Related papers: Symmetric Group Testing and Superimposed Codes
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…
We propose three test criteria each of which is appropriate for testing, respectively, the equivalence hypotheses of symmetry, of homogeneity, and of independence, with multivariate data. All quantities have the common feature of involving…
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 binary code is said to be a disjunctive list-decoding $s_L$-code (LD $s_L$-code), $s \ge 2$, $L \ge 1$, if the code is identified by the incidence matrix of a family of finite sets in which the union (or disjunctive sum) of any $s$ sets…
The increasing interest in subpopulation analysis has led to the development of various new trial designs and analysis methods in the fields of personalized medicine and targeted therapies. In this paper, subpopulations are defined in terms…
We consider nonparametric or universal sequential hypothesis testing problem when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution. These algorithms are…
In network tomography, one goal is to identify a small set of failed links in a network, by sending a few packets through the network and seeing which reach their destination. This problem can be seen as a variant of combinatorial group…
We investigate the problem of safety verification of infinite-state parameterized programs that are formed based on a rich class of topologies. We introduce a new proof system, called parametric proof spaces, which exploits the underlying…
In group testing, 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 testing, data…
The group synchronization problem involves estimating a collection of group elements from noisy measurements of their pairwise ratios. This task is a key component in many computational problems, including the molecular reconstruction…
We suggest a new approach to hypothesis testing for ergodic and stationary processes. In contrast to standard methods, the suggested approach gives a possibility to make tests, based on any lossless data compression method even if the…
The computation of the normaliser of a permutation group in the full symmetric group is an important and hard problem in computational group theory. This article reports on an algorithm that builds a descending chain of overgroups to…
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 original problem of group testing consists in the identification of defective items in a collection, by applying tests on groups of items that detect the presence of at least one defective item in the group. The aim is then to identify…
This paper is an attempt to compute the decomposition numbers of the blocks of the symmetric group which have "small defect"; that is, blocks of weight smaller than the characteristic. We present various methods for computing such…
Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for…
Labeling a training set is often expensive and susceptible to errors, making the design of robust loss functions for label noise an important problem. The symmetry condition provides theoretical guarantees for robustness to such noise. In…
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…
In the problem of classical group testing one aims to identify a small subset (of size $d$) diseased individuals/defective items in a large population (of size $n$). This process is based on a minimal number of suitably-designed group tests…
We explain an algorithm that approximately but efficiently assesses particular parity-check error-correcting codes of large, but finite, blocklength. This algorithm is based on the ``renormalization-group'' approach from physics: the idea…