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Let $\mathcal{C}\subseteq \mathbb{N}^p$ be an integer cone. A $\mathcal{C}$-semigroup $S\subseteq \mathcal{C}$ is an affine semigroup such that the set $\mathcal{C}\setminus S$ is finite. Such $\mathcal{C}$-semigroups are central to our study. We develop new algorithms for computing $\mathcal{C}$-semigroups with specified invariants, including genus, Frobenius element, and their combinations, among other invariants. To achieve this, we introduce a new class of $\mathcal{C}$-semigroups, termed $\mathcal{B}$-semigroups. By fixing the degree lexicographic order, we also research the embedding dimension for both ordinary and mult-embedded $\mathbb{N}^2$-semigroups. These results are applied to test some generalizations of Wilf's conjecture.

This work provides a complete rheological characterization of molybdenum disulfide (MoS2) inks in the presence of electric fields. Several concentrations of MoS2 are studied and dispersed in a viscoelastic fluid. The lubrication effects are present in the ink when the MoS2 concentration is higher than 0.10% w/w. The dielectric properties show the impossibility of a positive electrorheological effect for all MoS2-inks studied. The formation of vortices and electromigration of MoS2 particles occur under the influence of an external electric field. These two phenomena affect the rheological behavior of MoS2-inks under shear flow condition. Relatively to the extensional rheology experiments, the particle migration and the vortex formation promote anisotropy on the rheological properties of the inks which affects the relaxation time, the formation of beads-on-a-string and the uniaxial elongational flow condition is no longer valid. When the electric field strength is 1.5 kV/mm, the formation of Taylor's cone is observed and independent of MoS2 concentration.

Quasicrystals are unique materials characterized by long-range order without periodicity. They are observed in systems such as metallic alloys, soft matter, and particle simulations. Unlike periodic crystals, which are invariant under real-space symmetry operations, quasicrystals possess symmetry described by a space group in reciprocal space. In this study, we report the self-assembly of a six-fold chiral quasicrystal using molecular dynamics simulations of a two-dimensional particle system. These particles interact via the Lennard-Jones-Gauss pair potential and are subjected to a periodic substrate potential. Our findings confirm the presence of chiral symmetry through diffraction patterns and order parameters, revealing unique local motifs in both real and reciprocal space. We demonstrate that the quasicrystal's properties, including the tiling structure and symmetry and the extent of diffuse scattering, are influenced by substrate potential depth and temperature. Our results provide insights into the mechanisms of chiral quasicrystal formation and the role of external fields in tailoring quasicrystal structures.

The main aim of this work is to introduce and justify the study of semi-covarities. A {\it semi-covariety} is a non-empty family $\mathcal{F}$ of numerical semigroups such that it is closed under finite intersections, has a minimum, $\min(\mathcal{F}),$ and if $S\in \mathcal{F}$ being $S\neq \min(\mathcal{F})$, then there is $x\in S$ such that $S\backslash \{x\}\in \mathcal{F}$. As examples, we will study the semi-covariety formed by all the numerical semigroups containing a fixed numerical semigroup, and the semi-covariety composed by all the numerical semigroups of coated odd elements and fixed Frobenius number., Comment: 12 pages. arXiv admin note: text overlap with arXiv:2302.09121

A numerical semigroup $S$ is coated with odd elements (Coe-semigroup), if $\left\{x-1, x+1\right\}\subseteq S$ for all odd element $x$ in $S$. In this note, we will study this kind of numerical semigroups. In particular, we are interested in the study of the Frobenius number, gender and embedding dimension of a numerical semigroup of this type.

In this study, we investigate the problem of comparing gene trees reconciled with the same species tree using a novel semi-metric, called the Path-Label Reconciliation (PLR) dissimilarity measure. This approach not only quantifies differences in the topology of reconciled gene trees, but also considers discrepancies in predicted ancestral gene-species maps and speciation/duplication events, offering a refinement of existing metrics such as Robinson-Foulds (RF) and their labeled extensions LRF and ELRF. A tunable parameter {\alpha} also allows users to adjust the balance between its species map and event labeling components. We show that PLR can be computed in linear time and that it is a semi-metric. We also discuss the diameters of reconciled gene tree measures, which are important in practice for normalization, and provide initial bounds on PLR, LRF, and ELRF. To validate PLR, we simulate reconciliations and perform comparisons with LRF and ELRF. The results show that PLR provides a more evenly distributed range of distances, making it less susceptible to overestimating differences in the presence of small topological changes, while at the same time being computationally efficient. Our findings suggest that the theoretical diameter is rarely reached in practice. The PLR measure advances phylogenetic reconciliation by combining theoretical rigor with practical applicability. Future research will refine its mathematical properties, explore its performance on different tree types, and integrate it with existing bioinformatics tools for large-scale evolutionary analyses. The open source code is available at: https://pypi.org/project/parle/., Comment: Full version of WABI 2024 conference paper

In this work, we examined the impact of disorder in a ferromagnetic skyrmion lattice by introducing random-bond disorder based on two different models for both exchange and Dzyaloshinskii-Moriya interactions: Model I, where both interactions present the same disorder distribution and thus the same local distortion, and Model II, where both interactions have different disorder distributions. Through extensive Monte Carlo simulations, we explored the effect of bond disorder on the emergent phases induced by an external magnetic field at different temperatures, varying the disorder amplitude across a range from weak (10%) to strong (200%) regimes. Our study shows that for both models, moderate disorder at low magnetic fields breaks the helical order and induces a topologically non-trivial bimeron phase. We also found that the skyrmion lattice phase loses its periodicity, but surprisingly, the resulting phases retain topological characteristics up to high disorder amplitudes. Moreover, a significant difference between both disorder models is found at large magnetic fields: while in the first model, the high-field skyrmion phase is suppressed by disorder, in the second model, this phase is enhanced and expanded in temperature and magnetic field. Furthermore, for the second model, intermediate values of disorder induce a diluted skyrmion phase and chiral textures emerging from the ferromagnetic phase at low temperatures. Our results are relevant for layered magnets and provide valuable insights into the intricate behavior of skyrmion systems under varying disorder conditions., Comment: 11 pages, 8 figures

The extraplanar diffuse ionised gas is a key component for understanding the feedback processes that connect galactic discs and their halos. In this paper, we present the second study of the BETIS project, which aims to explore the ionisation mechanisms of the eDIG. We use a sample of eight edge-on galaxies observed with MUSE and apply the methodology developed in the first paper of the BETIS project. We found that the vertical and radial profiles of the [NII]/Ha, [SII]/Ha, [OIII]/Hb, and [OI]/Ha ratios depict a complex ionisation structure within galactic halos, influenced by the spatial distribution of HII regions across the galactic plane as observed from our line of sigh, with photon leakage from OB associations constituting the main ionisation source. Our analysis excludes low-mass, hot, and evolved stars as viable candidates for secondary ionisation sources to elucidate the unusual behaviour of the line ratios at greater distances from the galactic midplane. In contrast, we ascertain that shocks induced in the interstellar medium by star formation related feedback mechanisms represent a promising secondary ionisation source of the eDIG. We present a suite of models integrating ionisation mechanisms arising from fast shocks and photoionisation associated with star formation. When applied to the classical BPT diagrams, these models reveal that the ionisation budget of the eDIG ranges from 20% to 50% across our sample, with local variations of up to 20% within individual galaxy halos. This correlates with the presence of filaments and other structural components observed within galaxy halos. The presence of shocks is additionally supported by the observation of high-density, high [OI]/Ha ratios, characteristic of shock-compressed ionised gas, likely induced by feedback from regions of intense SF within the disk. These results are consistent across all galaxies analysed in this sample., Comment: 35 pages, 2 tables, 50 figures, A&A accepted

We determine the temperature fluctuations associated with the Higgs boson $p_T$ spectrum through the derivation of the string tension distribution corresponding to the QCD-based Hagedorn function, frequently used to fit the transverse momentum distribution (TMD). The identified string tension fluctuations are heavy tailed, behaving similarly to the $q$-Gaussian distribution. After the convolution with the Schwinger mechanism, both approaches correctly describe the entire TMD. This approach is the onset for the nonthermal description of the particle production in ultrarelativistic pp collisions. By analyzing the data of pp collisions at $\sqrt{s} =13$ TeV, we found that the average temperature associated with the Higgs boson differential cross section is around 85 times greater than the estimated value for the charged particle TMD. Our results show that the Higgs boson production exhibits the largest deviation from the thermal description., Comment: 7 pages, 3 figures, accepted for publication in PRC

In a recent work, assuming a Beer-Lambert optical absorption and a Gaussian laser time profile, the exact solutions for a 1D-photoacoustic(PA)-boundary value problem predict a null pressure for optically strong absorbent materials. To overcome this, a heuristic correction was introduced by assuming that heat flux travels a characteristic length during the duration of the laser pulse\cite{Ruiz-Veloz2021} $\tau_p$. In this work, we obtained exact solutions in the frequency domain for a 1D-boundary-value-problem for the Dual-Phase-Lag (DPL) heat equation coupled with a 1D PA-boundary-value-problem via the wave-equation. Temperature and pressure solutions were studied by assuming that the sample and its surroundings have a similar characteristic thermal lag response time $\tau_{_T}$, which was assumed to be a free parameter that can be adjusted to reproduce experimental results. Solutions for temperature and pressure were obtained for a three-layer 1D system. It was found that for $\tau_{_T}< \tau_{p}$, the DPL temperature has a similar thermal profile of the Fourier heat equation, however, when $\tau_{_T}\ge \tau_{p}$ this profile is very different from the Fourier case. Additionally, via a numerical Fourier transform the wave-like behavior of DPL temperature is explored, and it was found that as $\tau_{_T}$ increases, thermal wave amplitude is increasingly attenuated. Exact solutions for pressure were compared with experimental signals, showing a close resemblance between both data sets, particularly in the time domain, for an appropriated value of $\tau_{_T}$; the transference function was also calculated, which allowed us to find the maximum response in frequency for the considered experimental setup., Comment: 32 pages, 11 figures

Pair density Waves (PDW) are a inhomogeneous superconducting states whose Cooper pairs posses a finite momentum resulting in a oscillatory gap in space, even in the absence of an external magnetic field. There is growing evidence for the existence of PDW superconducting order in many strongly correlated materials particularly in the cuprate superconductios and in several other different types of systems. A feature of the PDW state is that inherently it has a CDW as a composite order associated with it. Here we study the structure of the electronic topological defects of the PDW, paying special attention to the half-vortex and its electronic structure that can be detected in STM experiments. We discuss tell-tale signatures of the defects in violations of inversion symmetry, in the excitation spectrum and their spectral functions in the presence of topological defects. We discuss the "Fermi surface" topology of Bogoliubov quasi-particle of the PDW phases and we briefly discuss the role of quasi-particle-interference., Comment: 26 pages and 14 figures, inserted a factor of 2 in the global gauge transform after eq 2.13, replaced Fig 3. with defects of smaller vortex radius (48 to 16 lattice spacing), updated the descriptions of Figs 3-5, and Fig 11 to include a statement on the normalization used

This paper proposes a feature-based Visual Servoing (VS) method for insertion task skills. A camera mounted on the robot's end-effector provides the pose relative to a cylinder (hole), allowing a contact-free and damage-free search of the hole and avoiding uncertainties emerging when the pose is computed via robot kinematics. Two points located on the hole's principal axis and three mutually orthogonal planes defining the flange's reference frame are associated with the pose of the hole and the flange, respectively. The proposed VS drives to zero the distance between the two points and the three planes aligning the robot's flange with the hole's direction. Compared with conventional VS where the Jacobian is difficult to compute in practice, the proposed featured-based uses a Jacobian easily calculated from the measured hole pose. Furthermore, the feature-based VS design considers the robot's maximum cartesian velocity. The VS method is implemented in an industrial robot and the experimental results support its usefulness., Comment: To be published in proceedings of The 19th IEEE Conference on Industrial Electronics and Applications (ICIEA 2024)

In this work, we will explore the effects of non-commutativity in fractional classical and quantum schemes using the anisotropicc Bianchi Type I cosmological model coupled to a scalar field in the K-essence formalism. We introduce non-commutative variables considering that all minisuperspace variables $q^i_{nc}$ do not commute, so the symplectic structure was modified, resulting in some changes with respect to the traditional formalism. In the quantum regime, the probability density presents a new structure in the scalar field corresponding to the value of the non-commutative parameter., Comment: 28 pages, 23 figures

In this manuscript, we put forward two new types of structured light beams, the vortex Pearcey-Gauss (VPeG) beam, with a homogeneous polarisation distribution, and the vector vortex Pearcey-Gauss (VVPeG) beam, with a non-homogeneous polarisation distribution. The later generated as a non-separable superposition of the spatial and polarisation degrees of freedom. We also achieve their experimental realization through the combination of a spatial light modulator, which creates a scalar Pearcey-Gauss beam, and a q-plate which transforms it into a vortex or a vortex vector beam, depending on its input polarisation state. Their intensity and polarisation distribution was performed through Stokes polarimetry, along the propagation direction, which was compared with numerical simulations. As demonstrated, the VVPeG beam evolves from a pure vector beam into a vector mode of quasi-homogeneous polarisation distribution. The proposed vector beams add to the already extensive family of non-separable states of light. We anticipate that both types of beams will find applications in fields as diverse as optical metrology, optical communications, and optical tweezers, amongst others., Comment: 10 pages, 4 figures

Stellar convection plays an important role in atmospheric dynamics, wind formation and the mass-loss processes in Asymptotic Giant Branch (AGB) stars. However, a direct characterization of convective surface structures in terms of size, contrast, and life-span is quite challenging. Spatially resolving these features requires the highest angular resolution. In this work, we aim at characterizing the size of convective structures on the surface of the O-rich AGB star R Car to test different theoretical predictions, based on mixing-length theory from solar models. We used infrared low-spectral resolution (R~35) interferometric data in the H-band (~1.76 $\mu$m) with the instrument PIONIER at the Very Large Telescope Interferometer (VLTI) to image the star's surface at two epochs separated by ~6 years. Using a power spectrum analysis, we estimate the horizontal size of the structures on the surface of R Car. The sizes of the stellar disk, at different phases of a pulsation cycle, were obtained using parametric model-fitting in the Fourier domain. Our analysis supports that the sizes of the structures in R Car are correlated with variations of the pressure scale height in the atmosphere of the target, as predicted by theoretical models based on solar convective processes. We observe that these structures grow in size when the star expands within a pulsation cycle. While the information is still scarce, this observational finding highlights the role of convection in the dynamics of those objects. New interferometric imaging campaigns with the renewed capabilities of the VLTI are envisioned to expand our analysis to a larger sample of objects., Comment: Accepted by A&A on 15/05/2024, 11 pages, 7 figures

We propose a new paradigm for machine translation that is particularly useful for no-resource languages (those without any publicly available bilingual or monolingual corpora): LLM-RBMT (LLM-Assisted Rule Based Machine Translation). Using the LLM-RBMT paradigm, we design the first language education/revitalization-oriented machine translator for Owens Valley Paiute (OVP), a critically endangered Indigenous American language for which there is virtually no publicly available data. We present a detailed evaluation of the translator's components: a rule-based sentence builder, an OVP to English translator, and an English to OVP translator. We also discuss the potential of the paradigm, its limitations, and the many avenues for future research that it opens up.

This paper explores the potential of large language models (LLMs) to make the Aeronautical Regulations of Colombia (RAC) more accessible. Given the complexity and extensive technicality of the RAC, this study introduces a novel approach to simplifying these regulations for broader understanding. By developing the first-ever RAC database, which contains 24,478 expertly labeled question-and-answer pairs, and fine-tuning LLMs specifically for RAC applications, the paper outlines the methodology for dataset assembly, expert-led annotation, and model training. Utilizing the Gemma1.1 2b model along with advanced techniques like Unsloth for efficient VRAM usage and flash attention mechanisms, the research aims to expedite training processes. This initiative establishes a foundation to enhance the comprehensibility and accessibility of RAC, potentially benefiting novices and reducing dependence on expert consultations for navigating the aviation industry's regulatory landscape. You can visit the dataset (https://huggingface.co/somosnlp/gemma-1.1-2b-it_ColombiaRAC_FullyCurated_format_chatML_V1) and the model (https://huggingface.co/datasets/somosnlp/ColombiaRAC_FullyCurated) here.

Our purpose is to study the effect of binary companions located within the first 10 stellar radii from the primary AGB star. In this work, we target the mass-losing carbon star V Hydrae (V Hya), looking for signatures of its companion in the dust forming region of the atmosphere. The star was observed in the L- and N-bands with the VLTI/MATISSE instrument at low spectral resolution. We reconstructed images of V Hya's photosphere and surroundings using the two bands and compared our interferometric observables with VLTI/MIDI and VISIR archival data. To constrain the dust properties, we used DUSTY to model the spectral energy distribution. The star is dominated by dust emission in the L- and N- bands. The VISIR image confirms the presence of a large-scale dusty circumstellar envelope surrounding V Hya. The MATISSE reconstructed images show asymmetric and elongated structures in both infrared bands. In the L-band, we detected an elongated shape of approximately 15 mas, likely to be of photospheric origin. In the N-band, we found a 20 mas extension North-East from the star, and perpendicular to the L-band elongated axis. The position angle and the size of the N-band extension match the prediction of the companion position at MATISSE epoch. By comparing MATISSE N-band with MIDI data, we deduce that the elongation axis in the N-band has rotated since the previous interferometric measurements 13 years ago, supporting the idea that the particle enhancement is related to the dusty clump moving along with the companion. The MATISSE images unveil the presence of a dust enhancement at the companion position, opening new doors for further analysis on the binary interaction with an AGB component., Comment: Accepted for publication in Astronomy & Astrophysics

Vector modes are well-defined field distributions with spatially varying polarisation states, rendering them irreducible to the product of a single spatial mode and a single polarisation state. Traditionally, the spatial degree of freedom of vector modes is constructed using two orthogonal modes from the same family. In this letter, we introduce a novel class of vector modes whose spatial degree of freedom is encoded by combining modes from both the Hermite- and Laguerre-Gaussian families. This particular superposition is not arbitrary, and we provide a detailed explanation of the methodology employed to achieve it. Notably, this new class of vector modes, which we term Hybrid Hermite-Laguerre-Gaussian (HHLG) vector modes, gives rise to subsets of modes exhibiting polarisation dependence on propagation due to the difference in mode orders between the constituent Hermite- and Laguerre-Gaussian modes. To the best of our knowledge, this is the first demonstration of vector modes composed of two scalar modes originating from different families. We anticipate diverse applications for HHLG vector modes in fields such as free-space communications, information encryption, optical metrology, and beyond., Comment: 4 pages, 5 figures

Sliding bilayers are systems that exploit the possibility of relatively translating two monolayers along a specific direction in real space, such that different stackings could be implemented in the process. This simple approach allows for manipulating the electronic properties of layered materials similarly as in twisted multilayers. In this work, the sliding of bilayers, composed of one type of monolayer with spatial symmetry described by space group P$\bar{3}1m$ is studied. Using a minimal tight-binding model along with symmetry analysis, we propose two effects that arise in a specific sliding direction. First, the sliding-induced control of the band gap magnitude, which produces a metal-insulator transition, is demonstrated. In addition, the potential to achieve a topological adiabatic charge pump for cyclic sliding is discussed. For each effect, we also present material implementations using first-principles calculations. Bilayer GaS is selected for the metal-insulator transition and bilayer transition metal dichalcogenide ZrS$_2$ is found to display the topological pump effect. Both realizations show good agreement with the predictions of the model., Comment: 9 pages, 3 figures + Supplementary information

The COVID-19 pandemic has had far-reaching consequences, highlighting the urgency for explanatory and predictive tools to track infection rates and burden of care over time and space. However, the scarcity and inhomogeneity of data is a challenge. In this research we develop a robust framework for estimating and predicting the occupied beds of Intensive Care Units by presenting an innovative Small Area Estimation methodology based on the definition of mixed models with random regression coefficients. We applied it to estimate and predict the daily occupancy of Intensive Care Unit beds by COVID-19 in health areas of Castilla y Le\'on, from November 2020 to March 2022., Comment: Main: 21 pages, 10 figures and 2 tables. Supplementary material: 16 pages, 10 figures and 4 tables

A search for hidden-charm pentaquark states decaying to a range of $\Sigma_{c}\bar{D}$ and $\Lambda_{c}\bar{D}$ final states, as well as doubly-charmed pentaquark states to $\Sigma_{c}D$ and $\Lambda_{c}^{+}D$, is made using samples of proton-proton collision data corresponding to an integrated luminosity of $5.7fb^{-1}$ recorded by the LHCb detector at $\sqrt{s} = 13Te\kern -0.1em V$. Since no significant signals are found, upper limits are set on the pentaquark yields relative to that of the $\Lambda_{c}^{+}$ baryon in the $\Lambda_{c}^{+}\to pK^{-}\pi^{+}$ decay mode. The known pentaquark states are also investigated, and their signal yields are found to be consistent with zero in all cases., Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2023-018.html (LHCb public pages)

The effects of disorder on the robustness of topological magnon states of two-dimensional ferromagnetic skyrmions is investigated. It is diagnosed by evaluating a real space topological invariant, the bosonic Bott index (BI). The disorder simultaneously breaks the axially symmetric shape and the crystalline ordering of the skyrmions array. The corresponding magnonic fluctuations and band spectrum are determined in terms of magnetic field and strength of disorder. We observe the closing of the existing band gaps as the individual skyrmions start to occupy random positions. The analysis reveals that topological states (TSs) persist beyond the perturbative limit when skyrmions reach the glassy phase. In addition, the localization of topologically protected edge states is weakened by the disordered skyrmion structure with increasing localization length. Our findings shed light on the physical understanding of the coexistence of disordered magnetic textures and their topological spin fluctuations., Comment: 6 pages, 4 figures

Bound states in the continuum (BICs) are exotic, localized states even though their energy lies in the continuum spectra. Since its discovery in 1929, the quest to unveil these exotic states in charge transport experiments remains an active pursuit in condensed matter physics. Here, we study charge transport in InSb nanowire networks in the ballistic regime and subject to a perpendicular magnetic field as ideal candidates to observe and control the appearance of BICs. We find that BICs reveal themselves as distinctive resonances or antiresonances in the conductance by varying the applied magnetic field and the Fermi energy. We systematically consider different lead connections in hashtag-like nanowire networks, finding the optimal configuration that enhances the features associated with the emergence of BICs. Finally, the investigation focuses on the effect of the Rashba spin-orbit interaction of InSb on the occurrence of BICs in nanowire networks. While the interaction generally plays a detrimental role in the signatures of the BICs in the conductance of the nanowire networks, it opens the possibility to operate these nanostructures as spin filters for spintronics. We believe that this work could pave the way for the unambiguous observation of BICs in charge transport experiments and for the development of advanced spintronic devices., Comment: 9 pages, 6 figures, supplementary material. Submission to SciPost

Vegetation phenology consists of studying synchronous stationary events, such as the vegetation green up and leaves senescence, that can be construed as adaptive responses to climatic constraints. In this paper, we propose a method to estimate the annual phenology curve from multi-annual observations of time series of vegetation indices derived from satellite images. We fitted the classical harmonic regression model to annual-based time series in order to construe the original data set as realizations of a functional process. Hierarchical clustering was applied to define a nearly homogeneous group of annual (smoothed) time series from which a representative and idealized phenology curve was estimated at the pixel level. This curve resulted from fitting a mixed model, based on functional principal components, to the homogeneous group of time series. Leveraging the idealized phenology curve, we employed standard calculus criteria to estimate the following phenological parameters (stationary events): green up, start of season, maturity, senescence, end of season and dormancy. By applying the proposed methodology to four different data cubes (time series from 2000 to 2023 of a popular satellite-derived vegetation index) recorded across grasslands, forests, and annual rainfed agricultural zones of a Flora and Fauna Protected Area in northern Mexico, we verified that our approach characterizes properly the phenological cycle in vegetation with nearly periodic dynamics, such as grasslands and agricultural areas. The R package sephora was used for all computations in this paper., Comment: 18 pages, 3 figures, 6 tables

We consider symmetric separately radial (with corresponding group $S_n\rtimes \mathbb{T}^n$) and alternating separately radial (with corresponding group $A_n\rtimes \mathbb{T}^n$) symbols, as well as the associated Toeplitz operators on the weighted Bergman spaces on the unit ball on $\mathbb{C}^n$. Using a purely representation theoretic approach we obtain that the $C^*$-algebras generated by each family of such Toeplitz operators is commutative. Furthermore, we show that the symmetric separately radial Toeplitz operators are more general than radial Toeplitz operators, i.e., every radial Toeplitz operator is a symmetric separately radial., Comment: 18 pages

Low-disorder two-dimensional electron systems in the presence of a strong, perpendicular magnetic field terminate at very small Landau level filling factors in a Wigner crystal (WC), where the electrons form an ordered array to minimize the Coulomb repulsion. The nature of this exotic, many-body, quantum phase is yet to be fully understood and experimentally revealed. Here we probe one of WC's most fundamental parameters, namely the energy gap that determines its low-temperature conductivity, in record-mobility, ultra-high-purity, two-dimensional electrons confined to GaAs quantum wells. The WC domains in these samples contain $\simeq$ 1000 electrons. The measured gaps are a factor of three larger than previously reported for lower quality samples, and agree remarkably well with values predicted for the lowest-energy, intrinsic, hyper-corelated bubble defects in a WC made of flux-electron composite fermions, rather than bare electrons. The agreement is particularly noteworthy, given that the calculations are done for disorder-free composite fermion WCs, and there are no adjustable parameters. The results reflect the exceptionally high quality of the samples, and suggest that composite fermion WCs are indeed more stable compared to their electron counterparts.

Monochromatic gamma-ray signals constitute a potential smoking gun signature for annihilating or decaying dark matter particles that could relatively easily be distinguished from astrophysical or instrumental backgrounds. We provide an updated assessment of the sensitivity of the Cherenkov Telescope Array (CTA) to such signals, based on observations of the Galactic centre region as well as of selected dwarf spheroidal galaxies. We find that current limits and detection prospects for dark matter masses above 300 GeV will be significantly improved, by up to an order of magnitude in the multi-TeV range. This demonstrates that CTA will set a new standard for gamma-ray astronomy also in this respect, as the world's largest and most sensitive high-energy gamma-ray observatory, in particular due to its exquisite energy resolution at TeV energies and the adopted observational strategy focussing on regions with large dark matter densities. Throughout our analysis, we use up-to-date instrument response functions, and we thoroughly model the effect of instrumental systematic uncertainties in our statistical treatment. We further present results for other potential signatures with sharp spectral features, e.g.~box-shaped spectra, that would likewise very clearly point to a particle dark matter origin., Comment: 44 pages JCAP style (excluding author list and references), 19 figures; minor changes to match published version

Inspired by Owings's problem, we investigate whether, for a given an Abelian group $G$ and cardinal numbers $\kappa,\theta$, every colouring $c:G\longrightarrow\theta$ yields a subset $X\subseteq G$ with $|X|=\kappa$ such that $X+X$ is monochromatic. (Owings's problem asks this for $G=\mathbb Z$, $\theta=2$ and $\kappa=\aleph_0$; this is known to be false for the same $G$ and $\kappa$ but $\theta=3$.) We completely settle the question for $\kappa$ and $\theta$ both finite (by obtaining sufficient and necessary conditions for a positive answer) and for $\kappa$ and $\theta$ both infinite (with a negative answer). Also, in the case where $\theta$ is infinite but $\kappa$ is finite, we obtain some sufficient conditions for a negative answer as well as an example with a positive answer., Comment: 14 pages. Some proofs (especially in Section 2) omit various details at the request of the referee; to see more detailed proofs the reader should refer to v2

In this work we shall explore the effects of non commutativity in fractional classical and quantum schemes using the flat Friedmmann-Robertson-Walker (FRW) cosmological model coupled to a scalar field in the K-essence formalism. In previous work we have obtained the commutative solutions in both regimes into the fractional framework. Here we introduce noncommutative variables, considering that all minisuperspace variables $\rm q^i_{nc}$ do not commute, so the symplectic structure was modified. In the quantum regime, the probability density presents new structure in the scalar field corresponding to the value of the non-commutative parameter, in the sense that this probability density undergoes a shift back to the direction of the scale factor, causing classical evolution to arise earlier than in the commutative world., Comment: Latex, 22 pages, 24 figures

We investigate the transverse momentum distribution (TMD) statistics from three different theoretical approaches. In particular, we explore the framework used for string models, wherein the particle production is given by the Schwinger mechanism. The thermal distribution arises from the Gaussian fluctuations of the string tension. The hard part of the TMD can be reproduced by considering heavy tailed string tension fluctuations, for instance, the Tsallis $q$-Gaussian function, giving rise to a confluent hypergeometric function that fits the entire experimental TMD data. We also discuss the QCD-based Hagerdon function, another family of fitting functions frequently used to describe the spectrum. We analyze the experimental data of minimum bias pp collisions reported by the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC) experiments (from $\sqrt{s}=0.2$ TeV to $\sqrt{s}=13$ TeV). We extracted the corresponding temperature by studying the behavior of the spectra at low transverse momentum values. For the three approaches, we compute all moments, highlighting the average, variance, and kurtosis. Finally, we compute the Shannon entropy and the heat capacity through the entropy derivative with respect to the temperature. We found that the $q$-Gaussian string tension fluctuations lead to a monotonically increasing heat capacity as a function of the center of mass energy, which is also observed for the Hagedorn fitting function. This behavior is consistent with the experimental observation that the temperature slowly rises with increments of the collision energy., Comment: 12 pages, 10 figures. Accepted for publication in Physical Review C

Given two numerical semigroups $S$ and $T$ we say that $T$ is a multiple of $S$ if there exists an integer $d \in \mathbb{N} \setminus \{0\}$ such that $S = \{x \in \mathbb{N} \mid d x \in T\}$. In this paper we study the family of multiples of a (fixed) numerical semigroup. We also address the open problem of finding numerical semigroups of embedding dimension $e$ without any quotient of embedding dimension less than $e$, and provide new families with this property., Comment: 15 pages

Astigmatic unitary transformations allow for the adiabatic connections of all feasible states of paraxial Gaussian beams on the same modal sphere, i.e., Hermite-Laguerre-Gaussian (HLG) modes. Here, we present a comprehensive investigation into the unitary modal evolution of complex structured Gaussian beams, comprised by HLG modes from disparate modal spheres, via astigmatic transformation. The non-synchronized higher-order geometric phases in cyclic transformations originates a Talbot-effect-like modal evolution in the superposition state of these HLG modes, resulting in pattern variations and revivals in transformations with specific geodesic loops. Using Ince-Gaussian modes as an illustrative example, we systematically analyze and experimentally corroborate the beamforming mechanism behind the pattern evolution. Our results outline a generic modal conversion theory of structured Gaussian beams via astigmatic unitary transformation, offering a new approach for shaping spatial modal structure. These findings may inspire a wide variety of applications based on structured light., Comment: 7 pages, 5 figures

3C84 is a nearby radio source with a complex total intensity structure, showing linear polarisation and spectral patterns. A detailed investigation of the central engine region necessitates the use of VLBI above the hitherto available maximum frequency of 86GHz. Using ultrahigh resolution VLBI observations at the highest available frequency of 228GHz, we aim to directly detect compact structures and understand the physical conditions in the compact region of 3C84. We used EHT 228GHz observations and, given the limited (u,v)-coverage, applied geometric model fitting to the data. We also employed quasi-simultaneously observed, multi-frequency VLBI data for the source in order to carry out a comprehensive analysis of the core structure. We report the detection of a highly ordered, strong magnetic field around the central, SMBH of 3C84. The brightness temperature analysis suggests that the system is in equipartition. We determined a turnover frequency of $\nu_m=(113\pm4)$GHz, a corresponding synchrotron self-absorbed magnetic field of $B_{SSA}=(2.9\pm1.6)$G, and an equipartition magnetic field of $B_{eq}=(5.2\pm0.6)$G. Three components are resolved with the highest fractional polarisation detected for this object ($m_\textrm{net}=(17.0\pm3.9)$%). The positions of the components are compatible with those seen in low-frequency VLBI observations since 2017-2018. We report a steeply negative slope of the spectrum at 228GHz. We used these findings to test models of jet formation, propagation, and Faraday rotation in 3C84. The findings of our investigation into different flow geometries and black hole spins support an advection-dominated accretion flow in a magnetically arrested state around a rapidly rotating supermassive black hole as a model of the jet-launching system in the core of 3C84. However, systematic uncertainties due to the limited (u,v)-coverage, however, cannot be ignored., Comment: 15 pages, 6 figures, published in A&A