6,434 research outputs found
Profile extrema for visualizing and quantifying uncertainties on excursion regions. Application to coastal flooding
We consider the problem of describing excursion sets of a real-valued
function , i.e. the set of inputs where is above a fixed threshold. Such
regions are hard to visualize if the input space dimension, , is higher than
2. For a given projection matrix from the input space to a lower dimensional
(usually ) subspace, we introduce profile sup (inf) functions that
associate to each point in the projection's image the sup (inf) of the function
constrained over the pre-image of this point by the considered projection.
Plots of profile extrema functions convey a simple, although intrinsically
partial, visualization of the set. We consider expensive to evaluate functions
where only a very limited number of evaluations, , is available, e.g.
, and we surrogate with a posterior quantity of a Gaussian process
(GP) model. We first compute profile extrema functions for the posterior mean
given evaluations of . We quantify the uncertainty on such estimates by
studying the distribution of GP profile extrema with posterior
quasi-realizations obtained from an approximating process. We control such
approximation with a bound inherited from the Borell-TIS inequality. The
technique is applied to analytical functions () and to a -dimensional
coastal flooding test case for a site located on the Atlantic French coast.
Here is a numerical model returning the area of flooded surface in the
coastal region given some offshore conditions. Profile extrema functions
allowed us to better understand which offshore conditions impact large flooding
events
Perception and steering control in paired bat flight
Animals within groups need to coordinate their reactions to perceived environmental features and to each other in order to safely move from one point to another. This paper extends our previously published work on the flight patterns of Myotis velifer that have been observed in a habitat near Johnson City, Texas. Each evening, these bats emerge from a cave in sequences of small groups that typically contain no more than three or four individuals, and they thus provide ideal subjects for studying leader-follower behaviors. By analyzing the flight paths of a group of M. velifer, the data show that the flight behavior of a follower bat is influenced by the
flight behavior of a leader bat in a way that is not well explained by existing pursuit laws, such as classical pursuit, constant bearing and motion camouflage. Thus we propose an
alternative steering law based on virtual loom, a concept we introduce to capture the geometrical configuration of the leader-follower pair. It is shown that this law may be integrated with our
previously proposed vision-enabled steering laws to synthesize trajectories, the statistics of which fit with those of the bats in our data set. The results suggest that bats use perceived information
of both the environment and their neighbors for navigation.2018-08-0
Investigation of a hopping transporter concept for lunar exploration
Performance and dynamic characteristics determined for hopping transporter for lunar exploratio
Unbounded Orbits for Outer Billiards
Outer billiards is a basic dynamical system, defined relative to a planar
convex shape. This system was introduced in the 1950's by B.H. Neumann and
later popularized in the 1970's by J. Moser. All along, one of the central
questions has been: is there an outer billiards system with an unbounded orbit.
We answer this question by proving that outer billiards defined relative to the
Penrose Kite has an unbounded orbit. The Penrose kite is the quadrilateral that
appears in the famous Penrose tiling. We also analyze some of the finer orbit
structure of outer billiards on the penrose kite. This analysis shows that
there is an uncountable set of unbounded orbits. Our method of proof relates
the problem to self-similar tilings, polygon exchange maps, and arithmetic
dynamics.Comment: 65 pages, computer-aided proof. Auxilliary program, Billiard King,
available from author's website. Latest version is essentially the same as
earlier versions, but with minor improvements and many typos fixe
Sensory Motor Remapping of Space in Human-Machine Interfaces
Studies of adaptation to patterns of deterministic forces have revealed the ability of the motor control system to form and use predictive representations of the environment. These studies have also pointed out that adaptation to novel dynamics is aimed at preserving the trajectories of a controlled endpoint, either the hand of a subject or a transported object. We review some of these experiments and present more recent studies aimed at understanding how the motor system forms representations of the physical space in which actions take place. An extensive line of investigations in visual information processing has dealt with the issue of how the Euclidean properties of space are recovered from visual signals that do not appear to possess these properties. The same question is addressed here in the context of motor behavior and motor learning by observing how people remap hand gestures and body motions that control the state of an external device. We present some theoretical considerations and experimental evidence about the ability of the nervous system to create novel patterns of coordination that are consistent with the representation of extrapersonal space. We also discuss the perspective of endowing human–machine interfaces with learning algorithms that, combined with human learning, may facilitate the control of powered wheelchairs and other assistive devices
Gravitational Collapse in One Dimension
We simulate the evolution of one-dimensional gravitating collisionless
systems from non- equilibrium initial conditions, similar to the conditions
that lead to the formation of dark- matter halos in three dimensions. As in the
case of 3D halo formation we find that initially cold, nearly homogeneous
particle distributions collapse to approach a final equilibrium state with a
universal density profile. At small radii, this attractor exhibits a power-law
behavior in density, {\rho}(x) \propto |x|^(-{\gamma}_crit), {\gamma}_crit
\simeq 0.47, slightly but significantly shallower than the value {\gamma} = 1/2
suggested previously. This state develops from the initial conditions through a
process of phase mixing and violent relaxation. This process preserves the
energy ranks of particles. By warming the initial conditions, we illustrate a
cross-over from this power-law final state to a final state containing a
homogeneous core. We further show that inhomogeneous but cold power-law initial
conditions, with initial exponent {\gamma}_i > {\gamma}_crit, do not evolve
toward the attractor but reach a final state that retains their original
power-law behavior in the interior of the profile, indicating a bifurcation in
the final state as a function of the initial exponent. Our results rely on a
high-fidelity event-driven simulation technique.Comment: 14 Pages, 13 Figures. Submitted to MNRA
The formation of CDM haloes I: Collapse thresholds and the ellipsoidal collapse model
In the excursion set approach to structure formation initially spherical
regions of the linear density field collapse to form haloes of mass at
redshift if their linearly extrapolated density contrast, averaged
on that scale, exceeds some critical threshold, .
The value of is often calculated from the
spherical or ellipsoidal collapse model, which provide well-defined predictions
given auxiliary properties of the tidal field at a given location. We use two
cosmological simulations of structure growth in a cold dark matter
scenario to quantify , its dependence on the
surrounding tidal field, as well as on the shapes of the Lagrangian regions
that collapse to form haloes at . Our results indicate that the
ellipsoidal collapse model provides an accurate description of the mean
dependence of on both the strength of the tidal
field and on halo mass. However, for a given , depends strongly on the halo's characteristic formation
redshift: the earlier a halo forms, the higher its initial density contrast.
Surprisingly, the majority of haloes forming fall below the ellipsoidal
collapse barrier, contradicting the model predictions. We trace the origin of
this effect to the non-spherical shapes of Lagrangian haloes, which arise
naturally due to the asymmetry of the linear tidal field. We show that a
modified collapse model, that accounts for the triaxial shape of protohaloes,
provides a more accurate description of the measured minimum overdensities of
recently collapsed objects.Comment: MNRAS in pres
Halo abundances within the cosmic web
We investigate the dependence of the mass function of dark-matter haloes on
their environment within the cosmic web of large-scale structure. A dependence
of the halo mass function on large-scale mean density is a standard element of
cosmological theory, allowing mass-dependent biasing to be understood via the
peak-background split. On the assumption of a Gaussian density field, this
analysis can be extended to ask how the mass function depends on the
geometrical environment: clusters, filaments, sheets and voids, as classified
via the tidal tensor (the Hessian matrix of the gravitational potential). In
linear theory, the problem can be solved exactly, and the result is
attractively simple: the conditional mass function has no explicit dependence
on the local tidal field, and is a function only of the local density on the
filtering scale used to define the tidal tensor. There is nevertheless a strong
implicit predicted dependence on geometrical environment, because the local
density couples statistically to the derivatives of the potential. We compute
the predictions of this model and study the limits of their validity by
comparing them to results deduced empirically from -body simulations. We
have verified that, to a good approximation, the abundance of haloes in
different environments depends only on their densities, and not on their tidal
structure. In this sense we find relative differences between halo abundances
in different environments with the same density which are smaller than 13%.
Furthermore, for sufficiently large filtering scales, the agreement with the
theoretical prediction is good, although there are important deviations from
the Gaussian prediction at small, non-linear scales. We discuss how to obtain
improved predictions in this regime, using the 'effective-universe' approach.Comment: 14 pages, 6 figures. Revision matching journal versio
The Brownian limit of separable permutations
We study random uniform permutations in an important class of
pattern-avoiding permutations: the separable permutations. We describe the
asymptotics of the number of occurrences of any fixed given pattern in such a
random permutation in terms of the Brownian excursion. In the recent
terminology of permutons, our work can be interpreted as the convergence of
uniform random separable permutations towards a "Brownian separable permuton".Comment: 45 pages, 14 figures, incorporating referee's suggestion
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