Unlike classical optimal transport, weak transport costs depend nonlinearly on the conditional law of couplings. This feature is essential in problems involving barycenter, conditional moments, and martingale-type constraints. Meanwhile, such conditional dependence makes ordinary Wasserstein geometry insufficient and calls instead for an adapted Wasserstein viewpoint. In this paper, we investigate the entropy-regularized weak optimal transport via gradient flows in adapted Wasserstein space. We derive, from the formal tangent structure of adapted Wasserstein space and the projection onto the set of couplings with prescribed marginals, a coupled McKean--Vlasov SDE. A novel and subtle term is a projection that, at each $Y$-location, averages a weak-transport force that already depends on the conditional law of $Y$ given $X$, thereby preserving marginals while retaining the nonlinear weak-transport structure. Under mild integrability and regularity assumptions, we prove weak existence and uniqueness in law for this projected McKean--Vlasov equation. We then prove that the flow converges, in the adapted Wasserstein topology, to the unique minimizer of the entropic weak optimal transport problem. We also describe a particle approximation and illustrate the dynamics on optimal transport and martingale optimal transport examples.

This work presents a conforming finite-element scheme for non-isothermal phase-field systems coupled to the incompressible Navier-Stokes equations. The proposed numerical scheme preserves entropy production and total energy conservation exactly by variable transformations using entropy as main variable instead of temperature. Convergence tests in space are conducted, and representative examples are provided to demonstrate the scheme's effectiveness.

Context: Neurodiversity is increasingly recognized as a valuable dimension of workplace diversity. However, in agile software development teams, the interplay between teamwork practices and the inclusion of neurodivergent employees remains underexplored. Objective: The study aims to explore how teamwork quality in agile software development is currently practiced and discussed in the context of neurodiversity, and to identify organizational barriers that hinder the effective inclusion of neurodivergent developers. Method: We applied a mixed-method approach combining a web content analysis covering Reddit and LinkedIn with 11 semi-structured expert interviews from a corporate neurodiversity network in a German organization. Results: The analysis shows that teamwork practices are highly fragmented and shaped by individual adaptation rather than a shared standard. While agile practices and supportive tools can enable neurodivergent participation, rigid structures, stereotypes, and one-size-fits-all approaches often undermine inclusion. Organizational awareness and tailored adjustments remain insufficient. Conclusion: Agile practices can promote inclusive teamwork, yet their benefits are constrained by rigid organizational structures and limited awareness of neurodiversity. Harnessing neurodiverse strengths demands flexible organizational conditions and tailored support.

By varying the symmetry energy slope ($L$), I investigate how the exotic content within the interiors of neutron stars changes and how it affects both macroscopic and microscopic quantities. Using two different parametrizations (L3$ωρ$ and BigApple), and three different possibilities about the neutron star core (nucleons+hyperons, nucleons+deltas, nucleons+hyperons+deltas), I show that, for the models analyzed in this work, changing the slope barely changes the amount of hyperons, but it can strongly suppress the $Δ$ resonances for large values of $L$. I also show that, in general, the presence of exotic content will be more evident for lower values of $L$ than for large ones. Differences and similarities between the two parametrizations are also analyzed.

Functional near-infrared spectroscopy (fNIRS) provides a noninvasive window into brain activity by measuring task-related changes in oxygenated and deoxygenated hemoglobin in the cortex. A key advantage of fNIRS is its promise of use with mobile participants in complex, real-world environments, such as walking, sports, classroom learning, driving simulations, or social interactions. However, analyzing fNIRS data is challenging because of motion artifacts, physiological noise, and other confounding factors. This challenge is further compounded by the limited availability of annotated datasets, which hinders the development and validation of new analysis pipelines, particularly given the growing use of AI methods. Recognizing these challenges, we introduce a 3D fNIRS simulator that uses mesh-based Monte Carlo simulations to create physiologically realistic, full-head synthetic recordings with high spatiotemporal fidelity. Our simulator combines anatomically accurate sensitivity profiles with parameterized models of hemodynamic responses, systemic physiology, and nonsystematic artifacts. As a result, users can generate virtually unlimited labeled datasets for testing denoising algorithms, data augmentation, mechanistic modeling, or \textit{in silico} experimentation. We validate the simulator using experimental fNIRS data from open-source finger-tapping, pain-assessment, and surgical-skill datasets and provide an open-source implementation to support reproducibility and broad adoption.

We study how retweet interactions in large-scale Twitter debates are organized beyond direct links alone. Focusing on Twitter debate in Italy during the first phase of the COVID-19 pandemic, we combine a validated community-reconstruction pipeline with a higher-order random-walk framework to examine how short multi-step pathways redistribute attention across discursive communities. Rather than reconstructing observed cascades of individual tweets, we use motif-based random-walk paths as a structural device to compare direct community-to-community connectivity with the distribution of multi-step endpoints. We find that attention is initially concentrated within communities, but that this concentration weakens as path length increases. At the same time, the resulting cross-community redistribution is not uniform: some communities become increasingly prominent as endpoints of longer pathways, while others lose relative prominence. These differences are not fully captured by community size or by first-order retweet connectivity alone, and they also display important directional asymmetries when the network is analyzed under the reversed orientation. Taken together, the results show that moving beyond direct retweets changes the community-level representation of online debate and reveals higher-order structural patterns that remain invisible in first-order analyses.

In this paper, we establish the expected asymptotic formula for the number of rational lines on a diagonal cubic hypersurface in 18 or more variables, improving on recent work of the second author. This is achieved via a refined mean value estimate for minor arcs that non-trivially exploits a shifting variables argument in both underlying dimensions.

We present three-dimensional general relativistic magnetohydrodynamics simulations of equal-mass binary neutron star mergers with varied neutron star spin configurations and second-moment neutrino transport, following the formation and early evolution of long-lived remnants. We compare a fiducial irrotational binary with binaries having spins that are aligned or antialigned with the orbital angular momentum, and examime how spin affects the merger dynamics, magnetic field evolution, outflows, and nucleosynthesis. Compared to the fiducial case, the aligned spin configuration releases more cold, neutron-rich tidal ejecta in the equatorial plane, which enables the development of a more tightly collimated polar outflow erupting from the remnant and inner accretion disk. Conversely, the case with spins antialigned with the orbit experiences a more violent collision at merger, disrupting magnetic amplification, loading the environment with debris, and impeding the propagation of magnetically driven winds. Strong neutrino reprocessing of the polar outflow in the irrotational and aligned spin cases produces $2.4\times 10^{-3}\,M_\odot$ of proton-rich ($Y_e \geq 0.49$) material, resulting in the synthesis of light r-process elements including $^{56}Ni$, whose subsequent decay potentially sends a unique electromagnetic signal from long-lived remnants. However, the outflows remain too dense and slow to be consistent with typical short gamma-ray bursts.

This paper introduces the Multi-Activity Transport & Mobility (MATraM) Agent-Based Model (ABM), a novel framework designed to advance activity-based transport modelling by incorporating dynamic activity adaptation. Traditional transport models simulate system performance using varying levels of abstraction, including flow-based, queue-based, and interaction-based mobility representations. While these approaches differ in their treatment of movement and congestion, they typically rely on pre-defined trip patterns that limit responsiveness to changing conditions. In particular, conventional activity-based models generate trips from fixed daily schedules, constraining their ability to capture behavioural flexibility and uncertainty. MATraM addresses this limitation by enabling agents to flag activities modification requests in response to sub-optimal travel conditions, such as increased travel times. By coupling with an activity scheduling and modification framework, the model integrates adaptive decision-making into the generation and execution of daily activity schedules. This allows for a more realistic representation of how individuals adjust their behaviour in response to transport system dynamics, leading to emergent mobility and congestion patterns. The ABM is presented following the ODD protocol, outlining its purpose, structure, and implementation. MATraM includes detailed representations of agents, their activity schedules, and the transport network, alongside submodels governing routing, scheduling, and behavioural adaptation. By bridging activity-based modelling with interaction-based mobility simulation, MATraM provides a flexible and extensible platform for exploring transport dynamics under uncertainty. This work contributes to the development of next-generation transport models capable of capturing the complex interplay between individual behaviour and system-level outcomes.

We study the aggregation problem in synchronous multi-hop radio networks with $O(\log n)$-bit messages and no collision detection. Each node initially holds a value, and the goal is to compute a global aggregate such as the sum of all values. Aggregation tasks arise naturally in wireless sensor networks, where nodes are often battery-powered and radio activity is the dominant source of energy consumption. Accordingly, our main objective is to minimize the energy complexity, defined as the maximum number of rounds in which any node is awake. Our main result is a randomized distributed algorithm that, with high probability, constructs and executes an aggregation schedule in $O(n \operatorname{polylog} n)$ rounds and using $O(Δ^\ast \operatorname{polylog} n)$ energy, where $Δ^\ast$ is the minimum possible maximum degree of a spanning tree of the network graph. This guarantee is nearly optimal: for any aggregation schedule and any graph, there exists a node that must be awake for at least $Δ^\ast$ rounds. As a by-product, the algorithm also computes a spanning tree whose maximum degree is within an $O(\log n)$ factor of $Δ^\ast$, with the same round and energy guarantees. For every tree edge, both endpoints learn that the edge belongs to the tree.

Computing within limits is a promising field, that follows principles of a) questioning endless growth narrative, b) considering and preparing for models of scarcity and c) reducing energy and material consumption, while considering d) a global spatial scale and e) long time frames. With computing's environmental impact growing and ecological limits becoming increasingly pressing, the LIMITS workshop has served as a central venue for this community since its inception in 2015, but an overview of the research published there has yet to be described. This paper addresses this gap by analyzing 160 publications from the LIMITS workshop in the period 2015 to 2025 to identify its international spread, contributions and developments in relation to field's core concerns, combining programmatic analysis with a manual review. Our findings indicate that the field has increasingly mentioned degrowth and post-growth, especially in 2024-2025. It has broadened its global perspective, with a growing, but still limited, representation of work beyond the Global North. The majority of papers are positional or observational, while artifact-producing research remains relatively scarce, though solution-oriented output has grown in recent years. This paper contributes to the LIMITS community by mapping its first decade and current trends to support future research and enhance its global impact.

We introduce a method to numerically compute the entanglement entropy of an acoustic black hole. It is shown that the entanglement entropy of sufficiently large subregions scales linearly with size and thus shows a volume law instead of an area law. The origin of this scaling can be traced back to the non-separable long-distance correlations due to the production of phonon pairs at the horizon. The system is shown to be locally thermal, such that the part of the entanglement entropy scaling with volume is well approximated by the thermal entropy of the outgoing Hawking radiation.

LLM pedagogical agents are proliferating, yet recent findings have raised questions about their adherence to established theories of learning and, by extension, their educational value. Concerns regarding cognitive offloading, over-reliance, and "gaming" behaviors persist and remain largely unaddressed. In response, we developed Copa, an agentic, multi-agent, multimodal Collaborative Peer Agent for STEM+C learning. Copa is built on top of the Evidence-Decision-Feedback (EDF) framework, grounding its interactions in Social Cognitive Theory and Social Constructivism and promoting sense-making through adaptive, dialogic support rather than answer-seeking. In an authentic high school computational-modeling study (n=33 dyads), we demonstrate that Copa (1) supports students' confidence building and ability to verbalize conceptual understanding without causing dependence; and (2) provides adaptive feedback personalized to learners that is interpretable with respect to students' multimodal input data. These findings position theory-guided, multimodal LLM agents as a promising path toward classroom AI integration that amplifies students' reasoning rather than replacing it.

Motivated by the open problem of whether all one-relator groups have decidable Diophantine problem, in this paper we prove a collection of undecidability results about the Diophantine problem for several families of groups that are close to one-relator groups in various ways. We prove that there is a generalised Baumslag--Solitar group with an undecidable Diophantine problem. Using our example we show there is a group with an undecidable Diophantine problem that is quasi-isometric to a one-relator group. Also, we prove that there is a one-relator product of cyclic groups with an undecidable Diophantine problem. In addition, we show that there there is a one-relator group $G$, with a single fixed finite rank free subgroup $H$, such that the Diophantine problem for $G$ with $H$-constraints is undecidable. The related open question of whether there is a free-by-cyclic group with undecidable Diophantine problem is also discussed, and we prove that there is a free-by-free group of the form $F_3 \rtimes F_2$ with an undecidable Diophantine problem.

Polymorphic Prompt Assembling (PPA) defends LLM agents against prompt injections by randomly selecting separator pairs from a fixed pool to isolate user input from system instructions. Although effective, static pool reuse exposes a blast-radius vulnerability: once a separator leaks, it can be exploited in future requests. We propose a dynamic per-request separator generation using domain-separated SHA-256 digests keyed on the timestamp, session identifier, and cryptographic nonce. Each assembled prompt receives a unique (BEGIN, END) canary pair, thereby limiting leakage exposure to a single request. We evaluated our extension against 16 injection payloads on Llama-3.3-70B-Instruct-Turbo, with cross-model validation on DeepSeek-V4-Flash model. Against the M1 obfuscation payload (leetspeak + urgency), the dynamic mode reduces the Attack Success Rate (ASR) from 0.88 to 0.38, yielding a statistically significant 2.3 x mitigation verified by non-overlapping 95% Wilson confidence intervals. Against format_breakout_salad, static separator leakage (leak_rate = 0.467) is eliminated entirely in the dynamic mode (0.000), confirming the blast-radius reduction in practice. The implementation requires no model fine-tuning, adds 2.7 microseconds prompt-assembly overhead per request, and is backward compatible with the existing PPA SDK.

We identify voids in NGC 628 from the JWST MIRI F770W image using a deep_learning method (BlendMask) and refine them by intensity contrast. These voids may be feedback_driven bubbles or dynamically formed structures. Cross_matching with archival star cluster/association catalogs shows that only up to 17.6% of voids are associated with such stellar populations. HST B_band peak_flux distributions of voids with and without these populations overlap substantially, suggesting many related clusters/associations remain unidentified or misclassified. Voids associated with star clusters/associations tend to have lower intensity contrast and larger sizes. An anti_correlation between void size and intensity contrast indicates larger voids have emptier centers, possibly due to stronger feedback. Thus, voids may provide a complementary tracer for identifying stellar populations and constraining their physical properties. To quantify spatial relationships among CO, 21$μ$m, H$_α$ sources, and voids, we construct networks linking each source pair. Among the nine networks, 21$μ$m and H$_α$ sources show the strongest spatial association. Compared to small voids, large voids exhibit progressively increasing separations from CO to 21$μ$m to H$_α$ sources to voids, consistent with an evolutionary sequence in space and time. Smaller voids lie closer to molecular clouds, while larger voids are more displaced. Compared with molecular clouds not associated with voids, those associated with voids are significantly more massive and appear more evolved. Indeed, 68% of molecular clouds associated with voids are also associated with 21$μ$m sources. These results support an evolutionary scenario where some voids originate within molecular clouds, grow through stellar feedback, and gradually detach from their parent clouds.

Bilevel optimization involves an upper-level and a lower-level decision maker. The lower-level optimization problem is nested within the constraints of the upper-level one. A point is said to be admissible for the bilevel problem if it satisfies all constraints and is optimal for the lower-level decision-maker. Bilevel derivative-free optimization (BL-DFO) algorithms address bilevel optimization problems in which either the upper-level or the lower-level problem is solved using a derivative-free optimization method. In this context, existing BL-DFO benchmarking techniques often do not rigorously validate the admissibility of proposed solutions, and do not adequately account for the computational effort deployed by the upper- and lower-level solvers. This work proposes a benchmarking methodology for BL-DFO algorithms. A post-optimization procedure, named refereeing procedure, is introduced to discard non-admissible points and ensure a fair comparison between the algorithms. The computational effort deployed by upper- and lower-level solvers are also taken into account into the overall computational cost. Numerical experiments illustrate the benchmarking methodology.

For an abelian variety $X$ and $α\in Br(X)$, we propose a new invariance $Ind_{SH}(α)$ that refines the known period index relations. It is closely related to the geometry of $\mathcal{X}$, the $\mathbb{G}_m$-gerbe over $X$ that corresponds to $α$: we study the minimal trivializing isogenies for $\mathcal{X}$ via its $μ_n$-lifts and the $1-$twisted semi-homogeneous vector bundles on $\mathcal{X}$. As an application, we show that the period index conjecture holds true for products of elliptic curves of any dimension.

Rainfall measurement with high spatial and temporal resolution is critical for flood forecasting, drought mitigation, and disaster preparedness. Rainfall patterns are highly variable, both geographically and over time. This variability presents a significant challenge for monitoring, as rain gauges can accurately capture temporal patterns only at a single location. Furthermore, the high cost of commercial instruments restricts their widespread deployment, and rain gauge networks often fail to adequately capture the spatial heterogeneity of precipitation patterns. To address these limitations, this study introduces a low-cost IoT-based rainfall monitoring system developed upon the Low-cost Efficient Wireless Intelligent Sensor (LEWIS) platform. Four rainfall sensors were designed, developed, and deployed at different locations across the semi-arid region of the United States, in the State of New Mexico, to capture localized precipitation variability. Each sensor node integrates a rainfall detection module with an LTE-enabled microcontroller and is powered by a compact solar-battery system, ensuring autonomous and self-sufficient operation. Real-time precipitation data are transmitted to a cloud server for continuous access, visualization, and integration with early-warning frameworks. The results demonstrate that IoT-based rainfall monitoring can achieve reliable accuracy at a fraction of the cost of conventional gauges, while supporting dense deployment for microscale precipitation analysis. Comparative validation with model-based precipitation data and in situ observations shows strong agreement in the detection and timing of recorded precipitation events, highlighting the system potential for early warning, disaster risk reduction, and bias correction of remotely sensed precipitation products by filling observational gaps in under-instrumented semi-arid areas.

Diagrammatic Monte Carlo provides a systematically improvable framework for stochastically resumming many-body expansions to high orders through direct sampling of diagram topologies. We advance our earlier work by introducing a novel time-ordered Diagrammatic Monte Carlo algorithm for the single-particle Green's function. The algorithm is tailored to finite nuclei, formulated in discrete model spaces and applicable to arbitrary two-body interactions. The new time-ordered diagrammatic Monte Carlo algorithm is based on the on-the-fly evaluation of time-ordered Goldstone diagrams, avoiding explicit diagram enumeration and expensive frequency integration. We show the algorithm by computing ${}^{16}$O up to fifth order in a reduced model space using optimized reference state orbitals and including effective three-body forces. Benchmarking against established truncation schemes in ab initio nuclear theory demonstrates its potential to overcome the limitations of current many-body approaches.

Artificial intelligence-driven radio propagation models provide agile and robust solutions for mobile network operators in their effort to ensure the optimal performance of the wireless ecosystem and support its efficient expansion. In this paper, we introduce GRAPHWAVE, a neural graph-driven propagation solver hinging on the governing principles of ray tracing. The proposed model leverages a digitized version of the propagation environment to build a point cloud and extract an equivalent graph representation of the radio environment. By applying neural message passing over the equivalent graph, it allows the model to accurately infer radio-related quantities, e.g., received signal strength, in a three-dimensional environment. We showcase the use of GRAPHWAVE as a radio environment digital twin and we demonstrate that the model can learn from synthetic and real-world data while achieving low inference times.

Collective information acquisition requires groups to combine personal evidence with social information while remaining coupled to the external state. Communication noise can affect this process, but the role of noise remains unclear. In an online experiment, 600 participants worked in four-person human groups estimating a room temperature across 25 rounds while receiving either faithful social information, comprehension noise in which each receiver saw independently perturbed social information, or production noise in which perturbations were stored before display and could be seen by multiple receivers. The thermometer cue was objectively veridical, but its reliability was subjectively uncertain and the unitless 50--250 room-temperature range created a task-induced conflict between displayed evidence and everyday temperature expectations. Production-noise groups spent more rounds tightly clustered around a wrong value than comprehension-noise groups (\(p=0.016\), group-level permutation). Production noise more often created a wrong common signal (\(p=0.025\), Fisher's exact test) and made that signal persist across more rounds (\(p=0.004\), permutation). Dynamic update models showed that production noise was not more harmful because people followed peers more strongly, but because the same peer influence acted on more correlated production-noise perturbations. Exploratory human analyses linked the mechanism to psychological patterns while a GPT-agent experiment clarified a boundary condition: GPT agents registered uncertainty through reduced confidence without reproducing human-scale production-noise vulnerability. Overall, noise did not simply degrade collective information acquisition. Comprehension noise could sometimes improve correction relative to the faithful control, whereas production noise could turn perturbations into common evidence and stabilize consensus on error.

This paper investigates scheduling strategies for wireless sensor-actuator networks (WSANs) in Industry 4.0 scenarios. In particular, we address the problem of real-time scheduling for multi-rate control systems by proposing a novel framework. Our framework features four strategies that improve reliability, schedulability and execution time, and reduce communication and storage costs. Two-phase scheduling is our first strategy, devised to improve communication reliability. Our second strategy is the least-laxity-first with remaining conflicts (LLF-RC) scheduling algorithm, which has high schedulability and affordable execution time. LLF-RC also keeps the maximum queue length at a moderate level, making it suitable for storage-constrained devices. Our third and fourth strategies are opportunistic aggregation and repetitive scheduling. Opportunistic aggregation performs simple and effective packet aggregation, enhancing schedulability by up to 97% and reducing execution time by up to 29%, in our simulation. Repetitive scheduling has negligible execution time, and contributes to minimize communication and storage costs. It reduces the maximum execution time by 92% and the maximum communication and storage cost by 99%, in our simulation. We compare our proposed framework against existing approaches, and evaluate the advantages of our strategies in realistic scenarios.

Dynamic conformational changes of proteins are crucial for their cellular functions. Here we present a unified refinement pipeline for flexible protein structures in both CryoEM and in situ CryoET. Using a Gaussian mixture model-based focused alignment procedure, we improve resolution of small domains in highly dynamic proteins and reveal intricate conformational changes. The method corrects the per-subunit motion of TRPV1 and captures the rotary dynamics of ATP synthase within mitochondria.

This paper introduces software implemented in the mets R-package for calculating non-parametric and regression estimates of Restricted Mean Survival Time (RMST) and Restricted Mean Time Lost (RMTL), including RMTL due to specific causes. A unique feature is the ability to compute the non-parametric estimates of RMST and RMTL, as well as their standard errors, for all time horizons simultaneously. Regression modeling in mets is based on Inverse Probability of Censoring Weighting (IPCW) methods. The package implements different versions of IPCW adjusted estimating equations. A critical technical contribution is the provision of influence functions for all models, which enables the computation of standard errors and allows the estimates to be used as building blocks for more complex statistics, such as the while-alive estimate in recurrent events settings. To expand capabilities in causal inference, the mets package also implements methods for standardization estimates (G-computation) and the estimation of Average Treatment Effects (ATE) for both RMST and RMTL in the competing risks setting. Importantly, the computations scale linearly with the number of observations, making the software efficient for use with large datasets.

Simulation-based inference (SBI) has become an increasingly important framework for parameter estimation in models for which simulation is feasible, including cases where likelihood evaluation is unavailable or costly. While recent work has introduced benchmark frameworks to compare likelihood-free methods, these studies often do not account for structural features such as heavy-tails or discreteness. In this article, we investigate how the performance of likelihood-free inference methods depends on these structural properties. We consider four approaches: MLE, NBE, EOT and AW--NBE and evaluate them using simulations. This study highlights the importance of carefully selecting evaluation tools in the presence of extremes and discrete data.

We study obviously strategy-proof implementation in the framework of social choice over acts introduced by Bahel and Sprumont (2020). We characterize the class of unanimous social choice functions that are implementable via obviously strategy-proof mechanisms. Our main result shows that a unanimous social choice function is obviously strategy-proof implementable if and only if it is dictatorial.

We present measurements of the mass-metallicity relation (MZR) and fundamental metallicity relation (FMR) at $1.4<z<7.0$ using stacked JWST/NIRSpec spectra of 601 star-forming galaxies from the JWST Advanced Deep Extragalactic Survey (JADES). Using the most up-to-date strong-line metallicity calibrations based on high-redshift galaxies, we derive gas-phase metallicities from composite spectra binned by stellar mass, redshift, and star-forming main sequence (SFMS) offset. We find that the MZR slope evolves weakly from $z\sim0$ out to $z\sim5$, with $γ\sim0.21\pm0.03$, while the normalization decreases smoothly with redshift at a rate of $d\log(\mathrm{O/H})/dz\sim-0.1$ out to $z\sim4$. Beyond $z\gtrsim5$, the low-mass end continues to decline in metallicity while the high-mass end remains broadly consistent with lower-redshift relations, producing a steeper overall MZR. We additionally find evidence for a shallow anti-correlation between deviations from the MZR and SFMS at fixed stellar mass at $z\sim1.4-5$. This anti-correlation, albeit with weaker SFR coupling than observed locally, suggests that an FMR is already beginning to emerge by $z\sim5$. Comparisons with recent observations and cosmological simulations show broad agreement, though no single simulation simultaneously reproduces the observed slopes and normalizations across all redshifts. Our results support a picture in which bursty star formation and strong stellar feedback increasingly shape the regulation of galaxy growth at high redshift, while also highlighting the need for substantially larger spectroscopic samples to robustly constrain the evolution of galaxy scaling relations at high-redshift.

Rational functions make sense over any commutative ring, as long as the denominators are invertible. When there is no subtraction involved, they even apply over semirings (rings without subtraction). It is particularly worthwhile to evaluate them over the *tropical semiring*, in which the roles of addition and multiplication are played by maxima and addition. Over this semiring, algebraic results often acquire combinatorial meaning. We give a few examples.

We present a conservation-based feedback-circuit decomposition specifically for general linear forced systems. In a role parallel to that of eigenvalues and eigenvectors for initial-value problems, the complete set of independent intrinsic circuit gains and their associated forcing-transformation vectors provide a complete analytical representation of both transient and equilibrium forced solutions. The sign of intrinsic circuit gains determines whether successive feedback cycles exhibit monotonic or oscillatory convergence to transformed forcing, while the forcing-transformation vectors determine the structure of transformed forcing. The exact transient and equilibrium solutions are represented analytically through the convergence of the finite-cycle forcing-transformation kernel to the equilibrium forcing-transformation kernel, which is guaranteed regardless of whether the magnitudes of circuit gains exceed one or unstable modes exist in the system. The feedback-circuit decomposition provides a new generic foundational mathematical tool for understanding, predicting, and controlling forced responses in a broad range of coupled linear systems across science and engineering.