2,315 research outputs found
Topological stability for conservative systems
We prove that the C1-interior of the set of all topologically stable
C1-incompressible flows is contained in the set of Anosov incompressible flows.
Moreover, we obtain an analogous result for the discrete-time case.Comment: 8 page
Topological Stability of Kinetic -Centers
We study the -center problem in a kinetic setting: given a set of
continuously moving points in the plane, determine a set of (moving)
disks that cover at every time step, such that the disks are as small as
possible at any point in time. Whereas the optimal solution over time may
exhibit discontinuous changes, many practical applications require the solution
to be stable: the disks must move smoothly over time. Existing results on this
problem require the disks to move with a bounded speed, but this model is very
hard to work with. Hence, the results are limited and offer little theoretical
insight. Instead, we study the topological stability of -centers.
Topological stability was recently introduced and simply requires the solution
to change continuously, but may do so arbitrarily fast. We prove upper and
lower bounds on the ratio between the radii of an optimal but unstable solution
and the radii of a topologically stable solution---the topological stability
ratio---considering various metrics and various optimization criteria. For we provide tight bounds, and for small we can obtain nontrivial
lower and upper bounds. Finally, we provide an algorithm to compute the
topological stability ratio in polynomial time for constant
Topological stability of stored optical vortices
We report an experiment in which an optical vortex is stored in a vapor of Rb
atoms. Due to its 2\pi phase twist, this mode, also known as the Laguerre-Gauss
mode, is topologically stable and cannot unwind even under conditions of strong
diffusion. To supplement our finding, we stored a flat phase Gaussian beam with
a dark center. Contrary to the optical vortex, which stays stable for over 100
microseconds, the dark center in the retrieved flat-phased image was filled
with light at storage times as small as 10 microseconds. This experiment proves
that higher electromagnetic modes can be converted into atomic coherences, and
that modes with phase singularities are robust to decoherence effects such as
diffusion. This opens the possibility to more elaborate schemes for two
dimensional information storage in atomic vapors.Comment: 4 pages, 4 figures v2: minor grammatical corrections v3: problem with
references fixed v4: minor clarifications added to the tex
Embedded Vortices
We present a discussion of embedded vortices in general Yang-Mills theories.
The origin of a family structure of solutions is shown to be group theoretic in
nature and a procedure for its determination is developed. Vortex stability can
be quantified into three types: Abelian topological stability, non-Abelian
topological stability, and dynamical stability; we relate these to the family
structure of vortices, in particular discussing how Abelian topological and
dynamical stability are related. The formalism generally encompasses embedded
domain walls and embedded monopoles also.Comment: final corrections. latex fil
A remark on the topological stability of symplectomorphisms
We prove that the C1 interior of the set of all topologically stable C1
symplectomorphisms is contained in the set of Anosov symplectomorphisms.Comment: 4 page
Evolutionary stable strategies in networked games: the influence of topology
Evolutionary game theory is used to model the evolution of competing
strategies in a population of players. Evolutionary stability of a strategy is
a dynamic equilibrium, in which any competing mutated strategy would be wiped
out from a population. If a strategy is weak evolutionarily stable, the
competing strategy may manage to survive within the network. Understanding the
network-related factors that affect the evolutionary stability of a strategy
would be critical in making accurate predictions about the behaviour of a
strategy in a real-world strategic decision making environment. In this work,
we evaluate the effect of network topology on the evolutionary stability of a
strategy. We focus on two well-known strategies known as the Zero-determinant
strategy and the Pavlov strategy. Zero-determinant strategies have been shown
to be evolutionarily unstable in a well-mixed population of players. We
identify that the Zero-determinant strategy may survive, and may even dominate
in a population of players connected through a non-homogeneous network. We
introduce the concept of `topological stability' to denote this phenomenon. We
argue that not only the network topology, but also the evolutionary process
applied and the initial distribution of strategies are critical in determining
the evolutionary stability of strategies. Further, we observe that topological
stability could affect other well-known strategies as well, such as the general
cooperator strategy and the cooperator strategy. Our observations suggest that
the variation of evolutionary stability due to topological stability of
strategies may be more prevalent in the social context of strategic evolution,
in comparison to the biological context
Exploring Topology Conserving Gauge Actions for Lattice QCD
We explore gauge actions for lattice QCD, which are constructed such that the
occurrence of small plaquette values is strongly suppressed. By choosing strong
bare gauge couplings we arrive at values for the physical lattice spacings of
O(0.1 fm). Such gauge actions tend to confine the Monte Carlo history to a
single topological sector. This topological stability facilitates the
collection of a large set of configurations in a specific sector, which is
profitable for numerical studies in the epsilon-regime. The suppression of
small plaquette values is also expected to be favourable for simulations with
dynamical quarks. We use a local Hybrid Monte Carlo algorithm to simulate such
actions, and we present numerical results for the static potential, the
physical scale, the topological stability and the kernel condition number of
the overlap Dirac operator. In addition we discuss the question of reflection
positivity for a class of such gauge actions.Comment: 28 pages, 8 figure
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