The Suzaku X-ray spectrum of NGC 3147. Further insights on the best "true" Seyfert 2 galaxy candidate

NGC 3147 is so far the most convincing case of a "true" Seyfert 2 galaxy, i.e. a source genuinely lacking the Broad Line Regions. We obtained a Suzaku observation with the double aim to study in more detail the iron line complex, and to check the Compton-thick hypothesis for the lack of observed optical broad lines. The Suzaku XIS and HXD/PIN spectra of the source were analysed in detail. The line complex is composed of at least two unresolved lines, one at about 6.45 keV and the other one at about 7 keV, most likely identified with Fe XVII/XIX, the former, and Fe XXVI, the latter. The high-ionization line can originate either in a photoionized matter or in an optically thin thermal plasma. In the latter case, an unusually high temperature is implied. In the photoionized model case, the large equivalent width can be explained either by an extreme iron overabundance or by assuming that the source is Compton-thick. In the Compton-thick hypothesis, however, the emission above 2 keV is mostly due to a highly ionized reflector, contrary to what is usually found in Compton-thick Seyfert 2s, where reflection from low ionized matter dominates. Moreover, the source flux varied between the XMM-Newton and the Suzaku observations, taken 3.5 years apart, confirming previous findings and indicating that the size of the emitting region must be smaller than a parsec. The hard X-ray spectrum is also inconclusive on the Compton-thick hypothesis. Weighting the various arguments, a "true" Seyfert 2 nature of NGC 3147 seems to be still the most likely explanation, even if the "highly ionized reflector" Compton-thick hypothesis cannot at present be formally rejected.Comment: 6 pages, accepted for publication in Astronomy & Astrophysic

On the existence of solutions to adversarial training in multiclass classification

We study three models of the problem of adversarial training in multiclass classification designed to construct robust classifiers against adversarial perturbations of data in the agnostic-classifier setting. We prove the existence of Borel measurable robust classifiers in each model and provide a unified perspective of the adversarial training problem, expanding the connections with optimal transport initiated by the authors in previous work and developing new connections between adversarial training in the multiclass setting and total variation regularization. As a corollary of our results, we prove the existence of Borel measurable solutions to the agnostic adversarial training problem in the binary classification setting, a result that improves results in the literature of adversarial training, where robust classifiers were only known to exist within the enlarged universal $\sigma$-algebra of the feature space

Stirling Numbers of Sunflower Graphs

A Stirling number of the second kind, S(n, k), is the number of ways to take all of the elements from an n element set and put them into k subsets, so that the subsets are non-empty and pairwise disjoint. To get the graphical Stirling number for a graph G, we add the restriction that any two vertices that are adjacent in G cannot be in the same subset. The traditional Stirling numbers are the graphical Stirling number where the graph is empty. We find graphical Stirling numbers for sunflower graphs, which are powers of paths joined at a single vertex. We approach the problem in two different ways, (1) by finding the chromatic polynomial and (2) recursively. Our results include the Stirling number for what we refer to as a complete sunflower graph, as well as a few other cases for sunflower graphs. We then form a general conjecture for the chromatic polynomial of a sunflower graph, which would then provide us with the graphical Stirling number for a sunflower graph using the Principle of Inclusion Exclusion. We also find several recursive formulas for finding graphical Stirling numbers, such as the graphical Stirling number for graph G with vertex v with a complete neighborhood, S(G, k) = S(G − v, k − 1) + (k − deg(v)) · S(G − v, k). We end with a discussion of possible future work

Chandra monitoring of UGC 4203: the structure of the X-ray absorber

We present a Chandra monitoring campaign of the highly variable Seyfert galaxy UGC 4203 (the "Phoenix Galaxy") which revealed variations in the X-ray absorbing column density on time scales of two weeks. This is the third, clear case, after NGC 1365 and NGC 7582, of dramatic N_H variability on short time scales observed in a "changing look" source, i.e. an AGN observed in the past in both a reflection-dominated and a Compton-thin state. The inferred limits on the distance of the X-ray absorber from the center suggest that the X-ray "torus" could be one and the same with the broad emission line region. This scenario, first proposed for an "ad-hoc" picture for NGC 1365, may be the common structure of the circumnuclear medium in AGN.Comment: 5 Pages, 4 figures. Accepted for publication in MNRAS. Missing references added and typos correcte

An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classification

Despite the success of deep learning-based algorithms, it is widely known that neural networks may fail to be robust. A popular paradigm to enforce robustness is adversarial training (AT), however, this introduces many computational and theoretical difficulties. Recent works have developed a connection between AT in the multiclass classification setting and multimarginal optimal transport (MOT), unlocking a new set of tools to study this problem. In this paper, we leverage the MOT connection to propose computationally tractable numerical algorithms for computing universal lower bounds on the optimal adversarial risk and identifying optimal classifiers. We propose two main algorithms based on linear programming (LP) and entropic regularization (Sinkhorn). Our key insight is that one can harmlessly truncate the higher order interactions between classes, preventing the combinatorial run times typically encountered in MOT problems. We validate these results with experiments on MNIST and CIFAR-$10$, which demonstrate the tractability of our approach

Turbulent Dynamo in Asymptotic Giant Branch Stars

Using recent results on the operation of turbulent dynamos, we show that a turbulent dynamo can amplify a large scale magnetic field in the envelopes of asymptotic giant branch (AGB) stars. We propose that a slow rotation of the AGB envelope can fix the symmetry axis, leading to the formation of an axisymmetric magnetic field structure. Unlike solar-type alpha-omega dynamos, the rotation has only a small role in amplifying the toroidal component of the magnetic field. The large-scale magnetic field is strong enough for the formation of magnetic cool spots on the AGB stellar surface. The spots can regulate dust formation, hence mass loss rate, leading to axisymmetric mass loss and the formation of elliptical planetary nebulae (PNe). Despite its role in forming cool spots, the large scale magnetic field is too weak to play a dynamic role and directly influence the wind from the AGB star. We find other problems in models where the magnetic field plays a dynamic role in shaping the AGB winds, and argue that they cannot explain the formation of nonspherical PNe.Comment: 12 pages (1 ps file of a table); Submitted to MNRA

Nonradial and nonpolytropic astrophysical outflows IX. Modeling T Tauri jets with a low mass-accretion rate

Context: A large sample of T Tauri stars exhibits optical jets, approximately half of which rotate slowly, only at ten per cent of their breakup velocity. The disk-locking mechanism has been shown to be inefficient to explain this observational fact. Aims: We show that low mass accreting T Tauri stars may have a strong stellar jet component that can effectively brake the star to the observed rotation speed. Methods: By means of a nonlinear separation of the variables in the full set of the MHD equations we construct semi- analytical solutions describing the dynamics and topology of the stellar component of the jet that emerges from the corona of the star. Results: We analyze two typical solutions with the same mass loss rate but different magnetic lever arms and jet radii. The first solution with a long lever arm and a wide jet radius effectively brakes the star and can be applied to the visible jets of T Tauri stars, such as RY Tau. The second solution with a shorter lever arm and a very narrow jet radius may explain why similar stars, either Weak line T Tauri Stars (WTTS) or Classical T Tauri Stars (CTTS) do not all have visible jets. For instance, RY Tau itself seems to have different phases that probably depend on the activity of the star. Conclusions: First, stellar jets seem to be able to brake pre-main sequence stars with a low mass accreting rate. Second, jets may be visible only part time owing to changes in their boundary conditions. We also suggest a possible scenario for explaining the dichotomy between CTTS and WTTS, which rotate faster and do not have visible jets