We interpret the $B$-lattice flavor framework as a compositeness hierarchy: all three fermion generations are elementary chiral fields, but third-generation Yukawa couplings are undressed ($Q=0$), while lighter generations acquire their Yukawa couplings through chains of spin-$0$ subconstituents (``hops'') whose depth is counted by the $\mathbb{Z}_9$ discrete gauge symmetry. The $\mathbb{Z}_9$ charge admits a two-index decomposition $q_9\mapsto(a,b)$ that identifies two hop species ($α$, $β$) and organizes all fundamental scales from $v_{\rm EW}$ to $M_{\rm Pl}$ on a ``ninths ladder'' $Λ\timesε^{n/9}$. The lattice structure yields the CKM and PMNS mixing parameterizations (with all mixing exponents expressible as charge differences $ΔQ$ dressed by a universal Fritzsch--Xing phase shift of $\pm 1/9$), a seesaw benchmark $m_3\simeq 51$~meV, the axion mass window $m_a\sim 7$--$12\;μ$eV, and the prediction $\tanβ\simeq 10$--$16$ (from the chain internal factor combined with the DFSZ-II two-Higgs-doublet structure), all from two parameters ($Λ$ and $ε= 14/75$). Generation-dependent Peccei--Quinn charges restore the axion--photon coupling ($C_{aγ}\simeq 0.6$--$1.0$) from ``back to invisible'' suppression. An illustrative UV realization in terms of hypercolor-confined scalars communicated to the SM by a gauge-invariant messenger chain is presented as an existence proof.

With the widespread application of location-based services, fingerprint-based localization has demonstrated advantages in environments with complex signal propagation. Deep learning has significantly improved the efficiency of both offline training and online matching in localization processes. However, existing fingerprints only contain terminal position information without capturing motion states, and neural network designs have not fully incorporated structural features such as fingerprint sparsity. In this paper, we propose a triple-beam fingerprint (TBF) incorporating Doppler information and design a Transformer-based localization and orientation awareness network (LOA-Net) to simultaneously estimate user position and motion direction in massive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. We first show the correlation between TBF and multipath information, and investigate the collinearity of different TBFs, demonstrating that TBF is an effective small-size sparse fingerprint. Then, we propose LOA-Net containing a mask-augmented detection Transformer for regression (MaskDETR-Reg) module and a fusion-enhanced Transformer for direction classification (Fusion-TDC) module to process angle-delay domain information and Doppler domain information, respectively. Finally, in the simulation of indoor scenarios defined in 3GPP 38.901, the proposed method achieves significantly better localization accuracy than weighted $K$-nearest neighbors (WKNN), 2D and 3D convolutional neural networks (CNNs), and achieves satisfactory motion direction estimation accuracy.

This work investigates additional gravitational features of a newly proposed black hole spacetime within Kalb-Ramond gravity, incorporating non-commutative corrections arising from a gauge-theoretic approach recently introduced in the literature [arXiv:2507.17390]. Accordingly, null geodesics are solved numerically to trace photon paths; the photon sphere and shadow are determined. From Event Horizon Telescope (EHT) measurements of $Sgr A^{*}$, constraints on the parameters $Θ$ (which encapsulates the non-commutativity) and $\ell$ (the Lorentz-violating parameter) are established. To examine the stability of critical orbits and the deflection angle (gravitational lensing) in the weak field scenario, we compute the Gaussian curvature in order to use the Gauss-Bonnet theorem. Moreover, the deflection angle has been calculated as well in the strong deflection limit. Furthermore, Lensing observables are estimated using EHT data for $Sgr A^{*}$ and $M87$. Topological features such as the topological photon sphere are also explored.

The exact solution of a two-dimensional (2D) Ising model with the next nearest interactions at zero magnetic field is derived. At first, the transfer matrices are analyzed in three representations, i.e., Clifford algebraic representation, transfer tensor representation and schematic representation, to inspect nontrivial topological structures in this system. The system is equivalent to a triangular Ising model plus an interaction along the z axis, so that the approaches developed for the 3D Ising model are modified to be appropriable for solving the exact solution of the 2D Ising model with the next nearest interactions. The partition function and the spontaneous magnetization are obtained. The comparison with the exact solutions of other Ising lattices reveals that either the increase of the number of interactions in a unit cell or the presence/increase of topological contributions enhances the critical point of the Ising lattices. The results obtained in this work are helpful for understanding the physical properties of the 2D magnetic materials.

Structured reduced-order modeling is a central component in the computer-aided design of control systems in which cheap-to-evaluate low-dimensional models with physically meaningful internal structures are computed. In this work, we develop a new approach for the structured data-driven surrogate modeling of linear dynamical systems described by second-order time derivatives via balanced truncation model-order reduction. The proposed method is a data-driven reformulation of position-velocity balanced truncation for second-order systems and generalizes the quadrature-based balanced truncation for unstructured first-order systems to the second-order case. The computed surrogates encode a generalized proportional damping structure, and we propose a computational procedure for inferring the damping coefficients from data by minimizing a least-squares error over the coefficients. Several numerical examples demonstrate the effectiveness of the proposed method.

An atomic Josephson junction realized with dipolar bosons in a double-well potential can be described by an extended Bose-Hubbard model in which dipolar interactions generate an effective on-site interaction and nearest-neighbor pair tunneling. Using mean-field theory and exact diagonalization, we investigate how this correlated process affects zero-temperature equilibrium and dynamical properties of the system. In equilibrium, we show that pair tunneling induces ground-state parity modulations and significantly reshapes the phase diagram, producing qualitative changes in the quantum phase transitions toward NOON and phase-NOON states, as well as quantitative shifts of the critical points. Out of equilibrium, we demonstrate that it modifies the conditions for macroscopic quantum self-trapping, and assess its impact by comparing mean-field and fully quantum evolution, including the emergence of dynamical quantum phase transitions.

We investigate circular current in both ordered and disordered Hubbard quantum rings threaded by magnetic flux, employing exact diagonalization and the Hartree-Fock mean-field approach within the tight-binding framework. The influence of on-site and extended Hubbard interactions, disorder, and electron filling on the persistent current is systematically analyzed. To construct the full many-body Hamiltonian, we introduce a linear table formalism, which, to our knowledge, has been rarely used in this context. In ordered rings, the current decreases monotonically with increasing on-site repulsion, while the impact of the extended interaction depends strongly on the filling factor. At low filling, stronger extended interaction suppresses the current, whereas near half-filling, it enhances the current up to a critical ratio, half of the on-site strength, before reducing it. Disorder significantly modifies these behaviors, notably enhancing the current at less than quarter-filling with increasing extended interaction. The localization properties of eigenstates, examined via the inverse participation ratio, further support the crucial roles of filling and the interplay between on-site and extended interactions in governing persistent current.

We systematically study the commutative factorization categories over the Ran space. We fill in what we consider as a gap in the construction of the factorizable Satake functor in the constructible setting in arXiv:1708.07205, arXiv:1608.00284. To do so, we summarize four different constructions of commutative factorization sheaves of categories on Ran and establish some relations between them. We also generalize the Drinfeld-Plücker formalism from arXiv:1708.07205, arXiv:2310.0638. In addition, we study the commutative factorization categories Fact(C) with an additional grading of C. We apply our results to relate the versions of the Satake functors for the Ran space with that of the configuration space of colored divisors on a curve. This paper is a companion of arXiv:2508.01527.

Supernovae are observed to occur approximately 1-2 times per century in a galaxy like the Milky Way. Based on historical records, however, the last core-collapse galactic supernova observed by humans occurred almost 1,000 years ago. Luckily, we are well positioned to catch the next one with the advent of new neutrino detectors and astronomical observatories. Neutrino observatories can provide unprecedented triggers for a galactic supernova event as they are likely to see a supernova neutrino signal anywhere from minutes to days before the shock breakout causes the supernova to brighten in optical wavelengths. Given its large etendue, the Vera C. Rubin Observatory is ideally positioned to rapidly localize the optical counterpart based on the neutrino trigger. In this paper we simulate events to study the efficiency with which supernovae are optimally localized by the Vera C. Rubin Observatory. We find that the observatory is ideal for initial localization of nearly all observable supernova triggers and has a 57-97% chance of catching any supernova based on theoretical stellar mass density predictions and observations. We provide an analysis of optimal filter selection and exposure times and discuss observational caveats.

We introduce TensorMixedStates, a Julia library built on top of ITensor which allows the simulation of quantum systems in the presence of dissipation using matrix product states (MPS). It offers three key features: i) it implements the MPS representation for mixed states along with associated operations, in particular the time evolution according to a Lindblad equation or discrete time evolution using non-unitary gates (quantum channels), ii) it is based on ITensor, which has proven its effectiveness and which gives access to efficient low-level tensor manipulation as well as state-of-the-art algorithms (like DMRG or TDVP), finally iii) it presents a user-friendly interface allowing users to write sophisticated simulations for pure and mixed quantum states in a few lines of code.

In this review, we aim to utilize the bootstrap method to study models that have received significant interest in high energy theory and holography recently. Matrix bootstrap is proposed to determine the range of the solution up to an impressively high precision merely through positive conditions rooted in fundamental quantum mechanical structures or reality of matrix integral saddle points, together with specific kinematical and dynamical constraints of the theory, whose precision increases exponentially with the number of variables taken into consideration in principle. It plays the role of an equivalently effective substitute for the numerical Monte Carlo method. Models that could potentially be explored with this approach include BFSS MQM (conjectured to be the first non-perturbative definition of M theory in 11d and dual to D0 brane black hole solutions in 10d supergravity), D-instanton/IKKT matrix integral (which has recently attracted particular attention for its relations with spacetime emergence) and mass deformed BMN theory. Apart from exploring the stationary state properties of the theory, we can extend the method to thermal or time-dependent cases to study the dynamical information of the properties and help to verify or predict the possibility of holographic realization in these models.

This study examines the development of reflective practice among students on a four-year work-based Software Engineering program. Using two established models of reflection - Boud et al.'s Model of Reflective Process and Bain et al.'s 5R Framework for Reflection - we analyse a series of reflective assignments submitted by students over four years. Our longitudinal analysis reveals clear trends in how students' reflective abilities evolve over the course of the program. We find that more sophisticated forms of reflection, such as integration of knowledge, appropriation of skills, and reconstruction of practice, increase markedly in prevalence in later years. The complementary nature of workplace experience and university study is highlighted in students' reflections, demonstrating a key benefit of the work-based learning approach. By the final year, all students demonstrate the ability to reconstruct their experiences to inform future practice. Our findings provide insight into how reflective practice develops in Software Engineering education and suggest potential value in incorporating more structured reflection into traditional degree programs. The study also reveals instances of meta-reflection, where students reflect on the value of reflection itself, indicating a deep engagement with the reflective process. While acknowledging limitations, this work offers a unique longitudinal perspective on the development of reflective practice in work-based Software Engineering education.

We consider the quantum creation of a closed universe within the Euclidean path-integral formalism. An analytical expression for the tunneling probability is derived, including both the exponential suppression and the exact Gaussian prefactor due to quadratic fluctuations around the instanton. The calculation is performed in a fixed-interval minisuperspace formulation, where the Hamiltonian constraint is imposed at the level of the classical instanton, while the full lapse integration is not included beyond the leading semiclassical approximation. The result provides a transparent and self-consistent semiclassical estimate of the nucleation rate, refining previous analyses with the inclusion of Gaussian fluctuations.

Quantum entanglement provides a unique perspective for probing nuclear structure. In this work, we employ quantum entanglement measures, including proton-neutron entanglement entropy, mutual information, and quantum relative entropy, to investigate the evolution of entanglement patterns as we approach neutron-rich nuclei. The study is carried out in the vicinity of the $N=20$ island of inversion region consisting of even-$A$ Ne, Mg, and Si isotopes, and also for isotones corresponding to $N=20$. The state-of-the-art \textit{ab initio} valence space in-medium similarity renormalization group method has been used for this purpose. We have highlighted the role of proton-neutron entanglement entropy in the formation of the island of inversion region. Mutual information provides insight into the strength of correlations between proton-proton, neutron-neutron, and proton-neutron single-particle states. While these correlations are relatively weak between protons and neutrons in the ground states, they become comparable to like-particle correlations in excited states. The quantum relative entropy is also studied between $0^+$ and $2^+$ states of the Ne, Mg, and Si isotopes, as well as $N=20$ isotones, using the Kullback-Leibler divergence and Jensen-Shannon divergence. We have performed these calculations by expressing the nuclear wavefunctions in a Slater-determinant basis and analyzing them through complementary partitions, including proton-neutron and mode-resolved factorizations.

We use semidefinite programming to bound the fractional cut-cover parameter of graphs in association schemes in terms of their smallest eigenvalue. We also extend the equality cases of a primal-dual inequality involving the Goemans-Williamson semidefinite program, which approximates MAXCUT, to graphs in certain coherent configurations. Moreover, we obtain spectral bounds for MAX 2-SAT when the underlying graphs belong to a symmetric association scheme by means of a certain semidefinite program used to approximate quadratic programs, and we further develop this technique in order to explicitly compute the optimum value of its gauge dual in the case of distance-regular graphs.

Removing the shape noise from the observed weak lensing field, i.e., denoising, enhances the potential of WL by accessing information at small scales where the shape noise dominates without denoising. We utilise two machine learning (ML) models for denosing: generative adversarial network (GAN) and diffusion model (DM). We evaluate the performance of denosing with GAN and DM utilising the large suite of mock WL observations, which serve as the training and test data sets. We apply denoising to 1,000 noisy mass maps with GAN and DM models trained with 39,000 mock observations. Both models can fairly well reproduce the true convergence map on large scales. Then, we measure cosmological statistics: power spectrum, bispectrum, one-point probability distribution function, peak and minima counts, and scattering transform coefficients. We find that DM outperforms GAN in almost all considered statistics and recovers the correct statistics down to small scales. For example, the angular power spectrum can be recovered with DM up to multipoles $\ell \lesssim 6000$ while the noise power spectrum dominates from $\ell \simeq 2000$. We also conduct stress tests on the trained model; denoising the maps with different characteristics, e.g., different source redshifts, from the training data. The performance degrades at small scales, but the statistics can still be recovered at large scales. Though the training of DM is more computationally demanding compared with GAN, there are several advantages: numerically stable training, higher performance in the reconstruction of cosmological statistics, and sampling multiple realisations once the model is trained. It has been known that DM can generate higher-quality images in real-world problems than GAN, the superiority has been confirmed as well in the WL denoising problem.

A random number generator for the Kappa velocity distribution in particle simulations is proposed. Approximating the cumulative distribution function with the q-exponential function, an inverse transform procedure is constructed. The proposed method provides practically accurate results, in particular for k<4. It runs fast on graphics processing units (GPUs). The derivation, numerical validation, and relevance to GPU execution models are discussed.

We develop a structure-preserving ADMM method, denoted SP-ADMM, for learning energy-stable spatial derivative stencils for Maxwell equations from noisy data. Starting from the source-free Maxwell system, we focus on a one-dimensional reduction whose energy conservation depends on the skew-adjointness of the spatial derivative operator. The learned derivative is represented by a compact periodic convolution stencil. Unlike standard constrained ADMM, which learns the full stencil and imposes skew-adjointness through equality constraints, SP-ADMM enforces skew-adjointness by construction through a reduced parameterization using only the independent positive-side stencil coefficients. Numerical experiments show that SP-ADMM is especially effective in hidden operator and noisy-data regimes. Across clean data, noisy derivative data, multiple initial conditions, different hidden skew-adjoint operators, training-set sizes, regularization parameters, constraint ablations, and long-time simulations, SP-ADMM achieves the smallest final-time electric-field error while preserving energy to roundoff accuracy. A layered-medium Maxwell propagation test further shows that the learned structure-preserving stencil remains competitive with classical finite differences in a physical reflection/transmission setting. Overall, SP-ADMM provides a data-driven way to learn accurate Maxwell stencils while retaining the energy-conserving structure of the underlying equations.

We identify compact groups of galaxies (CGs) in the IllustrisTNG-300 simulation using a Friends-of-Friends (FoF) algorithm. Our approach is designed to be comparable to systematic CG searches based on spectroscopic surveys, while avoiding the conventional Hickson selection criteria, which can bias samples toward relatively low-density environments. We construct two CG catalogs: one based on a three-dimensional distance linking length of 73 kpc (i.e., $50~h^{-1}$ kpc), and another based on projected and radial linking lengths of 73 kpc and $1000~\rm km~s^{-1}$. We refer to these as the position-position-position (PPP) and position-position-velocity (PPV) CG catalogs, respectively. The PPV catalog provides a direct analog to observed CG samples. At $z = 0$ in TNG300, we identify 383 PPP CGs and 1666 PPV CGs. A large fraction ($\sim 80\%$) of PPV CGs are not physically compact systems but are contaminated by line-of-sight interlopers. We demonstrate that the scaling relation between total group stellar mass and velocity dispersion is an effective diagnostic for identifying false positives with line-of-sight interlopers. We further examine the large-scale environments of CGs and show that they reside in a wide range of densities, including the central regions of galaxy clusters. These CG catalogs provide a robust foundation for studying the formation and evolution of CGs in cosmological simulations.

The quaternionic equations ax-xb=0 and ax-xb=c are investigated, which are called homogeneous and inhomogeneous Sylvester equations, respectively. Conditions for the existence of solutions are provided. In addition, the general and nonzero solutions to these equations are derived applying quaternion square roots.

Collaborative Optimization (CO) is a multidisciplinary design optimization (MDO) framework that decomposes large-scale engineering problems into parallel, independently solvable subsystems coordinated by a system-level optimizer. Its practical utility is limited by the high frequency of expensive black-box disciplinary evaluations arising from the bi-level consistency constraints. This paper introduces BACO, a Bayesian Algorithm for Collaborative Optimization, which replaces the direct black-box calls at both levels with Gaussian process (GP) surrogates and acquisition function maximization. At the subsystem level, an acquisition function subject to GP-predicted feasibility constraints identifies the next evaluation point. At the system level, the same surrogate framework enforces consistency through predicted discrepancy constraints. This architecture reduces the number of true black-box evaluations required per major iteration. BACO is benchmarked against state-of-the-art CO variants on a Scalable MDO problem over 50 randomized instances. On this problem, BACO consistently achieves lower objective values and drives both constraint violation and interdisciplinary discrepancy to near-zero within the evaluation budget, outperforming all three CO variants across all tested DoE sizes. Further validation is conducted on a coupled aero-structural wing optimization problem based on the Common Research Model (CRM) geometry, where BACO identifies a feasible solution within 886 of 1000 allocated evaluations, recovering results physically consistent with active bending stress and tip deflection constraints. The BACO software, the state-of-the-art CO solvers, as well as standard MDO benchmarking problems are open-source and publicly available at https://moebehfn.github.io/mdotoolbox/.

We introduce a three-dimensional quantum field theory with an infinite-dimensional symmetry, realized explicitly through a centrally extended affine graded Lie algebra. This symmetry is a direct three-dimensional generalization of the chiral symmetry in the Wess-Zumino-Witten model. Upon performing radial quantization, we construct the Fock space of the theory and, via a three-dimensional analogue of the state-operator correspondence, we demonstrate that the algebra of local operators is endowed with the structure of a raviolo vertex algebra. Accordingly, this setup provides a framework for extending the methods of two-dimensional conformal field theory to three dimensions, and we expect it to lay the groundwork for exact methods in three-dimensional quantum field theory.

Competing risks occur in survival analysis when multiple causes of death are present. They play a prominent role in several domains extending beyond biostatistics to encompass epidemiology, actuarial sciences, and reliability theory. This paper adopts a multi-state modeling framework to competing risks. We introduce a class of flexible nonparametric priors, defined through hierarchical completely random measures, to model the transition probabilities, and identify the specific (conditionally) conjugate member of this general class. Furthermore, we determine the joint marginal distribution of the data and of a latent random partition, and characterize the posterior distribution of the model. Leveraging these distributional results, we evaluate the predictive probability that a future event is of a specific type (e.g. death from a particular cause), as a function of the time at which the event occurs. The resulting function, derived on sound principles, is termed the prediction curve, and represents a major innovation in the literature. In addition, we provide posterior estimates for the survival function, and for the cause-specific incidence and subdistribution functions. Suitable simulation algorithms for posterior inference are also devised. The model's performance, as well as the algorithms' effectiveness, is evaluated through simulation studies. Finally, we illustrate our approach on clinical datasets.

Time-fractional telegraph equations provide fundamental mathematical models for transport processes that exhibit memory and nonlocal effects in industrial and physical systems. These models arise naturally in heat transport in materials with thermal memory, wave propagation in viscoelastic media, and charge transport in spatially heterogeneous semiconductor devices. In this study, we investigate a class of time-fractional telegraph systems with spatially varying coefficients using Lie symmetry analysis and the Riemann--Liouville fractional derivative. We establish a complete Lie group classification for sufficiently differentiable coefficient functions and determine all functional forms that admit such symmetry extensions. The symmetry structure is shown to depend fundamentally on the relationship between the transport coefficient and the potential function, resulting in three distinct symmetry classes. For each case, optimal systems of one-dimensional Lie subalgebras are constructed, and the governing fractional partial differential equations are systematically reduced to fractional ordinary differential equations. Exact invariant solutions are obtained in closed form and expressed in terms of Mittag--Leffler functions, generalized Wright functions, and Fox $H$-functions. These analytical solutions provide valuable insights into fractional telegraph-type transport phenomena and serve as important benchmarks for validating numerical methods in industrial transport modeling and fractional evolution systems.

Accurate modeling of supernova (SN) feedback in galaxy formation simulations is complicated by energy conservation violations arising from the vector nature of momentum injection. We present a mechanical feedback scheme addressing two key sources: the relative motion between gas elements and the SN-hosting star particle, and multiple momentum injections into a single gas element within one timestep. Computing the kinetic energy increment in the rest frame of the gas element ensures energy conservation while avoiding the momentum inversion that can occur when this calculation is instead performed in the lab frame. This correction inherently violates momentum conservation, disturbing the angular momentum distribution and hindering disk formation when momentum is coupled on galactic scales. To prevent unphysical large-scale momentum coupling without an ad hoc maximum coupling radius, we switch to purely thermal feedback when the cooling radius is resolved by the local inter-element separation. Our scheme is designed for high- to intermediate-resolution zoom-in simulations with star particle masses up to $\sim 10^5\,M_\odot$. Through cosmological zoom-in simulations of dwarf galaxies ($M_\mathrm{vir} \sim 10^{11}\,M_\odot$) at two mass resolutions, we demonstrate good convergence in star formation histories; without the momentum correction, stellar mass in low-resolution runs falls to as low as 59\% of that in high-resolution counterparts. At the feedback strength reproducing dwarf galaxy stellar masses, a Milky Way-mass simulation overproduces stellar mass, suggesting additional processes, such as active galactic nuclei feedback, are required at this mass scale.

This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block coordinate descent methods. We provide a convergence rate analysis ranging from minimal assumptions to more practical settings, such as sharpness and strong convexity. While most existing studies on block coordinate descent methods focus on nonoverlapping decompositions and smooth or strongly convex problems, our framework extends to more general settings involving arbitrary space decompositions, inexact local solvers, and problems with weaker smoothness or convexity assumptions. The proposed framework is broadly applicable to convex optimization problems arising in areas such as nonlinear partial differential equations, imaging, and data science.

We study the real-time chiral dynamics of Dirac fermions in AdS$_2$ and AdS$_2$ black hole backgrounds. The spacetime curvature generates a spin connection term, acting as an effective magnetic field and a position-dependent chiral chemical potential. This leads to strongly asymmetric wave propagation, confined within an inhomogeneous Lieb-Robinson cone. The front velocities decrease with increasing fermion mass and horizon radius. The entanglement entropy grows inside the causal cone, and it saturates due to screening/dephasing in the finite inhomogeneous chain. In dipole-dipole collision, the central bipartite entropy rises when the inward Lieb-Robinson fronts intersect, forming a bright ridge in the local entanglement profile. Charge and current correlators peak at the front arrival, providing a real-time diagnostic of chiral transport. These results establish a causality-respecting framework, linking curvature and horizons to transport and entanglement in (1+1)-dimensional fermionic matter.

This paper introduces a new method to search for unresolved binary stars in open star clusters. The work aims at improving the approach introduced previously, which employs the (H-W2)-W1 versus W2-(BP-K) photometric diagram. This diagram, in tandem with the Gaia Color Magnitude Diagram (CMD) and using theoretical isochrones as reference sequences, is used to estimate the binary star fraction and the distribution of the component mass ratio $q$ in eight nearby open star clusters, including Pleiades, Alpha Per, and Praesepe, which we investigated in previous studies. In this study, to alleviate the uncertainties associated with the use of theoretical isochrones, we propose an empirical isochrones approach. We show that this is an effective approach to exploring a wider primary-mass interval, in particular for the region of low-mass sources. Box-and-whisker plots are used to present the distribution of the component mass ratio $q$. The mode of distribution turns out to be in the range $0.43-0.83$ and $0.38-0.63$ for Gaia and infrared-visible photometry, respectively. In addition, we update the algorithm to obtain the binary fraction, whose estimate lies in the range $0.16 - 0.36$ and $0.21 - 0.44$, depending on the adopted method, and show that in previous studies the binary fraction was overestimated. We do not find evidence that the variable spatial resolution of the employed catalogs (Gaia, 2MASS, and WISE) affects the precision of the binary fraction estimate.

Using the convergent Leaver method, we investigate the quasinormal modes of a massive scalar field propagating in the background of the Casadio--Fabbri--Mazzacurati (CFM) brane-world black hole. We show that the spectrum exhibits two distinct types of modes, depending on their behavior as the field mass increases. In one class, the real oscillation frequency decreases and eventually approaches zero, while in the other the damping rate tends to vanish. When either the real or imaginary part of the frequency reaches zero, the corresponding mode disappears from the spectrum, and the first overtone replaces it. The emergence of modes with a vanishing real part at certain critical values of the field mass is a distinctive feature of the CFM spectrum.

The electronic band structure of CaSnN$_2$ in the wurtzite-based $Pna2_1$ structure is calculated using the Quasiparticle Self-consistent (QS)GW$^{BSE}$ method, including ladder diagrams in the screened Coulomb interaction W$^{BSE}$ and is found to have a direct gap of 2.59 eV at Γ, which corresponds to blue light wavelength of 478 nm and makes it an attractive candidate for sustainable blue light-emitting diodes (LEDs), avoiding Ga and In. The valence band splitting is analyzed in terms of symmetry labeling, and the effective mass tensor is calculated for several bands at Γ. The valence band maximum has a1 symmetry and gives allowed transitions to the conduction band minimum for light polarized along the {\bf c}-direction. While this is unfavorable for light emission with transverse electric (TE) or s-polarization from the basal plane, this would not be an impediment if another surface other than the basal plane is used. Furthermore, the crystal field splitting between the $a_1$ and $b_1$ states, corresponding to polarizations along {\bf c} and {\bf a} respectively, reverses under an applied uniaxial tensile strain of 3.7% along the {\bf c} direction, which might occur under biaxial compressive strain in the basal plane. The optical dielectric function, including electron-hole interaction effects is also reported, and the excitons are analyzed, including several dark excitons.