Semiquantitative Group Testing in at Most Two Rounds

通过非自适应半定量分组测试寻找正样本的突发

Finding a Burst of Positives via Nonadaptive Semiquantitative Group Testing

本文研究非自适应半定量分组测试中正样本突发识别问题，提出阶数最优测试方案，证明所需最少测试数仅取决于最大阈值，大饱和水平比精细量化更重要。

The Communication Complexity of Set Intersection and Multiple Equality Testing

In this paper we explore fundamental problems in randomized communication complexity such as computing Set Intersection on sets of size $k$ and Equality Testing between vectors of length $k$. Sağlam and Tardos and Brody et al. showed that for these types of problems, one can achieve optimal communication volume of $O(k)$ bits, with a randomized protocol that takes $O(\log^* k)$ rounds. Aside from rounds and communication volume, there is a \emph{third} parameter of interest, namely the \emph{error probability} $p_{\mathrm{err}}$. It is straightforward to show that protocols for Set Intersectio…

Heuristic Random Designs for Exact Identification of Defectives Using Single Round Non-adaptive Group Testing and Compressed Sensing

Among the challenges that the COVID-19 pandemic outbreak revealed is the problem to reduce the number of tests required for identifying the virus carriers in order to contain the viral spread while preserving the tests reliability. To cope with this issue, a prevalence testing paradigm based on group testing and compressive sensing approach or GTCS was examined. In these settings, a non-adaptive group testing algorithm is designed to rule out sure-negative samples. Then, on the reduced problem, a compressive sensing algorithm is applied to decode the positives without requiring any further tes…

隔离然后识别：重新思考自适应群体检测

Isolate and then Identify: Rethinking Adaptive Group Testing

本文提出“隔离然后识别”（I@I）的自适应群体检测策略，先分组隔离至每组最多一个患病者，再识别，首次在通用信道下实现最优系数，且模块化可分别优化。

Collaborative Distributed Hypothesis Testing

A collaborative distributed binary decision problem is considered. Two statisticians are required to declare the correct probability measure of two jointly distributed memoryless process, denoted by $X^n=(X_1,\dots,X_n)$ and $Y^n=(Y_1,\dots,Y_n)$, out of two possible probability measures on finite alphabets, namely $P_{XY}$ and $P_{\bar{X}\bar{Y}}$. The marginal samples given by $X^n$ and $Y^n$ are assumed to be available at different locations. The statisticians are allowed to exchange limited amount of data over multiple rounds of interactions, which differs from previous work that deals mai…

统计两轮搜索寻找一个优秀元素

Statistical two-round search for one excellent element

本文研究了统计意义上的两轮搜索问题，旨在以最小的测试次数找到至少一个优秀元素，证明在稀疏泊松条件下，测试次数随人口规模对数增长。