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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 51 (1979), S. 175-188 
    ISSN: 1432-2234
    Keywords: Configuration interaction method, coupling constants in the direct ∼
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A general algorithm of evaluation of the coefficients of molecular integrals (coupling constants) appearing in the direct configuration interaction method is derived. The configurations are assumed to be spin-adapted antisymmetrized products of orthonormal orbitals. No limitation is imposed either upon the reference state (the number of the singly occupied orbitals may be arbitrary) or upon the excitation multiplicity.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 71 (1987), S. 187-199 
    ISSN: 1432-2234
    Keywords: Configuration interaction method ; Symmetric group graphical approach ; Electron correlation problem ; Multi-reference CI program
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Specific features of an SGGA-based multireference direct CI program working in large internal spaces are discussed. In particular, advantages resulting from the explicit separation of the orbital and the spin spaces are explored. Concepts allowing for the efficient creation of a flexible and symmetry-adapted CI basis, for the high-speed generation of the coupling coefficients and for structuring a simple permutation driven algorithm to handle the orbital space are briefly discussed.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 67 (1985), S. 263-269 
    ISSN: 1432-2234
    Keywords: Configuration interaction method ; configuration selection ; high-spin systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A proof is given that in a configuration interaction method the first-order interaction space contains at most only twice as many spin functions as the zeroth-order space. This allows for a dramatic reduction of the size of CI expansion. For most of the high-spin systems only two spin functions for each configuration are needed.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Open systems & information dynamics 2 (1994), S. 295-302 
    ISSN: 1573-1324
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Natural Sciences in General
    Notes: Abstract Self-organizing topographic maps have found many applications as systems capable of unsupervised learning. They are based on the competitive learning algorithm applied to low-dimensional (in practice one, two or three-dimensional) structure of artificial neurons. The iterative algorithm used for competitive learning converges slowly and is computationally very intensive. In this paper, direct mapping on the continuous space based on the minimization principle is used to map the high-dimensional input data to the low-dimensional target space. The problem of finding the best low-dimensional representation of the data is reduced to a minimization problem or to the solution of a system of nonlinear algebraic equations.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Neural processing letters 10 (1999), S. 201-210 
    ISSN: 1573-773X
    Keywords: neural networks ; learning ; minimal distance methods ; similarity-based methods ; machine learning ; interpretation of neural functions ; classification
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Multilayer Perceptrons (MLPs) use scalar products to compute weighted activation of neurons providing decision borders using combinations of soft hyperplanes. The weighted fun-in activation function may be replaced by a distance function between the inputs and the weights, offering a natural generalization of the standard MLP model. Non-Euclidean distance functions may also be introduced by normalization of the input vectors into an extended feature space. Both approaches influence the shapes of decision borders dramatically. An illustrative example showing these changes is provided.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Neural processing letters 7 (1998), S. 211-219 
    ISSN: 1573-773X
    Keywords: backpropagation ; feature selection ; logical rule extraction ; MLP ; neural networks ; probability density estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Three neural-based methods for extraction of logical rules from data are presented. These methods facilitate conversion of graded response neural networks into networks performing logical functions. MLP2LN method tries to convert a standard MLP into a network performing logical operations (LN). C-MLP2LN is a constructive algorithm creating such MLP networks. Logical interpretation is assured by adding constraints to the cost function, forcing the weights to ±1 or 0. Skeletal networks emerge ensuring that a minimal number of logical rules are found. In both methods rules covering many training examples are generated before more specific rules covering exceptions. The third method, FSM2LN, is based on the probability density estimation. Several examples of performance of these methods are presented.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 50 (1994), S. 243-271 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The superdirect configuration interaction (Sup-CI) method has the usual versatility and stability of the CI methods with computational efficiency typical to that of the many-body methods, such as the many-body perturbation theory (MBPT). The Hamilton operator is projected into a space of a few trial vectors, such as Krylov, Nesbet, or Møller-Plesset correction vectors. In this space, Hamiltonian matrix elements may be directly computed in the many-body fashion, as weighted sums of integral products over orbital indices. The variation-perturbation method based on the first-order wave function is equivalent to the Sup-CI method with a single correction vector of the Møller-Plesset type. Different points of view on the superdirect CI method are discussed and a version in which third-order contributions are computed for a relatively small (10-100) space of reference and correction vectors is tested. Selection of the best “effective first-order spaces” and size-extensivity corrections in Sup-CI are briefly discussed. Møoller-Plesset, Epstein-Nesbet, and other correction vectors are included in the model calculations on the symmetric stretch of bonds in water, acetylene, and the NH2 molecule. Errors are almost independent of molecular geometry and the method appears to be superior than the multireference second-order perturbation methods. © 1994 John Wiley & Sons, Inc.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 30 (1986), S. 799-807 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Calculation of blocks of matrix elements between determinants associated with two fixed orbital configurations is very easy. A simple method to obtain the whole blocks and then transform them to the spinadapted basis is described. The method is suitable for many-particle operators, the number of operations to obtain matrix elements being independent of the number of orbitals or electrons. Some applications of the proposed algorithm, and possible extensions to eigenfunctions of Ľ2 and other operators, are discussed.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 38 (1990), S. 683-692 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A configuration interaction (CI) method is presented in which the space of configuration state functions expands in every iteration until all numerically significant configurations are taken into account. The algorithm is based on a new scheme of addressing unstructured sets of configurations and on the projection into the space of intermediate spin-adapted configurations with 2 electrons fixed on “ghost” orbitals.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 783-824 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An approach to the configuration interaction method based on symmetric groups (SGA) is developed. The formalism is an alternative of the unitary group approach (UGA). In many aspects the present formulation seems to be superior to UGA. In particular, in SGA the orbital and the spin parts of the configuration state functions may be processed separately. In consequence its graphical formulation is much simpler and the coupling constant expressions are more compact than the UGA analogs. A special emphasis is put on direct CI implementations. In addition to formulas for coupling constants, explicit expressions allowing for separation of external and internal space contributions are also presented.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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