Theorem 1. Let (S2, g) be the two dimensional sphere with a metric of class C1,1 whose Gaussian curvature satisfies 0 ≤ K ≤ 1. Then any simple closed geodesic γ on (S2, g) has length at least 2π. If the length of γ is 2π, then (S2, g) is isometric to the standard round sphere (S2, g0) and γ is a great circle on (S2, g0) or (S 2, g) is isometric to a circular cylinder of circumference 2π capped ...

CORRECTION Following publication of the original article [1], the authors pointed out that the figure shown as figure S1 is actually figure S2 and vice versa. Figure S1 should show the barcharts, and figure S2 should shows the heatmaps. Figures captions are in the correct order. 1) "...SILVA-only OTUs (37,066 97% OTUs and 1266 85% clusters) (Additional file 3: Figure S2 )..." - > ...SILVA-only ...

Given sequences S1, S2, . . . Sn, and a pattern string P the constrained multiple sequence alignment problem (CMSA) is to align similar subsequences of these sequences with the constraint that the alignment “contains” P . The CMSA problem can be considered as an optimal path search problem in the dynamic programming matrix. The problem has a dynamic programming solution that requires O(2|S1||S2...

The severe acute respiratory syndrome coronavirus enters cells through the activities of a spike protein (S) which has receptor-binding (S1) and membrane fusion (S2) regions. We have characterized four sequential states of a purified recombinant S ectodomain (S-e) comprising S1 and the ectodomain of S2. They are S-e monomers, uncleaved S-e trimers, cleaved S-e trimers, and dissociated S1 monome...

A double-loop digraph G(N ; s1, s2) = G(V,E) is defined by V = ZN and E = {(i, i + s1), (i, i + s2)| i ∈ V }, for some fixed steps 1 ≤ s1 < s2 < N with gcd(N, s1, s2) = 1. Let D(N ; s1, s2) be the diameter of G and let us define D(N) = min 1≤s1<s2<N, gcd(N,s1,s2)=1 D(N ; s1, s2), D1(N) = min 1<s<N D(N ; 1, s). Some early works about the diameter of these digraphs studied the minimization of D(N...

Myosin II, like many molecular motors, is a two-headed dimer held together by a coiled-coil rod. The stability of the (S2) rod has implications for head-head interactions, force generation, and possibly regulation. Whether S2 uncoils has been controversial. To test the stability of S2, we constructed a series of "zippered" dimeric smooth muscle myosin II compounds, containing a high-melting tem...

System L (SL), a basolateral amino acid transporter, transports large neutral amino acids (LNAAs) in a Na(+)-independent manner. Previously, we identified two isoforms of transporters: L-type amino acid transporter 1 (LAT1) and 2 (LAT2) and revealed their distinct substrate selectivity and transport properties. In this study, to establish more stable human LAT1 (hLAT1) and LAT2 (hLAT2) in vitro...

The P50 is an early component of auditory evoked potentials and a measure of sensory gating deficits. This evoked potential component is thought to be an important endophenotype candidate for schizophrenia. Recent research suggests that instead of the P50 ratio, S1 and S2 amplitudes should be evaluated for sensory gating. However, no studies have focused on the relationship between cognitive dy...

In this technical report we present a complete proof of the Marcinkiewicz-Zygmund inequality on the bi-Sphere from [1, Theorem 4.5]. We use the same notation as in [1]. The Theorem 4.5 of [1] reads as follows: Theorem 1. Let N ∈ N2 and R be a admissible decomposition of S2 × S2 according to a sampling set X such that ‖R‖ ≤ η 21 Ñ , (1) where η ∈ (0, 1) is arbitrarily fixed. Then for r = 1 or r ...

OBJECTIVE To examine the relationship between acoustic characteristics of the first and second heart sounds (S1 and S2) and underlying cardiac structure and haemodynamics in patients with isolated pulmonary arterial hypertension (PAH) and controls. DESIGN Prospective multicentre cohort study. SETTING Tertiary referral and community hospitals. PARTICIPANTS We prospectively evaluated 40 PAH...