Relevant bibliographies by topics / Foundations of homotopy theory

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Foundations of homotopy theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 11 February 2022

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Journal articles on the topic "Foundations of homotopy theory"

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RIJKE, EGBERT, and BAS SPITTERS. "Sets in homotopy type theory." Mathematical Structures in Computer Science 25, no. 5 (January 30, 2015): 1172–202. http://dx.doi.org/10.1017/s0960129514000553.

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Homotopy type theory may be seen as an internal language for the ∞-category of weak ∞-groupoids. Moreover, weak ∞-groupoids model the univalence axiom. Voevodsky proposes this (language for) weak ∞-groupoids as a new foundation for Mathematics called the univalent foundations. It includes the sets as weak ∞-groupoids with contractible connected components, and thereby it includes (much of) the traditional set theoretical foundations as a special case. We thus wonder whether those ‘discrete’ groupoids do in fact form a (predicative) topos. More generally, homotopy type theory is conjectured to be the internal language of ‘elementary’ of ∞-toposes. We prove that sets in homotopy type theory form a ΠW-pretopos. This is similar to the fact that the 0-truncation of an ∞-topos is a topos. We show that both a subobject classifier and a 0-object classifier are available for the type theoretical universe of sets. However, both of these are large and moreover the 0-object classifier for sets is a function between 1-types (i.e. groupoids) rather than between sets. Assuming an impredicative propositional resizing rule we may render the subobject classifier small and then we actually obtain a topos of sets.
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Pelayo, Álvaro, and Michael A. Warren. "Homotopy type theory and Voevodsky’s univalent foundations." Bulletin of the American Mathematical Society 51, no. 4 (May 9, 2014): 597–648. http://dx.doi.org/10.1090/s0273-0979-2014-01456-9.

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AWODEY, STEVE, NICOLA GAMBINO, and ERIK PALMGREN. "Introduction – from type theory and homotopy theory to univalent foundations." Mathematical Structures in Computer Science 25, no. 5 (March 10, 2015): 1005–9. http://dx.doi.org/10.1017/s0960129514000474.

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We give an overview of the main ideas involved in the development of homotopy type theory and the univalent foundations of Mathematics programme. This serves as a background for the research papers published in the special issue.
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Thomas, Jean-Claude, and Micheline Vigué-Poirrier. "Daniel Quillen, the father of abstract homotopy theory." Journal of K-theory 11, no. 3 (March 1, 2013): 479–91. http://dx.doi.org/10.1017/is013001006jkt204.

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AbstractIn this short paper we try to describe the fundamental contribution of Quillenin the development of abstract homotopy theory and we explain how he uses this theory to lay the foundations of rational homotopy theory.
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Lumsdaine, Peter Lefanu, and Nicolas Tabareau. "Preface: Special Issue on Homotopy Type Theory and Univalent Foundations." Journal of Automated Reasoning 63, no. 2 (October 30, 2018): 157–58. http://dx.doi.org/10.1007/s10817-018-9491-3.

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Ahrens, Benedikt, Simon Huber, and Anders Mörtberg. "Preface to the MSCS Issue 31.1 (2021) Homotopy Type Theory and Univalent Foundations." Mathematical Structures in Computer Science 31, no. 1 (January 2021): 1–2. http://dx.doi.org/10.1017/s0960129521000244.

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GYLTERUD, HÅKON ROBBESTAD. "FROM MULTISETS TO SETS IN HOMOTOPY TYPE THEORY." Journal of Symbolic Logic 83, no. 3 (September 2018): 1132–46. http://dx.doi.org/10.1017/jsl.2017.84.

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AbstractWe give a model of set theory based on multisets in homotopy type theory. The equality of the model is the identity type. The underlying type of iterative sets can be formulated in Martin-Löf type theory, without Higher Inductive Types (HITs), and is a sub-type of the underlying type of Aczel’s 1978 model of set theory in type theory. The Voevodsky Univalence Axiom and mere set quotients (a mild kind of HITs) are used to prove the axioms of constructive set theory for the model. We give an equivalence to the model provided in Chapter 10 of “Homotopy Type Theory” by the Univalent Foundations Program.
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Joyal, André, and Myles Tierney. "On the homotopy theory of sheaves of simplicial groupoids." Mathematical Proceedings of the Cambridge Philosophical Society 120, no. 2 (August 1996): 263–90. http://dx.doi.org/10.1017/s0305004100074855.

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The aim of this paper is to contribute to the foundations of homotopy theory for simplicial sheaves, as we believe this is the natural context for the development of non-abelian, as well as extraordinary, sheaf cohomology.In [11] we began constructing a theory of classifying spaces for sheaves of simplicial groupoids, and that study is continued here. Such a theory is essential for the development of basic tools such as Postnikov systems, Atiyah-Hirzebruch spectral sequences, characteristic classes, and cohomology operations in extraordinary cohomology of sheaves. Thus, in some sense, we are continuing the program initiated by Illusie[7], Brown[2], and Brown and Gersten[3], though our basic homotopy theory of simplicial sheaves is different from theirs. In fact, the homotopy theory we use is the global one of [10]. As a result, there is some similarity between our theory and the theory of Jardine[8], which is also partially based on [10]
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Escardó, Martín Hötzel. "The Cantor–Schröder–Bernstein Theorem for $$\infty $$-groupoids." Journal of Homotopy and Related Structures 16, no. 3 (June 28, 2021): 363–66. http://dx.doi.org/10.1007/s40062-021-00284-6.

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AbstractWe show that the Cantor–Schröder–Bernstein Theorem for homotopy types, or $$\infty $$ ∞ -groupoids, holds in the following form: For any two types, if each one is embedded into the other, then they are equivalent. The argument is developed in the language of homotopy type theory, or Voevodsky’s univalent foundations (HoTT/UF), and requires classical logic. It follows that the theorem holds in any boolean $$\infty $$ ∞ -topos.
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Corfield, David. "Expressing ‘the structure of’ in homotopy type theory." Synthese 197, no. 2 (November 20, 2017): 681–700. http://dx.doi.org/10.1007/s11229-017-1569-7.

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Abstract As a new foundational language for mathematics with its very different idea as to the status of logic, we should expect homotopy type theory to shed new light on some of the problems of philosophy which have been treated by logic. In this article, definite description, and in particular its employment within mathematics, is formulated within the type theory. Homotopy type theory has been proposed as an inherently structuralist foundational language for mathematics. Using the new formulation of definite descriptions, opportunities to express ‘the structure of’ within homotopy type theory are explored, and it is shown there is little or no need for this expression.
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Dissertations / Theses on the topic "Foundations of homotopy theory"

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Bordg, Anthony. "Modèles de l'univalence dans le cadre équivariant." Thesis, Nice, 2015. http://www.theses.fr/2015NICE4083.

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Cette thèse de doctorat a pour sujet les modèles de la théorie homotopique des types avec l'Axiome d'Univalence introduit par Vladimir Voevodsky. L'auteur prend pour cadre de travail les définitions de type-theoretic model category, type-theoretic fibration category (cette dernière étant la notion de modèle considérée dans cette thèse) et d'univers dans une type-theoretic fibration category, définitions dues à Michael Shulman. La problématique principale de cette thèse consiste à approfondir notre compréhension de la stabilité de l'Axiome d'Univalence pour les catégories de préfaisceaux, en particulier pour les groupoïdes équipés d'une involution
This PhD thesis deals with some new models of Homotopy Type Theory and the Univalence Axiom introduced by Vladimir Voevodsky. Our work takes place in the framework of the definitions of type-theoretic model categories, type-theoretic fibration categories (the notion of model under consideration in this thesis) and universe in a type-theoretic fibration category, definitions due to Michael Shulman. The goal of this thesis consists mainly in the exploration of the stability of the Univalence Axiom for categories of functors , especially for groupoids equipped with involutions
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Saleh, Bashar. "Formality and homotopy automorphisms in rational homotopy theory." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-160835.

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This licentiate thesis consists of two papers treating subjects in rational homotopy theory. In Paper I, we establish two formality conditions in characteristic zero. We prove that adg Lie algebra is formal if and only if its universal enveloping algebra is formal. Wealso prove that a commutative dg algebra is formal as a dg associative algebra if andonly if it is formal as a commutative dg algebra. We present some consequences ofthese theorems in rational homotopy theory. In Paper II, we construct a differential graded Lie model for the universal cover of the classifying space of the grouplike monoid of homotopy automorphisms of a space that fix a subspace.

At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 2: Manuscript.

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Wang, Guozhen Ph D. Massachusetts Institute of Technology. "Unstable chromatic homotopy theory." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/99321.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 57-58).
In this thesis, I study unstable homotopy theory with chromatic methods. Using the v, self maps provided by the Hopkins-Smith periodicity theorem, we can decompose the unstable homotopy groups of a space into its periodic parts, except some lower stems. For fixed n, using the Bousfield-Kuhn functor [Phi]n, we can associate to any space a spectrum, which captures the vo-periodic part of its homotopy groups. I study the homotopy type of the spectra LK(n)[Phi]nfSk, which would tell us much about the vn-periodic part of the homotopy groups of spheres provided we have a good understanding of the telescope conjecture. I make use the Goodwillie tower of the identity functor, which resolves the unstable spheres into spectra which are the Steinberg summands of classifying spaces of the additive groups of vector spaces over F,. By understanding the attaching maps of the Goodwillie tower after applying the Bousfield-Kuhn functor, we would be able to determine the homotopy type of LK(n)[Phi]nSk. As an example of how this works in concrete computations, I will compute the homotopy groups of LK(2)[Phi]nS3 at primes p >/= 5. The computations show that the unstable homotopy groups not only have finite p-torsion, their K(2)-local parts also have finite vo-torsion, which indicates there might be a more general finite v-torsion phenomena in the unstable world.
by Guozhen Wang.
Ph. D.
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Beke, Tibor 1970. "Homotopy theory and topoi." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/47465.

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Douglas, Christopher L. "Twisted stable homotopy theory." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/33095.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
Includes bibliographical references (p. 133-137).
There are two natural interpretations of a twist of stable homotopy theory. The first interpretation of a twist is as a nontrivial bundle whose fibre is the stable homotopy category. This kind of radical global twist forms the basis for twisted parametrized stable homotopy theory, which is introduced and explored in Part I of this thesis. The second interpretation of a twist is as a nontrivial bundle whose fibre is a particular element in the stable homotopy category. This milder notion of twisting leads to twisted generalized homology and cohomology and is central to the well established field of parametrized stable homotopy theory. Part II of this thesis concerns a computational problem in parametrized stable homotopy, namely the determination of the twisted K-homology of the simple Lie groups. In more detail, the contents of the two parts of the thesis are as follows. Part I: I describe a general framework for twisted forms of parametrized stable homotopy theory. An ordinary parametrized spectrum over a space X is a map from X into the category Spec of spectra; in other words, it is a section of the trivial Spec- bundle over X. A twisted parametrized spectrum over X is a section of an arbitrary bundle whose fibre is the category of spectra. I present various ways of characterizing and classifying these twisted parametrized spectra in terms of invertible sheaves and local systems of categories of spectra. I then define homotopy-theoretic invariants of twisted parametrized spectra and describe a spectral sequence for computing these invariants.
(cont.) In a more geometric vein, I show how a polarized infinite-dimensional manifold gives rise to a twisted form of parametrized stable homotopy, and I discuss how this association should be realized explicitly in terms of semi-infinitely indexed spectra. This connection with polarized manifolds provides a foundation for applications of twisted parametrized stable homotopy to problems in symplectic Floer and Seiberg-Witten-Floer homotopy theory. Part II: I prove that the twisted K-homology of a simply connected simple Lie group G of rank n is an exterior algebra on n - 1 generators tensor a cyclic group. I give a detailed description of the order of this cyclic group in terms of the dimensions of irreducible representations of G and show that the congruences determining this cyclic order lift along the twisted index map to relations in the twisted ... bordism group of G.
by Christopher Lee Douglas.
Ph.D.
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Heggie, Murray. "Tensor products in homotopy theory." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=72792.

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Miller, David. "Homotopy theory for stratified spaces." Thesis, University of Aberdeen, 2010. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=158352.

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There are many different notions of stratified spaces. This thesis concerns homotopically stratified spaces. These were defined by Frank Quinn in his paper Homotopically Stratified Sets ([16]). His definition of stratified space is very general and relates strata by “homotopy rather than geometric conditions”. This makes homotopically stratified spaces the ideal class of stratified spaces on which to define and study stratified homotopy theory. In the study of stratified spaces it is useful to examine spaces of popaths (paths which travel from lower strata to higher strata) and holinks (those spaces of popaths which immediately leave a lower stratum for their final stratum destination). It is not immediately clear that for adjacent strata these two path spaces are homotopically equivalent and even less clear that this equivalence can be constructed in a useful way. The first aim of this thesis is to prove such an equivalence exists for homotopically stratified spaces. We will define stratified analogues of the usual definitions of maps, homotopies and homotopy equivalences. Then we will provide an elementary criterion for deciding when a strongly stratified map is a stratified homotopy equivalence. This criterion states that a strongly stratified map is a stratified homotopy equivalence if and only if the induced maps on strata and holink spaces are homotopy equivalences. Using this criterion we will prove that any homotopically stratified space is stratified homotopy equivalent to a homotopically stratified space where neighborhoods of strata are mapping cylinders. Finally we will develop categorical descriptions of the class of homotopically stratified spaces up to stratified homotopy. The first of these categorical descriptions will involve categories with a topology on their object and morphism sets. The second categorical description will involve only categories with discrete object spaces.
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Antolini, Rosa. "Cubical structures and homotopy theory." Thesis, University of Warwick, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338578.

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Hollander, Sharon Joy 1975. "A homotopy theory for stacks." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/8637.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.
Includes bibliographical references (p. 69-70).
We give a homotopy theoretic characterization of stacks on a site C which allows one to think of stacks as the homotopy sheaves of groupoids on C. We use this characterization to construct a model category, that is a formal homotopy theory, in which stacks play the special role of the fibrant objects. This allows us to compare the different definitions of stacks and show that they lead to Quillen equivalent model categories. In addition, these model structures are Quillen equivalent to the S2-nullification of Jardine's model structure on sheaves of simplicial sets on e.
by Sharon Joy Hollander.
Ph.D.
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Ochi, Yoshihiro. "Iwasawa modules via homotopy theory." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624327.

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Books on the topic "Foundations of homotopy theory"

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R, Anderson Douglas. Boundedly controlled topology: Foundations of algebraic topology and simple homotopy theory. Berlin: Springer-Verlag, 1988.

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Combinatorial foundation of homology and homotopy: Applications to spaces, diagrams, transformation groups, compactifications, differential algebras, algebraic theories, simplicial objects, and resolutions. Berlin: Springer, 1999.

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Baues, Hans J. Combinatorial foundation of homology and homotopy: Applications to spaces, diagrams, transformation groups, compactifications, differential algebras, algebraic theories, simplicial objects, and resolutions. Berlin: Springer, 1999.

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Kamps, Klaus Heiner. Abstract homotopy and simple homotopy theory. Singapore: World Scientific, 1997.

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F, Jardine John, and SpringerLink (Online service), eds. Simplicial Homotopy Theory. Basel: Birkhäuser Basel, 2009.

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Antonio, Quintero, ed. Infinite homotopy theory. Dordrecht: Kluwer Academic Publishers, 2001.

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Crabb, M. C. Fibrewise homotopy theory. London: Springer, 1998.

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1975-, Sigurdsson J., ed. Parametrized homotopy theory. Providence, R.I: American Mathematical Society, 2006.

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Jardine, John F. Local Homotopy Theory. New York, NY: Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4939-2300-7.

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Félix, Yves, Stephen Halperin, and Jean-Claude Thomas. Rational Homotopy Theory. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0105-9.

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Book chapters on the topic "Foundations of homotopy theory"

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Baues, Hans-Joachim, and Antonio Quintero. "Foundations of Homotopy Theory and Proper Homotopy Theory." In K-Monographs in Mathematics, 7–70. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-009-0007-3_2.

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Buchholtz, Ulrik. "Higher Structures in Homotopy Type Theory." In Reflections on the Foundations of Mathematics, 151–72. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15655-8_7.

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Palmgren, Erik. "From Intuitionistic to Point-Free Topology: On the Foundation of Homotopy Theory." In Logicism, Intuitionism, and Formalism, 237–53. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-1-4020-8926-8_12.

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Weintraub, Steven H. "Homotopy Theory." In Graduate Texts in Mathematics, 127–38. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-1844-7_7.

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Banagl, Markus. "Homotopy Theory." In Lecture Notes in Mathematics, 1–106. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12589-8_1.

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Borisovich, Yuri G., Nikolai M. Bliznyakov, Tatyana N. Fomenko, and Yakov A. Izrailevich. "Homotopy Theory." In Kluwer Texts in the Mathematical Sciences, 161–215. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-017-1959-9_3.

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Basu, Samik, and Soma Maity. "Homotopy theory." In Topology and Condensed Matter Physics, 45–63. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6841-6_3.

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Bredon, Glen E. "Homotopy Theory." In Graduate Texts in Mathematics, 430–517. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4757-6848-0_7.

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Aubry, Marc. "Basic Homotopy Theory." In Homotopy Theory and Models, 1–13. Basel: Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9086-1_1.

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Dodson, C. T. J., and Phillip E. Parker. "Homotopy Group Theory." In A User’s Guide to Algebraic Topology, 51–103. Boston, MA: Springer US, 1997. http://dx.doi.org/10.1007/978-1-4615-6309-9_4.

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Conference papers on the topic "Foundations of homotopy theory"

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Hess, Kathryn. "Homotopic Hopf–Galois extensions: Foundations and examples." In New topological contexts for Galois theory and algebraic geometry. Mathematical Sciences Publishers, 2009. http://dx.doi.org/10.2140/gtm.2009.16.79.

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Mörtberg, Anders, and Loïc Pujet. "Cubical synthetic homotopy theory." In POPL '20: 47th Annual ACM SIGPLAN Symposium on Principles of Programming Languages. New York, NY, USA: ACM, 2020. http://dx.doi.org/10.1145/3372885.3373825.

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Devinatz, Ethan S. "Homotopy groups of homotopy fixed point spectra associated to En." In International Conference in Homotopy Theory. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2007.10.131.

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Furuta, Mikio, Yukio Kametani, Hirofumi Matsue, and Norihiko Minami. "Homotopy theoretical considerations of the Bauer–Furuta stable homotopy Seiberg–Witten invariants." In International Conference in Homotopy Theory. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2007.10.155.

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Lazarus, Francis, and Julien Rivaud. "On the Homotopy Test on Surfaces." In 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2012. http://dx.doi.org/10.1109/focs.2012.12.

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Frumin, Dan, Herman Geuvers, Léon Gondelman, and Niels van der Weide. "Finite sets in homotopy type theory." In the 7th ACM SIGPLAN International Conference. New York, New York, USA: ACM Press, 2018. http://dx.doi.org/10.1145/3176245.3167085.

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Awodey, Steve, Nicola Gambino, and Kristina Sojakova. "Inductive Types in Homotopy Type Theory." In 2012 27th Annual IEEE Symposium on Logic in Computer Science (LICS 2012). IEEE, 2012. http://dx.doi.org/10.1109/lics.2012.21.

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Kunii, Tosiyasu L., and Masaki Hilaga. "Homotopy Type Theory for Big Data." In 2015 International Conference on Cyberworlds (CW). IEEE, 2015. http://dx.doi.org/10.1109/cw.2015.9.

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Buchholtz, Ulrik, Floris van Doorn, and Egbert Rijke. "Higher Groups in Homotopy Type Theory." In LICS '18: 33rd Annual ACM/IEEE Symposium on Logic in Computer Science. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3209108.3209150.

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Buchholtz, Ulrik, and Kuen-Bang Hou Favonia. "Cellular Cohomology in Homotopy Type Theory." In LICS '18: 33rd Annual ACM/IEEE Symposium on Logic in Computer Science. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3209108.3209188.

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Reports on the topic "Foundations of homotopy theory"

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Watson, Layne T. Theory and Application of Homotopy Techniques in Nonlinear Programming and Control Systems. Fort Belvoir, VA: Defense Technical Information Center, April 1995. http://dx.doi.org/10.21236/ada294934.

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McCullough, Daryl. Foundations of Ulysses: The Theory of Security. Fort Belvoir, VA: Defense Technical Information Center, July 1988. http://dx.doi.org/10.21236/ada200110.

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Helmbold, Robert L. Foundations of the General Theory of Volley Fire. Fort Belvoir, VA: Defense Technical Information Center, September 1992. http://dx.doi.org/10.21236/ada263181.

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Protopopescu, V. (Discrete kinetic theory, lattice gas dynamics and foundations of hydrodynamics). Office of Scientific and Technical Information (OSTI), October 1988. http://dx.doi.org/10.2172/6804923.

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Lehmann, Bruce, and David Modest. The Empirical Foundations of the Arbitrage Pricing Theory I: The Empirical Tests. Cambridge, MA: National Bureau of Economic Research, October 1985. http://dx.doi.org/10.3386/w1725.

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Brot-Goldberg, Zarek, Timothy Layton, Boris Vabson, and Adelina Yanyue Wang. The Behavioral Foundations of Default Effects: Theory and Evidence from Medicare Part D. Cambridge, MA: National Bureau of Economic Research, January 2021. http://dx.doi.org/10.3386/w28331.

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Lehmann, Bruce, and David Modest. The Empirical Foundations of the Arbitrage Pricing Theory II: The Optimal Construction of Basis Portfolios. Cambridge, MA: National Bureau of Economic Research, October 1985. http://dx.doi.org/10.3386/w1726.

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Duersch, Jed, Thomas Catanach, and Ming Gu. CIS-LDRD Project 218313 Final Technical Report. Parsimonious Inference Information-Theoretic Foundations for a Complete Theory of Machine Learning. Office of Scientific and Technical Information (OSTI), September 2020. http://dx.doi.org/10.2172/1668936.

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Lewis, Alain A. Some Aspects of Constructive Mathematics That Are Relevant to the Foundations of Neoclassical Mathematical Economics and the Theory of Games. Fort Belvoir, VA: Defense Technical Information Center, April 1988. http://dx.doi.org/10.21236/ada198446.

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