Spanning trails containing given edges

A graph G is Eulerian-connected if for any u and v in V ( G ) , G has a spanning ( u , v ) -trail. A graph G is edge-Eulerian-connected if for any e ′ and e ″ in E ( G ) , G has a spanning ( e ′ , e ″ ) -trail. For an integer r ⩾ 0 , a graph is called r -Eulerian-connected if for any X ⊆ E ( G ) with | X | ⩽ r , and for any u , v ∈ V ( G ) , G has a spanning ( u , v ) -trail T such that X ⊆ E ( T ) . The r -edge-Eulerian-connectivity of a graph can be defined similarly. Let θ ( r ) be the minimum value of k such that every k -edge-connected graph is r -Eulerian-connected. Catlin proved that θ ( 0 ) = 4 . We shall show that θ ( r ) = 4 for 0 ⩽ r ⩽ 2 , and θ ( r ) = r + 1 for r ⩾ 3 . Results on r -edge-Eulerian connectivity are also discussed

Chain-of-Choice Hierarchical Policy Learning for Conversational Recommendation

Conversational Recommender Systems (CRS) illuminate user preferences via multi-round interactive dialogues, ultimately navigating towards precise and satisfactory recommendations. However, contemporary CRS are limited to inquiring binary or multi-choice questions based on a single attribute type (e.g., color) per round, which causes excessive rounds of interaction and diminishes the user's experience. To address this, we propose a more realistic and efficient conversational recommendation problem setting, called Multi-Type-Attribute Multi-round Conversational Recommendation (MTAMCR), which enables CRS to inquire about multi-choice questions covering multiple types of attributes in each round, thereby improving interactive efficiency. Moreover, by formulating MTAMCR as a hierarchical reinforcement learning task, we propose a Chain-of-Choice Hierarchical Policy Learning (CoCHPL) framework to enhance both the questioning efficiency and recommendation effectiveness in MTAMCR. Specifically, a long-term policy over options (i.e., ask or recommend) determines the action type, while two short-term intra-option policies sequentially generate the chain of attributes or items through multi-step reasoning and selection, optimizing the diversity and interdependence of questioning attributes. Finally, extensive experiments on four benchmarks demonstrate the superior performance of CoCHPL over prevailing state-of-the-art methods.Comment: Release with source cod

Transactive Energy and Flexibility Provision in Multi-microgrids using Stackelberg Game

Aggregating the demand side flexibility is essential to complementing the inflexible and variable renewable energy supply in achieving low carbon energy systems. Sources of demand side flexibility, e.g., dispatchable generators, storages, and flexible loads, can be structured in a form of microgrids and collectively provided to utility grids through transactive energy in local energy markets. This paper proposes a framework of local energy markets to manage the transactive energy and facilitate the flexibility provision. The distribution system operator aims to achieve local energy balance by scheduling the operation of multi-microgrids and determining the imbalance prices. Multiple microgrid traders aim to maximise profits for their prosumers through dispatching flexibility sources and participating in localised energy trading. The decision making and interactions between a distribution system operator and multiple microgrid traders are formulated as the Stackelberg game-theoretic problem. Case studies using the IEEE 69-bus distribution system demonstrate the effectiveness of the developed model in terms of facilitating the local energy balance and reducing the dependency on the utility grids

Multi-Range Attentive Bicomponent Graph Convolutional Network for Traffic Forecasting

Traffic forecasting is of great importance to transportation management and public safety, and very challenging due to the complicated spatial-temporal dependency and essential uncertainty brought about by the road network and traffic conditions. Latest studies mainly focus on modeling the spatial dependency by utilizing graph convolutional networks (GCNs) throughout a fixed weighted graph. However, edges, i.e., the correlations between pair-wise nodes, are much more complicated and interact with each other. In this paper, we propose the Multi-Range Attentive Bicomponent GCN (MRA-BGCN), a novel deep learning model for traffic forecasting. We first build the node-wise graph according to the road network distance and the edge-wise graph according to various edge interaction patterns. Then, we implement the interactions of both nodes and edges using bicomponent graph convolution. The multi-range attention mechanism is introduced to aggregate information in different neighborhood ranges and automatically learn the importance of different ranges. Extensive experiments on two real-world road network traffic datasets, METR-LA and PEMS-BAY, show that our MRA-BGCN achieves the state-of-the-art results.Comment: Accepted by AAAI 202

Fluorescent Probes for Molecular Imaging of ROS/RNS Species in Living Systems

Reactive Oxygen Species (ROS) and Reactive Nitrogen Species (RNS) are highly reactive species which play crucial roles in many fundamental physiological processes including cellular signalling pathways. Over-production of these reactive species by various stimuli leads to cellular oxidative stress which is linked to various disease conditions. Therefore, the development of novel detection methods for ROS and RNS is of great interest and indispensable for monitoring the dynamic changes of ROS and RNS in cells and for elucidating their mechanisms of trafficking and connections to diseases. We have been recently developing various fluorescent sensors which can selectively detect metal ions, ROS or RNS species in live cells or animals. Our turn-on profluorescent sensors are capable of imaging oxidative stress promoted by metal and H2O2 (i.e. the Fenton Reaction conditions) in living cells (Chem Commun 2010); our highly selective and sensitive iron sensors can image the endogenous exchangeable iron pools and their dynamic changes with subcellular resolution in living neuronal cells (ChemBioChem 2012 and unpublished data), and so do our superoxide sensors (ChemBioChem 2012 and unpublished data). Moreover, we have recently developed nitric oxide (NO) sensors for molecular imaging of stimulated NO production in live cells with subcellular resolution as well as novel near infra red (NIR) sensors for NO imaging in live animals