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and Mathematical Representations
, 2001
"... SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peerreviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for pap ..."
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SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peerreviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty, papers must be based on work done at SFI, inspired by an invited visit to or collaboration at SFI, or funded by an SFI grant. ©NOTICE: This working paper is included by permission of the contributing author(s) as a means to ensure timely distribution of the scholarly and technical work on a noncommercial basis. Copyright and all rights therein are maintained by the author(s). It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may be reposted only with the explicit permission of the copyright holder. www.santafe.edu
Representation Theory of Artin Algebras
 Studies in Advanced Mathematics
, 1994
"... The representation theory of artin algebras, as we understand it today, is a relatively new area of mathematics, as most of the main developments have occurred ..."
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Cited by 645 (10 self)
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The representation theory of artin algebras, as we understand it today, is a relatively new area of mathematics, as most of the main developments have occurred
Mathematical representations in musculoskeletal physiology and cell motility
 Thesis (Ph.D.)–The University of Iowa
, 2012
"... Mathematical representations in musculoskeletal physiology and cell motility ..."
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Cited by 1 (1 self)
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Mathematical representations in musculoskeletal physiology and cell motility
Electromagnetic concepts in mathematical representation of physics
 Journal of Science Education and Technology
, 2001
"... 1 Our paper deals with the use of mathematics when studying the physics of electromagnetism. We have concentrated on common electromagnetic concepts (magnetic field and flux) and their associated mathematical representation and arithmetical tools. Our studies showed that most students do not unders ..."
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Cited by 3 (0 self)
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1 Our paper deals with the use of mathematics when studying the physics of electromagnetism. We have concentrated on common electromagnetic concepts (magnetic field and flux) and their associated mathematical representation and arithmetical tools. Our studies showed that most students do
Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations
 Biophys. J
, 2001
"... ABSTRACT Transcriptional regulation is an inherently noisy process. The origins of this stochastic behavior can be traced to the random transitions among the discrete chemical states of operators that control the transcription rate and to finite number fluctuations in the biochemical reactions for t ..."
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Cited by 130 (1 self)
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ABSTRACT Transcriptional regulation is an inherently noisy process. The origins of this stochastic behavior can be traced to the random transitions among the discrete chemical states of operators that control the transcription rate and to finite number fluctuations in the biochemical reactions for the synthesis and degradation of transcripts. We develop stochastic models to which these random reactions are intrinsic and a series of simpler models derived explicitly from the first as approximations in different parameter regimes. This innate stochasticity can have both a quantitative and qualitative impact on the behavior of generegulatory networks. We introduce a natural generalization of deterministic bifurcations for classification of stochastic systems and show that simple noisy genetic switches have rich bifurcation structures; among them, bifurcations driven solely by changing the rate of operator fluctuations even as the underlying deterministic system remains unchanged. We find stochastic bistability where the deterministic equations predict monostability and viceversa. We derive and solve equations for the mean waiting times for spontaneous transitions between quasistable states in these switches.
A solution to Plato’s problem: The latent semantic analysis theory of acquisition, induction, and representation of knowledge
 PSYCHOLOGICAL REVIEW
, 1997
"... How do people know as much as they do with as little information as they get? The problem takes many forms; learning vocabulary from text is an especially dramatic and convenient case for research. A new general theory of acquired similarity and knowledge representation, latent semantic analysis (LS ..."
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Cited by 1816 (10 self)
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How do people know as much as they do with as little information as they get? The problem takes many forms; learning vocabulary from text is an especially dramatic and convenient case for research. A new general theory of acquired similarity and knowledge representation, latent semantic analysis
The DLV System for Knowledge Representation and Reasoning
 ACM Transactions on Computational Logic
, 2002
"... Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely believ ..."
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Cited by 456 (102 self)
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Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely
VERBAL PROTOCOLS, GAZES AND SKETCHES ON EXTERNAL MATHEMATICAL REPRESENTATIONS
"... and other research outputs ’There’s more than meets the eye’: analysing verbal protocols, gazes and sketches on external mathematical representations ..."
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and other research outputs ’There’s more than meets the eye’: analysing verbal protocols, gazes and sketches on external mathematical representations
Mathematical representations: Graphs, curves and formulas
 NONVISUAL HUMANCOMPUTER INTERACTIONS: PROSPECTS FOR THE VISUALLY HANDICAPPED. PARIS, JOHN LIBBEY EUROTEXT. EDITION
, 1993
"... Mathematics is communicated in visual forms, such as algebra and diagrams. This means that blind people are greatly disadvantaged with respect to education and employment in mathematics, science and technology. A number of ideas are presented regarding the representation of mathematics in nonvisual ..."
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Cited by 14 (5 self)
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Mathematics is communicated in visual forms, such as algebra and diagrams. This means that blind people are greatly disadvantaged with respect to education and employment in mathematics, science and technology. A number of ideas are presented regarding the representation of mathematics in non
Toward Principles for the Design of Ontologies Used for Knowledge Sharing
 IN FORMAL ONTOLOGY IN CONCEPTUAL ANALYSIS AND KNOWLEDGE REPRESENTATION, KLUWER ACADEMIC PUBLISHERS, IN PRESS. SUBSTANTIAL REVISION OF PAPER PRESENTED AT THE INTERNATIONAL WORKSHOP ON FORMAL ONTOLOGY
, 1993
"... Recent work in Artificial Intelligence is exploring the use of formal ontologies as a way of specifying contentspecific agreements for the sharing and reuse of knowledge among software entities. We take an engineering perspective on the development of such ontologies. Formal ontologies are viewed a ..."
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Cited by 2003 (3 self)
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are applied in case studies from the design of ontologies for engineering mathematics and bibliographic data. Selected design decisions are discussed, and alternative representation choices and evaluated against the design criteria.
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