369 research outputs found
Ramsey Properties of Permutations
The age of each countable homogeneous permutation forms a Ramsey class. Thus,
there are five countably infinite Ramsey classes of permutations.Comment: 10 pages, 3 figures; v2: updated info on related work + some other
minor enhancements (Dec 21, 2012
Promotion of Cooperation by Selective Group Extinction
Multilevel selection is an important organizing principle that crucially
underlies evolutionary processes from the emergence of cells to eusociality and
the economics of nations. Previous studies on multilevel selection assumed that
the effective higher-level selection emerges from lower-level reproduction.
This leads to selection among groups, although only individuals reproduce. We
introduce selective group extinction, where groups die with a probability
inversely proportional to their group fitness. When accounting for this the
critical benefit-to-cost ratio is substantially lowered. Because in game theory
and evolutionary dynamics the degree of cooperation crucially depends on this
ratio above which cooperation emerges previous studies may have substantially
underestimated the establishment and maintenance of cooperation.Comment: Accepted for publication in New Journal of Physic
An extension of Tur\'an's Theorem, uniqueness and stability
We determine the maximum number of edges of an -vertex graph with the
property that none of its -cliques intersects a fixed set .
For , the -partite Turan graph turns out to be the unique
extremal graph. For , there is a whole family of extremal graphs,
which we describe explicitly. In addition we provide corresponding stability
results.Comment: 12 pages, 1 figure; outline of the proof added and other referee's
comments incorporate
A density Corr\'adi-Hajnal Theorem
We find, for all sufficiently large and each , the maximum number of
edges in an -vertex graph which does not contain vertex-disjoint
triangles.
This extends a result of Moon [Canad. J. Math. 20 (1968), 96-102] which is in
turn an extension of Mantel's Theorem. Our result can also be viewed as a
density version of the Corradi-Hajnal Theorem.Comment: 41 pages (including 11 pages of appendix), 4 figures, 2 table
Impact of embedding on predictability of failure-recovery dynamics in networks
Failure, damage spread and recovery crucially underlie many spatially
embedded networked systems ranging from transportation structures to the human
body. Here we study the interplay between spontaneous damage, induced failure
and recovery in both embedded and non-embedded networks. In our model the
network's components follow three realistic processes that capture these
features: (i) spontaneous failure of a component independent of the
neighborhood (internal failure), (ii) failure induced by failed neighboring
nodes (external failure) and (iii) spontaneous recovery of a component.We
identify a metastable domain in the global network phase diagram spanned by the
model's control parameters where dramatic hysteresis effects and random
switching between two coexisting states are observed. The loss of
predictability due to these effects depend on the characteristic link length of
the embedded system. For the Euclidean lattice in particular, hysteresis and
switching only occur in an extremely narrow region of the parameter space
compared to random networks. We develop a unifying theory which links the
dynamics of our model to contact processes. Our unifying framework may help to
better understand predictability and controllability in spatially embedded and
random networks where spontaneous recovery of components can mitigate
spontaneous failure and damage spread in the global network.Comment: 22 pages, 20 figure
Triphenylmethyl Thionitrite: An Efficient NO Transfer Reagent During the Synthesis of a Triruthenium Nitrosyl Cluster
The synthesis and structural characterization of the novel triruthenium nitrosyl cluster [Ru-3(mu-NO)(CO)(5)(mu-H)(mu-PBu2t)(2)(mu-dppm)] (2) is described. Compound 2 was obtained by the reaction of the 46-valence electron cluster [Ru-3(mu-CO)(CO)(4)(mu(3)-H)(mu-H)(mu-PBu2t)(2)(mu-dppm)] (1) with nitric oxide and on the other hand in a more efficient way by the reaction of 1 with the nitrosyl transfer reagent triphenylmethyl thionitrite (TTN). The reaction of 1 with NO was outlined in dichloromethane whereas the reaction with TTN was realized in THF. Both methods worked at ambient temperature affording compound 2 in high yield. Temporarily we found that the transformation of 1 with NO was accompanied by a fast side-reaction resulting in a further substitution of CO ligands. The molecular structure of 2 in the crystal was confirmed by single-crystal X-ray diffraction
- …