Publications of Larry A Lambe
1980s to present
Notice: Copyrights to some of the following papers are held by the publishers. Copies made available here are preprints or are out of print. Please treat these materials in a way consistent with the "fair use" provisions of appropriate copyright law. The copies here are for individual use only for research purposes.
1980s to present
Notice: Copyrights to some of the following papers are held by the publishers. Copies made available here are preprints or are out of print. Please treat these materials in a way consistent with the "fair use" provisions of appropriate copyright law. The copies here are for individual use only for research purposes.
Some Selected Publications
Homological Perturbation Theory (HPT)
- Applications of perturbation theory to
iterated fibrations, with Jim Stasheff, Manuscripta Mathematica, 58 (1987) No. 3, 363-376.
manuscripta mathematica
Note: Click on the link above for an abstract and the list of references. - Perturbation Theory in Differential
Homological Algebra I, with V.K.A.M. Gugenheim,
IL. J. Math., 33 (1989), 566-582.
Full-text: Open access
-- Here is a related picture - 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.
Full-text: Open access - Perturbation Theory in Differential
Homological Algebra II, with V.K.A.M. Gugenheim and J.D.
Stasheff, IL. J. Math., 35 (1991),
359-373.
Full-text: Open access - A Fixed Point Approach to Homological
Perturbation Theory, with Don Barnes, Proc. AMS, 112 (1991), 881-892.
Full-text PDF Free Access
Note: Click on the link above for an abstract and the list of references. - Homological Perturbation Theory Hochschild
Homology and Formal Groups, Cont. Math.
134 (1992), Amer. Math. Soc.
Table of Contents (scroll down a bit)
click here for a preprint
direct any inquiries here - Entry on Homological Perturbation
Theory, Encyclopaedia of Mathematics,
Supplement II, Kluwer Academic Press, (2000), 264-267.
direct any inquiries here -
Transferring Algebra
Structures Up to Homology Equivalence, with Leif
Johansson, Scand. Math., 89 (2001),
no. 2, 181-200.
Download (Free)
Note: Click on the link above for an abstract.
-- Here is a related picture - Resolutions which Split off of the Bar
Construction, J. Pure and Appl. Alg.,
84 (1993) 311-329.
Download full text in pdf at this page
Note: Click on the link above for an abstract and the list of references. -
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.
Full-text Open access
Note: Click on the link above for an abstract.
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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.
direct any inquiries here - Scratchpad II as a tool for mathematical
research, Notices of the Amer.
Mathematics Soc. 36 No. 2, February 1989, 141-148.
Note: The system described in this article was still a research project and not commercially available. See the article "The AXIOM system" below for more information. download article - A computation of Green functions for some classical groups, with Bhama Srinivasan, Communications in Algebra, 18 No. 10, 1990, 3507-3545. Comms in Alg
- The AXIOM system, Notices of the Amer. Mathematics Soc. 41 No. 1, January
1994, 14-18.
Note: The AXIOM system became an open source project in the early 2000s. See "An Algebraic Study of the Klein Bottle" below for a example of its use in algebraic topology/homological algebra. download article. Several branches of open source AXIOM have evolved, click this for Info and Download for FriCAS . - Resolutions via homological perturbation, J. Symbolic Comput. 12 (1991), 71--87. Download full text in pdf
- 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,
Luleå Univ. of Technology, Sweden, 1992. New York, NY: Marcel
Dekker. Lect. Notes Pure Appl. Math. 156 (1994),
201-222.
(axiom-21congress) AXIOM Wiki
direct any inquiries here -
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
Note: Click on the link above for an abstract and the list of references. -- click here for a preprint - An Algebraic Study of the Klein
Bottle, Journal of Homotopy and Related
Structures, 11(4), 885-891. SpringerLink
direct any inquiries here
Note: Click on the first link above for an abstract and the list of references. click this for Info and Download for FriCAS -
Hopf Algebra and the Quantum Yang-Baxter Equation
- 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
- On the Quantum Yang-Baxter Equation with Spectral Parameter I, Lond. Maths. Soc. Proc. 68 (1994), 31-50. TOC
- 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
Note: Click on the link above for an abstract and the list of references. - 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
Note: Click on the link above for a preview and table of contents. - 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
- Cohomology of nilmanifolds and
torsion-free, nilpotent groups, with Stewart B. Priddy,
Trans. Amer. Math. Soc. 273 No. 1, 1982,
39-55. Free Access
Note: Click on the link above for an abstract and the list of references. - Two exact sequences in rational homotopy
theory relating cup products and commutators,
Proc. Amer. Math. Soc. 96 No. 2, 1986,
360-364. Free Access
Note: Click on the link above for an abstract and the list of references. - Cohomology of principal G-bundles over a torus when H^*(BG;R) is polynomial, Bull. Soc. Math. Belg. Ser. A 38 (1987), 247-264.
- 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.
direct any inquiries here - 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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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 - Mathematical Foundation for Physics-based
Simulations, VKI LS 2012-05:
Physics-Based Modeling & Simulation for Aerospace Systems
Aug. 21-23, 2012.
information page.
click here for a preprint
direct any inquiries here - 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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- 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.
download article
direct any inquiries here
-- Here is a related picture
- 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
Note: Click on the link above for an abstract and the list of references.
-- Here is another picture - See the listing for more Hybrid Symbolic Numeric Methods once there, use the 'back button' to return here
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