7,313 research outputs found
Topological invariants for semigroups of holomorphic self-maps of the unit disc
Let , be two one-parameter semigroups of holomorphic
self-maps of the unit disc . Let be a homeomorphism. We prove that, if for all , then extends to a homeomorphism of
outside exceptional maximal contact arcs (in particular, for
elliptic semigroups, extends to a homeomorphism of ).
Using this result, we study topological invariants for one-parameter semigroups
of holomorphic self-maps of the unit disc.Comment: 28 pages, final version, to appear in J. Math. Pures App
Hyperfine-induced decoherence in triangular spin-cluster qubits
We investigate hyperfine-induced decoherence in a triangular spin-cluster for
different qubit encodings. Electrically controllable eigenstates of spin
chirality (C_z) show decoherence times that approach milliseconds, two orders
of magnitude longer than those estimated for the eigenstates of the total spin
projection (S_z) and of the partial spin sum (S_{12}). The robustness of
chirality is due to its decoupling from both the total- and individual-spin
components in the cluster. This results in a suppression of the effective
interaction between C_z and the nuclear spin bath
Irreversibility-inversions in 2 dimensional turbulence
In this paper we consider a recent theoretical prediction (Bragg \emph{et
al.}, Phys. Fluids \textbf{28}, 013305 (2016)) that for inertial particles in
2D turbulence, the nature of the irreversibility of the particle-pair
dispersion inverts when the particle inertia exceeds a certain value. In
particular, when the particle Stokes number, , is below a certain
value, the forward-in-time (FIT) dispersion should be faster than the
backward-in-time (BIT) dispersion, but for above this value, this
should invert so that BIT becomes faster than FIT dispersion. This non-trivial
behavior arises because of the competition between two physically distinct
irreversibility mechanisms that operate in different regimes of . In
3D turbulence, both mechanisms act to produce faster BIT than FIT dispersion,
but in 2D turbulence, the two mechanisms have opposite effects because of the
flux of energy from the small to the large scales. We supplement the
qualitative argument given by Bragg \emph{et al.} (Phys. Fluids \textbf{28},
013305 (2016)) by deriving quantitative predictions of this effect in the short
time limit. We confirm the theoretical predictions using results of inertial
particle dispersion in a direct numerical simulation of 2D turbulence. A more
general finding of this analysis is that in turbulent flows with an inverse
energy flux, inertial particles may yet exhibit a net downscale flux of kinetic
energy because of their non-local in-time dynamics
Sharing rides with friends: a coalition formation algorithm for ridesharing
We consider the Social Ridesharing (SR) problem, where a set of commuters, connected through a social network, arrange one-time rides at short notice. In particular, we focus on the associated optimisation problem of forming cars to minimise the travel cost of the overall system modelling such problem as a graph constrained coalition formation (GCCF) problem, where the set of feasible coalitions is restricted by a graph (i.e., the social network). Moreover, we significantly extend the state of the art algorithm for GCCF, i.e., the CFSS algorithm, to solve our GCCF model of the SR problem. Our empirical evaluation uses a real dataset for both spatial (GeoLife) and social data (Twitter), to validate the applicability of our approach in a realistic application scenario. Empirical results show that our approach computes optimal solutions for systems of medium scale (up to 100 agents) providing significant cost reductions (up to -36.22%). Moreover, we can provide approximate solutions for very large systems (i.e., up to 2000 agents) and good quality guarantees (i.e., with an approximation ratio of 1.41 in the worst case) within minutes (i.e., 100 seconds
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