We propose to extend this approach to high-dimensional settings, that is where the number of parameters to be optimized exceeds 10--20. In this thesis, we scale Bayesian optimization by exploiting different types of projections and the intrinsic low-dimensionality assumption of the objective function. We reformulate the problem in a low-dimensional subspace and learn a response surface and maximize an acquisition function in this low-dimensional projection. Contributions include i) a probabilistic model for axis-aligned projections, such as the quantile-Gaussian process and ii) a probabilistic model for learning a feature space by means of manifold Gaussian processes. In the latter contribution, we propose to learn a low-dimensional feature space jointly with (a) the response surface and (b) a reconstruction mapping. Finally, we present empirical results against well-known baselines in high-dimensional Bayesian optimization and provide possible directions for future research in this field.Open Acces

WKB Approximation for the Polymer Quantization of the Taub Model

We develop a suitable technical algorithm to implement a separation of the Minisuperspace configurational variables into quasi-classical and purely quantum degrees of freedom, in the framework of a Polymer quantum Mechanics reformulation of the canonical dynamics. We then implement the obtained general scheme to the specific case of a Taub Universe, in the presence of a free massless scalar field. In particular, we identify the quasi-classical variables in the Universe volume and a suitable function of the scalar field, while the purely quantum degree of freedom corresponds to the Universe anisotropy. We demonstrate that the Taub cosmology is associated to a cyclical Universe, oscillating between a minimum and maximum volume turning points, respectively. The pure quantum Universe anisotropy has always a finite value.Comment: 12 pages, 4 figure

Dynamical systems in quantum cosmology

The work presented in this Ph.D. thesis has the purpose to provide new quantization procedures for the minisuperspace cosmological models in order to better understand the nature of the initial singularity. The possibility to perform a quantum analysis of the primordial Universe able to provide information about its first instants of life is of absolute interest for the comprehension of the properties of the initial singularity, and, consequently, of the mechanisms at the ground of the birth of our Universe. The original contribution of the thesis starts considering a quadratic correction in the Einstein-Hilbert Action, which in the context of the equivalent scalar-tensor picture behaves as a self-interacting scalar field coupled with the ordinary General Relativity. Once it is considered the Mixmaster Model for this particular f(R) theory, it emerges the existence of a free Kasner regime (formally a Bianchi I model coupled with a scalar field) towards the singularity, i.e. a regime in which the chaos is absent. Always in the context of the extended theories of gravity the presence of the Gauss-Bonnet invariant in the modified action that describe the gravitational field is considered. We demonstrate how, in the Noether Symmetry Approach and following the prescriptions of the Hartle criterion, the framework of Gauss-Bonnet cosmology when a simple flat FRW model is taken into account brings to the selection of possible solutions of the wave function of the Universe from which it is possible to extract the emerging classical cosmological trajectories. Then, the classical and quantum dynamics of a Bianchi I model in the presence of a small negative cosmological constant when a Gaussian Reference Dust Fluid is taken into account. In the framework of the canonical metric approach it is showed that the initial cosmological singularity is removed and it is replaced by a bounce in correspondence to a positive defined value of the dust energy density. A physical interpretation of the Bounce will be provide in term of a correlation between the Cosmological Constant and a characteristic polymer scale related to polymer discretization of the Universe volume. Finally, the final part of this work is focused on the analysis of a homogeneous Bianchi I model in presence of a stiff matter contribution, applying the Vilenkin interpretation of the Wave Function of the Universe when a Polymer quantization procedure is performed to the isotropic component of the spatial metric. The goal of this work is to understand if and how the singularity is avoided, how it changes the behaviour of the anisotropies and if it is possible to extend the results of the above mentioned application to the Bianchi IX model

Bianchi I model as a prototype for a cyclical Universe

We analyze the dynamics of the Bianchi I model in the presence of stiff matter, an ultrarelativistic component and a small negative cosmological constant. We quantize this model in the framework of the polymer quantum mechanics, in order to introduce cut-off features in the minisuperspace dynamics. We then apply to the polymer Wheeler-DeWitt equation, emerging from the Dirac constraint, an adiabatic approximation a la Vilenkin, which treats the Universe volume as a quasi-classical variable, becoming de facto the dynamical clock for the pure quantum degrees of freedom, here identified in the Universe anisotropies. The main issue of the present analysis consists of determining a cyclical evolution for the Bianchi I model, oscillating between the Big-Bounce induced by the cut-off physics and the turning point due to the small cosmological constant. Furthermore, the mean value of the Universe anisotropy variables remains finite during the whole evolution, including the phase across the Big-Bounce. Such a feature, according to a suitable choice of the initial conditions makes the present cosmological paradigm, a viable scenario for the description of a possible primordial and late phases of the actual Universe.Comment: 12 pages, 6 figure

INSIDIA:a FIJI macro delivering high-throughput and high-content spheroid invasion analysis

Time-series image capture of in vitro 3D spheroidal cancer models embedded within an extracellular matrix affords examination of spheroid growth and cancer cell invasion. However, a customizable, comprehensive and open source solution for the quantitative analysis of such spheroid images is lacking. Here, the authors describe INSIDIA (INvasion SpheroID ImageJ Analysis), an open-source macro implemented as a customizable software algorithm running on the FIJI platform, that enables high-throughput high-content quantitative analysis of spheroid images (both bright-field gray and fluorescent images) with the output of a range of parameters defining the spheroid “tumor” core and its invasive characteristics

Chaos removal inR+qR2gravity: The mixmaster model

We study the asymptotic dynamics of the Mixmaster Universe, near the cosmological singularity, considering $f(R)$ gravity up to a quadratic corrections in the Ricci scalar $R$. The analysis is performed in the scalar-tensor framework and adopting Misner-Chitr\'e-like variables to describe the Mixmaster Universe, whose dynamics resembles asymptotically a billiard-ball in a given domain of the half-Poincar\'e space. The form of the potential well depends on the spatial curvature of the model and on the particular form of the self-interacting scalar field potential. We demonstrate that the potential walls determine an open domain in the configuration region, allowing the point-Universe to reach the absolute of the considered Lobachevsky space. In other words, we outline the existence of a stable final Kasner regime in the Mixmaster evolution, implying the chaos removal near the cosmological singularity. The relevance of the present issue relies both on the general nature of the considered dynamics, allowing its direct extension to the BKL conjecture too, as well as the possibility to regard the considered modified theory of gravity as the first correction to the Einstein-Hilbert action as a Taylor expansion of a generic function $f(R)$ (as soon as a cut-off on the space-time curvature takes place).Comment: 7 pages, 2 figure

Skill of the immigrants and vote of the natives: Immigration and nationalism in European elections 2007–2016

International audienceWe analyze the impact of local immigration on natives’ preferences for “nationalism” as measured in parties’ programs by the Manifesto Project Database in European election data between 2007 and 2016. Using a 2SLS strategy with a shift-share IV based on immigrant shares by origin in 2005 and inflows by education-origin groups, we estimate that larger inflows of highly-educated immigrants were associated with a decrease in the “nationalistic” vote of natives, while less-educated immigrants produced an opposite-direction shift towards nationalistic parties. The aggregate results derive from individual shifts toward nationalism in response to less-skilled immigration, and from greater participation of young voters and more pro-European attitudes in response to high-skilled immigration