Maximizing the Total Resolution of Graphs

A major factor affecting the readability of a graph drawing is its resolution. In the graph drawing literature, the resolution of a drawing is either measured based on the angles formed by consecutive edges incident to a common node (angular resolution) or by the angles formed at edge crossings (crossing resolution). In this paper, we evaluate both by introducing the notion of "total resolution", that is, the minimum of the angular and crossing resolution. To the best of our knowledge, this is the first time where the problem of maximizing the total resolution of a drawing is studied. The main contribution of the paper consists of drawings of asymptotically optimal total resolution for complete graphs (circular drawings) and for complete bipartite graphs (2-layered drawings). In addition, we present and experimentally evaluate a force-directed based algorithm that constructs drawings of large total resolution

Classification and nondegeneracy of SU(n+1)SU(n+1) Toda system with singular sources

We consider the following Toda system \Delta u_i + \D \sum_{j = 1}^n a_{ij}e^{u_j} = 4\pi\gamma_{i}\delta_{0} \text{in}\mathbb R^2, \int_{\mathbb R^2}e^{u_i} dx -1$,$\delta_0$is Dirac measure at 0, and the coefficients$a_{ij}$form the standard tri-diagonal Cartan matrix. In this paper, (i) we completely classify the solutions and obtain the quantization result:$$\sum_{j=1}^n a_{ij}\int_{\R^2}e^{u_j} dx = 4\pi (2+\gamma_i+\gamma_{n+1-i}), \;\;\forall\; 1\leq i \leq n.$$This generalizes the classification result by Jost and Wang for$\gamma_i=0$,$\forall \;1\leq i\leq n$. (ii) We prove that if$\gamma_i+\gamma_{i+1}+...+\gamma_j \notin \mathbb Z$for all$1\leq i\leq j\leq n$, then any solution$u_i$ is \textit{radially symmetric} w.r.t. 0. (iii) We prove that the linearized equation at any solution is \textit{non-degenerate}. These are fundamental results in order to understand the bubbling behavior of the Toda system.Comment: 28 page

An improved geometric inequality via vanishing moments, with applications to singular Liouville equations

We consider a class of singular Liouville equations on compact surfaces motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the Gaussian curvature prescription with conical singularities and Onsager's description of turbulence. We analyse the problem of existence variationally, and show how the angular distribution of the conformal volume near the singularities may lead to improvements in the Moser-Trudinger inequality, and in turn to lower bounds on the Euler-Lagrange functional. We then discuss existence and non-existence results.Comment: some references adde

Training Psychologists for Rural Practice: Exploring Opportunities and Constraints

Purpose: To examine trends in the psychologist workforce and training opportunities, including factors that may influence the decision of clinical psychologists to practice in rural settings. Methods: We use a mixed-methods approach to examine the psychologist workforce nationally and in North Carolina (NC), including (1) an analysis of the location of programs awarding doctoral degrees; (2) an analysis of the practice, demographic, and educational characteristics of the psychologist workforce; and (3) interviews with directors of doctoral programs in clinical psychology to understand where current graduates are getting jobs and why they may or may not be choosing to practice in rural communities. Findings: Fewer than 1% of programs and institutions awarding doctoral degrees in psychology in the United States are located in rural areas. In NC, approximately 80% of practicing psychologists have out-of-state degrees and about 80% of recent NC graduates are not currently licensed in the state. This juxtaposition undermines the utility of adding more in-state degree programs. While expansion of training programs within rural areas could help alleviate the shortages of mental health providers, adding new degree-granting programs alone will not necessarily increase supply. We discuss complementary recruitment and retention strategies, including greater incentives for rural training and practice as well as training in emerging technologies that don't require providers to be physically located in underserved areas, such as telemedicine. Conclusions: Increasing the supply of psychologists practicing in rural areas will require a thoughtful, multipronged approach to training this critical part of the behavioral health workforce

C-axis lattice dynamics in Bi-based cuprate superconductors

We present results of a systematic study of the c axis lattice dynamics in single layer Bi2Sr2CuO6 (Bi2201), bilayer Bi2Sr2CaCu2O8 (Bi2212) and trilayer Bi2Sr2Ca2Cu3O10 (Bi2223) cuprate superconductors. Our study is based on both experimental data obtained by spectral ellipsometry on single crystals and theoretical calculations. The calculations are carried out within the framework of a classical shell model, which includes long-range Coulomb interactions and short-range interactions of the Buckingham form in a system of polarizable ions. Using the same set of the shell model parameters for Bi2201, Bi2212 and Bi2223, we calculate the frequencies of the Brillouin-zone center phonon modes of A2u symmetry and suggest the phonon mode eigenvector patterns. We achieve good agreement between the calculated A2u eigenfrequencies and the experimental values of the c axis TO phonon frequencies which allows us to make a reliable phonon mode assignment for all three Bi-based cuprate superconductors. We also present the results of our shell model calculations for the Gamma-point A1g symmetry modes in Bi2201, Bi2212 and Bi2223 and suggest an assignment that is based on the published experimental Raman spectra. The superconductivity-induced phonon anomalies recently observed in the c axis infrared and resonant Raman scattering spectra in trilayer Bi2223 are consistently explained with the suggested assignment.Comment: 29 pages, 13 figure

Quantum saturation and condensation of excitons in Cu2_2O: a theoretical study

Recent experiments on high density excitons in Cu$_2$O provide evidence for degenerate quantum statistics and Bose-Einstein condensation of this nearly ideal gas. We model the time dependence of this bosonic system including exciton decay mechanisms, energy exchange with phonons, and interconversion between ortho (triplet-state) and para (singlet-state) excitons, using parameters for the excitonic decay, the coupling to acoustic and low-lying optical phonons, Auger recombination, and ortho-para interconversion derived from experiment. The single adjustable parameter in our model is the optical-phonon cooling rate for Auger and laser-produced hot excitons. We show that the orthoexcitons move along the phase boundary without crossing it (i.e., exhibit a ``quantum saturation''), as a consequence of the balance of entropy changes due to cooling of excitons by phonons and heating by the non-radiative Auger two-exciton recombination process. The Auger annihilation rate for para-para collisions is much smaller than that for ortho-para and ortho-ortho collisions, explaining why, under the given experimental conditions, the paraexcitons condense while the orthoexcitons fail to do so.Comment: Revised to improve clarity and physical content 18 pages, revtex, figures available from G. Kavoulakis, Physics Department, University of Illinois, Urban

Ownership and control in a competitive industry

We study a differentiated product market in which an investor initially owns a controlling stake in one of two competing firms and may acquire a non-controlling or a controlling stake in a competitor, either directly using her own assets, or indirectly via the controlled firm. While industry profits are maximized within a symmetric two product monopoly, the investor attains this only in exceptional cases. Instead, she sometimes acquires a noncontrolling stake. Or she invests asymmetrically rather than pursuing a full takeover if she acquires a controlling one. Generally, she invests indirectly if she only wants to affect the product market outcome, and directly if acquiring shares is profitable per se. --differentiated products,separation of ownership and control,private benefits of control

Merger rates of dark matter haloes: a comparison between EPS and N-body results

We calculate merger rates of dark matter haloes using the Extended Press-Schechter approximation (EPS) for the Spherical Collapse (SC) and the Ellipsoidal Collapse (EC) models. Merger rates have been calculated for masses in the range $10^{10}M_{\odot}\mathrm{h}^{-1}$ to $10^{14}M_{\odot}\mathrm{h}^{-1}$ and for redshifts $z$ in the range 0 to 3 and they have been compared with merger rates that have been proposed by other authors as fits to the results of N-body simulations. The detailed comparison presented here shows that the agreement between the analytical models and N-body simulations depends crucially on the mass of the descendant halo. For some range of masses and redshifts either SC or EC models approximate satisfactory the results of N-body simulations but for other cases both models are less satisfactory or even bad approximations. We showed, by studying the parameters of the problem that a disagreement --if it appears-- does not depend on the values of the parameters but on the kind of the particular solution used for the distribution of progenitors or on the nature of EPS methods. Further studies could help to improve our understanding about the physical processes during the formation of dark matter haloes.Comment: 29 pages, 9 figure

Search for \bar{B}^0\to\Lambda_c^+\bar{\Lambda}_c^- decay at Belle

We search for the doubly charmed baryonic decay $\bar{B}^0\to\Lambda_c^+\bar{\Lambda}_c^-$, in a data sample of $520\times10^6$ $B{\bar B}$ events accumulated at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric e^+e^- collider. We find no significant signal and set an upper limit of ${\cal B}(\bar{B}^0\to\Lambda_c^+\bar{\Lambda}_c^-)<6.2\times10^{-5}$ at 90% confidence level. The result is significantly below a naive extrapolation from ${\cal B}(B^-\to\Xi_c^0\bar{\Lambda}_c^)$ assuming a simple Cabibbo-suppression factor of $|V_{cd}/V_{cs}|^2$. The small branching fraction could be attributed to a suppression due to the large momentum of the baryonic decay products, which has been observed in other charmed baryonic two-body B decays. trend observed in other charmed baryonic two-body B decays.Comment: 12 page, 5 figures. Contribution paper for conferences EPS2007 and Lepton Photon 2007, Belle-Conference-070

Quantum Interference in Superconducting Wire Networks and Josephson Junction Arrays: Analytical Approach based on Multiple-Loop Aharonov-Bohm Feynman Path-Integrals

We investigate analytically and numerically the mean-field superconducting-normal phase boundaries of two-dimensional superconducting wire networks and Josephson junction arrays immersed in a transverse magnetic field. The geometries we consider include square, honeycomb, triangular, and kagome' lattices. Our approach is based on an analytical study of multiple-loop Aharonov-Bohm effects: the quantum interference between different electron closed paths where each one of them encloses a net magnetic flux. Specifically, we compute exactly the sums of magnetic phase factors, i.e., the lattice path integrals, on all closed lattice paths of different lengths. A very large number, e.g., up to $10^{81}$ for the square lattice, exact lattice path integrals are obtained. Analytic results of these lattice path integrals then enable us to obtain the resistive transition temperature as a continuous function of the field. In particular, we can analyze measurable effects on the superconducting transition temperature, $T_c(B)$, as a function of the magnetic filed $B$, originating from electron trajectories over loops of various lengths. In addition to systematically deriving previously observed features, and understanding the physical origin of the dips in $T_c(B)$ as a result of multiple-loop quantum interference effects, we also find novel results. In particular, we explicitly derive the self-similarity in the phase diagram of square networks. Our approach allows us to analyze the complex structure present in the phase boundaries from the viewpoint of quantum interference effects due to the electron motion on the underlying lattices.Comment: 18 PRB-type pages, plus 8 large figure