Search results for " basis"
showing 10 items of 224 documents
Forward Kinematic Modelling with Radial Basis Function Neural Network Tuned with a Novel Meta-Heuristic Algorithm for Robotic Manipulators
2022
The complexity of forward kinematic modelling increases with the increase in the degrees of freedom for a manipulator. To reduce the computational weight and time lag for desired output transformation, this paper proposes a forward kinematic model mapped with the help of the Radial Basis Function Neural Network (RBFNN) architecture tuned by a novel meta-heuristic algorithm, namely, the Cooperative Search Optimisation Algorithm (CSOA). The architecture presented is able to automatically learn the kinematic properties of the manipulator. Learning is accomplished iteratively based only on the observation of the input–output relationship. Related simulations are carried out on a 3-Degrees…
Experimental studies on continuous speech recognition using neural architectures with “adaptive” hidden activation functions
2010
The choice of hidden non-linearity in a feed-forward multi-layer perceptron (MLP) architecture is crucial to obtain good generalization capability and better performance. Nonetheless, little attention has been paid to this aspect in the ASR field. In this work, we present some initial, yet promising, studies toward improving ASR performance by adopting hidden activation functions that can be automatically learned from the data and change shape during training. This adaptive capability is achieved through the use of orthonormal Hermite polynomials. The “adaptive” MLP is used in two neural architectures that generate phone posterior estimates, namely, a standalone configuration and a hierarch…
On the Ward theorem for P-adic-path bases associated with a bounded sequence
2004
In this paper we prove that each differentiation basis associated with a $\mathcal P$-adic path system defined by a bounded sequence satisfies the Ward Theorem.
Towards Stable Radial Basis Function Methods for Linear Advection Problems
2021
In this work, we investigate (energy) stability of global radial basis function (RBF) methods for linear advection problems. Classically, boundary conditions (BC) are enforced strongly in RBF methods. By now it is well-known that this can lead to stability problems, however. Here, we follow a different path and propose two novel RBF approaches which are based on a weak enforcement of BCs. By using the concept of flux reconstruction and simultaneous approximation terms (SATs), respectively, we are able to prove that both new RBF schemes are strongly (energy) stable. Numerical results in one and two spatial dimensions for both scalar equations and systems are presented, supporting our theoret…
Estimating the temperature evolution of foodstuffs during freezing with a 3D meshless numerical method
2015
Abstract Freezing processes are characterised by sharp changes in specific heat capacity and thermal conductivity for temperatures close to the freezing point. This leads to strong nonlinearities in the governing PDE that may be difficult to resolve using traditional numerical methods. In this work we present a meshless numerical method, based on a local Hermite radial basis function collocation approach in finite differencing mode, to allow the solution of freezing problems. By introducing a Kirchhoff transformation and solving the governing equations in Kirchhoff space, the strength of nonlinearity is reduced while preserving the structure of the heat equation. In combination with the hig…
Pressure-Driven Isostructural Phase Transition in InNbO4: In Situ Experimental and Theoretical Investigations
2017
[EN] The high-pressure behavior of technologically important visible-light photocatalytic semiconductor In.NbO4, adopting a monoclinic wolframite-type structure at ambient conditions, was investigated using synchrotron-based X-ray diffraction, Raman spectroscopic measurements, and first-principles calculations. The experimental results indicate the occurrence of a pressure-induced isostructural phase transition in the studied compound beyond 10.8 GPa. The large volume collapse associated with the phase transition and the coexistence of two phases observed over a wide range of pressure shows the nature of transition to be first-order. There is an increase in the oxygen anion coordination num…
Complete basis set prediction of methanol isotropic nuclear magnetic shieldings and indirect nuclear spin–spin coupling constants (SSCC) using polari…
2009
Efficient B3LYP and BHandH density functionals were used to estimate methanol's nuclear magnetic isotropic shieldings and spin–spin coupling constants in the basis set limit. Polarization‐consistent pcS‐n and pcJ‐n (n = 0, 1, 2, 3 and 4), and segmented contracted XZP, where X = D, T, Q and 5, basis sets were used and the results fitted with simple mathematical formulas. The performance of the methods was assessed from comparison with experiment and higher level calculations. 1J(CH) and 3J(HH) values were determined from very diluted solutions in deuterochloroform and compared with theoretical predictions. The agreement between complete basis set (CBS) density functional theory (DFT) predict…
H2O, H2, HF, F2 and F2O nuclear magnetic shielding constants and indirect nuclear spin–spin coupling constants (SSCCs) in the BHandH/pcJ‐n and BHandH…
2009
Good performance of segmented contracted basis sets XZP, where X = D, T, Q and 5, for obtaining H2O, H2, HF, F2 and F2O nuclear isotropic shielding constants in the BHandH Kohn–Sham basis set limit was shown. The results of two‐ and three‐parameter complete basis set limit extrapolation schemes were compared with experimental results, earlier literature data and benchmark ab initio results. Similar convergence patterns of shieldings obtained from calculations using general purpose XZP basis sets and from polarization‐consistent basis sets pcS‐n and pcJ‐n, where n = 0, 1, 2, 3 and 4, designed to accurately predict magnetic properties were observed. On the contrary, the SSCCs were more sensit…
Polynomial Spline-Wavelets
2015
This chapter presents wavelets in the spaces of polynomial splines. The wavelets’ design is based on the Zak transform, which provides an integral representation of spline-wavelets. The exponential wavelets which participate in the integral representation are counterparts of the exponential splines that were introduced in Chap. 4. Fast algorithms for the wavelet transforms of splines are presented. Generators of spline-wavelet spaces are described, such as the B-wavelets and their duals and the Battle-Lemarie wavelets whose shifts form orthonormal bases of the spline-wavelet spaces.
OPTIMIZATIONS FOR TENSORIAL BERNSTEIN–BASED SOLVERS BY USING POLYHEDRAL BOUNDS
2010
The tensorial Bernstein basis for multivariate polynomials in n variables has a number 3n of functions for degree 2. Consequently, computing the representation of a multivariate polynomial in the tensorial Bernstein basis is an exponential time algorithm, which makes tensorial Bernstein-based solvers impractical for systems with more than n = 6 or 7 variables. This article describes a polytope (Bernstein polytope) with a number of faces, which allows to bound a sparse, multivariate polynomial expressed in the canonical basis by solving several linear programming problems. We compare the performance of a subdivision solver using domain reductions by linear programming with a solver using a c…