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12,050
Formalising trust as a computational concept
, 1994
"... Trust is a judgement of unquestionable utility — as humans we use it every day of our lives. However, trust has suffered from an imperfect understanding, a plethora of definitions, and informal use in the literature and in everyday life. It is common to say “I trust you, ” but what does that mean? T ..."
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Cited by 518 (5 self)
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? This thesis provides a clarification of trust. We present a formalism for trust which provides us with a tool for precise discussion. The formalism is implementable: it can be embedded in an artificial agent, enabling the agent to make trustbased decisions. Its applicability in the domain of Distributed
Fronts propagating with curvature dependent speed: algorithms based on Hamilton–Jacobi formulations
 Journal of Computational Physics
, 1988
"... We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvaturedependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion, w ..."
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Cited by 1183 (64 self)
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in the moving fronts. The algorithms handle topological merging and breaking naturally, work in any number of space dimensions, and do not require that the moving surface be written as a function. The methods can be also used for more general HamiltonJacobitype problems. We demonstrate our algorithms
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory
HOMOGENIZATION AND TWOSCALE CONVERGENCE
, 1992
"... Following an idea of G. Nguetseng, the author defines a notion of "twoscale" convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in L2(f) are proven to be relatively compact with respect to this new type of convergence. A corrector ..."
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Cited by 445 (14 self)
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Following an idea of G. Nguetseng, the author defines a notion of "twoscale" convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in L2(f) are proven to be relatively compact with respect to this new type of convergence. A correctortype theorem (i.e., which permits, in some cases, replacing a sequence by its "twoscale " limit, up to a strongly convergent remainder in L2(12)) is also established. These results are especially useful for the homogenization of partial differential equations with periodically oscillating coefficients. In particular, a new method for proving the convergence of homogenization processes is proposed, which is an alternative to the socalled energy method of Tartar. The power and simplicity of the twoscale convergence method is demonstrated on several examples, including the homogenization of both linear and nonlinear secondorder elliptic equations.
Efficient Implementation of Weighted ENO Schemes
, 1995
"... In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially nonoscillatory) finite difference schemes of Liu, Osher and Chan [9]. It was shown by Liu et al. that WENO schemes constructed from the r th order (in L¹ norm) ENO schemes are (r +1) th order accur ..."
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Cited by 415 (40 self)
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In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially nonoscillatory) finite difference schemes of Liu, Osher and Chan [9]. It was shown by Liu et al. that WENO schemes constructed from the r th order (in L¹ norm) ENO schemes are (r +1) th order
Lax Factorization Algebras
"... It is shown that many weak factorization systems appearing in functorial Quillen model categories, including all those that are cofibrantly generated, come with a rich computational structure, defined by a certain lax algebra with respect to the "squaring monad" on CAT. This structure larg ..."
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Cited by 12 (4 self)
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It is shown that many weak factorization systems appearing in functorial Quillen model categories, including all those that are cofibrantly generated, come with a rich computational structure, defined by a certain lax algebra with respect to the "squaring monad" on CAT. This structure
On Language and Connectionism: Analysis of a Parallel Distributed Processing Model of Language Acquisition
 COGNITION
, 1988
"... Does knowledge of language consist of mentallyrepresented rules? Rumelhart and McClelland have described a connectionist (parallel distributed processing) model of the acquisition of the past tense in English which successfully maps many stems onto their past tense forms, both regular (walk/walked) ..."
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Cited by 404 (12 self)
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Does knowledge of language consist of mentallyrepresented rules? Rumelhart and McClelland have described a connectionist (parallel distributed processing) model of the acquisition of the past tense in English which successfully maps many stems onto their past tense forms, both regular (walk/walked) and irregular (go/went), and which mimics some of the errors and sequences of development of children. Yet the model contains no explicit rules, only a set of neuronstyle units which stand for trigrams of phonetic features of the stem, a set of units which stand for trigrams of phonetic features of the past form, and an array of connections between the two sets of units whose strengths are modified during learning. Rumelhart and McClelland conclude that linguistic rules may be merely convenient approximate fictions and that the real causal processes in language use and acquisition must be characterized as the transfer of activation levels among units and the modification of the weights of their connections. We analyze both the linguistic and the developmental assumptions of the model in detail and discover that (1) it cannot represent certain words, (2) it cannot learn many rules, (3) it can learn rules found in no human language, (4) it cannot explain morphological and phonological regularities, (5) it cannot explain the differences between irregular and regular forms, (6) it fails at its assigned task of mastering the past tense of English, (7) it gives an incorrect explanation for two developmental phenomena: stages of overregularization of irregular forms such as bringed, and the appearance of doublymarked forms such as ated, and (8) it gives accounts of two others (infrequent overregularization of verbs ending in t/d, and the order of acquisition of different irregula...
A perspective on judgment and choice: Mapping bounded rationality
 American psychologist
, 2003
"... Early studies of intuitive judgment and decision making conducted with the late Amos Tversky are reviewed in the context of two related concepts: an analysis of accessibility, the ease with which thoughts come to mind; a distinction between effortless intuition and deliberate reasoning. Intuitive th ..."
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Cited by 393 (0 self)
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for extensional attributes. Variations in the accessibility of rules explain the occasional corrections of intuitive judgments. The study of biases is compatible with a view of intuitive thinking and decision making as generally skilled and successful.
Exponentiability in Categories of Lax Algebras
, 2003
"... For a complete cartesianclosed category V with coproducts, and for any pointed endofunctor T of the category of sets satisfying a suitable BeckChevalleytype condition, it is shown that the category of lax reflexive (T , V)algebras is a quasitopos. This result encompasses many known and new examp ..."
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Cited by 10 (5 self)
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For a complete cartesianclosed category V with coproducts, and for any pointed endofunctor T of the category of sets satisfying a suitable BeckChevalleytype condition, it is shown that the category of lax reflexive (T , V)algebras is a quasitopos. This result encompasses many known and new
Quantified Lax Logic
, 1997
"... Lax Logic is an intuitionistic modal logic which has so far been investigated at the propositional level. It has shown itself to have applications in the formal verification of hardwarea logical modality is used to capture and express the correctness of specifications `up to' behavioural con ..."
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Cited by 2 (1 self)
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constraints. A translation from Quantified Lax Logic to a quantified classical modal logic is presented which enables both model and syntactic embedding theorems to be proved. By investigating the links between these logics, the nature of the single Lax Logic modality is revealed and results of soundness
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