2,894 research outputs found
The best constant for the centered maximal operator on radial decreasing functions
We show that the lowest constant appearing in the weak type (1,1) inequality
satisfied by the centered Hardy-Littlewood maximal operator on radial
integrable functions is 1.Comment: corrected typo
Laplace Approximation for Divisive Gaussian Processes for Nonstationary Regression
The standard Gaussian Process regression (GP) is usually formulated under stationary hypotheses: The noise power is considered constant throughout the input space and the covariance of the prior distribution is typically modeled as depending only on the difference between input samples. These assumptions can be too restrictive and unrealistic for many real-world problems. Although nonstationarity can be achieved using specific covariance functions, they require a prior knowledge of the kind of nonstationarity, not available for most applications. In this paper we propose to use the Laplace approximation to make inference in a divisive GP model to perform nonstationary regression, including heteroscedastic noise cases. The log-concavity of the likelihood ensures a unimodal posterior and makes that the Laplace approximation converges to a unique maximum. The characteristics of the likelihood also allow to obtain accurate posterior approximations when compared to the Expectation Propagation (EP) approximations and the asymptotically exact posterior provided by a Markov Chain Monte Carlo implementation with Elliptical Slice Sampling (ESS), but at a reduced computational load with respect to both, EP and ESS
Pseudospectral Model Predictive Control under Partially Learned Dynamics
Trajectory optimization of a controlled dynamical system is an essential part
of autonomy, however many trajectory optimization techniques are limited by the
fidelity of the underlying parametric model. In the field of robotics, a lack
of model knowledge can be overcome with machine learning techniques, utilizing
measurements to build a dynamical model from the data. This paper aims to take
the middle ground between these two approaches by introducing a semi-parametric
representation of the underlying system dynamics. Our goal is to leverage the
considerable information contained in a traditional physics based model and
combine it with a data-driven, non-parametric regression technique known as a
Gaussian Process. Integrating this semi-parametric model with model predictive
pseudospectral control, we demonstrate this technique on both a cart pole and
quadrotor simulation with unmodeled damping and parametric error. In order to
manage parametric uncertainty, we introduce an algorithm that utilizes Sparse
Spectrum Gaussian Processes (SSGP) for online learning after each rollout. We
implement this online learning technique on a cart pole and quadrator, then
demonstrate the use of online learning and obstacle avoidance for the dubin
vehicle dynamics.Comment: Accepted but withdrawn from AIAA Scitech 201
Reduced kinetic mechanisms for modelling LPP combustión in gas turbines
Reduced kinetic mechanisms for modelling LPP combustión in gas turbine
Vivencia interior de la ley natural en San Buenaventura: sindéresis, superación de la dialéctica sujeto-objeto
Saint Bonaventure did not write specifically on the natural law;
nevertheless, interesting contributions on the issue can be derived
from his theological reflection. The natural law, understood in the
context of his doctrine of exemplarism, is a characterization of the
interior experience, where “synderesis” appears as a fundamental
faculty. Within this context, the Franciscan teacher derives a conception
wherein the subject-object dialectic is overcome at several
levels: epistemological, anthropological, metaphysical and moral
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