26,036 research outputs found
Maximal randomness expansion from steering inequality violations using qudits
We consider the generation of randomness based upon the observed violation of
an Einstein-Podolsky-Rosen (EPR) steering inequality, known as one-sided
device-independent randomness expansion. We show that in the simplest scenario
-- involving only two parties applying two measurements with outcomes each
-- that there exist EPR steering inequalities whose maximal violation certifies
the maximal amount of randomness, equal to log(d) bits. We further show that
all pure partially entangled full-Schmidt-rank states in all dimensions can
achieve maximal violation of these inequalities, and thus lead to maximal
randomness expansion in the one-sided device-independent setting. More
generally, the amount of randomness that can be certified is given by a
semidefinite program, which we use to study the behaviour for non-maximal
violations of the inequalities.Comment: 6 pages, 1 figur
On Seat Congestion, Passenger Comfort and Route Choice in Urban Transit: a Network Equilibrium Assignment Model with Application to Paris
16 pagesInternational audienceIn network assignment models of urban transit, traffic congestion has been modelled either as vehicle congestion along the route track, or by reducing the service frequency with respect to excess flow of passenger arrivals. A third type of congestion has been modelled by Leurent (1), (2): that of seat congestion, because being seated or standing make distinct on-board states for a transit rider, resulting in distinct discomfort costs, with potential influence on route choice on the transit network. The paper has a twofold objective of, first, providing a concise statement of the seat congestion model, and second, reporting on its application to the Paris metropolitan area – a problem of very large size. The model makes explicit the residual set capacity and its evolution at any stage along a service line; the priority rules amongst riders depending on their order of arrival in the competition to get a seat; and the randomness in leg cost to the rider. Line algorithms and consistent network algorithms are provided
Agent-based pedestrian modelling
When the focus of interest in geographical systems is at the very fine scale, at the level of
streets and buildings for example, movement becomes central to simulations of how spatial
activities are used and develop. Recent advances in computing power and the acquisition of
fine scale digital data now mean that we are able to attempt to understand and predict such
phenomena with the focus in spatial modelling changing to dynamic simulations of the
individual and collective behaviour of individual decision-making at such scales. In this
Chapter, we develop ideas about how such phenomena can be modelled showing first how
randomness and geometry are all important to local movement and how ordered spatial
structures emerge from such actions. We focus on developing these ideas for pedestrians
showing how random walks constrained by geometry but aided by what agents can see,
determine how individuals respond to locational patterns. We illustrate these ideas with three
types of example: first for local scale street scenes where congestion and flocking is all
important, second for coarser scale shopping centres such as malls where economic
preference interferes much more with local geometry, and finally for semi-organised street
festivals where management and control by police and related authorities is integral to the
way crowds move
Universality aspects of the d=3 random-bond Blume-Capel model
The effects of bond randomness on the universality aspects of the simple
cubic lattice ferromagnetic Blume-Capel model are discussed. The system is
studied numerically in both its first- and second-order phase transition
regimes by a comprehensive finite-size scaling analysis. We find that our data
for the second-order phase transition, emerging under random bonds from the
second-order regime of the pure model, are compatible with the universality
class of the 3d random Ising model. Furthermore, we find evidence that, the
second-order transition emerging under bond randomness from the first-order
regime of the pure model, belongs to a new and distinctive universality class.
The first finding reinforces the scenario of a single universality class for
the 3d Ising model with the three well-known types of quenched uncorrelated
disorder (bond randomness, site- and bond-dilution). The second, amounts to a
strong violation of universality principle of critical phenomena. For this case
of the ex-first-order 3d Blume-Capel model, we find sharp differences from the
critical behaviors, emerging under randomness, in the cases of the
ex-first-order transitions of the corresponding weak and strong first-order
transitions in the 3d three-state and four-state Potts models.Comment: 12 pages, 12 figure
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