Lattice-point enumerators of ellipsoids

Minkowski's second theorem on successive minima asserts that the volume of a 0-symmetric convex body K over the covolume of a lattice \Lambda can be bounded above by a quantity involving all the successive minima of K with respect to \Lambda. We will prove here that the number of lattice points inside K can also accept an upper bound of roughly the same size, in the special case where K is an ellipsoid. Whether this is also true for all K unconditionally is an open problem, but there is reasonable hope that the inductive approach used for ellipsoids could be extended to all cases.Comment: 9 page

Optical interferometry-based array of seafloor environmental sensors using a trans-oceanic submarine cable

Optical fiber–based sensing technology can drastically improve Earth observations by enabling the use of existing submarine communication cables as seafloor sensors. Previous interferometric and polarization-based techniques demonstrated environmental sensing over cable lengths up to 10,500 kilometers. However, measurements were limited to the integrated changes over the entire length of the cable. We demonstrate the detection of earthquakes and ocean signals on individual spans between repeaters of a 5860-kilometer-long transatlantic cable rather than the whole cable. By applying this technique to the existing undersea communication cables, which have a repeater-to-repeater span length of 45 to 90 kilometers, the largely unmonitored ocean floor could be instrumented with thousands of permanent real-time environmental sensors without changes to the underwater infrastructure

Non-uniform recovery of left ventricular transmural mechanics in ST-segment elevation myocardial infarction

<p>Abstract</p> <p>Background</p> <p>After a transient ischemic episode, the subendocardial region is more severely injured than outer subepicardial layers and may regain a proportionately greater degree of mechanical function in the longitudinal direction. We sought to explore left ventricular (LV) transmural mechanics in patients with ST-segment elevation myocardial infarction (STEMI) for determining the mechanism underlying recovery of global LV function after primary percutaneous coronary intervention (PCI).</p> <p>Methods</p> <p>A total of 42 patients (62 ± 11 years old, 71% male) with a first STEMI underwent serial assessments of LV longitudinal, circumferential and radial strains (LS, CS and RS) by selective tracking of subendocardial and subepicardial regions within 48 hours and a median of 5 months after PCI. LV mechanical parameters were compared with sixteen age and gender matched normal controls.</p> <p>Results</p> <p>In comparison with controls, endocardial and epicardial LS were markedly attenuated at 48 hours following PCI (P < 0.001). An improvement in LV ejection fraction (EF > 5%) following PCI was seen in 24 (57%) patients and was associated with improvement in endocardial and epicardial LS (P < 0.001 and P = 0.003, respectively) and endocardial CS (P = 0.01). Radial strain and wall motion score index, however, remained persistently abnormal. The change in endocardial LS (OR 1.2, 95% CI 1.03 to 1.42, P = 0.01) and the change in epicardial LS (OR 1.2, 95% 1.03 to 1.46, P = 0.02) were significantly associated with the improvement in LVEF, independent of the location of STEMI and the presence of underlying multivessel disease.</p> <p>Conclusions</p> <p>In patients with STEMI treated by PCI, the recovery of LV subendocardial shortening strain seen in the longitudinal direction underlies the improvement in LV global function despite persistent abnormalities in radial mechanics and wall motion score index.</p

Left ventricular volume: an optimal parameter to detect systolic dysfunction on prospectively triggered 64-multidetector row computed tomography: another step towards reducing radiation exposure

In this study, we define the correlation between LV volumes (both LV end-diastolic volume [LVEDV] and LV end-systolic volume [LVESV]) and ejection fraction (EF) on 64 slice multi-detector computed tomography (MDCT). We also determine the accuracy of all the LV volume (LVV) parameters to detect LV systolic dysfunction (LVSD) and investigate the feasibility of using LVV as a surrogate of LVSD on prospectively gated imaging to prevent the radiation exposure of retrospective imaging. 568 patients undergoing 64-detector MDCT were divided into 2 groups: Group 1—subjects without any heart disease and LVEF ≥ 50%; and Group 2—patients with coronary artery disease and LVEF < 50% (defined as LVSD). The LVV (LV cavity only) and Total LV volume (cavity + LV mass) at end-systole and end-diastole (LVESV, Total LVESV, LVEDV and Total LVEDV) were measured. The upper limit values (mean + 2 SD) of all LVV parameters in Group 1 were used as the reference criterion to diagnose LVSD in Group 2. An exponential correlation was found between LVEF and all the LVV parameters. The specificity to detect LVSD in Group 2 was >90% and the sensitivity was 88.9, 83.3, 61.3 and 74.9% by using LVESV, Total LVESV, LVEDV and Total LVEDV, respectively. Systolic and diastolic LV volumes had a high correlation with LVEF and a high accuracy to detect LVSD. Thus, on prospectively triggered imaging, ventricular volumes can predict patients with reduced LVEF, and appropriate referrals can be made

Treatment options in end-stage heart failure: where to go from here?

Chronic heart failure is a major healthcare problem associated with high morbidity and mortality. Despite significant progress in treatment strategies, the prognosis of heart failure patients remains poor. The golden standard treatment for heart failure is heart transplantation after failure of medical therapy, surgery and/or cardiac resynchronisation therapy. In order to improve patients’ outcome and quality of life, new emerging treatment modalities are currently being investigated, including mechanical cardiac support devices, of which the left ventricular assist device is the most promising treatment option. Structured care for heart failure patients according to the most recent international heart failure guidelines may further contribute to optimal decision-making. This article will review the conventional and novel treatment modalities of heart failure

Parental sense of competence, paternal stress and perceived construction of the relationship with the premature newborn: A mixed method study

Objective: The aim of this study is to investigate the parental sense of competence, the paternal stress and the perceived construction of the relationship with the infant of during the hospitalization in a neonatal intensive care unit. Methods: Forty-eight French fathers of premature infants participated in this study, which took place in the Toulouse University Hospital in France. Mixed methods are used, a semi-structured interview and two self-reported questionnaires. Results: Main results show that fathers perceive the construction of the first relationship with their infant through the skin-to-skin and eye contact, along with their immediate presence by their child. The physical contact, although it may induce more stress, it motivates the father to be more involved in the caregiving process. Child&apos;s fragile appearance generates more stress to fathers. Finally, the stress linked to the construction of their relationship with the infant will affect their parental sense of competence. Conclusion: Results are discussed with respect to recent literature and ways to improve professional practice are proposed. © 2022 Elsevier B.V