Global characteristic problem for Einstein vacuum equations with small initial data: (I) The initial data constraints

We show how to prescribe the initial data of a characteristic problem satisfying the costraints, the smallness, the regularity and the asymptotic decay suitable to prove a global existence result. In this paper, the first of two, we show in detail the construction of the initial data and give a sketch of the existence result. This proof, which mimicks the analogous one for the non characteristic problem in [Kl-Ni], will be the content of a subsequent paper.Comment: 77 pages, no figures; corrected misprints and minor errors, to appear on Journal of Hyperbolic Differential Equations (JHDE

The ABACOC Algorithm: a Novel Approach for Nonparametric Classification of Data Streams

Stream mining poses unique challenges to machine learning: predictive models are required to be scalable, incrementally trainable, must remain bounded in size (even when the data stream is arbitrarily long), and be nonparametric in order to achieve high accuracy even in complex and dynamic environments. Moreover, the learning system must be parameterless ---traditional tuning methods are problematic in streaming settings--- and avoid requiring prior knowledge of the number of distinct class labels occurring in the stream. In this paper, we introduce a new algorithmic approach for nonparametric learning in data streams. Our approach addresses all above mentioned challenges by learning a model that covers the input space using simple local classifiers. The distribution of these classifiers dynamically adapts to the local (unknown) complexity of the classification problem, thus achieving a good balance between model complexity and predictive accuracy. We design four variants of our approach of increasing adaptivity. By means of an extensive empirical evaluation against standard nonparametric baselines, we show state-of-the-art results in terms of accuracy versus model size. For the variant that imposes a strict bound on the model size, we show better performance against all other methods measured at the same model size value. Our empirical analysis is complemented by a theoretical performance guarantee which does not rely on any stochastic assumption on the source generating the stream

Measurement-induced quantum operations on multiphoton states

We investigate how multiphoton quantum states obtained through optical parametric amplification can be manipulated by performing a measurement on a small portion of the output light field. We study in detail how the macroqubit features are modified by varying the amount of extracted information and the strategy adopted at the final measurement stage. At last the obtained results are employed to investigate the possibility of performing a microscopic-macroscopic non-locality test free from auxiliary assumptions.Comment: 13 pages, 13 figure

What is so special about analogue simulations?

Contra Dardashti, Th\'ebault, and Winsberg (2017), this paper defends an analysis of arguments from analogue simulations as instances of a familiar kind of inductive inference in science: arguments from material analogy (Hesse, Models and Analogies in Science, Univ Notre Dame Press, 1963). When understood in this way, the capacity of analogue simulations to confirm hypotheses about black holes can be deduced from a general account - fully consistent with a Bayesian standpoint - of how ordinary arguments from material analogy confirm. The proposed analysis makes recommendations about what analogue experiments are worth pursuing that are more credible than Dardashti, Hartmann, Th\'ebault, and Winsberg's (2019). It also offers a more solid basis for addressing the concerns by Crowther, Linneman, and W\"utrich (2019), according to which analogue simulations are incapable of sustaining hypotheses concerning black hole radiation.Comment: 26 pages, 1 figur

Reasoning by Analogy in Mathematical Practice

The testimony and practice of notable mathematicians indicate that there is an important phenomenological and epistemological difference between superficial and deep analogies in mathematics. In this paper, we offer a descriptive theory of analogical reasoning in mathematics, stating general conditions under which an analogy may provide genuine inductive support to a mathematical conjecture (over and above fulfilling the merely heuristic role of 'suggesting' a conjecture in the psychological sense). The proposed conditions generalize the criteria put forward by Hesse (1963) in her influential work on analogical reasoning in the empirical sciences. By reference to several case-studies, we argue that the account proposed in this paper does a better job in vindicating the use of analogical inference in mathematics than the prominent alternative defended by Bartha (2009). Moreover, our proposal offers novel insights into the practice of extending to the infinite case mathematical properties known to hold in finite domains.Comment: 35 pages, 4 figures. Forthcoming in Philosophia Mathematic