Flow fields are often partitioned into data blocks for massively parallel
computation and analysis based on blockwise relationships. However, most of the
previous techniques only consider the first-order dependencies among blocks,
which is insufficient in describing complex flow patterns. In this work, we
present FlowHON, an approach to construct higher-order networks (HONs) from
flow fields. FlowHON captures the inherent higher-order dependencies in flow
fields as nodes and estimates the transitions among them as edges. We formulate
the HON construction as an optimization problem with three linear
transformations. The first two layers correspond to the node generation and the
third one corresponds to edge estimation. Our formulation allows the node
generation and edge estimation to be solved in a unified framework. With
FlowHON, the rich set of traditional graph algorithms can be applied without
any modification to analyze flow fields, while leveraging the higher-order
information to understand the inherent structure and manage flow data for
efficiency. We demonstrate the effectiveness of FlowHON using a series of
downstream tasks, including estimating the density of particles during tracing,
partitioning flow fields for data management, and understanding flow fields
using the node-link diagram representation of networks.

使用 FlowHON 方法构建高阶网络来分析流场，并通过节点生成和边估计解决对流场的密度估计、数据管理和结构理解等下游任务。

FlowHON: 使用高阶网络表示流场

FlowHON: Representing Flow Fields Using Higher-Order Networks

We study the task of estimating the number of edges in a graph with access to
only an independent set oracle. Independent set queries draw motivation from
group testing and have applications to the complexity of decision versus
counting problems. We give two algorithms to estimate the number of edges in an
$n$-vertex graph, using (i) $\mathrm{polylog}(n)$ bipartite independent set
queries, or (ii) ${n}^{2/3} \cdot\mathrm{polylog}(n)$ independent set queries.

本研究探讨了使用独立集合查询进行图边估计的问题，并提出了两种算法来估计 n 个顶点的图中边的数量。