Uniqueness and Nondegeneracy of Ground States for (−Δ)sQ+Q−Qα+1=0(-\Delta)^s Q + Q - Q^{\alpha+1} = 0 in R\mathbb{R}

We prove uniqueness of ground state solutions $Q = Q(|x|) \geq 0$ for the nonlinear equation $(-\Delta)^s Q + Q - Q^{\alpha+1}= 0$ in $\mathbb{R}$, where $0 < s < 1$ and $0 < \alpha < \frac{4s}{1-2s}$ for $s < 1/2$ and $0 < \alpha < \infty$ for $s \geq 1/2$. Here $(-\Delta)^s$ denotes the fractional Laplacian in one dimension. In particular, we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for $s=1/2$ and $\alpha=1$ in [Acta Math., \textbf{167} (1991), 107--126]. As a technical key result in this paper, we show that the associated linearized operator $L_+ = (-\Delta)^s + 1 - (\alpha+1) Q^\alpha$ is nondegenerate; i.\,e., its kernel satisfies $\mathrm{ker}\, L_+ = \mathrm{span}\, \{Q'\}$. This result about $L_+$ proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for nonlinear dispersive PDEs with fractional Laplacians, such as the generalized Benjamin-Ono (BO) and Benjamin-Bona-Mahony (BBM) water wave equations.Comment: 45 page

Open charm and charmonium production at relativistic energies

We calculate open charm and charmonium production in $Au+Au$ reactions at $\sqrt{s}$ = 200 GeV within the hadron-string dynamics (HSD) transport approach employing open charm cross sections from $pN$ and $\pi N$ reactions that are fitted to results from PYTHIA and scaled in magnitude to the available experimental data. Charmonium dissociation with nucleons and formed mesons to open charm ($D+\bar{D}$ pairs) is included dynamically. The 'comover' dissociation cross sections are described by a simple phase-space model including a single free parameter, i.e. an interaction strength $M_0^2$, that is fitted to the $J/\Psi$ suppression data for $Pb+Pb$ collisions at SPS energies. As a novel feature we implement the backward channels for charmonium reproduction by $D \bar{D}$ channels employing detailed balance. From our dynamical calculations we find that the charmonium recreation is comparable to the dissociation by 'comoving' mesons. This leads to the final result that the total $J/\Psi$ suppression at $\sqrt{s}$ = 200 GeV as a function of centrality is slightly less than the suppression seen at SPS energies by the NA50 Collaboration, where the 'comover' dissociation is substantial and the backward channels play no role. Furthermore, even in case that all directly produced $J/\Psi$ mesons dissociate immediately (or are not formed as a mesonic state), a sizeable amount of charmonia is found asymptotically due to the $D+\bar{D} \to J/\Psi$ + meson channels in central collisions of $Au+Au$ at $\sqrt{s}$ = 200 GeV which, however, is lower than the $J/\Psi$ yield expected from binary scaling of $pp$ collisions.Comment: 42 pages, including 14 eps figures, discussions extended and references added, to be published in Phys. Rev.

MacB ABC transporter is a dimer whose ATPase activity and macrolide-binding capacity are regulated by the membrane fusion protein MacA

Gram-negative bacteria utilize specialized machinery to translocate drugs and protein toxins across the inner and outer membranes, consisting of a tripartite complex composed of an inner membrane secondary or primary active transporter (IMP), a periplasmic membrane fusion protein, and an outer membrane channel. We have investigated the assembly and function of the MacAB/TolC system that confers resistance to macrolides in Escherichia coli. The membrane fusion protein MacA not only stabilizes the tripartite assembly by interacting with both the inner membrane protein MacB and the outer membrane protein TolC, but also has a role in regulating the function of MacB, apparently increasing its affinity for both erythromycin and ATP. Analysis of the kinetic behavior of ATP hydrolysis indicated that MacA promotes and stabilizes the ATP-binding form of the MacB transporter. For the first time, we have established unambiguously the dimeric nature of a noncanonic ABC transporter, MacB that has an N-terminal nucleotide binding domain, by means of nondissociating mass spectrometry, analytical ultracentrifugation, and atomic force microscopy. Structural studies of ABC transporters indicate that ATP is bound between a pair of nucleotide binding domains to stabilize a conformation in which the substrate-binding site is outward-facing. Consequently, our data suggest that in the presence of ATP the same conformation of MacB is promoted and stabilized by MacA. Thus, MacA would facilitate the delivery of drugs by MacB to TolC by enhancing the binding of drugs to it and inducing a conformation of MacB that is primed and competent for binding TolC. Our structural studies are an important first step in understanding how the tripartite complex is assembled

Serological response in RT-PCR confirmed h1n1-2009 influenza a by hemagglutination inhibition and virus neutralization assays: An observational study

10.1371/journal.pone.0012474PLoS ONE58

SAFE-clustering: Single-cell Aggregated (from Ensemble) clustering for single-cell RNA-seq data

Motivation: Accurately clustering cell types from a mass of heterogeneous cells is a crucial first step for the analysis of single-cell RNA-seq (scRNA-Seq) data. Although several methods have been recently developed, they utilize different characteristics of data and yield varying results in terms of both the number of clusters and actual cluster assignments. Results: Here, we present SAFE-clustering, single-cell aggregated (From Ensemble) clustering, a flexible, accurate and robust method for clustering scRNA-Seq data. SAFE-clustering takes as input, results from multiple clustering methods, to build one consensus solution. SAFE-clustering currently embeds four state-of-the-art methods, SC3, CIDR, Seurat and t-SNE þ k-means; and ensembles solutions from these four methods using three hypergraph-based partitioning algorithms. Extensive assessment across 12 datasets with the number of clusters ranging from 3 to 14, and the number of single cells ranging from 49 to 32, 695 showcases the advantages of SAFEclustering in terms of both cluster number (18.2-58.1% reduction in absolute deviation to the truth) and cluster assignment (on average 36.0% improvement, and up to 18.5% over the best of the four methods, measured by adjusted rand index). Moreover, SAFE-clustering is computationally efficient to accommodate large datasets, taking <10 min to process 28 733 cells

Does theory of quantum correction to conductivity agree with experimental data in 2D systems?

The quantum correction to the conductivity have been studied in two types of 2D heterostructures: with doped quantum well and doped barriers. The consistent analysis shows that in the structures where electrons occupy the states in quantum well only, all the temperature and magnetic field dependencies of the components of resistivity tensor are well described by the theories of quantum corrections. The contribution of electron-electron interaction to the conductivity have been determined reliably in the structures with different electron density. A possible reason of large scatter in experimental data concerning the contribution of electron-electron interaction, obtained in previous papers, and the role of the carriers, occupied the states of the doped layers, is discussed.Comment: 10 pages with 9 figure

On non-local variational problems with lack of compactness related to non-linear optics

We give a simple proof of existence of solutions of the dispersion manage- ment and diffraction management equations for zero average dispersion, respectively diffraction. These solutions are found as maximizers of non-linear and non-local vari- ational problems which are invariant under a large non-compact group. Our proof of existence of maximizer is rather direct and avoids the use of Lions' concentration compactness argument or Ekeland's variational principle.Comment: 30 page

Frozen spatial chaos induced by boundaries

We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion equation in a two-dimensional undulated domain. Concepts from the theory of dynamical systems, and a transverse-single-mode approximation are used to describe the spatially chaotic structures.Comment: 9 pages, 6 figures, submitted for publication; for related work visit http://www.imedea.uib.es/~victo

Independent Eigenstates of Angular Momentum in a Quantum N-body System

The global rotational degrees of freedom in the Schr\"{o}dinger equation for an $N$-body system are completely separated from the internal ones. After removing the motion of center of mass, we find a complete set of $(2\ell+1)$ independent base functions with the angular momentum $\ell$. These are homogeneous polynomials in the components of the coordinate vectors and the solutions of the Laplace equation, where the Euler angles do not appear explicitly. Any function with given angular momentum and given parity in the system can be expanded with respect to the base functions, where the coefficients are the functions of the internal variables. With the right choice of the base functions and the internal variables, we explicitly establish the equations for those functions. Only (3N-6) internal variables are involved both in the functions and in the equations. The permutation symmetry of the wave functions for identical particles is discussed.Comment: 24 pages, no figure, one Table, RevTex, Will be published in Phys. Rev. A 64, 0421xx (Oct. 2001

Ultra-low Ultraviolet Radiation in Office Lighting Can Moderate Seasonal Vitamin D Cycle: A Pilot Study

Background/Aim: Ultraviolet-B (UV-B) radiation initiates vitamin D synthesis in the skin, making sun exposure a major source of vitamin D. We aimed to determine whether office lighting containing ultra-low levels of UV-B radiation could modify the winter decline in vitamin D status in the UK, while being safe and well tolerated. Patients and Methods: Twenty commercial office desk lamps were modified with the addition of UV-B LEDs. Ten hospital office administrative staff received UV-modified lamps with UV-on, and 10 staff received identical placebo lamps with UV switched off, in a double-blind, cross-over pilot study during the winter of 2021/22. Circulating 25-hydroxyvitamin D [25(OH)D] was measured every 4 weeks for 20 weeks: at baseline and during an 8-week trial period, 4-week washout, and a cross-over 8-week trial period. Results: The linear regression combining the complete datasets for phase 1 and 2 of the trial showed that an 8-week UV light intervention significantly increased 25OHD by 7.13 nmol/l with a p-Value=0.02, compared to the placebo group. Similar results were confirmed by cross-over analyses using the datasets of those completing both phases of the trial both with and without using the inverse probability weighing method to handle dropouts. Conclusion: The UV-B-modified lighting was well-tolerated and safe with weekly doses of UV-B of 0.5 - 0.9 Standard Erythema Dose [SED=100 Jm -2 erythema weighted UV radiation] measured at chest level. This ultra-low dosing was effective in reducing the winter decline in vitamin D status