Omid Amini
On explosions in heavy-tailed branching random walks.
Mon, 02/07/2011 - 16:01 — SomNambulAuthors: Luc Devroye, Omid Amini, Simon Griffiths, Neil Olver
Subjects: Probability
AbstractConsider a branching random walk on $\mathbb R$, with offspring distribution
$Z$ and non-negative displacement distribution $W$. We say that explosion
occurs if an infinite number of particles may be found within a finite distance
of the origin. In this paper, we investigate this phenomenon when the offspring
distribution $Z$ is heavy-tailed.Geometric Tomography With Topological Guarantees.
Fri, 07/16/2010 - 15:01 — SomNambulAuthors: Omid Amini, Jean-Daniel Boissonnat, Pooran Memari
Subjects: Computational Geometry
AbstractWe consider the problem of reconstructing a compact 3-manifold (with
boundary) embedded in $\mathbb{R}^3$ from its cross-sections $\mathcal S$ with
a given set of cutting planes $\mathcal P$ having arbitrary orientations. Using
the obvious fact that a point $x \in \mathcal P$ belongs to the original object
if and only if it belongs to $\mathcal S$, we follow a very natural
reconstruction strategy: we say that a point $x \in \mathbb{R}^3$ belongs to
the reconstructed object if (at least one of) its nearest point(s) in $\mathcal
P$ belongs to $\mathcal S$.Subgraphs of quasi-random oriented graphs.
Mon, 11/23/2009 - 16:01 — SomNambulAuthors: Florian Huc, Omid Amini, Simon Griffiths
Subjects: Combinatorics
AbstractOne cannot guarantee the presence of an oriented four-cycle in an oriented
graph $D$ simply by demanding it has many edges, as an acyclic orientation of
the complete graph on $n$ vertices has $\binom{n}{2}$ edges -- the most
possible -- but contains no oriented cycle. We show that a simple
quasi-randomness condition on the orientation of $D$ does allow one to
guarantee the presence of an oriented four-cycle. Significantly our results
work even for sparse oriented graphs. Furthermore, we give examples which show
that, in a sense, our result is best possible.
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