A stochastic model for the evolution of the web allowing link deletion

Recently several authors have proposed stochastic evolutionary models for the growth of the web graph and other networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer'' phenomenon. We present a generalisation of the basic model by allowing deletion of individual links and show that it also gives rise to a power-law distribution. We derive the mean-field equations for this stochastic model and show that by examining a snapshot of the distribution at the steady state of the model, we are able to tell whether any link deletion has taken place and estimate the link deletion probability. Our model enables us to gain some insight into the distribution of inlinks in the web graph, in particular it suggests a power-law exponent of approximately 2.15 rather than the widely published exponent of 2.1

A complex flow phantom for medical imaging : ring vortex phantom design and technical specification

Cardiovascular fluid dynamics exhibit complex flow patterns, such as recirculation and vortices. Quantitative analysis of these complexities supports diagnosis, leading to early prediction of pathologies. Quality assurance of technologies that image such flows is challenging but essential, and to this end, a novel, cost-effective, portable, complex flow phantom is proposed and the design specifications are provided. The vortex ring is the flow of choice because it offers patterns comparable to physiological flows and is stable, predictable, reproducible and controllable. This design employs a piston/cylinder system for vortex ring generation, coupled to an imaging tank full of fluid, for vortex propagation. The phantom is motor-driven and by varying piston speed, piston displacement and orifice size, vortex rings with different characteristics can be produced. Two measurement methods, namely Laser-PIV and an optical/video technique, were used to test the phantom under a combination of configurations. Vortex rings with a range of travelling velocities (approximately 1–80 cm/s) and different output-orifice diameters (10–25 mm) were produced with reproducibility typically better than ±10%. Although ultrasound compatibility has been demonstrated, longer-term ambitions include adapting the design to support comparative studies with different modalities, such as MRA and X-ray-CTA

A relational quantum computer using only two-qubit total spin measurement and an initial supply of highly mixed single qubit states

We prove that universal quantum computation is possible using only (i) the physically natural measurement on two qubits which distinguishes the singlet from the triplet subspace, and (ii) qubits prepared in almost any three different (potentially highly mixed) states. In some sense this measurement is a `more universal' dynamical element than a universal 2-qubit unitary gate, since the latter must be supplemented by measurement. Because of the rotational invariance of the measurement used, our scheme is robust to collective decoherence in a manner very different to previous proposals - in effect it is only ever sensitive to the relational properties of the qubits.Comment: TR apologises for yet again finding a coauthor with a ridiculous middle name [12

The Chemical Evolution of Helium in Globular Clusters: Implications for the Self-Pollution Scenario

We investigate the suggestion that there are stellar populations in some globular clusters with enhanced helium (Y from 0.28 to 0.40) compared to the primordial value. We assume that a previous generation of massive Asymptotic Giant Branch (AGB) stars have polluted the cluster. Two independent sets of AGB yields are used to follow the evolution of helium and CNO using a Salpeter initial mass function (IMF) and two top-heavy IMFs. In no case are we able to produce the postulated large Y ~ 0.35 without violating the observational constraint that the CNO content is nearly constant.Comment: accepted for publication in Ap

A stochastic evolutionary model generating a mixture of exponential distributions

Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic urn-based model proposed in \cite{FENN15} so that it can generate mixture models, in particular, a mixture of exponential distributions. The model is designed to capture the dynamics of survival analysis, traditionally employed in clinical trials, reliability analysis in engineering, and more recently in the analysis of large data sets recording human dynamics. The mixture modelling approach, which is relatively simple and well understood, is very effective in capturing heterogeneity in data. We provide empirical evidence for the validity of the model, using a data set of popular search engine queries collected over a period of 114 months. We show that the survival function of these queries is closely matched by the exponential mixture solution for our model

A quantum search for zeros of polynomials

A quantum mechanical search procedure to determine the real zeros of a polynomial is introduced. It is based on the construction of a spin observable whose eigenvalues coincide with the zeros of the polynomial. Subsequent quantum mechanical measurements of the observable output directly the numerical values of the zeros. Performing the measurements is the only computational resource involved

Abundance Anomalies in NGC6752 - Do AGB Stars Have a Role?

We are in the process of testing a popular theory that the observed abundance anomalies in the Globular Cluster NGC 6752 are due to `internal pollution' from intermediate mass asymptotic giant branch stars. To this end we are using a chemical evolution model incorporating custom-made stellar evolution yields calculated using a detailed stellar evolution code. By tracing the chemical evolution of the intracluster gas, which is polluted by two generations of stars, we are able to test the internal pollution scenario in which the Na- and Al-enhanced ejecta from intermediate mass stars is either accreted onto the surfaces of other stars, or goes toward forming new stars. In this paper we focus mainly on the nucleosynthetic yields of the AGB stars and discuss whether these stars are the source of the observed Na-O anticorrelation. Comparing our preliminary results with observational data suggests that the qualitative theory is not supported by this quantitative study.Comment: To be published in: Nuclear Physics, Section A. 4 pages, 2 figures. Conference: "The Eighth International Symposium on Nuclei in the Cosmos", Canada, July 200