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Courses
(at Johns Hopkins)
- 050.109
Minds, Brains & Computers
- 050.313/613 Introduction to Cognition for Mathematical Scientists
- 050.325/625 Phonology I
- 050.326/626
Foundations of Cognitive Science
- 050.327/627 Phonology II
- 050.329/629 Phonology III
- 050.372/672 Formal Methods in Cognitive Science: Neural Networks
- 050.382/682 Intermediate Formal Methods in Cognitive Science: Neural
Networks
- 050.823 Research Seminar
in Phonology
- 050.830 Topics in Cognitive
Science
Research
Primary
Area: Universal grammar --
Optimality Theory: phonology, syntax, acquisition, learnability, processing.
Secondary Areas: Integration
of connectionist ('neural') and symbolic computation: computational, linguistic,
and philosophical issues.
Precise theories of higher cognitive domains like language and reasoning
rely crucially on complex symbolic rule systems like those of grammar
and logic. According to traditional cognitive science and artificial intelligence,
such symbolic systems are the very essence of higher intelligence. Yet
intelligence resides in the brain, where computation appears to be numerical,
not symbolic; parallel, not serial; quite distributed, not as highly
localized as in symbolic systems. Furthermore, when observed carefully,
much of human behavior is remarkably sensitive to the detailed statistical
properties of experience; hard-edged rule systems seem ill-equipped to
handle these subtleties. My research attempts to identify the proper roles within a unified theory of cognition
for symbolic computation, numerical neural computation, and statistical
computation.
More specifically, the basic questions driving this research include:
What are the central general principles of computation in connectionist
-- abstract neural -- networks? How can these principles be reconciled
with those of symbolic computation? Addressing these questions over the
past two decades, my work has led to a new computational architecture
for cognition which integrates connectionist and symbolic computation.
Can this framework further the theory of higher cognition, by connecting
it with lower-level principles derived from neural computation?
The connectionist conception of intuitive knowledge as a collection of
conflicting soft constraints, interacting via optimization of well-formedness
or Harmony, led in joint research with Géraldine
Legendre to the connectionist-based formalism of Harmonic Grammar.Incorporating
the richly tructured representations and universal well-formedness constraints
of symbolic linguistic theory,
Alan Prince and I developed a grammar formalism called
Optimality Theory which brings general connectionist computational
principles of optimization into the heart of the symbolic theory of universal
grammar. The optimization that emerges is no longer inherently numerical:
constraint strengths are encoded in a hierarchy of constraints, ranked
from strongest to weakest; each constraint is stronger than all weaker
constraints combined.
According to Optimality Theory (OT), possible human languages share
a common set of universal constraints on well-formedness. These constraints
are highly general, and hence conflict; thus some must be violated in
optimal, i.e., grammatical, structures. The different surface patterns
of the world's languages emerge via different priority rankings of the
fixed set of universal constraints: each ranking is a language-particular
grammar, a means of resolving the inherent conflicts among the universal
constraints.
My current research addresses multiple aspects of OT. These include
superadditive constraint interaction ('local conjunction' of constraints),
especially in phonology (vowel harmony; Obligatory Contour Principle;
sonority and syllable structure), as well as numerical and connectionist
implementation of OT constraint interaction.
Ph.D. Students (since 1995)
|
Current
position |
Ph.D. Dissertation, Cognitive Science, Johns Hopkins or Research
Topic |
| |
|
|
Adam
Buchwald
Oren Schwartz |
Ph.D. students, Cognitive Science,
JHU |
Recoverability Optimality Theory: Discourse
anaphora in a bidirectional framework. |
| Lisa
Davidson |
Ph.D. student, Cognitive Science, JHU |
The interaction of articulatory, perceptual,
and temporal elements in consonant cluster production.Expected:
June 2003. |
John
Hale
|
Ph.D. student, Cognitive Science, JHU |
Grammar, uncertainty, and sentence processing.
Expected: June 2003. |
| Matt
Goldrick |
Postdoctoral Research Associate, Cognitive and Linguistic
Sciences, Brown |
Patterns in sound, patterns in mind: Phonological
regularities in speech production. 2002. |
|
Colin Wilson |
Assistant Professor of Linguistics, UCLA |
Targeted Constraints: An Approach to Positional Neutralization
in Optimality Theory. 2000. |
| Adamantios
Gafos |
Assistant Professor of Linguistics, NYU |
The Articulatory Basis of Locality in
Phonology. 1996. |
|
Bruce Tesar |
Assistant Professor of Linguistics, Rutgers |
Computational Optimality Theory. 1995. Computer
Science, U. of Colorado |
Education
- Ph.D. in mathematical physics, Indiana University, 1981.
- M.S. in physics, Indiana University, 1977.
- A.B. summa cum laude in physics, Harvard University, 1976.
Positions
- Full Professor, Department of Cognitive Science, Johns Hopkins University,
1994-present.
- Chair, Department of Cognitive Science, Johns Hopkins University,
Jan. 1997 - June 1998 (Acting), July 1998 - June 2000.
- Adjunct Professor, Department of Linguistics, University of Maryland
at College Park, 1994-present.
- Assistant Director, Center for Language and Speech Processing, Johns
Hopkins University, 1995-present.
- Director, NSF IGERT Training Program in the Cognitive Science of Language,
1999-2004.
- Professor, Department of Computer Science, University of Colorado
at Boulder,
Full Professor, 1994-95 (on leave, 1994-95).
Associate Professor, 1990-94.
Assistant Professor, 1985-90.
- Assistant Research Cognitive Scientist (Assistant Professor - Research),
Institute for Cognitive Science, University of California at San Diego,
1982-85.
- Visiting Scholar, Program in Cognitive Science, University of California
at San Diego, 1981-82.
- Faculty, First International Summer Institute in Cognitive Science,
SUNY Buffalo, 1994.
- Faculty, Linguistic Institute, University of California at Santa
Cruz, 1991.
- Faculty, Connectionist Models Summer School; Carnegie-Mellon University,
1986, 1988; University of California, San Diego, 1990; University of
Colorado, Boulder, 1993.
- National Science Foundation, John H. Edwards, and Indiana University
Graduate Fellow, 1976-81.
Recent
Presentations
- An Integrated Connectionist/Symbolic (ICS) Cognitive Architecture.
Seoul National University. November, 2002. [4.4Mb
ppt file]
- Jakobson's Grand Unified Theory of Linguistic Cognition. Seoul National
University. November, 2002. [.5Mb
ppt file]
- Constraint Conjunction andStrong Harmonic Completeness. Korean Phonological
Society. November, 2002.[0.6Mb
ppt file]
- The Harmonic Mind. Cognition Workshop. North American Summer School
for Logic, Language, and Information. Stanford University. July, 2002.
[2.4Mb ppt
file]
- Markedness Optimization in Grammar and Cognition. Plenary Lecture,
Annual Meeting of the Linguistic Society of America. San Francisco.
January, 2002. [1Mb ppt file]
- Formal Typology: Explanation in Optimality Theory. Phonology Forum.
Tokyo, Japan. August, 2001. [0.5Mb
ppt file]
- The Harmonic Mind. International Cognitive Science Conference. Beijing,
China. August, 2001.[2Mb
ppt file]
- The Harmonic Mind. Presidential Address, Annual Meeting of the Society
for Philosophy and Psychology. Cincinnati, OH. June, 2001. [4Mb
ppt file]
Publications
For
a complete list, see the
Complete Vita
ROA = http://ruccs.rutgers.edu/roa.html,
the Rutgers Optimality Archive

Books
- Smolensky, P., & Legendre, G. To appear. The harmonic mind:
From neural computation to optimality-theoretic grammar.
- Prince, A. & Smolensky, P. To appear.
Optimality Theory: Constraint interaction in generative grammar.
Blackwell. Complete ms. distributed April 1993 as Technical Report
CU-CS-696-93, Department of Computer Science, University of Colorado
at Boulder, and Technical Report TR-2, Rutgers Center for Cognitive
Science, Rutgers University, New Brunswick, NJ. (234 pages). ROA 537.
- Tesar, B. & Smolensky, P. 2000. Learnability
in Optimality Theory. MIT Press.
- Smolensky, P., Mozer, M. C., & Rumelhart, D. E. (eds.). 1996. Mathematical
perspectives on neural networks. Lawrence Erlbaum Publishers.
- Macdonald, C. & Macdonald, G. (eds.). 1995. Connectionism:
Debates on psychological explanation, Volume 2. Basil Blackwell.
[Contributed 4 chapters, 183 of 412 pp.]
- Mozer, M.C., Smolensky, P., Touretzky, D., Elman, J., & Weigend,
A. (eds.). 1993. Proceedings
of the Connectionist Models Summer School 1993.Lawrence
Erlbaum Publishers.
- Smolensky, P. 1992. Il Connessionismo: Tra simboli e neuroni.
Italian translation of the entire treatment, including peer commentary:
On the proper treatment of connectionism, Behavioral and Brain Sciences,
11, 1-74; with introduction by Marcello Frixione. Genova: Marietti/Cambridge
University Press.
Papers
Grammar
- Hale, John & Smolensky, Paul. To appear. Harmonic Grammars and
harmonic parsers for formal languages. In [1]. Chapter 10.
- Legendre, Géraldine, Smolensky, Paul, & Miyata, Yoshiro. To appear.
Harmonic Grammar and its subsymbolic foundations. In [1]. Chapter
11.
- Smolensky, Paul & Tesar, Bruce. To appear. Principles of Optimality
Theory. In [1]. Chapter 12.
- Smolensky, Paul. To appear. Optimality in phonology II: Markedness,
feature domains, and Local Constraint Conjunction. In [1]. Chapter
14.
- Smolensky, Paul & Stevenson, Suzanne. To appear. Optimality in
sentence processing. In [1]. Chapter 19.
- Legendre, Géraldine, Sorace, Antonella & Smolensky, Paul. To appear.
The Optimality Theory -- Harmonic Grammar connection. In [1].
Chapter 20.
- Smolensky, Paul, Davidson, Lisa, and Jusczyk, Peter W. In press.
The initial and final states: Theoretical implications and experimental
explorations of richness of the base. In René Kager, Joe Pater and
Wim Zonneveld, eds. Fixing Priorities: Constraints in Phonological
Acquisition. Cambridge, England: Cambridge University Press. Reprinted
in [1], Chapter 17. Rutgers Optimality Archive 428.
- Moreton, Elliott, and Smolensky, Paul. 2002. Typological consequences
of Local Constraint Conjunction. Proceedings of the 21st West
Coast Conference on Formal Linguistics.
- Jusczyk, P., Smolensky, P., and Allocco, T. 2002. How English-learning
infants respond to markedness and faithfulness constraints. Language
Acquisition .
- Smolensky, P. 2000. Grammar-based
connectionist approaches to language. Cognitive Science 23:
589-613. Reprinted in M. Christiansen and N. Chater. 2000. Connectionist
Psycholinguistics. Ablex.
- Tesar, B. & Smolensky, P. 1998. Learning
Optimality-Theoretic grammars. Lingua, 106: 161-196.
Reprinted in Sorace, A., Heycock, C. and Shillcock, R. (eds.) Language
Acquisition: Knowledge Representation and Processing. Amsterdam:
Elsevier.
- Legendre, G., Smolensky, P., & Wilson, C. 1998. When
is less more? Faithfulness and minimal links in wh-chains.
In Pilar Barbosa, Danny Fox, Paul Hagstrom, Martha McGinnis, and David
Pesetsky, eds., Is the Best Good Enough? Optimality and Competition
in Syntax. MIT Press. 249-289
- Tesar, B. & Smolensky, P. 1998. Learnability
in Optimality Theory. Linguistic Inquiry, 29: 229-268
- Prince, A. & Smolensky, P. 1997. Optimality:
From neural networks to universal grammar. Science 275:
1604-1610.
- Smolensky, P. 1996. On
the comprehension/production dilemma in child language.
Linguistic Inquiry 27: 720-731. ROA-118.
- Smolensky, P. 1996. The
initial state and 'richness of the base' in Optimality Theory.
Accepted for publication in Linguistic Inquiry in 1997.Technical
Report JHU-CogSci-96-4, Cognitive Science Department, Johns Hopkins
University. ROA-154.
- Legendre, G., Wilson, C., Smolensky, P., Homer, K., & Raymond, W.
1995. Optimality
in wh-chains. University of Massachusetts Occasional
Papers in Linguistics 18: Papers in Optimality Theory, J.
Beckman, S. Urbanczyk, & L. Walsh, eds. Amherst, MA: GLSA, University
of Massachusetts. 607-636. ROA-85.
- Tesar, B. & Smolensky, P. 1994. The
learnability of Optimality Theory. Proceedings of
the West Coast Conference on Formal Linguistics XIII. 122-137.
- Legendre, G., Raymond, W., & Smolensky, P. 1993. An
Optimality-Theoretic typology of case and grammatical voice systems.
Proceedings of the Nineteenth Annual Meeting of the Berkeley
Linguistics Society. Berkeley, CA. February. 464-478. ROA-3.
- Legendre, G., Miyata, Y., & Smolensky, P. 1991. Unifying syntactic
and semantic approaches to unaccusativity: A connectionist approach.
In L. Sutton & C. Johnson (with Ruth Shields) (Eds.), Proceedings
of the Seventeenth Annual Meeting of the Berkeley Linguistics Society.
Berkeley, CA. February. 156-167.
- Prince, A. & Smolensky, P. 1991. Notes on Connectionism and Harmony
Theory in Linguistics. Technical Report CU-CS-533-91, Department
of Computer Science, University of Colorado at Boulder. July. [Notes
from the course, 'Connectionism and Harmony Theory in Linguistics,'
LSA Linguistic Institute, University of California, Santa Cruz; July,
1991.]
- Smolensky, P. 1991. Connectionism. In W. Bright (Ed.) The
International Encyclopedia of Linguistics. Oxford University Press.
294-297.
- Legendre, G., Miyata, Y., & Smolensky, P. 1990. Can connectionism
contribute to syntax? Harmonic Grammar, with an application. Proceedings
of the 26th Meeting of the Chicago Linguistic Society. Chicago,
IL. April.
- Legendre, G., Miyata, Y., & Smolensky, P. 1990. Harmonic Grammar
-- A formal multi-level connectionist theory of linguistic well-formedness:
An application. Proceedings of the Twelfth Annual Conference
of the Cognitive Science Society, Cambridge, MA. July. 884-891.
- Legendre, G., Miyata, Y., & Smolensky, P. 1990. Harmonic Grammar
-- A formal multi-level connectionist theory of linguistic well-formedness:
Theoretical foundations. Proceedings of the Twelfth Annual Conference
of the Cognitive Science Society, Cambridge, MA. July. 388-395.
Computation
- Smolensky, P. (1996). Computational, dynamical, and statistical
perspectives on the processing and learning problems in neural network
theory. In [4]. 1-15.
- Smolensky, P. (1996). Computational perspectives on neural networks.
In [4]. 17-40.
- Smolensky, P. (1996). Dynamical perspectives on neural networks.
In [4]. 245-270.
- Smolensky, P. (1996). Statistical perspectives on neural networks.
In [4]. 453-496.
- Tesar, B. & Smolensky, P. (1994). Synchronous-firing variable
binding is spatio-temporal tensor product representation. Proceedings
of the 16th Annual Conference of the Cognitive Science Society.
Atlanta, GA. August.
- Smolensky, P. (1993). Harmonic Grammars for formal languages.
In S. Hanson, J. D. Cowan, & C. L. Giles, (Eds.), Advances in Neural
Information Processing Systems 5, San Mateo, CA: Morgan Kaufmann.
[Collected papers of the IEEE Conference on Neural Information Processing
Systems-Natural and Synthetic, Denver, Nov. 1992.] 847-854.
- Miyata, Y, Smolensky, P., & Legendre, G. (1993). Distributed representation
and parallel processing of recursive structures. Proceedings
of the 15th Annual Conference of the Cognitive Science Society,
Boulder, CO. June. 759-764.
- Legendre, G., Miyata, Y., & Smolensky, P. (1991). Distributed recursive
structure processing. In Touretzky, D. S., Lippman, R. (Eds.), Advances
in Neural Information Processing Systems 3. San Mateo, CA: Morgan
Kaufmann. [Collected papers of the IEEE Conference on Neural Information
Processing Systems-Natural and Synthetic, Denver, Nov. 1990.] 591-597.
Slightly expanded version in Mayoh, B. (Ed.), Scandinavian Conference
on Artificial Intelligence-91, 47-53. Amsterdam: IOS Press.
- Smolensky, P. (1990). Tensor product variable binding and the representation
of symbolic structures in connectionist networks. Artificial
Intelligence, 46, 159-216. [Reprinted in G. Hinton, (Ed.), (1990),
Connectionist symbol processing, Elsevier/MIT Press.]
- Brousse, O. & Smolensky, P. (1990). Connectionist generalization
and incremental learning in combinatorial domains. In H. Haken (Ed.),
Synergetics of Cognition. Springer-Verlag. 70-80.
- Smolensky, P. (1990). Representation in connectionist networks.
Intellectica: The Journal of the French Association for Cognitive
Research, 9-10, 127-165.
- Mozer, M. C., & Smolensky, P. (1989). Using relevance to reduce
network size automatically. Connection Science, 1, 3-16.
- Dolan, C. & Smolensky, P. (1989). Tensor Product Production System:
A modular architecture and representation. Connection Science,
1, 53-68.
- Brousse, O. & Smolensky, P. (1989). Virtual memories and massive
generalization in connectionist combinatorial learning. Proceedings
of the Eleventh Annual Meeting of the Cognitive Science Society.
Ann Arbor, MI. August. 380-387.
- Smolensky, P. (1988). Analysis of distributed representation of
constituent structure in connectionist systems. Proceedings of
Neural Information Processing Systems-87. Denver, CO. November.
730-739.
- McMillan, C. & Smolensky, P. (1988). Analyzing a connectionist
model as a system of soft rules. Proceedings of the Tenth Annual
Meeting of the Cognitive Science Society. Montreal, Canada. August.
62-68.
- Smolensky, P. (1987). On variable binding and the representation
of symbolic structures in connectionist systems. Technical Report
CU-CS-355-87, Department of Computer Science, University of Colorado
at Boulder. February.
- Smolensky, P. (1986). Information processing in dynamical systems:
Foundations of harmony theory. In D. E. Rumelhart, J. L. McClelland,
& the PDP Research Group, Parallel Distributed Processing: Explorations
in the Microstructure of Cognition. Volume 1: Foundations. Cambridge,
MA: MIT Press/Bradford Books. 194-281.
- Smolensky, P. (1986). Neural and conceptual interpretations of
parallel distributed processing models. In J. L. McClelland, D.
E. Rumelhart, & the PDP Research Group, Parallel Distributed Processing:
Explorations in the Microstructure of Cognition. Volume 2: Psychological
and Biological Models. Cambridge, MA: MIT Press/Bradford Books.
390-431.
- Rumelhart, D. E., Smolensky, P., McClelland, J. L., & Hinton, G.
E. (1986). Schemata and sequential thought processes in parallel
distributed processing. J. L. McClelland, D. E. Rumelhart, & the
PDP Research Group, Parallel Distributed Processing: Explorations
in the Microstructure of Cognition. Volume 2: Psychological and Biological
Models. Cambridge, MA: MIT Press/Bradford Books. 7-57. [Reprinted
in A. Collins & E. Smith (Eds), 1988, Readings in Cognitive Science,
San Mateo, CA: Morgan Kaufmann.]
- Smolensky, P. (1984). The mathematical role of self-consistency
in parallel computation. Proceedings of the Sixth Annual Conference
of the Cognitive Science Society. Boulder, CO. June. 319-325.
- Riley, M. S. & Smolensky, P. (1984). A parallel model of (sequential)
problem solving. Proceedings of the Sixth Annual Conference of
the Cognitive Science Society. Boulder, CO. June. 286-292.
- Smolensky, P. (1983). Schema selection and stochastic inference
in modular environments. Proceedings of the National Conference
on Artificial Intelligence. Washington, DC. August. 378-382.
Foundations
- Smolensky, P. (1995). Constituent structure and explanation in
an integrated connectionist/symbolic cognitive architecture. In
[5]. 221-290.
- Smolensky, P. (1994). Computational theories of mind. In S.
Guttenplan (Ed.), A Companion to the Philosophy of Mind. Blackwell
Publishers. 176-185.
- Smolensky, P. (1991). Connectionism, constituency, and the language
of thought. In B. Loewer & G. Rey (Eds.), Meaning in Mind: Fodor
and his Critics. Oxford: Basil Blackwell. 201-227. Reprinted in
[5].
- Smolensky, P. (1989). Connectionist modeling: Neural computation/mental
connections. In L. Nadel (Ed.), P. Culicover, L. A. Cooper, R. M.
Harnish (Assoc. Eds.), Neural connections, mental computation.
Cambridge, MA: MIT Press/Bradford. 49-67. [Reprinted in J. Haugeland,
(Ed.). (1997). Mind Design II: Philosophy, Psychology, Artificial
Intelligence, MIT Press/Bradford Books.]
- Smolensky, P. (1987). The constituent structure of connectionist
mental states: A reply to Fodor and Pylyshyn. Southern Journal
of Philosophy, 26 (Supplement), 137-63. [Reprinted in T. Horgan
& J. Tienson (Eds.), (1991), Connectionism and the Philosophy of
Mind, Dordrecht: Kluwer Academic. 281-308; Spanish translation in
E. Rabossi (Ed.), Filosofía y Ciencia Cognitiva, Buenos Aires-Barcelona:
Editorial Paidós.]
Integration
- Smolensky, P., Legendre, G., & Miyata, Y. (1993). Integrating connectionist
and symbolic computation for the theory of language. Current Science
64, 381-391. Reprinted in: V. Honavar & L. Uhr, Artificial Intelligence
and Neural Networks: Steps Toward Principled Integration, 509-530.
Academic Press.
- Smolensky, P., Legendre, G., & Miyata, Y. (1992). Principles for
an Integrated Connectionist/Symbolic Theory of Higher Cognition.
Technical Report CU-CS-600-92, Department of Computer Science and 92-8,
Institute of Cognitive Science. University of Colorado at Boulder. (75
pages). Expanded to [1].
- McNaughton, B. L. & Smolensky, P. (1991). Connectionist and neural
modeling: Converging in the hippocampus. In R. G. Lister & H. J.
Weingartner (Eds.), Perspectives on Cognitive Neuroscience. Oxford
University Press. 93-109.
- Smolensky, P. (1990). In defense of PTC: Reply to continuing commentary.
Behavioral and Brain Sciences. 13, 407-411.
- Smolensky, P. (1988). Putting Together Connectionism-again.
Behavioral and Brain Sciences, 11, 59-74.
- Smolensky, P. (1988). On the proper treatment of connectionism.
Behavioral and Brain Sciences, 11, 1-23. [Reprinted in D. Cole,
J. Fetzer, & T. Rankin (Eds.), (1990), Philosophy, Mind, and Cognitive
Inquiry, Dordrecht: Kluwer Academic; A. I. Goldman, (1994), Readings
in Philosophy and Cognitive Science, Cambridge: MIT Press/Bradford
Books; and [5]; Italian translation published as monograph [7]; Hungarian
translation in A Cognitive Science Reader, Budapest: Osiris Publishing
House. (1997)]
- Smolensky, P. (1987). Connectionist AI, symbolic AI, and the brain.
Artificial Intelligence Review, 1, 95-109. [French translation
with added post scriptum in D. Andler, (Ed.). (1992). Introduction
aux sciences cognitives, Editions Gallimard.]
Others
- Smolensky, P., Fox, B., King, R., Lewis, C. (1988). Computer-aided
reasoned discourse, or, How to argue with a computer. In R. Guindon
(Ed.), Cognitive Science and Its Applications For Human-Computer
Interaction. Hillsdale, NJ: Erlbaum. 109-62.
- Smolensky, P., Bell, B., Fox, B., King, R., & Lewis, C. (1987). Constraint-based
hypertext for argumentation. Proceedings of Hypertext-87. Chapel
Hill, NC. November. 215-245.
- Smolensky, P., Monty, M. L. & Conway, E. (1984). Formalizing task
descriptions for command specification and documentation. Proceedings
of the International Federation of Information Processing Conference
on Human-Computer Interaction. London, England. September. 603-609.
- Greenspan, S. & Smolensky, P. (1984). DESCRIBE: Environments for
Specifying Commands and Retrieving Information By Elaboration. In User
centered system design, Part II, Technical Report No. 8402. Institute
for Cognitive Science, University of California at San Diego. March.
- O'Malley, C., Smolensky, P, Bannon, L., Conway, E., Graham, J., Sokolov,
J., & Monty, M. L. (1983). A proposal for user centered system documentation.
Proceedings of the CHI 1983 Conference on Human Factors in Computing
Systems. Boston, MA. December.
- Freedman, B., Smolensky, P, & Weingarten, D. H. (1982). Monte Carlo
evaluation of the continuum limit of (j^4)_4
and (j^4)_3 field theory. Physics Letters
B, 113, 481-486.
- Smolensky, P. (1981). Lattice Renormalization of j^4
Theory. Doctoral thesis in mathematical physics, Indiana University.
- Bradbury, K., Danziger, S., Smolensky, E., & Smolensky, P. (1979).
Public assistance, female headship and economic well-being. Journal
of Marriage and the Family, 519-535. [Reprinted in G. McDonald &
F. Nye (Eds.), (1979), Family policy, National Council on Family
Relations.]
- Cicchetti, C., Gillen, W., & Smolensky, P. (1977). The Marginal
Cost and Pricing of Electricity: An Applied Approach. Ballinger.
Revised: March 2, 2003
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