Phase transitions in the fractional three-dimensional Navier-Stokes equations

The fractional Navier-Stokes equations on a periodic domain $[0,\,L]^{3}$ differ from their conventional counterpart by the replacement of the $-\nu\Delta\mathbf{u}$ Laplacian term by $\nu_{s}A^{s}\mathbf{u}$, where $A= - \Delta$ is the Stokes operator and $\nu_{s} = \nu L^{2(s-1)}$ is the viscosity parameter. Four critical values of the exponent $s\geq 0$ have been identified where functional properties of solutions of the fractional Navier-Stokes equations change. These values are\,: $s=\frac{1}{3}$\,; $s=\frac{3}{4}$\,; $s=\frac{5}{6}$ and $s=\frac{5}{4}$. In particular: i) for $s > \frac{1}{3}$ we prove an analogue of one of the Prodi-Serrin regularity criteria; ii) for $s \geq \frac{3}{4}$ we find an equation of local energy balance and; iii) for $s > \frac{5}{6}$ we find an infinite hierarchy of weak solution time averages. The existence of our analogue of the Prodi-Serrin criterion for $s > \frac{1}{3}$ suggests the sharpness of the construction using convex integration of Hölder continuous solutions with epochs of regularity in the range $0 < s < \frac{1}{3}$

Risk Prediction Models for Oral Cancer: A Systematic Review

Peer reviewed: TrueAcknowledgements: We would like to thank Isla Kuhn for her help in developing the search strategy.Publication status: PublishedIn the last 30 years, there has been an increasing incidence of oral cancer worldwide. Earlier detection of oral cancer has been shown to improve survival rates. However, given the relatively low prevalence of this disease, population-wide screening is likely to be inefficient. Risk prediction models could be used to target screening to those at highest risk or to select individuals for preventative interventions. This review (a) systematically identified published models that predict the development of oral cancer and are suitable for use in the general population and (b) described and compared the identified models, focusing on their development, including risk factors, performance and applicability to risk-stratified screening. A search was carried out in November 2022 in the Medline, Embase and Cochrane Library databases to identify primary research papers that report the development or validation of models predicting the risk of developing oral cancer (cancers of the oral cavity or oropharynx). The PROBAST tool was used to evaluate the risk of bias in the identified studies and the applicability of the models they describe. The search identified 11,222 articles, of which 14 studies (describing 23 models), satisfied the eligibility criteria of this review. The most commonly included risk factors were age (n = 20), alcohol consumption (n = 18) and smoking (n = 17). Six of the included models incorporated genetic information and three used biomarkers as predictors. Including information on human papillomavirus status was shown to improve model performance; however, this was only included in a small number of models. Most of the identified models (n = 13) showed good or excellent discrimination (AUROC &gt; 0.7). Only fourteen models had been validated and only two of these validations were carried out in populations distinct from the model development population (external validation). Conclusions: Several risk prediction models have been identified that could be used to identify individuals at the highest risk of oral cancer within the context of screening programmes. However, external validation of these models in the target population is required, and, subsequently, an assessment of the feasibility of implementation with a risk-stratified screening programme for oral cancer.</jats:p

Visualization of Cerebral Pressure Autoregulatory Insults in Traumatic Brain Injury.

OBJECTIVES: The first aim was to investigate the combined effect of insult intensity and duration of the pressure reactivity index (PRx) and deviation from the autoregulatory cerebral perfusion pressure target (∆CPPopt = actual CPP - optimal CPP [CPPopt]) on outcome in traumatic brain injury. The second aim was to determine if PRx influenced the association between intracranial pressure (ICP), CPP, and ∆CPPopt with outcome. DESIGN: Observational cohort study. SETTING: Neurocritical care unit, Cambridge, United Kingdom. PATIENTS: Five hundred fifty-three traumatic brain injury patients with ICP and arterial blood pressure monitoring and 6-month outcome data (Glasgow Outcome Scale [GOS]). INTERVENTION: None. MEASUREMENTS AND MAIN RESULTS: The insult intensity (mm Hg or PRx coefficient) and duration (minutes) of ICP, PRx, CPP, and ∆CPPopt were correlated with GOS and visualized in heatmaps. In these plots, there was a transition from favorable to unfavorable outcome when PRx remained positive for 30 minutes and this was also the case for shorter durations when the intensity was higher. In a similar plot of ∆CPPopt, there was a gradual transition from favorable to unfavorable outcome when ∆CPPopt went below -5 mm Hg for 30-minute episodes of time and for shorter durations for more negative ∆CPPopt. Furthermore, the percentage of monitoring time with certain combinations of PRx with ICP, CPP, and ∆CPPopt were correlated with GOS and visualized in heatmaps. In the combined PRx/ICP heatmap, ICP above 20 mm Hg together with PRx above 0 correlated with unfavorable outcome. In a PRx/CPP heatmap, CPP below 70 mm Hg together with PRx above 0.2-0.4 correlated with unfavorable outcome. In the PRx-/∆CPPopt heatmap, ∆CPPopt below 0 together with PRx above 0.2-0.4 correlated with unfavorable outcome. CONCLUSIONS: Higher intensities for longer durations of positive PRx and negative ∆CPPopt correlated with worse outcome. Elevated ICP, low CPP, and negative ∆CPPopt were particularly associated with worse outcomes when the cerebral pressure autoregulation was concurrently impaired

Evaluating the cost-effectiveness of polygenic risk score-stratified screening for abdominal aortic aneurysm

AbstractAs the heritability of abdominal aortic aneurysm (AAA) is high and AAA partially shares genetic architecture with other cardiovascular diseases, genetic information could help inform AAA screening strategies. Exploiting pleiotropy and meta-analysing summary data from large studies, we construct a polygenic risk score (PRS) for AAA. Leveraging related traits improves PRS performance (R2) by 22.7%, relative to using AAA alone. Compared with the low PRS tertile, intermediate and high tertiles have hazard ratios for AAA of 2.13 (95%CI 1.61, 2.82) and 3.70 (95%CI 2.86, 4.80) respectively, adjusted for clinical risk factors. Using simulation modelling, we compare PRS- and smoking-stratified screening with inviting men at age 65 and not inviting women (current UK strategy). In a futuristic scenario where genomic information is available, our modelling suggests inviting male current smokers with high PRS earlier than 65 and screening female smokers with high/intermediate PRS at 65 and 70 respectively, may improve cost-effectiveness.</jats:p

Current Legal Fictions in Public Law

Abstract The use of legal fiction in public law has shown no sign of abating, as demonstrated in the enactment of the Safety of Rwanda (Asylum and Immigration) Act 2024. Accompanying questions or concerns are about the degree to which they are problematic, useful, or detrimental, what is to be done about them, and whether their prevalence is specific to British or English legal culture. This article examines what has been done, or what has happened, to deal or to cope with them, in orthodox constitutional legal doctrine and administrative law liability. After adopting a working definition of legal fiction and showing Dicey’s own preoccupation with the constitution’s legal forms and fiction, it does so through two case studies. Both involve basic orthodox constitutional legal doctrines—parliamentary sovereignty and the rule of law—with which Dicey has long been associated. The one case study is of Parliament’s sovereignty, limitless in law, and limited in actuality. The other case study is of legal fiction in relation to developments in public authority liability under equality before the law, particularly for omissions, or non-conferrals of benefit. Through these studies, this article will argue that the fortunes of legal fiction in the British or English legal context have been not simply of all-or-nothing rejection or retention. They have been, because of the unease accompanying the use of legal fiction, also of their domestication, in analytical distinctions, and refinement of judicial language in common law reasoning. The extraordinary legal forms have been made more ordinary or so to appear, showing them as domesticated to have been and to remain of current, ongoing and present, relevance.License CC BY-NC-ND agreed 18/09/202

Roadmapping Roadmapping: Strategic planning for roadmapping systems

Acknowledgements: The authors are grateful to collaborating organizations for enabling the development and testing of the approach described in this paper, academic colleagues (Clare Farrukh, Dr Michèle Routley, Dr Clive Kerr, Dr Imoh Ilevbare, Dr Nicky Athanassopoulou), and the University of Cambridge STIM industry-academic consortium program for feedback and providing access for template testing.AbstractRoadmapping is a well-established technique in the context of innovation and strategy, with the potential to support organizations address the complex transformative challenges facing humanity in the 21st century. This is enabled by its systems-based architecture and visual form of roadmaps, supporting communication and reduction of information asymmetries in complex sociotechnical systems. This paper focuses on an adaptation of the roadmapping method to support strategic planning for roadmapping systems in organizations, addressing implementation challenges. This represents a novel application of roadmapping to business processes and systems, demonstrating the flexibility of the roadmapping approach. A workshop template (‘R2’) and process for supporting the roadmapping of roadmapping systems is presented, developed and refined through a series of six industrial cases, and illustrated with an application example in the additive manufacturing sector.</jats:p

GoFish: a foray into open‐source, aquatic behavioral automation

Publication status: PublishedAs the most species‐rich vertebrate group, fish provide an array of opportunities to investigate the link between ecological interactions and the evolution of behavior and cognition, yet, as an animal model, they are relatively underutilized in studies of comparative cognition. To address this gap, we developed a fully automated platform for behavioral experiments in aquatic species, GoFish. GoFish includes closed‐loop control of task contingencies using real‐time video tracking, presentation of visual stimuli, automatic food reward dispensers, and built‐in data acquisition. The hardware is relatively inexpensive and accessible, and all software components of the platform are open‐source. GoFish facilitates experimental automation, allowing for customization of high‐throughput protocols and the efficient acquisition of rich behavioral data. We hope this platform proves to be a useful tool for the research community, facilitating refined, reproducible behavioral experiments on aquatic species in comparative cognition, behavioral ecology, and neuroscience

Transverse polarization measurement of Λ hyperons in pNe collisions at sNN \sqrt{{\textrm{s}}_{\textrm{NN}}} = 68.4 GeV with the LHCb detector

Abstract A measurement of the transverse polarization of the Λ and $$\overline{\varLambda}$$ Λ ¯ hyperons in pNe fixed-target collisions at $$\sqrt{{\textrm{s}}_{\textrm{NN}}}$$ s NN = 68.4 GeV is presented using data collected by the LHCb detector. The polarization is studied using the decay Λ → pπ− together with its charge conjugated process, the integrated values measured are$${\displaystyle \begin{array}{c}{P}_{\varLambda }=0.029\pm 0.019\left(\textrm{stat}\right)\pm 0.012\left(\textrm{syst}\right),\\ {}{P}_{\overline{\varLambda}}=0.003\pm 0.023\left(\textrm{stat}\right)\pm 0.014\left(\textrm{syst}\right).\end{array}}$$ P Λ = 0.029 ± 0.019 stat ± 0.012 syst , P Λ ¯ = 0.003 ± 0.023 stat ± 0.014 syst . Furthermore, the results are shown as a function of the Feynman x variable, transverse momentum, pseudorapidity and rapidity of the hyperons, and are compared with previous measurements.</jats:p

Recognition as Resilience: How an Unrecognized Indigenous Nation is Using Visibility as a Pathway Towards Restorative Justice

Resilience has been conceptualized within international development as the ability to “return to a state of equilibrium” after exogenous shocks. For many Indigenous communities, however, there is no equilibrium to which to return. This article explores how the federally unrecognized Nevada City Rancheria Nisenan Tribe (NCRNT) has developed a creative strategy of resilience beyond a return to “equilibrium” in the face of their almost complete erasure by genocide and the illegal termination of their sovereign rights by US state and federal government agencies. The NCRNT’s experience reveals how activities underlying Indigenous resilience include a need for historical redress and reconciliation, thereby creating a “new normal” that is reflective of Native history as well as the ongoing social, political, and economic realities of existing within a settler state. This article bridges history and development studies, revealing how both disciplines must learn from Indigenous groups seeking restorative justice. It further employs oral histories, artwork, and documentation from the newly created NCRN Tribal archive, and so is presented as an interactive digital article using hyperlinked archival materials

Enhancing mathematical problem posing competence: a meta-analysis of intervention studies

Acknowledgements: The authors are grateful to the Editor and five anonymous reviewers for their helpful comments and feedback on earlier versions of this paper. The authors would also like to thank Shengya Wang and Murou Li for their assistance with the literature search and data coding as research assistants on this project.Mathematical problem posing, generally defined as the process of interpreting given situations and formulating meaningful mathematical problems, is academically important, and thus several interventions have been used to enhance this competence among students and teachers. Yet little is known about the interventions’ various components and their relative or combined effectiveness. In this meta-analysis of 26 intervention studies in mathematics, we identified nine intervention components and found that the interventions had a medium, positive, and significant mean weighted effect size. A stepwise meta-regression analysis revealed that intervention efficacy varied by moderators relevant to the research design, sample characteristics, and intervention characteristics. The findings obtained from this meta-analysis are expected to serve as a foundation for future efforts to design and implement (more) effective interventions to improve mathematical problem posing competence.The study was supported by a Chongqing Postdoctoral Fellowship (No. 2020379) to the first author, hosted at the University of Cambridge under the co-mentorship of the other authors