Practical designs for permutation-symmetric problem Hamiltonians on hypercubes

We present a method to experimentally realize large-scale permutation-symmetric Hamiltonians for continuous-time quantum protocols such as quantum walks and adiabatic quantum computation. In particular, the method can be used to perform an encoded continuous-time quantum search on a hypercube graph with 2n vertices encoded into 2n qubits. We provide details for a realistically achievable implementation in Rydberg atomic systems. Although the method is perturbative, the realization is always achieved at second order in perturbation theory, regardless of the size of the mapped system. This highly efficient mapping provides a natural set of problems which are tractable both numerically and analytically, thereby providing a powerful tool for benchmarking quantum hardware and experimentally investigating the physics of continuous-time quantum protocols

Aperiodic dynamics in a deterministic adaptive network model of attitude formation in social groups

Adaptive network models, in which node states and network topology coevolve, arise naturally in models of social dynamics that incorporate homophily and social influence. Homophily relates the similarity between pairs of nodes’ states to their network coupling strength, whilst social influence causes coupled nodes’ states to convergence. In this paper we propose a deterministic adaptive network model of attitude formation in social groups that includes these effects, and in which the attitudinal dynamics are represented by an activator–inhibitor process. We illustrate that consensus, corresponding to all nodes adopting the same attitudinal state and being fully connected, may destabilise via Turing instability, giving rise to aperiodic dynamics with sensitive dependence on initial conditions. These aperiodic dynamics correspond to the formation and dissolution of sub-groups that adopt contrasting attitudes. We discuss our findings in the context of cultural polarisation phenomena

Genome-wide survey of SNP variation uncovers the genetic structure of cattle breeds

status: publishe

Rehabilitation versus surgical reconstruction for non-acute anterior cruciate ligament injury (ACL SNNAP): a pragmatic randomised controlled trial

BackgroundAnterior cruciate ligament (ACL) rupture is a common debilitating injury that can cause instability of the knee. We aimed to investigate the best management strategy between reconstructive surgery and non-surgical treatment for patients with a non-acute ACL injury and persistent symptoms of instability.MethodsWe did a pragmatic, multicentre, superiority, randomised controlled trial in 29 secondary care National Health Service orthopaedic units in the UK. Patients with symptomatic knee problems (instability) consistent with an ACL injury were eligible. We excluded patients with meniscal pathology with characteristics that indicate immediate surgery. Patients were randomly assigned (1:1) by computer to either surgery (reconstruction) or rehabilitation (physiotherapy but with subsequent reconstruction permitted if instability persisted after treatment), stratified by site and baseline Knee Injury and Osteoarthritis Outcome Score—4 domain version (KOOS4). This management design represented normal practice. The primary outcome was KOOS4 at 18 months after randomisation. The principal analyses were intention-to-treat based, with KOOS4 results analysed using linear regression. This trial is registered with ISRCTN, ISRCTN10110685, and ClinicalTrials.gov, NCT02980367.FindingsBetween Feb 1, 2017, and April 12, 2020, we recruited 316 patients. 156 (49%) participants were randomly assigned to the surgical reconstruction group and 160 (51%) to the rehabilitation group. Mean KOOS4 at 18 months was 73·0 (SD 18·3) in the surgical group and 64·6 (21·6) in the rehabilitation group. The adjusted mean difference was 7·9 (95% CI 2·5–13·2; p=0·0053) in favour of surgical management. 65 (41%) of 160 patients allocated to rehabilitation underwent subsequent surgery according to protocol within 18 months. 43 (28%) of 156 patients allocated to surgery did not receive their allocated treatment. We found no differences between groups in the proportion of intervention-related complications.InterpretationSurgical reconstruction as a management strategy for patients with non-acute ACL injury with persistent symptoms of instability was clinically superior and more cost-effective in comparison with rehabilitation management

Correlations between physical and chemical defences in plants: tradeoffs, syndromes, or just many different ways to skin a herbivorous cat?

� Most plant species have a range of traits that deter herbivores. However, understanding of how different defences are related to one another is surprisingly weak. Many authors argue that defence traits trade off against one another, while others argue that they form coordinated defence syndromes. � We collected a dataset of unprecedented taxonomic and geographic scope (261 species spanning 80 families, from 75 sites across the globe) to investigate relationships among four chemical and six physical defences. � Five of the 45 pairwise correlations between defence traits were significant and three of these were tradeoffs. The relationship between species’ overall chemical and physical defence levels was marginally nonsignificant (P = 0.08), and remained nonsignificant after accounting for phylogeny, growth form and abundance. Neither categorical principal component analysis (PCA) nor hierarchical cluster analysis supported the idea that species displayed defence syndromes. � Our results do not support arguments for tradeoffs or for coordinated defence syndromes. Rather, plants display a range of combinations of defence traits. We suggest this lack of consistent defence syndromes may be adaptive, resulting from selective pressure to deploy a different combination of defences to coexisting species