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Search for integrable two-component versions of the lattice equations in the ABS-list
Full text linkWe search and classify two-component versions of the quad equations in the
ABS list, under certain assumptions. The independent variables will be called
and in addition to multilinearity and irreducibility the equation pair is
required to have the following specific properties: (1) The two equations
forming the pair are related by exchange. (2) When
both equations reduce to one of the equations in the ABS list. (3) Evolution in
any corner direction is by a multilinear equation pair. One straightforward way
to construct such two-component pairs is by taking some particular equation in
the ABS list (in terms of ), using replacement for
some particular shifts, after which the other equation of the pair is obtained
by property (1). This way we can get 8 pairs for each starting equation. One of
our main results is that due to condition (3) this is in fact complete for H1,
H3, Q1, Q3. (For H2 we have a further case, Q2, Q4 we did not check.) As for
the CAC integrability test, for each choice of the bottom equations we could in
principle have possible side-equations. However, we find that only
equations constructed with an even number of replacements
are possible, and for each such equation there are two sets of "side" equation
pairs that produce (the same) genuine B\"acklund transformation and Lax pair.Comment: 14 pages, final versio
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Searching for integrable lattice maps using factorization
No full textTo appear in Journal of Physics A. Some changes in referencesInternational audienceWe analyze the factorization process for lattice maps, searching for integrable cases. The maps were assumed to be at most quadratic in the dependent variables, and we required minimal factorization (one linear factor) after 2 steps of iteration. The results were then classified using algebraic entropy. Some new models with polynomial growth (strongly associated with integrability) were found. One of them is a nonsymmetric generalization of the homogeneous quadratic maps associated with KdV (modified and Schwarzian), for this new model we have also verified the ``consistency around a cube''
Degree growth of lattice equations defined on a 3x3 stencil
Full text linkWe study complexity in terms of degree growth of one-component lattice equations defined on a stencil. The equations include two in Hirota bilinear form and the Boussinesq equations of regular, modified and Schwarzian type. Initial values are given on a staircase or on a corner configuration and depend linearly or rationally on a special variable, for example , in which case we count the degree in of the iterates. Known integrable cases have linear growth if only one initial values contains , and quadratic growth if all initial values contain . Even a small deformation of an integrable equation changes the degree growth from polynomial to exponential, because the deformation will change factorization properties and thereby prevent cancellations.19 pages, to appear in Open Communications in Nonlinear Mathematical Physics , Special Issue in Memory of Decio Lev
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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