Remarks on the boundary set of spectral equipartitions

Given a bounded open set $\Omega$ in $\mathbb{R}^n$ (or a compact Riemannian manifold with boundary), and a partition of $\Omega$ by $k$ open sets $\omega_j$, we consider the quantity $\max_j \lambda(\omega_j)$, where $\lambda(\omega_j)$ is the ground state energy of the Dirichlet realization of the Laplacian in $\omega_j$. We denote by $\mathfrak{L}_k(\Omega)$ the infimum of $\max_j \lambda(\omega_j)$ over all $k$-partitions. A minimal $k$-partition is a partition which realizes the infimum. The purpose of this paper is to revisit properties of nodal sets and to explore if they are also true for minimal partitions, or more generally for spectral equipartitions. We focus on the length of the boundary set of the partition in the 2-dimensional situation.Comment: Final version to appear in the Philosophical Transactions of the Royal Society

Some Applications of Detailed Wind Profile Data to Launch Vehicle Response Problems

The response of a launch vehicle to a number of detailed wind profiles has been determined. The wind profiles were measured by two techniques which are briefly described. One of these techniques uses an angle-of-attack sensor in conjunction with guidance data to measure the wind profile traversed by some particular launch vehicle. The other wind-measuring technique is a photographic triangulation method, whereby two cameras take simultaneous pictures of a vertical trail of smoke left by a launch vehicle or sounding rocket. The response of a vehicle flying these detailed profiles is compared with the response of the same vehicle flying through balloon-measured profiles. The response to the detailed wind profiles, relative t o the balloon-measured profiles, is characterized by the large excitation of the rigid pitch and elastic bending modes. This is found to cause higher loads on the launch vehicle structure. Established design criteria which utilize balloon measured wind profiles have arbitrarily accounted-for this increased load by adding a load due to some type of discrete gust

Perspectives on financial incentives to health service providers for increasing breast feeding and smoking quit rates during pregnancy: a mixed methods study

Objective: To explore the acceptability, mechanisms and consequences of provider incentives for smoking cessation and breast feeding as part of the Benefits of Incentives for Breastfeeding and Smoking cessation in pregnancy (BIBS) study. Design: Cross-sectional survey and qualitative interviews. Setting: Scotland and North West England. Participants: Early years professionals: 497 survey respondents included 156 doctors; 197 health visitors/maternity staff; 144 other health staff. Qualitative interviews or focus groups were conducted with 68 pregnant/postnatal women/family members; 32 service providers; 22 experts/decision-makers; 63 conference attendees. Methods: Early years professionals were surveyed via email about the acceptability of payments to local health services for reaching smoking cessation in pregnancy and breastfeeding targets. Agreement was measured on a 5-point scale using multivariable ordered logit models. A framework approach was used to analyse free-text survey responses and qualitative data. Results: Health professional net agreement for provider incentives for smoking cessation targets was 52.9% (263/497); net disagreement was 28.6% (142/497). Health visitors/maternity staff were more likely than doctors to agree: OR 2.35 (95% CI 1.51 to 3.64; p<0.001). Net agreement for provider incentives for breastfeeding targets was 44.1% (219/497) and net disagreement was 38.6% (192/497). Agreement was more likely for women (compared with men): OR 1.81 (1.09 to 3.00; p=0.023) and health visitors/maternity staff (compared with doctors): OR 2.54 (95% CI 1.65 to 3.91; p<0.001). Key emergent themes were 'moral tensions around acceptability', 'need for incentives', 'goals', 'collective or divisive action' and 'monitoring and proof'. While provider incentives can focus action and resources, tensions around the impact on relationships raised concerns. Pressure, burden of proof, gaming, box-ticking bureaucracies and health inequalities were counterbalances to potential benefits. Conclusions: Provider incentives are favoured by non-medical staff. Solutions which increase trust and collaboration towards shared goals, without negatively impacting on relationships or increasing bureaucracy are required

Transient Heat Analysis of a Carbon Composite Scramjet Combustion Chamber

A preliminary 2D transient analysis for a predicted trajectory in a representative scramjet flight path is presented. This model incorporates hypersonic convection and radiation heat transfer at the combustor walls and heat transfer to the fuel which is used as an endothermic heat sink. A heavy hydrocarbon fuel is selected due to the high density and energy release required for combustion, whilst still providing the necessary heat sink for cooling. In this process the fuel can be cracked to smaller carbon chained molecules for improved ignition and combustion. This analysis will be used in parallel with materials development to ensure appropriate composites are available in Australia for flight structures. The results show that for a postulated Mach 8 scramjet flight at 27km altitude that a combustor structure comprising of 1mm RCC, 1mm graphite foam insulation and a 3mm inconel fuel manifold the maximum temperatures reached are of the order of 1950K in the RCC. This falls within the temperature range allowed for the chosen materials to ensure that structural integrity is maintained. These results justify the further investigation into the use of composite materials and regenerative cooling with the aim of potentially using the analysis for the design of flight vehicles, including the upcoming HiFire series of experiments

First-principles prediction of redox potentials in transition-metal compounds with LDA+U

First-principles calculations within the Local Density Approximation (LDA) or Generalized Gradient Approximation (GGA), though very successful, are known to underestimate redox potentials, such as those at which lithium intercalates in transition metal compounds. We argue that this inaccuracy is related to the lack of cancellation of electron self-interaction errors in LDA/GGA and can be improved by using the DFT+$U$ method with a self-consistent evaluation of the $U$ parameter. We show that, using this approach, the experimental lithium intercalation voltages of a number of transition metal compounds, including the olivine Li$_{x}$MPO$_{4}$ (M=Mn, Fe Co, Ni), layered Li$_{x}$MO$_{2}$ ($x=$Co, Ni) and spinel-like Li$_{x}$M$_{2}$O$_{4}$ (M=Mn, Co), can be reproduced accurately.Comment: 19 pages, 6 figures, Phys. Rev. B 70, 235121 (2004

Improving Detection of DeepFakes through Facial Region Analysis in Images

\ua9 2023 by the authors. In the evolving landscape of digital media, the discipline of media forensics, which encompasses the critical examination and authentication of digital images, videos, and audio recordings, has emerged as an area of paramount importance. This heightened significance is predominantly attributed to the burgeoning concerns surrounding the proliferation of DeepFakes, which are highly realistic and manipulated media content, often created using advanced artificial intelligence techniques. Such developments necessitate a profound understanding and advancement in media forensics to ensure the integrity of digital media in various domains. Current research endeavours are primarily directed towards addressing a common challenge observed in DeepFake datasets, which pertains to the issue of overfitting. Many suggested remedies centre around the application of data augmentation methods, with a frequently adopted strategy being the incorporation of random erasure or cutout. This method entails the random removal of sections from an image to introduce diversity and mitigate overfitting. Generating disparities between the altered and unaltered images serves to inhibit the model from excessively adapting itself to individual samples, thus leading to more favourable results. Nonetheless, the stochastic nature of this approach may inadvertently obscure facial regions that harbour vital information necessary for DeepFake detection. Due to the lack of guidelines on specific regions for cutout, most studies use a randomised approach. However, in recent research, face landmarks have been integrated to designate specific facial areas for removal, even though the selection remains somewhat random. Therefore, there is a need to acquire a more comprehensive insight into facial features and identify which regions hold more crucial data for the identification of DeepFakes. In this study, the investigation delves into the data conveyed by various facial components through the excision of distinct facial regions during the training of the model. The goal is to offer valuable insights to enhance forthcoming face removal techniques within DeepFake datasets, fostering a deeper comprehension among researchers and advancing the realm of DeepFake detection. Our study presents a novel method that uses face cutout techniques to improve understanding of key facial features crucial in DeepFake detection. Moreover, the method combats overfitting in DeepFake datasets by generating diverse images with these techniques, thereby enhancing model robustness. The developed methodology is validated against publicly available datasets like FF++ and Celeb-DFv2. Both face cutout groups surpassed the Baseline, indicating cutouts improve DeepFake detection. Face Cutout Group 2 excelled, with 91% accuracy on Celeb-DF and 86% on the compound dataset, suggesting external facial features’ significance in detection. The study found that eyes are most impactful and the nose is least in model performance. Future research could explore the augmentation policy’s effect on video-based DeepFake detection

Mechanisms of vascular smooth muscle contraction and the basis for pharmacologic treatment of smooth muscle disorders

The smooth muscle cell directly drives the contraction of the vascular wall and hence regulates the size of the blood vessel lumen. We review here the current understanding of the molecular mechanisms by which agonists, therapeutics, and diseases regulate contractility of the vascular smooth muscle cell and we place this within the context of whole body function. We also discuss the implications for personalized medicine and highlight specific potential target molecules that may provide opportunities for the future development of new therapeutics to regulate vascular function.Accepted manuscrip

A Consistent Picture Emerges: A Compact X-ray Continuum Emission Region in the Gravitationally Lensed Quasar SDSS J0924+0219

We analyze the optical, UV, and X-ray microlensing variability of the lensed quasar SDSS J0924+0219 using six epochs of Chandra data in two energy bands (spanning 0.4-8.0 keV, or 1-20 keV in the quasar rest frame), 10 epochs of F275W (rest-frame 1089A) Hubble Space Telescope data, and high-cadence R-band (rest-frame 2770A) monitoring spanning eleven years. Our joint analysis provides robust constraints on the extent of the X-ray continuum emission region and the projected area of the accretion disk. The best-fit half-light radius of the soft X-ray continuum emission region is between 5x10^13 and 10^15 cm, and we find an upper limit of 10^15 cm for the hard X-rays. The best-fit soft-band size is about 13 times smaller than the optical size, and roughly 7 GM_BH/c^2 for a 2.8x10^8 M_sol black hole, similar to the results for other systems. We find that the UV emitting region falls in between the optical and X-ray emitting regions at 10^14 cm < r_1/2,UV < 3x10^15 cm. Finally, the optical size is significantly larger, by 1.5*sigma, than the theoretical thin-disk estimate based on the observed, magnification-corrected I-band flux, suggesting a shallower temperature profile than expected for a standard disk.Comment: Replaced with accepted version to Ap

Lorentz and CPT Invariance Violation In High-Energy Neutrinos

High-energy neutrino astronomy will be capable of observing particles at both extremely high energies and over extremely long baselines. These features make such experiments highly sensitive to the effects of CPT and Lorentz violation. In this article, we review the theoretical foundation and motivation for CPT and Lorentz violating effects, and then go on to discuss the related phenomenology within the neutrino sector. We describe several signatures which might be used to identify the presence of CPT or Lorentz violation in next generation neutrino telescopes and cosmic ray experiments. In many cases, high-energy neutrino experiments can test for CPT and Lorentz violation effects with much greater precision than other techniques.Comment: 27 pages, 8 figure