Single crystals of \ce{AgInCr4S8} were grown by chemical vapor transport and crystallographic ordering of Ag/In that results in a breathing pyrochlore motif of Cr$^{3+}$ was verified by x-ray and neutron diffraction. Long-range antiferromagnetic order is observed below a Néel temperature of $T_{\mathrm N}$ $\approx$ 9.6 K. The magnetic properties are characterized using ac and dc magnetization, specific heat capacity, and single crystal neutron diffraction measurements. The specific heat data are characterized by a small lambda anomaly near 9.5 K and the estimated magnetic entropy reaches $\approx$ $\frac{1}{3}$ of the expected value by 3$T_{\mathrm N}$, suggesting significant short-range order in the paramagnetic phase. Single crystal neutron diffraction evidences an incommensurate spin structure with propagation vector $\textbf{\textit{k}}$ = (0,0,$δ$) and $δ$ = 0.343 at 5 K. The minimal model that accounts for the data consists of ferromagnetic layers of Cr atoms, with magnetic moments lying in the plane of the layers and modulating in the perpendicular direction to form a helical structure propagating along $\textbf{\textit{k}}$. This study represents a rare investigation of single crystals within the family of breathing pyrochlore materials.

Within the framework of QCD sum rules, we investigate hidden-heavy tetraquark states with the exotic quantum number $J^{PC}=0^{--}$ in color-octet configurations, namely $[Q\bar q]_{8_c}\otimes[q\bar Q]_{8_c}$ and $[Q\bar Q]_{8_c}\otimes[\bar q q]_{8_c}$ with $Q=c,b$. Since the $0^{--}$ quantum number cannot be realized by conventional $q\bar q$ mesons, the observation of such a state would provide a particularly clean signal for exotic hadronic structures. We construct four color-octet interpolating currents for the hidden-heavy systems and carry out the operator product expansion up to dimension-eight condensates. Our numerical analysis indicates that the hidden-bottom sector exhibits the clearest sum-rule stability, with flatter Borel platforms than the corresponding hidden-charm sector. We obtain four $0^{--}$ hidden-bottom tetraquark candidates in the mass range $10.8$--$11.1~\mathrm{GeV}$, while their hidden-charm partners are predicted around $4.3$--$4.6~\mathrm{GeV}$. The extracted masses suggest a compact spectral pattern with a mild dependence on the underlying color-octet clustering structure. We also discuss possible decay patterns and emphasize that the absence of the lowest pseudoscalar--pseudoscalar heavy-meson channels is a distinctive consequence of the exotic $0^{--}$ assignment. These results provide useful theoretical guidance for future searches for hidden-heavy exotic states at Belle II and LHCb, with complementary probes of the hidden-charm partners at BESIII.

Reset systems can overcome fundamental limitations of linear time-invariant control. The recently introduced notion of scaled (relative) graphs provides a promising framework for developing graphical analysis and design tools for reset systems, in line with widely adopted loopshaping methods for linear systems. The aim of this paper is to derive techniques for over-bounding the scaled graph of reset systems, and obtain insights in their accuracy. We exploit connections between quadratic dissipativity and scaled graphs to recast the over-bounding problem as the search for piecewise quadratic storage functions. Using specific sampling techniques, we reveal a fundamental limitation of general scaled graph approximation methods that are based on quadratic dissipativity.

We study an Arrow-Debreu economy with externalities generated by multiplex networks. Market equilibrium prices reflect both the preferences and scarcity of goods, consumers' network centralities arising from goods' externalities, as well as linkages across goods (layers) through the budget constraint. Despite the presence of externalities, competitive markets can still be efficient: the First and Second Welfare Theorems hold if either all networks are regular or all layers share the same network structure. When markets allocate goods inefficiently, a Lindahl equilibrium-implemented through personalized prices-can restore efficiency, but may leave some consumers worse off.

Existing Synthetic Aperture Radar (SAR) image generation methods still lack reliable controllability over key imaging parameters, particularly azimuth angle, depression angle, and polarization mode. Our preliminary GeoDiff-SAR supported limited azimuth completion, but remained ineffective for large missing azimuth sectors and did not provide unified control over multiple imaging conditions. To address this problem, we propose GeoDiff-SAR II, a 3D model-guided decoupled framework for controllable SAR image generation. The proposed framework imposes controllability through physically grounded geometric-electromagnetic cues rather than image intensity alone. We introduce a Geometric-Electromagnetic Conditioning Map (GECM), a structured intermediate representation that encodes the target pose map and dominant scattering centers, thereby decoupling macroscopic geometry from microscopic scattering responses. During training, GECMs are derived from real sparse-azimuth SAR images. During inference, the same representation is rendered directly from a 3D CAD model under specified azimuth, depression angle, and polarization conditions, enabling physically consistent control across large viewpoint gaps. The imaging parameters are further converted into text conditions, while the GECM is injected through ControlNet to provide explicit spatial guidance. Combined with Low-Rank Adaptation (LoRA) on a FLUX backbone, the proposed framework unifies geometric-electromagnetic conditioning and parameter-aware generation within a single process. Experiments on simulated and real datasets demonstrate controllable generation over key SAR imaging parameters, stable generalization across large azimuth gaps, and consistent improvements in image fidelity, physical consistency, and downstream Automatic Target Recognition (ATR) performance.

The far-field emission of large-area vertical-cavity surface-emitting lasers (VCSELs) is commonly associated with multimode, high-divergence beam profiles, limiting applicability in high-brightness free-space systems. We investigate angular emission characteristics of a 1 mm-diameter ring-aperture watt-class VCSEL and establish a theoretical framework capturing the formation of its far-field radiation patterns. Modeling the near field as an azimuthally modulated ring distribution and evaluating the far field within the Fresnel approximation, we demonstrate that a quasi-Gaussian far-field profile emerges from combined lower-order azimuthal modes, even in a highly multimode cavity. Experimentally, we observe a current-driven transition of the far-field distribution from a high-divergence ring at low injection levels to a narrow central beam at elevated currents. At high drive currents, the emission approaches a near-Gaussian profile with a full width at half maximum of 8°, while maintaining watt-class output power. Angle-resolved spectroscopy associates the central emission with longer-wavelength, lower-order modes, whereas the outer ring originates from shorter-wavelength, higher-order contributions. Combined with electroluminescence measurements and wavelength-dependent photon lifetime analysis, these results demonstrate that spectral and angular emission are determined by the interplay between wavelength-dependent material gain and angle-dependent cavity losses. This approach establishes a general framework for controlling beam divergence and modal content in large-area VCSELs, enabling high-power operation with near-Gaussian, low-divergence beam profiles.

When multiple electron temperature diagnostics converge on the same value, the standard inference is that the measurement is robust. We show that this convergence is a structural consequence of the shared ionization bottleneck in any plasma where the electron Knudsen number exceeds $\sim 0.01$: all diagnostics downstream of collisional ionization report the effective temperature $T_{\rm eff}$, not the core temperature $T_{\rm core}$. Their agreement is a single measurement reported $N$ times. We introduce a taxonomy: Type A (ionization-gated, $T_{\rm eff}$), Type B (bulk-sampling, $T_{\rm core}$), Type C (distribution-resolving). The ratio $R = T_A/T_B$ yields $κ= 3R/[2(R-1)]$ directly. Applied to the solar corona ($R = 2.4$, $κ\approx 2.5$) and the tokamak scrape-off layer, single kappa distributions ($κ\approx 2$--$10$) reproduce published bi-Maxwellian EEDF decompositions to 3--8\% RMS with one fewer parameter, and Thomson scattering confirms the predicted Type B temperature. We test applicability in planetary nebulae (the 80-year CEL--ORL abundance discrepancy). Knudsen calculations with the Shoub $v^4$ mean-free-path scaling show ionizing electrons are collisionless in the corona even when the bulk is fluid; in PNe, both ionizing ($\sim 55$ eV) and excitation ($\sim 5$ eV) electrons are collisional over nebular scales, identifying PNe as the falsification boundary; in the SOL, non-local parallel transport maintains tails even where local collisionality is high. For $κ\approx 3$--$5$, the raw Spitzer--Härm formula with spectroscopic $T_e$ overestimates parallel heat flux by factors of 3--25$\times$; flux-limited models inherit the bias through their boundary conditions, relevant to ITER divertor predictions. Every diagnostic campaign on a weakly collisional plasma should include at least one Type B measurement.

We present an information-theoretic assessment of atomic and molecular densities in the ground state and under a range of physical scenarios--excitation, confinement, and ensemblization. Comparisons across densities obtained from single-reference methods are facilitated through information entropy measures evaluated in position space. We demonstrate that the J-divergence serves as a key metric for benchmarking electron densities against coupled cluster and configuration interaction references. Mean-field orbital information is further compared with that of Brueckner and Dyson orbitals, and informational changes in multiple self-consistent-field solutions are examined under various symmetry-breaking conditions. We also explore the relationship between entropic measures of electron delocalization and the accuracy of the CO dipole moment computed with different methods. Our work offers insights into the selection of optimal reference determinants for a given chemical application and highlights potential benefits of incorporating information-entropy concepts in the development of new density functionals.

In our Galaxy, the average star formation efficiency is of the order of a few percent. We investigated the high-latitude molecular cloud MBM12 as part of the B-fields and star formation across scales (B-FROST) survey with the Taeduk Radio Astronomical Observatory (TRAO) to assess why star formation activity in MBM12 is low. We combine {\it Herschel}-based, locally $κ_ν$-calibrated $N$(H$_2$) estimates with $^{12}$CO and $^{13}$CO ($J=1-0$) observations (2.5$^\circ \times$3$^\circ$ at 48$''$) to map $N$(CO), $X$(CO), and [CO/H$_2$], compute multi-scale $α_{\rm vir}$ and mass-size scaling laws from dendrograms, and derive the histogram of relative orientations from {\it Planck} dust polarisation. We identify four main regions based on velocities that have H$_2$ column densities ranging from $2\times10^{20}$ cm$^{-2} - 1.3\times10^{22}$ cm$^{-2}$. The average $X$(CO) is close to the galactic average, with variations below $X_{\rm Gal}$ from collisional de-excitation in low-density gas, and above $X_{\rm Gal}$ from CO photodissociation at cloud edges. The hierarchical structures follow a broken power law mass-size relation $M=AR^α$. The values of $α_{\rm vir}$ ranged from $3-60$, with the smallest values at 0.1 pc scales. The mass-size relations for the structures with the lowest $α_{\rm vir}$ have scaling factors $A$ three times larger than those of high $α_{\rm vir}$ structures, indicating external pressure one order of magnitude larger. We found a transition of parallel to perpendicular between column density structures and magnetic field orientations at $N$(H$_2$) $= 4.5 \times 10^{21}$ cm$^{-2}$. We provide the first integrated chemical, dynamical, and magnetic field analysis of MBM12. Scale-dependent mass-size and virial analysis can further constrain the role of external pressure in regulating the star formation efficiency.

Modern serving systems for Mixture-of-Experts (MoE) models adopt hybrid data-expert parallelism: expert parallelism (EP) shards experts across GPUs to scale capacity, while data parallelism (DP) replicates attention layers across instances to process independent requests. Existing systems bind each request's attention, MoE communication, and KV cache to a single instance. Because attention latency scales with KV cache size while MoE communication latency scales with batch size, this binding cannot balance both simultaneously, producing EP stragglers; it also fragments KV memory across instances, inflating tail latency under long contexts. While existing context parallelism (CP) mitigates these constraints, its uniform parallelism degree incurs prohibitive communication and attention-side overheads. We present \work, which decouples MoE communication from KV cache placement and achieves dual balance through dynamic context parallelism (DCP). DCP assigns each request a context-parallel degree sized to its KV footprint: long requests distribute attention across multiple instances; short requests remain local. This dynamic parallelism effectively liquefies the KV cache across the cluster, balancing both the per-instance KV cache occupancy and batch sizes without unnecessary load-balancing costs. To bridge DCP with static execution, \work introduces an ahead-of-time (AOT) graph engine paired with a custom routing-based communication backend. Experimental results show that \work maintains up to $1.88\times$--$3.27\times$ higher request rates under strict time-per-output-token (TPOT) service level objectives (SLOs). Furthermore, \work significantly mitigates stragglers, reducing P99 tail latency by up to $1.79\times$--$2.12\times$.

In 2008, Dan Romik studied in this journal Primitive Pythagorean Triples, or PPTs. In order to do so, he introduced a modified slow (subtractive) Euclidean algorithm, and showed that the underlying dynamical system of this Euclidean algorithm (the ``Romik system''), is ergodic and has a $σ$-finite, infinite measure, of which is explicitly given. In this paper, the Romik system is further studied. Various basic properties are determined, such as the expansion of rational numbers and quadratic irrationals. Also (a version of) the planar natural extension of the Romik system is obtained, and the $σ$-finite, invariant measure is explicitly given, and it is shown that it is ergodic. Furthermore, for Lebesgue almost every $x$ asymptotically half of the regular continued fraction (RCF) convergents of $x$ are among the Romik convergents. We also show that related to the Romik map a ``strange'' continued fraction can be given. ``Strange,'' as the set of possible partial quotients (i.e., digits) for any $x\in [0,1]$ in this expansion is $\{ 0, \pm 2\}$. Various properties of this ``Romik expansion'' are given.

This paper proposes a joint alignment and denoising method for event-based vision sensors (EVSs). Existing signal processing methods for EVSs typically perform event alignment (EA) and event denoising (ED) as separate modules. However, this separation creates a dilemma: without ED, EA is biased by noise, whereas without EA, ED struggles to distinguish signal events from noise ones. To address this dilemma, we jointly optimize EA and ED by formulating a bi-objective Pareto optimization problem. Our formulation is built upon a contrast map that counts the number of events localized in each pixel. With a contrast map, we can formulate EA as maximizing its variance and ED as minimizing the variance. We cast these two conflicting problems as a Pareto optimization and use a regret strategy to obtain a solution. Experimental results on denoising and motion estimation demonstrate that our method achieves improvements against alternative ones.

Affordances and permissions are promising and timely safety levers for mitigating Loss of Control (LoC) threats in high-stakes deployment contexts, such as national security. Deployers in defense and intelligence could rely on several approaches to identify which affordances and permissions should be prioritized, such as structured threat modelling, pre-deployment agentic evaluations, post-deployment continuous monitoring, and AI safety cases. This paper proposes a complementary and empirical methodology that leverages existing use-case-specific benchmarks: backchaining LoC mitigations from the errors an AI system makes on national security benchmarks. The approach proceeds in three steps and allows national security deployers to start building LoC mitigations today, from evidence they can generate themselves. First, deployers evaluate AI systems on mission-specific benchmarks approximating real use-cases. Second, deployers concentrate on the incorrect responses that the AI system provides to the benchmark questions, and backchain the affordances and permissions that would enable the AI system to cause downstream harm if it pursued the actions described in the incorrect answers. Third, deployers intervene selectively on those affordances and permissions, bottlenecking the paths to harm while preserving the AI system's ability to carry out the correct action. We illustrate this methodology through a demonstrative benchmark question on derivative security classification.

This paper aims to review the diverse range of technosignatures that have been proposed in the literature. We organize the review by scales, starting carefully from Earth, then zooming out to Earth's orbit, the solar system, including the Moon, the Earth-Moon Lagrange points, the inner solar system, the asteroid belt, interstellar objects, the outer solar system, the Kuiper belt, the solar gravitational lens region, and the Oort cloud. We then introduce the Kardashev and Barrow scale before exploring exoplanetary technosignatures, from surface, atmospheric to orbital sources. We next consider stellar technosignatures that may involve massive energy utilization, stellar modification or stellar pollution, and end with a section about compact objects. We then review attempts to detect interstellar communication, and discuss many dimensions of the search space from first principles. Then we consider interstellar travel technosignatures, and end with galactic, extragalactic and universal signatures. We end with a discussion about synergies between biosignatures and technosignatures searches, anomaly detection, multimodal strategies, instruments for detecting technosignatures, how to evaluate and prioritize the search, as well as epistemological issues.

Identifying dark matter candidates that simultaneously generate multiple observable cosmological signatures is a key goal in connecting particle physics with upcoming observations. Axion-like particles coupled to the Standard Model photon offer a promising framework. In the trapped misalignment mechanism, the onset of axion oscillations is delayed, inducing a period of supercooling in the early Universe. This can lead to exponential production of photon quanta via a tachyonic instability, generating observable gravitational wave signatures. Simultaneously, reheating of the Standard Model plasma produces strong, helical magnetic fields on intergalactic scales. The parameter space most promising for gravitational wave detection yields magnetic field strengths that exceed lower bounds from blazar observations.

We investigate the large-space and large-time asymptotic behavior of a soliton gas for the focusing nonlinear Schrödinger equation. The soliton gas is constructed as the continuum limit of pure $N$-soliton solutions as $N\to\infty$, with the discrete spectrum confined to two segments $Σ_1$ and $Σ_2$. In particular, our framework does not require the discrete spectrum to be confined to the imaginary axis. By combining the nonlinear steepest descent method with an appropriate $g$-function mechanism, we show that, as $x\to-\infty$, the soliton gas is asymptotically described by a finite-gap elliptic solution with constant coefficients. In the large-time regime $t\to+\infty$, we assume that the endpoint $F$ lies on the trajectory of $H(ξ)$ with $ξ=\frac{x}{2t}\in(-E_1-\sqrt{2}E_2,-E_1)$, namely, $F=H(\hatξ)$, $\hatξ\in (-E_1-\sqrt{2}E_2,-E_1)$. Under this assumption, we prove that the solution exhibits distinct asymptotic behaviors in different regions of the variable $ξ=\frac{x}{2t}$. More precisely, there exist an exponentially decaying region $ξ\in(-E_1,+\infty)$, a modulated elliptic-wave region $ξ\in(\hatξ,-E_1)$, and an unmodulated elliptic-wave region $ξ\in(-\infty,\hatξ)$.

Enterprise software supply chains are increasingly vulnerable to infrastructure attacks, resulting in financial and reputational damage. Ensuring the integrity and provenance of software artifacts remains a significant challenge, where re-execution of the build and tests by every consumer to guarantee provenance produces a verification bottleneck and credibility reduction. This paper presents an evidence-driven protocol for trustworthy Continuous Integration (CI) pipelines that combines Deterministic Build Systems (DBS) with Trusted Execution Environments (TEEs). The approach provides cryptographically verifiable guarantees of integrity, authenticity, and attestation for CI artifacts in distributed environments, reducing implicit trust without requiring costly re-execution by consumers. We introduce a protocol that binds deterministic builds with TEE-based attestations, formalizing the evidence life cycle, together with a practical implementation using Nix and Intel TDX. Experimental results show that artifact verification is reduced from redundant computation to lightweight signature and policy checks. These findings demonstrate that evidence-driven CI pipelines establish scalable and verifiable trust in digital infrastructure, effectively amortizing the initial computational overhead introduced by TEEs.

In this work, we theoretically investigate the spin-Peltier effect in a heterostructure composed of graphene and a ferromagnetic insulator (FI). Using a microscopic formalism based on the characteristic spin-flip scattering length at the graphene/FI interface, we analyze how spin accumulation in graphene gives rise to a temperature difference across the junction. We show that, in the presence of an external magnetic field, the electronic spectrum of graphene is quantized into Landau levels, which strongly modifies the available spin-flip scattering channels. In particular, crossings between Landau levels significantly enhance the spin-flip scattering amplitude, leading to a pronounced amplification of the spin-Peltier response. Our results suggest that measurements of the spin-induced temperature difference in graphene-FI heterostructures can serve as a sensitive probe of discrete electronic energy levels. More broadly, this work provides a theoretical framework for understanding spin-driven thermal effects in hybrid systems combining Dirac materials and magnetic insulators.

Post-translational modifications (PTMs) play essential roles in regulating protein structure, function, and cellular signalling. However, peptide level discrimination of hydroxylation at the single-molecule level remains difficult. Here, we report a particle-in-pore single-molecule surface-enhanced Raman spectroscopy (SERS) platform combined with peak occurrence frequency (POF) analysis and a one-dimensional convolutional neural network (1D-CNN) for discriminating hydroxylated and non-hydroxylated HIF peptide fragments. Three peptide pairs containing the Pro-564 hydroxylation site, with lengths of 7, 9, and 15 amino acids (AAs), were investigated. POF analysis revealed reproducible hydroxylation-dependent spectral changes in the 7AA and 9AA peptide pairs, which were attributed to changes in adsorption conformation and surface interactions. CNN-based classification achieved post-evaluation accuracies of 72.98%, 78.55%, and 89.74% for the 7AA, 9AA, and 15AA peptide pairs, respectively, with AUC values above 0.80 for all the pairs, indicating a reliable discrimination. Gradient-weighted feature visualization further showed that CNN-sensitive regions overlapped with recurrent POF features, supporting the chemical relevance of the learned classification patterns. Notably, for the 15AA peptide pair, the enhanced citrate-associated band suggests that hydroxylation can substantially alter peptide-gold nanoparticle adsorption behaviour. This adsorption-mediated effect may amplify hydroxylation-induced spectral differences and contribute to the improved discrimination accuracy despite the increased structural complexity. These results demonstrate that the particle-in-pore sensor, assisted by deep learning, can capture hydroxylation-induced spectral and adsorption changes in peptide fragments, providing a promising strategy for ultrasensitive analysis of weak PTM signatures in peptides.

We study two nonlocal versions of the kinetic $p$-Laplace equation: a Gagliardo-type model defined through differences and a Bessel-type model defined via Fourier multiplication. Using critical kinetic trajectories, we derive representation formulas adapted to the kinetic transport-diffusion geometry and establish homogeneous and scale-invariant kinetic Gagliardo-Nirenberg inequalities for nonlocal diffusion, which yield gain-of-integrability estimates for weak solutions to the kinetic $p$-Laplace equations with nonlocal diffusion.

In this paper, we study the complete gradient Ricci solitons $(M^n, g,f)$ with zero radial Weyl curvature, which means that the interior product of $\nabla f$ with the Weyl tensor $W$ is zero, i.e., $i_{\nabla f}W=0$. We classify completely the complete gradient Ricci solitons with zero radial Weyl curvature for the dimension $n\geq 4$.

Galluccio--Loebl and Tesler showed that the perfect-matching polynomial of a graph embedded in an orientable surface of genus $g$ can be written as a linear combination of at most $4^g$ Pfaffians. We show that, in general, exponentially many Pfaffians are necessary. More precisely, among all graphs of orientable genus at most $g$, the maximum possible Pfaffian number is at least $(8/3)^g$. This lower bound holds even for connected matching-covered graphs. We also obtain exponential lower bounds for the Pfaffian number of complete bipartite graphs, and hence for even complete graphs, improving asymptotically on a recent linear lower bound of Junchaya, Lucchesi, and Miranda.

Thin-film lithium niobate (TFLN) electro-optic modulators are attractive for high-speed optical interconnects, but scalable transmitter architectures require not only high modulation bandwidth but also multi-channel optical power distribution and practical laser-to-chip integration. Here, we demonstrate a hybrid-integrated 1 * 8 TFLN electro-optic modulator array passively butt-coupled to a 1550 nm distributed-feedback laser. The chip integrates a three-stage cascaded 1 * 2 multimode-interference splitter, spot-size converters, eight traveling-wave Mach-Zehnder modulators, thermal tuning electrodes, and on-chip 50 Ω terminations. The cascaded splitter provides uniform optical power distribution with a maximum normalized power deviation of 9.7%, while the optimized electrodes enable electro-optic 3 dB bandwidths exceeding 40 GHz for all channels. The measured half-wave voltages are 3.60-3.83 V, corresponding to VπL products of 2.52-2.68 V cm for a 7 mm modulation length, and the extinction ratio reaches approximately 25 dB. The bare-chip insertion loss is 15.19-16.55 dB, and DFB laser bonding introduces an additional coupling loss of approximately 5 dB while preserving channel uniformity. These results establish a practical TFLN-based multi-channel modulator platform and represent a step toward compact hybrid-integrated optical transmitters for high-speed parallel interconnects.

We study the complex property $\partial\partial = 0$ of the boundary operator $\partial$ on a weighted, infinite, and possibly non-locally finite simplicial complex. We give a characterization of this property in $\ell^2$ in terms of the recurrence of the links of simplices. The complex property is essential to ensure that Hodge Laplacians $Δ^H $ indeed act as $δ\partial + \partialδ$ and to decompose $Δ^H$ into a direct sum of operators acting on $k$-forms. Furthermore, it allows us to define relative cohomology classes, show a respective weak Hodge decomposition, and prove the existence of harmonic Dirichlet eigenforms. We also discuss a transience property for simplicial complexes, that was introduced by Parzanchevski and Rosenthal.

The Galactic supernova remnant (SNR) Cygnus Loop emerges as an ideal laboratory for analyzing the different radiation mechanisms, as well as the particle acceleration mechanisms at different types of shocks. In order to determine radio spectral indices of non-radiative and radiative filaments in Cygnus Loop, we observed previously optically analyzed filaments with the Karl G. Jansky Very Large Array (VLA). At 1 and 5 GHz, we detected only radiative filaments in the field of view. Non-radiative optical filaments are also present, but were not detected in radio. Contrary to the expected non-thermal spectral slopes characteristic of SNRs, we instead observed spectral slopes characteristic of the thermal radiation mechanism from the radiative filaments in Cygnus Loop. These evolutionary older parts of Cygnus Loop radiate at radio frequencies predominantly via the thermal bremsstrahlung mechanism, and in that sense their emission more closely resembles the radio emission of HII regions rather than the radio emission of SNRs.

We utilize the structure of quasiautomorphic forms over a Hecke triangle group to define a mapping from a quasiautomorphic form to a vector-valued automorphic form (vvaf). This kind of vvaf we call a Hecke vector-form. First we supply a proof of the functional equations that hold for Hecke vector-forms modulo the group generators. Then, utilizing the multiplier system for these Hecke vector-forms, we prove the opposite direction and complete the bijection. Since the modular group is a special instance of the Hecke triangle groups, our results hold for quasimodular forms.

We investigate the phenomenology of light long-lived neutralinos in R-parity violating supersymmetric models, focusing on the proposed remote detectors $\texttt{ANUBIS}$, $\texttt{CODEX-b}$, $\texttt{FACET}$, $\texttt{FASER}$, $\texttt{FASER2}$, $\texttt{MAPP}$, $\texttt{MAPP2}$, and $\texttt{MATHUSLA}$ at the LHC. We assume the production of the neutralinos at the ATLAS or CMS interaction points via rare scalar meson decays induced by R-parity violating couplings. We study six supersymmetric R-parity violating benchmark scenarios in which the dominant neutralino decay is $\tildeχ^0_1 \rightarrow γ+ ν$. For each scenario, we determine the projected search sensitivity at the above listed detectors. Extending previous work focused primarily on $\texttt{FASER}$ and $\texttt{FASER2}$, we improve the simulation by taking into account the extended flight path of the parent meson. We find that $\texttt{ANUBIS}$ provides the best sensitivity to our benchmark scenarios and $\texttt{FASER}$ the least among the considered experiments, while of course $\texttt{FASER}$ has already taken data.

Some arguments are considered in favor of the idea that the canonical anticommutation relations for fermions should be modified in curved spacetime near the event horizon of a black hole. Such a modification is expected to lead to a change in the source term of the inhomogeneous Dirac equation describing the two-point Green's function. By introducing an {\it ad hoc} source into the Dirac equation that mimics the modification of these anticommutation relations, stationary solutions are obtained and interpreted as two-point Green's functions of fermions located near the event horizon. Owing to their stationarity, these Green's functions describe a fermion condensate near the event horizon.

Most massive stars live in binary systems. When the first supernova (SN) in a binary occurs, the ejecta hit the companion, which may inflate as a consequence, and then interacts with the newly formed compact object. The recent Type Ic SN2022jli shows a periodic modulation in its emission, which is interpreted as evidence for such interaction. We derive predictions for the occurrence rate and observables of SNe exhibiting these companion - compact-object interactions (CCIs). We analyze a comprehensive, state-of-the-art grid of detailed binary stellar evolution models, and implement analytic prescriptions for the expansion of the companion star following its interaction with the SN ejecta. We employ the newly developed population synthesis code SN-ORACLE to derive the distribution functions of the properties of the SNe affected by CCI and their companions, where we use different explodability and neutron star birth kick distributions. We find that periodic CCI is expected to occur in more than half of the binary systems that produce a hydrogen-poor core collapse SN and are not disrupted, while the occurrence rate in systems producing hydrogen-rich SNe is small. We find broad period ranges, peaking around 20-50 days, with the interaction lasting for 0.5-10 years. We identify specific binary evolution models that reproduce the observed period of the light curve undulations of SN2022jli, SN2015ap, and SN2022esa. The inflation of the companion also increases its luminosity and brightness, increasing its detectability with current instruments. For SN2022jli, our best fitting models predict a J-band magnitude of 21-23 for up to 10 years. We find that up to 27% of H-poor SNe could show periodicity in their light curves, while only a few such events have been identified so far. Our results may help find periodic CCI features in future and archival SN observations.

Legal citation in common-law systems depends not only on factual similarity, but also on the legal principle for which a precedent is invoked. However, existing benchmarks for legal citation retrieval use case facts, citation context, or full judgments as inputs, where the governing legal principle is often missing or only implicitly expressed and entangled with broader context. As a result, models may retrieve precedents that are factually similar yet doctrinally irrelevant. This limitation is particularly consequential in Singapore, where the legal system has evolved independently: only domestic precedents are binding, while foreign authorities serve merely as persuasive references. Thus, we propose a new retrieval paradigm that ranks cited cases based on queries integrating case facts and explicit legal principles, inspired by real-world legal reasoning workflows. To support this paradigm, we introduce SG-LegalCite, a dataset of 100,890 case-principle pairs extracted from 8,523 Singapore Supreme Court judgments spanning from 2000 to 2025. Experiments across 11 baselines demonstrate the effectiveness of our principle-augmented retrieval paradigm, showing that explicit legal principles provide strong discriminative signals for legal citation retrieval.