Optimal strategies for a game on amenable semigroups

The semigroup game is a two-person zero-sum game defined on a semigroup S as follows: Players 1 and 2 choose elements x and y in S, respectively, and player 1 receives a payoff f(xy) defined by a function f from S to [-1,1]. If the semigroup is amenable in the sense of Day and von Neumann, one can extend the set of classical strategies, namely countably additive probability measures on S, to include some finitely additive measures in a natural way. This extended game has a value and the players have optimal strategies. This theorem extends previous results for the multiplication game on a compact group or on the positive integers with a specific payoff. We also prove that the procedure of extending the set of allowed strategies preserves classical solutions: if a semigroup game has a classical solution, this solution solves also the extended game.Comment: 17 pages. To appear in International Journal of Game Theor

Conflict-free connection numbers of line graphs

A path in an edge-colored graph is called \emph{conflict-free} if it contains at least one color used on exactly one of its edges. An edge-colored graph $G$ is \emph{conflict-free connected} if for any two distinct vertices of $G$, there is a conflict-free path connecting them. For a connected graph $G$, the \emph{conflict-free connection number} of $G$, denoted by $cfc(G)$, is defined as the minimum number of colors that are required to make $G$ conflict-free connected. In this paper, we investigate the conflict-free connection numbers of connected claw-free graphs, especially line graphs. We first show that for an arbitrary connected graph $G$, there exists a positive integer $k$ such that $cfc(L^k(G))\leq 2$. Secondly, we get the exact value of the conflict-free connection number of a connected claw-free graph, especially a connected line graph. Thirdly, we prove that for an arbitrary connected graph $G$ and an arbitrary positive integer $k$, we always have $cfc(L^{k+1}(G))\leq cfc(L^k(G))$, with only the exception that $G$ is isomorphic to a star of order at least~$5$ and $k=1$. Finally, we obtain the exact values of $cfc(L^k(G))$, and use them as an efficient tool to get the smallest nonnegative integer $k_0$ such that $cfc(L^{k_0}(G))=2$.Comment: 11 page

Quantum entanglement between a nonlinear nanomechanical resonator and a microwave field

We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semi-classical approximation of this system has an interesting fixed point bifurcation structure. In the semi-classical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positive to negative detuning. We show that signatures of this bifurcation structure are also present in the full dissipative quantum system and further show that it leads to mixed state entanglement between the nanomechanical resonator and the microwave cavity in the dissipative quantum system that is a maximum close to the semi-classical bifurcation. Quantum signatures of the semi-classical limit-cycles are presented.Comment: 36 pages, 18 figure

Parallel Mapper

The construction of Mapper has emerged in the last decade as a powerful and effective topological data analysis tool that approximates and generalizes other topological summaries, such as the Reeb graph, the contour tree, split, and joint trees. In this paper, we study the parallel analysis of the construction of Mapper. We give a provably correct parallel algorithm to execute Mapper on multiple processors and discuss the performance results that compare our approach to a reference sequential Mapper implementation. We report the performance experiments that demonstrate the efficiency of our method

Emergence of Symmetry in Complex Networks

Many real networks have been found to have a rich degree of symmetry, which is a very important structural property of complex network, yet has been rarely studied so far. And where does symmetry comes from has not been explained. To explore the mechanism underlying symmetry of the networks, we studied statistics of certain local symmetric motifs, such as symmetric bicliques and generalized symmetric bicliques, which contribute to local symmetry of networks. We found that symmetry of complex networks is a consequence of similar linkage pattern, which means that nodes with similar degree tend to share similar linkage targets. A improved version of BA model integrating similar linkage pattern successfully reproduces the symmetry of real networks, indicating that similar linkage pattern is the underlying ingredient that responsible for the emergence of the symmetry in complex networks.Comment: 7 pages, 7 figure

Sometimes Sperm Whales (Physeter macrocephalus) Cannot Find Their Way Back to the High Seas: A Multidisciplinary Study on a Mass Stranding

BACKGROUND: Mass strandings of sperm whales (Physeter macrocephalus) remain peculiar and rather unexplained events, which rarely occur in the Mediterranean Sea. Solar cycles and related changes in the geomagnetic field, variations in water temperature and weather conditions, coast geographical features and human activities have been proposed as possible causes. In December 2009, a pod of seven male sperm whales stranded along the Adriatic coast of Southern Italy. This is the sixth instance from 1555 in this basin. METHODOLOGY/PRINCIPAL FINDINGS: Complete necropsies were performed on three whales whose bodies were in good condition, carrying out on sampled tissues histopathology, virology, bacteriology, parasitology, and screening of veins looking for gas emboli. Furthermore, samples for age determination, genetic studies, gastric content evaluation, stable isotopes and toxicology were taken from all the seven specimens. The animals were part of the same group and determined by genetic and photo-identification to be part of the Mediterranean population. Causes of death did not include biological agents, or the "gas and fat embolic syndrome", associated with direct sonar exposure. Environmental pollutant tissue concentrations were relatively high, in particular organochlorinated xenobiotics. Gastric content and morphologic tissue examinations showed a prolonged starvation, which likely caused, at its turn, the mobilization of lipophilic contaminants from the adipose tissue. Chemical compounds subsequently entered the blood circulation and may have impaired immune and nervous functions. CONCLUSIONS/SIGNIFICANCE: A multi-factorial cause underlying this sperm whales' mass stranding is proposed herein based upon the results of postmortem investigations as well as of the detailed analyses of the geographical and historical background. The seven sperm whales took the same "wrong way" into the Adriatic Sea, a potentially dangerous trap for Mediterranean sperm whales. Seismic surveys should be also regarded as potential co-factors, even if no evidence of direct impact has been detected

Morbillivirus Glycoprotein Expression Induces ER Stress, Alters Ca2+ Homeostasis and Results in the Release of Vasostatin

Although the pathology of Morbillivirus in the central nervous system (CNS) is well described, the molecular basis of neurodegenerative events still remains poorly understood. As a model to explore Morbillivirus-mediated CNS dysfunctions, we used canine distemper virus (CDV) that we inoculated into two different cell systems: a monkey cell line (Vero) and rat primary hippocampal neurons. Importantly, the recombinant CDV used in these studies not only efficiently infects both cell types but recapitulates the uncommon, non-cytolytic cell-to-cell spread mediated by virulent CDVs in brain of dogs. Here, we demonstrated that both CDV surface glycoproteins (F and H) markedly accumulated in the endoplasmic reticulum (ER). This accumulation triggered an ER stress, characterized by increased expression of the ER resident chaperon calnexin and the proapoptotic transcription factor CHOP/GADD 153. The expression of calreticulin (CRT), another ER resident chaperon critically involved in the response to misfolded proteins and in Ca2+ homeostasis, was also upregulated. Transient expression of recombinant CDV F and H surface glycoproteins in Vero cells and primary hippocampal neurons further confirmed a correlation between their accumulation in the ER, CRT upregulation, ER stress and disruption of ER Ca2+ homeostasis. Furthermore, CDV infection induced CRT fragmentation with re-localisation of a CRT amino-terminal fragment, also known as vasostatin, on the surface of infected and neighbouring non-infected cells. Altogether, these results suggest that ER stress, CRT fragmentation and re-localization on the cell surface may contribute to cytotoxic effects and ensuing cell dysfunctions triggered by Morbillivirus, a mechanism that might potentially be relevant for other neurotropic viruses

Counting independent sets in graphs with bounded bipartite pathwidth

The Glauber dynamics can efficiently sample independent sets almost uniformly at random in polynomial time for graphs in a certain class. The class is determined by boundedness of a new graph parameter called bipartite pathwidth. This result, which we prove for the more general hardcore distribution with fugacity λ, can be viewed as a strong generalisation of Jerrum and Sinclair’s work on approximately counting matchings. The class of graphs with bounded bipartite path-width includes line graphs and claw-free graphs, which generalise line graphs. We consider two further generalisations of claw-free graphs and prove that these classes have bounded bipartite pathwidth