Lyrical drama and the “turbid mountebanks”: Styles of dialogue in romantic and renaissance tragedy

Critics have condemned English Romantic tragedies as a series of poor imitations of Renaissance tragedy. This paper tests such “literary-critical” questions through statistical comparisons of ten plays from each group. The measures chosen give evidence of a strong and consistent difference between the groups, going beyond historical changes in the language. The Romantic tragedies are more expository; the Renaissance ones include more commonplace interactions between characters. The later plays do not show the marked variations in function-word frequencies of their predecessors. Of the Renaissance plays, Shakespeare's show the closest affinity to the Romantic tragedies, and the most telling contrasts.     

And then there were none: Winnowing the Shakespeare claimants

The Shakespeare Clinic has developed 51 computer tests of Shakespeare play authorship and 14 of poem authorship, and applied them to 37 claimed true Shakespeares, to 27 plays of the Shakespeare Apocrypha, and to several poems of unknown or disputed authorship. No claimant, and none of the apocryphal plays or poems, matched Shakespeare. Two plays and one poem from the Shakespeare Canon,Titus Andronicus, Henry VI, Part 3, and A Lover's Complaint, do not match the others.Ward Elliott is the Burnet C. Wohlford Professor of American Political Institutions at Claremont McKenna College. He is interested in, and has published in, almost everything,including politics, pollution, transportation, smog and Shakespeare.Robert J. Valenza is W.M. Keck Professor of Mathematics and Computer Science at Claremont McKenna College. He has written research articles in mathematics and metaphysics, as well as stylometrics. He is author ofLinear Algebra: An Introduction to Abstract Mathematics (Springer-Verlag, 1993).     

Defaults as restrictions on classical Hilbert-style proofs

Since the earliest formalisation of default logic by Reiter many contributions to this appealing approach to nonmonotonic reasoning have been given. The different formalisations are here presented in a general framework that gathers the basic notions, concepts and constructions underlying default logic. Our view is to interpret defaults as special rules that impose a restriction on the juxtaposition of monotonic Hubert-style proofs of a given logicL. We propose to describe default logic as a logic where the juxtaposition of default proofs is subordinate to a restriction condition . Hence a default logic is a pair (L, ) where properties of the logic , like compactness, can be interpreted through the restriction condition . Different default systems are then given a common characterization through a specific condition on the logicL. We also prove cumulativity for any default logic (L, ) by slightly modifying the notion of default proof. We extend, in fact, the language ofL in a way close to that followed by Brewka in the formulation of his cumulative default system. Finally we show the existence of infinitely many intermediary default logics, depending on and called linear logics, which lie between Reiter's and ukaszewicz' versions of default logic.Work carried out in the framework of the agreement between Italian PT Administration and FUBLaforia, Université Paris VI Pierre et Marie Curie, 4 Place Jussieu,Tour 46, 75252 Paris, France     

An average complexity measure that yields tight hierarchies

A new definition is given for the average growth of a functionf: ^* N with respect to a probability measure on ^* This allows us to define meaningful average distributional complexity classes for arbitrary time bounds (previously, one could not guarantee arbitrary good precision). It is shown that, basically, only the ranking of the inputs by decreasing probabilities is of importance.To compare the average and worst case complexity of problems, we study average complexity classes defined by a time bound and a bound on the complexity of possible distributions. Here, the complexity is measured by the time to compute the rank functions of the distributions. We obtain tight and optimal separation results between these average classes. Also, the worst case classes can be embedded into this hierarchy. They are shown to be identical to average classes with respect to distributions of exponential complexity.     

The plane with parallel coordinates

By means ofParallel Coordinates planar graphs of multivariate relations are obtained. Certain properties of the relationship correspond tothe geometrical properties of its graph. On the plane a point line duality with several interesting properties is induced. A new duality betweenbounded and unbounded convex sets and hstars (a generalization of hyperbolas) and between Convex Unions and Intersections is found. This motivates some efficient Convexity algorithms and other results inComputational Geometry. There is also a suprising cusp inflection point duality. The narrative ends with a preview of the corresponding results inR ^N .     

Constructing sets of functions which have a givenF-cardinality

The termF-cardinality of (=F-card()) is introduced whereF: ^{n n} is a partial function and is a set of partial functionsf: ^{n n} . TheF-cardinality yields a lower bound for the worst-case complexity of computingF if only functionsf can be evaluated by the underlying abstract automaton without conditional jumps. This complexity bound isindependent from the oracles available for the abstract machine. Thus it is shown that any automaton which can only apply the four basic arithmetic operations needs (n logn) worst-case time to sortn numbers; this result is even true if conditional jumps witharbitrary conditions are possible. The main result of this paper is the following: Given a total functionF: ^{n n} and a natural numberk, it is almost always possible to construct a set such that itsF-cardinality has the valuek; in addition, can be required to be closed under composition of functionsf,g . Moreover, ifF is continuous, then consists of continuous functions.     

Unitary immersions of nonlinear systems

In this paper, we define what we call a unitary immersion of a nonlinear system. We observe that, for classical Hamiltonian systems, this notion contains, in some sense, the concept of quantization. We restrict our attention to degree-zero unitary immersions, where all observation functions must be represented by operators of the type multiplication by a function. We show that the problem of classifying such degree-zero unitary immersions of a given nonlinear system is not obvious. In some cases, we solve this problem.Chargé de Recherche au CNRS.Maître de Conférences.     

Computer enhanced assessment of case-notes in studies of psychopathology: The example of an autistic subject

Case report notes on encounters and exchanges between a clinician and a patient are a rich and irreplaceable source of information in studies of psychopathology. The analysis and exploitation of these notes may be considerably enhanced by transcribing the original notes to computer text files, and subsequently submitting these files to computerized reading. This makes it possible to take account both of qualitative and quantitative features of the behaviour and events described in the notes. Notes taken during encounters with an autistic subject were analyzed in this way. The subject's verbal and gestural repertoires were identified, together with their relative frequencies, their principal associations, and their trends over successive encounters for the items described. The method also made it possible to specify the way in which the Observer was involved in encounters, and his role in them. Major conclusions were that the autistic subject distinctly avoided triadic situations, preferentially pronounced words and phonemes similar to those of his own name, and did not distinguish between the representations he had of persons, objects, places, gestures and words. He also failed to distinguish between the representation he had of himself and of his own name.J.-M. Vidal (Docteur d'Etat, 1976) is Chargé de Recherche CNRS. He studied the behavioral process of attachment in animals before studying discontinuities of mind between animals and humans, and psychopathological processes of non-attachment in autistic subjects. He has published, Motivation et attachement, inEncyclopédie de la Pléiade, Paris: Gallimard, 1987, and Evolution des psychismes et évolution des organismes, inDarwinisme et Société, Paris: Presses Universitaires de France, 1992. R. Quris is Ingénieur de Recherche CNRS. He specializes in the application of linear algebraic models in multivariate analysis which he originally applied to behavioral data from animals. More recently, he extended these applications, with his ANATEXT program, to the analysis of lexical data drawn from clinical dialogues. He is also the author of other multivariate analysis programs:Calmat Matrix Computation Tool, v. 1.4 (1993), Exeter Software, 100 North Country Road, Setauket, NY 11733, andGTABM, gestionnaire de tableaux multiples, v. 2.0 (1994), CNRS 74E, rue de Paris, 3069 Rennes, France.     

On the number of Eulerian orientations of a graph

An Eulerian orientation of an undirected Eulerian graph is an orientation of the edges of the graph such that for every vertex the in-degree is equal to the out-degree. Eulerian orientations are natural flow-like structures, and Welsh has pointed out that computing their number corresponds to evaluating the Tutte polynomial at the point (0, –2) [JVW], [Wl], and is further equivalent to evaluating ice-type partition functions in statistical physics [W2]. In this paper we resolve the complexity of counting the number of Eulerian orientations of an arbitrary Eulerian graph.We give an efficient randomized approximation algorithm for counting Eulerian orientations of any Eulerian graph. Our algorithm is based on a reduction to counting perfect matchings for a class of graphs for which the methods of Broder [B], Jerrum and Sinclair [JS1], and others [DL] [DS] apply. A crucial step of the reduction is the Monotonicity Lemma (Lemma 3.1) which is of independent combinatorial interest. Roughly speaking, the Monotonicity Lemma establishes the intuitive fact that increasing the number of constraints applied on a flow problem cannot increase the number of solutions. The proof of the lemma involves a new decomposition technique which decouples problematically overlapping structures (a recurrent obstacle in handling large combinatorial populations) and allows detailed enumeration arguments. As a by-product, we exhibit a class of graphs for which perfect and near-perfect matchings are polynomially related, and hence the permanent can be approximated, for reasons other than short augmenting paths (previously the only known approach).We also give the complementary hardness result, namely, that counting exactly Eulerian orientations is #P-complete. Finally, we provide some connections with counting Euler tours.