## Publications

98 results found

Gutin G, Jones N, Rafiey A,
et al., 2005, Mediated digraphs and quantum nonlocality, *Discrete Applied Mathematics*, Vol: 150, Pages: 41-50, ISSN: 0166-218X

A digraph D = ( V , A ) is mediated if for each pair x , y of distinct vertices of D , either xy ∈ A or yx ∈ A or there is a vertex z such that both xz , yz ∈ A . For a digraph D , Δ - ( D ) is the maximum in-degree of a vertex in D . The n th mediation number μ ( n ) is the minimum of Δ - ( D ) over all mediated digraphs on n vertices. Mediated digraphs and μ ( n ) are of interest in the study of quantum nonlocality. We obtain a lower bound f ( n ) for μ ( n ) and determine infinite sequences of values of n for which μ ( n ) = f ( n ) and μ ( n ) > f ( n ) , respectively. We derive upper bounds for μ ( n ) and prove that μ ( n ) = f ( n ) ( 1 + o ( 1 ) ) . We conjecture that there is a constant c such that μ ( n ) ⩽ f ( n ) + c . Methods and results of design theory and number theory are used.

Jones NS, Linden N, Massar S, 2005, Extent of multiparticle quantum nonlocality, *Physical Review A*, Vol: 71, Pages: 042329-042329, ISSN: 1050-2947

Jones NS, Linden N, 2005, Parts of quantum states, *Physical Review A*, Vol: 71, Pages: 012324-012324, ISSN: 1050-2947

Hadjipantelis PZ, Jones NS, Moriarty J, et al., Ancestral Inference from Functional Data: Statistical Methods and Numerical Examples

Many biological characteristics of evolutionary interest are not scalarvariables but continuous functions. Here we use phylogenetic Gaussian processregression to model the evolution of simulated function-valued traits. Givenfunction-valued data only from the tips of an evolutionary tree and utilisingindependent principal component analysis (IPCA) as a method for dimensionreduction, we construct distributional estimates of ancestral function-valuedtraits, and estimate parameters describing their evolutionary dynamics.

Jones NS, Ces O, Democratizing University Research

We detail an experimental programme we have been testing in our university.Our Advanced Hackspace, attempts to give all members of the university, fromstudents to technicians, free access to the means to develop their owninterdisciplinary research ideas, with resources including access tospecialized fellows and biological and chemical hacklabs. We assess the aspectsof our programme that led to our community being one of the largest collectivesin our university and critically examine the successes and failures of ourtrial programmes. We supply metrics for assessing progress and outlinechallenges. We conclude with future directions that advance interdisciplinaryresearch empowerment for all university members.

Hoffmann T, Jones NS, Unified treatment of the asymptotics of asymmetric kernel density estimators

We extend balloon and sample-smoothing estimators, two types ofvariable-bandwidth kernel density estimators, by a shift parameter and derivetheir asymptotic properties. Our approach facilitates the unified study of awide range of density estimators which are subsumed under these two generalclasses of kernel density estimators. We demonstrate our method by deriving theasymptotic bias, variance, and mean (integrated) squared error of densityestimators with gamma, log-normal, Birnbaum-Saunders, inverse Gaussian andreciprocal inverse Gaussian kernels. We propose two new density estimators forpositive random variables that yield properly-normalised density estimates.Plugin expressions for bandwidth estimation are provided to facilitate easyexploratory data analysis.

Bui-Xuan B-M, Jones NS, How modular structure can simplify tasks on networks

By considering the task of finding the shortest walk through a network wefind an algorithm for which the run time is not as O(2^n), with n being thenumber of nodes, but instead scales with the number of nodes in a coarsenednetwork. This coarsened network has a number of nodes related to the number ofdense regions in the original graph. Since we exploit a form of local communitydetection as a preprocessing, this work gives support to the project ofdeveloping heuristic algorithms for detecting dense regions in networks:preprocessing of this kind can accelerate optimization tasks on networks. Ourwork also suggests a class of empirical conjectures for how structural featuresof efficient networked systems might scale with system size.

Onnela J-P, Fenn DJ, Reid S, et al., Taxonomies of Networks

The study of networks has grown into a substantial interdisciplinaryendeavour that encompasses myriad disciplines in the natural, social, andinformation sciences. Here we introduce a framework for constructing taxonomiesof networks based on their structural similarities. These networks can arisefrom any of numerous sources: they can be empirical or synthetic, they canarise from multiple realizations of a single process, empirical or synthetic,or they can represent entirely different systems in different disciplines.Since the mesoscopic properties of networks are hypothesized to be importantfor network function, we base our comparisons on summaries of network communitystructures. While we use a specific method for uncovering network communities,much of the introduced framework is independent of that choice. Afterintroducing the framework, we apply it to construct a taxonomy for 746individual networks and demonstrate that our approach usefully identifiessimilar networks. We also construct taxonomies within individual categories ofnetworks, and in each case we expose non-trivial structure. For example wecreate taxonomies for similarity networks constructed from both politicalvoting data and financial data. We also construct network taxonomies to comparethe social structures of 100 Facebook networks and the growth structuresproduced by different types of fungi.

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