Publications of Larry A Lambe

1980s to present

• Applications of perturbation theory to iterated fibrations, with Jim Stasheff, Manuscripta Mathematica, 58 (1987) No. 3, 363-376.
  manuscripta mathematica
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• Perturbation Theory in Differential Homological Algebra I, with V.K.A.M. Gugenheim, IL. J. Math., 33 (1989), 566-582.
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• Algebraic aspects of Chen's twisting cochain, with V.K.A.M. Gugenheim and J.D. Stasheff, Illinois Journal of Mathematics 34 (1990) No. 2, 485-502.
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• Perturbation Theory in Differential Homological Algebra II, with V.K.A.M. Gugenheim and J.D. Stasheff, IL. J. Math., 35 (1991), 359-373.
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• A Fixed Point Approach to Homological Perturbation Theory, with Don Barnes, Proc. AMS, 112 (1991), 881-892.
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• Homological Perturbation Theory Hochschild Homology and Formal Groups, Cont. Math. 134 (1992), Amer. Math. Soc.
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• Entry on Homological Perturbation Theory, Encyclopaedia of Mathematics, Supplement II, Kluwer Academic Press, (2000), 264-267.
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• Transferring Algebra Structures Up to Homology Equivalence, with Leif Johansson, Scand. Math., 89 (2001), no. 2, 181-200.
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• Resolutions which Split off of the Bar Construction, J. Pure and Appl. Alg., 84 (1993) 311-329.
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• On Constructing Resolutions Over the Polynomial Algebra, with Leif Johansson and Emil Sköldberg, Special Issue of Homology, Homotopy and Applications in honor of Jan-Erik's Roos' 65th birthday, Homology, Homotopy and Applications, 4 (2002), no. 2, 315-336.
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• Symbolic Computation and Research in Mathematics

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• Algorithms for computing the cohomology of nilpotent groups, Computers in geometry and topology (Chicago, IL, 1986), Lecture Notes in Pure and Appl. Math., 114 (1989), 189-209.
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• Scratchpad II as a tool for mathematical research, Notices of the Amer. Mathematics Soc. 36 No. 2, February 1989, 141-148.
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• A computation of Green functions for some classical groups, with Bhama Srinivasan, Communications in Algebra, 18 No. 10, 1990, 3507-3545. Comms in Alg
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• The AXIOM system, Notices of the Amer. Mathematics Soc. 41 No. 1, January 1994, 14-18.
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• Resolutions via homological perturbation, J. Symbolic Comput. 12 (1991), 71--87. Download full text in pdf
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• Next generation computer algebra systems AXIOM and the Scratchpad concept: Applications to research in algebra, Gyllenberg, Mats (ed.) et al., Analysis, algebra, and computers in mathematical research. Proceedings of the 21st Nordic congress of mathematicians, Lulea Univ. of Technology, Sweden, 1992. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 156 (1994), 201-222.
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• Computing Resolutions Over Finite p-Groups, with Johannes Grabmeier, Algebraic Combinatorics and Applications, Proceedings of the Euroconference, Algebraic Combinatorics and Applications (ALCOMA), held in Gößweinstein, Germany, September 12-19, 1999, A. Betten, A. Kohnert, R. Laue, and A. Wassermann (Eds), Springer-Verlag, Heidelberg, (2001). 157-195. Springer Link
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• An Algebraic Study of the Klein Bottle, Journal of Homotopy and Related Structures, 11(4), 885-891. Here is the submitted version (freely available) -- -- The published version at SpringerLink
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• Hopf Algebra and the Quantum Yang-Baxter Equation

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• Algebraic Aspects of the Quantum Yang-Baxter Equation, with David Radford, Journal of Algebra, 154 (1993), 228-288. Open Archive or Download full text in pdf
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• On the Quantum Yang-Baxter Equation with Spectral Parameter I, Lond. Maths. Soc. Proc. 68 (1994), 31-50. TOC
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• Construction of Quantum Groups and the Yang-Baxter Equation with Spectral Parameter, with Paolo Cotta-Ramusino and Maurizio Rinaldi, in Symmetries in Science VI, editor B. Gruber, Plenum Press, New York (1993), 171-186. Symmetries in Science VI
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• Introduction to the quantum Yang-Baxter equation and quantum groups: an algebraic approach, with David E. Radford, Mathematics and its Applications Series 423 (1997), Springer, xx+293pp. Springer online listing
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• Solutions to the Quantum Yang-Baxter Equation Having Certain Bialgebras as Their Reduced FRT Construction, with David E. Radford, IL. J. Math., 42 (1998), 630-654. Full-test Open access
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• Homological Algebra and Algebraic Topology/Differential Equations

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• Cohomology of nilmanifolds and torsion-free, nilpotent groups, with Stewart B. Priddy, Trans. Amer. Math. Soc. 273 No. 1, 1982, 39-55. Free Access
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• Two exact sequences in rational homotopy theory relating cup products and commutators, Proc. Amer. Math. Soc. 96 No. 2, 1986, 360-364. Free Access
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• Cohomology of principal G-bundles over a torus when H^*(BG;R) is polynomial, Bull. Soc. Math. Belg. Ser. A 38 (1987), 247-264.
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• The Cohomology Ring of the Free Loop Space of a Wedge of Spheres and Cyclic Homology, with Clas Löfwall, CR Acad. Sci., Paris, 320 (1995), 1237-1242.
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• Differential Equations, Spencer Cohomology, and Computing Resolutions, with Werner M. Seiler, Georgian Math. J. 9 (2002), No. 4, 723-772. Full PDF
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• Machine Learning and Big Data

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• Decision trees for binary classification variables grow equally with the Gini impurity measure and Pearson's chi-square test, with Johannes Grabmeier, International Journal of Business Intelligence and Data Mining, 2 (2007), No. 2, 213-226.
  
  Abstract: It is shown that for binary classification variables, Gini and Pearson purity measures yield exactly the same tree, provided all the other parameters of the algorithms are identical. A counter-example for ternary classification variables is given.
  
  Keywords: decision trees, Gini, impurity measure, Pearson, chi-square test, entropy, binary classification, variables, contingency matrix, power series expansion, symmetric polynomials, purity measures, ternary classification, data mining.
  Inderscience Online
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• Mathematical Foundation for Physics-based Simulations, VKI LS 2012-05: Physics-Based Modeling & Simulation for Aerospace Systems Aug. 21-23, 2012. information page.
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• Mathematical Analysis and Computational Integration of Massive Heterogeneous Data from the Human Retina, with Arash Sangari, Adel Ardalan, Hamid Eghbalnia, and Amir Assadi, IFIP Advances in Information and Communication Technology, AICT-372, pp.571-578, 2012, Technological Innovation for Value Creation, 10.1007/978-3-642-28255-3_63.
  
  Abstract: Modern epidemiology integrates knowledge from heterogeneous collections of data consisting of numerical, descriptive and imaging. Large-scale epidemiological studies use sophisticated statistical analysis, mathematical models using differential equations and versatile analytic tools that handle numerical data. In contrast, knowledge extraction from images and descriptive information in the form of text and diagrams remain a challenge for most fields, in particular, for diseases of the eye. In this article we provide a roadmap towards extraction of knowledge from text and images with focus on forthcoming applications to epidemiological investigation of retinal diseases, especially from existing massive heterogeneous collections of data distributed around the globe.
  
  Keywords : Retina Vasculature, Image Analysis, Text Analysis, Massive Data, Symbolic computation.
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• Hybrid Symbolic and Numeric Computation

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• Object-Oriented Mathematical Programming and Symbolic/Numeric Interface, with Richard Luczak, 3rd International Conf. on Expert Systems for Numerical Computing, May, 1993, in MATCOM 981, Mathematics and Computers in Simulation 36 (1994), no. 4-6, 493-503, Elsevier Science B.V, The Netherlands.
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• A New Finite Difference Method for the Helmholtz Equation Using Symbolic Computation, with Richard Luczak and John W. Nehrbass, International Journal of Computational Engineering Science, Mar 2003, Vol. 4 Issue 1, 121-144. World Scientific
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