Search results for "vector [form factor]"
showing 10 items of 770 documents
Plane foliations with a saddle singularity
2012
Abstract We study the set of planar vector fields with a unique singularity of hyperbolic saddle type. We found conditions to assure that a such vector field is topologically equivalent to a linear saddle. Furthermore, we describe the plane foliations associated to these vector fields. Such a foliation can be split in two subfoliations. One without restriction and another one that is topologically characterized by means of trees.
Finite element approximation of vector fields given by curl and divergence
1981
In this paper a finite element approximation scheme for the system curl is considered. The use of pointwise approximation of the boundary condition leads to a nonconforming method. The error estimate is proved and numerically tested.
The Lie algebra of polynomial vector fields and the Jacobian conjecture
1998
The Jacobian conjecture for polynomial maps ϕ:Kn→Kn is shown to be equivalent to a certain Lie algebra theoretic property of the Lie algebra\(\mathbb{D}\) of formal vector fields inn variables. To be precise, let\(\mathbb{D}_0 \) be the unique subalgebra of codimensionn (consisting of the singular vector fields),H a Cartan subalgebra of\(\mathbb{D}_0 \),Hλ the root spaces corresponding to linear forms λ onH and\(A = \oplus _{\lambda \in {\rm H}^ * } H_\lambda \). Then every polynomial map ϕ:Kn→Kn with invertible Jacobian matrix is an automorphism if and only if every automorphism Φ of\(\mathbb{D}\) with Φ(A)\( \subseteq A\) satisfies Φ(A)=A.
Machine Learning Regression Approaches for Colored Dissolved Organic Matter (CDOM) Retrieval with S2-MSI and S3-OLCI Simulated Data
2018
The colored dissolved organic matter (CDOM) variable is the standard measure of humic substance in waters optics. CDOM is optically characterized by its spectral absorption coefficient, a C D O M at at reference wavelength (e.g., ≈ 440 nm). Retrieval of CDOM is traditionally done using bio-optical models. As an alternative, this paper presents a comparison of five machine learning methods applied to Sentinel-2 and Sentinel-3 simulated reflectance ( R r s ) data for the retrieval of CDOM: regularized linear regression (RLR), random forest regression (RFR), kernel ridge regression (KRR), Gaussian process regression (GPR) and support vector machines (SVR). Two different datasets of radiative t…
More limit cycles than expected in Liénard equations
2007
The paper deals with classical polynomial Lienard equations, i.e. planar vector fields associated to scalar second order differential equations x"+ f(x)x' + x = 0 where f is a polynomial. We prove that for a well-chosen polynomial f of degree 6, the equation exhibits 4 limit cycles. It induces that for n ≥ 3 there exist polynomials f of degree 2n such that the related equations exhibit more than n limit cycles. This contradicts the conjecture of Lins, de Melo and Pugh stating that for Lienard equations as above, with f of degree 2n, the maximum number of limit cycles is n. The limit cycles that we found are relaxation oscillations which appear in slow-fast systems at the boundary of classic…
Distributed learning automata-based scheme for classification using novel pursuit scheme
2020
Learning Automata (LA) is a popular decision making mechanism to “determine the optimal action out of a set of allowable actions” (Agache and Oommen, IEEE Trans Syst Man Cybern-Part B Cybern 2002(6): 738–749, 2002). The distinguishing characteristic of automata-based learning is that the search for the optimising parameter vector is conducted in the space of probability distributions defined over the parameter space, rather than in the parameter space itself (Thathachar and Sastry, IEEE Trans Syst Man Cybern-Part B Cybern 32(6): 711–722, 2002). Recently, Goodwin and Yazidi pioneered the use of Ant Colony Optimisation (ACO) for solving classification problems (Goodwin and Yazidi 2016). In th…
A Machine Learning Model to Predict Intravenous Immunoglobulin-Resistant Kawasaki Disease Patients: A Retrospective Study Based on the Chongqing Popu…
2021
Objective: We explored the risk factors for intravenous immunoglobulin (IVIG) resistance in children with Kawasaki disease (KD) and constructed a prediction model based on machine learning algorithms.Methods: A retrospective study including 1,398 KD patients hospitalized in 7 affiliated hospitals of Chongqing Medical University from January 2015 to August 2020 was conducted. All patients were divided into IVIG-responsive and IVIG-resistant groups, which were randomly divided into training and validation sets. The independent risk factors were determined using logistic regression analysis. Logistic regression nomograms, support vector machine (SVM), XGBoost and LightGBM prediction models wer…
Generalised power series solutions of sub-analytic differential equations
2006
Abstract We show that if a solution y ( x ) of a sub-analytic differential equation admits an asymptotic expansion ∑ i = 1 ∞ c i x μ i , μ i ∈ R + , then the exponents μ i belong to a finitely generated semi-group of R + . We deduce a similar result for the components of non-oscillating trajectories of real analytic vector fields in dimension n. To cite this article: M. Matusinski, J.-P. Rolin, C. R. Acad. Sci. Paris, Ser. I 342 (2006).
Minimal learning machine in hyperspectral imaging classification
2020
A hyperspectral (HS) image is typically a stack of frames, where each frame represents the intensity of a different wavelength of light. Each spatial pixel has a spectrum. In the classification of the HS image, each spectrum is classified pixel-by-pixel. In some of the real-time applications, the amount of the HS image data causes performance challenges. Those issues relate to the platforms (e.g. drones) payload restrictions, the issues of the available energy and to the complexity of the machine learning models. In this study, we introduce the minimal learning machine (MLM) as a computationally cheap training and classification machine learning method for the hyperspectral imaging classificatio…
Characterization of the atmospheric muon flux in IceCube
2015
Muons produced in atmospheric cosmic ray showers account for the by far dominant part of the event yield in large-volume underground particle detectors. The IceCube detector, with an instrumented volume of about a cubic kilometer, has the potential to conduct unique investigations on atmospheric muons by exploiting the large collection area and the possibility to track particles over a long distance. Through detailed reconstruction of energy deposition along the tracks, the characteristics of muon bundles can be quantified, and individual particles of exceptionally high energy identified. The data can then be used to constrain the cosmic ray primary flux and the contribution to atmospheric …