34,478 research outputs found
Universal targets for homomorphisms of edge-colored graphs
A -edge-colored graph is a finite, simple graph with edges labeled by
numbers . A function from the vertex set of one -edge-colored
graph to another is a homomorphism if the endpoints of any edge are mapped to
two different vertices connected by an edge of the same color. Given a class
of graphs, a -edge-colored graph (not necessarily
with the underlying graph in ) is -universal for
when any -edge-colored graph with the underlying graph in
admits a homomorphism to . We characterize graph classes that admit
-universal graphs. For such classes, we establish asymptotically almost
tight bounds on the size of the smallest universal graph.
For a nonempty graph , the density of is the maximum ratio of the
number of edges to the number of vertices ranging over all nonempty subgraphs
of . For a nonempty class of graphs, denotes
the density of , that is the supremum of densities of graphs in
.
The main results are the following. The class admits
-universal graphs for if and only if there is an absolute constant
that bounds the acyclic chromatic number of any graph in . For any
such class, there exists a constant , such that for any , the size
of the smallest -universal graph is between and
.
A connection between the acyclic coloring and the existence of universal
graphs was first observed by Alon and Marshall (Journal of Algebraic
Combinatorics, 8(1):5-13, 1998). One of their results is that for planar
graphs, the size of the smallest -universal graph is between and
. Our results yield that there exists a constant such that for all
, this size is bounded from above by
Anisotropic Flow of Strange Particles at SPS
The elliptic flow for Lambda hyperons and K0s mesons was measured by the NA49
experiment in semicentral Pb+Pb collisions at 158A GeV. The standard method of
correlating particles with an event plane has been used. Measurements of v2
near mid-rapidity are reported as a function of centrality, rapidity and
transverse momentum. Elliptic flow of Lambda and K0s particles increases both
with the impact parameter and with the transverse momentum. It is compared with
v2 for pions and protons as well as with various model predictions. The NA49
results are compared with data from NA45/CERES and STAR experiments
ON THE RESAMPLING METHOD IN SAMPLE MEDIAN ESTIMATION
Bootstrap is one of the resampling statistical methods. This method was proposed by B. Efron. The main idea of bootstrap is to treat the original sample of values as a stand-in for the population and to resample with replacement from it repeatedly. Bootstrap allows estimation of the sampling distribution of almost any statistics using only very simple methods. This paper presents a modification of a resampling procedure based on bootstrap sampling. The proposal leads to sampling from population with density function f(x), where f(x) is estimated based on the kernel estimation. The properties of the method were analyzed in the median estimation in Monte Carlo study.The proposal could be useful for the parameters estimation in the case of a small sample. This method could be used in quality control procedures such as control charts or in the acceptance sampling
Is a "homogeneous" description of dynamic heterogeneities possible?
We study the simplest model of dynamic heterogeneities in glass forming
liquids: one-spin facilitated kinetic Ising model introduced by Fredrickson and
Andersen [G.H. Fredrickson and H.C. Andersen, Phys. Rev. Lett. 53, 1244 (1984);
J. Chem. Phys. 83, 5822 (1985)]. We show that the low-temperature, long-time
behavior of the density autocorrelation function predicted by a scaling
approach can be obtained from a self-consistent mode-coupling-like
approximation.Comment: accepted for publication in the Journal of Chemical Physic
Construction of an A-manifold on a principal torus bundle
We construct a new example of an A-manifold, i.e. a Riemannian manifold with
a cyclic-parallel Ricci tensor, which can be viewed as a generalization of the
Einstein condition. The underlying manifold for our construction is a principal
torus bundle over K\"ahler-Einstein manifold a with fibre a torus of arbitrary
dimension
- …