Nonlocal Flow of Convex Plane Curves and Isoperimetric Inequalities

In the first part of the paper we survey some nonlocal flows of convex plane curves ever studied so far and discuss properties of the flows related to enclosed area and length, especially the isoperimetric ratio and the isoperimetric difference. We also study a new nonlocal flow of convex plane curves and discuss its evolution behavior. In the second part of the paper we discuss necessary and sufficient conditions (in terms of the (mixed) isoperimetric ratio or (mixed) isoperimetric difference) for two convex closed curves to be homothetic or parallel.Comment: 23 page

Perspective of monochromatic gamma-ray line detection with the High Energy cosmic-Radiation Detection (HERD) facility onboard China's Space Station

HERD is the High Energy cosmic-Radiation Detection instrument proposed to operate onboard China's space station in the 2020s. It is designed to detect energetic cosmic ray nuclei, leptons and photons with a high energy resolution ($\sim1\%$ for electrons and photons and $20\%$ for nuclei) and a large geometry factor ($>3\,{ m^2\,sr}$ for electrons and diffuse photons and $>2\,{ m^2\,sr}$ for nuclei). In this work we discuss the capability of HERD to detect monochromatic $\gamma$-ray lines, based on simulations of the detector performance. It is shown that HERD will be one of the most sensitive instruments for monochromatic $\gamma$-ray searches at energies between $\sim10$ to a few hundred GeV. Above hundreds of GeV, Cherenkov telescopes will be more sensitive due to their large effective area. As a specific example, we show that a good portion of the parameter space of a supersymmetric dark matter model can be probed with HERD.Comment: 9 pages, 7 figures, matches version published in Astropart.Phy

Assessment of density functional approximations for the hemibonded structure of water dimer radical cation

Due to the severe self-interaction errors associated with some density functional approximations, conventional density functionals often fail to dissociate the hemibonded structure of water dimer radical cation (H2O)2+ into the correct fragments: H2O and H2O+. Consequently, the binding energy of the hemibonded structure (H2O)2+ is not well-defined. For a comprehensive comparison of different functionals for this system, we propose three criteria: (i) The binding energies, (ii) the relative energies between the conformers of the water dimer radical cation, and (iii) the dissociation curves predicted by different functionals. The long-range corrected (LC) double-hybrid functional, omegaB97X-2(LP) [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2009, 131, 174105.], is shown to perform reasonably well based on these three criteria. Reasons that LC hybrid functionals generally work better than conventional density functionals for hemibonded systems are also explained in this work.Comment: 10 pages, 5 figures, 4 table

A high performance dye-sensitized solar cell with a novel nanocomposite film of PtNP/MWCNT on the counter electrode

An imide-functionalized material, poly(oxyethylene)-segmented polymer, was synthesized from the reaction of poly(oxyethylene) diamine of 2000 g mol(-1) M(w) and 4,4'-oxydiphthalic anhydride and used to disperse hybrid nanomaterials of platinum nanoparticles and multi-wall carbon nanotubes (PtNP/MWCNT). The composite material was spin-coated into film and further prepared as the counter electrode (PtNP/MWCNT-CE) for a dye-sensitized solar cell (DSSC). The short-circuit current density (J(SC)) and power-conversion efficiency (eta) of the DSSC with PtNP/MWCNT-CE were found to be 18.01 +/- 0.91 mA cm(-2) and 8.00 +/- 0.23%, respectively, while the corresponding values were 14.62 +/- 0.19 mA cm(-2) and 6.92 +/- 0.07% for a DSSC with a bare platinum counter electrode (Pt-CE). The presence and distribution of PtNP/MWCNT on the CE were characterized by using scanning electron microscopy (SEM), atomic force microscopy (AFM), energy dispersive spectroscopy (EDS), and X-ray diffraction (XRD). The attachment of PtNPs on MWCNTs was observed by transmission electron microscopy (TEM). Cyclic voltammetry (CV), incident-photo-to-current efficiency (IPCE) and electrochemical impedance spectra (EIS) were correlated to explain the efficacy of this nanocomposite system

BIOSMILE web search: a web application for annotating biomedical entities and relations

BIOSMILE web search (BWS), a web-based NCBI-PubMed search application, which can analyze articles for selected biomedical verbs and give users relational information, such as subject, object, location, manner, time, etc. After receiving keyword query input, BWS retrieves matching PubMed abstracts and lists them along with snippets by order of relevancy to protein–protein interaction. Users can then select articles for further analysis, and BWS will find and mark up biomedical relations in the text. The analysis results can be viewed in the abstract text or in table form. To date, BWS has been field tested by over 30 biologists and questionnaires have shown that subjects are highly satisfied with its capabilities and usability. BWS is accessible free of charge at http://bioservices.cse.yzu.edu.tw/BWS

Role of tissue transglutaminase 2 in the acquisition of a mesenchymal-like phenotype in highly invasive A431 tumor cells

<p>Abstract</p> <p>Background</p> <p>Cancer progression is closely linked to the epithelial-mesenchymal transition (EMT) process. Studies have shown that there is increased expression of tissue tranglutaminase (TG2) in advanced invasive cancer cells. TG2 catalyzes the covalent cross-linking of proteins, exhibits G protein activity, and has been implicated in the modulation of cell adhesion, migration, invasion and cancer metastasis. This study explores the molecular mechanisms associated with TG2's involvement in the acquisition of the mesenchymal phenotype using the highly invasive A431-III subline and its parental A431-P cells.</p> <p>Results</p> <p>The A431-III tumor subline displays increased expression of TG2. This is accompanied by enhanced expression of the mesenchymal phenotype, and this expression is reversed by knockdown of endogenous TG2. Consistent with this, overexpression of TG2 in A431-P cells advanced the EMT process. Furthermore, TG2 induced the PI3K/Akt activation and GSK3β inactivation in A431 tumor cells and this increased Snail and MMP-9 expression resulting in higher cell motility. TG2 also upregulated NF-κB activity, which also enhanced Snail and MMP-9 expression resulting in greater cell motility; interestingly, this was associated with the formation of a TG2/NF-κB complex. TG2 facilitated acquisition of a mesenchymal phenotype, which was reversed by inhibitors of PI3K, GSK3 and NF-κB.</p> <p>Conclusions</p> <p>This study reveals that TG2 acts, at least in part, through activation of the PI3K/Akt and NF-κB signaling systems, which then induce the key mediators Snail and MMP-9 that facilitate the attainment of a mesenchymal phenotype. These findings support the possibility that TG2 is a promising target for cancer therapy.</p

An alternative approach to regularity for the Navier-Stokes equations in critical spaces

In this paper we present an alternative viewpoint on recent studies of regularity of solutions to the Navier-Stokes equations in critical spaces. In particular, we prove that mild solutions which remain bounded in the space $\dot H^{1/2}$ do not become singular in finite time, a result which was proved in a more general setting by L. Escauriaza, G. Seregin and V. Sverak using a different approach. We use the method of "concentration-compactness" + "rigidity theorem" which was recently developed by C. Kenig and F. Merle to treat critical dispersive equations. To the authors' knowledge, this is the first instance in which this method has been applied to a parabolic equation. We remark that we have restricted our attention to a special case due only to a technical restriction, and plan to return to the general case (the $L^3$ setting) in a future publication.Comment: 41 page

Neurochemical Properties of the Synapses in the Pathways of Orofacial Nociceptive Reflexes

The brainstem premotor neurons of the facial nucleus (VII) and hypoglossal (XII) nucleus can integrate orofacial nociceptive input from the caudal spinal trigeminal nucleus (Vc) and coordinate orofacial nociceptive reflex (ONR) responses. However, the synaptoarchitectures of the ONR pathways are still unknown. In the current study, we examined the distribution of GABAergic premotor neurons in the brainstem local ONR pathways, their connections with the Vc projections joining the brainstem ONR pathways and the neurochemical properties of these connections. Retrograde tracer fluoro-gold (FG) was injected into the VII or XII, and anterograde tracer biotinylated dextran amine (BDA) was injected into the Vc. Immunofluorescence histochemical labeling for inhibitory/excitatory neurotransmitters combined with BDA/FG tracing showed that GABAergic premotor neurons were mainly distributed bilaterally in the ponto-medullary reticular formation with an ipsilateral dominance. Some GABAergic premotor neurons made close appositions to the BDA-labeled fibers coming from the Vc, and these appostions were mainly distributed in the parvicellular reticular formation (PCRt), dorsal medullary reticular formation (MdD), and supratrigeminal nucleus (Vsup). We further examined the synaptic relationships between the Vc projecting fibers and premotor neurons in the VII or XII under the confocal laser-scanning microscope and electron microscope, and found that the BDA-labeled axonal terminals that made asymmetric synapses on premotor neurons showed vesicular glutamate transporter 2 (VGluT2) like immunoreactivity. These results indicate that the GABAergic premotor neurons receive excitatory neurotransmission from the Vc and may contribute to modulating the generation of the tonic ONR