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Spontaneous brain activity generically displays transient spatiotemporal coherent structures, which can selectively be affected in various neurological and psychiatric pathologies. Here we model the full brain's electroencephalographic activity as a high-dimensional functional network performing a trajectory in a latent graph phase space. This approach allows us to investigate the orbital stability of brain's activity and in particular its short-term predictability. We do this by constructing a non-parametric statistic quantifying the expansion of initially close functional network trajectories. We apply the method to cohorts of healthy ageing individuals, and patients previously diagnosed with Parkinson's or Alzheimer's disease. Results not only characterise brain dynamics from a new angle, but further show that functional network predictability varies in a marked scale-dependent way across healthy controls and patient groups. The path towards both pathologies is markedly different. Furthermore, healthy ageing's predictability appears to strongly differ from that of Parkinson's disease, but much less from that of patients with Alzheimer's disease., Comment: 24 pages

This study examines the Lyapunov stability under coordinate $q$-contraction and $q$-dilatation in three dynamical systems: the discrete-time dissipative H\'enon map, and the conservative, non-integrable, continuous-time H\'enon-Heiles and diamagnetic Kepler problems. The stability analysis uses the $q$-deformed Jacobian and $q$-derivative, with trajectory stability assessed for $q > 1$ (dilatation) and $q < 1$ (contraction). Analytical curves in the parameter space mark boundaries of distinct low-periodic motions in the H\'enon map. Numerical simulations compute the maximal Lyapunov exponent across the parameter space, in Poincar\'e surfaces of section, and as a function of total energy in the conservative systems. Simulations show that $q$-contraction ($q$-dilatation) generally decreases (increases) positive Lyapunov exponents relative to the $q = 1$ case, while both transformations tend to increase Lyapunov exponents for regular orbits. Some exceptions to this trend remain unexplained regarding Kolmogorov-Arnold-Moser (KAM) tori stability., Comment: 15 pages, 8 figures

Let $R_{\lambda,j}$ be the $j$-th Bessel--Riesz transform, where $n\geq 1$, $\lambda>0$, and $j=1,\ldots,n+1$. In this article, we establish a Weyl type asymptotic for $[M_f,R_{\lambda,j}]$, the commutator of $R_{\lambda,j}$ with multiplication operator $M_f$, based on building a preliminary result that the endpoint weak Schatten norm of $[M_f,R_{\lambda,j}]$ can be characterised via homogeneous Sobolev norm $\dot{W}^{1,n+1}(\mathbb{R}_+^{n+1})$ of the symbol $f$. Specifically, the asymptotic coefficient is equivalent to $\|f\|_{\dot{W}^{1,n+1}(\mathbb{R}_+^{n+1})}.$ Our main strategy is to relate Bessel--Riesz commutator to classical Riesz commutator via Schur multipliers, and then to establish the boundedness of Schur multipliers., Comment: 37 pages

Functional networks representing human brain dynamics have become a standard tool in neuroscience, providing an accessible way of depicting the computation performed by the brain in healthy and pathological conditions. Yet, these networks share multiple characteristics with those representing other natural and man-made complex systems, leading to the question of whether they are actually capturing the uniqueness of the human brain. By resorting to a large set of data representing multiple financial, technological, social, and natural complex systems, and by relying on Deep Learning classification models, we show how they are highly similar. We specifically reach the conclusion that, under some general reconstruction methodological choices, it is as difficult to understand whether a network represents a human brain or a financial market, as to diagnose a major pathology. This suggests that functional networks are describing information processing mechanisms that are common across complex systems; but that are not currently defining the uniqueness of the human mind. We discuss the consequence of these findings for neuroscience and complexity science in general, and suggest future avenues for exploring this interesting topic., Comment: 5 pages plus SI, 3 figures

From the viewpoint of $*$-homomorphism on $C^{*}$-algebras, we establish the principal symbol mapping for filtered manifolds which are locally isomorphic to stratified Lie groups. Let $\mathbb{G}$ be a stratified Lie group, and let $M$ be a filtered manifold with a $\mathbb{G}$-atlas and a smooth positive density $\nu$. For the $C^{*}$-algebra bundle $E_{hom}$ of $M$ constructed from quasi-Riesz transforms on $\mathbb{G}$, we show that there exists a surjective $*$-homomorphism $${\rm sym}_{M}:\Pi_{M}\to C_{b}(E_{hom})$$ such that $${\rm ker}({\rm sym}_{M})=\mathcal{K}(L_{2}(M,\nu))\subset \Pi_{M}$$ where the domain $\Pi_{M}\subset\mathcal{B}(L_{2}(M,\nu))$ is a $C^{*}$-algebra and $C_{b}(E_{hom})$ is the $C^{*}$-algebra of bounded continuous sections of $E_{hom}$. Especially, we do not make any assumptions on the lattice of the osculating group of $M$ or the assumption of compactness on manifolds in \cite{DAO3,DAO4}.

We present the results of a multi-wavelength study of blazars selected from the 5th ROMABZCAT catalog. We selected from this sample a subsample of 2435 objects having at least one counterpart in one of the three main archival X-ray catalogs, which is, the fourth release of the XMM-Newton Survey Science Catalogue, the second release of the Chandra Source Catalog, and the second Swift X-ray Point Source catalog of detections by Swift-XRT, or in the recently released eROSITA-DE Data Release 1 catalog. We first searched for different multi-wavelength trends between sources with a Gamma-ray counterpart in the Fermi-LAT 14-year Source Catalog (4FGL-DR4) and sources lacking one. We find that the non-4FGL sources are on average fainter both in the X-rays and in the radio with respect to the 4FGL-detected ones, but the two samples have similar X-ray-to-radio flux ratios, as well as synchrotron peak frequencies. We then focused on the 1007 non-Gamma-ray detected population, to determine if there is a sample of X-ray sources that could be TeV emitters. We find that a large number of sources, mostly BL Lacs or BL Lacs with host-galaxy contribution to the spectral energy distribution, have large synchrotron peak frequency and X-ray to radio flux ratio, two properties that characterize the vast majority of known TeV emitters. With respect to these known TeV emitters, our targets have X-ray fluxes ~1 order of magnitude fainter. We then computed the 0.2-12 keV and 20 GeV - 300 TeV fluxes for the known 5BZCAT TeV emitters, and determined the existence of a direct correlation between X-ray and TeV fluxes in the BL Lacs population. We used this trend to estimate the VHE flux of our targets, and found a promising sample of sources for follow-up observations with current or future, more sensitive, Cherenkov telescopes, first and foremost the Cherenkov Telescope Array Observatory., Comment: 14 pages, 5 figures. Accepted for publication in Astronomy and Astrophysics

Let $\mathcal{M}$ be a semifinite von Neumann algebra and let $E$ be a symmetric function space on $(0,\infty)$. Denote by $E(\mathcal{M})$ the non-commutative symmetric space of measurable operators affiliated with $\mathcal{M}$ and associated with $E.$ Suppose $n\in \mathbb{N}$ and $E\cap L_{\infty}\not\subset L_{n,1}$, where $L_{n,1}$ is the Lorentz function space with the fundamental function $\varphi(t)=t^{1/n}$. We prove that for every $\varepsilon>0$ and every commuting self-adjoint $n$-tuple $(\alpha(j))_{j=1}^n,$ where $\alpha(j)$ is affiliated with $\mathcal{M}$ for each $1\leq j\leq n,$ there exists a commuting $n$-tuple $(\delta(j))_{j=1}^n$ of diagonal operators affiliated with $\mathcal{M}$ such that $\max\{\|\alpha(j)-\delta(j)\|_{E(\mathcal{M})},\|\alpha(j)-\delta(j)\|_{\infty}\}<\varepsilon$ for each $1\le j\le n$. In the special case when $\mathcal{M}=B(H)$, our results yield the classical Kuroda and Bercovici-Voiculescu theorems.

Let $E(\mathbb{T}^{d}_{\theta}),F(\mathbb{T}^{d}_{\theta})$ be two symmetric operator spaces on noncommutative torus $\mathbb{T}^{d}_{\theta}$ corresponding to symmetric function spaces $E,F$ on $(0,1)$. We obtain the Gagliardo--Nirenberg interpolation inequality with respect to $\mathbb{T}^{d}_{\theta}$: if $G=E^{1-\frac{l}{k}}F^{\frac{l}{k}}$ with $ 0\leq l\leq k$ and if the Ces\`{a}ro operator is bounded on $E$ and $F$, then \begin{align*} \|\nabla^lx\|_{G(\mathbb{T}^{d}_{\theta})}\leq 2^{3\cdot 2^{k-2}-2}(k+1)^d\|C\|_{E\to E}^{1-\frac{l}{k}}\|C\|_{F\to F}^{\frac{l}{k}}\|x\|_{E(\mathbb{T}^{d}_{\theta})}^{1-\frac{l}{k}}\|\nabla^kx\|_{F(\mathbb{T}^{d}_{\theta})}^{\frac{l}{k}},\; x\in W^{k,1}(\mathbb{T}^{d}_{\theta}), \end{align*} where $W^{k,1}(\mathbb{T}^{d}_{\theta})$ is the Sobolev space on $\mathbb{T}^{d}_{\theta}$ of order $k\in\mathbb{N}$. Our method is different from the previous settings, which is of interest in its own right.

The derivation of a function is a fundamental tool for solving problems in calculus. Consequently, the motivations for investigating physical systems capable of performing this task are numerous. Furthermore, the potential to develop an optical computer to replace conventional computers has led us to create an optical algorithm and propose an experimental setup for implementing the derivative of one-dimensional real-valued functions using a paraxial and monochromatic laser beam. To complement the differentiation algorithm, we have experimentally implemented a novel optical algorithm that can transfer a two-dimensional phase-encoded function to the intensity profile of a light beam. Additionally, we demonstrate how to implement the n-th derivative of functions encoded in the phase of the transverse profile of photons., Comment: 7 Pages, 9 figures

We study trace ideal properties of the commutators $[(-\Delta)^{\frac{\epsilon}{2}},M_f]$ of a power of the Laplacian with the multiplication operator by a function $f$ on $\mathbb R^d$. For a certain range of $\epsilon\in\mathbb R$, we show that this commutator belongs to the weak Schatten class $\mathcal L_{\frac d{1-\epsilon},\infty}$ if and only if the distributional gradient of $f$ belongs to $L_{\frac d{1-\epsilon}}$. Moreover, in this case we determine the asymptotics of the singular values. Our proofs use, among other things, the tool of Double Operator Integrals., Comment: 41 pages

We prove that the sequence space $\ell_{p,q}$ does not embed into $L_{p,q}(\mathcal{M},\tau)$ for any noncommutative probability space $(\mathcal{M},\tau)$, $1< p<\infty $, $1\le q<\infty$, $p\ne q$. Several applications to the isomorphic classification of noncommutative $L_{p,q}$-spaces are given, which extend and complement several earlier results.

In the study on the diagonality of an $n$-tuple $\alpha=(\alpha(j))_{j=1}^n$ of commuting self-adjoint operators modulo a given $n$-tuple $\Phi=(\mathcal{J}_1,\ldots,\mathcal{J}_n)$ of normed ideals in $B(H)$, Voiculescu introduced the notion of quasicentral modulus $k_{\Phi}(\alpha)$ and proved that $\alpha$ is diagonal modulo $(\mathcal{J}_1,\ldots,\mathcal{J}_n)$ if and only if $k_{\Phi}(\alpha)=0.$ We prove that the same assertion holds true when $B(H)$ is replaced with a $\sigma$-finite semifinite von Neumann algebra $\mathcal{M}$, and $\mathcal{J}_1,\ldots,\mathcal{J}_n$ are replaced with symmetric spaces $E_1(\mathcal{M}),\ldots,E_n(\mathcal{M})$ associated with $\mathcal{M}.$

The impact of air transport delays and their propagation has long been studied, mainly from environmental and mobility viewpoints, using a wide range of data analysis tools and simulations. Less attention has nevertheless been devoted to how delays create meso-scale structures around each airport. In this work we tackle this issue by reconstructing functional networks of delay propagation centred at each airport, and studying their identifiability (i.e. how unique they are) using Deep Learning models. We find that such delay propagation neighbourhoods are highly unique when they correspond to airports with a high share of Low Cost Carriers operations; and demonstrate the robustness of these findings for the EU and US systems, and to different methodological choices. We further discuss some operational implications of this uniqueness., Comment: 15 pages, 6 figures

We present a multi-epoch, multi-observatory X-ray analysis for 2FHL J1745.1-3035, a newly discovered very high energy Galactic source detected by the Fermi Large Area Telescope (LAT) located in close proximity to the Galactic Center (l=358.5319{\deg}; b=-0.7760{\deg}). The source shows a very hard gamma-ray photon index above 50 GeV, Gamma_gamma=1.2+-0.4, and is found to be a TeV-emitter by the LAT. We conduct a joint XMM-Newton, Chandra and NuSTAR observing campaign, combining archival XMM-Newton observations, to study the X-ray spectral properties of 2FHL J1745.1-3035 over a time-span of over 20 years. The joint X-ray spectrum is best-fitted as a broken power law model with break energy E_b~7 keV: the source is very hard at energies below 10 keV, with photon index Gamma_1~0.6, and significantly softer in the higher energy range measured by NuSTAR with photon index Gamma_2~1.9. We also perform a spatially resolved X-ray analysis with Chandra, finding evidence for marginal extension (up to an angular size r~5 arcsec), a result that supports a compact pulsar wind nebula scenario. Based on the X-ray and gamma-ray properties, 2FHL J1745.1-3035 is a powerful pulsar wind nebula candidate. Given its nature as an extreme TeV emitter, further supported by the detection of a coincident TeV extended source HESS J1745-303, 2FHL J1745.1-3035 is an ideal candidate for a follow-up with the upcoming Cherenkov Telescope Array., Comment: 21 pages, 13 figures; accepted for publication in ApJ

In mineral processing plants, grinding is a crucial step, accounting for approximately 50 percent of the total mineral processing costs. Semi-autogenous grinding mills are extensively employed in the grinding circuit of mineral processing plants. Maximizing SAG mill throughput is of significant importance considering its profound financial outcomes. However, the optimum process parameter setting aimed at achieving maximum mill throughput remains an uninvestigated domain in prior research. This study introduces a hybrid intelligent framework leveraging expert knowledge, machine learning techniques, and evolutionary algorithms to address this research need. In this study, we utilize an extensive industrial dataset comprising 36743 records and select relevant features based on the insights of industry experts. Following the removal of erroneous data, a comprehensive evaluation of 17 diverse machine learning models is undertaken to identify the most accurate predictive model. To improve the model performance, feature selection and outlier detection are executed. The resultant optimal model, trained with refined features, serves as the objective function within three distinct evolutionary algorithms. These algorithms are employed to identify parameter configurations that maximize SAG mill throughput while adhering to the working limits of input parameters as constraints. Notably, our analysis revealed that CatBoost, as an ensemble model, stands out as the most accurate predictor. Furthermore, differential evolution emerges as the preferred optimization algorithm, exhibiting superior performance in both achieving the highest mill throughput predictions and ensuring robustness in predictions, surpassing alternative methods.

Semi-autogenous grinding (SAG) mills play a pivotal role in the grinding circuit of mineral processing plants. Accurate prediction of SAG mill throughput as a crucial performance metric is of utmost importance. The potential of applying genetic programming (GP) for this purpose has yet to be thoroughly investigated. This study introduces an enhanced GP approach entitled multi-equation GP (MEGP) for more accurate prediction of SAG mill throughput. In the new proposed method multiple equations, each accurately predicting mill throughput for specific clusters of training data are extracted. These equations are then employed to predict mill throughput for test data using various approaches. To assess the effect of distance measures, four different distance measures are employed in MEGP method. Comparative analysis reveals that the best MEGP approach achieves an average improvement of 10.74% in prediction accuracy compared with standard GP. In this approach, all extracted equations are utilized and both the number of data points in each data cluster and the distance to clusters are incorporated for calculating the final prediction. Further investigation of distance measures indicates that among four different metrics employed including Euclidean, Manhattan, Chebyshev, and Cosine distance, the Euclidean distance measure yields the most accurate results for the majority of data splits.

Gamma-ray observations have established energetic isolated pulsars as outstanding particle accelerators and antimatter factories in the Galaxy. There is, however, no consensus regarding the acceleration mechanisms and the radiative processes at play, nor the locations where these take place. The spectra of all observed gamma-ray pulsars to date show strong cutoffs or a break above energies of a few gigaelectronvolt (GeV). Using the H.E.S.S. array of Cherenkov telescopes, we discovered a novel radiation component emerging beyond this generic GeV cutoff in the Vela pulsar's broadband spectrum. The extension of gamma-ray pulsation energies up to at least 20 teraelectronvolts (TeV) shows that Vela pulsar can accelerate particles to Lorentz factors higher than $4\times10^7$. This is an order of magnitude larger than in the case of the Crab pulsar, the only other pulsar detected in the TeV energy range. Our results challenge the state-of-the-art models for high-energy emission of pulsars while providing a new probe, i.e. the energetic multi-TeV component, for constraining the acceleration and emission processes in their extreme energy limit., Comment: 38 pages, 6 figures. This preprint has not undergone peer review or any post-submission improvements or corrections. The Version of Record of this article is published in Nature Astronomy, Nat Astron (2023), and is available online at https://doi.org/10.1038/s41550-023-02052-3

We treat the notion of principal symbol mapping on a compact smooth manifold as a $\ast$-homomorphism of $C^{\ast}$-algebras. Principal symbol mapping is built from the ground, without referring to the pseudodifferential calculus on the manifold. Our concrete approach allows us to extend Connes Trace Theorem for compact Riemannian manifolds.

In this article, we present Gammapy, an open-source Python package for the analysis of astronomical $\gamma$-ray data, and illustrate the functionalities of its first long-term-support release, version 1.0. Built on the modern Python scientific ecosystem, Gammapy provides a uniform platform for reducing and modeling data from different $\gamma$-ray instruments for many analysis scenarios. Gammapy complies with several well-established data conventions in high-energy astrophysics, providing serialized data products that are interoperable with other software packages. Starting from event lists and instrument response functions, Gammapy provides functionalities to reduce these data by binning them in energy and sky coordinates. Several techniques for background estimation are implemented in the package to handle the residual hadronic background affecting $\gamma$-ray instruments. After the data are binned, the flux and morphology of one or more $\gamma$-ray sources can be estimated using Poisson maximum likelihood fitting and assuming a variety of spectral, temporal, and spatial models. Estimation of flux points, likelihood profiles, and light curves is also supported. After describing the structure of the package, we show, using publicly available $\gamma$-ray data, the capabilities of Gammapy in multiple traditional and novel $\gamma$-ray analysis scenarios, such as spectral and spectro-morphological modeling and estimations of a spectral energy distribution and a light curve. Its flexibility and power are displayed in a final multi-instrument example, where datasets from different instruments, at different stages of data reduction, are simultaneously fitted with an astrophysical flux model., Comment: 26 pages, 16 figures

In very-high-energy (VHE) gamma-ray astronomy, the community is converging towards the use of a common open data format, called "Data formats for Gamma-ray Astronomy", for the high-level data products. This format is in use for ground-based TeV observatories like H.E.S.S., MAGIC or HAWC, some of whom plan to openly release high-level data products. These efforts are parallel to the development and use of open analysis software such as the Gammapy package. This open initiative has shown that it is possible to define common standards even without governance. With the advent of open VHE observatories (e.g. CTAO, KM3NeT) and an increase in both multi-wavelength and multi-messenger studies, such standards should evolve to support all of VHE multi-messenger astrophysics. For these reasons, a new initiative has been created to specify formats of high-level data from very and ultra high energy gamma-ray facilities and from VHE neutrino detectors. It also aims to better respect the FAIR principles and the IVOA recommendations.This communication will present the Very-high-energy Open Data Format (VODF) project that has been established by eleven VHE astroparticle facilities. Its structure, its organisation and its goal will be presented. Anchored in Open Science, our goal is to solicit comments and future contributions from the VHE astrophysics community., Comment: Proceedings paper presented at the 38th International Cosmic Ray Conference (ICRC2023), held 26 July - 3 August, 2023, in Nagoya, Japan

Motivated by the recent work of Gimperlein and Goffeng on Calder\'on's commutator on compact Heisenberg type manifolds and the related weak Schatten class estimates, we establish the characterisation of $L^p$ boundedness for Calderon's commutator on stratified Lie groups. We further study related weak Schatten class estimates for second order commutators on two step stratified Lie groups, which include the Heisenberg groups. This latter result is obtained using double operator integral techniques which are novel in this area., Comment: simplified the proof

Continuous variable encoding of quantum information requires the deterministic generation of highly correlated quantum states of light in the form of quantum networks, which, in turn, necessitates the controlled generation of a large number of squeezed modes. In this work, we present an experimental source of multimode squeezed states of light at telecommunication wavelengths. Generation at such wavelengths is especially important as it can enable quantum information processing, communication, and sensing beyond the laboratory scale. We use a single-pass spontaneous parametric down-conversion process in a non-linear waveguide pumped with the second harmonic of a femtosecond laser. Our measurements reveal significant squeezing in more than 21 frequency modes, with a maximum squeezing value exceeding 2.5 dB. We demonstrate multiparty entanglement by measuring the state's covariance matrix. Finally, we show the source reconfigurability by preparing few-node cluster states and measure their nullifier squeezing level. These results pave the way for a scalable implementation of continuous variable quantum information protocols at telecommunication wavelengths, particularly for multiparty, entanglement-based quantum communications. Moreover, the source is compatible with additional pulse-by-pulse multiplexing, which can be utilized to construct the necessary three-dimensional entangled structures for quantum computing protocols.

The Cherenkov Telescope Array Observatory (CTAO) is a next-generation facility for ground-based very high energy gamma ray astronomy. CTAO will be operated as an open observatory. With two sites, in the northern and southern hemispheres, the Cherenkov Telescope Array CTA will provide full-sky coverage, improving sensitivity by an order of magnitude over current instruments, with a wide gamma ray energy coverage from 20 GeV to 300 TeV. CTA will use telescope arrays composed of three types of telescopes, optimized to cover different energy ranges. The large telescopes covering the lowest energies provide rapid slewing capability, for follow-up of transients. Key Science Projects (KSPs) are developed to form a significant part of the CTAO observing program during the first decade of operation, providing legacy data sets such as surveys or deep observations of key targets., Comment: To appear in "Handbook of X-ray and Gamma-ray Astrophysics" by Springer (Eds. C. Bambi and A. Santangelo)

We explicitly compute the local invariants (heat kernel coefficients) of a conformally deformed non-commutative $d$-torus using multiple operator integrals. We derive a recursive formula that easily produces an explicit expression for the local invariants of any order $k$ and in any dimension $d$. Our recursive formula can conveniently produce all formulas related to the modular operator, which before were obtained in incremental steps for $d\in\{2,4\}$ and $k\in\{0,2,4\}$. We exemplify this by writing down some known ($k=2$, $d=2$) and some novel ($k=2$, $d\geq 3$) formulas in the modular operator., Comment: 34 pages, 1 figure, 1 python file

Air transportation is a complex system characterised by a plethora of interactions at multiple temporal and spatial scales; as a consequence, even simple dynamics like sequencing aircraft for landing can lead to the appearance of emergent behaviours, which are both difficult to control and detrimental to operational efficiency. We propose a model, based on a modulated Markov jitter, to represent ordinal pattern properties of real landing operations in European airports. The parameters of the model are tuned by minimising the distance between the probability distributions of ordinal patterns generated by the real and synthetic sequences, as estimated by the Permutation Jensen-Shannon Distance. We show that the correlation between consecutive hours in the landing flow changes between airports, and that it can be interpreted as a metric of efficiency. We further compare the dynamics pre and post COVID-19, showing how this has changed beyond what can be attributed to a simple reduction of traffic. We finally draw some operational conclusions, and discuss the applicability of these findings in a real operational environment., Comment: 12 pages, 11 figures, 2 tables

We obtain Weyl type asymptotics for the quantised derivative $\dbar f$ of a function $f$ from the homgeneous Sobolev space $\dot{W}^1_d(\mathbb{R}^d)$ on $\mathbb{R}^d.$ The asymptotic coefficient $\|\nabla f\|_{L_d(\mathbb R^d)}$ is equivalent to the norm of $\dbar f$ in the principal ideal $\mathcal{L}_{d,\infty},$ thus, providing a non-asymptotic, uniform bound on the spectrum of $\dbar f.$ Our methods are based on the $C^{\ast}$-algebraic notion of the principal symbol mapping on $\mathbb{R}^d$, as developed recently by the last two authors and collaborators., Comment: 41 pages; accepted for publication in Trans. Amer. Math. Soc

MAXI J1820+070 is a low-mass X-ray binary with a black hole as a compact object. This binary underwent an exceptionally bright X-ray outburst from March to October 2018, showing evidence of a non-thermal particle population through its radio emission during this whole period. The combined results of 59.5 hours of observations of the MAXI J1820+070 outburst with the H.E.S.S., MAGIC and VERITAS experiments at energies above 200 GeV are presented, together with Fermi-LAT data between 0.1 and 500 GeV, and multiwavelength observations from radio to X-rays. Gamma-ray emission is not detected from MAXI J1820+070, but the obtained upper limits and the multiwavelength data allow us to put meaningful constraints on the source properties under reasonable assumptions regarding the non-thermal particle population and the jet synchrotron spectrum. In particular, it is possible to show that, if a high-energy gamma-ray emitting region is present during the hard state of the source, its predicted flux should be at most a factor of 20 below the obtained Fermi-LAT upper limits, and closer to them for magnetic fields significantly below equipartition. During the state transitions, under the plausible assumption that electrons are accelerated up to ~ 500 GeV, the multiwavelength data and the gamma-ray upper limits lead consistently to the conclusion that a potential high-energy and very-high-energy gamma-ray emitting region should be located at a distance from the black hole ranging between 10^11 and 10^13 cm. Similar outbursts from low-mass X-ray binaries might be detectable in the near future with upcoming instruments such as CTA., Comment: 15 pages, 5 figures. Accepted for publication in MNRAS

We study the interaction of agents, where each one consists of an associative memory neural network trained with the same memory patterns and possibly different reinforcement-unlearning dreaming periods. Using replica methods, we obtain the rich equilibrium phase diagram of the coupled agents. It shows phases such as the student-professor phase, where only one network benefits from the interaction while the other is unaffected; a mutualism phase, where both benefit; an indifferent phase and an insufficient phase, where neither are benefited nor impaired; a phase of amensalism where one is unchanged and the other is damaged. In addition to the paramagnetic and spin glass phases, there is also one we call the reinforced delusion phase, where agents concur without having finite overlaps with memory patterns. For zero coupling constant, the model becomes the reinforcement and removal dreaming model, which without dreaming is the Hopfield model. For finite coupling and a single memory pattern, it becomes a Mattis version of the Ashkin-Teller model. In addition to the analytical results, we have explored the model with Monte Carlo simulations., Comment: 23 pages , 4 figures

We discuss the optimality of Cwikel-Solomyak estimates for the uniform operator norm and establish optimality of M.Z Solomyak's results \cite{Solomyak1995} within the class of Orlicz spaces. Our methods are based on finding the optimal version of the Sobolev embedding theorem.

In 2002, in a seminal article, Christoph Bandt and Bernd Pompe proposed a new methodology for the analysis of complex time series, now known as Ordinal Analysis. The ordinal methodology is based on the computation of symbols (known as ordinal patterns) which are defined in terms of the temporal ordering of data points in a time series, and whose probabilities are known as ordinal probabilities. With the ordinal probabilities, the Shannon entropy can be calculated, which is the permutation entropy. Since it was proposed, the ordinal method has found applications in fields as diverse as biomedicine and climatology. However, some properties of ordinal probabilities are still not fully understood, and how to combine the ordinal approach of feature extraction with machine learning techniques for model identification, time series classification or forecasting remains a challenge. The objective of this perspective article is to present some recent advances and to discuss some open problems., Comment: Accepted in EPL

During the last years, statistical physics has received an increasing attention as a framework for the analysis of real complex systems; yet, this is less clear in the case of international political events, partly due to the complexity in securing relevant quantitative data on them. Here we analyse a detailed data set of violent events that took place in Ukraine since January 2021, and analyse their temporal and spatial correlations through entropy and complexity metrics, and functional networks. Results depict a complex scenario, with events appearing in a non-random fashion, but with eastern-most regions functionally disconnected from the remainder of the country -- something opposing the widespread "two Ukraines" view. We further draw some lessons and venues for future analyses., Comment: 7 pages, 5 Figures

Let $(\mathcal{F}_n)_{n\ge 0}$ be the standard dyadic filtration on $[0,1]$. Let $\mathbb{E}_{\mathcal{F}_n}$ be the conditional expectation from $ L_1=L_1[0,1]$ onto $\mathcal{F} _n$, $n\ge 0$, and let $\mathbb{E}_{\mathcal{F} _{-1}} =0$. We present the sharp estimate for the distribution function of the martingale transform $T$ defined by \begin{align*} Tf=\sum_{m=0}^\infty \left( \mathbb{E}_{\mathcal{F}_{2m}} f-\mathbb{E}_{\mathcal{F}_{2m-1}}f \right), ~f\in L_1, \end{align*} in terms of the classical Calder\'{o}n operator. As an application, for a given symmetric function space $E$ on $[0,1]$, we identify the symmetric space $\mathcal{S}_E$, the optimal Banach symmetric range of martingale transforms/Haar basis projections acting on $E$.

For a certain class of discrete metric spaces, we provide a formula for the density of states. This formula involves Dixmier traces and is proven using recent advances in operator theory. Various examples are given of metric spaces for which this formula holds, including crystals, quasicrystals and the infinite cluster resulting from super-critical bond percolation on $\mathbb{Z}^d$., Comment: 28 pages, no figures

Along the line of singular value estimates for commutators by Rochberg-Semmes, Lord-McDonald-Sukochev-Zanin and Fan-Lacey-Li, we establish the endpoint weak Schatten class estimate for commutators of Riesz transforms with multiplication operator $M_f$ on Heisenberg groups via homogeneous Sobolev norm of the symbol $f$. The new tool we exploit is the construction of a singular trace formula on Heisenberg groups, which, together with the use of double operator integrals, allows us to bypass the use of Fourier analysis and provides a solid foundation to investigate the singular values estimates for similar commutators in general stratified Lie groups., Comment: 48 pages

We study Cwikel-type estimates for the singular values and Schatten $\mathcal{L}_p$-norms of compositions of multiplication and convolution operators acting on stratified Lie groups. This enables us to obtain novel spectral asymptotic formulas for certain operators derived from sub-Laplacians., Comment: 37 pages

Let $\theta \in(0,1)$ and $(\mathcal{M},\tau)$ be a semifinite von Neumann algebra. We consider the function spaces introduced by Sobolev (denoted by $S_{d,\theta}$), showing that there exists a constant $d>0 $ depending on $p$, $01$, we obtain a reverse of the Birman-Koplienko-Solomjak inequality, which extends a couple of existing results on fractional powers $t\mapsto t^\theta$ by Ando et al., Comment: accepted to be published in JLMS

Multifractal Detrended Fluctuation Analysis stands out as one of the most reliable methods for unveiling multifractal properties, specially when real-world time series are under analysis. However, little is known about how several aspects, like artefacts during the data acquisition process, affect its results. In this work we have numerically investigated the performance of Multifractal Detrended Fluctuation Analysis applied to synthetic finite uncorrelated data following a power-law distribution in the presence of additive noise, and periodic and randomly-placed outliers. We have found that, on one hand, spurious multifractality is observed as a result of data finiteness, while additive noise leads to an underestimation of the exponents $h_q$ for $q<0$ even for low noise levels. On the other hand, additive periodic and randomly-located outliers result in a corrupted inverse multifractality around $q=0$. Moreover, the presence of randomly-placed outliers corrupts the entire multifractal spectrum, in a way proportional to their density. As an application, the multifractal properties of the time intervals between successive aircraft landings at three major European airports are investigated., Comment: 17 pages, 11 figures, 2 tables

Magnetar hyperflares are the most plausible explanation for fast radio bursts (FRB) -- enigmatic powerful radio pulses with durations of several milliseconds and high brightness temperatures. The first observational evidence for this scenario was obtained in 2020 April when a FRB was detected from the direction of the Galactic magnetar and soft gamma-ray repeater SGR\,1935+2154. The FRB was preceded by two gamma-ray outburst alerts by the BAT instrument aboard the Swift satellite, which triggered follow-up observations by the High Energy Stereoscopic System (H.E.S.S.). H.E.S.S. has observed SGR\,1935+2154 for 2 hr on 2020 April 28. The observations are coincident with X-ray bursts from the magnetar detected by INTEGRAL and Fermi-GBM, thus providing the first very high energy (VHE) gamma-ray observations of a magnetar in a flaring state. High-quality data acquired during these follow-up observations allow us to perform a search for short-time transients. No significant signal at energies $E>0.6$~TeV is found and upper limits on the persistent and transient emission are derived. We here present the analysis of these observations and discuss the obtained results and prospects of the H.E.S.S. follow-up program for soft gamma-ray repeaters., Comment: Received 2021 June 13; accepted 2021 June 28; published 2021 September 29

Star-forming regions have been proposed as potential Galactic cosmic-ray accelerators for decades. Cosmic ray acceleration can be probed through observations of gamma-rays produced in inelastic proton-proton collisions, at GeV and TeV energies. We analyze more than 11 years of Fermi-LAT data from the direction of Westerlund 2, one of the most massive and best-studied star-forming regions in our Galaxy. The spectral and morphological characteristics of the LAT source agree with the ones in the TeV regime (HESS J1023-575), allowing the description of the gamma-ray source from a few hundreds of MeV to a few tens of TeVs. We will present the results and discuss the implications of the identification with the stellar cluster and the radiation mechanism involved., Comment: Proceeding for contribution to the 37th International Cosmic Ray Conference (ICRC2021)

Time irreversibility, defined as the lack of invariance of the statistical properties of a system or time series under the operation of time reversal, has received an increasing attention during the last decades, thanks to the information it provides about the mechanisms underlying the observed dynamics. Following the need of analysing real-world time series, many irreversibility metrics and tests have been proposed, each one associated with different requirements in terms of e.g. minimum time series length or computational cost. We here build upon previously proposed tests based on the concept of permutation patterns, but deviating from them through the inclusion of information about the amplitude of the signal and how this evolves over time. We show, by means of synthetic time series, that the results yielded by this method are complementary to the ones obtained by using permutation patterns alone, thus suggesting that "one irreversibility metric does not fit all" We further apply the proposed metric to the analysis of two real-world data sets., Comment: 10 pages, 6 figures

We analyzed 252 hours of High Energy Stereoscopic System (H.E.S.S.) observations towards the supernova remnant (SNR) LMC N132D that were accumulated between December 2004 and March 2016 during a deep survey of the Large Magellanic Cloud, adding 104 hours of observations to the previously published data set to ensure a > 5 sigma detection. To broaden the gamma-ray spectral coverage required for modeling the spectral energy distribution, an analysis of Fermi-LAT Pass 8 data was also included. We unambiguously detect N132D at very high energies (VHE) with a significance of 5.7 sigma. We report the results of a detailed analysis of its spectrum and localization based on the extended H.E.S.S. data set. The joint analysis of the extended H.E.S.S and Fermi-LAT data results in a spectral energy distribution in the energy range from 1.7 GeV to 14.8 TeV, which suggests a high luminosity of N132D at GeV and TeV energies. We set a lower limit on a gamma-ray cutoff energy of 8 TeV with a confidence level of 95%. The new gamma-ray spectrum as well as multiwavelength observations of N132D when compared to physical models suggests a hadronic origin of the VHE gamma-ray emission. SNR N132D is a VHE gamma-ray source that shows a spectrum extending to the VHE domain without a spectral cutoff at a few TeV, unlike the younger oxygen-rich SNR Cassiopeia A. The gamma-ray properties of N132D may be affected by an interaction with a nearby molecular cloud that partially lies inside the 95% confidence region of the source position. [Abridged], Comment: Accepted for publication in Astronomy & Astrophysics

In this short note we demonstrate that the definition of the density of states of a Schr\"{o}dinger operator with bounded potential in general depends on the choice of the domain undergoing the thermodynamic limit., Comment: 3 pages

Maxwell's Demon is at the heart of the interrelation between quantum information processing and thermodynamics. In this thought experiment, a demon generates a temperature gradient between two thermal baths initially at equilibrium by gaining information at the single-particle level and applying classical feed-forward operations, allowing for the extraction of work. Here we implement a photonic version of Maxwell's Demon with active feed-forward in a fibre-based system using ultrafast optical switches. We experimentally show that, if correlations exist between the two thermal baths, the Demon can generate a temperature difference over an order of magnitude larger than without correlations, and so extract more work. Our work demonstrates the great potential of photonic experiments -- which provide a unique degree of control on the system -- to access new regimes in quantum thermodynamics., Comment: 25 pages with appendix, 6 figures. Final version published on Quantum

The High Altitude Water Cherenkov (HAWC) observatory and the High Energy Stereoscopic System (H.E.S.S.) are two leading instruments in the ground-based very-high-energy gamma-ray domain. HAWC employs the water Cherenkov detection (WCD) technique, while H.E.S.S. is an array of Imaging Atmospheric Cherenkov Telescopes (IACTs). The two facilities therefore differ in multiple aspects, including their observation strategy, the size of their field of view and their angular resolution, leading to different analysis approaches. Until now, it has been unclear if the results of observations by both types of instruments are consistent: several of the recently discovered HAWC sources have been followed up by IACTs, resulting in a confirmed detection only in a minority of cases. With this paper, we go further and try to resolve the tensions between previous results by performing a new analysis of the H.E.S.S. Galactic plane survey data, applying an analysis technique comparable between H.E.S.S. and HAWC. Events above 1 TeV are selected for both datasets, the point spread function of H.E.S.S. is broadened to approach that of HAWC, and a similar background estimation method is used. This is the first detailed comparison of the Galactic plane observed by both instruments. H.E.S.S. can confirm the gamma-ray emission of four HAWC sources among seven previously undetected by IACTs, while the three others have measured fluxes below the sensitivity of the H.E.S.S. dataset. Remaining differences in the overall gamma-ray flux can be explained by the systematic uncertainties. Therefore, we confirm a consistent view of the gamma-ray sky between WCD and IACT techniques.

Feedback on the ASTRONET Science Vision and Infrastructure Roadmap from the CTA Consortium., Comment: Submitted as input to the ASTRONET Science Vision and Infrastructure roadmap on behalf of the CTA consortium

The identification of PeVatrons, hadronic particle accelerators reaching the knee of the cosmic ray spectrum (few $10^{15}$ eV), is crucial to understand the origin of cosmic rays in the Galaxy. We provide an update on the unidentified source HESS J1702-420, a promising PeVatron candidate. We present new observations of HESS J1702-420 made with the High Energy Stereoscopic System (H.E.S.S.), and processed using improved analysis techniques. The analysis configuration was optimized to enhance the collection area at the highest energies. We applied a three-dimensional (3D) likelihood analysis to model the source region and adjust non thermal radiative spectral models to the $\gamma$-ray data. We also analyzed archival data from the Fermi Large Area Telescope (LAT) to constrain the source spectrum at $\gamma$-ray energies >10 GeV. We report the detection of a new source component called HESS J1702-420A, that was separated from the bulk of TeV emission at a $5.4\sigma$ confidence level. The power law $\gamma$-ray spectrum of HESS J1702-420A extends with an index of $\Gamma=1.53\pm0.19_\text{stat}\pm0.20_\text{sys}$ and without curvature up to the energy band 64-113 TeV, in which it was detected by H.E.S.S. at a $4.0\sigma$ confidence level. This brings evidence for the source emission up to $100\,\text{TeV}$, which makes HESS J1702-420A a compelling candidate site for the presence of extremely high energy cosmic rays. Remarkably, in a hadronic scenario, the cut-off energy of the proton distribution powering HESS J1702-420A is found to be higher than 0.5 PeV at a 95% confidence level. HESS J1702-420A becomes therefore one of the most solid PeVatron candidates detected so far in H.E.S.S. data, altough a leptonic origin of its emission could not be ruled out either., Comment: Accepted for publication in the 2. Astrophysical processes section of Astronomy & Astrophysics

The physics of the non-thermal Universe provides information on the acceleration mechanisms in extreme environments, such as black holes and relativistic jets, neutron stars, supernovae or clusters of galaxies. In the presence of magnetic fields, particles can be accelerated towards relativistic energies. As a consequence, radiation along the entire electromagnetic spectrum can be observed, and extreme environments are also the most likely sources of multi-messenger emission. The most energetic part of the electromagnetic spectrum corresponds to the very-high-energy (VHE, E>100 GeV) gamma-ray regime, which can be extensively studied with ground based Imaging Atmospheric Cherenkov Telescopes (IACTs). The results obtained by the current generation of IACTs, such as H.E.S.S., MAGIC, and VERITAS, demonstrate the crucial importance of the VHE band in understanding the non-thermal emission of extreme environments in our Universe. In some objects, the energy output in gamma rays can even outshine the rest of the broadband spectrum. The Cherenkov Telescope Array (CTA) is the next generation of IACTs, which, with cutting edge technology and a strategic configuration of ~100 telescopes distributed in two observing sites, in the northern and southern hemispheres, will reach better sensitivity, angular and energy resolution, and broader energy coverage than currently operational IACTs. With CTA we can probe the most extreme environments and considerably boost our knowledge of the non-thermal Universe., Comment: Submitted as input to ASTRONET Science Vision and Infrastructure roadmap on behalf of the CTA consortium

We prove a Tauberian theorem for singular values of noncommuting operators which allows us to prove exact asymptotic formulas in noncommutative geometry at a high degree of generality. We explain how, via the Birman--Schwinger principle, these asymptotics imply that a semiclassical Weyl law holds for many interesting noncommutative examples. In Connes' notation for quantized calculus, we prove that for a wide class of $p$-summable spectral triples $(\mathcal{A},H,D)$ and self-adjoint $V \in \mathcal{A}$, there holds \[\lim_{h\downarrow 0} h^p\mathrm{Tr}(\chi_{(-\infty,0)}(h^2D^2+V)) = \int V_-^{\frac{p}{2}}|ds|^p.\] where $\int$ is Connes' noncommutative integral.

Cosmological $N$-body simulations show that Milky Way-sized galaxies harbor a population of unmerged dark matter subhalos. These subhalos could shine in gamma-rays and be eventually detected in gamma-ray surveys as unidentified sources. We performed a thorough selection among unidentified Fermi-LAT Objects (UFOs) to identify them as possible TeV-scale dark matter subhalo candidates. We search for very-high-energy (E $\gtrsim$ 100 GeV) gamma-ray emissions using H.E.S.S. observations towards four selected UFOs. Since no significant very-high-energy gamma-ray emission is detected in any dataset of the four observed UFOs nor in the combined UFO dataset, strong constraints are derived on the product of the velocity-weighted annihilation cross section $\langle \sigma v \rangle$ by the $J$-factor for the dark matter models. The 95% C.L. observed upper limits derived from combined H.E.S.S. observations reach $\langle \sigma v \rangle J$ values of 3.7$\times$10$^{-5}$ and 8.1$\times$10$^{-6}$ GeV$^2$cm$^{-2}$s$^{-1}$ in the $W^+W^-$ and $\tau^+\tau^-$ channels, respectively, for a 1 TeV dark matter mass. Focusing on thermal WIMPs, the H.E.S.S. constraints restrict the $J$-factors to lie in the range 6.1$\times$10$^{19}$ - 2.0$\times$10$^{21}$ GeV$^2$cm$^{-5}$, and the masses to lie between 0.2 and 6 TeV in the $W^+W^-$ channel. For the $\tau^+\tau^-$ channel, the $J$-factors lie in the range 7.0$\times$10$^{19}$ - 7.1$\times$10$^{20}$ GeV$^2$cm$^{-5}$ and the masses lie between 0.2 and 0.5 TeV. Assuming model-dependent predictions from cosmological N-body simulations on the $J$-factor distribution for Milky Way-sized galaxies, the dark matter models with masses greater than 0.3 TeV for the UFO emissions can be ruled out at high confidence level., Comment: 11 pages, 7 figures, matches accepted version in The Astrophysical Journal

Star-forming regions have been proposed as potential Galactic cosmic-ray accelerators for decades. Cosmic-ray acceleration can be probed through observations of gamma-rays produced in inelastic proton-proton collisions, at GeV and TeV energies. In this paper, we analyze more than 11 years of Fermi-LAT data from the direction of Westerlund 2, one of the most massive and best-studied star-forming regions in our Galaxy. In particular, we investigate the characteristics of the bright pulsar PSR J1023-5746 that dominates the gamma-ray emission below a few GeV at the position of Westerlund 2, and the underlying extended source FGES J1023.3-5747. The analysis results in a clear identification of FGES J1023.3-5747 as the GeV counterpart of the TeV source HESS J1023-575, through its morphological and spectral properties. This identification provides new clues about the origin of the HESS J1023-575 gamma-ray emission, favouring a hadronic origin of the emission, powered by Westerlund 2, rather than a leptonic origin related to either the pulsar wind nebula associated with PSR J1023-5746 or the cluster itself. This result indirectly supports the hypothesis that star-forming regions can contribute to the cosmic-ray sea observed in our Galaxy, Comment: In press in MNRAS