6,217 research outputs found
Improved Second-Order Bounds for Prediction with Expert Advice
This work studies external regret in sequential prediction games with both
positive and negative payoffs. External regret measures the difference between
the payoff obtained by the forecasting strategy and the payoff of the best
action. In this setting, we derive new and sharper regret bounds for the
well-known exponentially weighted average forecaster and for a new forecaster
with a different multiplicative update rule. Our analysis has two main
advantages: first, no preliminary knowledge about the payoff sequence is
needed, not even its range; second, our bounds are expressed in terms of sums
of squared payoffs, replacing larger first-order quantities appearing in
previous bounds. In addition, our most refined bounds have the natural and
desirable property of being stable under rescalings and general translations of
the payoff sequence
Recurrence relations for patterns of type in flattened permutations
We consider the problem of counting the occurrences of patterns of the form
within flattened permutations of a given length. Using symmetric
functions, we find recurrence relations satisfied by the distributions on
for the patterns 12-3, 21-3, 23-1 and 32-1, and develop a
unified approach to obtain explicit formulas. By these recurrences, we are able
to determine simple closed form expressions for the number of permutations
that, when flattened, avoid one of these patterns as well as expressions for
the average number of occurrences. In particular, we find that the average
number of 23-1 patterns and the average number of 32-1 patterns in
, taken over all permutations of the same length,
are equal, as are the number of permutations avoiding either of these patterns.
We also find that the average number of 21-3 patterns in
over all is the same as it is for 31-2 patterns.Comment: 19 pages. Final version will be published in Journal of Difference
Equations and Application
Modeling of the subgrid-scale term of the filtered magnetic field transport equation
Accurate subgrid-scale turbulence models are needed to perform realistic
numerical magnetohydrodynamic (MHD) simulations of the subsurface flows of the
Sun. To perform large-eddy simulations (LES) of turbulent MHD flows, three
unknown terms have to be modeled. As a first step, this work proposes to use a
priori tests to measure the accuracy of various models proposed to predict the
SGS term appearing in the transport equation of the filtered magnetic field. It
is proposed to evaluate the SGS model accuracy in term of "structural" and
"functional" performance, i.e. the model capacity to locally approximate the
unknown term and to reproduce its energetic action, respectively. From our
tests, it appears that a mixed model based on the scale-similarity model has
better performance.Comment: 10 pages, 5 figures; Center for Turbulence Research, Proceedings of
the Summer Program 2010, Stanford Universit
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