The Eisenhart lift is extended to the dynamics described by action-dependent Lagrangians. The resulting Brinkmann metrics depends on all coordinates. It is shown that the symmetries of the initial dynamics result in the existence of (conformal) Killing vectors of Brinkmann metric. An example is given of equivalent time- and action-dependent descriptions which result in conformally equivalent metrics.

It is demonstrated that nonlinear dynamical systems with analytic nonlinearities can be brought down to the abstract Schrödinger equation in Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion of solutions to the Schrödinger equation in the particular occupation number representation are expressed by means of the classical orthogonal polynomials. The introduced formalism amounts a generalization of the classical methods for linearization of nonlinear differential equations such as the Carleman embedding technique and Koopman approach.

Modelling the broadband emission of jetted active galactic nuclei (AGN) constitutes one of the main research topics of extragalactic astrophysics in the multi-wavelength and multi-messenger domain. We present agnpy, an open-source python package modelling the radiative processes of relativistic particles accelerated in the jets of active galactic nuclei. The package includes classes describing the galaxy components responsible for line and thermal emission and calculates the absorption due to $\gamma\gamma$ pair production on several photon fields. agnpy aims at extending the effort of modelling and interpreting the emission of extragalactic sources to a wide number of astrophysicists. We present the package content and illustrate a few examples of applications of its functionalities. We validate the software by comparing its results against the literature and against other open-source software. We illustrate the utility of agnpy in addressing the most common questions encountered while modelling the emission of jetted active galaxies. When comparing its results against the literature and other modelling tools adopting the same physical assumptions, we achieve an agreement within $10-30\%$. agnpy represents one of the first systematic and validated collection of established radiative processes for jetted active galaxies in an open-source python package. We hope it will stand also among the first endeavours providing reproducible and transparent astrophysical software not only for data reduction and analysis, but also for modelling and interpretation.

We have constructed and run a Bell test of local realism focusing on the objectivity criterion. The objectivity means that the outcomes are confirmed macroscopically by a few observers at each party. The IBM Quantum and IonQ devices turn out to be sufficiently accurate to pass such an extended Bell-type test, although at the price of communication loopholes and residual but statistically significant signaling. The test also serves as the benchmark of entanglement spread across larger sets of qubits.

Large Language Models (LLMs) are pretrained on textual data up to a specific temporal cutoff. This creates a strict knowledge boundary beyond which models cannot provide accurate information without querying external sources. More subtly, when this limitation is unknown or ignored, LLMs may inadvertently blend outdated time-sensitive information with general knowledge during reasoning tasks, potentially compromising response accuracy. We introduce LLMLagBench, an LLM freshness benchmark, as a systematic approach for identifying the earliest probable temporal boundaries of an LLM's training data by evaluating its knowledge of recent events. We then apply this benchmark to evaluate a large set of LLMs, including models with both explicitly declared and undeclared training cutoffs. The reliability of the benchmark is assessed by manual validation and comparison with publicly released information about LLM pretraining.

To discuss one-photon polarization states we find an explicit form of the Wigner's little group element in the massless case for arbitrary Lorentz transformation. As is well known, when analyzing the transformation properties of the physical states, only the value of the phase factor is relevant. We show that this phase factor depends only on the direction of the momentum $\vec{k}/|\vec{k}|$ and does not depend on the frequency $k^0$. Finally, we use this observation to discuss the transformation properties of the linearly polarized photons and the corresponding reduced density matrix. We find that they transform properly under Lorentz group.

Axion-like particles (ALPs) are pseudo-Nambu-Goldstone bosons that emerge in various theories beyond the standard model. These particles can interact with high-energy photons in external magnetic fields, influencing the observed gamma-ray spectrum. This study analyzes 41.3 hrs of observational data from the Perseus Galaxy Cluster collected with the MAGIC telescopes. We focused on the spectra the radio galaxy in the center of the cluster: NGC 1275. By modeling the magnetic field surrounding this target, we searched for spectral indications of ALP presence. Despite finding no statistical evidence of ALP signatures, we were able to exclude ALP models in the sub-micro electronvolt range. Our analysis improved upon previous work by calculating the full likelihood and statistical coverage for all considered models across the parameter space. Consequently, we achieved the most stringent limits to date for ALP masses around 50 neV, with cross sections down to $g_{a\gamma} = 3 \times 10^{-12}$GeV$^{-1}$.

This paper introduces the Hierarchical Kolmogorov-Arnold Network (HKAN), a novel network architecture that offers a competitive alternative to the recently proposed Kolmogorov-Arnold Network (KAN). Unlike KAN, which relies on backpropagation, HKAN adopts a randomized learning approach, where the parameters of its basis functions are fixed, and linear aggregations are optimized using least-squares regression. HKAN utilizes a hierarchical multi-stacking framework, with each layer refining the predictions from the previous one by solving a series of linear regression problems. This non-iterative training method simplifies computation and eliminates sensitivity to local minima in the loss function. Empirical results show that HKAN delivers comparable, if not superior, accuracy and stability relative to KAN across various regression tasks, while also providing insights into variable importance. The proposed approach seamlessly integrates theoretical insights with practical applications, presenting a robust and efficient alternative for neural network modeling.

We use the results of Neshveyev and Stormer to show that for a generic shift on a C*-algebra associated to a bitstream the Voiculescu topological entropy is strictly larger that the supremum of topological entropies of its classical subsystems.

This paper reports measurements of final-state proton multiplicity, muon and proton kinematics, and their correlations in charged-current pionless neutrino interactions, measured by the T2K ND280 near detector in its plastic scintillator (C$_8$H$_8$) target. The data were taken between years 2010 and 2013, corresponding to approximately 6$\times10^{20}$ protons on target. Thanks to their exploration of the proton kinematics and of kinematic imbalances between the proton and muon kinematics, the results offer a novel probe of the nuclear-medium effects most pertinent to the (sub-)GeV neutrino-nucleus interactions that are used in accelerator-based long-baseline neutrino oscillation measurements. These results are compared to many neutrino-nucleus interaction models which all fail to describe at least part of the observed phase space. In case of events without a proton above a detection threshold in the final state, a fully consistent implementation of the local Fermi gas model with multinucleon interactions gives the best description of the data. In the case of at least one proton in the final state the spectral function model agrees well with the data, most notably when measuring the kinematic imbalance between the muon and the proton in the plane transverse to the incoming neutrino. A clear indication of existence of multinucleon interactions is observed. The effect of final-state interactions is also discussed.

Background: The $^{35}Cl(n, p)^{35}S$ reaction is of special interest in three different applications. First, in Boron Neutron Capture Therapy due to the presence of $^{35}Cl$ in brain and skin tissue. Second, it is involved in the creation of $^{36}S$, whose astrophysical origin remains unresolved. Third, in the designing of fast nuclear reactors of new generation based on molten salts. Purpose: To measure the $^{35}Cl(n, p)^{35}S$ cross-section from thermal energy to 120 keV, determine the resonance parameters in this range and Maxwellian Averaged Cross-Section (MACS). Method: We made use of the Time-of-Flight technique with microMEGAS detectors at Experimental Area 2 (EAR-2) of n\_TOF facility at CERN. The $^{10}B(n, \alpha)^{7}Li$ and $^{235}U(n, f)$ reactions were used as references. Rutherford Back-scattering Spectrometry technique was performed at Centro Nacional de Aceleradores (CNA) in Sevilla, in order to accurately determine the masses of the irradiated samples. Results: We obtain a thermal cross-section of $0.470 \pm 0.009$ barns. The $1/v$ energy dependence of the cross-section is observed up to the first resonance at 0.398 keV, the resonances up to 120 keV are analyzed and MACS calculated for $k_{B} T$ from 1 to 100 keV. Conclusions: The $^{35}Cl(n, p)^{35}S$ cross-section has been obtained over a wide energy range for the first time, with high accuracy across the aforementioned range. The thermal cross-section and first two resonances are in agreement with latest evaluation in ENDF/B-VIII.1, while lower resonance strength was found for high energy resonances. These data are used to calculate the MACS for different $k_{B} T$.

We present two protocols, with one and two two-qubit gates, to noninvasively measure two incompatible observables on a qubit. Both protocols are completed with a projective measurement. By gathering sufficiently large statistics, we have been able to violate Leggett-Garg inequality and time-order invariance. The detailed analysis of the data on 10 qubit sets from 5 devices available on IBM Quantum and one on IonQ reveals violations beyond 5 standard deviations in almost all cases. We implemented our protocols using fractional gates, newly available on the IBM Heron devices, allowing us to benchmark them in application to weak measurements. The noninvasiveness is supported by a qualitative and quantitative agreement with the model of weak disturbance. These results show another characteristic feature of quantum measurements.

A geometric picture of conformally invariant mechanics is presented. Although the standard form of the model is recovered, the careful analysis of global geometry of phase space leads to the conclusion that, in the attractive case, the singularity related to the phenomenon of "falling on the center" is spurious. This opens new possibilities concerning both the interpretation and quantization of the model. Moreover, similar modification seem to be relevant in supersymmetric and multidimensional generalization of conformal mechanics.

Line-like features in TeV $\gamma$-rays constitute a ''smoking gun'' for TeV-scale particle dark matter and new physics. Probing the Galactic Center region with ground-based Cherenkov telescopes enables the search for TeV spectral features in immediate association with a dense dark matter reservoir at a sensitivity out of reach for satellite $\gamma$-ray detectors, and direct detection and collider experiments. We report on 223 hours of observations of the Galactic Center region with the MAGIC stereoscopic telescope system reaching $\gamma$-ray energies up to 100 TeV. We improved the sensitivity to spectral lines at high energies using large-zenith-angle observations and a novel background modeling method within a maximum-likelihood analysis in the energy domain. No line-like spectral feature is found in our analysis. Therefore, we constrain the cross section for dark matter annihilation into two photons to $\langle \sigma v \rangle \lesssim 5 \times 10^{-28}\,\mathrm{cm^3\,s^{-1}}$ at 1 TeV and $\langle \sigma v \rangle \lesssim 1 \times 10^{-25}\,\mathrm{cm^3\,s^{-1}}$ at 100 TeV, achieving the best limits to date for a dark matter mass above 20 TeV and a cuspy dark matter profile at the Galactic Center. Finally, we use the derived limits for both cuspy and cored dark matter profiles to constrain supersymmetric wino models.

The discovery of rapidly variable Very High Energy (VHE; E > 100 GeV) gamma-ray emission from 4C +21.35 (PKS 1222+216) by MAGIC on 2010 June 17, triggered by the high activity detected by the Fermi Large Area Telescope (LAT) in high energy (HE; E > 100 MeV) gamma-rays, poses intriguing questions on the location of the gamma-ray emitting region in this flat spectrum radio quasar. We present multifrequency data of 4C +21.35 collected from centimeter to VHE during 2010 to investigate the properties of this source and discuss a possible emission model. The first hint of detection at VHE was observed by MAGIC on 2010 May 3, soon after a gamma-ray flare detected by Fermi-LAT that peaked on April 29. The same emission mechanism may therefore be responsible for both the HE and VHE emission during the 2010 flaring episodes. Two optical peaks were detected on 2010 April 20 and June 30, close in time but not simultaneous with the two gamma-ray peaks, while no clear connection was observed between the X-ray an gamma-ray emission. An increasing flux density was observed in radio and mm bands from the beginning of 2009, in accordance with the increasing gamma-ray activity observed by Fermi-LAT, and peaking on 2011 January 27 in the mm regime (230 GHz). We model the spectral energy distributions (SEDs) of 4C +21.35 for the two periods of the VHE detection and a quiescent state, using a one-zone model with the emission coming from a very compact region outside the broad line region. The three SEDs can be fit with a combination of synchrotron self-Compton and external Compton emission of seed photons from a dust torus, changing only the electron distribution parameters between the epochs. The fit of the optical/UV part of the spectrum for 2010 April 29 seems to favor an inner disk radius of <6 gravitational radii, as one would expect from a prograde-rotating Kerr black hole.

Within Guney-Hillery approach a number of examples of classical and quantum bounds on sum of probabilities resulting from two orbits of $S_4$ is considered. It is shown that the violation of Bell's inequalities is rather rare and gentle.

A brief motivation for studying cosmic rays at energies 10^14 < E < 10^17 eV is given. Besides astrophysical interests in identifying and understanding their sources, there are also particle physics aspects related to their transport properties in the galaxy or to their detection via extensive air showers. The KASCADE air shower experiment taking data at Forschungszentrum Karlsruhe (Germany) provides important information to both of these topics of particle-astrophysics research. A target of particular interest is the so-called 'knee' in the cosmic ray energy spectrum at E_k = 4 x 10^15 eV. Recent results adding knowledge to an understanding its origin will be presented as well as results on tests of high-energy hadronic interaction models required for air shower simulations.

The flat spectrum radio quasar PKS 1510-089 is a monitored target in many wavelength bands due to its high variability. It was detected as a very-high-energy (VHE) $\gamma$-ray emitter with H.E.S.S. in 2009, and has since been a regular target of VHE observations by the imaging Cherenkov observatories H.E.S.S. and MAGIC. In this paper, we summarize the current state of results focusing on the monitoring effort with H.E.S.S. and the discovery of a particularly strong VHE flare in 2016 with H.E.S.S. and MAGIC. While the source has now been established as a weak, but regular emitter at VHE, no correlation with other energy bands has been established. This is underlined by the 2016 VHE flare, where the detected optical and high-energy $\gamma$-ray counterparts evolve differently than the VHE flux.

The recently discovered conserved quantity associated with Kepler rescaling is generalised by an extension of Noether's theorem which involves the classical action integral as an additional term. For a free particle the familiar Schroedinger dilations are recovered. A general pattern arises for homogeneous potentials. The associated conserved quantity allows us to derive the virial theorem. The relation to the Bargmann framework is explained and illustrated by exact plane gravitational waves.

In the first part of the paper, we prove a fractional fundamental (du Bois-Reymond) lemma and a fractional variant of the integration by parts formula. The proof of the second result is based on an integral representation of functions possessing Riemann-Liouville fractional derivatives, derived in this paper too. In the second part of the paper, we use the previous results to give necessary optimality conditions of Euler-Lagrange type (with boundary conditions) for fractional Bolza functionals and to prove an existence result for solutions of linear fractional boundary value problems. In the last case we use a Hilbert structure and the Stampacchia theorem.