250,783 research outputs found
Learning Sets with Separating Kernels
We consider the problem of learning a set from random samples. We show how
relevant geometric and topological properties of a set can be studied
analytically using concepts from the theory of reproducing kernel Hilbert
spaces. A new kind of reproducing kernel, that we call separating kernel, plays
a crucial role in our study and is analyzed in detail. We prove a new analytic
characterization of the support of a distribution, that naturally leads to a
family of provably consistent regularized learning algorithms and we discuss
the stability of these methods with respect to random sampling. Numerical
experiments show that the approach is competitive, and often better, than other
state of the art techniques.Comment: final versio
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
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
Efficiently Decodable Non-Adaptive Threshold Group Testing
We consider non-adaptive threshold group testing for identification of up to
defective items in a set of items, where a test is positive if it
contains at least defective items, and negative otherwise.
The defective items can be identified using tests with
probability at least for any or tests with probability 1. The decoding time is
. This result significantly improves the
best known results for decoding non-adaptive threshold group testing:
for probabilistic decoding, where
, and for deterministic decoding
Trajectory-Based Dynamic Map Labeling
In this paper we introduce trajectory-based labeling, a new variant of
dynamic map labeling, where a movement trajectory for the map viewport is
given. We define a general labeling model and study the active range
maximization problem in this model. The problem is NP-complete and W[1]-hard.
In the restricted, yet practically relevant case that no more than k labels can
be active at any time, we give polynomial-time algorithms. For the general case
we present a practical ILP formulation with an experimental evaluation as well
as approximation algorithms.Comment: 19 pages, 7 figures, extended version of a paper to appear at ISAAC
201
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
Convolution, Separation and Concurrency
A notion of convolution is presented in the context of formal power series
together with lifting constructions characterising algebras of such series,
which usually are quantales. A number of examples underpin the universality of
these constructions, the most prominent ones being separation logics, where
convolution is separating conjunction in an assertion quantale; interval
logics, where convolution is the chop operation; and stream interval functions,
where convolution is used for analysing the trajectories of dynamical or
real-time systems. A Hoare logic is constructed in a generic fashion on the
power series quantale, which applies to each of these examples. In many cases,
commutative notions of convolution have natural interpretations as concurrency
operations.Comment: 39 page
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