The best known methods for estimating hazard rate functions in survival analysis models are either purely parametric or purely nonparametric. The parametric ones are sometimes too biased while the nonparametric ones are sometimes too variable. In the present paper a certain semiparametric approach to hazard rate estimation, proposed in Hjort (1991), is developed further, aiming to combine parametric and nonparametric features. It uses a dynamic local likelihood approach to fit the locally most suitable member in a given parametric class of hazard rates, and amounts to a version of nonparametric parameter smoothing within the parametric class. Thus the parametric hazard rate estimate at time $s$ inserts a parameter estimate that also depends on $s$. We study bias and variance properties of the resulting estimator and methods for choosing the local smoothing parameter. It is shown that dynamic likelihood estimation often leads to better performance than the purely nonparametric methods, while also having capacity for not losing much to the parametric methods in cases where the model being smoothed is adequate.

This paper proposes an interpretation of Grothendieck's geometric universes as a foundational framework for \emph{information networks}. We argue that Grothendieck topologies, sheaves, and topoi provide a sheaf-theoretic semantics in which distributed and locally held information can be integrated into globally coherent structures. In this setting, local informational states are represented by sections, while the sheaf condition governs consistency, agreement, and consensus across a network. Logical validity and mathematical existence are therefore not imposed externally but arise intrinsically from geometric and categorical conditions. From this perspective, Grothendieck's geometric universes constitute a natural foundation for information networks governed by intrinsic logical principles. Moreover, we propose that Grothendieck's geometric universes themselves concretely instantiate what the author calls \emph{intrinsic logicism}. This position is intended as a contemporary reconstruction of the classical logicist program of Frege and Russell, reformulated within the framework of category theory and topos theory, where logical structure is generated internally by geometric and categorical organization rather than presupposed as an external foundational layer.

We propose CC-G2PnP, a streaming grapheme-to-phoneme and prosody (G2PnP) model to connect large language model and text-to-speech in a streaming manner. CC-G2PnP is based on Conformer-CTC architecture. Specifically, the input grapheme tokens are processed chunk by chunk, which enables streaming inference of phonemic and prosodic (PnP) labels. By guaranteeing minimal look-ahead size to each input token, the proposed model can consider future context in each token, which leads to stable PnP label prediction. Unlike previous streaming methods that depend on explicit word boundaries, the CTC decoder in CC-G2PnP effectively learns the alignment between graphemes and phonemes during training, making it applicable to unsegmented languages. Experiments on a Japanese dataset, which has no explicit word boundaries, show that CC-G2PnP significantly outperforms the baseline streaming G2PnP model in the accuracy of PnP label prediction.

This study compares the penetration characteristics of impact-induced jets with those of laser-induced jets, focusing on the underlying penetration mechanism rather than device performance for needle-free injection. Using an impact-induced jet system capable of ejecting a highly focused liquid jet at high speed without the use of lasers, we examine jet penetration into skin-simulating materials. Unlike conventional needle-free injectors that produce diffused liquid jets, the impact-induced method generates a highly focused jet that limits the injected area, thereby reducing invasiveness. Comparative experiments with laser-induced jets show that, even at similar jet tip velocities, impact-induced jets achieve greater penetration depth. The penetration depth remains constant regardless of the offset distance D from the target, owing to the high and nearly uniform velocity of the cylindrical jet root region, indicating that penetration is governed by the cylindrical jet structure. Furthermore, we systematically vary the liquid viscosity, jet inertia, and elastic modulus of the skin-simulating material. To account for cylindrical liquid jet penetration, a shear deformation model is proposed, in which the jet kinetic energy is dissipated through deformation of the gelatin. The model shows good agreement with experimental results and provides a unified physical basis for liquid jet penetration.

In this note, we prove that hereditary Mazur intersection property (MIP) does not imply Fréchet smoothness using an example by Borwein and Fabian (1993).

Monte Carlo sampling is the standard approach for estimating properties of solutions to stochastic differential equations (SDEs), but accurate estimates require huge sample sizes. Lyons and Victoir (2004) proposed replacing independently sampled Brownian driving paths with "cubature formulae", deterministic weighted sets of paths that match Brownian "signature moments" up to some degree $D$. They prove that cubature formulae exist for arbitrary $D$, but explicit constructions are difficult and have only reached $D=7$, too small for practical use. We present ARCANE, an algorithm that efficiently and automatically constructs cubature formulae of arbitrary degree. It reproduces the state of the art in seconds and reaches $\boldsymbol{D=19}$ within hours on modest hardware. In simulations across multiple different SDEs and error metrics, our cubature formulae robustly achieve an error orders of magnitude smaller than Monte Carlo with the same number of paths.

This paper explores cellular automata (CA) constructed from Yang-Baxter maps over finite fields $F_{2^n}$. We define $R$-matrices using a map $f$ on $F_{2^n}$ and establish necessary and sufficient conditions for $f$ to satisfy the Yang-Baxter equation. We show that these conditions become remarkably streamlined in characteristic two. An exhaustive search for bijective solutions in fields of order 4, 8, and 16 yields 16, 736, and 269,056 maps, respectively. Analysis of the resulting CA under helical boundary conditions reveals a consistent alignment between the temporal period and the field order. We propose the conjecture that this periodic identity holds generally for $F_{2^n}$, supported by analytical proofs for $n=2$ and $n=3$. Our results further indicate that bijectivity is a fundamental requirement for this periodic behavior.

We establish that ultralow lattice thermal conductivity in halide perovskites and related octahedral framework materials arises from two distinct and complementary mechanisms: (i) halogen-halogen-enabled rotational soft modes that reshape the low-frequency spectrum and intensify phonon scattering, and (ii) static octahedral distortions that further enhance anharmonicity and reduce phonon lifetimes. Using first-principles calculations on CsPbBr3, we demonstrate that Br-Br interactions induce rotational soft modes that decongest the phonon spectrum and enhance three- and four-phonon scattering, strongly suppressing particle-like thermal conductivity (kappa_p). Independently, static octahedral distortions further reduce kappa_p by amplifying anharmonicity while leaving wave-like conductivity (kappa_c) intact. Based on these mechanistic insights, we introduce a geometric distortion factor rho and perform a high-throughput screening that first selects materials with halogen-coordinated octahedral building blocks-ensuring the presence of rotational soft modes-and then identifies those with pronounced distortion. This strategy uncovers TaGaI8 with an ultralow kappa_L = 0.11 W/mK at room temperature. This work establishes halogen-halogen-enabled rotational soft modes and octahedral distortions as transferable design principles for octahedra-containing halides, spanning both extended frameworks and molecular-cluster motifs, for discovering ultralow-kappa_L materials.

Cognitive biases are often attributed to heuristics or limited information. Yet the structure of social networks is a key, often-overlooked source of perceptual bias. When information passes through social connections, the network alone can systematically distort how individuals view society. We use a simple model in which agents have a binary attribute (e.g., atheist or believer) and show that network topology alone can cause misperceptions of peers' attributes. These misperceptions persist even after aggregation and challenge the idea of the "wisdom of the crowd." We derive an estimator that predicts the size and direction of these biases from network features. We validate our findings using three large-scale opinion surveys. Our results show that network structure is a critical factor in collective perception, with major implications for reducing segregation, polarisation, and the marginalisation of minorities.

One of the key issues facing Direct-to-Cellular (D2C) satellite communication systems is ionospheric scintillation on the uplink and downlink, which can significantly degrade link quality. This work investigates the spatial and temporal characteristics of amplitude scintillation at D2C frequencies by scaling L-band scintillation observations from Global Navigation Satellite Systems (GNSS) receivers to bands relevant to D2C operation, including the low-band, and 3GPP's N255 and N256. These observations are then compared to scaled radio-occultation scintillation observations from the FORMOSAT-7/COSMIC-2 (F7/C2) mission, which can be used in regions that do not possess ground-based scintillation monitoring stations. As a proof of concept, five years of ground-based GNSS scintillation data from Sharjah, United Arab Emirates, together with two years of F7/C2 observations over the same region, corresponding to the ascending phase of Solar Cycle 25, are analyzed. Both space-based and ground-based observations indicate a pronounced diurnal scintillation peak between 20--22 local time, particularly during the equinoxes, with occurrence rates increasing with solar activity. Ground-based observations also reveal a strong azimuth dependence, with most scintillation events occurring on southward satellite links. The scintillation occurrence rate at the low-band is more than twice that observed at N255 and N256, highlighting the increased robustness of higher D2C bands to ionospheric scintillation. These results demonstrate how GNSS scintillation observations can be leveraged to characterize and anticipate scintillation-induced D2C link impairments, which help in D2C system design and the implementation of scintillation mitigation strategies.

Abstract interpretation has been shown to be a promising technique for the thread-modular verification of concurrent programs. Central to this is the generation of interferences, in the form of rely-guarantee conditions, conforming to a user-chosen structure. In this work, we introduce one such structure called the conditional-writes domain, designed for programs where it suffices to establish only the conditions under which particular variables are written to by each thread. We formalise our analysis within a novel abstract interpretation framework that is highly modular and can be easily extended to capture other structures for rely-guarantee conditions. We formalise two versions of our approach and evaluate their implementations on a simple programming language.

We establish Anderson localization for 1-d discrete Schrödinger operators with positive weights. The distinctive feature of this work lies in the degeneracy of the weights, with both the potentials and weights assumed to be analytic and quasi-periodic. Operators of this kind originate from distinct mathematical physics problems, which include the Frenkel-Kontorova model with impurities, the discretization of singular Sturm-Liouville operators, and the Fisher-KPP lattice equation in heterogeneous media.

We study compact orientable essential surfaces in knot exteriors in the 3-sphere. The genus $g$, the number of boundary components $b$, and the boundary slope $p/q$ are fundamental invariants of an essential surface. The \textit{realization problem} asks whether, for a given triple $(g, b, q)$ with $g \ge 0$, $b \ge 1$, and $q \ge 1$, there exists a knot $K \subset S^3$ whose exterior $E(K)$ contains a compact orientable essential surface $F$ of genus $g$ with $b$ boundary components and boundary slope $p/q$ for some $p$. In general, not all combinations of $(g, b, q)$ are realizable. First, we show that if $b$ is odd, then $q$ must be equal to $1$. Our main theorem states that for any given even $b \ge 2$ and $q \ge 1$, there exist a genus $g \ge 0$ and a knot $K$ such that $E(K)$ contains a compact orientable essential surface with these parameters.

We study an inverse design problem for the linear multiple fragmentation equation arising in particle dynamics. Our objective is to reconstruct an unknown initial size distribution that evolves, under a prescribed fragmentation law, into a desired size distribution at a specified final time. We first establish the existence of global mass-conserving solutions for a broad class of fragmentation kernels with unbounded rates, and subsequently prove the continuous dependence and uniqueness of these solutions under additional assumptions on the fragmentation kernels. We then formulate the inverse design problem as an optimal control problem constrained by the fragmentation dynamics and prove the existence of the optimal control problem. Also derive the corresponding continuous adjoint equation and propose a gradient-type iterative reconstruction method. For the numerical implementation, we develop finite volume schemes for both the forward and adjoint equations, including a weighted finite volume scheme designed to enhance mass conservation and accuracy. Two benchmark problems, involving linear and nonlinear fragmentation rates with known analytical solutions, are used to assess the accuracy and efficiency of the proposed approach and to compare the performance of the two discretizations in both forward simulations and inverse reconstructions.

Controlling flow-induced segregation in a granular mixture is highly relevant to many industrial settings. To enhance mixing or promote segregation, the continuous gravity flow of a bidisperse granular mixture through a series of narrow vertical channels with exit slots is investigated. The bidisperse mixture is composed of two different sizes of particles, but of the same density. In dense flow, segregation occurs, leading to formation of bands. The bands of large particles appear at a distance away from the walls. This finding is in contrast to that in shear-driven segregation in a dense flow where large particles segregate towards the walls. Using a phenomenological model, it has been shown that rolling and bouncing induced segregation is the dominant mechanism. When cylindrical inserts are placed to modify flow patterns, that significantly influences segregation patterns. The symmetrical placement of a cylindrical insert close to the exit slot vanishes the bands and enhances mixing. However, with two inserts placed symmetrically and close to the exit slot, the degree of segregation in the reverse direction is greatly enhanced compared to that without insert. In the former, small particles accumulate in thin regions adjacent to the walls, and large particles comprise the bulk of the domain and the flowing stream. The heap formation above the insert in a narrow channel, when the insert is close to the exit, enhances mixing in one configuration, whereas it amplifies reverse segregation in the other.

In multiphase flows, kinetic and interfacial energies coexist, and their mutual conversion can strongly influence the overall energy balance. However, in statistically steady flows these energy reservoirs remain constant, making such conversions undetectable. For them to be observed, a degree of unsteadiness must be introduced, here provided by the deliberate use of a fluctuating time-periodic input of kinetic energy into the system. The main focus of the present work is on the dynamical cycle connecting energy injection, conversion, and dissipation which we explore using numerical simulations of multiphase homogeneous isotropic turbulence, subjected to periodic forcing. The database includes various Reynolds and Weber numbers and volume fractions in the dense regime. To interpret and replicate the observed dynamics, we reformulate the \textit{Ka-Pi-bara} model of \cite{Bos2026} (an extension of the $k$--$ε$ model) in terms of total energy (the sum of kinetic and surface energy), which we further enhance by adding equations for the surface energy and its destruction. This model accurately captures a key feature of turbulence: non-equilibrium effects, seen as the phase lag between kinetic energy and its rate of dissipation, which are found to operate also in multiphase flows. Linearizing the model highlights the various relevant time scales of the system and provides predictions of how different observables are coupled and respond to the energy input. In particular, the model predicts that fluctuations of surface energy and its destruction are in phase, in good agreement with numerical simulations. Therefore, unlike kinetic energy, surface energy remains in equilibrium, indicating the absence of a surface energy cascade.

The maturity of the chemical vapor deposition graphene-based device processing has increased from chip level demonstrations to wafer-scale fabrication in the past few years. Due to this wafer-scale, electrical characterization and analysis of the fabricated devices has become increasingly important to enable extraction of multiple parameters with minimal number of measurements for the quality control purposes critical for industrial uptake of 2D materials-based devices. As a crucial step, we demonstrate optimization of complementary metal-oxide semiconductor (CMOS) back-end-of-line (BEOL) compatible graphene field-effect transistor (GFET) fabrication and analysis including the gate stack, bottom contact, graphene patterning and encapsulation process steps. The analysis methods include atomic force microscopy, scanning electron microscopy and most importantly electrical characterization. The electrical characterization focuses on comparing different test structures and extraction methods for mobility, contact resistance, IV-curve hysteresis and doping parameters. The comparison shows that the selected measurement test structures and analysis methods can have a large impact on the extracted values and should thus be considered when comparing data sets between different sources. The analysis shows that the optimized process offers high device yield of 98 % with good doping uniformity, contact resistance and mobility as well as low IV-curve hysteresis values on 200 mm wafers.

A classical theorem in the theory of minimal surfaces establishes a correspondence between minimal surfaces in $\mathbb{R}^n$ and null holomorphic curves in $\mathbb{C}^n$. A hyperbolic version of this correspondence is due to Bryant: null holomorphic curves in ${\rm SL}(2,\mathbb{C})$ correspond to CMC-1 surfaces in the hyperbolic space $\mathbb{H}^3$. We also have a relativistic Bryant type correspondence: CMC-1 immersions in the hyperbolic space are replaced by space-like CMC-1 immersion in the de Sitter space. We prove a mutual generalisation of all these results: let $H$ be a real Lie group, $π:P \to M$ a principal $H$-bundle, $A$ a connection on $P$ and $α\in A^1_{\rm Ad}(P,\mathfrak{h})$ a tensorial 1-form of type ${\rm Ad}$ which induces isomorphisms $A_ξ\to \mathfrak{h}$. Such a pair $(α,A)$ defines an almost complex structure $J^α_A$ on $P$, which is integrable if and only $(α,A)$ solves a gauge-invariant first order differential system. A non-degenerate symmetric ${\rm Ad}_H$-invariant bilinear form $g$ on $\mathfrak{h}$ defines pseudo-Riemannian metrics $g^α_M$, $\mathfrak{g}^α_A$ on $M$, respectively $P$, and a non-degenerate bilinear form $ω^{α,g}_A:T_P\times_P T_P\to \mathbb{C}$ which is holomorphic when $J^α_A$ is integrable. Assuming that this is the case, we have a Bryant type correspondence between space-like, $ω^{α,g}_A$-isotropic holomorphic immersions $Y\to P$ and space-like conformal immersions $Y\to (M,g^α_M)$ whose mean curvature vector field is given by a simple explicit formula. In particular, one obtains such a correspondence for any principal bundle of the form $G\to G/H$, where $G$ is a complex Lie group, and $H$ is a real form of $G$ endowed with a non-degenerate, ${\rm Ad}_H$-invariant, symmetric bilinear form $g$ on its Lie-algebra $\mathfrak{h}$.

Throughout the history of software, evolution has occurred in cycles of rise and fall driven by competition, and open-source software (OSS) is no exception. This cycle is accelerating, particularly in rapidly evolving domains such as web development and deep learning. However, the impact of competitive relationships among OSS projects on their survival remains unclear, and there are risks of losing a competitive edge to rivals. To address this, this study proposes a new automated method called ``Mutual Impact Analysis of OSS (MIAO)'' to quantify these competitive relationships. The proposed method employs a structural vector autoregressive model and impulse response functions, normally used in macroeconomic analysis, to analyze the interactions among OSS projects. In an empirical analysis involving mining and analyzing 187 OSS project groups, MIAO identified projects that were forced to cease development owing to competitive influences with up to 81\% accuracy, and the resulting features supported predictive experiments that anticipate cessation one year ahead with up to 77\% accuracy. This suggests that MIAO could be a valuable tool for OSS project maintainers to understand the dynamics of OSS ecosystems and predict the rise and fall of OSS projects.

The atomic properties of heavy, moderately-charged ions are important for a wide variety of applications, including precision tests of fundamental physics and for the study and development of atomic and nuclear clocks. In these systems it is known that relativistic effects, such as the Breit interaction and radiative quantum electrodynamics corrections, are important for an accurate understanding of atomic properties. It is also known that inclusion of correlations alongside the Breit effect is crucial. In this work we include the Breit interaction into all-orders calculations of energy levels and fine structure intervals of ions in the Cs and Fr isoelectronic sequences. This requires modifying the electron Green's function to account for Breit within the all-orders correlation potential method, which sums dominating series of perturbation diagrams exactly using a Feynman diagram technique. We find that Breit corrections to the energies of moderately ionized ions along these sequences are very large, particularly for the f states. We also observe a significant deviation from experiment for these levels. Incorporating Breit into the all-orders correlation potential provides a significant additional contribution beyond including Breit at the second-order level alone. While this does not resolve the disagreement in the energy levels, it does substantially improve the fine-structure intervals beyond what is achieved by including Breit only at second order. Furthermore, we include the frequency-dependent Breit interaction into the Dirac-Fock procedure, and find that this does not significantly modify the energy levels at this order of approximation.

Augmented reality (AR)-enabled Metaverse is a promising technique to provide immersive service experience for mobile users. However, the limited network resources and unpredictable wireless propagation environments are key design bottlenecks of AR-enabled Metaverse systems. Therefore, this paper presents a resource management framework for simultaneously transmitting and reflecting RIS (STAR-RIS)-assisted AR-enabled Metaverse, where the STAR-RIS is configured to improve the communication efficiency between AR users and the Metaverse server located at the base station (BS). Moreover, we formulate a service latency minimization problem via jointly optimizing the computation resource allocation of the BS, coefficient matrix of the STAR-RIS, central processing unit (CPU) frequency and transmit power of the AR users. To tackle the non-convex problem, we utilize an approximate method to transform it to a tractable form, and decouple the multi-dimensional variables via the alternating optimization method. Particularly, the optimal coefficient matrix is obtained by a penalty function-based method with proved convergence, the CPU frequencies of AR users are derived as the closed-form solution, and the transmit power of AR users and computation resource allocation of the BS are obtained by the Lagrange duality method and convex optimization theory. Finally, simulation results demonstrates that the proposed method achieves remarkable latency reduction than several benchmark methods.

We explore the operation of quantum batteries in the Lipkin-Meshkov-Glick (LMG) model, when they are charged either through a sudden quench in the magnetic field strength or by coupling them to a bosonic oscillator bath. Through initializing the battery in either the symmetric or broken symmetry phases of the LMG model we analyze how the different spectral properties can affect the performance of both the charging and discharging of the battery. In particular, we show that by quenching the magnetic field strength from the symmetric phase to the broken phase, we can achieve a significant enhancement in stored energy, as well as stable and efficient ergotropy extraction. Similar observations can be made when introducing weak coupling between the battery with the bosonic bath, while the amount of stored work and ergotropy saturate at strong coupling. These findings emphasize the importance of the magnetic field dynamics and environmental coupling in optimizing charging performance, which could lead to practical applications in quantum energy storage.

In Video on Demand (VoD) scenarios, traditional codecs are the industry standard due to their high decoding efficiency. However, they suffer from severe quality degradation under low bandwidth conditions. While emerging generative neural codecs offer significantly higher perceptual quality, their reliance on heavy frame-by-frame generation makes real-time playback on mobile devices impractical. We ask: is it possible to combine the blazing-fast speed of traditional standards with the superior visual fidelity of neural approaches? We present HybridPrompt, the first generative-based video system capable of achieving real-time 1080p decoding at over 150 FPS on a commercial smartphone. Specifically, we employ a hybrid architecture that encodes Keyframes using a generative model while relying on traditional codecs for the remaining frames. A major challenge is that the two paradigms have conflicting objectives: the "hallucinated" details from generative models often misalign with the rigid prediction mechanisms of traditional codecs, causing bitrate inefficiency. To address this, we demonstrate that the traditional decoding process is differentiable, enabling an end-to-end optimization loop. This allows us to use subsequent frames as additional supervision, forcing the generative model to synthesize keyframes that are not only perceptually high-fidelity but also mathematically optimal references for the traditional codec. By integrating a two-stage generation strategy, our system outperforms pure neural baselines by orders of magnitude in speed while achieving an average LPIPS gain of 8% over traditional codecs at 200kbps.

Domain-specific accelerators deliver exceptional performance on their target workloads through fabrication-time orchestrated datapaths. However, such specialized architectures often exhibit performance fragility when exposed to new kernels or irregular input patterns. In contrast, programmable architectures like FPGAs, CGRAs, and GPUs rely on compile-time orchestration to support a broader range of applications; but they are typically less efficient under irregular or sparse data. Pushing the boundaries of programmable architectures requires designs that can achieve efficiency and high-performance on par with specialized accelerators while retaining the agility of general-purpose architectures. We introduce Canon, a parallel architecture that bridges the gap between specialized and general purpose architectures. Canon exploits data-level and instruction-level parallelism through its novel design. First, it employs a novel dynamic data-driven orchestration mechanism using programmable Finite State Machines (FSMs). These FSMs are programmed at compile time to encode high-level dataflow per state and translate incoming meta-information (e.g., sparse coordinates) into control instructions at runtime. Second, Canon introduces a time-lapsed SIMD execution in which instructions are issued across a row of processing elements over several cycles, creating a staggered pipelined execution. These innovations amortize control overhead, allowing dynamic instruction changes while constructing a continuously evolving dataflow that maximizes parallelism. Experimental evaluation shows that Canon delivers high performance across diverse data-agnostic and data-driven kernels while achieving efficiency comparable to specialized accelerators, yet retaining the flexibility of a general-purpose architecture.

Electromagnetic transient (EMT) simulation is essential for analyzing sub-cycle switching phenomena in industrial power systems; however, commercial EMT platforms present significant cost barriers for smaller utilities, consultancies, and academic institutions, particularly in developing regions. This paper validates KESTREL EMT, a free and open-source electromagnetic transient solver with Python integration, through three progressive case studies involving industrial capacitor switching transients. This work investigates energization, switching resonance and VFD interactions with capacitor banks. The results demonstrate that KESTREL, when supported by appropriate circuit modeling techniques, produces EMT responses consistent with analytical predictions and established IEEE benchmarks. This work establishes a validated and reproducible methodology for conducting industrial EMT studies using freely available, open-source tools.

With the availability of automation machinery and its superiority, are being slothful and inviting many diseases to invade them. The world still has so many places where people lack basic health facilities. Due to early detection and intervention, CDV can be cured to an extreme extent. It heavily reduces travel and associated costs. A remote ECG monitoring system enables community health workers to support and empower patients through telemedicine. However, there remains some financial and logistical burden. Heart disease cannot be taken lightly. These patients require regular health check-ups and the attention of health personnel in a short period if their health deteriorates suddenly and rapidly. Chronic diseases are extremely variable in their symptoms and evolution of treatment. Some, if not treated early, will end the patient's life. The trend of the INTERNET OF THINGS, IoT, is spreading massively. This paper focuses on the three main: the operator, the doctor, and the server over which the data is being sent.

Many OSS projects join foundations such as Apache, Eclipse, and OSGeo, to aid their immediate plans and improve long-term prospects by getting governance advice, incubation support, and community-building mechanisms. But foundations differ in their policies, funding models, and support strategies. Moreover, since projects joining these foundations are diverse, coming at different lifecycle stages and having different needs, it can be challenging to decide on the appropriate project-foundation match and on the project-specific plan for sustainability. Here, we present an empirical study and quantitative analysis of the sustainability of incubator projects in the Apache, Eclipse, and OSGeo foundations, and, additionally, of OSS projects from GitHub outside of foundations. We develop foundation-specific sustainability models and a project triage, based on projects' sociotechnical trace profiles, and demonstrate their effectiveness across the foundations. Our results show that our models with triage can effectively forecast sustainability outcomes not only within but across foundations. In addition, the generalizability of the framework allows us to apply the approach to GitHub projects outside the foundations. We complement our findings with actionable recovery strategies from previous work and apply them to case studies of failed incubator projects. Our study highlights the value of sociotechnical frameworks in characterizing and addressing software project sustainability issues.

We investigate the class of $3$-decomposable genus two handlebody-knots and provide a complete classification of essential annuli in their exteriors. We introduce the notion of $τ$- and $ρ$-tangles and good rectangles and annuli. By classifying $τ$- and $ρ$-tangles whose exteriors admit a good rectangle or annulus, we categorize atoroidal $3$-decomposable genus two handlebody-knots into distinct classes, based on the number of essential annuli. As an application, the hyperbolicity of all genus two handlebody-knots with up to six crossings are determined, and numerous hyperbolic handlehody-knots with seven crossings identified. Furthermore, obstructions for a handlebody-knot to be $3$-decomposable are constructed with explicit examples provided.

The electronic band structure of Na$_{2}$KSb was studied by a combination of low-energy photoemission spectroscopy and density functional theory (DFT) calculations. The optical and photoemission quantum efficiency (QE) spectra, along with longitudinal energy distribution curves (EDCs) of multialkali Na$_{2}$KSb(Cs,Sb) photocathodes were measured in the temperature range of 80--295 K. The thresholds of various band-to-band transition in Na$_{2}$KSb were observed in the optical and QE spectra of Na$_{2}$KSb(Cs,Sb) photocathodes. The evolution of EDC derivatives with varying photon energy reveals a fine structure related to the emission of two types of electrons: (i) ballistic electrons, which are excited from heavy hole, light hole and split-off valence bands, and (ii) photoelectrons, that are captured in the side valleys of Na$_{2}$KSb conduction band. The analysis of EDCs and QE spectra allowed us to determine the band structure parameters of Na$_{2}$KSb at $T = 80$ K, including the band gap $E_{\text{g}} = 1.52 \pm 0.02$ eV, spin-orbit splitting $Δ_{\text{SO}} = 0.59 \pm 0.04$ eV and the energy separations between $Γ$ and side valleys of the conduction band: $Δ_{Γ-\text{X}1} = 0.41 \pm 0.05$ eV and $Δ_{Γ-\text{X}2} = 0.65 \pm 0.05$ eV. The experimentally determined band gaps and side valley positions, as well as the energies of the final electronic states of optical transitions are in good agreement with the DFT calculations. The obtained data on the hot electron dynamics and electronic band structure of Na$_{2}$KSb are crucial to improve the understanding of the photoemission processes in this material and will contribute to the development of the robust spin-polarized electron sources with multialkali photocathodes.

Large language model(LLM)-driven multi-agent systems(MAS) coordinate specialized agents through predefined interaction topologies and have shown promise for complex tasks such as competition-level code generation. Recent studies demonstrate that carefully designed multi-agent workflows and communication graphs can significantly improve code generation performance by leveraging collaborative reasoning. However, existing methods neither adapt topology density to task difficulty nor iteratively refine the topology within an instance using execution feedback, which leads to redundant communication and performance bottlenecks. To address these issues, we propose AgentConductor: a reinforcement learning-optimized MAS with an LLM-based orchestrator agent as its core, which enables end-to-end feedback-driven dynamic generation of interaction topologies. For each query, AgentConductor infers agent roles and task difficulty, then constructs a task-adapted, density-aware layered directed acyclic graph (DAG) topology, underpinned by two key innovations. First, we design a novel topological density function that captures communication-aware mathematical characterizations of multi-agent interactions. Second, we adopt difficulty interval partitioning to avoid excessive pruning for precise topological density upper bound measurement per difficulty level and finer-grained control. Empirically, across three competition-level and two foundational code datasets, AgentConductor achieves state-of-the-art accuracy, outperforming the strongest baseline by up to 14.6% in pass@1 accuracy, 13% in density reduction, and 68% in token cost reduction.