Geometric overconvergence of rational functions in unbounded domains

The basic aim of this paper is to study the phenomenon of overconvergence for rational functions converging geometrically on [0, + ∞)

Divergent estimation error in portfolio optimization and in linear regression

The problem of estimation error in portfolio optimization is discussed, in the limit where the portfolio size N and the sample size T go to infinity such that their ratio is fixed. The estimation error strongly depends on the ratio N/T and diverges for a critical value of this parameter. This divergence is the manifestation of an algorithmic phase transition, it is accompanied by a number of critical phenomena, and displays universality. As the structure of a large number of multidimensional regression and modelling problems is very similar to portfolio optimization, the scope of the above observations extends far beyond finance, and covers a large number of problems in operations research, machine learning, bioinformatics, medical science, economics, and technology.Comment: 5 pages, 2 figures, Statphys 23 Conference Proceedin

Shell model on a random gaussian basis

Pauli-projected random gaussians are used as a representation to solve the shell model equations. The elements of the representation are chosen by a variational procedure. This scheme is particularly suited to describe cluster formation and cluster decay in nuclei. It overcomes the basis-size problem of the ordinary shell model and the technical difficulties of the cluster-configuration shell model. The model reproduces the $\alpha$-decay width of $^{212}$Po satisfactorily.Comment: Latex, Submitted to Phys. Lett. B, 7 pages, 2 figures available upon request, ATOMKI-1994-

Identification of Young Stellar Object candidates in the GaiaGaia DR2 x AllWISE catalogue with machine learning methods

The second $Gaia$ Data Release (DR2) contains astrometric and photometric data for more than 1.6 billion objects with mean $Gaia$ $G$ magnitude $<$20.7, including many Young Stellar Objects (YSOs) in different evolutionary stages. In order to explore the YSO population of the Milky Way, we combined the $Gaia$ DR2 database with WISE and Planck measurements and made an all-sky probabilistic catalogue of YSOs using machine learning techniques, such as Support Vector Machines, Random Forests, or Neural Networks. Our input catalogue contains 103 million objects from the DR2xAllWISE cross-match table. We classified each object into four main classes: YSOs, extragalactic objects, main-sequence stars and evolved stars. At a 90% probability threshold we identified 1,129,295 YSO candidates. To demonstrate the quality and potential of our YSO catalogue, here we present two applications of it. (1) We explore the 3D structure of the Orion A star forming complex and show that the spatial distribution of the YSOs classified by our procedure is in agreement with recent results from the literature. (2) We use our catalogue to classify published $Gaia$ Science Alerts. As $Gaia$ measures the sources at multiple epochs, it can efficiently discover transient events, including sudden brightness changes of YSOs caused by dynamic processes of their circumstellar disk. However, in many cases the physical nature of the published alert sources are not known. A cross-check with our new catalogue shows that about 30% more of the published $Gaia$ alerts can most likely be attributed to YSO activity. The catalogue can be also useful to identify YSOs among future $Gaia$ alerts.Comment: 19 pages, 12 figures, 3 table

Conditional purity and quantum correlation measures in two qubit mixed states

We analyze and show experimental results of the conditional purity, the quantum discord and other related measures of quantum correlation in mixed two-qubit states constructed from a pair of photons in identical polarization states. The considered states are relevant for the description of spin pair states in interacting spin chains in a transverse magnetic field. We derive clean analytical expressions for the conditional local purity and other correlation measures obtained as a result of a remote local projective measurement, which are fully verified by the experimental results. A simple exact expression for the quantum discord of these states in terms of the maximum conditional purity is also derived.Comment: 16 pages, 5 figures, minor changes, to be published in J. Phys.

Gershgorin disks for multiple eigenvalues of non-negative matrices

Gershgorin's famous circle theorem states that all eigenvalues of a square matrix lie in disks (called Gershgorin disks) around the diagonal elements. Here we show that if the matrix entries are non-negative and an eigenvalue has geometric multiplicity at least two, then this eigenvalue lies in a smaller disk. The proof uses geometric rearrangement inequalities on sums of higher dimensional real vectors which is another new result of this paper

COVID has changed students’ needs and expectations. How do universities respond?

Flexibility is often understood as student preferences for modes of learning. Some students see benefits in fully online learning and may decide to continue in that mode. The majority, though, have expressed a strong desire to return to campus. But they want to retain the flexibility of online learning. This conversation piece explores how universities move forward with teaching post-pandemic