196,181 research outputs found
Preface to ”Mathematical Modelling and Machine Learning Methods for Bioinformatics and Data Science Applications”
No full textComputing the convolution and the Minkowski sum of surfaces
No full textIn many applications, such as NC tool path generation and robot motion planning, it is required to compute the Minkowski sum of two objects. Generally the Minkowski sum of two rational surfaces cannot be expressed in rational form. In this paper we show that for LN spline surfaces (surfaces with a linear field of normal vectors) a closed form representation is available. Copyright © 2005 by the Association for Computing Machinery, Inc
Adaptive Refinement in Advection--Diffusion Problems by Anomaly Detection: A Numerical Study
No full textWe consider advection--diffusion--reaction problems, where the advective or the reactive term is dominating with respect to the diffusive term. The solutions of these problems are characterized by the so-called layers, which represent localized regions where the gradients of the solutions are rather large or are subjected to abrupt changes. In order to improve the accuracy of the computed solution, it is fundamental to locally increase the number of degrees of freedom by limiting the computational costs. Thus, adaptive refinement, by a posteriori error estimators, is employed. The error estimators are then processed by an anomaly detection algorithm in order to identify those regions of the computational domain that should be marked and, hence, refined. The anomaly detection task is performed in an unsupervised fashion and the proposed strategy is tested on typical benchmarks. The present work shows a numerical study that highlights promising results obtained by bridging together standard techniques, i.e., the error estimators, and approaches typical of machine learning and artificial intelligence, such as the anomaly detection task
Computer simulation of polarizable fluids: A consistent and fast way for dealing with polarizability and hyperpolarizability
No full textBoolean Surfaces with Shape Constraints
No full textIn this paper we present a new method for the construction of
parametric surfaces reproducing an object from a set of spatial
data. We adopt a hybrid scheme, based on the Boolean sum of
variable degree spline operators, which both interpolates a set of
grid lines and approximates the data. As usual the variable
degrees can be chosen to satisfy proper shape constraints
Construction of G2 planar Hermite interpolants with prescribed arc lengths
No full textIn this paper we address the problem of constructing G^2 planar Pythagorean–hodograph (PH) spline curves, that interpolate points, tangent directions and curvatures, and have prescribed arc-length. The interpolation scheme is completely local. Each spline segment is defined as a PH biarc curve of degree 7, which results in having a closed form solution of the G^2 interpolation equations depending on four free parameters. By fixing two of them to zero, it is proven that the length constraint can be satisfied for any data and any chosen ratio between the two boundary tangents. Length interpolation equation reduces to one algebraic equation with four solutions in general. To select the best one, the value of the bending energy is observed. Several numerical examples are provided to illustrate the obtained theoretical results and to numerically confirm that the approximation order is 5
Mathematical Modelling and Machine Learning Methods for Bioinformatics and Data Science Applications
No full textGeometric Construction of Quintic Parametric B-splines
No full textThe aim of this paper is to present a new class of B-spline-like functions with tension properties. The main feature of these basis
functions consists in possessing C3 or even C4 continuity and, at the same time, being endowed by shape parameters that can be
easily handled. Therefore they constitute a useful tool for the construction of curves satisfying some prescribed shape constraints.
The construction is based on a geometric approach which uses parametric curves with piecewise quintic components
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