1,537 research outputs found
Detection of synchronization from univariate data using wavelet transform
A method is proposed for detecting from univariate data the presence of
synchronization of a self-sustained oscillator by external driving with varying
frequency. The method is based on the analysis of difference between the
oscillator instantaneous phases calculated using continuous wavelet transform
at time moments shifted by a certain constant value relative to each other. We
apply our method to a driven asymmetric van der Pol oscillator, experimental
data from a driven electronic oscillator with delayed feedback and human
heartbeat time series. In the latest case, the analysis of the heart rate
variability data reveals synchronous regimes between the respiration and slow
oscillations in blood pressure.Comment: 10 pages, 9 figure
On the viscous Cahn-Hilliard equation with singular potential and inertial term
We consider a relaxation of the viscous Cahn-Hilliard equation induced by the
second-order inertial term~. The equation also contains a semilinear
term of "singular" type. Namely, the function is defined only on a
bounded interval of corresponding to the physically admissible
values of the unknown , and diverges as approaches the extrema of that
interval. In view of its interaction with the inertial term , the term
is difficult to be treated mathematically. Based on an approach
originally devised for the strongly damped wave equation, we propose a suitable
concept of weak solution based on duality methods and prove an existence
result.Comment: 11 page
Attention and Anticipation in Fast Visual-Inertial Navigation
We study a Visual-Inertial Navigation (VIN) problem in which a robot needs to
estimate its state using an on-board camera and an inertial sensor, without any
prior knowledge of the external environment. We consider the case in which the
robot can allocate limited resources to VIN, due to tight computational
constraints. Therefore, we answer the following question: under limited
resources, what are the most relevant visual cues to maximize the performance
of visual-inertial navigation? Our approach has four key ingredients. First, it
is task-driven, in that the selection of the visual cues is guided by a metric
quantifying the VIN performance. Second, it exploits the notion of
anticipation, since it uses a simplified model for forward-simulation of robot
dynamics, predicting the utility of a set of visual cues over a future time
horizon. Third, it is efficient and easy to implement, since it leads to a
greedy algorithm for the selection of the most relevant visual cues. Fourth, it
provides formal performance guarantees: we leverage submodularity to prove that
the greedy selection cannot be far from the optimal (combinatorial) selection.
Simulations and real experiments on agile drones show that our approach ensures
state-of-the-art VIN performance while maintaining a lean processing time. In
the easy scenarios, our approach outperforms appearance-based feature selection
in terms of localization errors. In the most challenging scenarios, it enables
accurate visual-inertial navigation while appearance-based feature selection
fails to track robot's motion during aggressive maneuvers.Comment: 20 pages, 7 figures, 2 table
A Continuous-Time Perspective on Optimal Methods for Monotone Equation Problems
We study \textit{rescaled gradient dynamical systems} in a Hilbert space
, where implicit discretization in a finite-dimensional Euclidean
space leads to high-order methods for solving monotone equations (MEs). Our
framework can be interpreted as a natural generalization of celebrated dual
extrapolation method~\citep{Nesterov-2007-Dual} from first order to high order
via appeal to the regularization toolbox of optimization
theory~\citep{Nesterov-2021-Implementable, Nesterov-2021-Inexact}. More
specifically, we establish the existence and uniqueness of a global solution
and analyze the convergence properties of solution trajectories. We also
present discrete-time counterparts of our high-order continuous-time methods,
and we show that the -order method achieves an ergodic rate of
in terms of a restricted merit function and a pointwise rate
of in terms of a residue function. Under regularity conditions,
the restarted version of -order methods achieves local convergence with
the order . Notably, our methods are \textit{optimal} since they have
matched the lower bound established for solving the monotone equation problems
under a standard linear span assumption~\citep{Lin-2022-Perseus}.Comment: 35 Pages; Add the reference with lower bound constructio
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