Let ℱ⊆[n] k be a t-intersecting family. Define the t-covering number τ_t(ℱ) of ℱ as the minimum size of a subset S of [n] with |S∩ F|⩾ t for each F∈ℱ. In this paper, we characterize ℱ for which |ℱ| takes the maximum value under the condition that τ_t(ℱ)⩾ t+2 and n is sufficiently large, thereby generalizing two results by Frankl.
Large Language Models (LLMs) are rapidly transforming intelligent healthcare and medicine. However, their successful clinical deployment depends on reliable and explainable medical reasoning rather than surface-level text generation. This survey reviews LLM reasoning in medicine. It covers foundational datasets, training-time optimization, test-time reasoning, collaborative agents, and reasoning evaluation. We distinguish two complementary design axes. Individual-model optimization improves the reasoning behavior of a model or module through supervised fine-tuning, reinforcement-based fine-tuning, or test-time control. Collaborative-agent design specifies how one or more such modules exchange evidence, invoke tools, and aggregate decisions at the system level. Collaborative-agent design does not replace individual-model optimization. Contemporary agent systems commonly compose prompted or individually trained modules, including SFT- and GRPO-optimized planners, routers, and aggregators. This compositional view clarifies both the promise and the current limitations of agents. Structured collaboration can support transparency, error recovery, and heterogeneous evidence integration in workflow-oriented tasks. However, it does not provide an inherent advantage over a strong single LLM on narrowly scoped questions. Combining individual-model optimization with collaborative-agent design offers substantial potential for advancing future medical intelligence.
Capturing the rich, hierarchical information embedded in complex multivariate time series (MTS) necessitates modeling at multiple temporal scales. However, prevalent multi-scale forecasting methods suffer from critical limitations: a uniform scaling approach that overlooks individual variable characteristics, inconsistent modeling of temporal patterns and inter-variable dependency leading to modeling spurious correlations, and a neglect of global context. To overcome these challenges, we introduce LMSNet, a Lightweight Multi-Scale graph learning framework. Specifically, LMSNet introduces a novel variable-specific scaling mechanism, which leverages frequency-domain analysis to assign a tailored analytical window to each variable based on its intrinsic dynamics, establishing a robust foundation for accurately modeling multi-scale inter-variable dependencies. Furthermore, LMSNet synergizes global and local information and performs concurrent temporal and inter-variable dependency modeling at every network layer, aided by a momentum update mechanism that refines deep-layer graph node representations to mitigate the risk of modeling spurious correlations. LMSNet establishes a new state-of-the-art on eight benchmark datasets. Crucially, it achieves a 2.94% reduction in MAE with reducing GPU memory usage by 83% and accelerating training by 60% compared to strong baseline-TimeMixer. Our source code is provided at https://github.com/05Pikachu24/TSF-LMSNet.
The rapid expansion of global PV trade is accompanied by a notable “energy leakage” effect, where energy-intensive production processes are relocated via international trade to regions with lower energy efficiency, thereby undermining the overall emission reduction potential of the PV industry. This study integrates life-cycle data of PV products from 139 countries and constructs a multi-regional model based on 2021 actual trade flows, uncovering the embodied energy transfer characteristics across the entire supply chain from silicon feedstock, wafers to modules. The results reveal a profound fossil energy dependence (91.3–92.69%) throughout the supply chain. While current trade patterns enhance local energy efficiency through specialization, regional electricity mix disparities and cross-border transportation result in a net increase of 347.6 billion MJ energy input in the global supply chain, creating a vicious cycle of “scale expansion–energy leakage escalation”. Policy interventions show divergent effects: carbon tariffs and geopolitical conflicts reduce energy leakage through regionalized production reshoring at the cost of $2.3 billion trade losses, whereas technological breakthroughs achieve a win-win of “scale expansion and energy consumption reduction” (cutting 12.8 billion MJ fossil energy input). The study proposes a clean transition pathway leveraging process-specific differentiation and regional synergy to resolve the energy-environment paradox in PV trade.
