18,839 research outputs found
A Bernstein theorem for special Lagrangian graphs
We obtain a Bernstein theorem for special Lagrangian graphs in n-dimensional
complex space for arbitrary n only assuming bounded slope, but no quantitative
restriction.Comment: 17 page
Power Partial Isometry Index and Ascent of a Finite Matrix
We give a complete characterization of nonnegative integers and and a
positive integer for which there is an -by- matrix with its power
partial isometry index equal to and its ascent equal to . Recall that
the power partial isometry index of a matrix is the supremum,
possibly infinity, of nonnegative integers such that are all partial isometries while the ascent of is the smallest
integer for which equals . It was known
before that, for any matrix , either or
. In this paper, we prove more precisely that there is an
-by- matrix such that and if and only if one of the
following conditions holds: (a) , (b) and ,
and (c) and . This answers a question we asked in a previous
paper.Comment: 11 page
Functional Bandits
We introduce the functional bandit problem, where the objective is to find an
arm that optimises a known functional of the unknown arm-reward distributions.
These problems arise in many settings such as maximum entropy methods in
natural language processing, and risk-averse decision-making, but current
best-arm identification techniques fail in these domains. We propose a new
approach, that combines functional estimation and arm elimination, to tackle
this problem. This method achieves provably efficient performance guarantees.
In addition, we illustrate this method on a number of important functionals in
risk management and information theory, and refine our generic theoretical
results in those cases
On the Erdos-Sos Conjecture for Graphs on n=k+4 Vertices
The Erd\H{o}s-S\'{o}s Conjecture states that if is a simple graph of
order with average degree more than then contains every tree of
order . In this paper, we prove that Erd\H{o}s-S\'{o}s Conjecture is true
for .Comment: 18 page
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