We consider the optimization problem $\min_{x\in \mathbb R^n}{F(x):=f(x)+ω(Ax)}$, where $f$ is an $L$-Lipschitz smooth function, and $ω$ is a proper, lower semicontinuous, and convex function. We prove in this paper that when $ω$ is a conic polyhedral function, the inexact accelerated proximal gradient method (IAPG), employed in a double-loop structure, achieves a total complexity of $\mathcal O(\ln(1/\varepsilon)/\sqrt{\varepsilon})$ measured by the total number of calls to the proximal operator of the convex conjugate $ω^\star$ and the gradient of $f$ to achieve $\varepsilon$-optimality in function value. To the best of our knowledge, this improves upon the best-known complexity for IAPG. The key theoretical ingredient is a quadratic growth condition on the dual of the inexact proximal problem, which arises from the conic polyhedral structure of $ω$ and implies linear convergence of the inner proximal gradient loop. To validate these findings, we conduct numerical experiments on a robust TV-$\ell_2$ signal recovery problem, demonstrating fast convergence.

College students face well-being challenges driven by academic pressure, financial strain, and social expectations. While campus counseling and student-success programs offer support, access is often limited by stigma, waitlists, and scheduling constraints. Existing digital tools focus on emotional check-ins or chatbots and may overlook structured goal setting and aligning goals with personal values. We present GROW, a goal-centered well-being coaching system that puts values-aligned goals at the center of the student experience. GROW combines the SMART framework with principles from Acceptance and Commitment Therapy in a conversational AI coach that helps students clarify aspirations, break them into concrete steps, and reflect on progress. The system links action plans with Google Calendar, sends reminders, and provides a dashboard that shows progress and engagement. We evaluated GROW through interviews with clinical psychologists, student-success staff, and faculty, followed by a one-week deployment with 30 undergraduates. Findings offer design implications for interactive systems that support engagement, accountability, and sense of purpose in higher education.

We provide algorithmic versions of the Polynomial Freiman-Ruzsa theorem of Gowers, Green, Manners, and Tao (Ann. of Math., 2025). In particular, we give a polynomial-time algorithm that, given a set $A \subseteq \mathbb{F}_2^n$ with doubling constant $K$, returns a subspace $V \subseteq \mathbb{F}_2^n$ of size $|V| \leq |A|$ such that $A$ can be covered by $2K^C$ translates of $V$, for a universal constant $C>1$. We also provide efficient algorithms for several "equivalent" formulations of the Polynomial Freiman-Ruzsa theorem, such as the polynomial Gowers inverse theorem, the classification of approximate Freiman homomorphisms, and quadratic structure-vs-randomness decompositions. Our algorithmic framework is based on a new and optimal version of the Quadratic Goldreich-Levin algorithm, which we obtain using ideas from quantum learning theory. This framework fundamentally relies on a connection between quadratic Fourier analysis and symplectic geometry, first speculated by Green and Tao (Proc. of Edinb. Math. Soc., 2008) and which we make explicit in this paper.

We infer recoil (kick) velocities for all binary black hole merger events reported up to the GWTC--4 catalog, together with candidate intermediate-mass black hole events. We obtain informative kick constraints for GW231028\_153006 ($839^{+1018}_{-681}\,\mathrm{km\,s^{-1}}$) and GW231123\_135430 ($974^{+944}_{-760}\,\mathrm{km\,s^{-1}}$). Additionally, we compute recoil velocities for recently reported events from the ongoing fourth observing run: GW241011\_233834, GW241110\_124123, and GW250114\_082203, obtaining $v_{\rm kick} = 974^{+555}_{-466}\,\mathrm{km\,s^{-1}}$, $394^{+582}_{-207}\,\mathrm{km\,s^{-1}}$, and $115^{+301}_{-95}\,\mathrm{km\,s^{-1}}$, respectively. The remnant of GW241011\_233834 is therefore inferred to have one of the largest recoil velocities among currently known events. We find that present recoil kick constraints are driven primarily by measurements of the mass ratio and spin magnitudes, while the contribution from spin orientation angles remains subdominant in most cases. We estimate typical retention probabilities of the remnant black holes in GWTC catalogs to be $\sim 1$--$5\%$ for globular clusters, $\sim 15$--$30\%$ for nuclear star clusters, $\sim 5$--$40\%$ for dwarf galaxies, and $\sim 70$--$100\%$ for elliptical galaxies. We further show that, even for remnants retained in globular clusters, recoil-induced spatial displacements from the cluster core are often significant, which can substantially suppress the chances of hierarchical mergers. We find that the probability for a GWTC merger remnant to participate in hierarchical mergers is $\sim 0.1$--$1\%$ in globular clusters and $\sim 1$--$15\%$ in nuclear star clusters.

Supply chains involve geographically distributed manufacturing and assembly sites that must be coordinated under strict timing and resource constraints. While many existing approaches rely on Colored Petri Nets to model material flows, this work focuses on the temporal feasibility of supply chain processes. We propose a modular modelling approach based on Product Time Petri Nets (PTPNs), where each subsystem is represented independently and the global behaviour emerges through synchronised transition labels. A key feature of the model is the explicit representation of the supply chain manager as a critical shared and mobile resource, whose availability directly impacts system feasibility. We analyse how timing constraints and managerial capacity influence the system behaviour, identifying configurations that lead to successful executions, timeouts, or timelocks induced by incompatible timing constraints. This approach enables systematic what-if analysis of supply chain coordination policies and demonstrates the relevance of PTPNs for modelling and analysing synchronised timed systems.

Agent-based models (ABMs) are increasingly used to study complex economic phenomena such as endogenous growth, but their analysis typically relies on ad-hoc Monte Carlo exercises without formal statistical guarantees. We show how statistical model checking (SMC), and in particular Multi-VeStA, can automate and enrich the analysis of a seminal ABM: the Island Model of Fagiolo and Dosi, which captures the exploration-exploitation trade-off in technological search. We reproduce key stylized facts from the original model with formal confidence intervals, confirm the optimality of moderate exploration rates, and perform a counterfactual sensitivity analysis across returns to scale, skill transfer, and knowledge locality. Using MultiVeStA's built-in Welch's t-test, 6 out of 7 pairwise parameter comparisons yield statistically different growth trajectories, while the exception reveals a saturation effect in knowledge locality. Our results demonstrate that SMC offers a principled, reproducible methodology for the quantitative analysis of agent-based economic models.

The issue of privacy has gained significant attention in recent times. Many real-world applications increasingly require the use of sensitive data, such as in surveillance or tracking and assistance systems. To address these concerns, we propose a framework based on mm-wave radar technology that not only meets privacy requirements but also provides the necessary capabilities for these systems, including reliable current position tracking, sequence tracking, and feedback to the user. While the use of radar technology for surveillance purposes is gaining momentum, there has been no research to date on its application for prayer tracking and assistance systems. Furthermore, there is a lack of comprehensive research that covers all aspects of implementing such a system. Proposed approach offers a versatile solution that can be applied to a broad range of scenarios. Instead of utilizing raw I-Q data, we addressed the challenge of classification based on point cloud information generated by the conventional processing chain of the frequency-modulated continuous wave radar. This information contains corresponding range, reflection amplitude, Doppler and angular values. We have developed and compared different machine-learning classification algorithms to identify the most effective one. Our findings reveal that the convolutional neural network ResNet achieves the best results, with accuracy rates reaching up to 95.4 percent when applied to unknown data. The demonstration video of the developed system can be viewed at the following link: https://youtu.be/PnpGQZWqCr4.

Modern society relies on complex supply chains to sustain the flow of goods and services that are essential to daily life. While traditional supply chain theory assumes a clear, hierarchical flow from upstream suppliers to downstream customers, observable real-world transaction networks rarely exhibit this acyclic structure. Instead, detailed inter-firm data reveal that interwoven networks are heavily entangled by cyclic flows. Consequently, without appropriate partitioning of these massive inter-firm networks, the latent flow-hierarchical structures that are central to supply chain concepts remain obscure. To address this analytical challenge, we introduce the flow-Hierarchical Community Network Extraction (f-HiCoNE) framework. By applying combinatorial Hodge decomposition, this approach disentangles the complex inter-firm network by isolating the acyclic gradient flow to quantify the flow-hierarchical parts and partition the graph. By applying f-HiCoNE to a nationwide transaction dataset of approximately 650,000 firms, we successfully extracted functional supply-chain clusters. These clusters demonstrated strong flow-hierarchical organisation, wherein the upstream-downstream positioning of firms was accurately captured by local scalar potentials, revealing distinct geographically localised industrial ecosystems. This study provides a map that helps firms understand their surrounding environment and locate their position within an inter-firm network and opens a new research avenue focused on flow-hierarchy clustering in supply chain analysis.

This paper investigates the trajectory tracking problem of underactuated marine vessels within a polar coordinate framework. By introducing two polar coordinate transformations (PCTs), the original two-input-three-output second-order tracking model expressed in the Cartesian frame is reduced to a two-input-two-output feedback system. However, the resulting model does not necessarily satisfy the strict-feedback condition required by conventional backstepping approaches. To circumvent potential singularities arising in the controller design, a novel concept termed exponential modification of orientation (EMO) is proposed. While the PCTs yield substantial structural simplification, they also introduce inherent limitations, most notably singularities associated with angular coordinates. Addressing these singularities constitutes another key focus of this paper. Numerical simulation results are presented to demonstrate the effectiveness of the proposed control strategy.

An $r$-dimensional wheel is defined as the join of an $(r-2)$-simplex and a cycle. In this paper, we study the maximum signless Laplacian spectral radius of $n$-vertex $r$-dimensional pure simplicial complexes that contain no $r$-dimensional wheels. For sufficiently large $n$, we determine the extremal complexes that attain this maximum. Our result generalizes the corresponding extremal results of signless Laplacian on graphs and provides a spectral anlogue of a theorem of Sós, Erdős and Brown on the maximum number of facets of simplicial complexes in the case $r=2$.

Given a finite group $G$, we denote by $ν(G)$ the probability that two randomly chosen elements of $G$ generate a nilpotent subgroup. We prove that if $ν(G)>1/12,$ then $G$ is solvable.

We investigate the boost-invariant expansion of a recently developed first-order spin hydrodynamic framework in which the spin chemical potential is treated as a leading-order hydrodynamic variable. Considering a symmetric energy-momentum tensor and a separately conserved spin tensor, we derive the coupled evolution equations for the medium temperature and the independent components of the spin chemical potential in the presence of both viscous and spin-diffusive transport coefficients. For a boost-invariant system, only the magnetic-like components of the spin chemical potential survive, and their evolution is shown to depend sensitively on the spin transport coefficients. The transverse spin components decay more rapidly due to spin dissipation, while the longitudinal component survives for a longer duration. We further demonstrate that the evolution of the spin degrees of freedom modifies the temperature profile of the expanding medium. Using the resulting temperature profiles, we calculate thermal dilepton production rates from quark-antiquark annihilation. We find that the presence of spin dynamics enhances the dilepton yield relative to standard dissipative hydrodynamics, with the magnitude of the enhancement depending on the spin transport coefficients. Our results indicate that thermal dileptons can provide an indirect probe of spin dynamics and spin transport in the quark-gluon plasma.

We develop a dynamic factor stochastic volatility-in-mean (SVM) specification for vector autoregressions (VARs) that embeds an SVM component within a dynamic factor stochastic volatility structure. A small number of latent volatility factors capture common movements in conditional variances, while volatility enters the conditional mean of the VAR. This specification allows time-varying uncertainty to influence macroeconomic dynamics through both second moments and expected outcomes while preserving tractability in large panels. We construct an efficient Markov chain Monte Carlo algorithm for estimation in this high-dimensional, non-Gaussian setting. Using quarterly data on twenty variables from the FRED-QD database, we compare predictive performance with the benchmark stochastic volatility VAR model. The dynamic factor SVM specification delivers superior forecasts for more variables during major macroeconomic disruptions such as the 2008 global financial crisis. The results indicate that allowing volatility to enter the mean captures an important transmission channel in macroeconomic dynamics.

Let $f(x) \in K(x)$ be a quadratic polynomial where $K$ is a field of characteristic not equal to $2$. The associated arboreal Galois representation of the absolute Galois group of $K$ acts on a regular rooted binary tree. Boston and Jones conjectured that, for $f \in \mathbb{Z}[x]$, the image of this representation contains a dense set of settled elements. Roughly speaking, a cycle of an automorphism $τ$ of the tree is called stable if its length strictly increases at each subsequent level, and $τ$ is called settled if the proportion of vertices contained in stable cycles goes to $1$ as the level goes to infinity. In this article, we prove that the arithmetic iterated monodromy groups of postcritically finite quadratic polynomials in $K[x]$ with periodic postcritical orbits are densely settled. In the number field case, by a result of Benedetto--Ghioca--Juul--Tucker \cite{BGJT2025s}, it follows that for infinitely many $a \in K$, the associated arboreal Galois representations are densely settled. In particular, our results apply to the arithmetic IMG of the Basilica map $f(x)=x^2-1$.

Lookup tables (LUTs) have recently gained attention as an alternative compute mechanism that maps input operands to precomputed results, eliminating the need for arithmetic logic. LUTs not only reduce logic complexity, but also naturally support diverse numerical precisions without requiring separate circuits for each bitwidth-an increasingly important feature in quantized DNNs. This creates a favorable tradeoff in PIM: memory capacity can be used in place of logic to increase computational throughput, aligning well with DRAM-PIM architectures that offer high bandwidth and easily available memory but limited logic density. In this work, we explore this capacity-computation tradeoff in LUT-based PIM designs, where memory capacity is traded for performance by packing multiple MAC operations into a single LUT lookup. Building on this insight, we propose LOCALUT, a PIM-based design for efficient low-bit quantized DNN inference using operation-packed LUTs. First, we observe that these LUTs contain extensive redundancy and introduce LUT canonicalization, which eliminates duplicate entries to reduce LUT size. Second, we propose reordering LUT, a lightweight auxiliary LUT that remaps weight vectors to their canonical form required by LUT canonicalization with a simple LUT lookup. Third, we propose LUT slice streaming, a novel execution strategy that exploits the DRAM-buffer hierarchy by streaming only relevant LUT columns into the buffer and reusing them across multiple weight vectors. Evaluated on a real system based on UPMEM devices, we demonstrate a geometric mean speedup of 1.82x across various numeric precisions and DNN models. We believe LOCALUT opens a path toward scalable, low-logic PIM designs tailored for LUT-based DNN inference. Our implementation of LOCALUT is available at https://github.com/AIS-SNU/LoCaLUT.

Agentic AI systems increasingly execute consequential actions on behalf of human principals, delegating tasks through multi-step chains of autonomous agents. No existing standard addresses a fundamental accountability gap: verifying that terminal actions in a delegation chain were genuinely authorized by a human principal, through what chain of delegation, and under what scope. This paper presents the Human Delegation Provenance (HDP) protocol, a lightweight token-based scheme that cryptographically captures and verifies human authorization context in multi-agent systems. An HDP token binds a human authorization event to a session, records each agent's delegation action as a signed hop in an append-only chain, and enables any participant to verify the full provenance record using only the issuer's Ed25519 public key and the current session identifier. Verification is fully offline, requiring no registry lookups or third-party trust anchors. We situate HDP within the existing landscape of delegation protocols, identify its distinct design point relative to OAuth 2.0 Token Exchange (RFC 8693), JSON Web Tokens (RFC 7519), UCAN, and the Intent Provenance Protocol (draft-haberkamp-ipp-00), and demonstrate that existing standards fail to address the multi-hop, append-only, human-provenance requirements of agentic systems. HDP has been published as an IETF Internet-Draft (draft-helixar-hdp-agentic-delegation-00) and a reference TypeScript SDK is publicly available.

The evolution of wireless networks is driving new paradigms for consideration in upcoming generations. To this end, the 6G anticipates the development of several data-rate-hungry applications, in addition to a forecast growth in sensing-centric applications. Such an evolution, however, is unbalanced on the other side by the accentuated scarcity of spectrum, which opens up urgent needs to develop spectrum-efficient communication and sensing techniques. Due to the inability of the traditional multi-antenna schemes to enhance a wireless channel quality, increasing interest has been paid to wireless channel-altering schemes, such as reconfigurable intelligent surfaces and movable antennas. Recently, a new technique in this category, called pinching antennas (PAs), was introduced and tested. PA systems (PASS) are based on extending the reach of a base station by connecting its radio-frequency chains to long waveguides, on which one or many radiating antennas are pinched at custom positions of interest. Thus, such a technique can provide a means of overcoming several unfavorable channel conditions, such as the absence of a line-of-sight and increased free-space path loss. Importantly, such a channel-tuning feature can provide notable enhancements in terms of sensing, network coverage, data rate, and resilience against eavesdropping. In this work, we provide a comprehensive review of research on PASS, designed to meet various system design objectives, such as network coverage and data rate, information-theoretically secure transmission, sensing, integrated sensing and communication, and energy efficiency. A categorization of the surveyed work is established by comparing the various PASS schemes presented. Several takeaways are illustrated on the proposed schemes' potential and limitations, along with several directions forward discussed, in terms of future deployment and implementation.

We study nonreciprocal current response in noncentrosymmetric crystals under time-reversal symmetry. We show that the nonreciprocal current appears in a dissipative system through interband processes. The nonreciprocal current is inversely proportional to the lifetime $τ$ and has a close relationship to the geometric quantity called the shift vector. The current mechanism is suitable for minigap systems where the energy gap and relaxation strength are comparable. We present a numerical simulation of the nonreciprocal current in the one-dimensional Rice--Mele model.

We propose a unified mixture sampler (UMS) that provides a universal estimation framework for nonlinear state-space models with "exp-exp" likelihood kernels. Unlike existing methods that require deriving new mixture approximations for each specific distribution, our approach dynamically adapts the standard ten-component mixture from Omori et al. (2007) through a deterministic re-centering and rescaling algorithm. Applying this to the stochastic conditional duration (SCD) model, we demonstrate that the proposed sampler can efficiently handle unknown shape parameters - such as those in Weibull or Gamma distributions - by updating mixture components near-instantaneously during MCMC iterations. The UMS not only simplifies implementation but also ensures exact inference via a lightweight Metropolis-Hastings step. Numerical examples show that our method substantially outperforms the conventional slice sampling approach, significantly reducing autocorrelation in MCMC samples while maintaining high computational efficiency. This unified framework encompasses a wide range of applications, including logit, Poisson, and various SCD model specifications, providing a highly efficient alternative to model-specific samplers.

Detectors designed for the International Linear Collider have been studied over many years, and a good understanding of the relevant requirements and constraints has been developed. With the prospect of future Higgs Factory projects with different properties (for example, the FCC-ee), the adaptations required for use at such facilities are being investigated. We outline our current understanding in this note.

In this paper, we establish joint extreme values of Dirichlet (L)-functions and their logarithmic derivatives using the resonance method. Our results extend previous work of Aistleitner et al. (2019) and Yang (2023).

The AlF molecule, currently subject to laser cooling and trapping efforts, has the advantage that it can be efficiently produced in a thermochemical reaction between sublimated aluminum trifluoride and aluminum metal. Here we present a series of experiments with continuous molecular beam sources of AlF, utilising this reaction. We demonstrate a compact AlF molecular beam oven whose total far-field brightness is $5\times 10^{15}$ molecules per steradian per second at 923~K, just below the melting temperature of aluminum metal. The continuous output from the oven begins to exceed the peak brightness of a jet-cooled, ablation-based supersonic AlF source for the $v=0$, $J=7$ level, and we obtain an excellent signal-to-noise ratio with the oven in pulsed laser ionisation spectroscopy experiments. By delivering flux from the oven into a cryogenic Ne buffer gas cell, we lower the rotational temperature of the beam to around 30~K and reduce its most probable forward velocity from 600~ms$^{-1}$ to 200~ms$^{-1}$. In addition, we demonstrate that AlF can be made in a simple dispenser package, and observe that molecules thermalise to the laboratory temperature after colliding with vacuum chamber walls of the experiment. The resulting transient AlF vapour may enable direct loading of a molecular magneto-optical trap.

Group II-IV nitrides have recently emerged as a novel class of semiconductors composed of earth-abundant elements. Owing to their tunable bandgaps, comparable to those of III-nitrides, these materials are attractive candidates for replacing expensive Ga-based alloys in photovoltaics and green-gap optoelectronics. In this work, epitaxial growth of MgSnN2 layers on 4H-SiC(0001) substrates by direct current magnetron sputtering is demonstrated. Mg and Sn metal targets have been co-sputtered in nitrogen-containing atmosphere at growth temperatures up to 500 °C. X-ray diffraction and cross-sectional transmission electron microscopy confirm the MgSnN2 layers grow epitaxially in a wurtzite crystal structure, exhibiting the epitaxial relationships with the substrate: MgSnN2 [0001]//4H-SiC [0001] and MgSnN2 [10-10]//4H-SiC[10-10]. Improved crystalline quality is observed for higher deposition temperatures and near-stoichiometric composition, as evidenced by the narrowing of rocking curve linewidths. Optical characterization reveals high absorption coefficients (1e5 cm-1) in the visible spectrum, comparable to that of GaAs, highlighting the suitability of MgSnN2 for photovoltaic applications. A photoluminescence emission band at ~2.4 eV is detected, highly desirable for optoelectronic devices operating in the challenging green spectral region. These results establish MgSnN2 as an earth-abundant, environmentally friendly material, structurally compatible with III-nitrides, with potential for cost-efficient components in sustainable optoelectronics and photovoltaics.

We aim to investigate the feasibility of accurately determining the helium-to-metal enrichment ratio $ΔY/ΔZ$ for open clusters using Gaia DR3 photometry. To test the reliability of this calibration, we performed a theoretical investigation using mock open clusters. We generated synthetic photometric data from isochrones calculated by five different stellar evolution codes (FRANEC, PARSEC 1.2s, PARSEC 2.0, BASTI, and MIST), for which the true $ΔY/ΔZ$ is known. We then fitted these mock clusters with two sets of isochrones calculated with the FRANEC code, differing only in the implementation of bolometric corrections (BCs). The analysis focused on the G-band absolute magnitude range (4.3 to 6.5 mag) to minimise the impact of poorly constrained physics. Synthetic clusters were generated at [Fe/H] values from 0.0 to 0.15 dex, for different numbers of populating stars and different levels of photometric uncertainties. The Monte Carlo experiments revealed significant and code-dependent biases. Unbiased results were achieved only when the stellar models used for synthetic-cluster generation and fitting were identical. Using identical FRANEC stellar models but different BCs introduced a significant bias of up to 0.6. Furthermore, using different stellar models for synthetic cluster generations resulted in even larger biases: $ΔY/ΔZ$ was underestimated by up to 0.8 for PARSEC target isochrones, while it was overestimated for BASTI and MIST isochrones by up to 0.6 and 1.5, respectively. The magnitude and the inconsistency of these biases strongly suggest that the photometric calibration of $ΔY/ΔZ$ using open clusters is not reliably robust.

A torsion class $\mathcal{T}$ of the module category $\operatorname{\mathsf{mod}} A$ of a finite dimensional algebra $A$ over a field $K$ is said to be compact if there exists a module $M \in \operatorname{\mathsf{mod}} A$ such that $\mathcal{T}$ is the smallest torsion class containing $M$. If a torsion class satisfies this and the dual condition, then we call it a bicompact torsion class. We conjecture that bicompact torsion classes are precisely functorially finite torsion classes, and prove it for hereditary algebras and also for semistable torsion classes. This gives that Demonet Conjecture implies Enomoto Conjecture, both of which are important conjectures on brick infiniteness.

This paper studies the problem of steering large-scale multi-agent stochastic linear systems between Gaussian distributions under probabilistic collision avoidance constraints. We introduce a family of \textit{distributed covariance steering (DCS)} methods based on the Alternating Direction Method of Multipliers (ADMM), each offering different trade-offs between conservatism and computational efficiency. The first method, Full-Covariance-Consensus (FCC)-DCS, enforces consensus over both the means and covariances of neighboring agents, yielding the least conservative safe solutions. The second approach, Partial-Covariance-Consensus (PCC)-DCS, leverages the insight that safety can be maintained by exchanging only partial covariance information, reducing computational demands. The third method, Mean-Consensus (MC)-DCS, provides the most scalable alternative by requiring consensus only on mean states. Furthermore, we establish novel convergence guarantees for distributed ADMM with iteratively linearized non-convex constraints, covering a broad class of consensus optimization problems. This analysis proves convergence to stationary points for PCC-DCS and MC-DCS, while the convergence of FCC-DCS follows from standard ADMM theory. Simulations in 2D and 3D multi-agent environments verify safety, illustrate the trade-offs between methods, and demonstrate scalability to thousands of agents.

Satellite emulation software is essential for research due to the lack of access to physical testbeds. To be useful, emulators must generate observations that are well-aligned with real-world ones, and they must have acceptable resource overheads for setting up and running experiments. This study provides an in-depth evaluation of three open-source emulators: StarryNet, OpenSN, and Celestial. Running them side-by-side and comparing them with real-world measurements from the WetLinks study identifies shortcomings of current satellite emulation techniques as well as promising avenues for research and development.

This article proposes a category-theoretic formalization of Greimasian narrative programs (NPs) that makes their compositional structure mathematically precise. Building on a reconstruction of the actantial model as a categorical schema, we introduce a refined typological schema of actants and derive Set-valued instances corresponding to role-indexed elements of a narrative. NPs are represented within a categorical schema whose morphisms are interpreted using monads on Set. In particular, the List monad provides a Kleisli semantics for modeling non-atomic, list-valued actantial configurations, while the Maybe monad encodes optional dependencies between programs. This yields a minimal representation of narrative programs as structured data with an intrinsic compositional interpretation. To account for the dynamics of narrative formation, we lift these constructions into a diagrammatic setting by freely generating a symmetric monoidal category, and subsequently a hypergraph category, from the set of actants. In this framework, narrative programs act as generators of morphisms, and their composition is realized through wiring diagrams. A narrative trajectory is thereby interpreted as a single composite morphism. This approach provides a unified mathematical framework for structural semiotics, connecting data-level representations of narrative elements with their compositional realization in discourse.

We study oscillon/I-ball solutions in a real scalar version of the Friedberg-Lee-Sirlin (FLS) model. Using the two-timing analysis, we derive the conditions for oscillon solutions and explore multi-field oscillon configurations. In these configurations, the two fields form co-located oscillons that oscillate with frequencies set by their respective masses. These multi-field oscillons can be viewed as a bound state of two oscillons due to attractive interactions between the fields. We confirm these analytical predictions through numerical lattice calculations. This work extends the standard picture of single-field oscillons and may be relevant for cosmological scenarios involving multiple interacting real scalar fields.

The paper studies computability-theoretic aspects of topological $T_0$-spaces. We introduce effective versions of the notions of a countable $c$-poset and a (second-countable) topological space with base. Based on this, we prove an effective version of the known Stone-type duality between the category $\mathbf{AS}$ (whose objects are almost semispectral spaces with base and whose morphisms are spectral mappings) and the category $\mathbf{DP}$ (whose objects are distributive $c$-posets and whose morphisms are strict mappings). Namely, we show that for an arbitrary set $Z\subseteq ω$, this duality is preserved when one restricts to objects which have $Z$-computably enumerable presentations only. Following this approach, we establish several results in computable topology. We prove that every degree spectrum of a countable algebraic structure can be realized as the degree spectrum of a topological space with base. We show that for any non-zero natural number $N$, there is a computable topological space with base that has precisely $N$-many computable copies, up to effective spectral homeomorphisms.