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FEFERMAN’S COMPLETENESS THEOREM
No full textFeferman proved in 1962 [Fef62] that any arithmetical theorem is a consequence of a suitable transfinite iteration of full uniform reflection of PA. This result is commonly known as Feferman’s completeness theorem. The purpose of this paper is twofold. On the one hand this is an expository paper, giving two new proofs of Feferman’s completeness theorem that, we hope, shed light on this mysterious and often overlooked result. On the other hand, we combine one of our proofs with results from computable structure theory due to Ash and Knight to give sharp bounds on the order types of well-orders necessary to attain the completeness for levels of the arithmetical hierarchy
Understanding medical students’ intercalation decisions to preserve the clinical academic pipeline: a mixed-method survey
Get PDFIntroduction
Clinical academics are pivotal in advancing innovations by integrating clinical practice with education and research. The clinical academic workforce in the UK has struggled with a persistent shortage, now reaching a critical point. A recent nationwide decline in medical students opting for intercalated degrees, which provide early research exposure during undergraduate medical education, significantly contributed to the workforce crisis. However, the underlying factors for this recent decline in intercalation remain unclear. This study investigates the factors influencing medical students’ decisions to intercalate, focusing on personal motivations, and perceived value in the context of rising living costs and changing national policies.
Methods
We utilised a mixed-methods survey to explore the factors influencing medical students’ decisions regarding intercalation. Quantitative data from closed-ended questions were analysed using descriptive statistics and chi-square tests to identify associations between variables. Thematic analysis of qualitative data from open-ended questions was conducted using Vroom’s expectancy theory as an interpretive lens.
Results
A total of 50 students completed the questionnaire. The chi-square test demonstrated a significant association (p = 0.001) between the cost-of-living crisis and the decision to intercalate. The thematic analysis of non-intercalators highlighted the theme of financial burden, including reduced student loans, increased debt, and family financial stress. Conversely, we developed the theme of effective financial strategies and support systems from intercalators. The perception of career benefits significantly influenced intercalation decisions (p < 0.001). Furthermore, a change in policy to remove extra consideration for intercalated degree holders in UK foundation applications significantly affected decisions (p = 0.014). Thematic analysis of non-intercalators identified the lack of perceived career advantage, including a loss of extrinsic motivation and perceived non-recognition. Intercalators cited long-term career benefits, research skills and confidence, portfolio building and networking as their primary motivators.
Conclusions
Our study provided new insights into the socioeconomic, policy-related, and motivational differences among students that influence intercalation decisions. Financial constraints and the removal of extra consideration for intercalated degrees in physician training selection were major deterrents, particularly for students from diverse backgrounds. Future research should focus on developing targeted interventions to mitigate challenges and support a diverse and equitable clinical academic workforce
Relative testis size is associated with vagina length but not sperm storage traits in Galliformes
Get PDFPost-copulatory sexual selection, comprised of sperm competition and cryptic female choice, is a powerful evolutionary force that can drive the rapid diversification of reproductive traits across taxa. In birds, the female reproductive tract provides the arena for post-copulatory sexual selection, yet we lack a comprehensive understanding of the female specific processes that shape the evolution of sexually selected traits. Here, we use a comparative approach to explore the relationships between female reproductive tract morphology, sperm competition intensity, and sperm traits across Galliformes. Accounting for phylogenetic and allometric relationships, we find that species with relatively larger testes for their body size—a proxy for intense sperm competition—have relatively longer vaginas, suggesting that important co-evolutionary dynamics exist between male and female reproductive physiology. Surprisingly, we find no link between sperm length and sperm storage tubule morphology, challenging existing predictions. Our findings suggest that the vagina has a significant but currently overlooked influence on post-copulatory processes and emphasizes the need to better integrate female morphology into models of sexual selection
Computational screening of amino-functionalized molecules for direct air capture of CO2
Get PDFDirect air capture (DAC) of CO2 is a promising strategy for mitigating global carbon emissions by removing CO2 from the atmosphere. A critical factor in enhancing the efficiency of DAC is the design of functionalized materials with strong CO2 binding capabilities. This study screens a variety of amino-functionalized molecules, utilizing MP2 and density functional theory calculations, to identify promising candidates for CO2 capture under dry and humid conditions. The analysis determined the most stable configurations of CO2 and water with 15 amino-functionalized molecules. Amino acids such as arginine, 7-azaindole, 1,5,7-triazabicyclo-[4.4.0]dec-5-ene, and melamine demonstrated the strongest CO2 binding energies, ranging from -17 to -19 kJ/mol. This is the result of both Lewis acid-base interactions between the electron-deficient carbon of CO2 and a N atom and hydrogen bonding. Generally, all of the amino groups exhibited a stronger binding affinity with water, attributed to the formation of stable hydrogen bonds between an electron-rich N atom and the hydrogen atoms of water. To guide the design of porous host structures incorporating these molecules as functional groups, the study was extended to hypothetical systems where multiple functional groups can essentially "sandwich" CO2, promoting simultaneous binding. In these scenarios, the repulsion between functional molecules emerged as a critical factor increasing the overall CO2 binding energy to ca. -30 to -40 kJ/mol. This analysis enabled the identification of optimal pore sizes for the design of functionalized frameworks to maximize the CO2 capture efficiency
Inverted shear-strain magnetoelastic coupling at the Fe/BaTiO3 interface from polarised x-ray imaging
Get PDFThe elastic degree of freedom is widely exploited to mediate magnetoelectric coupling between ferromagnetic films and ferroelectric substrates. For epitaxial Fe films grown on clean BaTiO3 substrates, shear strain can determine the underlying magnetoelastic coupling. Here, we use PhotoEmission Electron Microscopy of ferroic Fe and BaTiO3 domains, combined with micromagnetic simulations, to directly reveal an inverted interfacial magnetoelastic coupling in the low-dimensional limit. We show that the magnetocrystalline anisotropy competes with the epitaxial shear strain to align the local magnetization of ultrathin Fe films close to the local polarization direction of the ferroelectric BaTiO3 in-plane domains. Poling the BaTiO3 substrate creates c-domains with no shear strain contribution with the local magnetization rotated by ~45°. Tuning shear strain magnetoelastic contributions suggests new routes for designing magnetoelectric devices
The (co)benefits portal—an evidence-based and climate policy-relevant tool for decision-making
Get PDFFrom improving health outcomes and health inequalities to ensuring energy and income security, the mitigation of and adaptation to climate change has extensive and diverse benefits. This paper describes a systematic evidence synthesis of climate action (co)benefits and trade-offs as well as the development of a decision-support tool that enables policy makers to explore that evidence-base. The term ‘(co)benefit’ is used deliberately to encompass both the direct benefits of averted impacts due to climate change as well as the indirect or ancillary benefits resulting from mitigation and adaptation interventions. We conducted a systematic search of the peer-reviewed literature in the IPCC 6th Assessment Report, Web of Science, and the Lancet Countdown on Health and Climate Change Reports. Our search strategy prioritised synthesised evidence (e.g. reviews, assessments) excluding primary studies and single case-studies. Data were extracted from 74 distinct records meeting our inclusion criteria and a total of 1785 rows of evidence were analysed. Scientific and technical teams then worked together to develop a tool interface that underwent iterative testing among a small group of potential users. The resulting (Co)Benefits Portal presents an assessment of the available scientific evidence of health, ecosystem, economic, energy, and socio-cultural (co)benefits and trade-offs associated with 40 different mitigation and adaptation actions for both global and regional scales. We then apply the (Co)Benefits Portal into a UK context, in combination with national policy documents and departmental guidance, to connect evidence about relevant climate interventions and reveal cross-sectoral policy implications that are essential for optimising opportunities and avoiding risks. We discuss how evidence-based tools can be developed to bridge critical climate adaptation and mitigation research, policy, and decision-making gaps
First ß-Delayed Two-Neutron Spectroscopy of the r-Process Nucleus 134In and Observation of the i13/2 Single-Particle Neutron State in 133Sn
Get PDFDisentangleFormer: Spatial-Channel Decoupling for Multi-Channel Vision
No full textVision Transformers face a fundamental limitation: standard self-attention jointly processes spatial and channel dimensions, leading to entangled representations that prevent independent modeling of structural and semantic dependencies. This problem is especially pronounced in hyperspectral imaging, from satellite hyperspectral remote sensing to infrared pathology imaging, where channels capture distinct biophysical or biochemical cues. We propose DisentangleFormer, an architecture that achieves robust multi-channel vision representation through principled spatial-channel decoupling. Motivated by information-theoretic principles of decorrelated representation learning, our parallel design enables independent modeling of structural and semantic cues while minimizing redundancy between spatial and channel streams. Our design integrates three core components: (1) Parallel Disentanglement: Independently processes spatial-token and channel-token streams, enabling decorrelated feature learning across spatial and spectral dimensions, (2) Squeezed Token Enhancer: An adaptive calibration module that dynamically fuses spatial and channel streams, and (3) Multi-Scale FFN: complementing global attention with multi-scale local context to capture fine-grained structural and semantic dependencies. Extensive experiments on hyperspectral benchmarks demonstrate that DisentangleFormer achieves state-of-the-art performance, consistently outperforming existing models on Indian Pine, Pavia University, and Houston, the large-scale BigEarthNet remote sensing dataset, as well as an infrared pathology dataset. Moreover, it retains competitive accuracy on ImageNet while reducing computational cost by 17.8% in FLOPs. The code will be made publicly available upon acceptance
To Signal or Not to Signal? A Non-cooperative Game-Theoretic Approach to Discretionary Communication Between Road Users
Get PDFReciprocal communication between road users is a vital element of road user interaction. Non-cooperative game theory is an effective framework for modelling and characterising communicative behaviour between road users, which enables the study of emergent benefits for both the issuer and recipient of communicative signals. In this paper, we introduce discretionary communication to gain an advantage over the other road user by masking one’s intent if beneficial to do so. We conduct a series of experiments with simulated interactions and compare interaction outcomes where communication is mandatory against those where communication is discretionary. Our findings further support the premise that non-cooperative game theory is an effective paradigm for modelling and producing emergent behaviours which benefit the network. Moreover, we see that including a layer of discretionary communication reaps benefits in interaction outcome to the communicator. It also provides benefits in safety to all parties involved above and beyond the benefits seen from mandatory communication
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