Search results for "Linear Algebra."
showing 10 items of 552 documents
Optimal Pruned K-Nearest Neighbors: OP-KNN Application to Financial Modeling
2008
The paper proposes a methodology called OP-KNN, which builds a one hidden-layer feed forward neural network, using nearest neighbors neurons with extremely small computational time. The main strategy is to select the most relevant variables beforehand, then to build the model using KNN kernels. Multi-response sparse regression (MRSR) is used as the second step in order to rank each k-th nearest neighbor and finally as a third step leave-one-out estimation is used to select the number of neighbors and to estimate the generalization performances. This new methodology is tested on a toy example and is applied to financial modeling.
Semi-Supervised Support Vector Biophysical Parameter Estimation
2008
Two kernel-based methods for semi-supervised regression are presented. The methods rely on building a graph or hypergraph Laplacian with both the labeled and unlabeled data, which is further used to deform the training kernel matrix. The deformed kernel is then used for support vector regression (SVR). The semi-supervised SVR methods are sucessfully tested in LAI estimation and ocean chlorophyll concentration prediction from remotely sensed images.
Ab Initio Study of BiFeO3: Thermodynamic Stability Conditions
2015
BiFeO3 is investigated intensively, mainly as a multiferroic material. In this paper, the state-of-the-art ab initio hybrid functional approach with atomic basis sets was employed for a study of the stability range of BiFeO3 with respect to its decomposition into binary oxides and elementary metals, as a function of temperature and oxygen partial pressure. The calculated atomic and electronic structure of BiFeO3 was compared with previous LDA+U calculations using plane-wave basis sets. Based on performed calculations, the phase diagram was constructed, which allows us to predict the stability region of stoichiometric BiFeO3.
The accuracy of molecular dipole moments in standard electronic structure calculations
2000
Abstract A systematic investigation has been carried out of the accuracy of calculated molecular equilibrium dipole moments of 11 polar closed-shell molecules, using the HF, MP2, CCSD and CCSD(T) models and correlation-consistent basis sets. Augmented basis sets are important for improving the basis-set convergence, but the quality of the results depends more on the correlation treatment than on the cardinal number of the basis set. Augmented triple-zeta basis sets are sufficient for most calculations. The mean absolute error of the HF calculations is 0.16 D, which is reduced at the MP2 and CCSD levels to 0.048 and 0.025 D, respectively. The CCSD(T) errors are small – typically
From CCSD(T)/aug-cc-pVTZ-J to CCSD(T) complete basis set limit isotropic nuclear magnetic shieldings via affordable DFT/CBS calculations
2011
It is shown that a linear correlation exists between nuclear shielding constants for nine small inorganic and organic molecules (N2, CO, CO2, NH3, CH4, C2H2, C2H4, C2H6 and C6H6) calculated with 47 methods (42 DFT methods, RHF, MP2, SOPPA, SOPPA(CCSD), CCSD(T)) and the aug-cc-pVTZ-J basis set and corresponding complete basis set results, estimated from calculations with the family of polarization-consistent pcS-n basis sets. This implies that the remaining basis set error of the aug-cc-pVTZ-J basis set is very similar in DFT and CCSD(T) calculations. As the aug-cc-pVTZ-J basis set is significantly smaller, CCSD(T)/aug-cc-pVTZ-J calculations allow in combination with affordable DFT/pcS-n com…
Theoretical spectroscopy of organic systems
1999
Abstract The complete active space (CAS) SCF method in conjunction with the multiconfigurational second-order perturbation theory (CASPT2) has been applied to study the electronically excited states of basic organic compounds. As shown in the lecture with a number of examples, the CASPT2 method is capable of yielding accurate results for relative energies and other properties of excited states, provided that flexible one-electron basis sets are employed. The applications comprise an ample range of systems and problems, including polyenes, conjugated and unconjugated dienes, alternant and nonalternant hydrocarbons, polyenals, etc. As a whole these studies enable both qualitative and quantita…
Cation Environment in BaCeO3-Based Protonic Conductors: a Computational Study
2009
Geometry calculations were performed on pure BaCeO(3) fragments and on Y- and In-doped derivatives. HF and DFT approaches were used to investigate monoclinic and orthorhombic structures. The computational methods, structural models, and electronic structure investigation protocols were tuned taking into consideration and balancing the consistency of the results against the computational cost. The calculated structures and energetics parameter, as well as the detailed orbital analysis performed on the corresponding BaCeO(3) derivatives allowed us to explain experimental findings and to develop a procedure to study the cationic octahedral environment of doped X:BaCeO(3) (X = Y, In) and undope…
Theoretical study of stationary structures of acetamidine unimolecular decomposition
1990
Abstract The unimolecular decomposition of acetamidine to ammonia and acetonitrile was examined by ab initio methods. Stationary points, i.e. the reactant, product and transition structures, have been characterized. The process has an asynchronous mechanism, the transition state being described as a four-membered ring. To establish the relevance of different basis sets, calculations with eight standard Gaussian basis sets, STO-3G, 3-21G, 4-21G, 4-31G, 6-31G, 6-311G, 6-31G*, and G-31G**, were carried out.
The electronic spectrum of pyrrole
1999
The electronic spectrum of pyrrole has been investigated by performing calculations using a hierarchy of coupled-cluster models consisting of CCS, CC2, CCSD, and CC3. Basis-set effects have been investigated by carrying out calculations using correlation-consistent basis sets augmented with functions especially designed for the description of Rydberg states. Oscillator strengths, excited state dipole moments, and second moments of the electronic charge distributions have been used to characterize the electronic transitions and final states. Structures and vibrational frequencies have been calculated for a few selected states, and the importance of distinguishing between vertical and adiabat…
An adaptive-PCA algorithm for reflectance estimation from color images
2008
This paper deals with the problem of spectral reflectance estimation from color camera outputs. Because the reconstruction of such functions is an inverse problem, stabilizing the reconstruction process is highly desirable. One way to do this is to decompose reflectance function on a basis functions like PCA. The present work proposes an algorithm making PCA adaptive in reflectance estimation from a color camera output. We propose to adapt the PCA basis derivation by selecting, for each sample, the more relevant elements from the training set elements. The adaptivity criterion is achieved by a likelihood measurement. Finally, the spectral reflectance estimation results are evaluated with th…