Experimental determination of Ramsey numbers

Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has been proposed that calculates the two-color Ramsey numbers $R(m,n)$. Here we present results of an experimental implementation of this algorithm and show that it correctly determines the Ramsey numbers R(3,3) and $R(m,2)$ for $4\leq m\leq 8$. The R(8,2) computation used 84 qubits of which 28 were computational qubits. This computation is the largest experimental implementation of a scientifically meaningful adiabatic evolution algorithm that has been done to date.Comment: manuscript: 5 pages; 1 table, 3 figures; Supplementary Information: 18 pages, 1 table, 13 figures; version to appear in Physical Review Letter

Methodological issues in the design and evaluation of supported communication for aphasia training: a cluster-controlled feasibility study

Objective: To assess the feasibility and acceptability of training stroke service staff to provide supported communication for people with moderate-severe aphasia in the acute phase; assess the suitability of outcome measures; collect data to inform sample size and Health Economic evaluation in a definitive trial. Design: Phase II cluster-controlled, observer-blinded feasibility study Settings: In-patient stroke rehabilitation units in the UK matched for bed numbers and staffing were assigned to control and intervention conditions. Participants: Seventy stroke rehabilitation staff from all professional groups, excluding doctors, were recruited. Twenty patients with moderate-severe aphasia were recruited. Intervention: Supported communication for aphasia training, adapted to the stroke unit context vs usual care. Training was supplemented by a staff learning log, refresher sessions and provision of communication resources. Main outcome measures: Feasibility of recruitment and acceptability of the intervention and of measures required to assess outcomes and Health Economic evaluation in a definitive trial. Staff outcomes: Measure of Support in Conversation; patient outcomes: Stroke and Aphasia Quality of Life Scale; Communicative Access Measure for Stroke; Therapy Outcome Measures for aphasia; EQ-5D-3L was used to assess health outcomes. Results: Feasibility of staff recruitment was demonstrated. Training in the intervention was carried out with 28 staff and was found to be acceptable in qualitative reports. Twenty patients consented to take part, 6 withdrew. Eighteen underwent all measures at baseline; 16 at discharge; and 14 at 6-month follow-up. Of 175 patients screened 71% were deemed to be ineligible, either lacking capacity or too unwell to participate. Poor completion rates impacted on assessment of patient outcomes. We were able to collect sufficient data at baseline, discharge and follow-up for economic evaluation. Conclusions: The feasibility study informed components of the intervention and implementation in day-to-day practice. Modifications to the design are needed before a definitive cluster-randomised trial can be undertaken

Ramsey numbers and adiabatic quantum computing

The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers $R(m,n)$ with $m,n\geq 3$, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers $R(m,n)$. We show how the computation of $R(m,n)$ can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for $5\leq s\leq 7$. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class QMA.Comment: 4 pages, 1 table, no figures, published versio

ENUMERATING LABELLED GRAPHS WITH CERTAIN NEIGHBORHOOD PROPERTIES

Properties of (connected) graphs whose closed or open neighborhood families are Sperner, anti-Sperner, distinct or none of the proceeding have been extensively examined. In this paper we examine 24 properties of the neighborhood family of a graph. We give asymptotic formulas for the number of (connected) labelled graphs for 12 of these properties. For the other 12 properties, we give bounds for the number of such graphs. We also determine the status (a.a.s. or a.a.n.) in Gn,1/2 of all 24 of these properties. Our methods are both constructive and probabilistic

Collective T=0 pairing in N=Z nuclei? Pairing vibrations around 56Ni revisited

We present a new analysis of the pairing vibrations around 56Ni, with emphasis on odd-odd nuclei. This analysis of the experimental excitation energies is based on the subtraction of average properties that include the full symmetry energy together with volume, surface and Coulomb terms. The results clearly indicate a collective behavior of the isovector pairing vibrations and do not support any appreciable collectivity in the isoscalar channel.Comment: RevTeX, two-column, 5 pages, 4 figure