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In the past ** Jean-Claude Falmagne** has collaborated on articles with

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AbstractAny semiorder on a finite set can be reached from any other semiorder on the same set by elementary steps consisting either in the addition or in the removal of a single ordered pair, in such a way that only semiorders are generated at every step, and also that the number of steps equals the distance between the two semiorders. Similar results are also established for other families of relations (partial orders, biorders, interval orders). These combinatorial results are used in another paper to develop a stochastic theory describing the emergence and the evolution of preference relations (Falmagne and Doignon, [7]).

AbstractThe highpoints of mathematical psychology between the first issue of the Journal of Mathematical Psychology in 1964 and the present are outlined, with an attempt to highlight its achievements, to understand its failures and to anticipate—and possibly influence—its fate.

AbstractThis paper presents a stochastic process describing the progress of subjects (for example, students learning a particular field) over a period of time. Typical data involve a fixed sample of subjects tested repeatedly. At the core of the model is a knowledge structure, that is, a possibly large collection Q of items, together with a family of its subsets representing the possible knowledge states. The basic prediction concerns the joint probabilities P(Rt1 = R1 , …, Rta = Rn ) of observing sets of correct responses R1, …, Rn at times t1 < · · · < tn (Thus, Rt1 , …, Rtn are jointly distributed random variables taking their values in 2Q, for any choice of the times t1 < · · · <.) The prediction is obtained by analyzing the possible learning paths of the subject through the knowledge structure, mapping out the visits of possible knowledge states at the times of the tests, and integrating over the possible learning rates of the subjects. The learning rate of the subjects, and the times required to master the items along a learning path, are assumed to be distributed gamma. These results elaborate, as a stochastic process, a model proposed earlier by the author.

AbstractFalmagne recently introduced the concept of a medium, a combinatorial object encompassing hyperplane arrangements, topological orderings, acyclic orientations, and many other familiar structures. We find efficient solutions for several algorithmic problems on media: finding short reset sequences, shortest paths, testing whether a medium has a closed orientation, and listing the states of a medium given a black-box description.

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