This paper provides necessary and sufficient conditions for the existence of free boundaries in overdetermined problems for the Laplacian, and sufficient conditions for the bi-Laplacian, when the overdetermined boundary condition is non-constant. Using classical integral inequalities (Cauchy-Schwarz, Hölder, Hardy, eigenvalue bounds, Pohozaev and Reilly identities), we derive existence results for a broad class of free boundary problems arising in potential theory, plate theory, electromagnetism, and shape optimization. A regularity result for minimizers in the $C$-GNP class is established using the thickness function and the Wiener criterion, based on the geometric description of cusp points given in \cite{Barkatou2002}. We provide a new, self-contained geometric result: for almost every $t$, the level sets of the solution inherit the $C$-GNP property. This inheritance theorem justifies the variational framework and guarantees that the entire foliation generated by the state function remains within the admissible class. New results include refined estimates via interpolation inequalities, stability under perturbations, and connections with isoperimetric inequalities. The physical interpretation of the bi-Laplacian problem $\mathcal{B}(f,g)$ in the Kirchhoff-Love theory of thin plates is emphasized.

We present the analysis of the stellar and interstellar medium (ISM) properties of MARTA-4327, a star-forming galaxy at z=2.224 observed by means of deep JWST/NIRSpec spectroscopy in both medium- and high-resolution gratings as part of the "Measuring Abundances at high Redshift with the Te Approach" (MARTA) programme. We report one of the highest-redshift detections of the Wolf-Rayet (WR) blue and red bumps in a non-lensed system. The broad He ii$λ$4686 feature is consistent with a young (${\sim 5-6}$ Myr) burst dominated by WN stars, although both SSP models and empirical templates struggle to reproduce the nitrogen stellar features at ${\approx}$ 4640 A. Based on the relative strength of the available optical stellar features, we disfavor the presence of very massive stars (VMS) in this system. Elemental abundance ratios such as Ne/O, N/O, and Ar/O align with observations of local star-forming galaxies (including WR galaxies), suggesting that any impact of the WR population on the chemical enrichment of the ISM is strongly localized. However, the gas-phase Fe/O ratio appears enhanced compared to local galaxies of similar metallicity, which we interpret as evidence for reduced Fe depletion onto dust grains, possibly linked to localized destruction in WR-driven wind environments. In addition, we detect a broad and blueshifted (~70 km/s) H$α$ component, revealing the presence of an ionized outflow with a mass loading factor ${η\sim 0.2}$. Finally, we report the robust detection of O I$λ$8446 emission (among the firsts at high redshift), which we interpret as originating from Ly$β$ fluorescence and/or collisional excitation in dense clumps. Overall, MARTA-4327 represents a unique system for studying the role of massive stars in shaping the ISM in galaxies at Cosmic Noon.

Bargmann invariants provide a rephasing-invariant description of phase relations among quantum states and offer a geometric perspective on interference phenomena. In this work, we investigate their role in neutral meson systems by constructing cyclic products involving the heavy and light mass eigenstates together with decay-projected states arising from correlated meson decays. Explicit expressions for third-order and fourth-order invariants are obtained in terms of mixing parameters and decay amplitudes. The analysis shows that the associated geometric phases encode CP-sensitive interference effects between meson-antimeson mixing and decay amplitudes and become trivial in the CP-conserving limit. Expressing the decay amplitudes in terms of CKM matrix elements reveals quartic combinations with analogous rephasing-invariant weak-phase structure to that of the Jarlskog invariant. We further introduce a rephasing-invariant ratio constructed from third- and fourth-order Bargmann invariants, which isolates correlated CP-violating structures that cannot, in general, be factorized into independent decay-channel contributions and can enhance sensitivity to small deviations from CP symmetry. The invariants can also be related to parameters governing time-dependent CP asymmetries in neutral meson decays, thereby providing a geometric interpretation of observable CP-violating interference effects.

Non-destructive testing using ultrasound is based on the interaction of sound waves with the object being tested and any defects it may contain. The aim is to extract as much information as possible about the object and its defects from the scattered wave field. In this paper, the concept of information in the context of ultrasonic testing is formalized and quantified physically for the first time. To this end, a balance equation for information is derived, analogous to Poynting's theorem for elastic energy. Various examples demonstrate how structural information is generated and annihilated within a component and along which pathways it travels from the defect to the sensor. Subsequently, the significance and potential of this new information concept for practical ultrasonic testing, structural health monitoring, numerical simulation, and machine learning are discussed. Finally, similarities and differences to mathematical Shannon information and statistical Fisher information are highlighted.

In this note, we study the equivalence of Morse and stable subgroups in the framework of the coset intersection complex. Under certain conditions on a coset intersection complex of a group, we prove that infinite-index Morse subgroups are stable.

Resource-constrained Internet of Things (IoT) devices, from medical implants to small drones, must transmit sensitive telemetry under adversarial wireless channels while operating under stringent computing and energy budgets. Authenticated Encryption (AE) is essential to ensure confidentiality, integrity, and authenticity. However, existing lightweight AE standards lack forward-security guarantees, compact tag aggregation, and offline-online (OO) optimizations required for modern high-throughput IoT pipelines. We introduce Diamond , the first provably secure Forward-secure and Aggregate Authenticated Encryption (FAAE) framework that extends and generalizes prior FAAE constructions through a lightweight key evolution mechanism, an OOoptimized computation pipeline, and a set of performance-tier instantiations. Diamond substantially reduces amortized offline preprocessing (up to 47%) and achieves up to an order-of-magnitude reduction in end-toend latency for large telemetry batches. Our comprehensive evaluation on 64-bit ARM Cortex-A72, 32-bit ARM Cortex-M4 and 8-bit AVR architectures confirms that Diamond outperforms baseline FAAE variants in authenticated encryption throughput and end-to-end verification latency while maintaining compact tag aggregation and strong breach resilience. Diamond outperforms NIST lightweight AE candidates for medium and large payloads, while remaining competitive for small messages when amortized across batches. We formally prove the security of Diamond and provide two concrete instantiations optimized for compliance and high efficiency. Our open-source release enables reproducibility and seamless integration into IoT platforms.

Decoding motor performance from brain signals offers promising avenues for adaptive deep brain stimulation (aDBS) for Parkinson's disease (PD). In a two-center cohort of 19 PD patients executing a drawing task, we decoded motor performance from electroencephalography (n=15) and, critically for clinical translation, electrocorticography (n=4). Within each session, patients performed the task under DBS on and DBS off. A total of 35 sessions were recorded. Instead of relying on single frequency bands, we derived patient-specific biomarkers using a filterbank-based machine-learning approach. DBS modulated kinematics significantly in 23 sessions. Significant neural decoding of kinematics was possible in 28 of the 35 sessions (average Pearson's $\text{r}= 0.37$). Our results further demonstrate modulation of speed-accuracy trade-offs, with increased drawing speed but reduced accuracy under DBS. Joint evaluation of behavioral and neural decoding outcomes revealed six prototypical scenarios, for which we provide guidance for future aDBS strategies.

We present a user-friendly, open-source Wolfram Language package that automates the construction of an effective homogeneous generalized Voigt rheology for a spherically symmetric, incompressible layered body with Maxwell solid layers. It provides a practical bridge between layered interior models and time-domain simulations of tidal evolution. The package combines three components: (i) a forward computation of the degree-2 tidal Love number based on the propagator-matrix formulation for incompressible stratified viscoelastic bodies; (ii) numerical identification of the secular relaxation poles and residues of the layered model; and (iii) inversion of the resulting response into the compliance of an equivalent homogeneous generalized Voigt body. The implementation is based on the equivalence established for multilayer Maxwell bodies and includes an optional dominant-mode selection procedure for obtaining reduced rheological models over a prescribed frequency range. The package returns the parameters of the equivalent homogeneous model, including elastic, gravitational, viscous, and Voigt-element contributions, in a format suitable for downstream numerical applications. As a case study, we apply the package to a five-layer lunar interior model and obtain its equivalent generalized Voigt representation, together with a reduced model that preserves the tidal response over the frequency interval relevant for orbital evolution while using fewer relaxation elements. This package makes the reduction from stratified viscoelastic interiors to effective homogeneous rheologies reproducible and accessible. It allows physical tidal dissipation models to be used in long-term orbital and spin-evolution studies without having to repeatedly solve the full layered boundary-value problem.

The evolutionary origin of Wolf-Rayet (WR) stars at Solar metallicity is unclear. Single-star evolution from massive O stars, possibly via a Luminous Blue Variable phase, is challenged by binary period distributions of different WR subtypes. Wd1-72 is a WN7b+O binary embedded in the collective wind of the Galactic young massive cluster Westerlund 1 (Wd 1). It is surrounded by highly structured nebulosity, with cometary tails pointing away from Wd 1 and quasi-spherical droplets towards it. In this letter, we demonstrate that this morphology can be qualitatively reproduced by a hydrodynamic simulation of non-conservative Roche Lobe Overflow (RLOF) mass-loss into a cluster wind. Our model is based on a detailed binary evolution track consistent with key known properties of Wd1-72. Our work suggests Wd1-72 could be only ~10 kyr post-RLOF, and the hydrogen-free nature of Wd1-72 favours this being a second or subsequent RLOF episode. Follow-up observations could make Wd1-72 a valuable benchmark for probing mass-loss and mass-transfer in forming gravitational-wave binary-progenitor systems.

Self-organized dynamic patterns in dense active matter are striking manifestations of non-equilibrium physics. A prominent example is the macroscopic elliptical motion observed in quasi-2D bacterial suspensions, which has lacked a physical explanation. Here, we examine a minimal linear response framework coupling bacterial swimming dynamics with fluid flow, treating long-range hydrodynamic interactions as a macroscopic communication channel. We demonstrate that microscopic swim motion, via Jeffery coupling, manifests as a ``phase-leading'' response to local shear flows. System-wide sustained oscillations, on the other hand, require both a critical bacterial density and strict geometric confinement. By analytically predicting the onset cell density and maximum film thickness, our model achieves excellent quantitative agreement with experiments, establishing a unified physical framework for self-organized periodic motion of elongated body in active fluids.

Timed automata (TAs) are an extension of finite automata that can measure and react to the passage of time, providing the ability to handle real-time constraints using clocks. In 2009, Franck Cassez showed that the timed opacity problem, where an attacker can observe some actions with their timestamps and attempts to deduce information, is undecidable for TAs. Moreover, he showed that the undecidability holds even for subclasses such as event-recording automata. In this article, we consider the same definition of opacity, by restricting either the system or the attacker. Our first contribution is to prove the inter-reducibility of two variants of opacity: full opacity (for which the observations should be the same regardless of the visit of a private location) and weak opacity (for which it suffices that the attacker cannot deduce whether the private location was visited, but for which it is harmless to deduce that it was not visited); we also prove further results including a connection with timed language inclusion. Our second contribution is to study opacity for several subclasses of TAs: with restrictions on the number of clocks, the number of actions, the nature of time, or a new subclass called observable event-recording automata. We show that opacity is mostly decidable in these cases, except for one-action TAs and for one-clock TAs with $ε$-transitions, for which undecidability remains. Our third (and arguably main) contribution is to propose a new definition of opacity in which the number of observations made by the attacker is limited to the first $N$ observations, or to a set of $N$ timestamps after which the attacker observes the first action that follows immediately. This set can be defined either a priori or at runtime; all three versions yield decidability for the whole TA class.

This paper presents a dynamic gamification architecture for an Extended Reality Artificial Intelligence virtual training environment designed to enhance STEM education through immersive adaptive, and kinesthetic learning. The proposed system can be introduced in four phases: Introduction Phase, Component Development Phase, Fault Introduction and Correction Phase and Generative AI XR scenarios Phase. Security and privacy are discussed via a defense-in-depth approach spanning client, middleware, and backend layers, incorporating AES 256 encryption, multi-factor authentication, role-based access control and GDPR or FERPA compliance. Risks such as sensor exploitation, perceptual manipulation, and virtual physical harm are identified, with mitigation strategies embedded at the design stage. Potential barriers to large scale adoption-including technical complexity, cost of deployment, and need for cybersecurity expertise are discussed.

Plasticity is a fundamental property of complex systems, such as the brain or an organism. Yet it typically remains a descriptive concept inferred retrospectively from observed outcomes, such as modifications in activity or morphology. Here, the network-based operationalization of plasticity is further formalized as the ratio between system size and connectivity strength among system elements. Within this framework, system size determines the dimensionality of the accessible state space, while connectivity strength tunes the system's regime. An optimal range of plasticity -- balancing capacity for change and capacity to maintain coherence -- emerges at intermediate connectivity strength. Notably, this balance coincides with the critical regime, which provides a theoretically motivated benchmark that enables a normalized unit of measure, termed effective plasticity, and comparisons of adaptive efficacy across diverse systems. Plasticity is thus transformed into a predictive tool that quantifies a system's capacity for change before it occurs. Its validity is supported across disciplines and, in particular, by evidence from psychopathology where it anticipates transitions between mental states. At a mechanistic level, plasticity acts as a structural tuning parameter for criticality, reframing their relationship as causal, with plasticity driving criticality rather than merely accompanying it. Furthermore, this network-based operationalization explains how larger systems can more robustly maintain critical dynamics. Crucially, the proposed perspective distinguishes functional regime shifts from thermodynamic phase changes, identifying plasticity as the system-level regulator that shapes and constrains the dynamic repertoire. This framework is applicable across domains, including ecology, economics, and social systems, and may foster cross-disciplinary integration within complexity science.

Spreading and storing erasure-coded data effectively in distributed systems is challenging in practical settings. The dissemination of erasure-coded information is typically designed to complete only after receiving messages from $(N-F)$ nodes, thereby preparing for the worst-case, but rare, scenario of $F$ failures. In steady state, the remaining $F$ nodes may in fact be healthy, but their resources are not counted. This leads to over-provisioning of storage for encoded data. This paper introduces eAID, a novel elastic information dispersal algorithm that addresses this conundrum through a two-stage approach. First, the core protocol estimates the actual number $f$ of faulty nodes, rather than assuming the worst-case bound $F$. Dissemination completes quickly when messages are received from $(N-f)$ nodes, and more gradually when fewer nodes respond. Second, after initial dissemination completes, eAID continues monitoring for additional responses. As responses arrive from up to $N$ nodes, the system prunes the information stored at responding nodes accordingly. A key technique enabling this seamless elasticity is an agile encoding scheme that varies the number of disseminated fragments while keeping both fragment size and the recovery threshold $(F+1)$ fixed. Not only does this enable varying the number of disseminated fragments on the fly, it also allows nodes to discard encoded fragments autonomously. Crucially, this is achieved without maintaining complex metadata, without requiring nodes to reconstruct or re-encode information, and without global coordination for storage decisions. We demonstrate the practicality of eAID by integrating it with a replicated key-value store, and evaluating it in network environments with unpredictable latencies. The results show that eAID improves overall performance while significantly reducing long-term storage consumption.

Variability monitoring provides an unparalleled insight into the atmospheric processes of brown dwarfs and directly imaged exo-planets. Inhomogeneous clouds, aurorae and magnetic spots have all been postulated as potential drivers of variability. While objects at the L/T transition have had their variability studied extensively, the variability of early L-dwarfs remains an understudied region of the parameter space. We use observations from the Hubble Space Telescope in the near-infrared, using WFC3/G141 to disentangle the drivers of variability in three known variable early L-dwarfs: 2MASS J1721039+334415, 2MASS J00361617+1821104 and 2MASS J19064801+4011089. We find that all three objects exhibit significant variability at all wavelengths, with white-light amplitudes of 0.53-1.41 %. We find that their colour variations are brighter and bluer compared to later spectral types, except for 2MASSJ19064801+4011089 which exhibits largely grey variations. We report a new period for 2MASS J1721039+334415, of 4.9^{+0.4}_{-0.2} hours. We find evidence of long term light curve stability in each object, which may indicate the presence of long lived features on their surfaces. We create a flexible modelling framework to model three potential drivers of variability: clouds, aurorae and magnetic spots. We fit our models to the spectral variability amplitude from 1.1-1.67 μm of each object. We find that changing cloud properties or magnetic spots are the most likely drivers of variability in each object. Auroral models do not reproduce the variability within the HST wavelengths, however future observations at longer wavelengths that probe higher in the atmosphere may be more sensitive to auroral effects. This work provides a foundation for future variability studies of early L-dwarfs and directly imaged exoplanets to disentangle auroral, cloud and magnetic spot driven variability.

A recurring question in continuum-discretized coupled-channels (CDCC) calculations is which continuum channels carry the breakup coupling, both to interpret the reaction and to decide which channels a model space can safely omit. The standard answer is bin deletion: remove a channel, re-solve the coupled equations, and read the change in the elastic $S$-matrix. We show that this cannot isolate an individual channel's contribution. Deleting a channel forces the surviving model space to reorganize, the neighboring bins rerouting through the off-diagonal Green's function, so the recorded change mixes the channel's own effect with the readjustment of all the others. Working instead from the channel-resolved Feshbach dynamic polarization potential (DPP), whose full-coupling Green's function is a fixed reference shared by every channel, we define an exclusion that removes one channel while holding that reference fixed, returning its contribution to the intact system. The two operations disagree on which continuum bins matter most, for $d$+$^{58}$Ni at 21.6~MeV even reversing their order of importance. The DPP further separates each channel's action into a direct path, virtual excitation and return, and a bridge path, relayed through neighboring bins, a split deletion cannot make; it shows the bins act on the elastic channel mainly as bridges, robustly across angular momentum, and that it is this bridge coupling that reorganizes under deletion. A deletion-based channel importance is therefore best read as the truncated calculation's sensitivity to a channel's removal, not as the channel's intrinsic coupling strength.

A field in which the (logarithmic) Weil height is bounded from below by a strictly positive constant is said to have the Bogomolov property (property (B)). Given a normalized eigenform $f\in S_k(Γ_0(N))$ Amoroso and Terracini proved (B) for the field "cut out" by the adelic representation associated to $f$ under some assumptions on $f$, generalizing the earlier work of Habegger on elliptic curves. In this paper we extend this result to the case of normalized eigenforms with nontrivial nebentypus character. We also introduce the notion of ADZ field, inspired by earlier work of Amoroso, David and Zannier, exhibiting a class of fields in which property (B) is preserved under (arbitrary) composition.

We introduce a new family of multi-mode, rotationally symmetric bosonic codes inspired by the group-theoretic framework of [Phys. Rev. Lett. 133, 240603 (2024)]. Such a construction inverts the traditional paradigm of code design by identifying codes from the requirement that a group of chosen logical gates should be implemented by means of physically simple logical operations, such as linear optics. Leveraging previously unexplored degrees of freedom within this framework, our construction preserves rotational symmetry across multiple modes, enabling linear-optics implementation of the full Pauli group. These codes exhibit improved protection against dephasing noise, outperforming both single-mode analogues and earlier multi-mode constructions. Notably, they allow exact correction of correlated dephasing and support qudit encoding in arbitrary dimensions. We analytically construct and numerically benchmark two-mode binomial codes instances, and demonstrate that, unlike single-mode rotationally symmetric bosonic codes, these exhibit no trade-off between protection against dephasing and photon loss.

Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework, which provides off-the-shelf compositionality results for first-order languages, so far does not apply to higher-order languages. In the present work, we develop a theory of abstract GSOS specifications for higher-order languages, in effect transferring the core principles of Turi and Plotkin's framework to a higher-order setting. In our theory, the operational semantics of higher-order languages is represented by certain dinatural transformations that we term (pointed) higher-order GSOS laws. We give a general compositionality result that applies to all systems specified in this way and discuss how compositionality of combinatory logics and the lambda-calculus w.r.t. a strong variant of Abramsky's applicative bisimilarity are obtained as instances.

Properties of the hot intracluster and intragroup medium are mostly set by the underlying gravitational potential well, although complex astrophysical processes at play during their buildup may leave a significant imprint. Observational constraints on the degree and scales of such non-gravitational processes require well-selected samples of objects and deep observations of their gas content. We aim to study the scaling relation between two global properties of the hot gas, namely its soft-band X-ray luminosity ($L_X$) and its temperature ($T$), by studying a sample of low-mass systems associated with precise redshifts, simultaneously accounting for sample selection biases and associated measurement uncertainties. This work takes as input a large catalogue of X-ray-selected galaxy clusters (X-CLASS). We perform a thorough revision of the redshifts of sources using deep photometric data from the Legacy Surveys and our own tailored spectroscopic follow-up of 52 low-redshift systems. We devise a spectroscopically complete sample of 155 low-redshift ($0.07<z<0.2$) systems, and we measure properties of their X-ray emitting gas, with median $\overline{T}=1.7$ keV and median $\overline{L_X}=10^{43}$ erg s$^{-1}$. We infer the relation between $L_X$ and $T$ in a Bayesian framework. Our sample of groups and clusters with median total mass $\sim 6 \times 10^{13}M_\odot$ reveals a relation $L_X-T$ steeper than predicted by the self-similar model, with a slope $B=3.2 \pm 0.1$. This result fits well within recent studies that together indicate a trend of increasing slope with decreasing median halo mass. This work supports a scenario of a stronger decrease in luminosity with decreasing mass in the group regime than for massive galaxy clusters. This effect is possibly due to strong and sustained feedback expelling gas efficiently from their relatively shallower potential wells.

Aims. We aim to investigate the connection between star formation histories (SFHs) and the inner dark matter density profiles of simulated galaxies. In particular, we test whether the burstiness and temporal distribution of star formation influence the formation of cored versus cuspy dark matter profiles. Methods. We homogeneously analysed simulated galaxies from the NIHAO and FIRE-2 projects. For each galaxy, we derived dark matter density profiles and measured the logarithmic slope in the inner region of the dark matter halo (1-2% of R$_{\rm vir}$). To characterise star formation burstiness, we introduced a criterion based on comparing the star formation rate (SFR) averaged over two distinct timescales. We further quantified the temporal concentration of SFHs by computing $M_{\star, \rm post}$ / $M_{\star, \rm pre}$, the ratio of stellar mass formed after versus before the epoch of reionisation at redshift z $\sim$ 6.5. Results. Homogeneous analysis reveals that inner slope versus stellar-to-halo mass ratio trends for NIHAO and FIRE-2 galaxies are in much better agreement than reported in previous works. The burstiness and post-to-pre reionisation stellar mass ratio of the SFH explain the scatter in the inner slope versus stellar-to-halo mass ratio relation, revealing that galaxies with above average burstiness and more extended SFHs are more efficient at developing cored dark matter profiles. In contrast, galaxies with smoother SFHs and earlier stellar mass assembly tend to maintain cuspier dark matter profiles. We present an analytic expression that improves predictions for the inner slope using the parameter $M_{\star \rm,post}$ / $M_{\star \rm,pre}$, which reduces the mean squared error in both simulation suites relative to previous formulations based solely on the stellar-to-halo mass ratio.

The polarization of $Λ$ hyperons is preserved in the angular distribution of their decay products. This property allows one to study the spin structure of the $Λ$. In Semi-Inclusive Deep Inelastic Scattering where a high energy lepton interacts with a nucleon target and one or more hadrons and the scattered lepton are detected in the final state, the probability for a struck quark to impart the polarization of the lepton to the $Λ$ may be measured. In particular, in electron-proton scattering this quantity may be related to the longitudinal light quark polarization of the $Λ$. Currently, limited experimental data cannot discriminate between different models of $Λ$ spin structure. This work reports on the measurement of the longitudinal spin transfer $D^Λ_{LL'}$ to the $Λ$ using data taken by the CLAS12 spectrometer at Jefferson Lab with a $10.6$ GeV longitudinally polarized electron beam and an unpolarized hydrogen target. This measurement is the most precise to date, and, in comparison with theory predictions, it offers valuable insight into the relative dominance of current and target fragmentation in $Λ$ production.

We identify a sample of 83 spatially resolved hot molecular cores (HMCs) in the QUARKS survey, aiming at investigating thermal feedback from massive stars. Using CH$_3$CN\,(12--11) line emission together with 1.3\,mm continuum data we derive the radial temperature, volume density and \ch3cn{} abundance profiles for the 83 HMCs. Based on the envelope temperature and density profiles, we compute the luminosities of the embedded massive protostars with \radmc{} radiation transfer model. The derived luminosities are comparable (within $\sim1$ dex) to the bolometric luminosities of their natal clumps and show strong correlations with several core-scale properties, including the HMC mass ($Log[ M_\mathrm{env}] = 1.01\,Log [L_\star] - 4.80$), the inner core radius (the flat radius of Plummer-like volume density profile) ($Log[a] = 0.46\,Log[L_\star] + 0.52$) and the central density $ (Log[n_c] = -0.55 Log[L_\star] +10.47) $. These empirical relations provide useful observational constraints for physical models of protostellar objects. Importantly, we find a strong positive correlation between the massive protostellar luminosity and the local thermal Jeans mass. The derived Jeans masses, $M_\mathrm{Jeans}$, exceed the HMC masses $M_\mathrm{env}$, with the average $M_\mathrm{Jeans}$ being two times larger than the average $M_\mathrm{env}$. This provides observational evidence that thermal feedback from massive protostars can effectively suppress further fragmentation of HMCs, thereby promoting massive star formation. In addition, the positive correlation between massive protostellar luminosity and natal clump mass suggests that more massive clumps preferentially host more luminous protostars, leading to stronger thermal feedback.

We consider a broad class of static, spherically symmetric generalized Schwarzschild-like solutions with multiple non-interacting anisotropic fluid sources and derive the coordinate transformation from Schwarzschild-like (curvature) to isotropic coordinates with conformally flat spatial slices. The isotropic form removes spatial-sector coordinate pathologies at the horizon, clarifies geometric quantities (e.g., ADM mass and curvature invariants), and enables the construction of well-posed initial data on t=const hypersurfaces, suitable for the Hamiltonian and conformal formulations of numerical relativity and for perturbation theory. The backgrounds in isotropic coordinates we develop make it straightforward to separate environmental effects from intrinsic strong-gravity signals and meet the growing interest in non-vacuum black hole phenomenology across scattering, lensing, and waveform modeling.

We study local verification of graph properties in distributed networks under the framework of \emph{locally checkable proofs} (LCPs). In an LCP, a prover assigns proof labels to nodes, and a distributed verifier must make all nodes accept if the graph satisfies the property, while at least one node rejects otherwise. Each node bases its decision on a local neighborhood, called its \emph{view distance}. Our focus is twofold. First, we study cycle existence, i.e., whether a graph contains a cycle (as opposed to cycle-freeness). We show that cycle existence admits verification with only $3$ proof labels and view distance $1$, and establish a matching lower bound. More importantly, inspired by direction-encoding techniques based on BFS distances, we introduce a novel gadget that encodes direction using only $2$ labels and view distance $3$ through repeated occurrences of the string $001101$. Although developed for cycle existence, this gadget may be useful for other verification tasks. Second, we introduce an \emph{erroneous proof} model in which an adversary may corrupt proof labels of at most $i$ nodes within the $(2i+1)$-hop neighborhood of each node. We present an algorithmic framework, called \textbf{\texttt{refix}}, that transforms an error-free verifier into one that tolerates such errors at the cost of a view distance of $2i+1$. We demonstrate the framework on cycle existence, cycle-freeness, and bipartiteness, and establish lower bounds relating the number of errors to the required view distance. Finally, we show that our $2$-label, view-distance-$3$ verifier for cycle existence admits a $3$-round implementation in the \textsc{CONGEST} model, providing a first step toward implementing LCPs under communication constraints.

Band alignment, namely the prediction of band-edge positions of semiconductors and insulators in aqueous solutions, is an important problem in physics and chemistry. Such a prediction is especially challenging for structurally and chemically complex, multi-component materials. Here we present an approach to align band structure of metal-organic frameworks (MOFs) on an absolute energy scale which can be used for direct comparison with experiments. Hydrogen defects are used as probes into the chemical bonding of the hybrid inorganic-organic materials. An effective hydrogen defect level, defined as the average of the charge-state transition levels of the defects at the secondary building unit and at the linker, is identified as a charge neutrality level to align band structures. This level captures subtle chemical details at both the building blocks and provides results that are in agreement with experiments in a wide range of different MOFs. We also compare with results obtained from using other approaches involving surface calculations and average pore-center electrostatic potentials.

The Atomki anomaly puts forward the hypothesis of an $X(17)$ particle to explain its observation. Utilizing experimental results from the Atomki experiments, measurements of the electron's anomalous magnetic moment, beam dump experiments, the KLOE-2 experiment, the PADME experiment, and the parity-violating Møller scattering experiment, we derive constraints on the $Xee$ coupling of the $X(17)$ boson to electrons. It is found that the scalar and pseudoscalar models can be excluded by Atomki experiments due to the parity conservation, and the pure axial-vector model is excluded at 98\% C.L. Meanwhile, the analyses in both pure vector and $V \pm A$ models consistently show that the $Xee$ coupling is of the vector type and has an almost fixed value, $\left(6.78 \pm 0.042\right) \times 10^{-4} \lesssim |\varepsilon_e^v| \lesssim \left(6.93 \pm 1.66\right) \times 10^{-4}$ in unit of electric charge $e$.

We explicitly compute Fourier coefficients of Eisenstein series on the special orthogonal group $G={\rm SO}(3,n+1)$ over $\mathbb{Q}$ with $n\ge 2$ which splits everywhere at finite places. We show that it has a bounded denominator.

Let $(M,h)$ be a connected, complete Riemannian manifold, $x\in M$, and $l>0$. Then $M$ is called a $Z^x$ manifold if all geodesics starting at $x$ return to $x$, and it is called a $Y^x_l$ manifold if every unit-speed geodesic starting at $x$ returns to $x$ at time $l$. It is unknown whether there are $Z^x$ manifolds that are not $Y^x_l$ manifolds for any $l>0$. By the Bérard-Bergery theorem, any $Y^x_l$ manifold of dimension at least $2$ is compact with finite fundamental group. We prove the same result for $Z^x$ manifolds $M$ for which all unit-speed geodesics starting at $x$ return to $x$ in uniformly bounded time. We also prove that any $Z^x$ manifold $(M,h)$ with $h$ analytic is a $Y^x_l$ manifold for some $l>0$. We start by defining a class of globally hyperbolic spacetimes (called observer-refocusing) such that any $Z^x$ manifold is the Cauchy surface of some observer-refocusing spacetime. We then prove that under suitable conditions the Cauchy surfaces of observer-refocusing spacetimes are compact with finite fundamental group, and we show that analytic observer-refocusing spacetimes of dimension at least $3$ are strongly refocusing. We end by stating a contact-theoretic conjecture analogous to our results in Riemannian and Lorentzian geometry.

Context. In the context of galactic archaeology, the study of the Small Magellanic Cloud (SMC) is of crucial importance, as it represents a unique opportunity to study a nearby massive dwarf system. However, theoretical studies of the chemical evolution of this galaxy are strikingly lacking. Aims. In this study, we investigate the chemical enrichment of the SMC galaxy. Besides alpha and Fe-peak elements, we devote particular attention to the evolution of neutron-capture elements with different origin, namely r-process (Eu), weak s-process (Zr) and main s-process (Ba, La). Methods. We develop chemical evolution models that use as input the star formation histories obtained from colour-magnitude diagram fitting. We follow in detail the chemical feedback provided by a large variety of nucleosynthetic sources. Model predictions are compared with recent abundance measurements for the SMC. Results. The developed framework reproduces well all the observables for elements up to the Fe-peak. The abundance patterns of n-capture elements are simultaneously reproduced only by assuming an enhanced contribution from the delayed r-process at low metallicity and a top-lighter IMF relative to the reference IMF by Kroupa (2001). In this way, both the observed very high plateau in [Eu/Fe] and the rising trends in [s-process/Fe] ratios can be reproduced by the models. Conclusions. This study provides for the first time information on the evolution of several n-capture elements in a massive dwarf irregular galaxy, also providing insight on several ingredients driving galactic evolution. Moreover, this work provides a test-bed for further modelling of the SMC in the context of the numerous surveys that will target the Magellanic Clouds in the next years.