The Minimum Wiener Connector

The Wiener index of a graph is the sum of all pairwise shortest-path distances between its vertices. In this paper we study the novel problem of finding a minimum Wiener connector: given a connected graph $G=(V,E)$ and a set $Q\subseteq V$ of query vertices, find a subgraph of $G$ that connects all query vertices and has minimum Wiener index. We show that The Minimum Wiener Connector admits a polynomial-time (albeit impractical) exact algorithm for the special case where the number of query vertices is bounded. We show that in general the problem is NP-hard, and has no PTAS unless $\mathbf{P} = \mathbf{NP}$. Our main contribution is a constant-factor approximation algorithm running in time $\widetilde{O}(|Q||E|)$. A thorough experimentation on a large variety of real-world graphs confirms that our method returns smaller and denser solutions than other methods, and does so by adding to the query set $Q$ a small number of important vertices (i.e., vertices with high centrality).Comment: Published in Proceedings of the 2015 ACM SIGMOD International Conference on Management of Dat

Supermetallic conductivity in bromine-intercalated graphite

Exposure of highly oriented pyrolytic graphite to bromine vapor gives rise to in-plane charge conductivities which increase monotonically with intercalation time toward values (for ~6 at% Br) that are significantly higher than Cu at temperatures down to 5 K. Magnetotransport, optical reflectivity and magnetic susceptibility measurements confirm that the Br dopes the graphene sheets with holes while simultaneously increasing the interplanar separation. The increase of mobility (~ 5E4 cm^2/Vs at T=300 K) and resistance anisotropy together with the reduced diamagnetic susceptibility of the intercalated samples suggests that the observed supermetallic conductivity derives from a parallel combination of weakly-coupled hole-doped graphene sheets.Comment: 5 pages, 4 figure

Conserved cosmological structures in the one-loop superstring effective action

A generic form of low-energy effective action of superstring theories with one-loop quantum correction is well known. Based on this action we derive the complete perturbation equations and general analytic solutions in the cosmological spacetime. Using the solutions we identify conserved quantities characterizing the perturbations: the amplitude of gravitational wave and the perturbed three-space curvature in the uniform-field gauge both in the large-scale limit, and the angular-momentum of rotational perturbation are conserved independently of changing gravity sector. Implications for calculating perturbation spectra generated in the inflation era based on the string action are presented.Comment: 5 pages, no figure, To appear in Phys. Rev.

Spectral dimensions of hierarchical scale-free networks with shortcuts

The spectral dimension has been widely used to understand transport properties on regular and fractal lattices. Nevertheless, it has been little studied for complex networks such as scale-free and small world networks. Here we study the spectral dimension and the return-to-origin probability of random walks on hierarchical scale-free networks, which can be either fractals or non-fractals depending on the weight of shortcuts. Applying the renormalization group (RG) approach to the Gaussian model, we obtain the spectral dimension exactly. While the spectral dimension varies between $1$ and $2$ for the fractal case, it remains at $2$, independent of the variation of network structure for the non-fractal case. The crossover behavior between the two cases is studied through the RG flow analysis. The analytic results are confirmed by simulation results and their implications for the architecture of complex systems are discussed.Comment: 10 pages, 3 figure

Cosmological perturbations in a gravity with quadratic order curvature couplings

We present a set of equations describing the evolution of the scalar-type cosmological perturbation in a gravity with general quadratic order curvature coupling terms. Equations are presented in a gauge ready form, thus are ready to implement various temporal gauge conditions depending on the problems. The Ricci-curvature square term leads to a fourth-order differential equation for describing the spacetime fluctuations in a spatially homogeneous and isotropic cosmological background.Comment: 5 pages, no figure, To appear in Phys. Rev.

COBE constraints on inflation models with a massive non-minimal scalar field

We derive power spectra of the scalar- and tensor-type structures generated in an inflation model based on a massive non-minimally coupled scalar field with the strong coupling assumption. We make analyses in both the original-frame and the conformally transformed Einstein-frame. We derive contributions of both structures to the anisotropy of the cosmic microwave background radiation, and compare the contributions with the four-year COBE-DMR data. Previous study showed that sufficient amount of inflation requires a small coupling parameter. In such a case the spectra become near Zeldovich spectra, and the gravitational wave contribution becomes negligible compared with the scalar-type contribution which is testable in future CMBR experiments.Comment: 4 pages, no figure, To appear in Phys. Rev.

Free Energy Approach to the Formation of an Icosahedral Structure during the Freezing of Gold Nanoclusters

The freezing of metal nanoclusters such as gold, silver, and copper exhibits a novel structural evolution. The formation of the icosahedral (Ih) structure is dominant despite its energetic metastability. This important phenomenon, hitherto not understood, is studied by calculating free energies of gold nanoclusters. The structural transition barriers have been determined by using the umbrella sampling technique combined with molecular dynamics simulations. Our calculations show that the formation of Ih gold nanoclusters is attributed to the lower free energy barrier from the liquid to the Ih phases compared to the barrier from the liquid to the face-centered-cubic crystal phases

Graphene Transport at High Carrier Densities using a Polymer Electrolyte Gate

We report the study of graphene devices in Hall-bar geometry, gated with a polymer electrolyte. High densities of 6 $\times 10^{13}/cm^{2}$ are consistently reached, significantly higher than with conventional back-gating. The mobility follows an inverse dependence on density, which can be correlated to a dominant scattering from weak scatterers. Furthermore, our measurements show a Bloch-Gr\"uneisen regime until 100 K (at 6.2 $\times10^{13}/cm^{2}$), consistent with an increase of the density. Ubiquitous in our experiments is a small upturn in resistivity around 3 $\times10^{13}/cm^{2}$, whose origin is discussed. We identify two potential causes for the upturn: the renormalization of Fermi velocity and an electrochemically-enhanced scattering rate.Comment: 13 pages, 4 figures, Published Versio

Equilibrium orbit analysis in a free-electron laser with a coaxial wiggler

An analysis of single-electron orbits in combined coaxial wiggler and axial guide magnetic fields is presented. Solutions of the equations of motion are developed in a form convenient for computing orbital velocity components and trajectories in the radially dependent wiggler. Simple analytical solutions are obtained in the radially-uniform-wiggler approximation and a formula for the derivative of the axial velocity $v_{\|}$ with respect to Lorentz factor $\gamma$ is derived. Results of numerical computations are presented and the characteristics of the equilibrium orbits are discussed. The third spatial harmonic of the coaxial wiggler field gives rise to group $III$ orbits which are characterized by a strong negative mass regime.Comment: 13 pages, 9 figures, to appear in phys. rev.

Formation of an Icosahedral Structure during the Freezing of Gold Nanoclusters: Surface-Induced Mechanism

The freezing behavior of gold nanoclusters was studied by employing molecular dynamics simulations based on a semi-empirical embedded-atom method. Investigations of the gold nanoclusters revealed that, just after freezing, ordered nano-surfaces with a fivefold symmetry were formed with interior atoms remaining in the disordered state. Further lowering of temperatures induced nano-crystallization of the interior atoms that proceeded from the surface towards the core region, finally leading to an icosahedral structure. These dynamic processes explain why the icosahedral cluster structure is dominantly formed in spite of its energetic metastability.Comment: 9 pages, 4 figures(including 14 eps-files