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.
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.
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. -- Here is a related picture
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 here 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,
Lulea 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.
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
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
t
Differential Equations, Spencer
Cohomology, and Computing Resolutions, with Werner M.
Seiler,Georgian Math. J. 9 (2002), No.
4, 723-772.Full
PDF
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. 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.
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