LLM agents have begun to find real security vulnerabilities that human auditors and automated fuzzers missed for decades, in source-available targets where the analyst can build and instrument the code. In practice the work is split among several agents, wired together by a harness: the program that fixes which roles exist, how they pass information, which tools each may call, and how retries are coordinated. When the language model is held fixed, changing only the harness can still change success rates by several-fold on public agent benchmarks, yet most harnesses are written by hand; recent harness optimizers each search only a narrow slice of the design space and rely on coarse pass/fail feedback that gives no diagnostic signal about why a trial failed. AgentFlow addresses both limitations with a typed graph DSL whose search space jointly covers agent roles, prompts, tools, communication topology, and coordination protocol, paired with a feedback-driven outer loop that reads runtime signals from the target program itself to diagnose which part of the harness caused the failure and rewrite it accordingly. We evaluate AgentFlow on TerminalBench-2 with Claude Opus 4.6 and on Google Chrome with Kimi K2.5. AgentFlow reaches 84.3% on TerminalBench-2, the highest score in the public leaderboard snapshot we evaluate against, and discovers ten previously unknown zero-day vulnerabilities in Google Chrome, including two Critical sandbox-escape vulnerabilities (CVE-2026-5280 and CVE-2026-6297).

We study a bulk-surface coupled Laplace system involving an embedded open boundary. The problem is reformulated as an integro-differential equation using boundary integral representations, for which we establish existence and uniqueness of the solution. A Wiener-Hopf technique is employed to study the solution regularity and derive asymptotic expressions for the edge singularity. Building on these results, we develop a finite element method that incorporates the singularity structure and provide a rigorous error analysis. Numerical experiments confirm the theoretical convergence rates.

In this paper, we study Hardy-type uncertainty principles and unique continuation properties for linear covariant Schrodinger equations with variable coefficients in the presence of bounded electric and magnetic potentials. Under suitable smallness assumptions on the leading coefficients, we prove that any solution exhibiting super-quadratic exponential decay at two distinct times must vanish identically. Under an additional structural assumption on the coefficient matrix $G$, we further establish a Hardy-type result at the quadratic exponential scale. We also obtain an analogous uniqueness result for the heat equation with variable-coefficient magnetic perturbations. Our results unify and extend previous works in two directions: they recover the constant-coefficient covariant case treated by Barcelo-Fanelli-Gutierrez-Ruiz-Vilela when $G=I$, and the variable-coefficient non-magnetic case considered by Federico-Li-Yu when $A=0$. The proofs combine logarithmic convexity arguments with Carleman estimates adapted to variable-coefficient covariant Schrödinger and parabolic flows. Although our approach follows the general strategy introduced by Escauriaza-Kenig-Ponce-Vega, substantial new difficulties arise from the interaction between the variable metric and the magnetic structure, which requires new weight functions and refined commutator estimates.

When a quantum electronic device is coupled to an electrical resonator, admittance changes of the quantum subsystem may be detected. The effective reactance may include capacitive and inductive terms that incorporate geometric, quantum, and tunneling components; while the effective resistance may be composed of Sisyphus and Hermes terms linked to relaxation and decoherence, respectively. Such reflectometry is usually studied when all characteristic times of the quantum system are much shorter than the resonator's period, in which case only stationary quantum states are probed. We present a rigorous description of a driven-dissipative qudit-resonator system. Our approach demonstrates how to strictly introduce quantum and tunneling capacitances as well as Hermes and Sisyphus resistances, and how these values are modified when the dynamics of the subsystems becomes mutually dependent. We present the cases of a Cooper-pair box, a single-Cooper-pair transistor, a double quantum dot, and a single-electron box. Our approach can be applied to describe any quantum system coupled to any classical resonator.

We introduce the E-measure: a measure-like generalization of the E-value to a class of hypotheses. Unlike classical measures, E-measures are closed under infimums instead of addition. They arise from a compatibility axiom with logical implications, that there should be at least as much evidence against more specific hypotheses. We show that E-measures are the only non-dominated such objects, if the hypothesis class is closed under intersections. We propose to use the E-measure to present all the relevant evidence for a problem, where the relevance is captured by the choice of hypothesis class. We showcase this by applying the E-measure to decision making, inducing a hypothesis class from the uncertain consequences of decisions. This results in uniform E-consequence bounds on decisions, which nest high-probability loss bounds. Correcting for multiplicity, we consider 'familywise evidence' and 'false evidence rate' control, generalizing from errors and discoveries to continuous evidence. Remarkably, E-measures control these without multiplicity correction if the hypothesis class is intersection-closed. Moreover, we obtain a 'frequentist' notion of updating from E-prior to E-posterior. Abstracting the notion of a 'hypothesis', we advocate for using E-measures for any unknown quantity, leading to predictive E-measures.

Given a graph $G$, a subset $S \subseteq V(G)$ is \textit{cycle convex}, if for any vertex $v \in V(G) \setminus S$, the induced subgraph, $G[S \cup \{v\}]$ cannot form a cycle containing the vertex $v$. The \textit{exchange number} of $G$, denoted by $e_{cc}(G)$ is the maximum cardinality of an $\textit{$E$-independent}$ set of $G$. This paper studies the computational complexity of determining the exchange number of graphs and provides exact values for some graph classes. Given a graph $G$ and a positive integer $k$, we show that deciding whether $e_{cc}(G) \geq k$ is NP-complete even if $G$ is a $K_5$-free graph. In contrast, we characterize all $n$-vertex graphs $G$ with exchange number $n-1$ and obtain closed formulas for chordal graphs $G$ whose blocks lie in a single chain, which leads to polynomial-time algorithms for computing $e_{cc}(G)$. We also establish a lower bound for the exchange number of the Cartesian product of general graphs and by using the results of Anand et al. \cite{bijo2}, we derive an explicit formula for the exchange number of strong and lexicographic graph products.

We study the following problem that is motivated by demand-aware network design: Given a tree~$G$, the task is to find a binary tree~$H$ on the same vertex set. The objective is to minimize the sum of distances in~$H$ between vertex pairs that are adjacent in~$G$. We present a linear-time factor-4 approximation for this problem.

Let $Y_-$ and $Y_+$ be two compact 3-manifolds with empty or toroidal boundary. A 4-dimensional ribbon homology cobordism is a homologically trivial cobordism built with 1-handles and 2-handles. In this note, following the work of Friedl and collaborators, we apply twisted Alexander polynomials to show that if there is a ribbon homology cobordism from $Y_-$ to $Y_+$ with $Y_-$ irreducible, then the unit ball of the Thurston norm of $Y_-$ contains that of $Y_+$. Moreover, we show in general that the fibered classes of $Y_+$ correspond to those of $Y_-$.

This paper reports on the process of designing the UK Co-Benefits Atlas, which communicates and publicizes data for climate mitigation. Visualization atlases -- an emerging type of platform to make data about complex topics comprehensive through interactive visualizations and explanatory content -- pose challenges beyond traditional visualization projects. Atlases must address diverse and often uncertain audiences and use cases, support both explanatory and guided exploration, and accommodate complex, evolving data. Over 10 months, our team of visualization and domain experts conducted 8 design workshops, iterative prototyping, 15 stakeholder onboarding sessions, and continuous reflection. These intertwined processes informed the development of the Atlas, comprising over 400 pages of visualizations and explanations. They also enabled a deeper understanding of how stakeholders may critically engage with the atlas in practice, in terms of interests, potential frictions when navigating huge amounts of data, and envisioned usage scenarios. Reflecting on our design process, we identify five driving forces in atlas design -- data, people, stories, context, and the atlas itself -- whose shifting dynamics influence different stages of visualization atlas design in different ways. Grounded in our case study, we discuss using these forces as a conceptual starting point for structuring and reflecting on future atlas design processes.

Discovery of instantons in colliders will provide experimental evidence for the topological properties of the QCD vacuum. In this work, we propose jet correlation observables that can unambiguously discriminate between instanton-induced processes and perturbative hard scattering events in pp collisions at LHC energies. By calculating the instanton sizes and their separations in 2+1 flavor QCD with physical quark masses, we provide constraints on the center-of-mass energies of the produced hadrons in an instanton-induced process. Our proposal is directly applicable for future ep measurements at the Electron-Ion Collider, offering a cleaner environment to probe instanton-induced processes.

We generalize the well-studied notion of a modular pair of a finite matroid to arbitrary families of sets in infinite matroids, and use it to develop the theory of infinite matroids in several as-yet-unexplored areas. Our results include a complete theory of single-element extensions, a description of the relationship between quotients and projections, a proof that matroids for which every flat is modular must be finitary, and two new perspectives on the infinite matroid connectivity parameter λ. In most cases, existing theory for finite matroids either fails completely or does not extend in obvious ways, and as a result we develop multiple new techniques for reasoning about infinite matroids, including establishing well-behaved infinite analogues of nullity, local connectivity and skewness. We also point to an online repository containing formalized proofs of all our results using the lean4 proof assistant

We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d \times \mathbb{Z}_d$ (with $d$ an odd prime), and the associated Weyl transform built from generalized displacement operators, we derive an exact evolution kernel that propagates the discrete Wigner function in time. By exploiting the composition law of the kernel and iterating the short-time approximation, we obtain a sum-over-paths expression for the propagator weighted by a discrete phase-space action that is the natural finite-dimensional counterpart of Marinov's functional. For Hamiltonians linear in the phase-space coordinates, we show that the fluctuation sum factorizes and, at times strictly commensurate with the lattice (the Clifford-covariant regime), collapses to a deterministic shift realizing the discrete analog of classical Hamiltonian flow. The formulation is applied to a single qutrit ($d=3$) under a diagonal Hamiltonian, and to two interacting qutrits, where we show explicitly that the full entanglement dynamics -- captured by a closed-form expression for the linear entropy valid for all times -- requires the coherent contribution of all fluctuation sectors of the action. The $\tildeμ= 0$ sector alone is non-real at finite time step and collapses to a trivial (uniform) kernel in the continuum limit, failing to reproduce the entanglement dynamics in either regime. We discuss the relevance of this construction for semiclassical simulation of many-body spin systems and the characterization of non-classicality through Wigner negativity.

We demonstrate a construction of products on the quantum torus $\mathbb{T}_θ^2$ that generalises the usual construction of finite Riesz products on the commutative torus $\mathbb{T}^2$. We explain why the former constitutes a natural analogue of the latter in the non-commutative setting and, based on this construction, as well as on previous results by K. Kazaniecki and the second author, we prove a non-commutative version of an Ornstein non-inequality.

The large-scale integration of inverter-based resources (IBRs), particularly distributed photovoltaics (DPVs), into distribution networks increases the need for integrated transmission and distribution (T&D) co-simulation. A key challenge in such co-simulation lies in accurately modeling system frequency across two asynchronous simulation environments. For example, the transmission system, simulated in the phasor domain, can operate with a simulation timestep of 10 ms, while the distribution system, simulated in the electromagnetic transient domain (EMT) to include IBR models, uses a much finer timestep of 100 microseconds. To ensure accurate PLL-based frequency estimation in distribution systems, it is essential to predict voltage magnitude and phase angle variations within the 10 ms transmission intervals, rather than using constant values that cause inaccurate frequency calculations. This issue becomes particularly critical when modeling primary and secondary frequency response services provided by IBRs. To address this challenge, we propose an automated Exponentially Weighted Moving Average Real-Time Threshold Adaptation (EWMA-RTTA) method, which utilizes Quadratic Extrapolation to predict voltage magnitude and phase angle trends more precisely. The proposed method is validated using two Opal-RT simulators: one simulating an IEEE 118-bus transmission system and the other simulating an IEEE 123-bus distribution network. Simulation results demonstrate that our approach improves the normalized mean absolute error (nMAE) by a factor of 25.7 compared to methods that do not account for time mismatches, offering a scalable and accurate solution for modeling IBR-based frequency response in modern power systems.

This thesis studies general relativity (GR) using chiral formulations, which take advantage of the decomposition of the four-dimensional Lorentz group into self-dual and anti-self-dual sectors. Within this framework, GR can be expressed using Plebanski's formulation, where the basic variables are triples of 2-forms rather than a metric, or alternatively through pure connection approaches. These viewpoints expose additional structure in Einstein's equations (EEs) and offer new analytical and numerical tools. Part I develops the geometric foundations using fibre bundles, where the 2-forms arise as soldering forms on an SO(3,C) bundle. Part II investigates the linearised form of EEs in the chiral setting, with particular attention to their gauge fixings. Part III extends this analysis to the nonlinear regime, and also examines the complex-geometric structure underlying black hole spacetimes. The final part turns to numerical relativity, exploring evolution schemes built from the chiral formulations and their associated gauge choices.

In this work, we study the dynamics of multiple random walkers on networks subject to a simultaneous resetting protocol, whereby all walkers are synchronously returned to their respective initial nodes. For this collective Markovian process, we derive exact analytical expressions for the mean first-encounter time, defined as the average time required for all walkers to meet for the first time at a given node. These results are formulated in terms of the eigenvalues and eigenvectors of the transition matrices governing the dynamics without resetting, providing a clear spectral interpretation of the impact of resetting on encounter processes. We further establish a general criterion for finite networks that determines when the introduction of a nonzero resetting probability reduces the mean first-encounter time and leads to an optimal resetting strategy. The theoretical predictions are illustrated through numerical results on regular and heterogeneous networks, for encounters involving two or more walkers, and for combinations of local and nonlocal dynamics. Our findings demonstrate that simultaneous resetting can significantly reduce encounter times for specific target nodes and initial conditions, while becoming ineffective for highly exploratory dynamics or distant targets. A comparison with independent resetting shows that simultaneous resetting is more efficient in homogeneous networks, whereas independent resetting can outperform it in heterogeneous structures, thereby revealing a trade-off between synchronization and exploration. The framework provides a unified approach to collective search and encounter problems on networks with resetting.

It has been 90 years since the discovery of geomagnetic pulsations in the Pc1 range (0.2-5 Hz), widely known as pearls. In the second half of the last century, the concept of pearls as multiple echoes of a wave packet that propagates along the lines of the geomagnetic field, periodically reflecting off the ionosphere at magnetically conjugate points emerged. This paper proposes an alternative interpretation of the pearls. It is assumed that high above the Earth in the narrow equatorial zone of the outer radiation belt there is a pulsed generator of ion-cyclotron waves. The generator excites a discrete sequence of wave packets, which are recorded in the magnetosphere and on the Earth's surface as a series of pearls. The generator is a Q-modulated ion cyclotron resonator with active filling. The presence of opacity domains adjacent to the resonator's end faces is reminiscent of the opacity layer in the atmosphere of a Cepheid. This association was strengthened by the fact that in both cases the formation of opaque layers is associated with the presence in the medium of ions with different charge-to-mass ratios. Based on this association, the idea of a ponderomotive valve arose, periodically changing the width of the opacity domains, thereby forming a periodic sequence of pearls. The ponderomotive valve in pearl theory is analogous to the Eddington valve in Cepheid theory.

Sufficiently strong first-order phase transitions (FOPTs) in the early Universe can simultaneously produce an observable stochastic gravitational wave background (SGWB) and a large-scale primordial magnetic field (PMF). The recent $3.8σ$ evidence for a non-zero intergalactic MF from anisotropic pair-halo searches using \textit{Fermi}-LAT data further motivates a cosmological origin of this MF. We investigate an FOPT-origin of both cosmic signatures, namely, PMF and SGWB, and the correlation between them, within a minimal axion-like particle (ALP) framework in which a global $U(1)$ symmetry is spontaneously broken through radiative corrections, with the ALP sector coupled to the Standard Model (SM) via Higgs-portal. We compute the present-day PMF amplitude and coherence length for both maximally helical and non-helical configurations, accounting for inverse cascade effects. For maximally helical configurations, we find peak field strengths up to $B_0 \sim 10^{-9}$ G at coherence length $λ_0 \sim 10^{-3}-10^{-1}$ Mpc, consistent with lower bounds on the IGMF inferred from blazar observations by MAGIC, H.E.S.S. and {\it Fermi}-LAT. We show that the ALP parameter region consistent with $γ$-ray blazar data (assuming maximal helicity) simultaneously produces SGWB detectable at future space-based interferometers, such as LISA, etc., over the ALP decay constant range $10^3~\text{GeV} \lesssim f_a \lesssim 10^5~\text{GeV}$. We directly map these onto effective ALP couplings to SM particles, e.g., photons, gluons, and fermions. This establishes a multi-messenger complementarity between cosmological observables and laboratory/astrophysical ALP searches, with the combined constraints preferring relatively heavy ALPs, $m_a \gtrsim 0.1~\text{GeV}$, in a regime accessible to next-generation intensity and energy-frontier experiments.

The eigenstates of two test-masses (where each test-mass is placed inside of a harmonic trap) separated by a distance, can get entangled where gravity acts as the mediator of entanglement and it has been argued in \href{https://doi.org/10.48550/arXiv.2511.07348}{arXiv:2511.07348 [quant-ph]} that this entanglement of masses cannot be generated without the underlying quantum nature of gravity. In this work, we consider two non-relativistic Bose-Einstein condensates (formed inside of harmonic trap potentials with identical trapping frequencies) separated by a distance. We take a linearized quantum gravity model and investigate the generation of entanglement while gravitons serve as the mediator of entanglement. The entanglement is generated between the phonon modes of the two condensates, and we observe that for very low separation distance, the entanglement generated is significantly higher than that observed for the quantum gravity induced entanglement of masses or QGEM protocol; however, the fall of entanglement is faster than the two-particle case for two separated Bose-Einstein condensates. We observe that when the number of particles in the condensate is increased, the degree of entanglement for a smaller separation distance becomes substantially higher compared to the case discussed in \href{https://doi.org/10.1103/PhysRevD.105.106028}{Phys. Rev. D 105 (2022) 106028}, which allows for a more robust experimental proposal using this quantum gravity induced entanglement of phonons or QGEP protocol.

We present a robust and accurate numerical method for the anisotropic diffusion equation in curvilinear coordinates. This study extends the recent work [Muir et al., Computer Physics Communications, 2025] for solving the anisotropic diffusion equation in magnetic fields from Cartesian meshes to to curvilinear coordinates and complex geometries. The method uses summation by parts with simultaneous approximation terms for computing the diffusion perpendicular to field lines. The diffusion along field lines is computed using a penalty approach, similar to a simultaneous approximation term, but applied across the volume. To extend the method to complex geometry we use a multi-block approach with piecewise smooth structured meshes. That is, the domain is split into sub-grids, with locally adjacent boundaries coupled weakly using penalties. We prove the semi-discrete stability for the curvilinear implementation by deriving discrete energy estimates. The approach is verified though a number of numerical tests, which demonstrate the convergence properties of the method in multi-domain approach. Finally, we present a qualitative result generated in complex geometry and magnetic field, which is generated by the Stepped Pressure Equilibrium Code.

Critical vulnerabilities with Common Vulnerability Scoring System scores of 9.0 or higher pose severe risks to organisations' information systems. Timely detection and remediation are essential to minimise economic and reputational damage from cyberattacks. This paper provides a thorough analysis of the identification and resolution timelines of such critical vulnerabilities. A mixed-methods approach is employed, integrating quantitative data from global vulnerability databases analysing 245,456 Common Vulnerabilities and Exposures records spanning from 2009 to 2024, of which 12.8 % were critical, with qualitative case studies of notable incidents. This methodical combination of quantitative and qualitative data sources enables the identification of patterns and delay factors in vulnerability management. The findings indicate significant delays in public disclosure and patch deployment, influenced by industry-specific factors, resource availability and organisational processes. The paper concludes with a series of actionable recommendations to improve the efficiency of vulnerability responses. Despite faster disclosure, the remediation gap for critical vulnerabilities remains a systemic risk, driven by organisational inertia and system complexity.

We propose a baryogenesis mechanism in which an electroweak phase boundary is induced by a wall-like configuration of a scalar field, such as a domain wall or a shock wave, coupled to the Higgs field. If the Higgs mass parameter depends on the scalar field value, the wall locally separates the electroweak-symmetric and broken phases, thereby providing an induced electroweak wall. We focus on the case where the scalar field is an axion-like particle coupled to the SU(2) Chern--Simons density. The motion of the wall then generates a local effective chemical potential for B+L, realizing a spontaneous baryogenesis mechanism. In the presence of unsuppressed sphaleron transitions in front of the wall, this biases the plasma and leads to baryon asymmetry generation. We discuss the parametric conditions for the induced wall, cosmological realizations based on domain walls and shock waves, and the associated implications for baryon inhomogeneities and gravitational waves. The axion coupling is predicted to be sufficiently weak to evade current experimental and observational bounds.

In this paper, we develop a novel privacy mechanism for Riemannian manifold-valued data. Our key contribution lies in uncovering unexpected connections among geometric analysis, heat diffusion models, and differential privacy (DP). We characterize the Renyi divergence via dimension-free Harnack inequalities on Riemannian manifolds and establish Renyi differential privacy guarantees governed by Ricci curvature. For manifolds with nonnegative Ricci curvature, we propose a mechanism based on heat diffusion. In contrast, for general manifolds we introduce a Langevin-process-based approach that yields intrinsic mechanisms supporting normalization-free sampling and continuous privacy-utility trade-offs. We derive detailed utility analyses for both mechanisms. As a statistical application, we develop privacy-preserving estimation of the generalized Frechet mean, including nontrivial sensitivity analysis and phase transition characterizations. Numerical experiments further demonstrate the advantages of the proposed DP mechanisms over existing approaches.

The development of visual analytics (VA) systems has traditionally been a labor-intensive process, balancing design methodologies with complex software engineering practices. In domain-specific fields like urban VA, this challenge is amplified by heterogeneous data streams and a reliance on complex, multi-service architectures that hinder fast development, deployment, and reproducibility. Despite the richness of the urban VA literature, the field lacks a consolidated toolkit that encapsulates the core components of these systems, such as spatial data management, analytical processing, and visualization, into a unified, lightweight framework. In this paper, we introduce Autark, a serverless toolkit designed for the rapid prototyping of urban VA systems. Autark provides domain-aware abstractions through a self-contained architecture, enabling researchers to transition from design intention to deployed, shareable systems within hours. Furthermore, Autark's structured, tightly scoped interfaces make it well-suited for AI-assisted coding workflows, where LLMs produce more reliable code when composing from well-defined abstractions rather than generating complex solutions from scratch. Our contributions are: (1) the Autark toolkit, a serverless architecture for rapid prototyping of urban VA; (2) a comparative study of LLM coding effectiveness with and without Autark; and (3) a series of usage scenarios demonstrating its capability to streamline the creation of robust, shareable urban VA prototypes. Autark is available at https://autarkjs.org/.

We study the stability under point-wise product and under composition in Carleman classes of holomorphic functions, defined on sectors of the Riemann surface of the logarithm, and admitting a uniform asymptotic expansion with remainders controlled by a given sequence of positive real numbers $\mathbf{M}$. On the one hand, the well-known conditions of algebrability and Faà di Bruno, imposed on the sequence $\mathbf{M}$, ensure the desired stability with respect to each operation in both the Roumieu and the Beurling settings. On the other hand, these conditions turn out to be necessary for the corresponding stability in the Roumieu case as long as the existence of suitable characteristic functions, in a precise sense, is guaranteed within the class. The construction of such functions rests on classical results of B. Rodríguez-Salinas, and is given in detail. Our results are inspired by, and thoroughly generalize, several partial statements by G.~Auberson and G.~Mennessier for Gevrey classes of order 1.

Sub-bandgap reflectors (SBR) can reduce the temperature of photovoltaic (PV) modules by reflecting the near-infrared region of the solar spectrum with photon energies smaller than the electronic bandgap of the solar cell absorber material. We consider an ideal SBR, which reflects 100 % of non-harvestable low-energy photons but does not alter the reflectivity of the PV module for usable high-energy photons, and estimate how reducing the module temperature with the SBR affects the annual and the cumulative energy yield of silicon PV modules for six locations in North America and Europe. An ideal SBR would increase the annual energy yield between 1.0 % and 1.5 % for open-rack mounted modules and between 1.6 % and 2.4 % for close-roof mounted PV modules. Whether a non-ideal SBR provides a benefit in actual deployments strongly depends on the location and the optical properties of the coating. Beyond effects on the instantaneous power conversion efficiency and hence the annual energy yield, reducing the temperature by a SBR might also reduce the degradation and increase the overall lifetime of the PV module. By describing degradation using a simple Arrhenius approach using typical activation energies between 0.4 eV and 0.8 eV, we find that an ideal SBR increases the cumulative energy yield over 30 years between 2.2 % and 4.0 % for an open-rack mounted PV module in Princeton, New Jersey, USA.

The main claim of arXiv:2206.08467 is that "functional (deterministic) no-signalling resources can be stronger than probabilistic ones" a certain nonlocal game on a Bell scenario with countably many parties. We disagree and argue that (i) under standard definitions, deterministic no-signalling resources are always probabilistic no-signalling resources; (ii) the deterministic strategy considered in arXiv:2206.08467 can be promoted to a genuinely probabilistic strategy with similar properties and (iii) a key step in the derivation in arXiv:2206.08467, claimed to hold for all no-signalling strategies, implicitly assumes measurability, leaving a gap in the argument. We propose measurability assumptions which we conjecture would make this derivation rigorous. Taken together, the phenomenon highlighted in arXiv:2206.08467 is best understood as a difference between measurable and non-measurable no-signalling resources.

It has been shown that, regarding a terminating right-linear overlay term rewrite system (TRS), any rewrite sequence ending with a normal form can be simulated by the innermost reduction. In this paper, using this simulation property, we show that for a right-linear overlay TRS, there is no infinite minimal dependency-pair chain if and only if there is no infinite innermost minimal dependency-pair chain. This implies that a right-linear overlay TRS is terminating if and only if it is innermost terminating.

Self-excited limit-cycle oscillations (LCOs) from Hopf bifurcations are a key feature of nonlinear aeroelasticity and depend sensitively on structural and aerodynamic parameters. Classical center-manifold and normal-form theory describe this local behavior, but can be cumbersome to apply in large discretized models and standard reduced-order modeling (ROM) workflows. A renormalization-group (RG)-based reduction is developed that directly yields a Hopf-type amplitude equation on a local invariant manifold, specialized for polynomial nonlinearities in tensor-based discretizations and compatible with finite-element-type settings. The method provides explicit coefficients governing the Hopf threshold, criticality, and leading LCO amplitude/frequency trends, and admits a companion slow-manifold approximation with selected stable modes retained as static coordinates. Representative nonlinear-aeroelastic examples illustrate how the proposed framework supplies compact, parameter-aware Hopf/LCO descriptors suitable for local ROM construction near flutter.

Inspired by the majority colorings and C-colorings, we introduce and study the majority C-coloring of graphs. In such a vertex coloring, every vertex shares its color with at least half of its neighbors. The maximum number of colors that can be used in a majority C-coloring of a graph $G$ is called the majority C-chromatic number and denoted by $\mc(G)$. An upper bound on $\mc(G)$ is proved in terms of the order, minimum, and maximum degree. Its sharpness is demonstrated by several results over different graph classes. In particular, $\mc(P_n^k)= \mc(C_n^k)= \lfloor n/(k+1)\rfloor$ is true for the $k$-th power of a path and a cycle if $n \ge k+1$. Further, $\mc(G) = (n-d)/3$ holds if $G$ is a $(\mbox{claw}, K_4)$-free cubic graph and contains $d$ diamonds. %claw-free cubic graph on $n \ge 6$ vertices and contains $d$ diamonds. It is further shown that the majority C-chromatic number is not monotone under edge deletion. In fact, both the lower and upper bounds are sharp in the inequality chain $\mc(G)-2 \leq \mc(G-e) \leq \mc(G) +1$. The minimum and maximum number of edges in an $n$-vertex graph $G$ with $\mc(G)=k$ are determined for every $n$ and $k$. It is also pointed out that the classical chromatic number $χ(G)$ and $\mc(G)$ are incomparable, and the difference $\mc(G)-χ(G)$ can take any positive or negative integer. On the other hand, $\mc(G)+χ(G) \leq n+1$ holds for every graph $G$ of order $n$. The decision problem of whether $\mc(G) \ge k$ holds is NP-complete for every fixed $k\ge 2$. In contrast, some sufficient conditions for $\mc(G) \ge 2$ are proved, and a linear-time algorithm is presented that determines $\mc(T)$ if $T$ is a tree.