We propose a high-precision phase estimation scheme in a hybrid interferometer by synergistically combining a Kerr nonlinear phase shifter and multi-photon subtraction operations. Using a coherent state and a vacuum state as input resources, we systematically evaluate the phase sensitivity via homodyne detection and analyze the quantum Fisher information as well as the quantum Cramér-Rao bound under both ideal and lossy conditions. Our results show that the joint integration of Kerr nonlinearity and multi-photon subtraction yields remarkable advantages over either technique used alone. The proposed scheme enables the phase sensitivity to surpass the standard quantum limit, exceed the conventional Heisenberg scaling ($1/N$), and approach the super-Heisenberg scaling ($1/N^{2}$)-a direct consequence of Kerr nonlinearity. More precisely, the super-Heisenberg scaling $\propto $ $1/N^{2}$ is the ultimate precision limit permitted by the $k=2$ Kerr nonlinearity and does not violate the fundamental Heisenberg limit for linear phase accumulation. Even under moderate internal photon loss, the system maintains high precision and exhibits enhanced robustness to decoherence. The Kerr nonlinearity introduces an intensity-dependent phase shift proportional to the squared photon number, while multi-photon subtraction tailors non-Gaussian states to strengthen phase information extraction. Compared with existing schemes based on hybrid interferometers or SU(1,1) interferometers, our architecture achieves superior precision and stronger loss resilience. All components are experimentally accessible with current quantum optical technologies. This work provides a promising route for practical high-precision quantum metrology and quantum sensing.

The topology of nanoporous metals is crucial for determining their mechanical response. In this work, we generated 6,000 gold and 422 silver nanoporous structures and calculated three components of elastic modulus with Molecular Dynamics simulations, resulting in 19,263 data points. This study compared two distinct approaches of predicting elastic modulus: a Fully-Connected neural network trained on precomputed topological descriptors, and several 3D Convolutional neural network architectures adapted from computer vision. The 3D CNNs outperformed the descriptor-based baseline model ($R^2 = 0.704$), with to-performing DenseNet-201 architecture achieving $R^2 = 0.955$. Additionally, the effects of training grid resolution, dataset size, and descriptor integration into a model were investigated. We further demonstrated model robustness through Transfer learning: a pretrained model was fine-tuned on a much smaller dataset of denser gold structures and the dataset of denser silver structures. Finally, the trained model was employed to evaluate the mechanical properties of 100,000 stochastic nanoporous gold structures and identify the Pareto optimal designs.

Numerical-relativity simulations with non-trivial matter configurations require initial data that satisfy the Hamiltonian and momentum constraints of the Einstein equations. We construct constraint-satisfying scalar-field initial data using the eXtended Conformally Flat Condition (XCFC) formalism, in which the matter variables are conformally rescaled and an auxiliary vector field is introduced. In doing so, we overcome the issues of local uniqueness and convergence of the solutions that arise in the second-order elliptic equations associated with the constraints. Using an iterative solver method, we demonstrate the convergence of the XCFC approach to a solution for several scalar-field matter systems. Those include Gaussian-like profiles, topological torus configurations, and equal-mass boson star binaries. In particular, for the latter case, it is common to employ the superposition of two isolated boson star solutions in order to build the initial data. We show that our formalism significantly improves upon a superposition approach by generating genuinely constraint-satisfying initial data for boson star binaries.

Using JWST observations in CANDELS fields, we measure the half-light radius ($r_{\rm e,light}$) and half-mass radius ($r_{\rm e,mass}$) for 14,333 galaxies with stellar masses $M_* > 10^9 M_\odot$ at redshifts $0.2 < z < 2.5$. To investigate the difference between $r_{\rm e,light}$ and $r_{\rm e,mass}$, we find that $r_{\rm e,light}$ is larger than $r_{\rm e,mass}$ for both quiescent galaxies (QGs) and star-forming galaxies (SFGs). Moreover, the difference between these two radii is clearly correlated with galaxy stellar mass, $r_{\rm e,light}$, and the rest-frame $U - V$ color. When examining the evolution of the $r_{\rm e,mass}/r_{\rm e,light}$ ratio, we observe a significant increase for SFGs at $z > 1.7$. In contrast, no clear increase is observed for QGs at $z > 1$, though a slight decreasing trend is seen between $0.2 < z < 1.0$. By fitting a linear relationship between galaxy size and stellar mass, we find that the slope for $r_{\rm e,light}$ is $\sim$ 0.1 to 0.3 dex larger than that for $r_{\rm e,mass}$. In terms of galaxy size evolution at a fixed stellar mass, the $r_{\rm e,mass}$ of QGs increases by a factor of $\sim$ 3 to 5 from $z \sim 2.5$ to $z \sim 0.2$. In contrast, the $r_{\rm e,mass}$ of SFGs increases by a factor of approximately 2 over the same redshift range, with this growth trend closely following that of their $r_{\rm e,light}$. These results indicate that previous insights into galaxy evolution based on $r_{\rm e,light}$ remain valid when considering $r_{\rm e,mass}$, although the specific slopes show some variations.

Context: Galaxy morphology is a fundamental property to describe galaxy evolution. However, the observed morphology of a particular galaxy may depend on the observed wavelength. Aims: Our aim is to investigate the wavelength dependence and the effect of dust attenuation on nonparametric morphology indicators. Methods: We use the TNG50-SKIRT Atlas, an atlas of synthetic UV to near-infrared (NIR) broadband images for a complete stellar-mass-selected sample of 1154 galaxies extracted from the TNG50 cosmological simulation at $z = 0$. For each image, we calculate four nonparametric morphology indicators using the StatMorph code. Results: We find that the known correlations between the stellar mass and the morphological parameters measured in the optical, together with the Gini-$M_{20}$, concentration-Gini, and concentration-$M_{20}$ planes, are fully consistent with observational data. However, nonparametric morphological indicators change significantly with wavelength and that this wavelength dependence is stronger for disc-dominated than for bulge-dominated galaxies. The wavelength dependence of the morphology of our simulated TNG50 galaxies is consistent with measurements of local galaxies from the SINGS survey. We demonstrate that the effect of dust attenuation on nonparametric morphology indicators is modest across the full galaxy population but can be significant for individual galaxies.

We present the Matlab toolbox MacaulayLab, which implements numerical linear algebra algorithms for solving multivariate polynomial systems and rectangular multiparameter eigenvalue problems. Its structure and functionality are the result of several years of research and algorithmic development. We demonstrate how the software works and compare its performance with other software packages, such as PNLA, PHCpack, and MultiParEig. Some core features of MacaulayLab are the fact that it solves two key problems via one common approach, works independently of the chosen polynomial basis and monomial order, and is capable of dealing with positive-dimensional solution sets at infinity. The toolbox (including its future updates) and a large collection of test problems are freely available online.

Selective adsorption in a two-dimensional model of a binary hard-disk mixture on patterned adhesive surfaces is studied using grand canonical Monte Carlo simulations. The two species have equal diameters and equal bulk chemical potentials, but different attraction strengths to adhesive domains. Thus, affinity-driven selectivity is separated from particle-size asymmetry and unequal chemical potentials. The surface pattern is defined by domain size, domain surface coverage, and ordered or disordered arrangement of circular domains. The results show that selectivity depends strongly on surface geometry, especially at low and intermediate chemical potentials. Domains comparable to the particle size enhance selectivity by forming adsorption regions with large particle-domain overlap, whereas larger domains can provide high selectivity at low chemical potentials. For small domains, further reduction in size can also increase selectivity as the system approaches a uniform attractive surface with corresponding effective affinity parameters of the species.

Large underwater telescopes have been proposed as a challenging method to measure high energy neutrinos from astrophysical objects. In recent years, The Antares collaboration has designed and realized the first detector of this type in the Mediterranean Sea. Muon tracks produced by the neutrino interaction in the surrounding medium are reconstructed from the arrival time and the number of photo-electrons of the Cherenkov light measured by the Photomultiplier tubes (PMT) array of the detector. In order to provide sufficient statistics, the events from various periods in the year must be summed together taking care of the various environmental conditions and detector configurations. In this note we describe effective criteria to group compatible runs based on the effective number of active PMTs in each run.

We study two new parameters for finite posets motivated by the problem of efficiently determining the set of successors of a given element. A plane map of a poset $P=(X,\leq)$ is an injective mapping of $X$ into the Cartesian plane $\mathbb{R}^2$. Given two different points $a$ and $b$ in the plane, we say that $b$ dominates $a$ if $a<b$ coordinatewise. We say that an element $x$ of $P$ is tight in a plane map $μ$ if the following holds: $x<y$ in $P$ if and only if $μ(y)$ dominates $μ(x)$. Note that, by definition, every 2-dimensional poset admits a map such that every element of the poset is tight. For any poset $P$, we define the mapability of $P$, $\mathrm{dmap}(P)$, to be the maximum number of elements that are tight in a single map, and we define the atlas thickness of $P$, $\mathrm{at}(P)$, to be the size of the smallest collection of maps such that every element is tight in at least one map of the collection. We relate these parameters to the classical notions of dimension and width: for every poset $P$, we show that $\mathrm{dim}(P) \le 2\mathrm{at}(P) \le \mathrm{width}(P)+1$. On the other hand, there exists a sequence of posets $(P_n)_{n \ge 1}$ such that the atlas thickness of $P_n$ is doubly exponential in the dimension of $P_n$. On the computational side, we prove that it is NP-complete, for a given poset $P$, to compute the mapability of $P$ and to decide whether $\mathrm{at}(P) \le 2$. In contrast to the latter, we show that computing the mapability of a poset is fixed-parameter tractable with respect to the natural parameter.

This paper presents a Markov-chain-based method for the early-phase analysis and design of hybrid spare-management architectures for large-scale satellite constellations.} The hybrid strategy combines two channels: an indirect path that stages spares in parking orbits via heavy launch for later transfer to constellation planes, and a direct path that delivers spares to in-plane orbits using small launch vehicles. {To assess the long-run viability of such concepts of operations, satellite failure and replenishment processes are modeled as a Markov chain:} the indirect channel follows a periodic-review reorder-point/order-quantity policy, while the direct channel uses a standard reorder-point/order-quantity policy. These coupled chains yield a periodic steady state over the right ascension of the ascending node cycle via fixed-point iteration, and the stationary distributions provide rigorous cost and resilience metrics. By directly modeling the stochastic, multi-echelon dynamics governed by orbital mechanics, our framework avoids the aggregation assumptions of prior works and remains valid across a wider operating domain. We also introduce an approximate analysis that preserves delay statistics while significantly reducing model size. Building on this fast, accurate analysis, we formulate a cost minimization problem with resilience constraints and solve it using a genetic algorithm. The framework is channel-neutral; the optimization autonomously selects the preferred path and roles. {A case study validates the analysis against Monte Carlo simulations and demonstrates the practical value of the framework in identifying the conditions under which the hybrid policy outperforms pure strategies.

We conduct a systematic robustness analysis of the unsupervised machine learning module within the hybrid framework \texttt{USmorph}. This module automatically discovers morphological structures from large-scale galaxy images, forming the foundation of the complete classification workflow. We evaluate five pre-trained models for feature extraction and identify an ImageNet-pretrained AlexNet as the most effective for capturing discriminative morphological features. UMAP is chosen for dimensionality reduction due to its optimal balance between preserving high-dimensional structure and computational efficiency. To enhance clustering stability, we propose a Bagging-based multi-cluster voting scheme, which significantly improves label consistency and cluster purity. We compare the convergence, scalability, and quality of five clustering algorithms, finding that the Bagging voting scheme has the best performance with the combination of K-means, Birch, and Agg. A bagging clustering number of $K=16$ is used to achieve the optimal balance between classification granularity and manual validation efficiency. Our tests show that: (1) the t-distributed stochastic neighbor embedding (t-SNE) reveals clear, compact cluster boundaries in low-dimensional space with strong feature separability; (2) the morphology classification results align with galaxy evolution theory, showing physically plausible distributions of different types in parameter space. These results demonstrate the technical robustness and scientific credibility of \texttt{USmorph}, establishing it as a reliable method for automated morphological classification in future large-scale surveys such as the China Space Station Telescope (CSST) mission.

Xenon is of high chemical-physical stability and health compatibility. The xenon triple point (Xe TP) is accounted for a promising candidate replacing the mercury triple point (Hg TP) from the set of the defining fixed points of the international temperature scale ITS-90. The success of the alternative highly depends on the level of the realization of the Xe TP using long-stem standard platinum resistance thermometers (LSPRTs). We report in this article our study on the development of an immersion-type Xe TP apparatus, which is suitable for calibration of both LSPRTs and capsule standard platinum resistance thermometers (CSPRT). We realize the melting plateaus of the Xe TP using the continuous heating method on the apparatus. The effective melting plateaus extend for 8-12 hours long with temperature flatness range of 0.37 mK-1.0 mK over the melted fractions from 0.2 to 0.75. We find the axial heat leak contributing a principal effect influencing measurements of the Xe TP. We investigate the effect by varying the offset temperatures on the outer wall of the Xe TP cell. We measure the Xe TP using two LSPRTs upon correction of the axial heat leak. The new measurement, giving the Xe TP of 161.405 71 (55) K (k=1) at the melted fraction F=1.0, agrees well with those previously obtained by the adiabatic apparatuses. Their differences fall within 0.11 mK to 0.42 mK. by. Those differences are well covered by the estimated measurement uncertainty.

Novel excitonic phenomena emerging in transition metal dichalcogenide (TMDC) heterostructures belong to the most exciting topics in contemporary physics of van der Waals materials. Interlayer excitons (IXs) stand out among those due to their long radiative lifetimes and tunability by electric fields, strain, and twist angle. However, many ambiguities persist in the optical identification and manipulation of IXs, highlighting the need for reliable spectroscopic criteria that distinguish interlayer species from spurious signals. Here, we present a decision-tree protocol that evaluates interlayer coupling via intralayer exciton quenching and correlates photoluminescence (PL) with atomic force microscopy (AFM) to correctly assign room-temperature PL features in TMDC-based heterostructures. Applying this protocol, we identify momentum-direct IX between the K valleys of the two layers (KK-IX) in MoS2-MoSe2 and MoS2-WSe2 heterostructures at room temperature. In contrast, our protocol contests the reported bright, momentum-indirect, twist-angle-independent $Γ$K-IX in MoS2-WSe2. Comprehensive experimental data, including infrared and tip-enhanced photoluminescence (TEPL) with sub-diffraction-limited resolution, show no compelling evidence for this excitonic species, despite numerous reports. Instead, the spectroscopic features previously assigned to this $Γ$K-IX originate from locally strained WSe2 at topographical inhomogeneities of the heterostructure interface, underscoring the need for robust, spatially resolved characterization of real-world samples in this highly accessible field and providing a generally applicable framework for identifying interlayer excitons in 2D semiconductor heterostructures.

Incoherent photonic neural networks (PNNs) provide a robust platform for analog optical computing, yet efficient implementation of native signed operations remains challenging. Existing incoherent PNNs approaches often require additional spatial channels or temporal encoding steps to represent bipolar input signals, resulting in hardware overhead that scales with system size. Here, we demonstrate a dual-wavelength incoherent photonic architecture that natively supports both signed inputs and signed weights on a thin-film lithium niobate platform. By encoding complementary signal components onto two wavelength channels and performing computation within a shared physical path, the proposed scheme eliminates duplicated weighting units. As a result, the additional hardware overhead associated with signed computation remains constant per multiply accumulate operation, independent of matrix size. The fabricated device exhibits a modulation bandwidth exceeding 40 GHz and achieves four-quadrant optical multiplication with a standard deviation error of 1.27%. System-level functionality is validated through neural-network classification, achieving 95.1% accuracy on the Moons dataset and 91.63% on MNIST. These results establish a practical route toward scalable incoherent photonic computing systems with native bipolar processing capability.

Next-generation solar spectrographs increasingly record dense wavelength windows in which tens to hundreds of spectral lines are sampled at each spatial location and time step. This expands the scope for multi-line, multi-height diagnostics of magnetohydrodynamic motions, but also raises a practical challenge: deriving stable line-core intensity and line-of-sight velocity time series when profiles evolve rapidly, become asymmetric, blend, or develop multi-lobed cores. Common fast estimators can perform well for simple, isolated absorption lines, yet can intermittently misidentify the core in crowded or morphologically complex cases. Even infrequent mis-tracking can leave step-like artefacts that redistribute power and bias spectral, phase, and coherence measures used in wave and dynamics analyses. We introduce LineFit, a fully reproducible adaptive multi-line fitting approach tailored to dense-window spectroscopy. LineFit models each line locally with bounded non-linear least-squares fits to a Voigt-family profile, including an asymmetric-Voigt option to accommodate unequal wing broadening, and incorporates close-pair ownership control together with conservative, per-line window adaptation and split-core-aware handling. Using a synthetic time series with unambiguous ground truth, we benchmark LineFit against four widely used fast baselines and assess both instantaneous centre errors and downstream time-series diagnostics. Several fast methods remain competitive for many lines, whereas LineFit is most robust in key stress cases involving intermittently split-core profiles and correspondingly yields power spectra that agree most closely with the truth. We also demonstrate a proof-of-principle that benchmarks hybrid acceleration of the LineFit software via supervised emulation, offering at least three orders-of-magnitude improvement in processing time.

Testing the unitarity of the lepton mixing matrix, in a manner analogous to the unitarity tests of the CKM matrix in the quark sector, is an important step toward probing physics beyond the standard three-generation framework. In long baseline neutrino oscillation experiments, the formula of the oscillation probabilities can be written as a sum of terms with various combinations of the mixing-matrix elements, and their coefficients depend differently on energy. By observing the spectral information of long baseline experiments such as T2HK and a future neutrino factory at J-PARC with a $ν_e$ beam, the elements of the mixing matrix can be extracted without assuming a specific parametrization of the mixing matrix. We investigate how such an extraction method can be applied to neutrino oscillations by taking into account matter effects, and discuss how one can test unitarity of the mixing matrix in future long baseline experiments. As a concrete example, we examine the unitarity test by using a four-generation model, where we look at a quantity which should be vanishing in a unitary model. Among possible combinations of measurements, the most powerful test can be provided from the energy spectra of the CP-conjugate appearance channels $ν_μ\to ν_e$ and $\barν_μ\to \barν_e$ at T2HK, as well as from the T-conjugate pair $ν_μ\to ν_e$ and $ν_e \to ν_μ$ available at neutrino factories.

Photoinduced force microscopy (PiFM) enables nanoscale visualization of optical responses by directly detecting photoinduced forces without relying on luminescence. In molecular assemblies, intermolecular polarization coupling can generate collective excitation modes and chiral optical responses that are absent in isolated molecules. In this study, we theoretically investigate PiFM images of ZnPc molecular assemblies using the discrete dipole approximation combined with nonlocal molecular susceptibilities. Under linearly polarized illumination, bonding and antibonding polarization-coupling modes are found to produce characteristic spatial distributions in both the optical force spectra and PiFM images of molecular dimers and tetramers. Furthermore, under circularly polarized illumination, intermolecular coupling and asymmetric molecular packing generate enhanced local circular dichroism distributions characterized by large asymmetric factors and spatially varying chiral contrasts. These results demonstrate that PiFM can spatially resolve collective polarization modes and local chiral optical responses in molecular assemblies, providing insight into nanoscale intermolecular optical interactions.

In this paper, we first confirm the Hamilton-Tian conjecture for the Sasaki-Ricci flow in a compact transverse Fano quasi-regular Sasakian $5$-manifold with klt foliation singularities. Secondly, we derive the compactness theorem of Sasaki-Ricci solitons on transverse Fano quasi-regular Sasakian $5$-manifolds. Then,by the second Sasakian structure theorem, we confirm the Hamilton-Tian conjecture for a compact transverse Fano Sasakian $5$-manifold. With its applications, we show that the gradient Sasaki-Ricci soliton orbifold metric on a compact Sasakian $5$-manifold is Sasaki-Einstein if $M$ is transverse $K$-stable.

By solving algebraic relations for the conditions of Haantjes structure on a Lie algebra ${\G}$ and by using the corresponding automorphism group we proceed to classify all inequivalent algebraic Haantjes structures on ${\G}$. In this manner, we obtain 34 inequivalent algebraic Haantjes structures on the ${h_{4}}$ Lie algebra. We deform the chiral sigma model on a Lie group by using Haantjes structure on it. Then we try to obtain conditions on this structure such that the deformed sigma model remains to be integrable. Finally, using the ${h_{4}}$ Haantjes structures and solving this conditions three new integrable sigma models on the ${H_{4}}$ Lie group are obtained.

Operations Research (OR) serves as a core decision-support methodology for complex systems, with significant applications across mathematics, management science, and computer science. Traditional approaches heavily rely on expert knowledge and often struggle to efficiently solve large-scale and multi-constraint problems. The rapid advancement of Large Language Models (LLMs) in recent years has offered a novel research paradigm to address these challenges. This paper presents a systematic survey of Large Language Models for Operations Research (LLM4OR). We begin by introducing the definition of OR problems and the fundamental principles of LLMs. We then focus on analyzing the roles of LLMs in OR, specifically covering such as model formulation, algorithm design, and solution verification. In addition, we discuss practical applications in representative scenarios and summarize benchmark datasets in this field. Finally, we outline the key challenges and provide perspectives on future research directions. A collection of related literature is available at https://github.com/xianchaoxiu/LLM4OR.

Identifying the regions responsible for plastic flow in amorphous solids remains an open problem, since structural disorder seems to prevent the direct application of concepts such as dislocations, topological defects that successfully describe irreversible deformations in crystalline systems. Here, we introduce fields of dislocation, disclination, and incompatibility densities, that reduce to the standard sources of plasticity in crystals and assess their predictive power in amorphous materials. We find that, in a simulated two-dimensional glass as well in two- and three-dimensional experimental granular systems, these fields exhibit strong spatial correlations with $D^2_{\text{min}}$, the standard measure used to locate plastic events under shear in disordered solids. Unlike $D^2_{\text{min}}$, these fields also allow to disentangle rotational and translational contributions to the plastic events, revealing that rotational defects becoming dominant in three dimensions. Our approach paves the way for a unified description of plasticity in crystalline and amorphous solids.

We give two presentations for bordisms of $S^2$ in the 3-dimensional oriented bordism category $\operatorname{Cob}(3) $, encoding the algebraic structures on $S^2$. After passing through topological field theories, we define two kinds of monoids which we call P-monoids and L-monoids. In addition to both being commutative Frobenius monoids, P-monoids are equipped with a class of endomorphisms while L-monoids are equipped with a class of unit morphisms, all of which are labelled by closed oriented irreducible prime 3-manifolds. They turn out to be equivalent. The new prime structures satisfy some countable relations with the commutative Frobenius structure, the most notable of which we call "legs relations." We then restrict to the setting of algebras and show that the legs relations place strong constraints on the new prime endomorphisms which forces them to act by multiplications by prime units, rendering the additional prime structures remarkably simple. We also propose an $\infty$-operad which encodes these prime structures and contains the $\infty$-little 3-cube operad as a sub-operad.% We briefly discuss the relations between P/L-algebras and J-algebras which classify 3-dimensional TFTs.

We study the $2\frac12$-dimensional electron magnetohydrodynamics (EMHD) system on $\mathbb T^2$ with componentwise fractional dissipation: $\partial_t a+a_yb_x-a_xb_y=-Λ^αa$ and $\partial_t b-a_yΔa_x+a_xΔa_y=-Λ^βb$, where $0<α,β<2$. This system is a $2\frac12$-dimensional reduction of the magnetic equation in Hall--MHD/EMHD under the ansatz $B=\nabla\times(ae_z)+be_z$. We prove local well-posedness for initial data $(a_0,b_0)\in H^{s+1}(\mathbb T^2)\times H^s(\mathbb T^2)$ with $s\geq 2-\varepsilon$, provided that $α+β>2$. Thus neither component is required to carry a full Laplacian dissipation; the smoothing effects of the two fractional dissipations can be combined to control the Hall nonlinearity. The proof is based on Littlewood--Paley energy estimates, commutator bounds, and cancellations between the leading low--high interactions.

It is proved by L.~Schneps that the double shuffle Lie algebra $\mathfrak{dmr}_0$ injects to the Kashiwara-Vergne Lie algebra $\mathfrak{krv}_2$ in \cite{Schneps2012,Schneps2025}. We show that $\mathfrak{dmr}_0$ with the infinitesimal hexagon equation $[x,φ(-x,-y,x)]+[y,φ(-x-y,y)]=0$ injects to the symmetric Kashiwara-Vergne Lie algebra $\mathfrak{krv}^{\mathrm{sym}}_2$. The proof is based on the inclusion of brunnian braids group on different genus 0 surfaces which is different from the method of mould calculus in \cite{Schneps2012,Schneps2025}. We generalize the inclusion in two directions, one using lower central series of brunnian Lie algebras and the other is to establish explicit links between the pentagon equation map, the stuffle coproduct, the divergence map and the necklace cobracket.

We conducted an analysis of gamma-ray variability in a large sample of jetted active galactic nuclei (AGNs) by utilizing archival Fermi-LAT light curves and applying damped random walk modeling to obtain variability amplitude. Our primary findings are summarized as follows: (1) The mean variability damping timescales of our sources are approximately 100 days. This damping timescale may imply that the diffusive shock acceleration plays an important role in the variability of gamma-ray emission. (2) Flat-spectrum radio quasars (FSRQs) demonstrate greater variability amplitude compared to BL Lacertae objects (BL Lacs). (3) The ratio of the distance of the emission region from the central supermassive black hole to the dusty torus radius for our sources is $R\approx2-4.5R_{\rm DT}$. In contrast, the ratio of the distance of the emission region from the central supermassive black hole to the BLR radius for our sources is $R\approx135-295R_{\rm BLR-in}$ and $R\approx123-270R_{\rm BLR-out}$. These findings indicate that the $γ$-ray emission region in jetted AGNs is likely located beyond the BLR, potentially could be associated with the dusty torus. (4) A statistical correlation is observed between variability amplitude and radio luminosity, radio loudness, X-ray luminosity, X-ray loudness, gamma-ray luminosity, and gamma-ray loudness, indicating a potential relationship between gamma-ray variability and jet activity. (5) Variability amplitude also shows a statistical correlations with synchrotron peak frequency luminosity, inverse Compton peak frequency luminosity, and Compton dominance. (6) Variability amplitude also correlates with black hole mass, accretion disk luminosity, and Eddington ratio, implying that the accretion disk may also contribute to gamma-ray variability.

In this paper, we discuss the 2D convection-diffusion-reaction equation with variable smooth coefficients and the Dirichlet boundary condition on a complicated, thin, and curved domain. We propose the fourth-order compact FDM at every grid point with the uniform Cartesian mesh. For the regular stencil center, we utilize the fourth-order compact 9-point FDM to approximate the solution. According to the preliminary analysis, we use vertical and horizontal transformations to derive fourth-order compact FDMs in 10 cases for all irregular stencil centers. To obtain the left-hand side of the stencil of the fourth-order FDM in each case, we only need to solve an at most $6 \times 24$ linear system which is presented with the explicit formula. The right-hand side of the FDM is constructed in explicit expression for any irregular stencil centers too. To achieve the fourth-order consistency, up to second-order partial derivatives of convection, diffusion, reaction, and source terms are used for the FDM at the regular stencil center, and the FDM at an irregular stencil center only requires first-order partial derivatives of convection, diffusion, reaction, and source terms, and up to third-order derivatives of the Dirichlet boundary function and the parametric expression of the boundary curve. We test challenging domains with 100-leaf, high-curvature, high-frequency, sharply varying, and nearly overlapping boundary curves, the proposed FDM produces the high accuracy and the stable fourth-order convergence rate in $l_2$ and $l_{\infty}$ norms. All stencils of our FDMs have a simple desired structure by only keeping grid points inside $Ω$ in the standard compact 9-point stencil for both regular stencils and boundary stencils, but without assuming any information outside the domain $Ω$.

There exist initial segments of both the Dyment lattice and the Dyment-Muchnik lattice that yield Brouwer algebras modeling exactly the intuitionistic propositional calculus. For the Dyment-Muchnik lattice, this result is obtained by constructing a splitting class of enumeration degrees. In contrast, the full Dyment lattice and the full Dyment-Muchnik lattice model the intuitionistic propositional calculus plus the weak law of excluded middle. We also observe that certain naturally definable classes of enumeration degrees, which are downwards closed under enumeration reducibility, fail to form splitting classes.

In a classical paper [20] in 2000, Lutwak-Yang-Zhang established the $L^p$ analog of the Petty projection inequality and the $L^p$ analog of the Busemann-Petty centroid inequality. In Section 7 of [20], Lutwak-Yang-Zhang proposed the important $L^p$ projection centroid conjecture. We give a positive solution to the $L^p$ projection centroid conjecture in this work.

Time-modulated systems have received growing interest in recent years. They allow us to tailor effects, such as frequency conversion, single-direction propagation, etc. For the microwave band, semiconductor elements, such as varactors, are usually used as time-modulated elements but their modulation frequency has been limited to the few-gigahertz range. Recent advances in nanoplasma switches, i.e., two-state electronic switches based on a gas discharge in a nanometer-scale gap, provide a new potential for developing time-modulated systems with high operating frequencies. Here, we develop an analytical framework based on the time-Floquet method for the design of nonreciprocal time-modulated devices based on two-state time-modulated elements, for instance, nanoplasma-based switches. A practical example of a microwave isolator operating at 100~GHz frequency is developed and studied both analytically and using full-wave simulations. A potential realization in a parallel-plate waveguide is also simulated numerically.

Stars are thought to form predominantly within filamentary molecular clouds. Recent studies have suggested that active star formation, including the formation of stellar clusters and massive stars, occurs within so-called "hub" structures, where multiple filaments converge. Understanding the formation and evolution of such hub-filament systems is therefore essential for unveiling the physical processes responsible for cluster and massive star formation, although the full picture remains incomplete. To address this, we have focused on filament-filament collisions as a potential formation mechanism of the hubs. In this study, we investigate the fundamental evolutionary processes of oblique collisions between two magnetized filaments using three-dimensional ideal magnetohydrodynamical simulations. As a model of initial filaments, we consider two identical finite-length magnetized filaments, varying the collision angle between their long axes, the collision velocity, which is set perpendicular to the long axes, and the initial line mass. We find that as the collision angle decreases from orthogonal to parallel, the compressed cloud becomes more prone to gravitational collapse. In addition, the instability of the post-collision compressed cloud can be explained by its energy balance. Specifically, if the absolute value of the gravitational energy exceeds the sum of the kinetic, thermal, and magnetic energies immediately after the collision, the cloud undergoes gravitational collapse. Conversely, if the gravitational energy is smaller, the cloud expands. In addition, we estimate the upper limit of the collision velocity that enables hub-filament formation and identify the collision conditions favorable for massive star formation.