Search results for "Vector"
showing 10 items of 2660 documents
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.
Uniform estimates for the X-ray transform restricted to polynomial curves
2012
We establish near-optimal mixed-norm estimates for the X-ray transform restricted to polynomial curves with a weight that is a power of the affine arclength. The bounds that we establish depend only on the spatial dimension and the degree of the polynomial. Some of our results are new even in the well-curved case.
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…
The Schur property on projective and injective tensor products
2008
The problem of whether the Schur property is passed from a Banach space to its (symmetric) projective n-fold tensor product is reformu lated in the language of polynomial ideals. As a result, a very closely related question is solved in the negative. It is also proved that the injective tensor product of infrabarrelled locally convex spaces with the Schur property has the Schur property as well.
Principal polynomial analysis for remote sensing data processing
2011
Inspired by the concept of Principal Curves, in this paper, we define Principal Polynomials as a non-linear generalization of Principal Components to overcome the conditional mean independence restriction of PCA. Principal Polynomials deform the straight Principal Components by minimizing the regression error (or variance) in the corresponding orthogonal subspaces. We propose to use a projection on a series of these polynomials to set a new nonlinear data representation: the Principal Polynomial Analysis (PPA). We prove that the dimensionality reduction error in PPA is always lower than in PCA. Lower truncation error and increased independence suggest that unsupervised PPA features can be b…
An Innovative Friction Stir Welding Based Technique to Produce Dissimilar Light Alloys to Thermoplastic Matrix Composite Joints
2016
Abstract Aluminum sheets can be joined to composite materials with different techniques. Each of them has advantages and weak points over the others. In literature, new techniques and patents are continuously developed to overcome these difficulties. In the paper a new Friction Stir Welding based approach is proposed to mechanically join AA6082-T6 to self-reinforced polypropylene. The aluminum sheet is pre-holed along both the sides of the weld line. A pinless tool generates the heat and pressure needed to activate back-extrusion of the composite. Joints have been produced with varying hole diameter and pitch. The mechanical resistance of the joint has been evaluated and the different failu…
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…
Digenean parasites of the bivalve mollusc Pisidium amnicum in a small river in eastern Finland
1998
The host-parasite relationship between digeneans and a semelparous population of the mollusc. Pisidium amnicum Müller in a small river in eastern Finland was studied during 1992/1993. The parasite prevalence of the population was high. The total prevalence was 45.6% in 1992 (n = 790) and 47.5% in 1993 (n = 160). The dominant digenean, Bunodera luciopercae (34.2% in 1992, 35.0% in 1993), had highest prevalences in July/August and in winter. Two other species, Palaeorchis crassus (7.8% in 1992, 7.5% in 1993) and Phyllodistomum elongatum (4.7% and 5.0%), were rare during the winter. The prevalence of B. luciopercae increased as clams aged, while the other species were most common in middle-siz…