21,932 research outputs found
3LP: a linear 3D-walking model including torso and swing dynamics
In this paper, we present a new model of biped locomotion which is composed
of three linear pendulums (one per leg and one for the whole upper body) to
describe stance, swing and torso dynamics. In addition to double support, this
model has different actuation possibilities in the swing hip and stance ankle
which could be widely used to produce different walking gaits. Without the need
for numerical time-integration, closed-form solutions help finding periodic
gaits which could be simply scaled in certain dimensions to modulate the motion
online. Thanks to linearity properties, the proposed model can provide a
computationally fast platform for model predictive controllers to predict the
future and consider meaningful inequality constraints to ensure feasibility of
the motion. Such property is coming from describing dynamics with joint torques
directly and therefore, reflecting hardware limitations more precisely, even in
the very abstract high level template space. The proposed model produces
human-like torque and ground reaction force profiles and thus, compared to
point-mass models, it is more promising for precise control of humanoid robots.
Despite being linear and lacking many other features of human walking like CoM
excursion, knee flexion and ground clearance, we show that the proposed model
can predict one of the main optimality trends in human walking, i.e. nonlinear
speed-frequency relationship. In this paper, we mainly focus on describing the
model and its capabilities, comparing it with human data and calculating
optimal human gait variables. Setting up control problems and advanced
biomechanical analysis still remain for future works.Comment: Journal paper under revie
Controlling Light Through Optical Disordered Media : Transmission Matrix Approach
We experimentally measure the monochromatic transmission matrix (TM) of an
optical multiple scattering medium using a spatial light modulator together
with a phase-shifting interferometry measurement method. The TM contains all
information needed to shape the scattered output field at will or to detect an
image through the medium. We confront theory and experiment for these
applications and we study the effect of noise on the reconstruction method. We
also extracted from the TM informations about the statistical properties of the
medium and the light transport whitin it. In particular, we are able to isolate
the contributions of the Memory Effect (ME) and measure its attenuation length
An extended collection of matrix derivative results for forward and reverse mode automatic differentiation
This paper collects together a number of matrix derivative results which are very useful in forward and reverse mode algorithmic differentiation (AD). It highlights in particular the remarkable contribution of a 1948 paper by Dwyer and Macphail which derives the linear and adjoint sensitivities of a matrix product, inverse and determinant, and a number of related results motivated by applications in multivariate analysis in statistics.\ud
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This is an extended version of a paper which will appear in the proceedings of AD2008, the 5th International Conference on Automatic Differentiation
Quark Pseudo-Distributions at Short Distances
We perform a one-loop study of the small- behavior of the Ioffe-time
distribution (ITD) , the basic function that may be
converted into parton pseudo- and quasi-distributions. We calculate the
corrections at the operator level, so that our results may be later used for
pseudo-distribution amplitudes and generalized parton pseudo-distributions. We
separate two sources of the -dependence at small . One is related
to the ultraviolet (UV) singularities generated by the gauge link, and another
to short-distance logarithms generating perturbative evolution of parton
densities. Our calculation explicitly shows that, for a finite UV cut-off, the
UV-singular terms vanish when . The UV divergences are absent in the
ratio ("reduced" ITD). Still, it
has a non-trivial short-distance behavior due to terms
generating perturbative evolution of the parton densities. We give an explicit
expression, up to constant terms, for the reduced ITD at one loop. It may be
used in extraction of PDFs from the lattice QCD simulations. We also use our
results to get new insights concerning the structure of parton
quasi-distributions at one-loop level.Comment: 10 pages, 4 figures, typos fixed, references added, some changes in
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A polynomial training algorithm for calculating perceptrons of optimal stability
Recomi (REpeated COrrelation Matrix Inversion) is a polynomially fast
algorithm for searching optimally stable solutions of the perceptron learning
problem. For random unbiased and biased patterns it is shown that the algorithm
is able to find optimal solutions, if any exist, in at worst O(N^4) floating
point operations. Even beyond the critical storage capacity alpha_c the
algorithm is able to find locally stable solutions (with negative stability) at
the same speed. There are no divergent time scales in the learning process. A
full proof of convergence cannot yet be given, only major constituents of a
proof are shown.Comment: 11 pages, Latex, 4 EPS figure
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