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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