38 research outputs found
Boxicity and separation dimension
A family of permutations of the vertices of a hypergraph is
called 'pairwise suitable' for if, for every pair of disjoint edges in ,
there exists a permutation in in which all the vertices in one
edge precede those in the other. The cardinality of a smallest such family of
permutations for is called the 'separation dimension' of and is denoted
by . Equivalently, is the smallest natural number so that
the vertices of can be embedded in such that any two
disjoint edges of can be separated by a hyperplane normal to one of the
axes. We show that the separation dimension of a hypergraph is equal to the
'boxicity' of the line graph of . This connection helps us in borrowing
results and techniques from the extensive literature on boxicity to study the
concept of separation dimension.Comment: This is the full version of a paper by the same name submitted to
WG-2014. Some results proved in this paper are also present in
arXiv:1212.6756. arXiv admin note: substantial text overlap with
arXiv:1212.675
Measurement of D+- and D0 production in deep inelastic scattering using a lifetime tag at HERA
The production of D-+/-- and D-0-mesons has been measured with the ZEUS detector at HERA using an integrated luminosity of 133.6 pb(-1). The measurements cover the kinematic range 5 < Q(2) < 1000 GeV2, 0.02 < y < 0.7, 1.5 < p(T)(D) < 15 GeV and |eta(D)| < 1.6. Combinatorial background to the D-meson signals is reduced by using the ZEUS microvertex detector to reconstruct displaced secondary vertices. Production cross sections are compared with the predictions of next-to-leading-order QCD, which is found to describe the data well. Measurements are extrapolated to the full kinematic phase space in order to obtain the open-charm contribution, F-2(c (c) over bar), to the proton structure function, F-2
Harnack inequalities and Bounds for Densities of Stochastic Processes
We consider possibly degenerate parabolic operators in the form of "sum of squares of vector fields plus a drif term" that are naturally associated to a suitable family of stochastic differential equations, and satisfying the H\uf6rmander condition. Note that, under this assumption, the operators considered have a smooth fundamental solution that agrees with the density of the corresponding stochastic process. We describe a method based on Harnack inequalities and on the construction of Harnack chains to prove lower bounds for the fundamental solution. We also briefly discuss PDE and SDE methods to prove analogous upper bounds. We eventually give a list of meaningful examples of operators to which the method applies
Harnack inequalities and Bounds for Densities of Stochastic Processes
We consider possibly degenerate parabolic operators in the form of "sum of squares of vector fields plus a drif term" that are naturally associated to a suitable family of stochastic differential equations, and satisfying the Hörmander condition. Note that, under this assumption, the operators considered have a smooth fundamental solution that agrees with the density of the corresponding stochastic process. We describe a method based on Harnack inequalities and on the construction of Harnack chains to prove lower bounds for the fundamental solution. We also briefly discuss PDE and SDE methods to prove analogous upper bounds. We eventually give a list of meaningful examples of operators to which the method applies