On a conjecture about tricyclic graphs with maximal energy

For a given simple graph $G$, the energy of $G$, denoted by $\mathcal {E}(G)$, is defined as the sum of the absolute values of all eigenvalues of its adjacency matrix, which was defined by I. Gutman. The problem on determining the maximal energy tends to be complicated for a given class of graphs. There are many approaches on the maximal energy of trees, unicyclic graphs and bicyclic graphs, respectively. Let $P^{6,6,6}_n$ denote the graph with $n\geq 20$ vertices obtained from three copies of $C_6$ and a path $P_{n-18}$ by adding a single edge between each of two copies of $C_6$ to one endpoint of the path and a single edge from the third $C_6$ to the other endpoint of the $P_{n-18}$. Very recently, Aouchiche et al. [M. Aouchiche, G. Caporossi, P. Hansen, Open problems on graph eigenvalues studied with AutoGraphiX, {\it Europ. J. Comput. Optim.} {\bf 1}(2013), 181--199] put forward the following conjecture: Let $G$ be a tricyclic graphs on $n$ vertices with $n=20$ or $n\geq22$, then $\mathcal{E}(G)\leq \mathcal{E}(P_{n}^{6,6,6})$ with equality if and only if $G\cong P_{n}^{6,6,6}$. Let $G(n;a,b,k)$ denote the set of all connected bipartite tricyclic graphs on $n$ vertices with three vertex-disjoint cycles $C_{a}$, $C_{b}$ and $C_{k}$, where $n\geq 20$. In this paper, we try to prove that the conjecture is true for graphs in the class $G\in G(n;a,b,k)$, but as a consequence we can only show that this is true for most of the graphs in the class except for 9 families of such graphs.Comment: 32 pages, 12 figure

Anomalous thermoelectric transport of Dirac particles in graphene

We report a thermoelectric study of graphene in both zero and applied magnetic fields. As a direct consequence of the linear dispersion of massless particles, we find that the Seebeck coefficient Sxx diverges with 1 /, where n2D is the carrier density. We observe a very large Nernst signal Sxy (~ 50 uV/K at 8 T) at the Dirac point, and an oscillatory dependence of both Sxx and Sxy on n2D at low temperatures. Our results underscore the anomalous thermoelectric transport in graphene, which may be used as a highly sensitive probe for impurity bands near the Dirac point

Spin Seebeck effect from antiferromagnetic magnons and critical spin fluctuations in epitaxial FeF2 films

We report a longitudinal spin Seebeck effect (SSE) study in epitaxially grown FeF2(110) antiferromagnetic (AFM) thin films with strong uniaxial anisotropy over the temperature range of 3.8 - 250 K. Both the magnetic field- and temperature-dependent SSE signals below the N\'eel temperature (TN=70 K) of the FeF2 films are consistent with a theoretical model based on the excitations of AFM magnons without any net induced static magnetic moment. In addition to the characteristic low-temperature SSE peak associated with the AFM magnons, there is another SSE peak at TN which extends well into the paramagnetic phase. All the SSE data taken at different magnetic fields up to 12 T near and above the critical point TN follow the critical scaling law very well with the critical exponents for magnetic susceptibility of 3D Ising systems, which suggests that the AFM spin correlation is responsible for the observed SSE near TN

Field-effect mobility enhanced by tuning the Fermi level into the band gap of Bi2Se3

By eliminating normal fabrication processes, we preserve the bulk insulating state of calcium-doped Bi2Se3 single crystals in suspended nanodevices, as indicated by the activated temperature dependence of the resistivity at low temperatures. We perform low-energy electron beam irradiation (<16 keV) and electrostatic gating to control the carrier density and therefore the Fermi level position in the nanodevices. In slightly p-doped Bi2-xCaxSe3 devices, continuous tuning of the Fermi level from the bulk valence band to the band-gap reveals dramatic enhancement (> a factor of 10) in the field-effect mobility, which suggests suppressed backscattering expected for the Dirac fermion surface states in the gap of topological insulators

A thermodynamically consistent quasi-particle model without density-dependent infinity of the vacuum zero point energy

In this paper, we generalize the improved quasi-particle model proposed in J. Cao et al., [ Phys. Lett. B {\bf711}, 65 (2012)] from finite temperature and zero chemical potential to the case of finite chemical potential and zero temperature, and calculate the equation of state (EOS) for (2+1) flavor Quantum Chromodynamics (QCD) at zero temperature and high density. We first calculate the partition function at finite temperature and chemical potential, then go to the limit $T=0$ and obtain the equation of state (EOS) for cold and dense QCD, which is important for the study of neutron stars. Furthermore, we use this EOS to calculate the quark-number density, the energy density, the quark-number susceptibility and the speed of sound at zero temperature and finite chemical potential and compare our results with the corresponding ones in the existing literature

Systems Biology of Gastric Cancer: Perspectives on the Omics-Based Diagnosis and Treatment

Gastric cancer is the fifth most diagnosed cancer in the world, affecting more than a million people and causing nearly 783,000 deaths each year. The prognosis of advanced gastric cancer remains extremely poor despite the use of surgery and adjuvant therapy. Therefore, understanding the mechanism of gastric cancer development, and the discovery of novel diagnostic biomarkers and therapeutics are major goals in gastric cancer research. Here, we review recent progress in application of omics technologies in gastric cancer research, with special focus on the utilization of systems biology approaches to integrate multi-omics data. In addition, the association between gastrointestinal microbiota and gastric cancer are discussed, which may offer insights in exploring the novel microbiota-targeted therapeutics. Finally, the application of data-driven systems biology and machine learning approaches could provide a predictive understanding of gastric cancer, and pave the way to the development of novel biomarkers and rational design of cancer therapeutics

Independent tuning of electronic properties and induced ferromagnetism in topological insulators with heterostructure approach

The quantum anomalous Hall effect (QAHE) has been recently demonstrated in Cr- and V-doped three-dimensional topological insulators (TIs) at temperatures below 100 mK. In those materials, the spins of unfilled d-electrons in the transition metal dopants are exchange coupled to develop a long-range ferromagnetic order, which is essential for realizing QAHE. However, the addition of random dopants does not only introduce excess charge carriers that require readjusting the Bi/Sb ratio, but also unavoidably introduces paramagnetic spins that can adversely affect the chiral edge transport in QAHE. In this work, we show a heterostructure approach to independently tune the electronic and magnetic properties of the topological surface states in (BixSb1-x)2Te3 without resorting to random doping of transition metal elements. In heterostructures consisting of a thin (BixSb1-x)2Te3 TI film and yttrium iron garnet (YIG), a high Curie temperature (~ 550 K) magnetic insulator, we find that the TI surface in contact with YIG becomes ferromagnetic via proximity coupling which is revealed by the anomalous Hall effect (AHE). The Curie temperature of the magnetized TI surface ranges from 20 to 150 K but is uncorrelated with the Bi fraction x in (BixSb1-x)2Te3. In contrast, as x is varied, the AHE resistivity scales with the longitudinal resistivity. In this approach, we decouple the electronic properties from the induced ferromagnetism in TI. The independent optimization provides a pathway for realizing QAHE at higher temperatures, which is important for novel spintronic device applications.Comment: Accepted by Nano Letter