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After Bershadsky-Cecotti-Ooguri-Vafa, we introduce an invariant of Calabi-Yau threefolds, which we call the BCOV invariant and which we obtain using analytic torsion. We give an explicit formula for the BCOV invariant as a function on the compactified moduli space, when it is isomorphic to a projective line. As a corollary, we prove the formula for the BCOV invariant of quintic mirror threefolds conjectured by Bershadsky-Cecotti-Ooguri-Vafa. Contents 1. Introduction 2. Calabi-Yau varieties with at most one ordinary double point 3. Quillen metrics 4. The BCOV invariant of Calabi-Yau manifolds 5. The singularity of the Quillen metric on the BCOV bundle 6. The cotangent sheaf of the Kuranishi space 7. Behaviors of the Weil-Petersson metric and the Hodge metric 8. The singularity of the BCOV invariant I -the case of ODP 9. The singularity of the BCOV invariant II -general degenerations 10. The curvature current of the BCOV invariant 11. The BCOV invariant of Calabi-Yau threefolds with h 1,2 = 1 12. The BCOV invariant of quintic mirror threefolds 13. The BCOV invariant of FHSV threefolds 1 ANALYTIC TORSION FOR CALABI-YAU THREEFOLDS 5an arbitrary Calabi-Yau manifold of arbitrary dimension, which we obtain using determinants of cohomologies [28], Quillen metrics [11], [44], and a Bott-Chern class like A(·). Then the BCOV Hermitian line of a Calabi-Yau manifold depends only on the complex structure of the manifold. The Hodge diamond of Calabi-Yau threefolds are so simple that the BCOV Hermitian line reduces to the scalar invariant τ BCOV in the case of threefolds. Hence Eq. (1.1) on P 1 \ D is deduced from the curvature formula for the BCOV Hermitian line bundles. (See Sect. 4).(b) To establish the formula for log τ BCOV near D, we fix a specific holomorphic extension of the BCOV bundle from P 1 \D to P 1 , which we call the Kähler extension. (See Sect. 5.) Since τ BCOV is the ratio of the Quillen metric and the L 2 -metric on the BCOV bundle, it suffices to determine the singularities of the Quillen metric and the L 2 -metric on the extended BCOV bundle. We determine the singularity of the Quillen metric on the extended BCOV bundle with respect to the metric on T X /P 1 induced from a Kähler metric on X . The anomaly formula for Quillen metrics of Bismut-Gillet-Soulé [11] and a formula for the singularity of Quillen metrics [9], [61] play the central role. (See Sect. 5.).(c) By the smoothness of Def(X ψ ) at ψ ∈ D * [26], [45], [54], the behavior of the L 2 -metric on the extended BCOV bundle near D * is determined by the singularity of Ω WP near D * , which was computed by Tian [54]. (See Sects. 6,7,8.) To determine the behavior of the L 2 metric on the extended BCOV bundle at ψ = ∞, one may assume that π : X → P 1 is semi-stable at ψ = ∞ by Mumford [27]. We consider another holomorphic extension of the BCOV bundle, i.e., the canonical extension in Hodge theory [48]. With respect to the canonical extension, the L 2 -metric has at most an algebraic singularity at ψ = ∞ by Schmid [48]. Comparing the two extensions, we sh...

BackgroundThe Hybrid Assistive Limb (HAL, CYBERDYNE) is a wearable robot that provides assistance to patients while walking, standing, and performing leg movements based on the intended movement of the wearer. We aimed to assess the effect of HAL training on the walking ability, range of motion (ROM), and muscle strength of patients after total knee arthroplasty (TKA) for osteoarthritis and rheumatoid arthritis, and to compare the functional status after HAL training to the conventional training methods after surgery.MethodsNine patients (10 knees) underwent HAL training (mean age 74.1 ± 5.7 years; height 150.4 ± 6.5 cm; weight 61.2 ± 8.9 kg), whereas 10 patients (11 knees) underwent conventional rehabilitation (mean age 78.4 ± 8.0 years; height 150.5 ± 10.0 cm; weight 59.1 ± 9.8 kg). Patients underwent HAL training during 10 to 12 (average 14.4 min a session) sessions over a 4-week period, 1 week after TKA. There was no significant difference in the total physical therapy time including HAL training between the HAL and control groups. Gait speed, step length, ROM, and muscle strength were evaluated.ResultsThe nine patients completed the HAL training sessions without adverse events. The walking speed and step length in the self-selected walking speed condition, and the walking speed in the maximum walking speed condition were greater in the HAL group than in the control group at 4 and 8 weeks (P < 0.05). The step length in the maximum walking speed condition was greater in the HAL group than in the control group at 2, 4, and 8 weeks (P < 0.05). The extension lag and knee pain were lower in the HAL group than in the control group at 2 weeks (P < 0.05). The muscle strength of knee extension in the HAL group was greater than that in the control group at 8 weeks (P < 0.05).ConclusionHAL training after TKA can improve the walking ability, ROM, and muscle strength compared to conventional physical therapy for up to 8 weeks after TKA. Since the recovery of walking ability was earlier in the HAL group than in the control group and adverse events were not observed in this pilot study, HAL training after TKA can be considered a safe and effective rehabilitation intervention.Trial registrationUMIN, UMIN000017623. Registered 19 May 2015

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Purpose To characterize the safety, pharmacodynamics, and pharmacokinetics (PK) of vericiguat in healthy males. Methods Six phase I studies were conducted in European, Chinese, and Japanese males. Subjects received oral vericiguat as a single dose (0.5–15.0 mg solution [for first-in-human study] or 1.25–10.0 mg immediate release [IR tablets]) or multiple doses (1.25–10.0 mg IR tablets once daily [QD] or 5.0 mg IR tablets twice daily for 7 consecutive days). Bioavailability and food effects on vericiguat PK (IR tablets) were also studied in European subjects. Results Overall, 255 of 265 randomized subjects completed their respective studies. There were no deaths or serious adverse events. Vericiguat was generally well tolerated at doses ≤ 10.0 mg. In the first-in-human study, the most frequent drug-related adverse events were headache and postural dizziness (experienced by five subjects each [7.2%]). Three of four subjects who received vericiguat 15.0 mg (oral solution, fasted) experienced orthostatic reactions. Vericiguat (≤ 10.0 mg, IR tablets) was rapidly absorbed (median time to reach maximum plasma concentration ≤ 2.5 h [fasted]) with a mean half-life of about 22.0 h (range 17.9–27.0 h for single and multiple doses). No evidence for deviation from dose proportionality or unexpected accumulation was observed. Administration of vericiguat 5.0 mg IR tablets with food increased bioavailability by 19% (estimated ratio 119% [90% confidence interval]: 108; 131]), reduced PK variability, and prolonged vericiguat absorption relative to the fasted state. Conclusion In general, vericiguat was well tolerated. These results supported further clinical evaluation of vericiguat QD in patients with heart failure. Registry numbers EudraCT: 2011-001627-21; EudraCT: 2012-000953-30