Correlations for pairs of periodic trajectories for open billiards

In this paper we prove two asymptotic estimates for pairs of closed trajectories for open billiards similar to those established by Pollicott and Sharp for closed geodesics on negatively curved compact surfaces. The first of these estimates holds for general open billiards in any dimension. The more intricate second estimate is established for open billiards satisfying the so called Dolgopyat type estimates. This class of billiards includes all open billiards in the plane and open billiards in $\R^N, N \geq 3$ satisfying some additional conditions

Landau quantization and neutron emissions by nuclei in the crust of a magnetar

Magnetars are neutron stars endowed with surface magnetic fields of the order of $10^{14}-10^{15}$~G, and with presumably much stronger fields in their interior. As a result of Landau quantization of electron motion, the neutron-drip transition in the crust of a magnetar is shifted to either higher or lower densities depending on the magnetic field strength. The impact of nuclear uncertainties is explored considering the recent series of Brussels-Montreal microscopic nuclear mass models. All these models are based on the Hartree-Fock-Bogoliubov method with generalized Skyrme functionals. They differ in their predictions for the symmetry energy coefficient at saturation, and for the stiffness of the neutron-matter equation of state. For comparison, we have also considered the very accurate but more phenomenological model of Duflo and Zuker. Although the equilibrium composition of the crust of a magnetar and the onset of neutron emission are found to be model dependent, the quantum oscillations of the threshold density are essentially universal.Comment: 7 pages, 2 figure

Artificial intelligence and automation in endoscopy and surgery

Modern endoscopy relies on digital technology, from high-resolution imaging sensors and displays to electronics connecting configurable illumination and actuation systems for robotic articulation. In addition to enabling more effective diagnostic and therapeutic interventions, the digitization of the procedural toolset enables video data capture of the internal human anatomy at unprecedented levels. Interventional video data encapsulate functional and structural information about a patient’s anatomy as well as events, activity and action logs about the surgical process. This detailed but difficult-to-interpret record from endoscopic procedures can be linked to preoperative and postoperative records or patient imaging information. Rapid advances in artificial intelligence, especially in supervised deep learning, can utilize data from endoscopic procedures to develop systems for assisting procedures leading to computer-assisted interventions that can enable better navigation during procedures, automation of image interpretation and robotically assisted tool manipulation. In this Perspective, we summarize state-of-the-art artificial intelligence for computer-assisted interventions in gastroenterology and surgery

Role of Landau-Rabi quantization of electron motion on the crust of magnetars within the nuclear energy density functional theory

Magnetic fields of order $10^{15}$ G have been measured at the surface of some neutron stars, and much stronger magnetic fields are expected to be present in the solid region beneath the surface. The effects of the magnetic field on the equation of state and on the composition of the crust due to Landau-Rabi quantization of electron motion are studied. Both the outer and inner crustal regions are described in a unified and consistent way within the nuclear-energy density functional theory.Comment: 23 pages, 11 figure

Analytical modeling of micelle growth. 2. Molecular thermodynamics of mixed aggregates and scission energy in wormlike micelles

Hypotheses: Quantitative molecular-thermodynamic theory of the growth of giant wormlike micelles in mixed nonionic surfactant solutions can be developed on the basis of a generalized model, which includes the classical phase separation and mass action models as special cases. The generalized model describes spherocylindrical micelles, which are simultaneously multicomponent and polydisperse in size. Theory: The model is based on explicit analytical expressions for the four components of the free energy of mixed nonionic micelles: interfacial-tension, headgroup-steric, chain-conformation components and free energy of mixing. The radii of the cylindrical part and the spherical endcaps, as well as the chemical composition of the endcaps, are determined by minimization of the free energy. Findings: In the case of multicomponent micelles, an additional term appears in the expression for the micelle growth parameter (scission free energy), which takes into account the fact that the micelle endcaps and cylindrical part have different compositions. The model accurately predicts the mean mass aggregation number of wormlike micelles in mixed nonionic surfactant solutions without using any adjustable parameters. The endcaps are enriched in the surfactant with smaller packing parameter that is better accommodated in regions of higher mean surface curvature. The model can be further extended to mixed solutions of nonionic, ionic and zwitterionic surfactants used in personal-care and house-hold detergency

H-alpha observations of the gamma-ray-emitting Be/X-ray binary LSI+61303: orbital modulation, disk truncation, and long-term variability

We report 138 spectral observations of the H-alpha emission line of the radio- and gamma-ray-emitting Be/X-ray binary LSI+61303 obtained during the period of September 1998 -- January 2013. From measuring various H-alpha parameters, we found that the orbital modulation of the H-alpha is best visible in the equivalent width ratio EW(B)/EW(R), the equivalent width of the blue hump, and in the radial velocity of the central dip. The periodogram analysis confirmed that the H-alpha emission is modulated with the orbital and superorbital periods. For the past 20 years the radius of the circumstellar disk is similar to the Roche lobe size at the periastron. It is probably truncated by a 6:1 resonance. The orbital maximum of the equivalent width of H-alpha emission peaks after the periastron and coincides on average with the X-ray and gamma-ray maxima. All the spectra are available upon request from the authors and through the CDS.Comment: 11 pages, accepted for publication in A&

FedDP: Dual Personalization in Federated Medical Image Segmentation

Personalized federated learning (PFL) addresses the data heterogeneity challenge faced by general federated learning (GFL). Rather than learning a single global model, with PFL a collection of models are adapted to the unique feature distribution of each site. However, current PFL methods rarely consider self-attention networks which can handle data heterogeneity by long-range dependency modeling and they do not utilize prediction inconsistencies in local models as an indicator of site uniqueness. In this paper, we propose FedDP, a novel federated learning scheme with dual personalization, which improves model personalization from both feature and prediction aspects to boost image segmentation results. We leverage long-range dependencies by designing a local query (LQ) that decouples the query embedding layer out of each local model, whose parameters are trained privately to better adapt to the respective feature distribution of the site. We then propose inconsistency-guided calibration (IGC), which exploits the inter-site prediction inconsistencies to accommodate the model learning concentration. By encouraging a model to penalize pixels with larger inconsistencies, we better tailor prediction-level patterns to each local site. Experimentally, we compare FedDP with the state-of-the-art PFL methods on two popular medical image segmentation tasks with different modalities, where our results consistently outperform others on both tasks. Our code and models will be available at https://github.com/jcwang123/PFL-Seg-Trans

Imaging skins: stretchable and conformable on-organ beta particle detectors for radioguided surgery

While radioguided surgery (RGS) traditionally relied on detecting gamma rays, direct detection of beta particles could facilitate the detection of tumour margins intraoperatively by reducing radiation noise emanating from distant organs, thereby improving the signal-to-noise ratio of the imaging technique. In addition, most existing beta detectors do not offer surface sensing or imaging capabilities. Therefore, we explore the concept of a stretchable scintillator to detect beta-particles emitting radiotracers that would be directly deployed on the targeted organ. Such detectors, which we refer to as imaging skins, would work as indirect radiation detectors made of light-emitting agents and biocompatible stretchable material. Our vision is to detect scintillation using standard endoscopes routinely employed in minimally invasive surgery. Moreover, surgical robotic systems would ideally be used to apply the imaging skins, allowing for precise control of each component, thereby improving positioning and task repeatability. While still in the exploratory stages, this innovative approach has the potential to improve the detection of tumour margins during RGS by enabling real-time imaging, ultimately improving surgical outcomes

Step Bunching with Alternation of Structural Parameters

By taking account of the alternation of structural parameters, we study bunching of impermeable steps induced by drift of adatoms on a vicinal face of Si(001). With the alternation of diffusion coefficient, the step bunching occurs irrespective of the direction of the drift if the step distance is large. Like the bunching of permeable steps, the type of large terraces is determined by the drift direction. With step-down drift, step bunches grows faster than those with step-up drift. The ratio of the growth rates is larger than the ratio of the diffusion coefficients. Evaporation of adatoms, which does not cause the step bunching, decreases the difference. If only the alternation of kinetic coefficient is taken into account, the step bunching occurs with step-down drift. In an early stage, the initial fluctuation of the step distance determines the type of large terraces, but in a late stage, the type of large terraces is opposite to the case of alternating diffusion coefficient.Comment: 8pages, 16 figure