65,014 research outputs found
Estimating statistical distributions using an integral identity
We present an identity for an unbiased estimate of a general statistical
distribution. The identity computes the distribution density from dividing a
histogram sum over a local window by a correction factor from a mean-force
integral, and the mean force can be evaluated as a configuration average. We
show that the optimal window size is roughly the inverse of the local
mean-force fluctuation. The new identity offers a more robust and precise
estimate than a previous one by Adib and Jarzynski [J. Chem. Phys. 122, 014114,
(2005)]. It also allows a straightforward generalization to an arbitrary
ensemble and a joint distribution of multiple variables. Particularly we derive
a mean-force enhanced version of the weighted histogram analysis method (WHAM).
The method can be used to improve distributions computed from molecular
simulations. We illustrate the use in computing a potential energy
distribution, a volume distribution in a constant-pressure ensemble, a radial
distribution function and a joint distribution of amino acid backbone dihedral
angles.Comment: 45 pages, 7 figures, simplified derivation, a more general mean-force
formula, add discussions to the window size, add extensions to WHAM, and 2d
distribution
Human Preference-Based Learning for High-dimensional Optimization of Exoskeleton Walking Gaits
Optimizing lower-body exoskeleton walking gaits for user comfort requires understanding users’ preferences over a high-dimensional gait parameter space. However, existing preference-based learning methods have only explored low-dimensional domains due to computational limitations. To learn user preferences in high dimensions, this work presents LINECOSPAR, a human-in-the-loop preference-based framework that enables optimization over many parameters by iteratively exploring one-dimensional subspaces. Additionally, this work identifies gait attributes that characterize broader preferences across users. In simulations and human trials, we empirically verify that LINECOSPAR is a sample-efficient approach for high-dimensional preference optimization. Our analysis of the experimental data reveals a correspondence between human preferences and objective measures of dynamicity, while also highlighting differences in the utility functions underlying individual users’ gait preferences. This result has implications for exoskeleton gait synthesis, an active field with applications to clinical use and patient rehabilitation
Safe Multi-Agent Interaction through Robust Control Barrier Functions with Learned Uncertainties
Robots operating in real world settings must navigate and maintain safety while interacting with many heterogeneous agents and obstacles. Multi-Agent Control Barrier Functions (CBF) have emerged as a computationally efficient tool to guarantee safety in multi-agent environments, but they assume perfect knowledge of both the robot dynamics and other agents' dynamics. While knowledge of the robot's dynamics might be reasonably well known, the heterogeneity of agents in real-world environments means there will always be considerable uncertainty in our prediction of other agents' dynamics. This work aims to learn high-confidence bounds for these dynamic uncertainties using Matrix-Variate Gaussian Process models, and incorporates them into a robust multi-agent CBF framework. We transform the resulting min-max robust CBF into a quadratic program, which can be efficiently solved in real time. We verify via simulation results that the nominal multi-agent CBF is often violated during agent interactions, whereas our robust formulation maintains safety with a much higher probability and adapts to learned uncertainties
Analysis of effects of macroscopic propagation and multiple molecular orbitals on the minimum in high-order harmonic generation of aligned CO
We report theoretical calculations on the effect of the multiple orbital
contribution in high-order harmonic generation (HHG) from aligned CO with
inclusion of macroscopic propagation of harmonic fields in the medium. Our
results show very good agreements with recent experiments for the dynamics of
the minimum in HHG spectra as laser intensity or alignment angle changes.
Calculations are carried out to check how the position of the minimum in HHG
spectra depends on the degrees of molecular alignment, laser focusing
conditions, and the effects of alignment-dependent ionization rates of the
different molecular orbitals. These analyses help to explain why the minima
observed in different experiments may vary.Comment: 7 figure
Semiclassical Time Evolution of the Holes from Luttinger Hamiltonian
We study the semi-classical motion of holes by exact numerical solution of
the Luttinger model. The trajectories obtained for the heavy and light holes
agree well with the higher order corrections to the abelian and the non-abelian
adiabatic theories in Ref. [1] [S. Murakami et al., Science 301, 1378(2003)],
respectively. It is found that the hole trajectories contain rapid oscillations
reminiscent of the "Zitterbewegung" of relativistic electrons. We also comment
on the non-conservation of helicity of the light holes.Comment: 4 pages, 5 fugure
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