Related papers: Statistical Physics of Group Testing
We consider sequential hypothesis testing based on observations which are received in groups of random size. The observations are assumed to be independent both within and between the groups. We assume that the group sizes are independent…
A two-stage collaborative exam is one in which students first complete the exam individually, and then complete the same or similar exam in collaborative groups immediately afterward. To quantify the learning effect from the group component…
Accurate detection of infected individuals is one of the critical steps in stopping any pandemic. When the underlying infection rate of the disease is low, testing people in groups, instead of testing each individual in the population, can…
In this paper, we introduce a variation of the group testing problem capturing the idea that a positive test requires a combination of multiple ``types'' of item. Specifically, we assume that there are multiple disjoint \emph{semi-defective…
In this paper, we propose algorithms that leverage a known community structure to make group testing more efficient. We consider a population organized in connected communities: each individual participates in one or more communities, and…
The paper describes an automated evaluation system for the learning of general Physics. The system whose name is Test on Line (ToL) is based on a questions bank from which an appropriate software generates individual multi-issue…
Group testing is a useful method that has broad applications in medicine, engineering, and even in airport security control. Consider a finite population of $N$ items, where item $i$ has a probability $p_i$ to be defective. The goal is to…
Hypothesis testing is a statistical inference approach used to determine whether data supports a specific hypothesis. An important type is the two-sample test, which evaluates whether two sets of data points are from identical…
Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their…
We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like ``a random element (or a tuple of elements) of a group G has a…
The paper addresses general aspects of experimental data analysis, dealing with the separation of ``signal vs. background''. It consists of two parts. Part I is a tutorial on statistical event classification, Bayesian inference, and test…
In this paper, we propose algorithms that leverage a known community structure to make group testing more efficient. We consider a population organized in disjoint communities: each individual participates in a community, and its infection…
The aim of this Thesis is to present five new tests for random numbers, which are widely used {\em e.g.} in computer simulations in physics applications. The first two tests, the cluster test and the autocorrelation test, are based on…
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
In one-stage or non-adaptive group testing, instead of testing every sample unit individually, they are split, bundled in pools, and simultaneously tested. The results are then decoded to infer the states of the individual items. This…
We present results of an extensive test program of a group of pseudorandom number generators which are commonly used in the applications of physics, in particular in Monte Carlo simulations. The generators include public domain programs,…
We study the inference problem in the group testing to identify defective items from the perspective of the decision theory. We introduce Bayesian inference and consider the Bayesian optimal setting in which the true generative process of…
Clustering is part of unsupervised analysis methods that consist in grouping samples into homogeneous and separate subgroups of observations also called clusters. To interpret the clusters, statistical hypothesis testing is often used to…
The conventional model of disjunctive group testing assumes that there are several defective elements (or defectives) among a large population, and a group test yields the positive response if and only if the testing group contains at least…
A new approach to adaptive design of clinical trials is proposed in a general multiparameter exponential family setting, based on generalized likelihood ratio statistics and optimal sequential testing theory. These designs are easy to…