Basic recursive summation and common dot product algorithm have a backward error bound that grows linearly with the vector dimension. Blanchard [1] proposed a class of fast and accurate summation and dot product algor...
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In this paper we analyze the graph-based approach to semi-supervised learning under a manifold assumption. We adopt a Bayesian perspective and demonstrate that, for a suitable choice of prior constructed with sufficie...
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In this paper we analyze the graph-based approach to semi-supervised learning under a manifold assumption. We adopt a Bayesian perspective and demonstrate that, for a suitable choice of prior constructed with sufficiently many unlabeled data, the posterior contracts around the truth at a rate that is minimax optimal up to a logarithmic factor. Our theory covers both regression and classification.
We explore the relationship between complexity and duality in quantum systems, focusing on how local and non-local operators evolve under time evolution. We find that non-local operators, which are dual to local opera...
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This paper investigates a novel nonlinear singular fractional SI model with the Φp operator and the Mittag-Leffler kernel. The initial investigation includes the existence, uniqueness, boundedness, and non-negativity...
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A Bayesian network approach is presented for probabilistic safety analysis(PSA)of railway *** idea consists of identifying and reproducing all the elements that the train encounters when circulating along a railway li...
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A Bayesian network approach is presented for probabilistic safety analysis(PSA)of railway *** idea consists of identifying and reproducing all the elements that the train encounters when circulating along a railway line,such as light and speed limit signals,tunnel or viaduct entries or exits,cuttings and embankments,acoustic sounds received in the cabin,curves,*** addition,since the human error is very relevant for safety evaluation,the automatic train protection(ATP)systems and the driver behaviour and its time evolution are modelled and taken into account to determine the probabilities of human *** nodes of the Bayesian network,their links and the associated probability tables are automatically constructed based on the line data that need to be carefully *** conditional probability tables are reproduced by closed formulas,which facilitate the modelling and the sensitivity analysis.A sorted list of the most dangerous elements in the line is obtained,which permits making decisions about the line safety and programming maintenance operations in order to optimize them and reduce the maintenance costs *** proposed methodology is illustrated by its application to several cases that include real lines such as the Palencia-Santander and the Dublin-Belfast lines.
We develop entropy dissipative higher order accurate local discontinuous Galerkin (LDG) discretizations coupled with Diagonally Implicit Runge-Kutta (DIRK) methods for nonlinear degenerate parabolic equations with a g...
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We consider the joint problem of system identification and inverse optimal control for discrete-time stochastic Linear Quadratic Regulators. We analyze finite and infinite time horizons in a partially observed setting...
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In this paper, we apply the Paired-Explicit Runge-Kutta (P-ERK) schemes by Vermeire et. al. (2019, 2022) to dynamically partitioned systems arising from adaptive mesh refinement. The P-ERK schemes enable multirate tim...
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We present a new approach for modeling avoidance constraints in 2D environments, in which waypoints are assigned to obstacle-free polyhedral regions. Constraints of this form are often formulated as mixed-integer prog...
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There has been a surge of interest in uncertainty quantification for parametric partial differential equations (PDEs) with Gevrey regular inputs. The Gevrey class contains functions that are infinitely smooth with a g...
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