Balanced and 1-balanced graph constructions

AbstractThere are several density functions for graphs which have found use in various applications. In this paper, we examine two of them, the first being given by b(G)=|E(G)|/|V(G)|, and the other being given by g(G)=|E(G)|/(|V(G)|−ω(G)), where ω(G) denotes the number of components of G. Graphs for which b(H)≤b(G) for all subgraphs H of G are called balanced graphs, and graphs for which g(H)≤g(G) for all subgraphs H of G are called 1-balanced graphs (also sometimes called strongly balanced or uniformly dense in the literature). Although the functions b and g are very similar, they distinguish classes of graphs sufficiently differently that b(G) is useful in studying random graphs, g(G) has been useful in designing networks with reduced vulnerability to attack and in studying the World Wide Web, and a similar function is useful in the study of rigidity. First we give a new characterization of balanced graphs. Then we introduce a graph construction which generalizes the Cartesian product of graphs to produce what we call a generalized Cartesian product. We show that generalized Cartesian product derived from a tree and 1-balanced graphs are 1-balanced, and we use this to prove that the generalized Cartesian products derived from 1-balanced graphs are 1-balanced

Highly efficient free-space fiber coupler with 45° tilted fiber grating to access remotely placed optical fiber sensors

In this work, a 45° tilted fiber grating (TFG) is used as a waveguide coupler for the development of a portable interrogation system to access remotely placed optical fiber sensors. The TFG is directly connected to a remote fiber sensor and serves as a highly efficient light coupler between the portable interrogation unit and the sensor. Variation of strain and temperatures are measured with a standard fiber Bragg grating (FBG) sensor, which serves as a remotely placed optical sensor. A light beam from the interrogation unit is coupled into the TFG by a system of lenses, mirrors and optical collimator and acted as the input of the FBG. Reflected light from the FBG sensor is coupled back to the interrogation unit via the same TFG. The TFG is being used as a receiver and transmitter of light and constituent the key part of the system to connect “light source to the optical sensor” and “optical sensor to detector.” A successful demonstration of the developed system for strain and temperature sensing applications have been presented and discussed. Signal to noise ratio of the reflected light from the sensors was greater than ∼ 40 dB

Improved field emission performance of carbon nanotube by introducing copper metallic particles

To improve the field emission performance of carbon nanotubes (CNTs), a simple and low-cost method was adopted in this article. We introduced copper particles for decorating the CNTs so as to form copper particle-CNT composites. The composites were fabricated by electrophoretic deposition technique which produced copper metallic particles localized on the outer wall of CNTs and deposited them onto indium tin oxide (ITO) electrode. The results showed that the conductivity increased from 10-5 to 4 × 10-5 S while the turn-on field was reduced from 3.4 to 2.2 V/μm. Moreover, the field emission current tended to be undiminished after continuous emission for 24 h. The reasons were summarized that introducing copper metallic particles to decorate CNTs could increase the surface roughness of the CNTs which was beneficial to field emission, restrain field emission current from saturating when the applied electric field was above the critical field. In addition, it could also improve the electrical contact by increasing the contact area between CNT and ITO electrode that was beneficial to the electron transport and avoided instable electron emission caused by thermal injury of CNTs

Atomic-scale visualization of quasiparticle interference on a type-II Weyl semimetal surface

We combine quasiparticle interference simulation (theory) and atomic resolution scanning tunneling spectro-microscopy (experiment) to visualize the interference patterns on a type-II Weyl semimetal Mo$_{x}$W$_{1-x}$Te$_2$ for the first time. Our simulation based on first-principles band topology theoretically reveals the surface electron scattering behavior. We identify the topological Fermi arc states and reveal the scattering properties of the surface states in Mo$_{0.66}$W$_{0.34}$Te$_2$. In addition, our result reveals an experimental signature of the topology via the interconnectivity of bulk and surface states, which is essential for understanding the unusual nature of this material.Comment: To appear in Phys. Rev. Let

Discovery of Lorentz-violating Weyl fermion semimetal state in LaAlGe materials

We report theoretical and experimental discovery of Lorentz-violating Weyl fermion semimetal type-II state in the LaAlGe class of materials. Previously type-II Weyl state was predicted in WTe2 materials which remains unrealized in surface experiments. We show theoretically and experimentally that LaAlGe class of materials are the robust platforms for the study of type-II Weyl physics.Comment: This paper reports theoretical prediction and experimental discovery together. A detailed theoretical paper describing the topology of the full family of X(Lanthanides)AlGe materials will follow. Other related papers can be found at http://physics.princeton.edu/zahidhasangroup/index_WS.htm

Original Article One stage laminoplasty and posterior herniotomy for the treatment of myelopathy caused by cervical stenosis with cervical disc herniation

Abstract: The aim of the study was to introduce a method of one stage laminoplasty and posterior herniotomy for myelopathy caused by cervical stenosis with cervical disc herniation and to evaluate the clinical efficacy of this surgery. From 1999 to 2008, 18 patients with myelopathy caused by cervical stenosis with cervical disc herniation who underwent this procedure were included. The average age was 63 years (range 48-74 years), and the average follow-up period was 46 months (range 3-108 months). Neurologic status was evaluated using the JOA scoring system. Neurological symptoms improvement was seen in all patients after surgery. The average JOA score was 14.22±1.86 by final follow-up, which was higher than preoperative values (P<0.01), and the average improvement in neurological function was 76.63%. Neurologic examination showed that excellent results had been obtained by 10 patients, good results by 8 patients, with no fair or poor results. 2 patients developed cerebrospinal fluid leakage after surgery and recovered during the follow-up period. One patient with cervical disc herniation developed postoperative C5 palsy on the axle side on the third day after surgery. She completely recovered by 1 month after surgery. No other patients experienced postoperative neurologic complications. Complete anterior and posterior decompression of the spinal cord was achieved after surgery. We concluded that one stage laminoplasty and posterior herniotomy is an effective, reliable, and safe procedure for the treatment of myelopathy caused by cervical stenosis with cervical disc herniation

MACROD1/LRP16 Enhances LPS-Stimulated Inflammatory Responses by Up-Regulating a Rac1-Dependent Pathway in Adipocytes

Background/Aims: Chronic inflammation contributes to the development of type 2 diabetes mellitus by targeting the insulin receptor substrate protein-1 (IRS-1) signaling pathway. Previous studies showed that Leukemia related protein 16 (LRP16) reduced insulin stimulated glucose uptake in adipocytes by impairing the IRS-1 signaling pathway. We explored the mechanism by which LRP16 promotes the inflammatory response. Methods: We screened LRP16 induced proteins in the lipopolysaccharide (LPS)-stimulated inflammatory response using liquid chromatography-mass spectrometry (LC-MS) and analyzed the potential biological functions of these proteins using online bioinformatics tools. mRNA expression and protein expression of target genes were measured by real time PCR and Western blot, respectively. Results: A total of 390 differentially expressed proteins were identified. The mitogen-activated protein kinase (MAPK) signaling pathway was the primary activated pathway in LRP16-expressing cells. Overexpression of LRP16 activated ERK1/2 and Rac1, which are two key players related to the MAPK signaling pathway. Furthermore, knock down of endogenous LRP16 by RNA interference (RNAi) reduced Rac1 expression, ERK activation, and inflammatory cytokine expression in human adipocytes stimulated by LPS. The stimulatory effect of LRP16 was diminished by suppressing Rac1 expression and treating the cells with the ERK specific inhibitor, PD98059. Conclusion: These findings revealed the functions of LRP16 in promoting the inflammatory response through activating the Rac1-MAPK1/ERK pathway in human adipocytes

Effects of tumor necrosis factor-α polymorphism on the brain structural changes of the patients with major depressive disorder

Single Nucleotide Polymorphic (SNP) variations of proinflammatory cytokines such as Tumor Necrosis Factor-α (TNF-α) have been reported to be closely associated with the major depressive disorder (MDD). However, it is unclear if proinflammatory genetic burden adversely affects the regional gray matter volume in patients with MDD. The aim of this study was to test whether rs1799724, an SNP of TNF-α, contributes to the neuroanatomical changes in MDD. In this cross-sectional study, a total of 144 MDD patients and 111 healthy controls (HC) well matched for age, sex and education were recruited from Shanghai Mental Health Center. Voxel-based morphometry (VBM) followed by graph theory based structural covariance analysis was applied to locate diagnosis x genotype interactions. Irrespective of diagnosis, individuals with the high-risk genotype (T-carriers) had reduced volume in left angular gyrus (main effect of genotype). Diagnosis x genotype interaction was exclusively localized to the visual cortex (right superior occipital gyrus). The same region also showed reduced volume in patients with MDD than HC (main effect of diagnosis), with this effect being most pronounced in patients carrying the high-risk genotype. However, neither global nor regional network of structural covariance was found to have group difference. In conclusion, a genetic variation which can increase TNF-α expression selectively affects the anatomy of the visual cortex among the depressed subjects, with no effect on the topographical organization of multiple cortical regions. This supports the notion that anatomical changes in depression are in part influenced by the genetic determinants of inflammatory activity

Straw and phosphorus applications promote maize (Zea mays L.) growth in saline soil through changing soil carbon and phosphorus fractions

IntroductionStraw return has been widely recognized as an important carbon (C) enhancement measure in agroecosystems, but the C-phosphorus (P) interactions and their effects on plants in saline soils are still unclear.MethodsIn this study, we investigated the effects of straw return and three P application levels, no P fertilizer (Non-P), a conventional application rate of P fertilizer (CP), and a high application rate of P fertilizer (HP), on maize growth and soil C and P fractions through a pot experiment.Results and discussionThe results revealed that the dry matter weight of maize plant was no difference between the two straw return levels and was 15.36% higher under HP treatments than under Non-P treatments. Plant nutrient accumulations were enhanced by straw addition and increased with increasing P application rate. Straw application reduced the activities of peroxidase (POD), superoxide dismutase (SOD), catalase, and the content of malondialdehyde (MDA) in maize plants by 31.69%, 38.99%, 45.96% and 27.04%, respectively. P application decreased SOD, POD activities and MDA content in the absence of straw. The contents of easily oxidized organic carbon (EOC), particulate organic carbon (POC) and the ratio of POC/SOC in straw-added soils were 10.23%, 17.00% and 7.27% higher, respectively, than those in straw-absent soils. Compared with Non-P treatments, HP treatments led to an increase of 12.05%, 23.04% in EOC, POC contents respectively, while a decrease of 18.12% in the contribution of MAOC to the SOC pool. Straw return improved the P status of the saline soil by increasing soil available P (14.80%), organic P (35.91%) and Ca2-P contents (4.68%). The structural equation model showed that straw and P applications could promote maize growth (indicated by dry matter weight, P accumulation, antioxidant enzyme activity and MDA content) through improving soil C and P availabilities.ConclusionThis study provides evidence that straw return together with adequate P supply in saline soil can promote crop nutrient accumulation, attenuate the oxidation damage on crop growth, and be beneficial for SOC turnover and soil P activation