27,572 research outputs found
Computing the permanent of (some) complex matrices
We present a deterministic algorithm, which, for any given 0< epsilon < 1 and
an nxn real or complex matrix A=(a_{ij}) such that | a_{ij}-1| < 0.19 for all
i, j computes the permanent of A within relative error epsilon in n^{O(ln n -ln
epsilon)} time. The method can be extended to computing hafnians and
multidimensional permanents.Comment: 12 pages, results extended to hafnians and multidimensional
permanents, minor improvement
Approximations for the boundary crossing probabilities of moving sums of normal random variables
In this paper we study approximations for boundary crossing probabilities for
the moving sums of i.i.d. normal random variables. We propose approximating a
discrete time problem with a continuous time problem allowing us to apply
developed theory for stationary Gaussian processes and to consider a number of
approximations (some well known and some not). We bring particular attention to
the strong performance of a newly developed approximation that corrects the use
of continuous time results in a discrete time setting. Results of extensive
numerical comparisons are reported. These results show that the developed
approximation is very accurate even for small window length
Approximated Symbolic Computations over Hybrid Automata
Hybrid automata are a natural framework for modeling and analyzing systems
which exhibit a mixed discrete continuous behaviour. However, the standard
operational semantics defined over such models implicitly assume perfect
knowledge of the real systems and infinite precision measurements. Such
assumptions are not only unrealistic, but often lead to the construction of
misleading models. For these reasons we believe that it is necessary to
introduce more flexible semantics able to manage with noise, partial
information, and finite precision instruments. In particular, in this paper we
integrate in a single framework based on approximated semantics different over
and under-approximation techniques for hybrid automata. Our framework allows to
both compare, mix, and generalize such techniques obtaining different
approximated reachability algorithms.Comment: In Proceedings HAS 2013, arXiv:1308.490
Regression Depth and Center Points
We show that, for any set of n points in d dimensions, there exists a
hyperplane with regression depth at least ceiling(n/(d+1)). as had been
conjectured by Rousseeuw and Hubert. Dually, for any arrangement of n
hyperplanes in d dimensions there exists a point that cannot escape to infinity
without crossing at least ceiling(n/(d+1)) hyperplanes. We also apply our
approach to related questions on the existence of partitions of the data into
subsets such that a common plane has nonzero regression depth in each subset,
and to the computational complexity of regression depth problems.Comment: 14 pages, 3 figure
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