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Polstar is a proposed NASA MIDEX space telescope that will provide high-resolution, simultaneous full-Stokes spectropolarimetry in the far ultraviolet, together with low-resolution linear polarimetry in the near ultraviolet. In this white paper, we describe the unprecedented capabilities this observatory would offer in order to obtain unique information on the magnetic and plasma properties of the magnetospheres of hot stars. This would enable a test of the fundamental hypothesis that magnetospheres should act to rapidly drain angular momentum, thereby spinning the star down, whilst simultaneously reducing the net mass-loss rate. Both effects are expected to lead to dramatic differences in the evolution of magnetic vs. non-magnetic stars., Comment: White paper, 40 pages

Approximately 7% of massive stars host stable surface magnetic fields that are strong enough to alter stellar evolution through their effect on the stellar wind. It is therefore crucial to characterize the strength and structure of these large-scale fields in order to quantify their influence on massive star evolution. This is traditionally done by measuring the circular polarization caused by Zeeman splitting in optical photospheric lines, but we investigate here the possibility of detecting Stokes $V$ signatures in the wind-sensitive resonance lines formed in magnetically confined winds in the high opacity ultraviolet (UV) domain. This unique diagnostic would be accessible to high-sensitivity spaceborne UV spectropolarimeters such as POLSTAR., Comment: Proceedings article from IAUS 360 -- Astronomical Polarimetry 2020: New Era of Multiwavelength Polarimetry. 2 pages, 1 figure

Recent large-scale spectropolarimetric surveys have established that a small but significant percentage of massive stars host stable, surface dipolar magnetic fields with strengths on the order of kG. These fields channel the dense, radiatively driven stellar wind into circumstellar magnetospheres, whose density and velocity structure can be probed using ultraviolet (UV) spectroscopy of wind-sensitive resonance lines. Coupled with appropriate magnetosphere models, UV spectroscopy provides a valuable way to investigate the wind-field interaction, and can yield quantitative estimates of the wind parameters of magnetic massive stars. We report a systematic investigation of the formation of UV resonance lines in slowly rotating magnetic massive stars with dynamical magnetospheres. We pair the Analytic Dynamical Magnetosphere (ADM) formalism with a simplified radiative transfer technique to produce synthetic UV line profiles. Using a grid of models, we examine the effect of magnetosphere size, the line strength parameter, and the cooling parameter on the structure and modulation of the line profile. We find that magnetic massive stars uniquely exhibit redshifted absorption at most viewing angles and magnetosphere sizes, and that significant changes to the shape and variation of the line profile with varying line strengths can be explained by examining the individual wind components described in the ADM formalism. Finally, we show that the cooling parameter has a negligible effect on the line profiles., Comment: 16 pages, 15 figures, accepted to MNRAS

The magnetic beta Cep pulsator xi^1 CMa has the longest rotational period of any known magnetic B-type star. It is also the only magnetic B-type star with magnetospheric emission that is known to be modulated by both rotation and pulsation. We report here the first unambiguous detection of a negative longitudinal magnetic field in xi^1 CMa (=-87 +/- 2 G in 2019 and =-207 +/- 3 G in 2020), as well as the results of ongoing monitoring of the star's Halpha variability. We examine evidence for deviation from a purely dipolar topology. We also report a new HST UV spectrum of xi^1 CMa obtained near magnetic null that is consistent with an equatorial view of the magnetosphere, as evidenced by its similarity to the UV spectrum of beta Cep obtained near maximum emission. The new UV spectrum of xi^1 CMa provides additional evidence for the extremely long rotation period of this star via comparison to archival data., Comment: 13 pages, Accepted 2021 May 14 to Monthly Notices of the Royal Astronomical Society 2021

The OPC UA protocol is an upcoming de-facto standard for building Industry 4.0 processes in Europe, and one of the few industrial protocols that promises security features to prevent attackers from manipulating and damaging critical infrastructures. Despite the importance of the protocol, challenges in the adoption of OPC UA's security features by product vendors, libraries implementing the standard, and end-users were not investigated so far. In this work, we systematically investigate 48 publicly available artifacts consisting of products and libraries for OPC UA and show that 38 out of the 48 artifacts have one (or more) security issues. In particular, we show that 7 OPC UA artifacts do not support the security features of the protocol at all. In addition, 31 artifacts that partially feature OPC UA security rely on incomplete libraries and come with misleading instructions. Consequently, relying on those products and libraries will result in vulnerable implementations of OPC UA security features. To verify our analysis, we design, implement, and demonstrate attacks in which the attacker can steal credentials exchanged between victims, eavesdrop on process information, manipulate the physical process through sensor values and actuator commands, and prevent the detection of anomalies.

We consider the Random Euclidean Assignment Problem in dimension $d=1$, with linear cost function. In this version of the problem, in general, there is a large degeneracy of the ground state, i.e. there are many different optimal matchings (say, $\sim \exp(S_N)$ at size $N$). We characterize all possible optimal matchings of a given instance of the problem, and we give a simple product formula for their number. Then, we study the probability distribution of $S_N$ (the zero-temperature entropy of the model), in the uniform random ensemble. We find that, for large $N$, $S_N \sim \frac{1}{2} N \log N + N s + \mathcal{O}\left( \log N \right)$, where $s$ is a random variable whose distribution $p(s)$ does not depend on $N$. We give expressions for the asymptotics of the moments of $p(s)$, both from a formulation as a Brownian process, and via singularity analysis of the generating functions associated to $S_N$. The latter approach provides a combinatorial framework that allows to compute an asymptotic expansion to arbitrary order in $1/N$ for the mean and the variance of

We provide strong evidence that the effective spin-spin interaction in a multimodal confocal optical cavity gives rise to a self-induced glassy phase, which emerges exclusively from the peculiar euclidean correlations and is not related to the presence of disorder as in standard spin glasses. As recently shown, this spin-spin effective interaction is both non-local and non-translational invariant, and randomness in the atoms positions produces a spin glass phase. Here we consider the simplest feasible disorder-free setting where atoms form a one-dimensional regular chain and we study the thermodynamics of the resulting effective Ising model. We present extensive results showing that the system has a low-temperature glassy phase. Notably, for rational values of the only free adimensional parameter $\alpha=p/q$ of the interaction, the number of metastable states at low temperature grows exponentially with $q$ and the problem of finding the ground state rapidly becomes computationally intractable, suggesting that the system develops high energy barriers and ergodicity breaking occurs.

In recent years, a number of process-based anomaly detection schemes for Industrial Control Systems were proposed. In this work, we provide the first systematic analysis of such schemes, and introduce a taxonomy of properties that are verified by those detection systems. We then present a novel general framework to generate adversarial spoofing signals that violate physical properties of the system, and use the framework to analyze four anomaly detectors published at top security conferences. We find that three of those detectors are susceptible to a number of adversarial manipulations (e.g., spoofing with precomputed patterns), which we call Synthetic Sensor Spoofing and one is resilient against our attacks. We investigate the root of its resilience and demonstrate that it comes from the properties that we introduced. Our attacks reduce the Recall (True Positive Rate) of the attacked schemes making them not able to correctly detect anomalies. Thus, the vulnerabilities we discovered in the anomaly detectors show that (despite an original good detection performance), those detectors are not able to reliably learn physical properties of the system. Even attacks that prior work was expected to be resilient against (based on verified properties) were found to be successful. We argue that our findings demonstrate the need for both more complete attacks in datasets, and more critical analysis of process-based anomaly detectors. We plan to release our implementation as open-source, together with an extension of two public datasets with a set of Synthetic Sensor Spoofing attacks as generated by our framework., Comment: An updated version of the paper has been published at ACSAC'2022: Assessing Model-free Anomaly Detection in Industrial Control Systems Against Generic Concealment Attacks https://dl.acm.org/doi/10.1145/3564625.3564633

In this manuscript we consider the set of Dyck paths equipped with the uniform measure, and we study the statistical properties of a deformation of the observable "area below the Dyck path" as the size $N$ of the path goes to infinity. The deformation under analysis is apparently new: while usually the area is constructed as the sum of the heights of the steps of the Dyck path, here we regard it as the sum of the lengths of the connected horizontal slices under the path, and we deform it by applying to the lengths of the slices a positive regular function $\omega(\ell)$ such that $\omega(\ell) \sim \ell^p$ for large argument. This shift of paradigm is motivated by applications to the Euclidean Random Assignment Problem in Random Combinatorial Optimization, and to Tree Hook Formulas in Algebraic Combinatorics. For $p \in \mathbb{R}^+ \smallsetminus \left\{ \frac{1}{2}\right\}$, we characterize the statistical properties of the deformed area as a function of the deformation function $\omega(\ell)$ by computing its integer moments, finding a generalization of a well-known recursion for the moments of the area-Airy distribution, due to Tak\'acs. Most of the properties of the distribution of the deformed area are \emph{universal}, meaning that they depend on the deformation parameter $p$, but not on the microscopic details of the function $\omega(\ell)$. We call \emph{$p$-Airy distribution} this family of universal distributions.

NGC 1624-2 is the most strongly magnetized O-type star known. Previous spectroscopic observations of this object in the ultraviolet provided evidence that it hosts a large and dense circumstellar magnetosphere. Follow-up observations obtained with the \textit{Hubble Space Telescope} not only confirm that previous inference, but also suggest that NGC 1624-2's magnetosphere has a complex structure. Furthermore, an expanded spectropolarimetric time series shows a potential departure from a dipolar magnetic field geometry, which could mean that the strongest field detected at the surface of an O-type star is also topologically complex. This result raises important questions regarding the origin and evolution of magnetic fields in massive stars., Comment: 12 pages, 3 figures, accepted for publication by MNRAS (2020 December 1)

An operational probabilistic theory where all systems are classical, and all pure states of composite systems are entangled, is constructed. The theory is endowed with a rule for composing an arbitrary number of systems, and with a nontrivial set of transformations. Hence, we demonstrate that the presence of entanglement is independent of the existence of incompatible measurements. We then study a variety of phenomena occurring in the theory -- some of them contradicting both Classical and Quantum Theories -- including: cloning, entanglement swapping, dense coding, additivity of classical capacities, non-monogamous entanglement, hypersignaling. We also prove the existence, in the theory, of a universal processor. The theory is causal and satisfies the no-restriction hypothesis. At the same time, it violates a number of information-theoretic principles enjoyed by Quantum Theory, most notably: local discriminability, purity of parallel composition of states, and purification. Moreover, we introduce an exhaustive procedure to construct generic operational probabilistic theories, and a sufficient set of conditions to verify their consistency. In addition, we prove a characterisation theorem for the parallel composition rules of arbitrary theories, and specialise it to the case of bilocal-tomographic theories. We conclude pointing out some open problems. In particular, on the basis of the fact that every separable state of the theory is a statistical mixture of entangled states, we formulate a no-go conjecture for the existence of a local-realistic ontological model., Comment: 24+7 pages, 2 figures, 1 table, plenty of diagrams; section "Conceptual Preview" added in v2; differently from the published version, a table of contents is herein present

The traditional approach of statistical physics to supervised learning routinely assumes unrealistic generative models for the data: usually inputs are independent random variables, uncorrelated with their labels. Only recently, statistical physicists started to explore more complex forms of data, such as equally-labelled points lying on (possibly low dimensional) object manifolds. Here we provide a bridge between this recently-established research area and the framework of statistical learning theory, a branch of mathematics devoted to inference in machine learning. The overarching motivation is the inadequacy of the classic rigorous results in explaining the remarkable generalization properties of deep learning. We propose a way to integrate physical models of data into statistical learning theory, and address, with both combinatorial and statistical mechanics methods, the computation of the Vapnik-Chervonenkis entropy, which counts the number of different binary classifications compatible with the loss class. As a proof of concept, we focus on kernel machines and on two simple realizations of data structure introduced in recent physics literature: $k$-dimensional simplexes with prescribed geometric relations and spherical manifolds (equivalent to margin classification). Entropy, contrary to what happens for unstructured data, is nonmonotonic in the sample size, in contrast with the rigorous bounds. Moreover, data structure induces a novel transition beyond the storage capacity, which we advocate as a proxy of the nonmonotonicity, and ultimately a cue of low generalization error. The identification of a synaptic volume vanishing at the transition allows a quantification of the impact of data structure within replica theory, applicable in cases where combinatorial methods are not available, as we demonstrate for margin learning., Comment: 19 pages, 3 figures

In this paper, we present results from the spectropolarimetric follow-up of photometrically selected candidate magnetic B stars from the MOBSTER project. Out of four observed targets, one (HD 38170) is found to host a detectable surface magnetic field, with a maximum longitudinal field measurement of 105$\pm$14 G. This star is chemically peculiar and classified as an $\alpha^2$ CVn variable. Its detection validates the use of TESS to perform a photometric selection of magnetic candidates. Furthermore, upper limits on the strength of a putative dipolar magnetic field are derived for the remaining three stars, and we report the discovery of a previously unknown spectroscopic binary system, HD 25709. Finally, we use our non-detections as case studies to further inform the criteria to be used for the selection of a larger sample of stars to be followed up using high-resolution spectropolarimetry., Comment: 9 pages, 6 figures, 4 tables, accepted by MNRAS (2021 March 23)

Many machine learning algorithms used for dimensional reduction and manifold learning leverage on the computation of the nearest neighbours to each point of a dataset to perform their tasks. These proximity relations define a so-called geometric graph, where two nodes are linked if they are sufficiently close to each other. Random geometric graphs, where the positions of nodes are randomly generated in a subset of $\mathbb{R}^{d}$, offer a null model to study typical properties of datasets and of machine learning algorithms. Up to now, most of the literature focused on the characterization of low-dimensional random geometric graphs whereas typical datasets of interest in machine learning live in high-dimensional spaces ($d \gg 10^{2}$). In this work, we consider the infinite dimensions limit of hard and soft random geometric graphs and we show how to compute the average number of subgraphs of given finite size $k$, e.g. the average number of $k$-cliques. This analysis highlights that local observables display different behaviors depending on the chosen ensemble: soft random geometric graphs with continuous activation functions converge to the naive infinite dimensional limit provided by Erd\"os-R\'enyi graphs, whereas hard random geometric graphs can show systematic deviations from it. We present numerical evidence that our analytical insights, exact in infinite dimensions, provide a good approximation also for dimension $d\gtrsim10$.

Recent spectropolarimetric surveys (MiMeS, BOB) have revealed that approximately 7% of massive stars host stable, surface dipolar magnetic fields with strengths on the order of kG. These fields channel the dense radiatively driven stellar wind into a circumstellar magnetosphere. Wind-sensitive UV spectral lines can probe the density and velocity structure of massive star magnetospheres, providing insight into wind-field interactions. To date, large-scale magnetohydrodynamic modeling of this phenomenon has been limited by the associated computational cost. Our analysis, using the Analytic Dynamical Magnetosphere model, solves this problem by applying a simple analytic prescription to efficiently calculate synthetic UV spectral lines. It can therefore be applied in the context of a larger parameter study to derive the wind properties for the population of known magnetic O stars. We also present the latest UV spectra of the magnetic O star NGC 1624-2 obtained with HST/COS, which test the limits of our models and suggest a particularly complex magnetospheric structure for this archetypal object., Comment: Stellar Magnetic Fields: A workshop in honor of the career and contributions of John Landstreet

Recent BRITE-Constellation space photometry of the slowly rotating, magnetic $\beta$ Cep pulsator $\xi^1$ CMa permits a new analysis of its pulsation properties. Analysis of the two-colour BRITE data reveals the well-known single pulsation period of $0.209$ d, along with its first and second harmonics. A similar analysis of SMEI and TESS observations yields compatible results, with the higher precision TESS observations also revealing several low-amplitude modes with frequencies below 5 d$^{-1}$; some of these are likely $g$ modes. The phase lag between photometric and radial velocity maxima - equal to 0.334 cycles - is significantly larger than the typical value of $1/4$ observed in other large-amplitude $\beta$ Cep stars. The phase lag, as well as the strong dependence of phase of maximum light on wavelength, can be reconciled with seismic models only if the dominant mode is the fundamental radial mode. We employ all published photometric and radial velocity measurements, spanning over a century, to evaluate the stability of the pulsation period. The $O-C$ diagram exhibits a clear parabolic shape consistent with a mean rate of period change $\dot P=0.34\pm 0.02$ s/cen. The residuals from the best-fit parabola exhibit scatter that is substantially larger than the uncertainties. In particular, dense sampling obtained during the past $\sim$20 years suggests more complex and rapid period variations. Those data cannot be coherently phased with the mean rate of period change, and instead require $\dot P\sim0.9$ s/cen. We examine the potential contributions of binarity, stellar evolution, and stellar rotation and magnetism to understand the apparent period evolution., Comment: 14 pages, accepted by MNRAS

Magnetic massive and intermediate-mass stars constitute a separate population whose properties are still not fully understood. Increasing the sample of known objects of this type would help answer fundamental questions regarding the origins and characteristics of their magnetic fields. The MOBSTER Collaboration seeks to identify candidate magnetic A, B and O stars and explore the incidence and origins of photometric rotational modulation using high-precision photometry from the Transiting Exoplanet Survey Satellite (\textit{TESS}) mission. In this contribution, we present an overview of our methods and planned targeted spectropolarimetric follow-up surveys., Comment: 7 pages, 1 figure, Conference proceedings: "Stellar Magnetic Fields - A workshop in honour of the career and contributions of John Landstreet", London, Canada, 2019 (to be published in the Proceedings of the Polish Astronomical Society)

In this contribution, we present the MOBSTER Collaboration, a large community effort to leverage high-precision photometry from the Transiting Exoplanet Survey Satellite (\textit{TESS}) in order to characterize the variability of magnetic massive and intermediate-mass stars. These data can be used to probe the varying column density of magnetospheric plasma along the line of sight for OB stars, thus improving our understanding of the interaction between surface magnetic fields and massive star winds. They can also be used to map out the brightness inhomogeneities present on the surfaces of Ap/Bp stars, informing present models of atomic diffusion in their atmospheres. Finally, we review our current and ongoing studies, which lead to new insights on this topic., Comment: 4 pages, Conference proceedings: "Stars and their variability observed from space", Vienna, Austria, 2019

We investigate operational probabilistic theories where the pure states of every system are the vertices of a simplex. A special case of such theories is that of classical theories, i.e. simplicial theories whose pure states are jointly perfectly discriminable. The usual Classical Theory satisfies also local discriminability. However, simplicial theories---including the classical ones---can violate local discriminability, thus admitting of entangled states. First, we prove sufficient conditions for the presence of entangled states in arbitrary probabilistic theories. Then, we prove that simplicial theories are necessarily causal, and this represents a no-go theorem for conceiving non-causal classical theories. We then provide necessary and sufficient conditions for simplicial theories to exhibit entanglement, and classify their system-composition rules. We conclude proving that, in simplicial theories, an operational formulation of the superposition principle cannot be satisfied, and that---under the hypothesis of $n$-local discriminability---no mixed state admits of a purification. Our results hold also in the general case where the sets of states fail to be convex., Comment: The definitions of simplicial and classical theories have been relaxed, in order to include the non-convex cases; the results hold also in the non-convex cases. Improved and extended presentation. Added results on superposition and purification. Enhanced the 'Discussion and Conclusions' section. Minor corrections. Layout fixed and mention to Ref. [13] corrected

Recently, reconstruction-based anomaly detection was proposed as an effective technique to detect attacks in dynamic industrial control networks. Unlike classical network anomaly detectors that observe the network traffic, reconstruction-based detectors operate on the measured sensor data, leveraging physical process models learned a priori. In this work, we investigate different approaches to evade prior-work reconstruction-based anomaly detectors by manipulating sensor data so that the attack is concealed. We find that replay attacks (commonly assumed to be very strong) show bad performance (i.e., increasing the number of alarms) if the attacker is constrained to manipulate less than 95% of all features in the system, as hidden correlations between the features are not replicated well. To address this, we propose two novel attacks that manipulate a subset of the sensor readings, leveraging learned physical constraints of the system. Our attacks feature two different attacker models: A white box attacker, which uses an optimization approach with a detection oracle, and a black box attacker, which uses an autoencoder to translate anomalous data into normal data. We evaluate our implementation on two different datasets from the water distribution domain, showing that the detector's Recall drops from 0.68 to 0.12 by manipulating 4 sensors out of 82 in WADI dataset. In addition, we show that our black box attacks are transferable to different detectors: They work against autoencoder-, LSTM-, and CNN-based detectors. Finally, we implement and demonstrate our attacks on a real industrial testbed to demonstrate their feasibility in real-time., Comment: Proceedings of the Annual Computer Security Applications Conference (ACSAC) 2020

High-dimensional data are ubiquitous in contemporary science and finding methods to compress them is one of the primary goals of machine learning. Given a dataset lying in a high-dimensional space (in principle hundreds to several thousands of dimensions), it is often useful to project it onto a lower-dimensional manifold, without loss of information. Identifying the minimal dimension of such manifold is a challenging problem known in the literature as intrinsic dimension estimation (IDE). Traditionally, most IDE algorithms are either based on multiscale principal component analysis (PCA) or on the notion of correlation dimension (and more in general on k-nearest-neighbors distances). These methods are affected, in different ways, by a severe curse of dimensionality. In particular, none of the existing algorithms can provide accurate ID estimates in the extreme locally undersampled regime, i.e. in the limit where the number of samples in any local patch of the manifold is less than (or of the same order of) the ID of the dataset. Here we introduce a new ID estimator that leverages on simple properties of the tangent space of a manifold to overcome these shortcomings. The method is based on the full correlation integral, going beyond the limit of small radius used for the estimation of the correlation dimension. Our estimator alleviates the extreme undersampling problem, intractable with other methods. Based on this insight, we explore a multiscale generalization of the algorithm. We show that it is capable of (i) identifying multiple dimensionalities in a dataset, and (ii) providing accurate estimates of the ID of extremely curved manifolds. In particular, we test the method on manifolds generated from global transformations of high-contrast images, relevant for invariant object recognition and considered a challenge for state-of-the-art ID estimators.

In this paper we introduce the MOBSTER collaboration and lay out its scientific goals. We present first results based on the analysis of nineteen previously known magnetic O, B and A stars observed in 2-minute cadence in sectors 1 and 2 of the Transiting Exoplanet Survey Satellite (TESS) mission. We derive precise rotational periods from the newly obtained light curves and compare them to previously published values. We also discuss the overall photometric phenomenology of the known magnetic massive and intermediate-mass stars and propose an observational strategy to augment this population by taking advantage of the high-quality observations produced by TESS., Comment: 15 pages, 3 figures, accepted for publication by MNRAS (2019 April 22)

We consider models of assignment for random $N$ blue points and $N$ red points on an interval of length $2N$, in which the cost for connecting a blue point in $x$ to a red point in $y$ is the concave function $|x-y|^p$, for $01$, where the optimal matching is trivially determined, here the optimization is non-trivial. The purpose of this paper is to introduce a special configuration, that we call the \emph{Dyck matching}, and to study its statistical properties. We compute exactly the average cost, in the asymptotic limit of large $N$, together with the first subleading correction. The scaling is remarkable: it is of order $N$ for $p<\frac{1}{2}$, order $N \ln N$ for $p=\frac{1}{2}$, and $N^{\frac{1}{2}+p}$ for $p>\frac{1}{2}$, and it is universal for a wide class of models. We conjecture that the average cost of the Dyck matching has the same scaling in $N$ as the cost of the optimal matching, and we produce numerical data in support of this conjecture. We hope to produce a proof of this claim in future work., Comment: 31 pages, 5 figures

Quantum walks (QWs) describe the evolution of quantum systems on graphs. An intrinsic degree of freedom---called the coin and represented by a finite-dimensional Hilbert space---is associated to each node. Scalar quantum walks are QWs with a one-dimensional coin. We propose a general strategy allowing one to construct scalar QWs on a broad variety of graphs, which admit embedding in Eulidean spaces, thus having a direct geometric interpretation. After reviewing the technique that allows one to regroup cells of nodes into new nodes, transforming finite spatial blocks into internal degrees of freedom, we prove that no QW with a two-dimensional coin can be derived from an isotropic scalar QW in this way. Finally we show that the Weyl and Dirac QWs can be derived from scalar QWs in spaces of dimension up to three, via our construction., Comment: 22 pages, 2 figures