52,762 research outputs found
Computationally Tractable Pairwise Complexity Profile
Quantifying the complexity of systems consisting of many interacting parts
has been an important challenge in the field of complex systems in both
abstract and applied contexts. One approach, the complexity profile, is a
measure of the information to describe a system as a function of the scale at
which it is observed. We present a new formulation of the complexity profile,
which expands its possible application to high-dimensional real-world and
mathematically defined systems. The new method is constructed from the pairwise
dependencies between components of the system. The pairwise approach may serve
as both a formulation in its own right and a computationally feasible
approximation to the original complexity profile. We compare it to the original
complexity profile by giving cases where they are equivalent, proving
properties common to both methods, and demonstrating where they differ. Both
formulations satisfy linear superposition for unrelated systems and
conservation of total degrees of freedom (sum rule). The new pairwise
formulation is also a monotonically non-increasing function of scale.
Furthermore, we show that the new formulation defines a class of related
complexity profile functions for a given system, demonstrating the generality
of the formalism.Comment: 18 pages, 3 figure
Joint segmentation of many aCGH profiles using fast group LARS
Array-Based Comparative Genomic Hybridization (aCGH) is a method used to
search for genomic regions with copy numbers variations. For a given aCGH
profile, one challenge is to accurately segment it into regions of constant
copy number. Subjects sharing the same disease status, for example a type of
cancer, often have aCGH profiles with similar copy number variations, due to
duplications and deletions relevant to that particular disease. We introduce a
constrained optimization algorithm that jointly segments aCGH profiles of many
subjects. It simultaneously penalizes the amount of freedom the set of profiles
have to jump from one level of constant copy number to another, at genomic
locations known as breakpoints. We show that breakpoints shared by many
different profiles tend to be found first by the algorithm, even in the
presence of significant amounts of noise. The algorithm can be formulated as a
group LARS problem. We propose an extremely fast way to find the solution path,
i.e., a sequence of shared breakpoints in order of importance. For no extra
cost the algorithm smoothes all of the aCGH profiles into piecewise-constant
regions of equal copy number, giving low-dimensional versions of the original
data. These can be shown for all profiles on a single graph, allowing for
intuitive visual interpretation. Simulations and an implementation of the
algorithm on bladder cancer aCGH profiles are provided
Simulating fluid flows in micro and nano devices : the challenge of non-equilibrium behaviour
We review some recent developments in the modelling of non-equilibrium (rarefied) gas flows at the micro- and nano-scale, concentrating on two different but promising approaches: extended hydrodynamic models, and lattice Boltzmann methods. Following a brief exposition of the challenges that non-equilibrium poses in micro- and nano-scale gas flows, we turn first to extended hydrodynamics, outlining the effective abandonment of Burnett-type models in favour of high-order regularised moment equations. We show that the latter models, with properly-constituted boundary conditions, can capture critical non-equilibrium flow phenomena quite well. We then review the boundary conditions required if the conventional Navier-Stokes-Fourier (NSF) fluid dynamic model is applied at the micro scale, describing how 2nd-order Maxwell-type conditions can be used to compensate for some of the non-equilibrium flow behaviour near solid surfaces. While extended hydrodynamics is not yet widely-used for real flow problems because of its inherent complexity, we finish this section with an outline of recent 'phenomenological extended hydrodynamics' (PEH) techniques-essentially the NSF equations scaled to incorporate non-equilibrium behaviour close to solid surfaces-which offer promise as engineering models. Understanding non-equilibrium within lattice Boltzmann (LB) framework is not as advanced as in the hydrodynamic framework, although LB can borrow some of the techniques which are being developed in the latter-in particular, the near-wall scaling of certain fluid properties that has proven effective in PEH. We describe how, with this modification, the standard 2nd-order LB method is showing promise in predicting some rarefaction phenomena, indicating that instead of developing higher-order off-lattice LB methods with a large number of discrete velocities, a simplified high-order LB method with near-wall scaling may prove to be just as effective as a simulation tool
Theory of weakly nonlinear self sustained detonations
We propose a theory of weakly nonlinear multi-dimensional self sustained
detonations based on asymptotic analysis of the reactive compressible
Navier-Stokes equations. We show that these equations can be reduced to a model
consisting of a forced, unsteady, small disturbance, transonic equation and a
rate equation for the heat release. In one spatial dimension, the model
simplifies to a forced Burgers equation. Through analysis, numerical
calculations and comparison with the reactive Euler equations, the model is
demonstrated to capture such essential dynamical characteristics of detonations
as the steady-state structure, the linear stability spectrum, the
period-doubling sequence of bifurcations and chaos in one-dimensional
detonations and cellular structures in multi- dimensional detonations
Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds
In this work we present a trajectory Optimization framework for whole-body
motion planning through contacts. We demonstrate how the proposed approach can
be applied to automatically discover different gaits and dynamic motions on a
quadruped robot. In contrast to most previous methods, we do not pre-specify
contact switches, timings, points or gait patterns, but they are a direct
outcome of the optimization. Furthermore, we optimize over the entire dynamics
of the robot, which enables the optimizer to fully leverage the capabilities of
the robot. To illustrate the spectrum of achievable motions, here we show eight
different tasks, which would require very different control structures when
solved with state-of-the-art methods. Using our trajectory Optimization
approach, we are solving each task with a simple, high level cost function and
without any changes in the control structure. Furthermore, we fully integrated
our approach with the robot's control and estimation framework such that
optimization can be run online. By demonstrating a rough manipulation task with
multiple dynamic contact switches, we exemplarily show how optimized
trajectories and control inputs can be directly applied to hardware.Comment: Video: https://youtu.be/sILuqJBsyK
The group fused Lasso for multiple change-point detection
We present the group fused Lasso for detection of multiple change-points
shared by a set of co-occurring one-dimensional signals. Change-points are
detected by approximating the original signals with a constraint on the
multidimensional total variation, leading to piecewise-constant approximations.
Fast algorithms are proposed to solve the resulting optimization problems,
either exactly or approximately. Conditions are given for consistency of both
algorithms as the number of signals increases, and empirical evidence is
provided to support the results on simulated and array comparative genomic
hybridization data
Quantitative Measurements of CME-driven Shocks from LASCO Observations
In this paper, we demonstrate that CME-driven shocks can be detected in white
light coronagraph images and in which properties such as the density
compression ratio and shock direction can be measured. Also, their propagation
direction can be deduced via simple modeling. We focused on CMEs during the
ascending phase of solar cycle 23 when the large-scale morphology of the corona
was simple. We selected events which were good candidates to drive a shock due
to their high speeds (V>1500 km/s). The final list includes 15 CMEs. For each
event, we calibrated the LASCO data, constructed excess mass images and
searched for indications of faint and relatively sharp fronts ahead of the
bright CME front. We found such signatures in 86% (13/15) of the events and
measured the upstream/downstream densities to estimate the shock strength. Our
values are in agreement with theoretical expectations and show good
correlations with the CME kinetic energy and momentum. Finally, we used a
simple forward modeling technique to estimate the 3D shape and orientation of
the white light shock features. We found excellent agreement with the observed
density profiles and the locations of the CME source regions. Our results
strongly suggest that the observed brightness enhancements result from density
enhancements due to a bow-shock structure driven by the CME.Comment: to be published in Astrophysical Journa
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