Higgs branches of 5d $Sp(k)$ theories with $N_f$ flavours, whether at weak or strong coupling, are described by a pair of instantons transforming as pure spinors of $SO(2N_f)$. The Poisson structure is constrained by symmetry arguments and implies that these Higgs branches are algebraic integrable systems; the degeneration of the symplectic form occurs when the spinor annihilators overlap. We argue that the stratification of the Higgs branch at infinite coupling corresponds to the alignment of the instantons weights, leading to a non vanishing magnetization, and their acquisition of a mass.

We develop a generalized resistance geometry based on Kron reduction and effective resistance for directed graphs, paralleling classical undirected graph theory. For strongly connected directed graphs, we prove a Fiedler--Bapat identity that links the resistance matrix and the Laplacian through the symmetrized pseudoinverse. This identity provides a canonical definition of the resistance curvature and resistance radius in the strongly connected directed setting. In the strongly connected weight-balanced case, it also implies that the operation of associating an undirected Laplacian with a directed Laplacian via the pseudoinverse of the symmetrized pseudoinverse commutes with Kron reduction. We further introduce a class of signed undirected Laplacians for which effective resistance defines a distance between nodes. We call this distance the generalized resistance metric and prove that it coincides with the class of strict negative type metrics. Within this framework, we investigate analytical and geometric properties of resistance curvature and resistance radius, characterize the maximum graph-variance problem, and generalize resistive embeddings. These results place signed undirected resistance geometry on a footing parallel to the classical unsigned undirected theory and provide a unified perspective on model reduction, graph variance, and resistance-based embedding.

We assess the dielectrically consistent reference interaction site model (DRISM) as an implicit electrolyte framework for modeling the electrochemical double layer, and compare it with the Poisson-Boltzmann model and explicit molecular dynamics results from the literature. We use the gold-electrolyte interface as the main test case and analyze solvent and ionic density profiles, the differential capacitance, and the solvation contribution to CO adsorption. The results show a strong sensitivity to the Lennard-Jones parametrization of metal-ion and metal-water interactions. In particular, we find that the default Lorentz-Berthelot mixing rules to be inadequate and lead to excessive Na+ accumulation at the interface, which results in an increase of the differential capacitance at negative electrode potentials. We demonstrate that introducing pair-specific metal-ion parameters yields more symmetric charging behavior and provides greater flexibility. Our findings suggest that using pair-specific parameters, rather than relying on Lorentz-Berthelot mixing rules, improves the accuracy of the model and opens the way for future studies with this improved yet equally performant model.

Identified hadron production is essential for the study of nucleon structure and QCD hadronization at high energies. We present the first calculation of unpolarized semi-inclusive deep-inelastic scattering (SIDIS) at next-to-next-to-next-to-leading order (N$^3$LO) in perturbative QCD. Our calculation is based on a novel method of two-dimensional transverse-momentum subtraction motivated by QCD factorization of soft and collinear singularities. The N$^3$LO corrections are moderate in general but can be significant in threshold regions, and exhibit excellent perturbative convergence and reduced scale variations. The fully differential framework allows for arbitrary selection cuts and directly enables precision nucleon tomography at the upcoming Electron-Ion Collider, establishing the theory foundation needed to match the anticipated experimental accuracy. Generalization of the method to calculations of polarized SIDIS is also feasible.

Hackathons are time-bound collaborative events that often target software creation. Although hackathons have been studied in the past, existing work focused on in-depth case studies limiting our understanding of hackathons as a software engineering activity. To complement the existing body of knowledge, we introduce HackRep, a dataset of 100,356 hackathon GitHub repositories. We illustrate the ways HackRep can benefit software engineering researchers by presenting a preliminary investigation of hackathon project continuation, hackathon team composition, and an estimation of hackathon geography. We further display the opportunities of using this dataset, for instance showing the possibility of estimating hackathon durations based on commit timestamps.

We investigate the gain in Shannon information that can be extracted from an X-ray image obtained after coherent free-space propagation of the transmitted beam and subsequent digital processing of the detected image. We show that simulated digital forward free-space propagation can produce a much higher formal information gain, both in projection imaging and in phase-contrast computed tomography, compared to conventional phase retrieval based on the Transport of Intensity equation. However, it appears that the extra information gained in the simulated free-space propagation may be due in part to superficial high-frequency content in the obtained images, rather than due to a genuine improvement of the spatial resolution. This points to the need to critically evaluate the performance of different types of image quality metrics and their relationship to the information content of the images.

Quantum key distribution is often regarded as an unconditionally secure method to exchange a secret key by harnessing fundamental aspects of quantum mechanics. Despite the robustness of key exchange, classical post-processing reveals vulnerabilities that an eavesdropper could target. In particular, many reconciliation protocols correct errors by comparing the parities of subsets between both parties. These communications occur over insecure channels, leaking information that an eavesdropper could exploit. Currently there is no holistic threat model that addresses how parity-leakage during reconciliation might be actively manipulated. In this paper we introduce a new form of attack, namely the Manipulate-and-Observe attack in which the adversary (1) partially intercepts a fraction $ρ$ of the qubits during key exchange, injecting the maximally tolerated amount of errors up to the 11 percent error threshold whilst remaining undetected and (2) probes the maximum amount of parity-leakage during reconciliation, and exploits it using a vectorised, parallel brute force filter to shrink the search space from 2n down to as few as a single candidate, for an n-bit reconciled key. We perform simulations of the attack, deploying it on the most widely used protocol, BB84, andthe benchmark reconciliation protocol, Cascade. Our simulation results demonstrate that the attack can significantly reduce the security below the theoretical bound and, in the worst case, fully recover the reconciled key material. The principles of the attack could threaten other parity-based reconciliation schemes, like Low Density Parity Check, which underscores the need for urgent consideration of the combined security of key exchange and post-processing.

Mobile messaging apps are a fundamental communication infrastructure, used by billions of people every day to share information, including sensitive data. Security and Privacy are thus critical concerns for such applications. Although the cryptographic protocols prevalent in messaging apps are generally well studied, other relevant implementation characteristics of such apps, such as their software architecture, permission use, and network-related runtime behavior, have not received enough attention. In this paper, we present a methodology for comparing implementation characteristics of messaging applications by employing static and dynamic analysis under reproducible scenarios to identify discrepancies with potential security and privacy implications. We apply this methodology to study the Android clients of the Meta Messenger, Signal, and Telegram apps. Our main findings reveal discrepancies in application complexity, attack surface, and network behavior. Statically, Messenger presents the largest attack surface and the highest number of static analysis warnings, while Telegram requests the most dangerous permissions. In contrast, Signal consistently demonstrates a minimalist design with the fewest dependencies and dangerous permissions. Dynamically, these differences are reflected in network activity; Messenger is by far the most active, exhibiting persistent background communication, whereas Signal is the least active. Furthermore, our analysis shows that all applications properly adhere to the Android permission model, with no evidence of unauthorized data access.

This paper presents results of two-dimensional direct numerical simulations (DNS) and global linear stability analyses (based on mean flow and base flow) of a viscous incompressible flow past a circular array of cylinders with six-fold rotational symmetry. Six cylinder arrays, with varied patch density $ϕ= N_c (d/D)^2$ (with $N_c$ cylinders of diameter $d$ within a patch of diameter $D$) is investigated by adjusting the $N_c$ and its arrangement. The simulations cover a wide parameter space, with $ϕ$ ranging from $0.043$ to $0.315$, and the free-stream flow Reynolds numbers ($Re_D = U_{\infty} D / ν= < 300$ based on $D$ and the uniform incoming velocity $U_{\infty}$ and the kinematic viscosity $ν$). We focus on the onset of vortex shedding with variant $ϕ$, since the onset of global instabilities in such arrays has not been discussed earlier in the literature. For the patch diameters and solid volume fractions considered here,three distinct regimes are identified: (I) a low-$ϕ$ regime where cylinders behave nearly independently, the flow is stable, forming steady wake without vortex street; (II) an intermediate-$ϕ$ regime where $Re_c$ varies logarithmically with $ϕ$, resembling a porous medium; and (III) a high-$ϕ$ regime where $Re_c$ approaches that of a solid cylinder ($ϕ= 1$).

Network-based approaches have become increasingly prominent in science education research as tools for analysing relational structures in learning, teaching, and knowledge production. This review presents a PRISMA-informed scoping analysis of 82 articles published in nine leading science education journals, which are organised into four main categories: concept networks, social networks, bibliographic networks, and attitudes or behavioural networks. We observe a sustained exponential growth in the use of network methods, indicating a still-emerging and expanding research area. Concept networks dominate the literature, followed by social network analyses linking interaction structure to learning outcomes and persistence, while bibliographic and abilities-oriented networks provide complementary meta-level and practice-focused perspectives. In addition, analysis of the coauthorship network reveals a highly fragmented field, characterised by many small and weakly connected research groups, typically organised within single application categories. Complementary analysis of a citation network that includes all referenced authors shows that, despite this limited collaboration structure, the field is intellectually organised around several major traditions--network science methodology, learning sciences, and argumentation in science education--linked by a small number of bridging authors. Overall, the literature remains largely descriptive, relying on static, single-layer representations and a narrow set of network metrics. We identify substantial opportunities for advancing science education research through stronger theoretical integration and the adoption of dynamic, multilayer, and coevolutionary network frameworks.

Mismatched junctions formed by two C$_3$N zigzag nanoribbons of different widths provide a useful setting for studying quantum interference effects involving edge state transport. A crucial ingredient for this interference to appear is, besides the presence of edge states, the formation of localized interface states at the mismatched interface of the junction. At the level of a tight-binding model it is shown that, by means of an external gate potential, one of the edge state energy bands can selectively be shifted into the energy range of the localized interface states. The resulting coupling between the edge and localized interface states gives rise to pronounced Fano resonances in both the density of states and the transmission spectrum with line shapes well described by the canonical Fano formula. Furthermore, it is found that the geometrical mismatch of the junction not only determines the number of resonances but also the energetic orientation of their asymmetric line shapes. These results identify mismatched C$_3$N nanojunctions as a tunable and robust platform for engineering interference-driven transport.

Certifying the Region of Attraction (ROA) for high-dimensional nonlinear dynamical systems remains a severe computational bottleneck. Traditional deterministic verification methods, such as Sum-of-Squares (SOS) programming and Satisfiability Modulo Theories (SMT), provide hard guarantees but suffer from the curse of dimensionality, typically failing to scale beyond 20 dimensions. To overcome these limitations, we propose SCORE, a statistical certification framework that shifts from seeking deterministic guarantees to bounding the worst-case safety violation with high statistical confidence. By integrating Projected Stochastic Gradient Langevin Dynamics (PSGLD) with Extreme Value Theory (EVT), we frame ROA certification as a constrained extreme-value estimation problem on the sublevel set boundary. We theoretically demonstrate that modeling the optimization process as a stochastic diffusion on a compact manifold places the local maxima of the Lyapunov derivative into the Weibull maximum domain of attraction. Since the Weibull domain features a finite right endpoint, we can compute a rigorous statistical upper bound on the global maximum of the Lyapunov derivative. Numerical experiments validate that our EVT-based approach achieves certification tightness competitive to exact SOS programming on a 2D Van der Pol benchmark. Furthermore, we demonstrate unprecedented scalability by successfully certifying a dense, unstructured 500-dimensional ODE system up to a confidence level of 99.99\%, effectively bypassing the severe combinatorial constraints that limit existing formal verification pipelines.

Recent theoretical studies on the nonlinear response of spin and orbital degrees of freedom have discovered spin and orbital analogs of the photocurrent, with potential for characterizing topological materials and for applications. In this paper, we develop a general theory for calculating spin and orbital currents in semiconductors and study the properties of optical responses in the Bernevig-Hughes-Zhang and Luttinger models, where nonlinear orbital responses and a topological phase transition occur. We study the evolution of optical responses at the topological phase transition and how they manifest. In addition, we find that the relaxation time dependence of the orbital conductivity is somewhat distinct from that of the photocurrent. The theory is straightforwardly applicable to complex models of real materials, allowing quantitative predictions of the nonlinear responses of orbital and spin.

We targeted with deep NOEMA observations the [CII]158$μ$m emission of three JWST-discovered AGN at z>6. Two of them have the typical features of Little Red Dots (LRDs), while the third one is a blue, extended, Type I AGN. We do not significantly detect [CII] emission or dust continuum in any of the targets, even after stacking. The resulting [CII] luminosity upper limits, $\log (L_{[CII]}/L_{\odot})<7.77-8.1$, lie $\sim2σ$ below the values expected from the [CII]-SFR relation, and we explore different scenarios to explain the lack of [CII]. We obtained upper limits on the gas masses of $\log (M_{gas}/M_{\odot})<9.26-9.59$ corresponding to $\log( M_{dust}/M_{\odot})<5.68-6.55$ assuming a metallicity dependent dust to gas ratio. Using the continuum non-detections (rms $\sim 16-25 ~μJy$) together with JWST/MIRI constraints, we performed a revised SED-fitting decomposition, resulting in stellar masses up to $\sim 2$ dex lower than previously reported, and implying $0.03\lesssim M_{BH}/M_{*}\lesssim0.7$. For the two LRDs, the SED is well reproduced by stellar emission in the rest-frame UV, while the rising rest-frame optical slope, flattening toward the near-infrared, is consistent with emission from a Type I AGN partially obscured along the polar direction with $E(B-V)_{\rm polar}\simeq 1$, in agreement with attenuation derived from the broad lines Balmer decrement. This decomposition demonstrates that a relatively standard AGN configuration can reproduce the SEDs of the two LRDs, without invoking more exotic scenarios. Finally, we investigate the positions of the three sources in the $IRX-β_{UV}$ plane, finding that they lie in a parameter space where galaxies are typically characterized by patchy dust distributions. Our analysis highlights the importance of millimeter constraints to characterize the different physical properties of high-z AGN.

It is a universal empirical observation that socks become unpaired in the laundry. We propose a quasiparticle theory of sock dynamics in which individual socks are modelled as bosonic excitations of the agitated laundry condensate. The sock dispersion relation is material-dependent: nondispersive materials retain their shape, while dispersive materials give rise to the well-documented phenomenon of sock shrinkage. In the convex regions of the dispersive spectrum, socks undergo Beliaev decay and spontaneously split into two lower-momentum socks, while in the concave regions the dominant process is Landau-Khalatnikov scattering, which degrades socks into lint and loose threads. In addition, the rotating drum creates sock-antisock pairs from the laundry vacuum via the dynamical Casimir effect. The coexistence of these creation and destruction channels gives rise to a fundamental ambiguity: an unpaired sock at the end of a wash cycle is equally consistent with the destruction of its partner or the spontaneous creation of an entirely new sock.

Task-oriented communication is a key enabler of emerging 6G systems, where the objective is to support decisions and actions rather than full message reconstruction. From an information-theoretic perspective, identification (ID) codes provide a natural abstraction for this paradigm by enabling receivers to test whether a task-relevant message was sent, without decoding the entire message. Motivated by the strong impact of feedback on ID and by the growing interest in integrated communication and sensing, this paper studies joint identification and sensing (JIDAS) over state-dependent discrete memoryless channels with noisy strictly causal feedback. The transmitter conveys identification messages while simultaneously estimating the channel state from the feedback signal. For both deterministic and randomized coding schemes, we derive lower and upper bounds on the capacity--distortion function. The results quantify the fundamental limits of JIDAS under noisy feedback and recover existing noiseless-feedback characterizations as special cases.

We introduce a novel coupling scheme for maximizing the synchronization of Kuramoto oscillator networks under a fixed coupling budget. We show that by scaling the interaction strength between oscillators according to their frequency detuning, synchronization is enhanced. The coupling scheme induces a change in criticality, driving the system from a continuous phase transition to an explosive transition by changing a single parameter. Our work offers a general route to efficient synchronization in engineered networks and provides insight into the critical behavior of the Kuramoto model.

Dynamic structural equation modeling (DSEM) is widely used for analyzing intensive longitudinal data (ILD). Although many ILD have categorical (Bernoulli or binomially distributed) responses, currently available Metropolis-within-Gibbs samplers for estimating DSEMs are limited to using the probit link and the Bernoulli distribution. These samplers scale poorly with increasing model complexity and/or data size. Here, we present a hybrid sampler -- alternating between one step of the No-U-Turn Sampler (NUTS) and one Gibbs step -- which solves both of these problems: the Gibbs step naturally handles Pólya-Gamma distributed latent variables arising from binomially distributed responses with a logit link, and the NUTS step utilizes a Kalman filter to exactly marginalize over latent states, alleviating the need to sample these variables. We demonstrate in simulation experiments that the proposed sampler is more efficient than alternative algorithms, and that it makes DSEM estimation with binomial data feasible for larger data and models than what has previously been possible. We also illustrate its use in an example application of predicting panic attacks.

The white book released by the International Telecommunications Union (ITU) calls for extremely high-security and low-latency communication over fading channels. Under the low-latency requirement, the corresponding fading model is quasi-static fading while high-security can be achieved via covert communication. In response to the call of ITU, we study the finite blocklength performance of optimal codes for covert communication over quasi-static multi-antenna fading channels, under the covertness metric of Kullback-Leibler (KL) divergence. In particular, we study all four cases regarding the availability of channel state information (CSI) for legitimate transmitter and receiver, and assume that the warden knows perfect CSI for the channel from the legitimate transmitter to itself. Specifically, we show that, when the blocklength is $n$, the first-order covert rate satisfies the square root law, scaling as $Θ(n^{-\frac{1}{2}})$ with the coefficient determined by the traces of the channel matrices of the legitimate users and the warden, and the second-order rate vanishes. In contrast to the non-covert result of Yang et al. (TIT, 2014), we show that CSI availability at the legitimate users does not affect the finite blocklength performance for covert communication. Furthermore, we reveal the significant spatial diversity gain provided by multiple-antenna systems for covert communication. For the covertness analysis, we extend the quasi-$η$-neighborhood framework to fading channels and address challenges arising from the random channel matrices. For the reliability analysis, due to the vanishing power imposed by the covertness constraint, we refine the non-covert analysis by Yang et al. (TIT, 2014), by carefully controlling higher-order terms and exploiting the properties of covert outage probability.

While spatial phonon coherence manifested through band folding is believed to be a key factor governing the anomalous thermal conductivity of periodic structures, we investigate phonon transport from the perspective of temporal coherence. Using mode-resolved analyses, we quantify temporal coherent contributions and elucidate the interplay between phonon coherence time and lifetime in heat conduction of graphene/hexagonal boron nitride superlattices. We find that intrinsic coherence of folded phonon modes dominates the enhancement in ultrashort-period superlattices. In contrast, Wigner transport equation yields only a minor effect of band folding on thermal conductivity. The predictions in temperature dependence of models with and without temporal coherence provide a falsifiable experimental signature of this effect. Temporal coherence therefore constitutes a previously overlooked but fundamental channel for heat conduction, extending the conventional picture of spatially coherent transport and deepening the understanding of phonon dynamics in superlattices.

Altermagnets constitute an emerging materials platform for spintronic technologies by combining compensated magnetic order with ferromagnet-like spin-split electronic bands. Here, we investigate the proposed d-wave altermagnetic material RuO2 using circularly polarized ultrashort laser pulses. Time-resolved magneto-optical Kerr effect measurements, which are intrinsically sensitive to surface and interface states, reveal the ultrafast spin response of RuO2. In contrast to the demagnetization dynamics characteristic of conventional ferromagnets, we observe a distinct coherent contribution to the complex Kerr rotation that appears during the light-matter interaction and lasts for about 200 fs. Similar signatures have been associated with spin-momentum locking and directional band splitting in spin-split surface states of topological insulators as well as spin-orbit-coupled semiconductors. They are governed by a finite Raman coherence time. We interpret this coherent response as evidence for transient spin-polarized surface states in RuO2, consistent with the emergence of altermagnetic surface states that are directly relevant to spin-polarized transport at surfaces and interfaces.

We classify equivalence classes of Hopf algebra quotient pairs $(D,θ)$ of the Drinfeld double $D(G)$ of a finite group scheme $G$ over an algebraically closed field $\mathbf{k}$ of characteristic $p\ge 0$, in terms of group scheme-theoretical data. We prove that such Hopf algebra quotients $D$ are Hopf algebra extensions $\mathscr{O}(K)^{\mathrm{cop}}\#_σ^τ \mathbf{k}[G/H]$, where $K$ and $H$ are normal subgroup schemes of $G$ that centralize each other and $B:\mathbf{k}[H]\to \mathscr{O}(K)$ is a $G$-equivariant Hopf algebra map, and describe the surjective Hopf algebra map $θ:D(G)\twoheadrightarrow D$. Using this classification, we determine the tensor subcategories of the center $\mathscr{Z}(G):=\Rep(D(G))$ of $G$, describe their centralizers, determine when they are symmetric or non-degenerate, and give a description of their simple and projective objects using \cite{GS}. Our categorical results generalize those found in \cite{NNW} in characteristic $0$.

Magnetic reconnection drives a wide range of astrophysical plasma phenomena, including solar flares, by converting magnetic energy into plasma energy through changes in magnetic field topology. Petschek reconnection is a magnetohydrodynamic (MHD) model in which magnetic field lines reconnect within a localized diffusion region, and a pair of switch-off slow shocks forms outside this region, enabling efficient energy conversion. Whether this picture remains valid when kinetic effects are included remains an open question. In this study, we examine the formation and properties of slow shocks associated with reconnection exhausts by solving a two-dimensional Riemann problem using a multi-hierarchy framework that couples MHD and particle-in-cell (PIC) simulations. We find that a slow shock close to the switch-off limit forms in the MHD domain even when slow shock formation is suppressed in the PIC domain, and that this behavior is insensitive to the size of the PIC domain. The formation of the slow shock further promotes plasma isotropization within the PIC domain. These results suggest that Petschek-like reconnection remains viable in collisionless-collisional systems, such as solar flares, where temperature anisotropy appears to be relaxed far from the reconnection region.

Using a field theory equivalent to a lattice version of the Poland-Scheraga (PS) model, the phase diagram for a long DNA molecule is derived in closed form. A one-loop renormalization group calculation for the generalized PS model with excluded volume interactions shows that there are two stable fixed points. At both fixed points, the excluded volume effect plays a role. At the fixed point reached when the original excluded volume effect is weak, the phase transition is continuous. At the other fixed point, the phase transition is first order.

Mobile networks are essential for modern societies. The most recent generation of mobile networks will be even more ubiquitous than previous ones. Therefore, the security of these networks as part of the critical infrastructure with essential communication services is of the uttermost importance. However, these systems are still vulnerable to being compromised, as showcased in the recent discussion on supply chain security and other challenges. This work addresses problems arising from compromised 5G core network components. The investigations reveal how attacks based on command and control communication can be designed so that they cannot be detected or prevented. This way, various attacks against the security and privacy of subscribers can be performed for which no effective countermeasures are available.

Anitmatter-based propulsion is often cited as a physically plausible route to relativistic interstellar travel, and thus as a potential mechanism by which technologically advanced civilizations could expand throughout the galaxy. Its difficulty may be central to the resolution of Fermi's paradox. Since the Universe should be teaming with advanced technological life, yet we see none, it may be that interstellar travel is simply too difficult. It has been suggested that the main difficulty with using antimatter as propulsion is its limited availability, assuming it must be artificially manufactured. In this paper, we demonstrate that naturally occurring potassium 40 - rich biological matter (specifically bananas) is a promising, overlooked antimatter source for interstellar propulsion.

This work presents a detailed covariance and correlation matrix analysis for experimentally measured cross sections obtained using the activation technique. Both statistical and systematic contributions to the covariance matrix were explicitly calculated using sensitivity coefficients. The detector efficiency was determined by refitting standard source data with an exponential function, and the associated covariance matrix of the fitted parameters was propagated to estimate the uncertainty in efficiency at the relevant $γ$-ray energy. The cross sections and the corresponding experimental parameters, such as beam flux, target thickness, $γ$-ray intensity, and decay corrections, were taken from previously published measurements and are used here for the purpose of illustrating the covariance formalism. The resulting covariance and correlation matrices provide a comprehensive representation of uncertainties and their interdependencies. This formalism demonstrates the importance of including correlated uncertainties for reliable interpretation and comparison of experimental cross section data.

We investigate `almost counterexamples' to Seymour's second neighbourhood conjecture. In what we call Seymour-tight orientations, the size of the first neighbourhood of each vertex equals the size of its second neighbourhood. We give several examples and constructions. Specifically, we prove that the class of Seymour-tight orientations is closed under taking (generalized) lexicographic products. Moreover, the lexicographic product of a putative counterexample to Seymour's second neighbourhood conjecture and a Seymour-tight orientation is again a counterexample. Using lexicographic products, we show that if the conjecture is false, then there exist counterexamples that are close to regular tournaments, and moreover that any digraph occurs as an induced subgraph of a counterexample. We then use this same machinery to construct special putative counterexamples to Sullivan's conjecture. The inherent symmetry of these orientations give access to an algebraic perspective. Seymour-tight orientations that are also Cayley digraphs correspond to special pairs of critical sets in groups, which connects potentially to additive combinatorics. We use Kemperman's theorem to characterize those Seymour-tight orientations that are the Cayley digraph of an abelian group.

The most elementary prepare-and-measure scenarios have no independent measurement inputs. No inputs mean that quantum advantages require two indispensable ingredients: shared entanglement and measurements that can be adapted to the communicated messages. Understanding these scenarios is therefore conceptually natural, but also practically relevant, since they act as testbeds for black-box certification of adaptive one-way LOCC. Here, we study them systematically and reveal several of their basic features. For classical messages, we first identify the minimal scenario with a quantum advantage and show that it is maximised by high-dimensional entanglement. Then, we identify the next-to-minimal scenario, and show that quantum advantages can be propelled by nonlocality of the Clauser-Horne-Shimony-Holt type, which makes this an appropriate setting for certification experiments. Proceeding further, we replace classical messages with quantum messages, but require the receiver to read the message before measuring the entangled particle. We show that this leads to amplified quantum advantages, that are made possible only thanks to non-projective message read-out. This in dispensable role of non-projective measurements challenges the common wisdom that they play a secondary role in revealing the power of quantum correlations in black-box experiments.

Scratch is the most popular programming environment for novices, with over 1.15 billion projects created worldwide. Unlike traditional languages, correctness in Scratch is defined by visible behavior on the stage rather than by code structure alone, so programs that appear correct in the workspace can still fail at runtime due to timing, event ordering, or cross-sprite interactions. Visual execution evidence such as gameplay videos can therefore be essential for diagnosis and repair. However, capturing and processing this evidence inside an automated repair loop introduces substantial overhead. Probing execution, recording stage behavior, rebuilding executable .sb3 projects, and verifying candidate fixes consume time, monetary cost, and resources across an entire repair trajectory rather than a single model call. We present EcoScratch, a repair pipeline that uses lightweight runtime signals to decide whether the next attempt stays text-only or escalates to multimodal prompting. The controller also sets the JSON Patch budget and verification effort, so evidence choice and repair budget are coupled inside the same decision. EcoScratch rebuilds candidate fixes into executable .sb3 projects and records per-trajectory traces, monetary cost, local-runtime energy. We evaluate 12 models on 100 executable Scratch repair projects under four controller settings, yielding 4800 repair trajectories. In this matrix, a selective multimodal policy gives the strongest observed success-cost-energy tradeoff. It reaches the highest generation success (30.3%) while using less average cost and local-runtime energy than the two non-adaptive multimodal baselines under the same bounded trajectory budget; text-only remains the lowest-cost floor. Across the evaluated matrix, multimodal evidence helps most when it is used to control escalation within a bounded trajectory budget rather than applied uniformly.