On the multiplicity of Laplacian eigenvalues of graphs

summary:In this paper we investigate the effect on the multiplicity of Laplacian eigenvalues of two disjoint connected graphs when adding an edge between them. As an application of the result, the multiplicity of 1 as a Laplacian eigenvalue of trees is also considered

Pinoresinol diglucoside exhibits protective effect on dexamethasone-induced osteoporosis in rats

Purpose: To investigate the effect of pinoresinol diglucoside (PDG) on dexamethasone-induced osteoporosis in rats.Methods: Sixty Wistar rats were randomly and equally divided into normal, control, alendronate and PDG (10, 20 or 40 mg/kg) groups. Bone tissue parameters, including length, transverse diameter, weight, bone mineral content (BMC) and bone mineral density (BMD), were determined using vernier caliper, electronic balance and single photon bone mineral density meter. Serum biochemical indices, including Ca2+, inorganic phosphorus (IP), IL-6, TNF-α and alkaline phosphatase (ALP), were determined using colorimetry and enzyme-linked immunosorbent assay (ELISA). Osteoprotegerin (OPG) and receptor activator of nuclear factor-κB ligand (RANKL) proteins were detected by Western blot.Results: PDG (10, 20 or 40 mg/kg) increased significantly (p < 0.05 or 0.01) transverse diameter (3.64 – 3.79 vs. 3.31 mm), weight (0.73 – 0.78 vs. 0.67 g), BMC (0.16 – 0.23 vs. 0.12 g/cm), BMD (0.27 – 0.35 vs. 0.22 g/cm2) of right femur, serum Ca2+ level (2.16 – 2.39 vs. 1.94 mmol/L), and OPG level of left femur, compared with those in the control group. PDG (10, 20 or 40 mg/kg) reduced significantly (p < 0.05 or 0.01) serum IP (1.34 – 1.14 vs. 1.76 mmol/L), IL-6 (103.25 – 95.38 vs. 108.74 ng/L), TNF-α (87.46 – 82.05 vs. 92.38 ng/L), ALP (334.79 – 276.32 vs. 486.45 U/L) levels or activities, and RANKL level of left femur, compared with those in the control group.Conclusion: PDG exhibits a protective effect on dexamethasone-induced osteoporosis by increasing bone mass and regulating bone metabolism. Thus, PDG may be a candidate drug for treating osteoporosis.Keywords: Pinoresinol diglucoside, Osteoporosis, Bone mass, Bone metabolism, Dexamethasone, Osteoprotegeri

Terretonin, ophiobolin, and drimane terpenes with absolute configurations from an algicolous Aspergillus ustus

One new meroterpene, 1,2-dihydroterretonin F (2), five new sesterterpenes, (6a)-21-deoxyophiobolin G(3), (6a)-16,17-dihydro-21-deoxyophiobolin G (4), phiobolin U (5), ophiobolin V (6), and ophiobolin W (7),two new sesquiterpenes, (6-strobilactone-B) esters of (E,E)-6,7-epoxy-2,4-octadienoic acids (13 and 14),and twelve known terpenes (1, 8–12, and 15–20) were isolated from Aspergillus ustus, a fungus from the fresh tissue of marine green alga Codium fragile. Their structures and absolute configurations were identified by NMR and mass spectroscopic methods as well as quantum chemical calculations. Some of the isolates exhibited antibacterial activity and brine shrimp toxicity.One new meroterpene, 1,2-dihydroterretonin F (2), five new sesterterpenes, (6 alpha)-21-deoxyophiobolin G (3), (6 alpha)-16,17-dihydro-21-deoxyophiobolin G (4), ophiobolin U (5), ophiobolin V (6), and ophiobolin W(7), two new sesquiterpenes, (6-strobilactone-B) esters of (E,E)-6,7-epoxy-2,4-octadienoic acids (13 and 14), and twelve known terpenes (1, 8-12, and 15-20) were isolated from Aspergillus ustus, a fungus from the fresh tissue of marine green alga Codium fragile. Their structures and absolute configurations were identified by NMR and mass spectroscopic methods as well as quantum chemical calculations. Some of the isolates exhibited antibacterial activity and brine shrimp toxicity

Activation of mammalian target of rapamycin mediates rat pain-related responses induced by BmK I, a sodium channel-specific modulator

The mammalian target of rapamycin (mTOR) is known to regulate cell proliferation and growth by controlling protein translation. Recently, it has been shown that mTOR signaling pathway is involved in long-term synaptic plasticity. However, the role of mTOR under different pain conditions is less clear. In this study, the spatiotemporal activation of mTOR that contributes to pain-related behaviors was investigated using a novel animal inflammatory pain model induced by BmK I, a sodium channel-specific modulator purified from scorpion venom. In this study, intraplantar injections of BmK I were found to induce the activation of mTOR, p70 ribosomal S6 protein kinase (p70 S6K) and eukaryotic initiation factor 4E-binding protein 1 (4E-BP1) in rat L5-L6 spinal neurons. In the spinal cord, mTOR, p70 S6K and 4E-BP1 were observed to be activated in the ipsilateral and contralateral regions, peaking at 1-2 h and recovery at 24 h post-intraplantar (i.pl.) BmK I administration. In addition, intrathecal (i.t.) injection of rapamycin - a specific inhibitor of mTOR - was observed to result in the reduction of spontaneous pain responses and the attenuation of unilateral thermal and bilateral mechanical hypersensitivity elicited by BmK I. Thus, these results indicate that the mTOR signaling pathway is mobilized in the induction and maintenance of pain-activated hypersensitivity

Superradiant Solid in Cavity QED Coupled to a Lattice of Rydberg Gas

We study an optical cavity coupled to a lattice of Rydberg atoms, which can be represented by a generalized Dicke model. We show that the competition between the atomic interaction and atom-light coupling induces a rich phase diagram. A novel "superradiant solid" (SRS) phase is found, where both the superradiance and crystalline orders coexist. Different from the normal second order superradiance (SR) transition, here both the Solid-1/2 and SRS to SR phase transitions are first order. These results are confirmed by the large scale quantum Monte Carlo simulations.Comment: 5 pages,4 figure

Multi-parameter Tests of General Relativity Using Bayesian Parameter Estimation with Principal Component Analysis for LISA

In the near future, space-borne gravitational wave (GW) detector LISA can open the window of low-frequency band of GW and provide new tools to test gravity theories. In this work, we consider multi-parameter tests of GW generation and propagation where the deformation coefficients are varied simultaneously in parameter estimation and the principal component analysis (PCA) method are used to transform posterior samples into new bases for extracting the most informative components. The dominant components can be better mesured and constrained and are more sensitive to potential departures from general relativity (GR). We extend previous works by employing Bayesian parameter estimation and performing both null tests and tests with injections of subtle GR-violated signals. We also apply multi-parameter tests with PCA in the phenomenological test of GW propagation. This work complements previous works and further demonstrates the enhancement provided by the PCA method. Considering a supermassive black hole binary system as the GW source, we find that $1\sigma$ bounds of the most dominant PCA parameter can be one order of magnitude tighter than the bounds of original deformation parameter of leading frequency order. The departures less than $1\sigma$ in original parameters can yield significant departures in first 5 dominant PCA parameters.Comment: 16 pages, 6 figure