149,641 research outputs found
Minimal Completely Separating Systems of k-Sets
AbstractLet n and k be fixed positive integers. A collection C of k-sets of [n] is a completely separating system if, for all distinct i, j∈[n], there is an S∈C for which i∈S and j∉S. Let R(n, k) denote the minimum size of such a C. Our results include showing that if nk is a sequence with k⪡nk⪡k1+ε for every ε>0, then[formula
On Almost Automorphic Dynamics in Symbolic Lattices
1991 Mathematics Subject Classification. Primary Primary 37B10, 37A35, 43A60; Secondary
37B20, 54H20.We study the existence, structure, and topological entropy of almost automorphic arrays in symbolic lattice dynamical systems. In particular we show that almost automorphic arrays with arbitrarily large entropy are typical in symbolic lattice dynamical systems. Applications to pattern formation and spatial chaos in infinite dimensional lattice systems are considered,
and the construction of chaotic almost automorphic signals is discussed.The first author was supported by a Max Kade Postdoctoral Fellowship (at Georgia Tech). The second author was partially supported by DFG grant Si 801 and CDSNS, Georgia Tech. The third author was partially supported by NSF Grant DMS-0204119
Separating path systems
We study separating systems of the edges of a graph where each member of the
separating system is a path. We conjecture that every -vertex graph admits a
separating path system of size and prove this in certain interesting
special cases. In particular, we establish this conjecture for random graphs
and graphs with linear minimum degree. We also obtain tight bounds on the size
of a minimal separating path system in the case of trees.Comment: 21 pages, fixed misprints, Journal of Combinatoric
Bell's local causality is a d-separation criterion
This paper aims to motivate Bell's notion of local causality by means of
Bayesian networks. In a locally causal theory any superluminal correlation
should be screened off by atomic events localized in any so-called
\textit{shielder-off region} in the past of one of the correlating events. In a
Bayesian network any correlation between non-descendant random variables are
screened off by any so-called \textit{d-separating set} of variables. We will
argue that the shielder-off regions in the definition of local causality
conform in a well defined sense to the d-separating sets in Bayesian networks.Comment: 13 pages, 8 figure
Some New Bounds For Cover-Free Families Through Biclique Cover
An cover-free family is a family of subsets of a finite set
such that the intersection of any members of the family contains at least
elements that are not in the union of any other members. The minimum
number of elements for which there exists an with blocks is
denoted by .
In this paper, we show that the value of is equal to the
-biclique covering number of the bipartite graph whose vertices
are all - and -subsets of a -element set, where a -subset is
adjacent to an -subset if their intersection is empty. Next, we introduce
some new bounds for . For instance, we show that for
and
where is a constant satisfies the
well-known bound . Also, we
determine the exact value of for some values of . Finally, we
show that whenever there exists a Hadamard matrix of
order 4d
Characterizations of Decomposable Dependency Models
Decomposable dependency models possess a number of interesting and useful
properties. This paper presents new characterizations of decomposable models in
terms of independence relationships, which are obtained by adding a single
axiom to the well-known set characterizing dependency models that are
isomorphic to undirected graphs. We also briefly discuss a potential
application of our results to the problem of learning graphical models from
data.Comment: See http://www.jair.org/ for any accompanying file
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