Related papers: Efficient Two-Stage Group Testing Algorithms for D…
We consider the probabilistic group testing problem where $d$ random defective items in a large population of $N$ items are identified with high probability by applying binary tests. It is known that $\Theta(d \log N)$ tests are necessary…
We consider two combinatorial problems. The first we call "search with wildcards": given an unknown n-bit string x, and the ability to check whether any subset of the bits of x is equal to a provided query string, the goal is to output x.…
Pathogenic infections pose a significant threat to global health, affecting millions of people every year and presenting substantial challenges to healthcare systems worldwide. Efficient and timely testing plays a critical role in disease…
We consider adaptive group testing in the linear regime, where the number of defective items scales linearly with the number of items. We analyse an algorithm based on generalized binary splitting. Provided fewer than half the items are…
PCR testing is an invaluable diagnostic tool that has most recently seen widespread use during the COVID-19 pandemic. A recent work by Wang, Gabrys and Vardy proposed tropical codes as a model for group PCR testing. For a known but…
The aim of staged compilation is to enable metaprogramming in a way such that we have guarantees about the well-formedness of code output, and we can also mix together object-level and meta-level code in a concise and convenient manner. In…
Computer based techniques for recognizing finitely presented groups are quite powerful. Tools available for this purpose are outlined. They are available both in stand-alone programs and in more comprehensive systems. A general…
Let $1 \le s < t$, $N \ge 1$ be integers and a complex electronic circuit of size $t$ is said to be an $s$-active, $\; s \ll t$, and can work as a system block if not more than $s$ elements of the circuit are defective. Otherwise, the…
A generative Bayesian model is developed for deep (multi-layer) convolutional dictionary learning. A novel probabilistic pooling operation is integrated into the deep model, yielding efficient bottom-up and top-down probabilistic learning.…
We investigate group coding for arbitrary finite groups acting linearly on a vector space. These yield robust codes based on real or complex matrix groups. We give necessary and sufficient conditions for correct subgroup decoding using…
Forensic scientists are often criticised for the lack of quantitative support for the conclusions of their examinations. While scholars advocate for the use of a Bayes factor to quantify the weight of forensic evidence, it is often…
In this paper, we consider the problem of noiseless non-adaptive group testing under the for-each recovery guarantee, also known as probabilistic group testing. In the case of $n$ items and $k$ defectives, we provide an algorithm attaining…
Autonomous materials discovery with desired properties is one of the ultimate goals for materials science, and the current studies have been focusing mostly on high-throughput screening based on density functional theory calculations and…
Thinning is the removal of contour pixels/points of connected components in an image to produce their skeleton with retained connectivity and structural properties. The output requirements of a thinning procedure often vary with…
Designing molecular structures with desired chemical properties is an essential task in drug discovery and material design. However, finding molecules with the optimized desired properties is still a challenging task due to combinatorial…
The study proves the existence of an algorithm to receive all elements of a class of binary matrices without obtaining redundant elements, e. g. without obtaining binary matrices that do not belong to the class. This makes it possible to…
The purpose of this article is to introduce a new iterative algorithm with properties resembling real life bipartite graphs. The algorithm enables us to generate wide range of random bigraphs, which features are determined by a set of…
The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of possibly-noisy tests, and is relevant in applications such as medical testing, communication protocols, pattern…
In small sample studies with binary outcome data, use of a normal approximation for hypothesis testing can lead to substantial inflation of the type-I error-rate. Consequently, exact statistical methods are necessitated, and accordingly,…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…