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Given a finite and noisy dataset generated with a closed-form mathematical model, when is it possible to learn the true generating model from the data alone? This is the question we investigate here. We show that this model-learning problem displays a transition from a low-noise phase in which the true model can be learned, to a phase in which the observation noise is too high for the true model to be learned by any method. Both in the low-noise phase and in the high-noise phase, probabilistic model selection leads to optimal generalization to unseen data. This is in contrast to standard machine learning approaches, including artificial neural networks, which in this particular problem are limited, in the low-noise phase, by their ability to interpolate. In the transition region between the learnable and unlearnable phases, generalization is hard for all approaches including probabilistic model selection. Learning analytical models from noisy data remains challenging and depends essentially on the noise level. The authors analyze the transition of the model-learning problem from a low-noise phase to a phase where noise is too high for the underlying model to be learned by any method, and estimate upper bounds for the transition noise.

Given a finite and noisy dataset generated with a closed-form mathematical model, when is it possible to learn the true generating model from the data alone? This is the question we investigate here. We show that this model-learning problem displays a transition from a low-noise phase in which the true model can be learned, to a phase in which the observation noise is too high for the true model to be learned by any method. Both in the low-noise phase and in the high-noise phase, probabilistic model selection leads to optimal generalization to unseen data. This is in contrast to standard machine learning approaches, including artificial neural networks, which in this particular problem are limited, in the low-noise phase, by their ability to interpolate. In the transition region between the learnable and unlearnable phases, generalization is hard for all approaches including probabilistic model selection.

Ever since Nikuradse's experiments on turbulent friction in 1933, there have been theoretical attempts to describe his measurements by collapsing the data into single-variable functions. However, this approach, which is common in other areas of physics and in other fields, is limited by the lack of rigorous quantitative methods to compare alternative data collapses. Here, we address this limitation by using an unsupervised method to find analytic functions that optimally describe each of the data collapses for the Nikuradse dataset. By descaling these analytic functions, we show that a low dispersion of the scaled data does not guarantee that a data collapse is a good description of the original data. In fact, we find that, out of all the proposed data collapses, the original one proposed by Prandtl and Nikuradse over 80 years ago provides the best description of the data so far, and that it also agrees well with recent experimental data, provided that some model parameters are allowed to vary across experiments.

Closed-form, interpretable mathematical models have been instrumental for advancing our understanding of the world; with the data revolution, we may now be in a position to uncover new such models for many systems from physics to the social sciences. However, to deal with increasing amounts of data, we need \"machine scientists\" that are able to extract these models automatically from data. Here, we introduce a Bayesian machine scientist, which establishes the plausibility of models using explicit approximations to the exact marginal posterior over models and establishes its prior expectations about models by learning from a large empirical corpus of mathematical expressions. It explores the space of models using Markov chain Monte Carlo. We show that this approach uncovers accurate models for synthetic and real data and provides out-of-sample predictions that are more accurate than those of existing approaches and of other nonparametric methods.

We analyze 3.5 years of public Fermi/LAT data around the position of the supernova remnant HB 21, where four point-like sources from the 2nd Fermi/LAT catalog are located. We determine that the gamma-ray source is produced by a single extended source. We model the observed morphology as a uniform circle. The spectral energy distribution is best described by a curved power law, with a maximum at 413+-11 MeV. We divide the circle into three regions defined by previously identified shocked molecular clouds, and find that one of these regions has a softer spectrum. The >3 GeV gamma-ray emission of the soft spectrum region is bow-shaped and coincident with the supernova remnant shell seen at radio wavelengths. We suggest that the gamma-ray emission from HB 21 can be understood as a combination of emission from shocked/illuminated molecular clouds, one of them coincident with the supernova remnant shell itself.

Located in a dense complex environment, W51C provides an excellent scenario to probe accelerated protons in SNRs and their interaction with surrounding target material. Here we report the observation of extended Very High Energy (VHE) gamma-ray emission from the W51C supernova remnant (SNR) with MAGIC. Detections of extended gamma-ray emission in the same region have already been reported by the Fermi and H.E.S.S. collaborations. Fermi/LAT measured the source spectrum in the energy range between 0.2 and 50 GeV, which was found to be well fit by a hadronic neutral-pion decay model. The VHE observations presented here, obtained with the improved MAGIC stereo system, allow us to pinpoint the VHE gamma-ray emission in the dense shocked molecular cloud surrounding the remnant shell. The MAGIC data also allow us to measure, for the first time, the VHE emission spectrum of W51C from the highest Fermi/LAT energies up to TeV. The spatial distribution and spectral properties of the VHE emission suggest a hadronic origin of the observed gamma rays. Therefore W51C is a prime candidate for a cosmic ray accelerator.

In the past decade imaging atmospheric Cherenkov telescope arrays such as H.E.S.S., MAGIC, VERITAS, as well as the Fermi-LAT space telescope have provided us with detailed images and spectra of the gamma-ray universe for the first time. Currently the gamma-ray community is preparing to build the next-generation Cherenkov Telecope Array (CTA), which will be operated as an open observatory. Gammapy (available at https://github.com/gammapy/gammapy under the open-source BSD license) is a new in-development Astropy affiliated package for high-level analysis and simulation of astronomical gamma-ray data. It is built on the scientific Python stack (Numpy, Scipy, matplotlib and scikit-image) and makes use of other open-source astronomy packages such as Astropy, Sherpa and Naima to provide a flexible set of tools for gamma-ray astronomers. We present an overview of the current Gammapy features and example analyses on real as well as simulated gamma-ray datasets. We would like Gammapy to become a community-developed project and a place of collaboration between scientists interested in gamma-ray astronomy with Python. Contributions welcome!

The Cherenkov Telescope Array (CTA) is the the next generation facility of imaging atmospheric Cherenkov telescopes; two sites will cover both hemispheres. CTA will reach unprecedented sensitivity, energy and angular resolution in very-high-energy gamma-ray astronomy. Each CTA array will include four Large Size Telescopes (LSTs), designed to cover the low-energy range of the CTA sensitivity (\\(\\)20 GeV to 200 GeV). In the baseline LST design, the focal-plane camera will be instrumented with 265 photodetector clusters; each will include seven photomultiplier tubes (PMTs), with an entrance window of 1.5 inches in diameter. The PMT design is based on mature and reliable technology. Recently, silicon photomultipliers (SiPMs) are emerging as a competitor. Currently, SiPMs have advantages (e.g. lower operating voltage and tolerance to high illumination levels) and disadvantages (e.g. higher capacitance and cross talk rates), but this technology is still young and rapidly evolving. SiPM technology has a strong potential to become superior to the PMT one in terms of photon detection efficiency and price per square mm of detector area. While the advantage of SiPMs has been proven for high-density, small size cameras, it is yet to be demonstrated for large area cameras such as the one of the LST. We are working to develop a SiPM-based module for the LST camera, in view of a possible camera upgrade. We will describe the solutions we are exploring in order to balance a competitive performance with a minimal impact on the overall LST camera design.

The MAGIC I telescope produces currently around 100TByte of raw data per year that is calibrated and reduced on-site at the Observatorio del Roque de los Muchachos (La Palma). Since February 2007 most of the data have been stored and further processed in the Port d'Informacio Cientifica (PIC), Barcelona. This facility, which supports the GRID Tier 1 center for LHC in Spain, provides resources to give the entire MAGIC Collaboration access to the reduced telescope data. It is expected that the data volume will increase by a factor 3 after the start-up of the second telescope, MAGIC II. The project to improve the MAGIC Data Center to meet these requirements is presented. In addition, we discuss the production of high level data products that will allow a more flexible analysis and will contribute to the international network of astronomical data (European Virtual Observatory). For this purpose, we will have to develop a new software able to adapt the analysis process to different data taking conditions, such as different trigger configurations or mono/stereo telescope observations.