A Note on: `Algorithms for Connected Set Cover Problem and Fault-Tolerant Connected Set Cover Problem'

A flaw in the greedy approximation algorithm proposed by Zhang et al. for minimum connected set cover problem is corrected, and a stronger result on the approximation ratio of the modified greedy algorithm is established. The results are now consistent with the existing results on connected dominating set problem which is a special case of the minimum connected set cover problem.Comment: 6 pages, 1 figure, submitted to Theoretical Computer Scienc

Numerical Simulation of Compressible Reactive Flows

Numerical simulation has been widely employed to investigate the compressible flows since it is difficult to carry out the experimental measurements, especially in the reactive flows. The shock-wave capturing scheme will be necessary for resolving the compressible flows, and moreover the careful treatments of chemical reaction should be considered for proceeding numerical simulation stable and fast. Recently, the present authors have tried to establish a high-resolution numerical solver for computing the compressible reactive flows. This chapter presents the numerical procedures acquired in this solver for computing the fluxes using weighted essentially non-oscillatory (WENO) scheme, dealing with chemical stiffness problems, and tracing droplets and their interaction with the compressible fluids. As examples, the Taylor-Green vortex (TGV) problem considering the passive scalar mixing, the spatially developing reactive mixing layer flows taken gas-phase hydrogen, and liquid n-decane as fuel are simulated, respectively. Many important characteristics of flow, flame, and ignition are analyzed under the supersonic condition

T-SaS: Toward Shift-aware Dynamic Adaptation for Streaming Data

In many real-world scenarios, distribution shifts exist in the streaming data across time steps. Many complex sequential data can be effectively divided into distinct regimes that exhibit persistent dynamics. Discovering the shifted behaviors and the evolving patterns underlying the streaming data are important to understand the dynamic system. Existing methods typically train one robust model to work for the evolving data of distinct distributions or sequentially adapt the model utilizing explicitly given regime boundaries. However, there are two challenges: (1) shifts in data streams could happen drastically and abruptly without precursors. Boundaries of distribution shifts are usually unavailable, and (2) training a shared model for all domains could fail to capture varying patterns. This paper aims to solve the problem of sequential data modeling in the presence of sudden distribution shifts that occur without any precursors. Specifically, we design a Bayesian framework, dubbed as T-SaS, with a discrete distribution-modeling variable to capture abrupt shifts of data. Then, we design a model that enable adaptation with dynamic network selection conditioned on that discrete variable. The proposed method learns specific model parameters for each distribution by learning which neurons should be activated in the full network. A dynamic masking strategy is adopted here to support inter-distribution transfer through the overlapping of a set of sparse networks. Extensive experiments show that our proposed method is superior in both accurately detecting shift boundaries to get segments of varying distributions and effectively adapting to downstream forecast or classification tasks.Comment: CIKM 202