Multi-fidelity classification using Gaussian processes: accelerating the prediction of large-scale computational models

Machine learning techniques typically rely on large datasets to create accurate classifiers. However, there are situations when data is scarce and expensive to acquire. This is the case of studies that rely on state-of-the-art computational models which typically take days to run, thus hindering the potential of machine learning tools. In this work, we present a novel classifier that takes advantage of lower fidelity models and inexpensive approximations to predict the binary output of expensive computer simulations. We postulate an autoregressive model between the different levels of fidelity with Gaussian process priors. We adopt a fully Bayesian treatment for the hyper-parameters and use Markov Chain Mont Carlo samplers. We take advantage of the probabilistic nature of the classifier to implement active learning strategies. We also introduce a sparse approximation to enhance the ability of themulti-fidelity classifier to handle large datasets. We test these multi-fidelity classifiers against their single-fidelity counterpart with synthetic data, showing a median computational cost reduction of 23% for a target accuracy of 90%. In an application to cardiac electrophysiology, the multi-fidelity classifier achieves an F1 score, the harmonic mean of precision and recall, of 99.6% compared to 74.1% of a single-fidelity classifier when both are trained with 50 samples. In general, our results show that the multi-fidelity classifiers outperform their single-fidelity counterpart in terms of accuracy in all cases. We envision that this new tool will enable researchers to study classification problems that would otherwise be prohibitively expensive. Source code is available at https://github.com/fsahli/MFclass

Nonlocal compensation of pure phase objects with entangled photons

We suggest and demonstrate a scheme for coherent nonlocal compensation of pure phase objects based on two-photon polarization and momentum entangled states. The insertion of a single phase object on one of the beams reduces the purity of the state and the amount of shared entanglement, whereas the original entanglement can be retrieved by adding a suitable phase object on the other beam. In our setup polarization and momentum entangled states are generated by spontaneous parametric downconversion and then purified using a programmable spatial light modulator, which may be also used to impose arbitrary space dependent phase functions to the beams. As a possible application, we suggest and demonstrate a quantum key distribution protocol based on nonlocal phase compensation.Comment: 7 pages, 5 figure

Marginal states of the resistive tearing mode with flow in cylindrical geometry

The linear stability of tearing modes in a cylindrical plasma subject to a sub-Alfvénic equilibrium shear flow along the equilibrium magnetic field is considered. The equations in the resistive boundary layer at the rational surface are solved numerically using a Fourier transform combined with a finite-element approach. The behaviour of the growth rate as a function of the flow and the various parameters (including a perpendicular fluid viscosity) is obtained. Marginal stability curves showing the dependence of the familiar matching parameter Δ' with flow and shear are also given

Phase transitions related to the pigeonhole principle

Since Paris introduced them in the late seventies (Paris1978), densities turned out to be useful for studying independence results. Motivated by their simplicity and surprising strength we investigate the combinatorial complexity of two such densities which are strongly related to the pigeonhole principle. The aim is to miniaturise Ramsey's Theorem for $1$-tuples. The first principle uses an unlimited amount of colours, whereas the second has a fixed number of two colours. We show that these principles give rise to Ackermannian growth. After parameterising these statements with respect to a function f:N->N, we investigate for which functions f Ackermannian growth is still preserved

Observing the very low-surface brightness dwarfs in a deep field in the VIRGO cluster: constraints on Dark Matter scenarios

We report the discovery of 11 very faint (r< 23), low surface brightness ({\mu}_r< 27 mag/arcsec^2) dwarf galaxies in one deep field in the Virgo cluster, obtained by the prime focus cameras (LBC) at the Large Binocular Telescope (LBT). These extend our previous sample to reach a total number of 27 galaxies in a field of just of 0.17 deg^2 located at a median distance of 390 kpc from the cluster center. Their association with the Virgo cluster is supported by their separate position in the central surface brightness - total magnitude plane with respect to the background galaxies of similar total magnitude. For a significant fraction (26\%) of the sample the association to the cluster is confirmed by spectroscopic follow-up. We show that the mere abundance of satellite galaxies corresponding to our observed number in the target field provides extremely tight constraints on Dark Matter models with suppressed power spectrum compared to the Cold Dark Matter case, independently of the galaxy luminosity distribution. In particular, requiring the observed number of satellite galaxies not to exceed the predicted abundance of Dark Matter sub-halos yields a limit m_X >3 keV at 1-{\sigma} and m_X > 2.3 keV at 2-{\sigma} confidence level for the mass of thermal Warm Dark Matter particles. Such a limit is competitive with other limits set by the abundance of ultra-faint satellite galaxies in the Milky Way, is completely independent of baryon physics involved in galaxy formation, and has the potentiality for appreciable improvements with next observations. We extend our analysis to Dark Matter models based on sterile neutrinos, showing that our observations set tight constraints on the combination of sterile neutrino mass m_{\nu} and mixing parameter sin^2(2{\theta}). We discuss the robustness of our results with respect to systematics.Comment: Accepted for publication in Astronomy & Astrophysic

On the reconstruction of diagonal elements of density matrix of quantum optical states by on/off detectors

We discuss a scheme for reconstructing experimentally the diagonal elements of the density matrix of quantum optical states. Applications to PDC heralded photons, multi-thermal and attenuated coherent states are illustrated and discussed in some details.Comment: 10 pages, presented at Palermo "TQMFA2005" Conference. To appear on "Open Systems & Information Dynamics" (2006

Neutrino energy transport in weak decoupling and big bang nucleosynthesis

We calculate the evolution of the early universe through the epochs of weak decoupling, weak freeze-out and big bang nucleosynthesis (BBN) by simultaneously coupling a full strong, electromagnetic, and weak nuclear reaction network with a multi-energy group Boltzmann neutrino energy transport scheme. The modular structure of our code provides the ability to dissect the relative contributions of each process responsible for evolving the dynamics of the early universe in the absence of neutrino flavor oscillations. Such an approach allows a detailed accounting of the evolution of the $\nu_e$, $\bar\nu_e$, $\nu_\mu$, $\bar\nu_\mu$, $\nu_\tau$, $\bar\nu_\tau$ energy distribution functions alongside and self-consistently with the nuclear reactions and entropy/heat generation and flow between the neutrino and photon/electron/positron/baryon plasma components. This calculation reveals nonlinear feedback in the time evolution of neutrino distribution functions and plasma thermodynamic conditions (e.g., electron-positron pair densities), with implications for: the phasing between scale factor and plasma temperature; the neutron-to-proton ratio; light-element abundance histories; and the cosmological parameter \neff. We find that our approach of following the time development of neutrino spectral distortions and concomitant entropy production and extraction from the plasma results in changes in the computed value of the BBN deuterium yield. For example, for particular implementations of quantum corrections in plasma thermodynamics, our calculations show a $0.4\%$ increase in deuterium. These changes are potentially significant in the context of anticipated improvements in observational and nuclear physics uncertainties.Comment: 37 pages, 12 Figures, 6 Table

Probing neutrino physics with a self-consistent treatment of the weak decoupling, nucleosynthesis, and photon decoupling epochs

We show that a self-consistent and coupled treatment of the weak decoupling, big bang nucleosynthesis, and photon decoupling epochs can be used to provide new insights and constraints on neutrino sector physics from high-precision measurements of light element abundances and cosmic microwave background observables. Implications of beyond-standard-model physics in cosmology, especially within the neutrino sector, are assessed by comparing predictions against five observables: the baryon energy density, helium abundance, deuterium abundance, effective number of neutrinos, and sum of the light neutrino mass eigenstates. We give examples for constraints on dark radiation, neutrino rest mass, lepton numbers, and scenarios for light and heavy sterile neutrinos.Comment: 29 pages, 10 figure

Non-classical correlations in non-Markovian continuous variable systems

We consider two identical and non-interacting harmonic oscillators coupled to either two independent bosonic baths or to a common bosonic bath. Under the only assumption of weak coupling, we analyze in details the non-Markovian short time-scale evolution of intensity correlations, entanglement and quantum discord for initial two-mode squeezed-thermal vacuum states. In the independent reservoirs case we observe the detrimental effect of the environment for all these quantities and we establish a hierarchy for their robustness against the environmental noise. In the common reservoir case, for initial uncorrelated states, we find that only quantum discord can be created via interaction with the bath, while entanglement and sub shot noise intensity correlations remain absent.Comment: 10 pages, 5 figure