18,948 research outputs found
On Partitions of Two-Dimensional Discrete Boxes
Let and be finite sets and consider a partition of the \emph{discrete
box} into \emph{sub-boxes} of the form where and . We say that such a partition has the
-piercing property for positive integers and if every
\emph{line} of the form intersects at least sub-boxes and
every line of the form intersects at least sub-boxes.
We show that a partition of that has the -piercing
property must consist of at least sub-boxes. This bound is nearly sharp (up
to one additive unit) for every and .
As a corollary we get that the same bound holds for the minimum number of
vertices of a graph whose edges can be colored red and blue such that every
vertex is part of red -clique and a blue -clique.Comment: 10 pages, 2 figure
A Species Sampling Model with Finitely many Types
A two-parameter family of exchangeable partitions with a simple updating rule
is introduced. The partition is identified with a randomized version of a
standard symmetric Dirichlet species-sampling model with finitely many types. A
power-like distribution for the number of types is derived
Asymptotic regimes for the occupancy scheme of multiplicative cascades
In the classical occupancy scheme, one considers a fixed discrete probability
measure and throws balls independently at
random in boxes labeled by , such that is the probability that
a given ball falls into the box . In this work, we are interested in
asymptotic regimes of this scheme in the situation induced by a refining
sequence of random probability measures which arise
from some multiplicative cascade. Our motivation comes from the study of the
asymptotic behavior of certain fragmentation chain
Tempered modules in exotic Deligne-Langlands correspondence
The main purpose of this paper is to identify the tempered modules for the
affine Hecke algebra of type with arbitrary, non-root of unity,
unequal parameters, in the exotic Deligne-Langlands correspondence in the sense
of Kato. Our classification has several applications to the Weyl group module
structure of the tempered Hecke algebra modules. In particular, we provide a
geometric and a combinatorial classification of discrete series which contain
the sign representation of the Weyl group. This last combinatorial
classification was expected from the work of Heckman-Opdam and Slooten.Comment: 51 page
Traffic Network Control from Temporal Logic Specifications
We propose a framework for generating a signal control policy for a traffic
network of signalized intersections to accomplish control objectives
expressible using linear temporal logic. By applying techniques from model
checking and formal methods, we obtain a correct-by-construction controller
that is guaranteed to satisfy complex specifications. To apply these tools, we
identify and exploit structural properties particular to traffic networks that
allow for efficient computation of a finite state abstraction. In particular,
traffic networks exhibit a componentwise monotonicity property which allows
reach set computations that scale linearly with the dimension of the continuous
state space
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