An algorithm for efficiently calculating the expected size of single-seed cascade dynamics on networks is proposed and tested. The expected size is a time-dependent quantity and so enables the identification of nodes who are the most influential early or late in the spreading process. The measure is accurate for both critical and subcritical dynamic regimes and so generalises the nonbacktracking centrality that was previously shown to successfully identify the most influential single spreaders in a model of critical epidemics on networks.

We present observations and analysis of the starburst, PACS-819, at z=1.45 ($M_*=10^{10.7}$ M$_{ \odot}$), using high-resolution ($0^{\prime \prime}.1$; 0.8 kpc) ALMA and multi-wavelength JWST images from the COSMOS-Web program. Dissimilar to HST/ACS images in the rest-frame UV, the redder NIRCam and MIRI images reveal a smooth central mass concentration and spiral-like features, atypical for such an intense starburst. Through dynamical modeling of the CO J=5--4 emission with ALMA, PACS-819 is rotation-dominated thus has a disk-like nature. However, kinematic anomalies in CO and asymmetric features in the bluer JWST bands (e.g., F150W) support a more disturbed nature likely due to interactions. The JWST imaging further enables us to map the distribution of stellar mass and dust attenuation, thus clarifying the relationships between different structural components, not discernable in the previous HST images. The CO J = 5 -- 4 and FIR dust continuum emission are co-spatial with a heavily-obscured starbursting core (<1 kpc) which is partially surrounded by much less obscured star-forming structures including a prominent arc, possibly a tidally-distorted dwarf galaxy, and a clump, either a sign of an ongoing violent disk instability or a recently accreted low-mass satellite. With spatially-resolved maps, we find a high molecular gas fraction in the central area reaching $\sim3$ ($M_{\text{gas}}$/$M_*$) and short depletion times ($M_{\text{gas}}/SFR\sim$ 120 Myrs) across the entire system. These observations provide insights into the complex nature of starbursts in the distant universe and underscore the wealth of complementary information from high-resolution observations with both ALMA and JWST.

Collective effects, such as Dicke superradiant emission, can enhance the performance of a quantum device. Here, we study the heat current flowing between a cold and a hot bath through an ensemble of $N$ qubits, which are collectively coupled to the thermal baths. We find a regime where the collective coupling leads to a quadratic scaling of the heat current with $N$ in a finite-size scenario. Conversely, when approaching the thermodynamic limit, we prove that the collective scenario exhibits a parametric enhancement over the non-collective case. We then consider the presence of a third uncontrolled {\it parasitic} bath, interacting locally with each qubit, that models unavoidable couplings to the external environment. Despite having a non-perturbative effect on the steady-state currents, we show that the collective enhancement is robust to such an addition. Finally, we discuss the feasibility of realizing such a Dicke heat valve with superconducting circuits. Our findings indicate that in a minimal realistic experimental setting with two superconducting qubits, the collective advantage offers an enhancement of approximately $10\%$ compared to the non-collective scenario.

Developing large language models (LLMs) to cooperate and compete effectively within multi-agent systems (MASs) is a critical step towards more advanced intelligence. While reinforcement learning (RL) has proven effective for enhancing reasoning in single-agent tasks, its extension to multi-turn, multi-agent scenarios remains underexplored due to the challenges of long-horizon credit assignment and agent-specific advantage estimation. To address these challenges, we introduce MARSHAL, an end-to-end RL framework that incentivizes Multi-Agent Reasoning through Self-play witH strAtegic LLMs in both cooperative and competitive games. MARSHAL features a turn-level advantage estimator that aligns learning signals with each interaction for credit assignment, and an agent-specific advantage normalization to stabilize multi-agent training. By learning with self-play across cooperative and competitive games, MARSHAL agent trained from Qwen3-4B develops strong strategic abilities that generalize to held-out games with up to 28.7% performance improvements. More importantly, the capability acquired through self-play generalizes beyond games, yielding consistent performance gains of MASs in reasoning benchmarks. When integrated into leading MASs, our MARSHAL agent achieves significant performance gains of up to 10.0% on AIME, 6.6% on GPQA-Diamond, and 3.5% on average across all benchmarks. These results establish end-to-end RL training with self-play in strategic games as a powerful approach for developing generalizable multi-agent reasoning capabilities in LLMs.

The recently proposed Temporal Ensembling has achieved state-of-the-art results in several semi-supervised learning benchmarks. It maintains an exponential moving average of label predictions on each training example, and penalizes predictions that are inconsistent with this target. However, because the targets change only once per epoch, Temporal Ensembling becomes unwieldy when learning large datasets. To overcome this problem, we propose Mean Teacher, a method that averages model weights instead of label predictions. As an additional benefit, Mean Teacher improves test accuracy and enables training with fewer labels than Temporal Ensembling. Without changing the network architecture, Mean Teacher achieves an error rate of 4.35% on SVHN with 250 labels, outperforming Temporal Ensembling trained with 1000 labels. We also show that a good network architecture is crucial to performance. Combining Mean Teacher and Residual Networks, we improve the state of the art on CIFAR-10 with 4000 labels from 10.55% to 6.28%, and on ImageNet 2012 with 10% of the labels from 35.24% to 9.11%.