A Characterization of Uniquely Representable Graphs

The betweenness structure of a finite metric space $M = (X, d)$ is a pair $\mathcal{B}(M) = (X,\beta_M)$ where $\beta_M$ is the so-called betweenness relation of $M$ that consists of point triplets $(x, y, z)$ such that $d(x, z) = d(x, y) + d(y, z)$. The underlying graph of a betweenness structure $\mathcal{B} = (X,\beta)$ is the simple graph $G(\mathcal{B}) = (X, E)$ where the edges are pairs of distinct points with no third point between them. A connected graph $G$ is uniquely representable if there exists a unique metric betweenness structure with underlying graph $G$. It was implied by previous works that trees are uniquely representable. In this paper, we give a characterization of uniquely representable graphs by showing that they are exactly the block graphs. Further, we prove that two related classes of graphs coincide with the class of block graphs and the class of distance-hereditary graphs, respectively. We show that our results hold not only for metric but also for almost-metric betweenness structures.Comment: 16 pages (without references); 3 figures; major changes: simplified proofs, improved notations and namings, short overview of metric graph theor

Phase transitions for rock-scissors-paper game on different networks

Monte Carlo simulations and dynamical mean-field approximations are performed to study the phase transitions in rock-scissors-paper game on different host networks. These graphs are originated from lattices by introducing quenched and annealed randomness simultaneously. In the resulting phase diagrams three different stationary states are identified for all structures. The comparison of results on different networks suggests that the value of clustering coefficient plays an irrelevant role in the emergence of a global oscillating phase. The critical behavior of phase transitions seems to be universal and can be described by the same exponents.Comment: 4 pages, 4 figures, to be published in PR

ExoMol line lists XXXI: Spectroscopy of lowest eights electronic states of C2_2

Accurate line lists for the carbon dimer, C$_2$, are presented. These line lists cover rovibronic transitions between the eight lowest electronic states: $X\,{}^{1}\Sigma_{g}^{+}$, $a\,{}^{3}\Pi_{u}$, $A\,{}^{1}\Pi_{u}$, b\,^{3}\Sigma_{g}^{-}, b\,^{3}\Sigma_{g}^{-}, c\,^{3}\Sigma_{u}^{+}, $d\,{}^{3}\Pi_{g}$, $B\,{}^{1}\Delta_{g}$, $B^\prime\,{}^{1}\Sigma_{g}^{+}$. Potential energy curves (PECs) and transition dipole moment curves are computed on a large grid of geometries using the aug-cc-pwCVQZ-DK/MRCI level of theory including core and core-valence correlations and scalar relativistic energy corrections. The same level of theory is used to compute spin-orbit and electronic angular momentum couplings. The PECs and couplings are refined by fitting to the empirical (MARVEL) energies of $^{12}$C$_2$ using the nuclear-motion program Duo. The transition dipole moment curves are represented as analytical functions to reduce the numerical noise when computing transition line strengths. Partition functions, full line lists, Land\'{e}-factors and lifetimes for three main isotopologues of C$_2$ ($^{12}$C$_2$,$^{13}$C$_2$ and $^{12}$C$^{13}$C) are made available in electronic form from the CDS (http://cdsarc.u-strasbg.fr) and ExoMol (www.exomol.com) databases

Causation, Measurement Relevance and No-conspiracy in EPR

In this paper I assess the adequacy of no-conspiracy conditions employed in the usual derivations of the Bell inequality in the context of EPR correlations. First, I look at the EPR correlations from a purely phenomenological point of view and claim that common cause explanations of these cannot be ruled out. I argue that an appropriate common cause explanation requires that no-conspiracy conditions are re-interpreted as mere common cause-measurement independence conditions. In the right circumstances then, violations of measurement independence need not entail any kind of conspiracy (nor backwards in time causation). To the contrary, if measurement operations in the EPR context are taken to be causally relevant in a specific way to the experiment outcomes, their explicit causal role provides the grounds for a common cause explanation of the corresponding correlations.Comment: 20 pages, 1 figur

Closed classes of functions, generalized constraints and clusters

Classes of functions of several variables on arbitrary non-empty domains that are closed under permutation of variables and addition of dummy variables are characterized in terms of generalized constraints, and hereby Hellerstein's Galois theory of functions and generalized constraints is extended to infinite domains. Furthermore, classes of operations on arbitrary non-empty domains that are closed under permutation of variables, addition of dummy variables and composition are characterized in terms of clusters, and a Galois connection is established between operations and clusters.Comment: 21 page

Vortex dynamics in a three-state model under cyclic dominance

The evolution of domain structure is investigated in a two-dimensional voter model with three states under cyclic dominance. The study focus on the dynamics of vortices, defined by the points where three states (domains) meet. We can distinguish vortices and antivortices which walk randomly and annihilate each other. The domain wall motion can create vortex-antivortex pairs at a rate which is increased by the spiral formation due to the cyclic dominance. This mechanism is contrasted with a branching annihilating random walk (BARW) in a particle antiparticle system with density dependent pair creation rate. Numerical estimates for the critical indices of the vortex density ($\beta=0.29(4)$) and of its fluctuation ($\gamma=0.34(6)$) improve an earlier Monte Carlo study [Tainaka and Itoh, Europhys. Lett. 15, 399 (1991)] of the three-state cyclic voter model in two dimensions.Comment: 5 pages, 6 figures, to appear in PR