257,400 research outputs found
Sensitivity of wardrop equilibria
We study the sensitivity of equilibria in the well-known game theoretic traffic model due to Wardrop. We mostly consider single-commodity networks. Suppose, given a unit demand flow at Wardrop equilibrium, one increases the demand by Îľ or removes an edge carrying only an Îľ-fraction of flow. We study how the equilibrium responds to such an Îľ-change.
Our first surprising finding is that, even for linear latency functions, for every Îľ>â0, there are networks in which an Îľ-change causes every agent to change its path in order to recover equilibrium. Nevertheless, we can prove that, for general latency functions, the flow increase or decrease on every edge is at most Îľ.
Examining the latency at equilibrium, we concentrate on polynomial latency functions of degree at most p with nonnegative coefficients. We show that, even though the relative increase in the latency of an edge due to an Îľ-change in the demand can be unbounded, the path latency at equilibrium increases at most by a factor of (1â+âÎľ) p . The increase of the price of anarchy is shown to be upper bounded by the same factor. Both bounds are shown to be tight.
Let us remark that all our bounds are tight. For the multi-commodity case, we present examples showing that neither the change in edge flows nor the change in the path latency can be bounded
Locally Stable Marriage with Strict Preferences
We study stable matching problems with locality of information and control.
In our model, each agent is a node in a fixed network and strives to be matched
to another agent. An agent has a complete preference list over all other agents
it can be matched with. Agents can match arbitrarily, and they learn about
possible partners dynamically based on their current neighborhood. We consider
convergence of dynamics to locally stable matchings -- states that are stable
with respect to their imposed information structure in the network. In the
two-sided case of stable marriage in which existence is guaranteed, we show
that the existence of a path to stability becomes NP-hard to decide. This holds
even when the network exists only among one partition of agents. In contrast,
if one partition has no network and agents remember a previous match every
round, a path to stability is guaranteed and random dynamics converge with
probability 1. We characterize this positive result in various ways. For
instance, it holds for random memory and for cache memory with the most recent
partner, but not for cache memory with the best partner. Also, it is crucial
which partition of the agents has memory. Finally, we present results for
centralized computation of locally stable matchings, i.e., computing maximum
locally stable matchings in the two-sided case and deciding existence in the
roommates case.Comment: Conference version in ICALP 2013; to appear in SIAM J. Disc Mat
On the dependence of the leak-rate of seals on the skewness of the surface height probability distribution
Seals are extremely useful devices to prevent fluid leakage. We present
experimental result which show that the leak-rate of seals depend sensitively
on the skewness in the height probability distribution. The experimental data
are analyzed using the critical-junction theory. We show that using the
top-power spectrum result in good agreement between theory and experiment.Comment: 5 pages, 9 figure
Topological surface state under graphene for two-dimensional spintronics in air
Spin currents which allow for a dissipationless transport of information can
be generated by electric fields in semiconductor heterostructures in the
presence of a Rashba-type spin-orbit coupling. The largest Rashba effects occur
for electronic surface states of metals but these cannot exist but under
ultrahigh vacuum conditions. Here, we reveal a giant Rashba effect ({\alpha}_R
~ 1.5E-10 eVm) on a surface state of Ir(111). We demonstrate that its spin
splitting and spin polarization remain unaffected when Ir is covered with
graphene. The graphene protection is, in turn, sufficient for the spin-split
surface state to survive in ambient atmosphere. We discuss this result along
with evidences for a topological protection of the surface state.Comment: includes supplementary informatio
Computer Algebra meets Finite Elements: an Efficient Implementation for Maxwell's Equations
We consider the numerical discretization of the time-domain Maxwell's
equations with an energy-conserving discontinuous Galerkin finite element
formulation. This particular formulation allows for higher order approximations
of the electric and magnetic field. Special emphasis is placed on an efficient
implementation which is achieved by taking advantage of recurrence properties
and the tensor-product structure of the chosen shape functions. These
recurrences have been derived symbolically with computer algebra methods
reminiscent of the holonomic systems approach.Comment: 16 pages, 1 figure, 1 table; Springer Wien, ISBN 978-3-7091-0793-
Algorithmic Thomas Decomposition of Algebraic and Differential Systems
In this paper, we consider systems of algebraic and non-linear partial
differential equations and inequations. We decompose these systems into
so-called simple subsystems and thereby partition the set of solutions. For
algebraic systems, simplicity means triangularity, square-freeness and
non-vanishing initials. Differential simplicity extends algebraic simplicity
with involutivity. We build upon the constructive ideas of J. M. Thomas and
develop them into a new algorithm for disjoint decomposition. The given paper
is a revised version of a previous paper and includes the proofs of correctness
and termination of our decomposition algorithm. In addition, we illustrate the
algorithm with further instructive examples and describe its Maple
implementation together with an experimental comparison to some other
triangular decomposition algorithms.Comment: arXiv admin note: substantial text overlap with arXiv:1008.376
Convergence to equilibrium under a random Hamiltonian
We analyze equilibration times of subsystems of a larger system under a
random total Hamiltonian, in which the basis of the Hamiltonian is drawn from
the Haar measure. We obtain that the time of equilibration is of the order of
the inverse of the arithmetic average of the Bohr frequencies. To compute the
average over a random basis, we compute the inverse of a matrix of overlaps of
operators which permute four systems. We first obtain results on such a matrix
for a representation of an arbitrary finite group and then apply it to the
particular representation of the permutation group under consideration.Comment: 11 pages, 1 figure, v1-v3: some minor errors and typos corrected and
new references added; v4: results for the degenerated spectrum added; v5:
reorganized and rewritten version; to appear in PR
Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV
The performance of muon reconstruction, identification, and triggering in CMS
has been studied using 40 inverse picobarns of data collected in pp collisions
at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection
criteria covering a wide range of physics analysis needs have been examined.
For all considered selections, the efficiency to reconstruct and identify a
muon with a transverse momentum pT larger than a few GeV is above 95% over the
whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4,
while the probability to misidentify a hadron as a muon is well below 1%. The
efficiency to trigger on single muons with pT above a few GeV is higher than
90% over the full eta range, and typically substantially better. The overall
momentum scale is measured to a precision of 0.2% with muons from Z decays. The
transverse momentum resolution varies from 1% to 6% depending on pseudorapidity
for muons with pT below 100 GeV and, using cosmic rays, it is shown to be
better than 10% in the central region up to pT = 1 TeV. Observed distributions
of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO
Implicit-Explicit Runge-Kutta schemes for numerical discretization of optimal control problems
Implicit-explicit (IMEX) Runge-Kutta methods play a major rule in the
numerical treatment of differential systems governed by stiff and non-stiff
terms. This paper discusses order conditions and symplecticity properties of a
class of IMEX Runge-Kutta methods in the context of optimal control problems.
The analysis of the schemes is based on the continuous optimality system. Using
suitable transformations of the adjoint equation, order conditions up to order
three are proven as well as the relation between adjoint schemes obtained
through different transformations is investigated. Conditions for the IMEX
Runge-Kutta methods to be symplectic are also derived. A numerical example
illustrating the theoretical properties is presented
Dark-matter particles and baryons from inflation and spontaneous CP violation in the early universe
We present aspects of a model which attempts to unify the creation of cold
dark matter, a CP-violating baryon asymmetry, and also a small, residual vacuum
energy density, in the early universe. The model contains a primary scalar
(inflaton) field and a primary pseudoscalar field, which are initially related
by a cosmological, chiral symmetry. The nonzero vacuum expectation value of the
pseudoscalar field spontaneously breaks CP invariance.Comment: 7 pages, appendix adde
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