Related papers: Optimal pooling designs with error detection

The task of learning to pick a single preferred example out a finite set of examples, an "optimal choice problem", is a supervised machine learning problem with complex, structured input. Problems of optimal choice emerge often in various…

We study Probabilistic Group Testing of a set of N items each of which is defective with probability p. We focus on the double limit of small defect probability, p<<1, and large number of variables, N>>1, taking either p->0 after…

We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In…

In combinatorial group testing (CGT), the objective is to identify the set of at most $d$ defective items from a pool of $n$ items using as few tests as possible. The celebrated result for the CGT problem is that the number of tests $t$ can…

In order to identify the infected individuals of a population, their samples are divided in equally sized groups called pools and a single laboratory test is applied to each pool. Individuals whose samples belong to pools that test negative…

In the group testing problem, the goal is to identify a subset of defective items within a larger set of items based on tests whose outcomes indicate whether any defective item is present. This problem is relevant in areas such as medical…

Property testing has been a major area of research in computer science in the last three decades. By property testing we refer to an ensemble of problems, results and algorithms which enable to deduce global information about some data by…

We show that for any n divisible by 3, almost all order-n Steiner triple systems have a perfect matching (also known as a parallel class or resolution class). In fact, we prove a general upper bound on the number of perfect matchings in a…

The decision to incorporate cross-validation into validation processes of mathematical models raises an immediate question - how should one partition the data into calibration and validation sets? We answer this question systematically: we…

Data pooling offers various advantages, such as increasing the sample size, improving generalization, reducing sampling bias, and addressing data sparsity and quality, but it is not straightforward and may even be counterproductive.…

Optimisation problems are ubiquitous in particle and astrophysics, and involve locating the optimum of a complicated function of many parameters that may be computationally expensive to evaluate. We describe a number of global optimisation…

Maximum diversity problems arise in many practical settings from facility location to social networks, and constitute an important class of NP-hard problems in combinatorial optimization. There has been a growing interest in these problems…

We consider the {\em clustering with diversity} problem: given a set of colored points in a metric space, partition them into clusters such that each cluster has at least $\ell$ points, all of which have distinct colors. We give a…

We study the problem of aggregating polygons by covering them with disjoint representative regions, thereby inducing a clustering of the polygons. Our objective is to minimize a weighted sum of the total area and the total perimeter of the…

We consider the dihedral hidden subgroup problem as the problem of distinguishing hidden subgroup states. We show that the optimal measurement for solving this problem is the so-called pretty good measurement. We then prove that the success…

Bloom filters are space-efficient probabilistic data structures that are used to test whether an element is a member of a set, and may return false positives. Recently, variations referred to as learned Bloom filters were developed that can…

In several interesting applications one is faced with the problem of simultaneous binary hypothesis testing and parameter estimation. Although such joint problems are not infrequent, there exist no systematic analysis in the literature that…

The Maximum Flow Problem with Conflict Constraints is a generalization that adds conflict constraints to a classical optimization problem on networks used to model several real-world applications. In the last few years several approaches,…

Several researchers have experimentally shown that substantial improvements can be obtained in difficult pattern recognition problems by combining or integrating the outputs of multiple classifiers. This chapter provides an analytical…

Duplicate detection is the problem of identifying whether a given item has previously appeared in a (possibly infinite) stream of data, when only a limited amount of memory is available. Unfortunately the infinite stream setting is…