865 research outputs found
Hierarchical Time-Dependent Oracles
We study networks obeying \emph{time-dependent} min-cost path metrics, and
present novel oracles for them which \emph{provably} achieve two unique
features: % (i) \emph{subquadratic} preprocessing time and space,
\emph{independent} of the metric's amount of disconcavity; % (ii)
\emph{sublinear} query time, in either the network size or the actual
Dijkstra-Rank of the query at hand
Approximate well-supported Nash equilibria in symmetric bimatrix games
The -well-supported Nash equilibrium is a strong notion of
approximation of a Nash equilibrium, where no player has an incentive greater
than to deviate from any of the pure strategies that she uses in
her mixed strategy. The smallest constant currently known for
which there is a polynomial-time algorithm that computes an
-well-supported Nash equilibrium in bimatrix games is slightly
below . In this paper we study this problem for symmetric bimatrix games
and we provide a polynomial-time algorithm that gives a
-well-supported Nash equilibrium, for an arbitrarily small
positive constant
Homogenization problems in random media
we study homogenization problems of partial differential equations in random domains. We give an overview of the classical techniques that are used to obtain homogenized equations over simple microstructures (for instance, periodic or almost periodic structures) and we show how we can obtain averaging equations over some particular random configurations. As it will be seen, such methods require ergodic theory, percolation, stochastic processes, in addition to the compactness of solutions and the convergence process
Revealing the nature of magnetic shadows with numerical 3D-MHD simulations
We investigate the interaction of magneto-acoustic waves with magnetic
network elements with the aim of finding possible signatures of the magnetic
shadow phenomenon in the vicinity of network elements. We carried out
three-dimensional numerical simulations of magneto-acoustic wave propagation in
a model solar atmosphere that is threaded by a complexly structured magnetic
field, resembling that of a typical magnetic network element and of
internetwork regions. High-frequency waves of 10 mHz are excited at the bottom
of the simulation domain. On their way through the upper convection zone and
through the photosphere and the chromosphere they become perturbed, refracted,
and converted into different mode types. We applied a standard Fourier analysis
to produce oscillatory power-maps of the line-of-sight velocity. In the power
maps of the upper photosphere and the lower chromosphere, we clearly see the
magnetic shadow: a seam of suppressed power surrounding the magnetic network
elements. We demonstrate that this shadow is linked to the mode conversion
process and that power maps at these height levels show the signature of three
different magneto-acoustic wave modes.Comment: Astronomy & Astrophysics Letters, in print 4 pages, 4 figure
Energy and helicity budgets of solar quiet regions
We investigate the free magnetic energy and relative magnetic helicity
budgets of solar quiet regions. Using a novel non-linear force-free method
requiring single solar vector magnetograms we calculate the instantaneous free
magnetic energy and relative magnetic helicity budgets in 55 quiet-Sun vector
magnetograms. As in a previous work on active regions, we construct here for
the first time the (free) energy-(relative) helicity diagram of quiet-Sun
regions. We find that quiet-Sun regions have no dominant sense of helicity and
show monotonic correlations a) between free magnetic energy/relative helicity
and magnetic network area and, consequently, b) between free magnetic energy
and helicity. Free magnetic energy budgets of quiet-Sun regions represent a
rather continuous extension of respective active-region budgets towards lower
values, but the corresponding helicity transition is discontinuous due to the
incoherence of the helicity sense contrary to active regions. We further
estimate the instantaneous free magnetic-energy and relative magnetic-helicity
budgets of the entire quiet Sun, as well as the respective budgets over an
entire solar cycle. Derived instantaneous free magnetic energy budgets and, to
a lesser extent, relative magnetic helicity budgets over the entire quiet Sun
are comparable to the respective budgets of a sizeable active region, while
total budgets within a solar cycle are found higher than previously reported.
Free-energy budgets are comparable to the energy needed to power fine-scale
structures residing at the network, such as mottles and spicules
Managing Known Clones: Issues and Open Questions
Many software systems contained cloned code, i.e., segments of code that
are highly similar to each other, typically because one has been copied
from the other, and then possibly modified. In some contexts, clones are
of interest because they are targets for refactoring. This paper
summarizes the results of a working session in which the problems of merely
managing clones that are already known to exist. Six key issues in the
space are briefly reviewed, and open questions raised in the working
session are listed
Polylogarithmic Supports are required for Approximate Well-Supported Nash Equilibria below 2/3
In an epsilon-approximate Nash equilibrium, a player can gain at most epsilon
in expectation by unilateral deviation. An epsilon well-supported approximate
Nash equilibrium has the stronger requirement that every pure strategy used
with positive probability must have payoff within epsilon of the best response
payoff. Daskalakis, Mehta and Papadimitriou conjectured that every win-lose
bimatrix game has a 2/3-well-supported Nash equilibrium that uses supports of
cardinality at most three. Indeed, they showed that such an equilibrium will
exist subject to the correctness of a graph-theoretic conjecture. Regardless of
the correctness of this conjecture, we show that the barrier of a 2/3 payoff
guarantee cannot be broken with constant size supports; we construct win-lose
games that require supports of cardinality at least Omega((log n)^(1/3)) in any
epsilon-well supported equilibrium with epsilon < 2/3. The key tool in showing
the validity of the construction is a proof of a bipartite digraph variant of
the well-known Caccetta-Haggkvist conjecture. A probabilistic argument shows
that there exist epsilon-well-supported equilibria with supports of cardinality
O(log n/(epsilon^2)), for any epsilon> 0; thus, the polylogarithmic cardinality
bound presented cannot be greatly improved. We also show that for any delta >
0, there exist win-lose games for which no pair of strategies with support
sizes at most two is a (1-delta)-well-supported Nash equilibrium. In contrast,
every bimatrix game with payoffs in [0,1] has a 1/2-approximate Nash
equilibrium where the supports of the players have cardinality at most two.Comment: Added details on related work (footnote 7 expanded
An Empirical Study of Finding Approximate Equilibria in Bimatrix Games
While there have been a number of studies about the efficacy of methods to
find exact Nash equilibria in bimatrix games, there has been little empirical
work on finding approximate Nash equilibria. Here we provide such a study that
compares a number of approximation methods and exact methods. In particular, we
explore the trade-off between the quality of approximate equilibrium and the
required running time to find one. We found that the existing library GAMUT,
which has been the de facto standard that has been used to test exact methods,
is insufficient as a test bed for approximation methods since many of its games
have pure equilibria or other easy-to-find good approximate equilibria. We
extend the breadth and depth of our study by including new interesting families
of bimatrix games, and studying bimatrix games upto size .
Finally, we provide new close-to-worst-case examples for the best-performing
algorithms for finding approximate Nash equilibria
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