Related papers: Test Groups for Whitehead Groups
Toric Duality arises as an ambiguity in computing the quiver gauge theory living on a D3-brane which probes a toric singularity. It is reviewed how, in simple cases Toric Duality is Seiberg Duality. The set of all Seiberg Dualities on a…
This paper will be concerned with proving that certain Whitehead groups of torsion-free elementary amenable groups are torsion groups and related results, and then applying these results to the Bass conjecture. In particular we shall…
In group testing, the task is to identify defective items by testing groups of them together using as few tests as possible. We consider the setting where each item is defective with a constant probability $\alpha$, independent of all other…
Building on work by Kasparov, we study the notion of Spanier-Whitehead K-duality for a discrete group. It is defined as duality in the KK-category between two C*-algebras which are naturally attached to the group, namely the reduced group…
This article reviews a class of adaptive group testing procedures that operate under a probabilistic model assumption as follows. Consider a set of $N$ items, where item $i$ has the probability $p$ ($p_i$ in the generalized group testing)…
Standard high-dimensional factor models assume that the comovements in a large set of variables could be modeled using a small number of latent factors that affect all variables. In many relevant applications in economics and finance,…
We give a survey on classical and recent results on dual spaces of topological tensor products as well as some examples where these are used.
In this article we define the twisted product of groups as the generalization of the semidirect product of groups. We will find the necessary and sufficient condition in order that the twisted product of groups to be a group. In particular,…
We explore the concept of conjugation between subgroupoids, providing several characterizations of the conjugacy relation (Theorem A in {\S}1.2). We show that two finite groupoid-sets, over a locally strongly finite groupoid, are…
This is the second of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we develop a basic machinery for studying homotopy classes of such maps. It contains two parts: (1) the…
We consider the problem of hypothesis testing in the situation where the first hypothesis is simple and the second one is local one-sided composite. We describe the choice of the thresholds and the power functions of different tests when…
We investigate the problem whether a given multiplier of a tensor product of two algebras belongs to the tensor product of multiplier algebras. We give a characterization of such multipliers in the case when one of the algebras is the…
We present a general framework for hypothesis testing on distributions of sets of individual examples. Sets may represent many common data sources such as groups of observations in time series, collections of words in text or a batch of…
The Surface Group Conjectures are statements about recognising surface groups among one-relator groups, using either the structure of their finite-index subgroups, or all subgroups. We resolve these conjectures in the two generator case.…
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…
Non-adaptive group testing refers to the problem of inferring a sparse set of defectives from a larger population using the minimum number of simultaneous pooled tests. Recent positive results for noiseless group testing have motivated the…
Given two tuples of subspaces, can you tell whether the tuples are isomorphic? We develop theory and algorithms to address this fundamental question. We focus on isomorphisms in which the ambient vector space is acted on by either a unitary…
We combine results about Whitehead groups of finite groups with results about genetic bases of finite $p$-groups to compute the Whitehead groups of some metacyclic $p$-groups. Let $C_{p^n}$ denote a cyclic group of order $p^n$ for $p$ an…
We construct a commutative version of the group ring and show that it allows one to translate questions about the normal generation of groups into questions about the generation of ideals in commutative rings. We demonstrate this with an…
Group testing is utilized in the case when we want to find a few defectives among large amount of items. Testing n items one by one requires n tests, but if the ratio of defectives is small, group testing is an efficient way to reduce the…