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In the non-metric gravity proposed by K. Krasnov, this is a theory in which the scalar constraint of the Ashtekar's formalism is modified in such way that the cosmological constant is replaced by a cosmological function that depends of the canonical variables $A_{a}{}^{i}$ and $E_{i}{}^{a}$, the General Relativity (GR) is the particular case when the cosmological function is a constant. Some years ago inspired by this theory Rosas-Rodr\'iguez proposed two cosmological functions, one for the Ashtekar's formalism and the other for the ADM formalism. In this paper we show that this cosmological functions are related thought the three-dimensional Ricci scalar.

In this paper we study germs of holomorphic foliations, at the origin of the complex plane, tangent to Pfaffian hypersurfaces - integral hypersurfaces of real analytic 1-forms - satisfying the Rolle-Khovanskii condition. This hypothesis leads us to conclude that such a foliation is defined by a closed meromorphic 1-form, also allowing the classification of the simple models in its reduction of singularities., Comment: 23 pages

Higher-order interactions underlie complex phenomena in systems such as biological and artificial neural networks, but their study is challenging due to the lack of tractable standard models. By leveraging the maximum entropy principle in curved statistical manifolds, here we introduce curved neural networks as a class of prototypical models for studying higher-order phenomena. Through exact mean-field descriptions, we show that these curved neural networks implement a self-regulating annealing process that can accelerate memory retrieval, leading to explosive order-disorder phase transitions with multi-stability and hysteresis effects. Moreover, by analytically exploring their memory capacity using the replica trick near ferromagnetic and spin-glass phase boundaries, we demonstrate that these networks enhance memory capacity over the classical associative-memory networks. Overall, the proposed framework provides parsimonious models amenable to analytical study, revealing novel higher-order phenomena in complex network systems.

We investigate entanglement in two-qubit systems using a geometric representation based on the minimum of essential parameters. The states are X-shaped and host pairs of identical populations while reducing the number of coherences involved. A geometric L-measure of entanglement is introduced as the distance between the points that represent entangled states and the closest point that defines separable states. Our results give a geometric meaning to the Hill-Wootters concurrence C since L coincides with C. Furthermore, unlike C, the measure L distinguishes the rank of states with maximum entanglement. We construct a time-dependent two-qubit state, traced out over the complementary components of a pure tetra-partite system, and find that its one-qubit states share the same entropy. The entanglement measure results bounded from above by the envelope of the minima of such entropy., Comment: 22 pages, 11 figures

We explore the interaction between a three-level atom and a single-mode quantized cavity, known as the three-level ladder-type Jaynes-Cummings model. By employing the exact solution of the Schr\"odinger equation, we investigate how the initial conditions of the atom influence the occupation probabilities of the atomic energy levels, average photon number, and the nonclassicality of light, assessed through the Mandel $\mathcal{Q} (t)$ parameter and the Wigner function. Our findings are rigorously validated through comprehensive numerical simulations, ensuring robust and consistent outcomes.

Nonlinear optical materials of atomic thickness--such as non-centrosymmetric 2H transition metal dichalcogenide monolayers--have a second order nonlinear susceptibility ($\chi^{(2)}$) whose intensity can be tuned by strain. However, whether $\chi^{(2)}$ is enhanced or reduced by tensile strain is a subject of conflicting reports. Here, we grow high-quality MoSe$_2$ monolayers under controlled biaxial strain created by two different substrates, and study their linear and non-linear optical responses with a combination of experimental and theoretical approaches. A 15-fold overall enhancement in second harmonic generation (SHG) intensity is observed on MoSe$_2$ monolayers grown on SiO$_2$ when compared to its value when on a Si$_3$N$_4$ substrate. A seven-fold enhancement was ascertained to substrate interference, and a factor of two to the enhancement of $\chi^{(2)}$ arising from biaxial strain: substrate interference and strain are independent handles to engineer the SHG strength of non-centrosymmetric 2D materials.

We present the first combinatorial proof of the Graham-Pollak Formula for the determinant of the distance matrix of a tree, via sign-reversing involutions and the Lindstr\"om-Gessel-Viennot Lemma. Our approach provides a cohesive and unified framework for the understanding of the existing generalizations and $q$-analogues of the Graham-Pollak Formula, and facilitates the derivation of a natural simultaneous generalizations for them.

In a recent study [1], we demonstrated a multi-heterodyne differential absorption lidar (DIAL) for greenhouse gas monitoring utilizing solid targets. The multi-frequency absorption measurement was achieved using electro-optic dual-comb spectroscopy (DCS) with a minimal number of comb teeth to maximize the optical power per tooth. In this work, we examine the lidar's working principle and architecture. Additionally, we present measurements of atmospheric CO2 at 1572 nm over a 1.4 km optical path conducted in summer 2023. Furthermore, we show that, due to the high power per comb tooth, multi-frequency Doppler wind speed measurements can be performed using the DCS signal from aerosol backscattering. This enables simultaneous radial wind speed and path-average gas concentration measurements, offering promising prospects for novel concepts of tunable multi-frequency lidar systems capable of simultaneously monitoring wind speed and gas concentrations. [1] W. Pati\~no Rosas and N. C\'ezard, "Greenhouse gas monitoring using an IPDA lidar based on a dual-comb spectrometer," Opt. Express 32, 13614-13627 (2024)., Comment: Conference paper for the 22nd Coherent Laser Radar Conference (2024)

We study the field of rational first integrals of distributions. We show that for a distribution on 3 dimensional manifolds there exists a tangent vector field with the same field of first integrals. We also show a similar result for integrable distributions in any dimension.

In the contemporary landscape of computer architecture, the demand for efficient parallel programming persists, needing robust optimization techniques. Traditional optimizing compilers have historically been pivotal in this endeavor, adapting to the evolving complexities of modern software systems. The emergence of Large Language Models (LLMs) raises intriguing questions about the potential for AI-driven approaches to revolutionize code optimization methodologies. This paper presents a comparative analysis between two state-of-the-art Large Language Models, GPT-4.0 and CodeLlama-70B, and traditional optimizing compilers, assessing their respective abilities and limitations in optimizing code for maximum efficiency. Additionally, we introduce a benchmark suite of challenging optimization patterns and an automatic mechanism for evaluating performance and correctness of the code generated by such tools. We used two different prompting methodologies to assess the performance of the LLMs -- Chain of Thought (CoT) and Instruction Prompting (IP). We then compared these results with three traditional optimizing compilers, CETUS, PLUTO and ROSE, across a range of real-world use cases. A key finding is that while LLMs have the potential to outperform current optimizing compilers, they often generate incorrect code on large code sizes, calling for automated verification methods. Our extensive evaluation across 3 different benchmarks suites shows CodeLlama-70B as the superior optimizer among the two LLMs, capable of achieving speedups of up to 2.1x. Additionally, CETUS is the best among the optimizing compilers, achieving a maximum speedup of 1.9x. We also found no significant difference between the two prompting methods: Chain of Thought (Cot) and Instructing prompting (IP)., Comment: 11 pages, 10 figures, under review for The International Symposium on Code Generation and Optimization (CGO) 2025, Las Vegas

Time-rescaling (TR) has been recently proposed as a method to engineer fast processes, also known as shortcuts to adiabaticity (STA), which enables the coherent control of quantum systems beyond the adiabatic regime [B. L. Bernardo, Phys. Rev. Res. 2, 013133 (2020)]. The method provides the Hamiltonians that generate the fast processes without requiring information about the instantaneous eigenstates of a reference protocol, whereas experimental implementations dismiss additional coupling fields when compared with adiabatic protocols. Here, we revisit the technique and show that the obtained fast dynamics are transitionless, similar to the ones designed via the famous counterdiabatic (CD) approach. We also show that the time evolution of the STA found via TR relates to that of the reference adiabatic protocol by a simple reparametrization of time. To illustrate our findings, we studied the problem of speeding up the stimulated Raman adiabatic passage (STIRAP) and found out that TR revealed quantum dynamics more robust to parameter variations than those provided by the CD technique. Our results shed new light on the application of TR in the control of larger quantum systems., Comment: 9 pages, 6 figures

We present a comprehensive multi-messenger study of NGC 1068, the prototype Seyfert II galaxy recently associated with high-energy IceCube neutrinos. Various aspects of the source, including its nuclear activity, jet, outflow, and starburst region, are analyzed in detail using a multi-wavelength approach and relevant luminosities are derived. We then explore its gamma-ray and neutrino emissions and investigate potential mechanisms underlying these phenomena and their relations with the different astrophysical components to try to understand which one is responsible for the IceCube neutrinos. By first using simple order-of-magnitude arguments and then applying specific theoretical models, we infer that only the region close to the accretion disc around the supermassive black hole has both the right density of X-ray photons needed to provide the targets for protons to sustain neutrino production and of optical/infrared photons required to absorb the associated but unobserved gamma rays. We conclude by highlighting ongoing efforts to constrain a possible broad connection between neutrinos and active galactic nuclei, as well as future synergies between astronomical and neutrino facilities., Comment: 18 pages, 4 figures, review paper accepted for publication in Nature Astronomy; authors' version before editorial review

We introduce a purely geometric formulation for two different measures addressed to quantify the entanglement between different parts of a tripartite qubit system. Our approach considers the entanglement-polytope defined by the smallest eigenvalues of the reduced density matrices of the qubit-components. The measures identify global and genuine entanglement, and are respectively associated with the projection and rejection of a given point of the polytope on the corresponding biseparable segments. Solving the so called `inverse problem', we also discuss a way to force the system to behave in a particular form, which opens the possibility of controlling and manipulating entanglement for practical purposes., Comment: 22 pages, 11 figures, 1 table

Systems of interest for theoretical or experimental work often exhibit high-order interactions, corresponding to statistical interdependencies in groups of variables that cannot be reduced to dependencies in subsets of them. While still under active development, the framework of partial information decomposition (PID) has emerged as the dominant approach to conceptualise and calculate high-order interdependencies. PID approaches can be grouped in two types: directed approaches that divide variables into sources and targets, and undirected approaches that treat all variables equally. Directed and undirected approaches are usually employed to investigate different scenarios, and hence little is known about how these two types of approaches may relate to each other, or if their corresponding quantities are linked in some way. In this paper we investigate the relationship between the redundancy-synergy index (RSI) and the O-information, which are practical metrics of directed and undirected high-order interdependencies, respectively. Our results reveal tight links between these two quantities, and provide interpretations of them in terms of likelihood ratios in a hypothesis testing setting, as well as in terms of projections in information geometry., Comment: 6 pages, 1 figure

In this paper, we study the problem of multi-reward reinforcement learning to jointly optimize for multiple text qualities for natural language generation. We focus on the task of counselor reflection generation, where we optimize the generators to simultaneously improve the fluency, coherence, and reflection quality of generated counselor responses. We introduce two novel bandit methods, DynaOpt and C-DynaOpt, which rely on the broad strategy of combining rewards into a single value and optimizing them simultaneously. Specifically, we employ non-contextual and contextual multi-arm bandits to dynamically adjust multiple reward weights during training. Through automatic and manual evaluations, we show that our proposed techniques, DynaOpt and C-DynaOpt, outperform existing naive and bandit baselines, showcasing their potential for enhancing language models.

The variations in metallicity and spatial patterns within star-forming regions of galaxies result from diverse physical processes unfolding throughout their evolutionary history, with a particular emphasis in recent events. Analysing MaNGA and \textsc{eagle} galaxies, we discovered an additional dependence of the mass-metallicity relation (MZR) on metallicity gradients ($\nabla_{{\rm (O/H)}}$). Two regimes emerged for low and high stellar mass galaxies, distinctly separated at approximately ${\rm M_{\star}} >10^{9.75}$. Low-mass galaxies with strong positive $\nabla_{{\rm (O/H)}}$ appear less enriched than the MZR median, while those with strong negative gradients are consistently more enriched in both simulated and observed samples. Interestingly, low-mass galaxies with strong negative $\nabla_{{\rm (O/H)}}$ exhibit high star-forming activity, regardless of stellar surface density or $\nabla_{{\rm (O/H)}}$. In contrast, a discrepancy arises for massive galaxies between MaNGA and \textsc{eagle} datasets. The latter exhibit a notable anticorrelation between specific star formation rate and stellar surface density, independent of $\nabla_{{\rm (O/H)}}$, while MaNGA galaxies show this trend mainly for strong positive $\nabla_{{\rm (O/H)}}$. Further investigation indicates that galaxies with strong negative gradients tend to host smaller central black holes in observed datasets, a trend not replicated in simulations. These findings suggest disparities in metallicity recycling and mixing history between observations and simulations, particularly in massive galaxies with varying metallicity gradients. These distinctions could contribute to a more comprehensive understanding of the underlying physics.

This contribution presents the recent research developments within the Cosmic Ray Extremely Distributed Observatory (CREDO) in the search for resolution of various scientific puzzles, ranging from fundamental physical questions to applications like the determination of earthquake precursors. The state-of-the art theoretical, numerical and computational aspects of these phenomena are addressed, as well as recent experimental developments for detection., Comment: 9 pages, 7 figures. Based on the contribution to the XVIII Mexican Workshop on Particles and Fields in Puebla, Mexico, November 2022. M\'exico

In the present article we define an integral analogue of Chow-K\"unneth decomposition for \'etale motives. By using families of conservative functors we are able to establish a decomposition of the \'etale motive of commutative group schemes over a base and we relate to an integral \'etale Chow-K\"unneth decomposition of abelian varieties. For a projective variety $X$ of dimension $d$ over an algebraically closed field, we construct integral sub-motives $h^1_{\text{\'et}}(X)$ and $h^{2d-1}_{\text{\'et}}(X)$ of the motive $h_{\text{\'et}}(X)$.

Optical metasurfaces can manipulate electromagnetic waves in unprecedented ways at ultra-thin engineered interfaces. Specifically, in the mid-infrared (mid-IR) region, metasurfaces have enabled numerous biochemical sensing, spectroscopy, and vibrational strong coupling (VSC) applications via enhanced light-matter interactions in resonant cavities. However, mid-IR metasurfaces are usually fabricated on solid substrates, which degrade resonance quality factors (Q) and hinder efficient sample access to the near-field electromagnetic hotspots. Besides, typical IR-transparent substrate materials, such as CaF2, NaCl, KBr, and ZnSe, are usually either water-soluble, expensive, or not compatible with low-cost mass manufacturing processes. To address these substrate-related technological limitations, we present novel substrate-less mid-IR metasurfaces with strong light-trapping capabilities in accessible air voids through the patterning of free-standing Si-membranes. We employed the Brillouin zone folding technique to excite high-Q quasi-bound states in the continuum (q-BIC) resonances. Leveraging the strong field localizations in accessible air cavities (|E/E0|>200), we demonstrated VSC between molecules and the q-BIC modes. Our new approach of fabricating mid-IR metasurfaces into semiconductor membranes enables low-cost manufacturing of MIR photonic devices and provides exciting opportunities for quantum-coherent light-matter interactions, biochemical sensing, and polaritonic chemistry.

Understanding the functional architecture of complex systems is crucial to illuminate their inner workings and enable effective methods for their prediction and control. Recent advances have introduced tools to characterise emergent macroscopic levels; however, while these approaches are successful in identifying when emergence takes place, they are limited in the extent they can determine how it does. Here we address this limitation by developing a computational approach to emergence, which characterises macroscopic processes in terms of their computational capabilities. Concretely, we articulate a view on emergence based on how software works, which is rooted on a mathematical formalism that articulates how macroscopic processes can express self-contained informational, interventional, and computational properties. This framework establishes a hierarchy of nested self-contained processes that determines what computations take place at what level, which in turn delineates the functional architecture of a complex system. This approach is illustrated on paradigmatic models from the statistical physics and computational neuroscience literature, which are shown to exhibit macroscopic processes that are akin to software in human-engineered systems. Overall, this framework enables a deeper understanding of the multi-level structure of complex systems, revealing specific ways in which they can be efficiently simulated, predicted, and controlled., Comment: 33 pages, 13 figures

Entanglement between distant quantum systems is a critical resource for implementing quantum communication. This property is affected by external agents and can be restored by employing efficient entanglement purification protocols. In this work, we propose an entanglement purification protocol based on two entangling two-qubit operations that replace the usual controlled-NOT (CNOT) gate. These operations arise from a generalized quantum measurement and can be understood as measurement operators in a positive operator-valued measure (POVM). Furthermore, two variants of the core protocol are introduced and shown to be more practical in certain scenarios. The performance of the protocols is studied in terms of the overall success probability of reaching a Bell state and the number of purifiable states. Based on rank-two states, we can obtain analytical expressions for the success probability that we extend and refine using numerical calculations to the case of maximally entangled states (MEMS). We also consider more general rank-three states to show that our procedure is in general more convenient compared to purification protocols based on Bell diagonal states. Finally, we test the protocols using initial random states. In all cases, we find a larger performance and larger amount of purifiable states using our schemes compared to the CNOT-based purification protocol., Comment: 14 pages, 5 figures

The Planetary Instrument for X-ray Lithochemistry (PIXL) is a rasterable focused-beam X-ray fluorescence (XRF) spectrometer mounted on the arm of National Aeronautics and Space Administration's (NASA) Mars 2020 Perseverance rover. To ensure that PIXL would be capable of performing accurate in-flight compositional analysis of martian targets, in situ, an elemental calibration was performed pre-flight on the PIXL flight instrument in a simulated martian environment. The details of this calibration, and implications for measuring unknown materials on Mars are the subjects of this paper. The major goals of this calibration were both to align the spectrometer to perform accurate elemental analysis and, to derive a matrix of uncertainties that are applied to XRF measurements of all elements in unknown materials. A small set of pure element and pure compound targets and geologically relevant reference materials were measured with the flight hardware in a simulated martian environment. Elemental calibration and quantifications were carried out using PIXL's XRF quantification software (PIQUANT). Uncertainties generated were implemented into the PIQUANT software version employed by the PIXL's data visualization software (PIXLISE). We outline in this work, a list of factors that impact micro-XRF accuracy, the methodology and steps involved in the calibration, details on the fabrication of the uncertainty matrix, instructions on the use and interpretations of the uncertainties applied to unknowns and an assessment on the limitations and areas open to future improvement as part of subsequent calibration efforts.

In the rapidly evolving field of bioimaging, the integration and orchestration of Findable, Accessible, Interoperable, and Reusable (FAIR) image analysis workflows remains a challenge. We introduce BIOMERO, a bridge connecting OMERO, a renowned bioimaging data management platform, FAIR workflows and high-performance computing (HPC) environments. BIOMERO, featuring our opensource Python library "OMERO Slurm Client", facilitates seamless execution of FAIR workflows, particularly for large datasets from High Content or High Throughput Screening. BIOMERO empowers researchers by eliminating the need for specialized knowledge, enabling scalable image processing directly from OMERO. BIOMERO notably supports the sharing and utilization of FAIR workflows between OMERO, Cytomine/BIAFLOWS, and other bioimaging communities. BIOMERO will promote the widespread adoption of FAIR workflows, emphasizing reusability, across the realm of bioimaging research. Its user-friendly interface will empower users, including those without technical expertise, to seamlessly apply these workflows to their datasets, democratizing the utilization of AI by the broader research community., Comment: 20 pages, 3 figures, 4 pages supplemental information; submitted to Cell Patterns; for software, see https://github.com/NL-BioImaging/biomero

We prove that, for each fixed genus, the portion of semigroups of that genus belonging to infinite chains in the semigroup tree approaches 0 as the genus grows to infinite. This means that most numerical semigroups have a finite number of descendants in the semigroup tree. This problem has been open since 2009.

We investigate the influence of the environment on the evolution of barred and unbarred disc galaxies with a mass $>10^{10}\Msun$ from z=1 down to z=0, employing the TNG50 magnetic-hydrodynamical simulation. We find that 49% of z=1 disc galaxies undergoes a morphological transformation, transitioning into either a lenticular or spheroidal, while the other 51% retains the massive disc. The morphological alteration is mostly influenced by the environment. Lenticular and spheroidal galaxies tend to exist in denser environments and have more frequent mergers compared to disc galaxies. We find that over half of the barred galaxies (60.2%) retain the bar structure and have experienced fewer mergers compared to those galaxies that lose their bars (5.6%). These latter ones start with weaker and shorter bars at z=1 influenced by tidal interactions and are frequently observed in more populated areas. Additionally, our study reveals that less than 20% of unbarred galaxies will never develop a bar and exhibit the quietest merger history. Unbarred galaxies that experience bar formation after z=1 exhibit more frequent instances of merging events. Furthermore, tidal interactions with a close companion may account for bar formation in at least one-third of the cases. Our findings highlight that stable bars are prevalent in disc galaxies. Bar evolution may nonetheless be affected by the environment. Interactions with nearby companions or tidal forces caused by mergers have the capacity to disrupt the disc. This perturbance may materialise as the dissolution of the bar, the formation of a bar, or, in its most severe form, the complete destruction of the disc, resulting in morphological transformation. Bars that are weak and short at z=1 and undergo major or minor mergers may eventually dissolve, whereas unbarred galaxies that enter crowded environments or experience a merger may develop a bar., Comment: 20 pages, 18 Figures, accepted for publication in A&A with language corrections and updates in some Figures

From Nov. 2019 to May 2020, the red supergiant star Betelgeuse experienced an unprecedented drop of brightness in the visible domain called the great dimming event. Large atmospheric dust clouds and large photospheric convective features are suspected to be responsible for it. To better understand the dimming event, we used mid-infrared long-baseline spectro-interferometric measurements of Betelgeuse taken with the VLTI/MATISSE instrument before (Dec. 2018), during (Feb. 2020), and after (Dec. 2020) the GDE. We present data in the 3.98 to 4.15\,$\mu$m range to cover SiO spectral features molecules as well as adjacent continuum. We have employed geometrical models, image reconstruction, as well as radiative transfer models to monitor the spatial distribution of SiO over the stellar surface. We find a strongly in-homogeneous spatial distribution of SiO that appears to be looking very different between our observing epochs, indicative of a vigorous activity in the stellar atmosphere. The contrast of our images is small in the pseudo-continuum for all epochs, implying that our MATISSE observations support both cold spot and dust cloud model.

Context. Rocky planets form by the concentration of solid particles in the inner few au regions of planet-forming disks. Their chemical composition reflects the materials in the disk available in the solid phase at the time the planets were forming. Aims. We aim to constrain the structure and dust composition of the inner disk of the young star HD 144432, using an extensive set of infrared interferometric data taken by the Very Large Telescope Interferometer (VLTI), combining PIONIER, GRAVITY, and MATISSE observations. Methods. We introduced a new physical disk model, TGMdust, to image the interferometric data, and to fit the disk structure and dust composition. We also performed equilibrium condensation calculations with GGchem. Results. Our best-fit model has three disk zones with ring-like structures at 0.15, 1.3, and 4.1 au. Assuming that the dark regions in the disk at ~0.9 au and at ~3 au are gaps opened by planets, we estimate the masses of the putative gap-opening planets to be around a Jupiter mass. We find evidence for an optically thin emission ($\tau<0.4$) from the inner two disk zones ($r<4$ au) at $\lambda>3\ \mu$m. Our silicate compositional fits confirm radial mineralogy gradients. To identify the dust component responsible for the infrared continuum emission, we explore two cases for the dust composition, one with a silicate+iron mixture and the other with a silicate+carbon one. We find that the iron-rich model provides a better fit to the spectral energy distribution. Conclusions. We propose that in the warm inner regions ($r<5$ au) of typical planet-forming disks, most if not all carbon is in the gas phase, while iron and iron sulfide grains are major constituents of the solid mixture along with forsterite and enstatite. Our analysis demonstrates the need for detailed studies of the dust in inner disks with new mid-infrared instruments such as MATISSE and JWST/MIRI., Comment: 29 pages, 24 figures

Resonant metasurfaces present extraordinary subwavelength light trapping capabilities, which have been critical to the development of high-performance biochemical sensors and surface-enhanced spectroscopy techniques. To date, metasurface-enhanced light-matter interactions in the mid-infrared region have been primarily leveraged in the weak coupling regime. Nevertheless, the strong coupling regime, characterized by the hybrid light-matter states - polaritons, has not been fully explored. Specifically, metasurfaces made from low-loss dielectric resonators underpinned by the bound states in the continuum (BIC) are well suited for quantum coherent energy exchange between their high-Q open cavities and molecules' resonant transitions. This paper delves into the light-matter interactions in metasurface cavities generated by quasi-BIC resonances at mid-infrared frequencies. We thoroughly investigate the material and cavity parameters that define the boundaries between weak and strong coupling. Our findings underscore the transformative potential of dielectric metasurfaces to harness vibrational strong coupling for applications such as cavity polaritonic chemistry, modulation of chemical reactivity with light, and highly sensitive molecular spectroscopy.

This work concerns the analysis of electromagnetic dispersive media modelled by generalized Lorentz models. More precisely, this paper is the second of two articles dedicated to the long time behaviour of solutions of Maxwell's equations in dissipative Lorentz media, via the long time decay rate of the electromagnetic energy for the corresponding Cauchy problem. In opposition to the frequency dependent Lyapunov functions approach used in [Cassier, Joly, Rosas Mart\'inez, Z. Angew. Math. Phys. 74 (2023), 115], we develop a method based on the spectral analysis of the underlying non-self-adjoint operator of the model. Although more involved, this approach is closer to physics, as it uses the dispersion relation of the model, and has the advantage to provide more precise and more optimal results, leading to distinguish the notion of weak and strong dissipation., Comment: 67 pages, 4 figures

The Very Large Telescope Interferometer (VLTI) has been providing breakthrough images of the dust in the central parsecs of Active Galactic Nuclei (AGN), a key component of the AGN unification scheme and AGN host galaxy interaction. In single IR bands, the images can have multiple interpretations some of which could challenge the unification scheme. This is the case for the archetypal type 2 AGN of NGC1068. The ambiguity is reduced by multi-band temperature maps which are hindered by uncertainty in intra-band alignment. We create a chromatic model capable of simultaneously explaining the VLTI GRAVITY+MATISSE 2$\mu$m-13$\mu$m observations of the AGN in NGC1068. We use a simple disk and wind geometry populated with spherical black body emitters and dust obscuration to create a versatile multi-wavelength model for IR interferometric data of dusty objects. This simple geometry is capable of reproducing the K-N-band VLTI data, explains the complex single band images, and solves the alignment between bands. We find that the resulting geometry is consistent with previous studies. Compared to molecular gas emission, our model wind position angle (PA) of $22^3_2{\deg}$ is close to the mas scale outflowing CO(6-5) PA of ~33{\deg} seen with the ALMA. The equivalent 90{\deg} offset model disk PA is also consistent with the CO(6-5) disk axis of 112{\deg} as well as the mas scale disk axis from CO(2-1), CO(3-2), and HCO$^+$(4-3) of 115$\pm$5{\deg}. Furthermore, the resulting model visually resembles the equivalent achromatic image reconstructions. We conclude that the IR emitting structure surrounding the AGN can indeed be explained by the clumpy disk+wind iteration of the AGN unification scheme. Within the scheme, we find it is best explained as a type 2 and the obscuring dust chemistry is consistent with a mix of olivine silicates and 16$\pm$1% amorphous carbon., Comment: 15 pages, 19 appendix pages, 23 figures, and 2 tables. Accepted for publication in A&A

Nonrelativistic (NR) string theory was discovered as a framework that underlies and unifies the various noncommutative open string (NCOS) theories, which were originally envisioned as surprising exceptions to the maxim that all string theories are gravitational in nature. In that view, the fact that NCOS has a gravitational dual was believed to be directly analogous to the AdS/CFT correspondence. When NCOS theories were understood to be simply the particular classes of states of the underlying NR theory that include longitudinal D-branes, it was suggested that the duality between NCOS and the corresponding gravitational theory is not an instance of gauge/gravity-type duality, but of open-string/closed-string duality between D-branes and black branes. The present paper provides direct evidence in support of this perspective, by starting from a stack of D-branes in NR string theory and deriving the long-distance profile of the curved geometry in the corresponding black brane., Comment: 25+1 pages; v2: typos corrected, references added

We present an analysis of nine bright spectroscopic binaries (HD 1585, HD 6613, HD 12390, HD 39923, HD 55201, HD 147430, HD 195543, HD 202699, HD 221643), which have orbital periods of P > 500 days. These well-separated binaries are the last stars of our sample that we observed with the TIGRE telescope obtaining intermediate-resolution spectra of R = 20,000. We applied the same method as described in our previous publication of this series. For the analysis of the radial velocity curves, we used the toolkit RadVel, which allowed us to determine all orbital parameters. Recently published orbital solutions of some systems from Gaia DR3 agree with our results. However, our solutions have much smaller uncertainties. We determined the basic stellar parameters of the primary stars with our automatic script using iSpec. The parameter determination allowed us to place all nine stars in the Hertzsprung-Russell diagram. We found that all stars have already evolved to the giant phase. A comparison with stellar evolution tracks of the Eggleton code was applied to determine the stellar masses and ages. As a result of our analysis, we were able to estimate the masses of the secondary stars and the orbital inclinations of the binary systems., Comment: Accepted for publication in AN, 13 pages