Lower bounds on the dilation of plane spanners

(I) We exhibit a set of 23 points in the plane that has dilation at least $1.4308$, improving the previously best lower bound of $1.4161$ for the worst-case dilation of plane spanners. (II) For every integer $n\geq13$, there exists an $n$-element point set $S$ such that the degree 3 dilation of $S$ denoted by $\delta_0(S,3) \text{ equals } 1+\sqrt{3}=2.7321\ldots$ in the domain of plane geometric spanners. In the same domain, we show that for every integer $n\geq6$, there exists a an $n$-element point set $S$ such that the degree 4 dilation of $S$ denoted by $\delta_0(S,4) \text{ equals } 1 + \sqrt{(5-\sqrt{5})/2}=2.1755\ldots$ The previous best lower bound of $1.4161$ holds for any degree. (III) For every integer $n\geq6$, there exists an $n$-element point set $S$ such that the stretch factor of the greedy triangulation of $S$ is at least $2.0268$.Comment: Revised definitions in the introduction; 23 pages, 15 figures; 2 table

Nondegenerate Optical Parametric Chirped Pulse Amplification

We present the first recompression of amplified pulses in a highly nondegenerate optical parametric chirped pulse amplifier. 60-fs recompressed pulse width and up to 2 mJ pulses were obtained in our experiments

Novel insights into diminished cardiac reserve in non-obstructive hypertrophic cardiomyopathy from four-dimensional flow cardiac magnetic resonance component analysis

Aims: Hypertrophic cardiomyopathy (HCM) is characterized by hypercontractility and diastolic dysfunction, which alter blood flow haemodynamics and are linked with increased risk of adverse clinical events. Four-dimensional flow cardiac magnetic resonance (4D-flow CMR) enables comprehensive characterization of ventricular blood flow patterns. We characterized flow component changes in non-obstructive HCM and assessed their relationship with phenotypic severity and sudden cardiac death (SCD) risk. Methods and results: Fifty-one participants (37 non-obstructive HCM and 14 matched controls) underwent 4D-flow CMR. Left-ventricular (LV) end-diastolic volume was separated into four components: direct flow (blood transiting the ventricle within one cycle), retained inflow (blood entering the ventricle and retained for one cycle), delayed ejection flow (retained ventricular blood ejected during systole), and residual volume (ventricular blood retained for >two cycles). Flow component distribution and component end-diastolic kinetic energy/mL were estimated. HCM patients demonstrated greater direct flow proportions compared with controls (47.9 ± 9% vs. 39.4 ± 6%, P = 0.002), with reduction in other components. Direct flow proportions correlated with LV mass index (r = 0.40, P = 0.004), end-diastolic volume index (r = −0.40, P = 0.017), and SCD risk (r = 0.34, P = 0.039). In contrast to controls, in HCM, stroke volume decreased with increasing direct flow proportions, indicating diminished volumetric reserve. There was no difference in component end-diastolic kinetic energy/mL. Conclusion: Non-obstructive HCM possesses a distinctive flow component distribution pattern characterised by greater direct flow proportions, and direct flow-stroke volume uncoupling indicative of diminished cardiac reserve. The correlation of direct flow proportion with phenotypic severity and SCD risk highlight its potential as a novel and sensitive haemodynamic measure of cardiovascular risk in HCM

Gemini multi-conjugate adaptive optics system review II: Commissioning, operation and overall performance

The Gemini Multi-conjugate Adaptive Optics System - GeMS, a facility instrument mounted on the Gemini South telescope, delivers a uniform, near diffraction limited images at near infrared wavelengths (0.95 microns- 2.5 microns) over a field of view of 120 arc seconds. GeMS is the first sodium layer based multi laser guide star adaptive optics system used in astronomy. It uses five laser guide stars distributed on a 60 arc seconds square constellation to measure for atmospheric distortions and two deformable mirrors to compensate for it. In this paper, the second devoted to describe the GeMS project, we present the commissioning, overall performance and operational scheme of GeMS. Performance of each sub-system is derived from the commissioning results. The typical image quality, expressed in full with half maximum, Strehl ratios and variations over the field delivered by the system are then described. A discussion of the main contributor to performance limitation is carried-out. Finally, overheads and future system upgrades are described.Comment: 20 pages, 11 figures, accepted for publication in MNRA

Comprehensive 4D velocity mapping of the heart and great vessels by cardiovascular magnetic resonance

<p>Abstract</p> <p>Background</p> <p>Phase contrast cardiovascular magnetic resonance (CMR) is able to measure all three directional components of the velocities of blood flow relative to the three spatial dimensions and the time course of the heart cycle. In this article, methods used for the acquisition, visualization, and quantification of such datasets are reviewed and illustrated.</p> <p>Methods</p> <p>Currently, the acquisition of 3D cine (4D) phase contrast velocity data, synchronized relative to both cardiac and respiratory movements takes about ten minutes or more, even when using parallel imaging and optimized pulse sequence design. The large resulting datasets need appropriate post processing for the visualization of multidirectional flow, for example as vector fields, pathlines or streamlines, or for retrospective volumetric quantification.</p> <p>Applications</p> <p>Multidirectional velocity acquisitions have provided 3D visualization of large scale flow features of the healthy heart and great vessels, and have shown altered patterns of flow in abnormal chambers and vessels. Clinically relevant examples include retrograde streams in atheromatous descending aortas as potential thrombo-embolic pathways in patients with cryptogenic stroke and marked variations of flow visualized in common aortic pathologies. Compared to standard clinical tools, 4D velocity mapping offers the potential for retrospective quantification of flow and other hemodynamic parameters.</p> <p>Conclusions</p> <p>Multidirectional, 3D cine velocity acquisitions are contributing to the understanding of normal and pathologically altered blood flow features. Although more rapid and user-friendly strategies for acquisition and analysis may be needed before 4D velocity acquisitions come to be adopted in routine clinical CMR, their capacity to measure multidirectional flows throughout a study volume has contributed novel insights into cardiovascular fluid dynamics in health and disease.</p

Removal of Lattice Imperfections that Impact the Optical Quality of Ti:Sapphire using Advanced Magnetorheological Finishing Techniques

Ti:sapphire has become the premier lasing medium material for use in solid-state femtosecond high-peak power laser systems because of its wide wavelength tuning range. With a tuneable range from 680 to 1100 nm, peaking at 800 nm, Ti:sapphire lasing crystals can easily be tuned to the required pump wavelength and provide very high pump brightness due to their good beam quality and high output power of typically several watts. Femtosecond lasers are used for precision cutting and machining of materials ranging from steel to tooth enamel to delicate heart tissue and high explosives. These ultra-short pulses are too brief to transfer heat or shock to the material being cut, which means that cutting, drilling, and machining occur with virtually no damage to surrounding material. Furthermore, these lasers can cut with high precision, making hairline cuts of less than 100 microns in thick materials along a computer-generated path. Extension of laser output to higher energies is limited by the size of the amplification medium. Yields of high quality large diameter crystals have been constrained by lattice distortions that may appear in the boule limiting the usable area from which high quality optics can be harvested. Lattice distortions affect the transmitted wavefront of these optics which ultimately limits the high-end power output and efficiency of the laser system, particularly when operated in multi-pass mode. To make matters even more complicated, Ti:sapphire is extremely hard (Mohs hardness of 9 with diamond being 10) which makes it extremely difficult to accurately polish using conventional methods without subsurface damage or significant wavefront error. In this presentation, we demonstrate for the first time that Magnetorheological finishing (MRF) can be used to compensate for the lattice distortions in Ti:sapphire by perturbing the transmitted wavefront. The advanced MRF techniques developed allow for precise polishing of the optical inverse of lattice distortions with magnitudes of about 70 nm in optical path difference onto one or both of the optical surfaces to produce high quality optics from otherwise unusable Ti:sapphire crystals. The techniques include interferometric, software, and machine modifications to precisely locate and polish sub-millimeter sites onto the optical surfaces that can not be polished into the optics conventionally. This work may allow extension of Ti:sapphire based systems to peak powers well beyond one petawatt

Frequency Conversion Activation on the Mercury Laser

High efficiency frequency conversion while operating at average power is critical for the Mercury laser. We will demonstrate average power frequency conversion of face-cooled DKDP and YCOB crystals using a sapphire heat spreader approach

Short-pulse Laser Capability on the Mercury Laser System

Applications using high energy ''petawatt-class'' laser drivers operating at repetition rates beyond 0.01 Hz are only now being envisioned. The Mercury laser system is designed to operate at 100 J/pulse at 10 Hz. We investigate the potential of configuring the Mercury laser to produce a rep-rated, ''petawatt-class'' source. The Mercury laser is a prototype of a high energy, high repetition rate source (100 J, 10 Hz). The design of the Mercury laser is based on the ability to scale in energy through scaling in aperture. Mercury is one of several 100 J, high repetition rate (10 Hz) lasers sources currently under development (HALNA, LUCIA, POLARIS). We examine the possibility of using Mercury as a pump source for a high irradiance ''petawatt-class'' source: either as a pump laser for an average power Ti:Sapphire laser, or as a pump laser for OPCPA based on YCa{sub 4}O(BO{sub 3}){sub 3} (YCOB), ideally producing a source approaching 30 J /30 fs /10 Hz--a high repetition rate petawatt. A comparison of the two systems with nominal configurations and efficiencies is shown in Table 1