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Generalization Algorithms for Second-Order Terms [chapter]

Kouichi Hirata, Takeshi Ogawa, Masateru Harao
2004 Lecture Notes in Computer Science  
First, we extend the least generalization algorithm lg for a pair of first-order terms under , introduced by Plotkin and Reynolds, to the one for a pair of second-order terms.  ...  In this paper, we study the generalization algorithms for second-order terms, which are treated as first-order terms with function variables, under an instantiation order denoted by .  ...  Acknowledgment The authors would like to thank the anonymous referees for valuable comments to revise the preliminary version of this paper.  ... 
doi:10.1007/978-3-540-30109-7_14 fatcat:4ivuqdmj6bhhpevcm3qzgpmmla

Second-Order Learning Algorithm with Squared Penalty Term

Kazumi Saito, Ryohei Nakano
2000 Neural Computation  
Our experiments showed that for a reasonably adequate penalty factor, the combination of the squared penalty term and the second-order learning algorithm drastically improves the convergence performance  ...  This paper compares three penalty terms with respect to the efficiency of supervised learning, by using first-and second-order learning algorithms.  ...  This paper evaluates the efficiency of first-and second-order learning algorithms with three penalty terms.  ... 
doi:10.1162/089976600300015763 pmid:10769328 fatcat:rcwbomvs35alrnxxxisuvtvydq

A self-correcting matrix iteration for the Moore-Penrose generalized inverse

William H Pierce
1996 Linear Algebra and its Applications  
The popular algorithm Xk+ t = Xk(2I -AXt) has a first-order error component, but the more eomplieated algorithm given here has no first-order error eomponent for general A and X~.  ...  Let X k be the k th iterate of an algorithm fbr finding the Moore-Penrose generalized inverse of a singular matrix A.  ...  The convergence of various algorithms for successive improvements with general initial errors depends upon the second-and higher-order error terms not discussed here.  ... 
doi:10.1016/0024-3795(94)00306-8 fatcat:7zwsuee63bcxrpzdj327wu75ou

Automatic thesaurus construction for cross generation corpus

Hadas Zohar, Chaya Liebeskind, Jonathan Schler, Ido Dagan
2013 ACM Journal on Computing and Cultural Heritage  
We evaluated different first and second order methods, and introduced a special annotation scheme for this problem, which showed that first order methods performed surprisingly well.  ...  This article describes methods for semiautomatic thesaurus construction, for a cross generation, cross genre, and cross cultural corpus.  ...  Therefore, we used an approximation for the representation of a term as a vector in all second-order algorithms.  ... 
doi:10.1145/2442080.2442084 fatcat:caedcdqwjnczbgu6fowhygvlzi

Runge-Kutta neural network for identification of dynamical systems in high accuracy

Yi-Jen Wang, Chin-Teng Lin
1998 IEEE Transactions on Neural Networks  
Two types of learning algorithms are investigated for the RKNN's, gradientand nonlinear recursive least-squares-based algorithms.  ...  We show theoretically the superior generalization and long-term prediction capability of the RKNN's over the normal neural networks.  ...  ACKNOWLEDGMENT The authors would like to thank the reviewers for their helpful suggestions in improving the quality of the final manuscript.  ... 
doi:10.1109/72.661124 pmid:18252453 fatcat:vfqst2epvfaavf7pzytcky7esq

Unification in lambda-calculi with if-then-else [chapter]

Michael Beeson
1998 Lecture Notes in Computer Science  
This unification algorithm can be used to generalize first-order proofsearch algorithms to second-order logic, making possible for example a straighforward treatment of McCarthy's circumscription schema  ...  A new unification algorithm is introduced, which (unlike previous algorithms for unification in λ-calculus) shares the pleasant properties of first-order unification.  ...  second-order unification algorithm is more general than each of Huet's two answers.  ... 
doi:10.1007/bfb0054251 fatcat:2l2szw5fdfg6jig4jmcnfiv6x4

Deterministic second-order patterns

Tetsuo Yokoyama, Zhenjiang Hu, Masato Takeichi
2004 Information Processing Letters  
The time-complexity of our deterministic matching algorithm is linear in the size of a term for a fixed pattern.  ...  However, second-order matching in general is nondeterministic, and the matching algorithm is so expensive that the matching is NP-complete.  ...  However, second-order matching in general is nondeterministic [9] (there is more than a single match).  ... 
doi:10.1016/j.ipl.2003.12.008 fatcat:6rqesghd5jcjhnekqejadgkyey

Using Windmill Expansion for Document Retrieval

Shao Fen Liang, Paul Smart, Alistair Russell, Nigel Shadbolt
2009 The Open Information Systems Journal  
WE is based on the extraction of human-generated written phases for automated query expansion. Top and Second Level expansion terms have been generated and their usefulness evaluated.  ...  The algorithm uses retrieval feedback techniques for automated query expansion in order to improve the effectiveness of information retrieval.  ...  This proves the WE algorithm is a generic algorithm for query expansion.  ... 
doi:10.2174/1874133900903010001 fatcat:qri6wttgvbfrhb7jtpbcatqvje

Monadic Second-Order Logic for Graphs: Algorithmic and Language Theoretical Applications [chapter]

Bruno Courcelle
2009 Lecture Notes in Computer Science  
This tutorial will present an overview of the use of Monadic Second-Order Logic to describe sets of finite graphs and graph transformations, in relation with the notions of tree-width and clique-width.  ...  It will review applications to the construction of algorithms, to Graph Theory and to the extension to graphs of Formal Language Theory concepts.  ...  As mentioned above every monadic second-order graph property has, for each k, a polynomial time checking algorithm for graphs of tree-width at most k.  ... 
doi:10.1007/978-3-642-00982-2_2 fatcat:ryjvoaa7dnefrcruygfnpqso2i

Explicit symplectic algorithms based on generating functions for charged particle dynamics

Ruili Zhang, Hong Qin, Yifa Tang, Jian Liu, Yang He, Jianyuan Xiao
2016 Physical review. E  
To overcome this difficulty, we combine the familiar sum-split method and a generating function method to construct second and third order explicit symplectic algorithms for dynamics of charged particle  ...  For long-term simulations with high efficiency, explicit symplectic algorithms are desirable.  ...  However, for product-separable Hamiltonian with the form of Eq. (5) or Eq. (6), second and third order symplectic algorithms based on generating functions can be constructed explicitly.  ... 
doi:10.1103/physreve.94.013205 pmid:27575228 fatcat:dexdcetupbadnphgpxajatusaa

Application of the Hori Method in the Theory of Nonlinear Oscillations

Sandro da Silva Fernandes
2012 Mathematical Problems in Engineering  
Two simplified algorithms for determining the generating function and the new system of differential equations are derived from a general algorithm proposed by Sessin.  ...  These simplified algorithms are applied in determining second-order asymptotic solutions of two well-known equations in the theory of nonlinear oscillations: van der Pol equation and Duffing equation.  ...  In this paper, this new approach is applied to the theory of nonlinear oscillations for a second-order differential equation and two simplified versions of the general algorithm are derived.  ... 
doi:10.1155/2012/239357 fatcat:3z2lnevzcbasvfuobdicnqgofu

A note on the operator compact implicit method for the wave equation

Melvyn Ciment, Stephen H. Leventhal
1978 Mathematics of Computation  
In this note we implement the operator compact implicit spatial discretization method for the second order wave equation when first order terms are present.  ...  The resulting algorithm is completely analogous to the compact implicit algorithm when lower order terms were not present.  ...  In this note we implement the operator compact implicit spatial discretization method for the second order wave equation when first order terms are present.  ... 
doi:10.1090/s0025-5718-1978-0483507-7 fatcat:igvx2ie2tncrrpgviymzzgc33e

A Note on the Operator Compact Implicit Method for the Wave Equation

Melvyn Ciment, Stephen H. Leventhal
1978 Mathematics of Computation  
In this note we implement the operator compact implicit spatial discretization method for the second order wave equation when first order terms are present.  ...  The resulting algorithm is completely analogous to the compact implicit algorithm when lower order terms were not present.  ...  In this note we implement the operator compact implicit spatial discretization method for the second order wave equation when first order terms are present.  ... 
doi:10.2307/2006263 fatcat:m4m7ylhujjerzj63fer6ct2l3y

ON ALGORITHMS FOR BROWNIAN DYNAMICS COMPUTER SIMULATIONS

ARKADIUSZ C. BRAŃKA
1998 Computational Methods in Science and Technology  
Mutual merits of the second-order algorithms are discussed.  ...  stochastic expansion and second-order stochastic Runge-Kutta algorithms.  ...  Acknowledgment The work has been supported by the Polish Committee for Scientific Research (KBN) grant No. 8T11F01214.  ... 
doi:10.12921/cmst.1998.04.01.35-42 fatcat:ssngfyoam5eqloo7whmofnjdqq

A second-order scheme for integration of one-dimensional dynamic analysis

Hang Ma, Qing-Hua Qin
2005 Computers and Mathematics with Applications  
This paper proposes a second-order scheme of precision integration for dynamic analysis with respect to long-term integration.  ...  Rather than transforming into first-order equations, a recursive scheme is presented in detail for direct solution of the homogeneous part of second-order algebraic and differential equations.  ...  The CPU time used for the second-order algorithm required only about 37.5% of that used for the first-order algorithm for the same amount of computation.  ... 
doi:10.1016/j.camwa.2004.08.009 fatcat:wkrycdcezvbt7jhezwr4bwfnd4
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