Hamiltonicity of 3-arc graphs

An arc of a graph is an oriented edge and a 3-arc is a 4-tuple $(v,u,x,y)$ of vertices such that both $(v,u,x)$ and $(u,x,y)$ are paths of length two. The 3-arc graph of a graph $G$ is defined to have vertices the arcs of $G$ such that two arcs $uv, xy$ are adjacent if and only if $(v,u,x,y)$ is a 3-arc of $G$. In this paper we prove that any connected 3-arc graph is Hamiltonian, and all iterative 3-arc graphs of any connected graph of minimum degree at least three are Hamiltonian. As a consequence we obtain that if a vertex-transitive graph is isomorphic to the 3-arc graph of a connected arc-transitive graph of degree at least three, then it is Hamiltonian. This confirms the well known conjecture, that all vertex-transitive graphs with finitely many exceptions are Hamiltonian, for a large family of vertex-transitive graphs. We also prove that if a graph with at least four vertices is Hamilton-connected, then so are its iterative 3-arc graphs.Comment: in press Graphs and Combinatorics, 201

Dietary Cholesterol Protects Anesthesia-Induced Cognitive Deficits in Wistar Rats

Purpose: To evaluate the effect of cholesterol on frequent exposure of anesthesia-induced cognitive impairment in wistar rats.Methods: Healthy wistar rats were divided in two groups, the gp I rats fed with regular diet and gp II with cholesterol diet. These groups were further divided into sub-groups as gp Ia (n=8) and gp IIa (n=8). These sub-groups received weekly exposure of anesthesia for 6 weeks. Animals were anesthetized by subcutaneous sodium thiopental injection. Cortical nerve growth factor levels were measured by indirect sandwich enzyme-linked immunosorbent assay (ELISA) while total protein was determined by Bradford protein assay.Results: Group IIa (cholesterol-fed animals) as well as Group IIb (cholesterol-fed followed by anesthesia) showed significant increase in body weight (25 to 50 g, p < 0.03), but no such increase was observed in other groups. However, group Ib showed a significant (43.07 %, p ˂ 0.001) decrease in the level of nerve growth factor when compared with group Ia. Moreover, significantly decreased cytokines IL-1β levels (59.09 %, p < 0.005) and TNF-α (20 %, p < 0.025) of group IIa more effectively than in group Ia rats. Microglial marker showed significantly increase (16.66 %, p < 0.025) in cholesterol diet group. Overall increase in leakage of anti-rat IgG (blood brain barrier marker) was found in both groups (IIa and IIb).Conclusion: The results suggest that dietary cholesterol protects or neutralizes anesthesia-induced cognitive deficits in rats.Keywords: Cognitive deficit, Cholesterol diet, Blood-brain barrier, Nerve growth factor, Inflammation marker, Microglial marker, Cytokine

Probing Spin-Flip Scattering in Ballistic Nanosystems

Because spin-flip length is longer than the electron mean-free path in a metal, past studies of spin-flip scattering are limited to the diffusive regime. We propose to use a magnetic double barrier tunnel junction to study spin-flip scattering in the nanometer sized spacer layer near the ballistic limit. We extract the voltage and temperature dependence of the spin-flip conductance Gs in the spacer layer from magnetoresistance measurements. In addition to spin scattering information including the mean-free path (70 nm) and the spin-flip length (1:0–2:6 m) at 4.2 K, this technique also yields information on the density of states and quantum well resonance in the spacer laye

Genetic differentiation in Japanese flounder in the Yellow Sea and East China Sea by amplified fragment length polymorphism (AFLP) and mitochondrial DNA markers

The population structure of Japanese flounder (Paralichthys olivaceus) in the Yellow and East China Seas were analyzed using amplified fragment length polymorphism (AFLP) and cytochrome c oxidase subunit I (COI) gene sequencing. A total of 390 reproducible bands were generated by 10 AFLP primer combinations in two populations collected from the coasts of Qingdao (located at the Yellow Sea) and Zhoushan (located at the East China Sea). The percentage of polymorphic loci (P), Nei’s genetic diversity (H) and Shannon’s information index (I) values were higher in the Qingdao population (P = 72.85%, H = 0.243 and I = 0.364) than those in the Zhoushan population (P = 56.35%, H = 0.189 and I = 0.284). The genetic diversity reduction in the Zhoushan population may be attributed to fishing pressure and habitat loss in this area. Based on the COI sequencing analysis, a total of 25 polymorphic sites were examined, and 15 haplotypes were identified in the two populations. The haplotype diversity (h) and nucleotide diversity (π) values in the Qingdao population were 0.746 ± 0.0728 and 0.00334 ± 0.00103, respectively. The corresponding values in the Zhoushan population were 0.712 ± 0.0470 and 0.00318 ± 0.00049. Both the AFLP and mtDNA data revealed significant genetic differentiation between the two populations. The present study discussed the factors that may result in genetic differentiation between the populations in the Yellow and East China Seas.Keywords: Japanese flounder, amplified fragment length polymorphism (AFLP), cytochrome c oxidase subunit I (COI) gene, genetic diversity, population structur

Obvious enhancement of the total reaction cross sections for 27,28^{27,28}P with 28^{28}Si target and the possible relavent mechanisms

The reaction cross sections of $^{27,28}$P and the corresponding isotones on Si target were measured at intermediate energies. The measured reaction cross sections of the N=12 and 13 isotones show an abrupt increase at $$. The experimental results for the isotones with $Z\leq 14$ as well as $$P can be well described by the modified Glauber theory of the optical limit approach. The enhancement of the reaction cross section for $^{28}$P could be explained in the modified Glauber theory with an enlarged core. Theoretical analysis with the modified Glauber theory of the optical limit and few-body approaches underpredicted the experimental data of $^{27}$P. Our theoretical analysis shows that an enlarged core together with proton halo are probably the mechanism responsible for the enhancement of the cross sections for the reaction of $^{27}$P+$^{28}$Si.Comment: 16 pages, 5 figures, to be published in Phys.Rev.

Extended magic phase in twisted graphene multilayers

Theoretical and experimental studies have verified the existence of ``magic angles'' in twisted bilayer graphene, where the twist between layers gives rise to flat bands and consequently highly correlated phases. Narrow bands can also exist in multilayers with alternating twist angles, and recent theoretical work suggests that they can also be found in trilayers with twist angles between neighboring layers in the same direction. We show here that flat bands exist in a variety of multilayers where the ratio between twist angles is close to coprime integers. We generalize previous analyses, and, using the chiral limit for interlayer coupling, give examples of many combinations of twist angles in stacks made up of three and four layers which lead to flat bands. The technique we use can be extended to systems with many layers. Our results suggest that flat bands can exist in graphene multilayers with angle disorder, that is, narrow samples of turbostatic graphite.Comment: Main text: 4 pages, 4 figures -- Supplementary Material: 15 pages, 13 figure

A comprehensive study of the open cluster NGC 6866

We present CCD $UBVRI$ photometry of the field of the open cluster NGC 6866. Structural parameters of the cluster are determined utilizing the stellar density profile of the stars in the field. We calculate the probabilities of the stars being a physical member of the cluster using their astrometric data and perform further analyses using only the most probable members. The reddening and metallicity of the cluster were determined by independent methods. The LAMOST spectra and the ultraviolet excess of the F and G type main-sequence stars in the cluster indicate that the metallicity of the cluster is about the solar value. We estimated the reddening $E(B-V)=0.074 \pm 0.050$ mag using the $U-B$ vs $B-V$ two-colour diagram. The distance modula, the distance and the age of NGC 6866 were derived as $\mu = 10.60 \pm 0.10$ mag, $d=1189 \pm 75$ pc and $t = 813 \pm 50$ Myr, respectively, by fitting colour-magnitude diagrams of the cluster with the PARSEC isochrones. The Galactic orbit of NGC 6866 indicates that the cluster is orbiting in a slightly eccentric orbit with $e=0.12$. The mass function slope $x=1.35 \pm 0.08$ was derived by using the most probable members of the cluster.Comment: 14 pages, including 16 figures and 7 tables, accepted for publication in MNRAS. Table 4 in the manuscript will be published electronicall