16,101 research outputs found
Natural maps between CAT(0) boundaries
It is shown that certain natural maps between the ideal, Gromov, and end
boundaries of a complete CAT(0) space can fail to be either injective or
surjective. Additionally the natural map from the Gromov boundary to the end
boundary of a complete CAT(-1) space can fail to be either injective or
surjective.Comment: 8 page
Optimal Switching for Hybrid Semilinear Evolutions
We consider the optimization of a dynamical system by switching at discrete
time points between abstract evolution equations composed by nonlinearly
perturbed strongly continuous semigroups, nonlinear state reset maps at mode
transition times and Lagrange-type cost functions including switching costs. In
particular, for a fixed sequence of modes, we derive necessary optimality
conditions using an adjoint equation based representation for the gradient of
the costs with respect to the switching times. For optimization with respect to
the mode sequence, we discuss a mode-insertion gradient. The theory unifies and
generalizes similar approaches for evolutions governed by ordinary and delay
differential equations. More importantly, it also applies to systems governed
by semilinear partial differential equations including switching the principle
part. Examples from each of these system classes are discussed
Instanton constituents in the O(3) model at finite temperature
It is shown that instantons in the O(3) model at finite temperature consist
of fractional charge constituents and the (topological) properties of the
latter are discussed.Comment: 5 pages, 12 plots in 3 figure
Rough CAT(0) spaces
We investigate various notions of rough CAT(0). These conditions define
classes of spaces that strictly include the union of all Gromov hyperbolic
length spaces and all CAT(0) spaces.Comment: Corrected typos and updated Corollaries 3.22 and 3.2
Asymptotic Conditional Distribution of Exceedance Counts: Fragility Index with Different Margins
Let be a random vector, whose components are not
necessarily independent nor are they required to have identical distribution
functions . Denote by the number of exceedances among
above a high threshold . The fragility index, defined by
if this limit exists, measures the
asymptotic stability of the stochastic system as the threshold
increases. The system is called stable if and fragile otherwise. In this
paper we show that the asymptotic conditional distribution of exceedance counts
(ACDEC) , , exists, if the
copula of is in the domain of attraction of a multivariate extreme
value distribution, and if
exists for
and some . This enables the computation of
the FI corresponding to and of the extended FI as well as of the
asymptotic distribution of the exceedance cluster length also in that case,
where the components of are not identically distributed
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