Low Reynolds number flow near a poroelastic interface can be found across scales in biological and engineered systems. We develop a 2D model of peristaltic flow confined under a poroelastic solid. In this geometry, the lower boundary is an infinite train of traveling waves which pump fluid along a channel. The upper boundary of the flow is a poroelastic half space. The flow and deformation are solved analytically by an asymptotic expansion in the peristaltic amplitude and depend nonlinearly on dimensionless poroelastic stiffness, permeability, and interfacial slip. We quantify the effect of material properties on the poroelastic fluid-structure interaction. Peristaltic flow through the channel is inhibited by poroelastic confinement owing to increased viscous dissipation across the interface and energy loss in deforming the elastic solid. Permeability and slip interact with the material stiffness to produce material dependent regimes of forward or backward interstitial flow within the poroelastic domain. The maximum Darcy flow is found to occur at permeability values that optimize the elastic matrix interaction.

The European colonization of sub-Saharan Africa drove a massive shift from indigenous religions to Christianity, yet the channels through which this transformation occurred remain poorly understood. Using a geographic regression discontinuity design at colonial borders in sub-Saharan Africa, I find that Christian adherence is substantially higher under French and Portuguese direct rule than under British indirect rule -- a gap that implies a correspondingly greater persistence of traditional religions where indirect rule prevailed. Neither mission presence nor pre-colonial political centralization can account for the discontinuity. Instead, the evidence points to the disruption of the inherited social order as the key channel: where direct rule eroded rigid traditional social structures, Christianity -- which bypassed hereditary boundaries -- expanded to fill the void; where indirect rule preserved them, indigenous religions endured. These findings shed light on the dynamics of religious identity change and how it was shaped by colonialism.

In this paper we establish optimal $C^{1,α}$ regularity up to the boundary for viscosity solutions of fully nonlinear elliptic equations with double phase degeneracy law and oblique boundary conditions. The approach developed here relies on first deriving uniform boundary Hölder estimates for perturbed models with oblique boundary data in ``almost $C^{1}$-flat'' domains. Building upon these estimates, the desired regularity is obtained through a compactness and stability framework for viscosity solutions. As a byproduct of our analysis, we determine the optimal Hölder exponent for solutions when the governing operator is quasiconvex or quasiconcave. In addition, we establish an improved regularity result along vanishing points of the source term.

Road traffic crashes claim approximately 1.19 million lives annually worldwide, and human error accounts for the vast majority, yet the autonomous vehicle acceptance literature models adoption almost exclusively through technology-centered pull factors such as perceived usefulness and trust. This study examines a moderated mediation model in which perceived community driving-safety concern (PCSC) predicts evaluations of AI versus human driving capability, mediated by Generalized AI Orientation and moderated by personal driving frequency. Weighted structural equation modeling is applied to a nationally representative U.S. probability sample from Pew Research Center's American Trends Panel Wave 152, using Weighted Least Squares Mean and Variance Adjusted (WLSMV)-estimated confirmatory factor analysis on ordinal indicators, bias-corrected bootstrap inference, and seven robustness checks including Imai sensitivity analysis, E-value confounding thresholds, and propensity score matching. Results reveal a dual-pathway mechanism constituting an inconsistent mediation: PCSC exerts a small positive direct effect on AI driving evaluation, consistent with a domain-specific push interpretation, while simultaneously suppressing Generalized AI Orientation, which is itself a strong positive predictor of AI driving evaluation. Conditional indirect effects are negative and statistically significant at low, mean, and high levels of driving frequency. These findings establish a risk-spillover mechanism whereby community driving-safety concern promotes domain-specific AI endorsement yet suppresses domain-general AI enthusiasm, yielding a near-zero net total effect.

This paper presents a novel framework for ensuring safety in dynamically coupled multi-agent systems through collaborative control. Drawing inspiration from ecological models of altruism, we develop collaborative control barrier functions that allow agents to cooperatively enforce individual safety constraints under coupling dynamics. We introduce an altruistic safety condition based on the so-called Hamilton's rule, enabling agents to trade off their own safety to support higher-priority neighbors. By incorporating these conditions into a distributed optimization framework, we demonstrate increased feasibility and robustness in maintaining system-wide safety. The effectiveness of the proposed approach is illustrated through simulation in a simplified formation control scenario.

Balanced spiking networks can transition between silent, asynchronous-irregular, and oscillatory states depending on interacting synaptic and temporal time scales, while their joint parameter structure remains incompletely characterized. In this work, we systematically map how postsynaptic decay (τs), conduction delay (d), and plasticity rate (λp) jointly shape oscillatory regimes in recurrent leaky integrate-and-fire networks. By combining Brian2 simulations across the (τs, d, λp) space with a coarse Hopf-reference boundary, we construct regime maps that directly visualize SIL-AI-OSC transitions and corresponding spectral prominence landscapes. The mapped results show that increasing λp expands oscillatory regions toward shorter τs and moderate-to-long delays, while prominence maps identify parameter regions with the strongest rhythmic coherence. Representative control experiments further connect this global landscape to local rhythm-forming mechanisms, showing that STDP freezing weakens rhythmic coherence whereas delay jitter enhances it with minimal change in mean firing rate. As a result, these findings provide a useful reference for operating-point selection, synchrony modulation studies, and future biologically grounded spiking-network modeling within similar balanced-network settings.

Stochastic resetting has emerged as a powerful mechanism for driving systems into nonequilibrium stationary states with tunable properties. While most existing studies focus on global resetting, where all degrees of freedom are simultaneously reset, recent work has shown that resetting only a subset of degrees of freedom (subsystem resetting) can qualitatively alter collective behavior in interacting many-body systems. In this work, we develop a general theoretical framework for analysing subsystem resetting in Kuramoto-type coupled-oscillator systems. Building on a continued-fraction approach, we derive self-consistent equations for the stationary-state order parameter of the non-reset subsystem, applicable to both noisy and noiseless dynamics and to models with arbitrary interaction harmonics. Using this framework, we systematically investigate how the stationary state and phase transitions depend on the resetting rate, the size of the reset subsystem, and the reset configuration. We show that subsystem resetting can shift or even suppress synchronization transitions, and can give rise to nontrivial features such as re-entrant behavior and restructuring of phase boundaries. In specific cases, including the noiseless Kuramoto model with a Lorentzian frequency distribution, our results recover known analytical predictions and extend them to more general settings. These results establish subsystem resetting as a versatile control protocol for engineering collective dynamics in nonequilibrium interacting systems.

Cygnus X-3 has recently been established as a variable ultra-high-energy(UHE) gamma-ray source with photons detected up to 3.7~PeV. The temporal correlation between its PeV activity and GeV flares, together with the possible orbital modulation, suggests that the emission is produced within or close to the binary system. In this work, we test whether the contemporaneous GeV emission zone can also host the acceleration of the parent protons responsible for the multi-PeV photons. We jointly model the contemporaneous \textit{Fermi}-LAT spectrum and orbital light curve with a one-zone leptonic scenario dominated by anisotropic external inverse-Compton scattering. The fit places the GeV emission region at $H\sim2.8\times10^{11}\,$cm and constrains the magnetic field--size product to $BH\lesssim10^{13.3}\,$G\,cm at the $3σ$ level. This implies a maximum proton energy of only $\sim0.3$~PeV from the Hillas criterion, far below that required by the observed PeV emission. We therefore conclude that the GeV zone cannot be the main PeV acceleration site. Instead, the PeV emission should originate from a more compact inner region, and the jet magnetic field must dissipate rapidly between the PeV and GeV emitting zones.

We construct simple analytical solutions of renormalization group equations for the running coupling and for the Green functions in QCD in the asymptotic regime. These solutions have an explicit form and subsequently sum up the leading, subleading, and so on logarithms in all orders of PT. They easily reproduce the inverse logarithm expansion and allow for further summation and improvement of the asymptotic behaviour.

This document summarizes the discussions at the program "Precision QCD with the Electron Ion Collider", held from May to June 2025 at the Institute for Nuclear Theory (INT) at the University of Washington. The program was co-sponsored by the INT and by the Center for Frontiers in Nuclear Science (CFNS, Stony Brook University). Over its five-week duration it brought together about 70 theorists, experimentalists and computer scientists all interested in the physics program at the future Electron Ion Collider in preparation at Brookhaven National Laboratory. Key topics at the program were: higher-order perturbative-QCD calculations and techniques; nuclear structure and tomography; comparisons of phenomenological and lattice determinations of parton distribution functions; identification of signature observables for saturated gluons; assessment of the importance of AI techniques for EIC studies and detector development.

In this paper, we investigate the production of gravitational waves during the preheating era. To achieve this purpose, we consider Gauss-Bonnet inflation model with Power{\textendash}law potential, $V(ϕ)= V_0 ϕ^n$, and monomial Gauss-Bonnet coupling function, $ξ(ϕ)= ξ_0 ϕ^n$. We examine our model by comparing our findings with the current observational data. After that, we study the preheating stage by adopting an approach in which we establish a link between preheating duration, reheating phase and inflationary parameters. This step allows us to benefit from observational constraints imposed on inflation. Furthermore, we examine the production of gravitational waves during preheating epoch connecting the energy density to the preheating duration, $N_{pre}$, and then with the spectral index $n_s$. The generation of gravitational waves during preheating can satisfy observational constraints. In particular, the predicted present-day gravitational-wave energy density, expressed as a function of the scalar spectral index, is consistent with the Planck constraints for the choice of a dimensionless Gauss-Bonnet coupling parameter $α\equiv 4V_{0}ξ_{0}/3 = -1.5\times 10^{-6}$, an effective equation of state parameter $ω= 1/6$, and a preheating efficiency parameter $δ= 10^{5}$.

This collection presents a selected set of unsolved problems in semigroup theory, a fundamental branch of modern algebra. The publication is dedicated to the 110th anniversary of the birth of E. S. Lyapin, one of the founders of the field and the author of the world's first monograph on semigroups. The collection covers several major directions of contemporary research: potential properties and embeddability of semigroups; structural problems and finiteness conditions in varieties; endomorphisms; solvable and unsolvable classes of finite semigroups and groups; power semigroups; inclusive varieties; and the theory of partial groupoids. It serves both as a tribute to Lyapin's memory and as a roadmap for current and future research in algebraic systems.

We say that a locally nilpotent derivations $δ$ is maximal if there are no inequivalent locally nilpotent derivations that commute with $δ$. The paper gives a description of isotropy groups of maximal homogeneous locally nilpotent derivations on affine toric varieties and on certain trinomial hypersurfaces. Moreover, the criteria for homogeneous locally nilpotent derivations to be maximal were obtained for these classes of varieties.

The phrase ``buy a quantum computer'' hides several different procurement problems. An institution may be seeking cloud access for teaching, reserved capacity for research, a local instrument for hardware training, an optimization appliance, or a strategic installation that reshapes facilities, staffing, and budgets. Because these choices differ in purpose, operating burden, and useful lifetime, the decision should be framed as acquisition of \emph{quantum capability} rather than selection of a presumed hardware winner. This manuscript develops a practical procurement framework that distinguishes five capability layers, separates peer-reviewed results from commercial offerings, pricing anchors, and public roadmaps, and compares the main commercial platform families -- superconducting circuits, trapped ions, neutral atoms, quantum annealing, and photonics -- through the lens of institutional fit, access model, and refresh pressure. The main conclusion is that most institutions should begin with the smallest layer of capability that produces repeatable near-term value, builds internal expertise, and preserves strategic flexibility. Large on-premises systems are justified only when mission requirements, site readiness, staffing, governance, and upgrade paths are already clear.

A notorious open question in circuit complexity is whether Boolean operations of arbitrary arity can efficiently be expressed using modular counting gates only. Håstad's celebrated switching lemma yields exponential lower bounds for the dual problem - realising modular arithmetic with Boolean gates - but, a similar lower bound for modular circuits computing the Boolean AND function has remained elusive for almost 30 years. We solve this problem for the restricted model of symmetric circuits: We consider MOD$_m$-circuits of arbitrary depth, and for an arbitrary modulus $m \in \mathbb{N}$, and obtain subexponential lower bounds for computing the $n$-ary Boolean AND function, under the assumption that the circuits are syntactically symmetric under all permutations of their $n$ input gates. This lower bound is matched precisely by a construction due to (Idziak, Kawałek, Krzaczkowski, LICS'22), leading to the surprising conclusion that the optimal symmetric circuit size is already achieved with depth $2$. Motivated by another construction from (LICS'22), which achieves smaller size at the cost of greater depth, we also prove tight size lower bounds for circuits with a more liberal notion of symmetry characterised by a nested block structure on the input variables.

This paper addresses the conservatism in data-driven reachability analysis for discrete-time linear systems subject to bounded process noise, where the system matrices are unknown and only input--state trajectory data are available. Building on the constrained matrix zonotope (CMZ) framework, two complementary strategies are proposed to reduce conservatism in reachable-set over-approximations. First, the standard Moore--Penrose pseudoinverse is replaced with a row-norm-minimizing right inverse computed via a second-order cone program (SOCP), which directly reduces the size of the resulting model set, yielding tighter generators and less conservative reachable sets. Second, an online A-optimal input design strategy is introduced to improve the informativeness of the collected data and the conditioning of the resulting model set, thereby reducing uncertainty. The proposed framework extends naturally to piecewise affine systems through mode-dependent data partitioning. Numerical results on a five-dimensional stable LTI system and a two-dimensional piecewise affine system demonstrate that combining designed inputs with the row-norm right inverse significantly reduces conservatism compared to a baseline using random inputs and the pseudoinverse, leading to tighter reachable sets for safety verification.

This work considers the problem of detecting signals from multiple sequentially observed data streams, where only one stream can be observed at every time instant. The goal is to detect signals as quickly as possible while controlling the global probabilities of false alarm and missed detection. In this active sampling setup, it is impossible to minimize the expected detection time simultaneously for every signal, so we formulate a novel set of performance criteria that aim to minimize the expectations of the order statistics of the detection times. A novel procedure is proposed, which incorporates an exploration mechanism to a "follow-the-leader" procedure, and is shown to optimize all the criteria asymptotically as the global error probabilities go to zero. Its finite-sample performance is compared with existing and oracle procedures in simulation studies.

In this paper, we present the discrete-time unbiased extremum seeking (ES) algorithm for n-dimensional (nD) static quadratic maps in the presence of unknown time-varying measurement delays bounded by known constants which can be large. The existing ES results in the presence of large delays are usually confined to known constant or slowly-varying delays, which is restrictive. We provide the first ES algorithm, which is robust with respect to unknown large time-varying delays. Moreover, we achieve the unbiased exponential convergence. We manage with such delays by choosing dithers with frequencies of the order of \sqrtε, where the small parameter ε > 0 appears in the dynamics of the real-time estimator. As expected, larger delays lead to a slower convergence. We provide qualitative and quantitative results based on the averaging analysis via delay-free transformation. For the quantitative bounds on the controller parameters that ensure the exponential unbiased convergence of the ES system, we assume that the Hessian of the map is uncertain and lies within a known range. Differently from its continuous-time counterpart, the small parameter in the discrete-time case defines the decay rate of the estimation error system, making a quantitative bound on this parameter particularly important. We present also constructive conditions for the practical stability of the classical ES system. Our results are semi-global for globally quadratic maps, while for locally quadratic static maps, we provide a bound on the region of convergence. Our analysis shows that appropriate ES parameters can be found for any large unknown time-varying bounded delay. A numerical example highlights the efficiency of the method.

We show that every directed graph $G$ with $n$ vertices and $m$ edges admits a directed acyclic graph (DAG) with $m^{1+o(1)}$ edges, called a DAG projection, that can either $(1+1/\text{polylog} (n))$-approximate distances between all pairs of vertices $(s,t)$ in $G$, or $n^{o(1)}$-approximate maximum flow between all pairs of vertex subsets $(S,T)$ in $G$. Previous similar results suffer a $Ω(\log n)$ approximation factor for distances [Assadi, Hoppenworth, Wein, STOC'25] [Filtser, SODA'26] and, for maximum flow, no prior result of this type is known. Our DAG projections admit $m^{1+o(1)}$-time constructions. Further, they admit almost-optimal parallel constructions, i.e., algorithms with $m^{1+o(1)}$ work and $m^{o(1)}$ depth, assuming the ones for approximate shortest path or maximum flow on DAGs, even when the input $G$ is not a DAG. DAG projections immediately transfer results on DAGs, usually simpler and more efficient, to directed graphs. As examples, we improve the state-of-the-art of $(1+ε)$-approximate distance preservers [Hoppenworth, Xu, Xu, SODA'25] and single-source minimum cut [Cheung, Lau, Leung, SICOMP'13], and obtain simpler construction of $(n^{1/3},ε)$-hop-set [Kogan, Parter, SODA'22] [Bernstein, Wein, SODA'23] and combinatorial max flow algorithms [Bernstein, Blikstad, Saranurak, Tu, FOCS'24] [Bernstein, Blikstad, Li, Saranurak, Tu, FOCS'25]. Finally, via DAG projections, we reduce major open problems on almost-optimal parallel algorithms for exact single-source shortest paths (SSSP) and maximum flow to easier settings: (1) From exact directed SSSP to exact undirected ones, (2) From exact directed SSSP to $(1+1/\text{polylog}(n))$-approximation on DAGs, and (3) From exact directed maximum flow to $n^{o(1)}$-approximation on DAGs.

Hydrogen Inventory Simulations for Plasma facing components (HISP) is an open-source simulation tool to model the evolution of hydrogen (H) isotopes inventory in plasma-facing-components (PFCs) of magnetic confinement fusion devices. The objective was to produce a demonstrative study describing the efficiency of tritium (T) removal strategies in ITER. HISP transforms plasma code outputs to spatial-averaged inputs along ITER's first wall (FW) and divertor for 1D H transport models using FESTIM. Exposure conditions were tested in three scenarios that included DT operation and varied T removal methods. Generally, DT operation resulted in $\approx$ \SI{35}{g} of T in FW and divertor components after 10 days of DT pulses. Almost \SI{80}{\%} of the total T inventory resided in co-deposited boron layers in the divertor. Baking proved to be the most effective T removal method in the divertor, decreasing T inventory by almost \SI{88}{\%} for tungsten and almost \SI{30}{\%} for boron. T removal was also evaluated from Glow Discharge Conditioning (GDC) - with a peak efficiency of \SI{23}{\%} in the tungsten FW - and low power deuterium (DD) pulses - with a peak efficiency of \SI{13}{\%} in the entire divertor. Due to the high removal efficiency of baking, inclusion of GDC and DD pulses in the tested scenarios did not meaningfully change final T inventory values, which varied by less than \SI{2}{\%} in the FW and \SI{10}{\%} in the divertor between scenarios.

Optimistic rollups provide scalable smart-contract execution but remain unsuitable for regulated financial applications due to three structural gaps: semantic legitimacy, cross-layer state consistency, and ordering fairness. We introduce RegGuard, a unified framework that enhances optimistic rollups with comprehensive legitimacy guarantees. RegGuard integrates three coordinated mechanisms: a decidable semantic validator powered by the RegSpec rule language for encoding regulatory constraints; a cross-layer state pre-synchronization validator that detects inconsistent L1-L2 dependencies with probabilistic reliability bounds; and a cryptographically verifiable fair-ordering service that ensures transaction sequencing fairness with negligible violation probability. We implement a 15,000-line prototype integrated into an Optimism-based rollup and evaluate it under adversarial conditions. RegGuard reduces settlement failures by over 90%, prevents detectable ordering manipulation, and maintains 85% of baseline throughput.

GPUs are becoming a major contributor to data center power, yet unlike CPUs, they can remain at high power even when visible activity is near zero. We call this state execution-idle. Using per-second telemetry from a large academic AI cluster, we characterize execution-idle as a recurring low-activity yet high-power state in real deployments. Across diverse workloads and multiple GPU generations, it accounts for 19.7% of in-execution time and 10.7% of energy. This suggests a need to both reduce the cost of execution-idle and reduce exposure to it. We therefore build two prototypes: one uses automatic downscaling during execution-idle, and the other uses load imbalance to reduce exposure, both with performance trade-offs. These findings suggest that future energy-efficient GPU systems should treat execution-idle as a first-class operating state.

Randomness beacons based on Verifiable Delay Functions (VDFs) are increasingly proposed for blockchains and distributed systems, promising publicly verifiable delay and bias resistance. Existing analyses, however, treat adversaries purely as cryptographic entities and overlook that real attackers are economically motivated. A VDF may be sequentially secure, yet still vulnerable if a rational adversary can profit by purchasing faster hardware and exploiting reward spikes such as MEV opportunities. We develop a formal framework for economic security of VDF-based randomness beacons. Modeling the attacker as a rational agent facing hardware speedup, operating costs, and stochastic rewards, we cast the attack decision as an optimal-stopping problem and prove that optimal behavior has a monotone threshold structure. This yields tight necessary and sufficient conditions relating delay parameters to adversarial cost and reward distributions. We extend the analysis to grinding, selective abort, and multi-adversary competition, demonstrating how each amplifies effective rewards and increases required delays. Using realistic cloud costs, hardware benchmarks, and MEV data, we show that many proposed VDF delays, on the order of a few seconds, are economically insecure under plausible conditions. We conclude with deployable guidelines and introduce Economically Secure Delay Parameters (ESDPs) to support principled parameter selection in practical systems.

Digital twins are becoming an important tool for designing, developing, testing, and optimizing next-generation wireless communication systems. Over the past decade, system softwarization has become a reality, and wireless communication systems are no exception. Software-Defined Radios (SDRs), in general, and Universal Software Radio Peripherals (USRPs), in particular, are often used for prototyping and testing advanced wireless systems. Unfortunately, there is currently no end-to-end, software-based, general-purpose testing environment for SDR-based systems: developers often rely on benchtop setups or even small testbeds, but those are costly and cumbersome to build. At the other end of the spectrum, simulations often rely on simplified channel/radio models and typically do not execute full-stack production code, which can increase development effort and reduce fidelity. In this paper, we propose ACHEM (A Channel Emulator), the first software-based, end-to-end wireless channel emulation environment and toolset for communication systems based on SDRs, specifically USRPs. With the proposed emulator and toolkit, any USRP-based system can be fully emulated at the I/Q level in a pure digital environment without requiring specialized hardware (e.g., vehicles, USRPs, FPGAs, or GPUs). The proposed emulator supports multiple transmitters and receivers, MIMO communications, multiple frequencies, heterogeneous sampling rates, real-time node mobility through vehicle emulation, antenna radiation patterns, and various channel models. ACHEM facilitates wireless digital twin development and deployment. ACHEM is validated with several popular open-source USRP-based wireless communication applications, including GNU Radio, srsRAN 4G/5G, and OpenAirInterface.

We study the Generalized Multiple Strip Packing Problem (GMSPP) with heterogeneous per-unit-area costs, in which rectangular items of fixed dimensions must be packed without overlap into multiple open-ended strips of different widths, each incurring a cost proportional to the area used. This cost-weighted area objective is introduced here for the first time and unifies several objectives studied separately in the literature, including total area, total height for identical strips, and makespan. We propose two exact integer programming formulations for this problem: a big-M formulation adapted from recent work, and a normal-position formulation extending an earlier single-strip approach to multiple heterogeneous strips. For the normal-position formulation, we develop an exact Benders decomposition algorithm, called BendM (Benders' Method for Multiple strips). Comprehensive computational experiments on 180 instances derived from standard strip-packing benchmarks compare both formulations and demonstrate the effectiveness of BendM across three cost structures.

Two-dimensional (2D) ferromagnetic materials with high Curie temperature ($T_{\rm c}$) and large magnetic anisotropy energy (MAE) are critical for nanoscale spintronics but remain rare. We propose, via first-principles calculations, that adsorbing alkali atoms ($A$ = Li, Na, K, Rb, Cs) onto a tetragonal CoSe monolayer transforms it into a series of stable 2D ferromagnetic metals, $A$CoSe, with an in-plane easy axis. Notably, LiCoSe is a half-metal. These functionalized monolayers exhibit dramatically enhanced ferromagnetism compared to the pristine layer, with $T_{\rm c}$ > 300 K and MAE > 800 $μ$eV/Co. The coupled alkali atoms amplify the local magnetic moment of Co ions, reinforce ferromagnetic Ruderman-Kittel-Kasuya-Yosida (RKKY) and superexchange couplings, and concurrently weaken the direct antiferromagnetic exchange between Co ions. Furthermore, tensile strain can further elevate the MAE (via band shifting) and increase $T_{c}$ (by strengthening the nearest-neighbor exchange $J_1$). Among them, NaCoSe exhibits the highest MAE and excellent strain-modulated $T_{c}$, rendering it the most promising candidate material. Our results establish alkali-metal decoration as an effective strategy for realizing 2D ferromagnets with high $T_{\rm c}$ and large MAE in tetragonal lattices.

Thermodynamic interpretations of gravity often arise from applying the Clausius relation to spacetime horizons. In modified gravity theories with higher-order equations of motion, such as f(R) and scalar-tensor gravity, this relation generally acquires additional entropy-production term. In this context, two distinct formulations have been proposed in literature: the non-equilibrium approach of Eling, Guedens, and Jacobson based on local Rindler horizons, and the thermodynamic formulation of cosmological apparent horizons in FLRW spacetimes. In this article, we present a detailed analysis of these approaches, and show that, even though both employ identical entropy balance relations that resemble non-equilibrium thermodynamics, the exact origin and role of each entropy-production term is fundamentally different. In the Rindler-horizon framework the extra term follows directly from consistency requirements related to the Bianchi identity, whereas in the apparent-horizon approach it is introduced solely to recover the Friedmann equations. Furthermore, we will see that the latter non-equilibrium contribution enters directly into dynamical equations of gravity, while the former does not. Finally, we also highlight the fact that thermodynamic descriptions of horizons in such modified gravity are not unique, and that equilibrium, and non-equilibrium descriptions can arise from different choices of thermodynamic variables. A clear understanding of these distinctions is therefore crucial for establishing a consistent and physically meaningful thermodynamic foundation for gravity beyond general relativity.

Heat engines that convert thermal energy into work are a cornerstone of classical thermodynamics and remain an active area of contemporary research. Notable examples include microscopic heat engines, trade-off relations between power and efficiency, and the attainability of Carnot efficiency at finite power. We propose a cyclic heat engine based on the Ising model, in which the thermodynamic cycle involves variations of both temperature and magnetic field. We analyze the one-dimensional and mean-field Ising models, which allow for simple analytical results and provide new insight into the role of interactions in cyclic heat engines. In particular, we show that interactions can enhance both power and efficiency. Moreover, a system that does not operate as an engine in the absence of interactions can become an engine upon tuning the interaction strength. The mean-field model enables us to investigate the relevance of the phase transition for the performance of this Ising heat engine. Owing to the emergence of spontaneous magnetization, the mean-field model can still operate as an engine even when one of the magnetic fields is set to zero. Remarkably, when the work is maximized, we find that the optimal parameters are numerically consistent with this regime, in which one magnetic field vanishes and the cycle explores the phase transition. We also consider an alternative cycle for the mean-field model, obtained by varying the interaction strength while keeping both temperatures below the critical temperature and setting the magnetic field to zero throughout the cycle. The power and efficiency of this cycle are analyzed as well. Finally, while our analytical results are valid for the limit of large period we use numerical simulations for finite periods and show that the power decreases monotonically with the period.

We investigate the convexity of cooperative games arising from network flow problems. While it is well-known that flow games are totally balanced, a complete characterization of their convexity has remained an open problem. In this paper, we provide a necessary and sufficient characterization of the networks that induce convex flow games. We show that a flow game is convex if and only if the underlying network is acyclic and admits an arc cover by $s$-$t$ paths that are disjoint at their bottleneck arcs. Specifically, every bottleneck arc must belong to exactly one path, and every non-bottleneck arc must possess sufficient capacity. To derive this characterization, we establish six structural properties of convex flow games. Additionally, we prove that our characterization can be verified efficiently, yielding a polynomial-time algorithm to recognize convex flow games. Since the class of flow games coincides exactly with the class of non-negative totally balanced games, as established by Kalai and Zemel (1982), our structural and algorithmic characterization applies to all such games, provided they are represented in their network form.

Generative AI (GenAI) combined with Extended Reality (XR) offers potential for K-12 education, yet classroom adoption remains limited by the high technical barrier of XR content authoring. Moreover, the probabilistic nature of GenAI introduces risks of hallucination that may cause severe consequences in K-12 education settings. In this work, we present a multi-agent XR authoring framework. Our prototype system coordinates four specialized agents: a Pedagogical Agent outlining grade-appropriate content specifications with learning objectives; an Execution Agent assembling 3D assets and XR contents; a Safeguard Agent validating generated content against five safety criteria; and a Tutor Agent embedding educational notes and quiz questions within the scene. Our teacher-facing system combines pedagogical intent, safety validation, and educational enrichment. It does not require technical expertise and targets commodity devices.