1,720,962 research outputs found
Monotonicity of equilibria in nonatomic congestion games
Get PDFThis paper studies the monotonicity of equilibrium costs and equilibrium loads in nonatomic congestion games, in response to variations of the demands. The main goal is to identify conditions under which a paradoxical non-monotone behavior can be excluded. In contrast with routing games with a single commodity, where the network topology is the sole determinant factor for monotonicity, for general congestion games with multiple commodities the structure of the strategy sets plays a crucial role.
We frame our study in the general setting of congestion games, with a special focus on singleton congestion games, for which we establish the monotonicity of equilibrium loads with respect to every demand. We then provide conditions for comonotonicity of the equilibrium loads, i.e.,we investigate when they jointly increase or decrease after variations of the demands. We finally extend our study from singleton congestion games to the larger class of constrained series-parallel congestion games, whose structure is reminiscent of the concept of a series-parallel network
Phase Transitions of the Price-of-Anarchy Function in Multi-Commodity Routing Games
Get PDFWe consider the behavior of the price of anarchy and equilibrium flows in
nonatomic multi-commodity routing games as a function of the traffic demand. We
analyze their smoothness with a special attention to specific values of the
demand at which the support of the Wardrop equilibrium exhibits a phase
transition with an abrupt change in the set of optimal routes. Typically, when
such a phase transition occurs, the price of anarchy function has a breakpoint,
\ie is not differentiable. We prove that, if the demand varies proportionally
across all commodities, then, at a breakpoint, the largest left or right
derivatives of the price of anarchy and of the social cost at equilibrium, are
associated with the smaller equilibrium support. This proves -- under the
assumption of proportional demand -- a conjecture of O'Hare et al. (2016), who
observed this behavior in simulations. We also provide counterexamples showing
that this monotonicity of the one-sided derivatives may fail when the demand
does not vary proportionally, even if it moves along a straight line not
passing through the origin
Modular Curves with many Points over Finite Fields
Get PDFWe describe an algorithm to compute the number of points over finite fields
on a broad class of modular curves: we consider quotients for a
subgroup of \GL_2(\mathbb Z/n\mathbb Z) such that for each prime dividing
, the subgroup at is either a Borel subroup, a Cartan subgroup, or
the normalizer of a Cartan subgroup of \GL_2(\mathbb Z/p^e\mathbb Z), and for
any subgroup of the Atkin-Lehner involutions of . We applied our
algorithm to more than ten thousands curves of genus up to 50, finding more
than one hundred record-breaking curves, namely curves X/\FF_q with genus
that improve the previously known lower bound for the maximum number of points
over \FF_q of a curve with genus . As a key technical tool for our
computations, we prove the generalization of Chen's isogeny to all the Cartan
modular curves of composite level
The Price of Anarchy in Routing Games as a Function of the Demand
Get PDFThe price of anarchy has become a standard measure of the efficiency of
equilibria in games. Most of the literature in this area has focused on
establishing worst-case bounds for specific classes of games, such as routing
games or more general congestion games. Recently, the price of anarchy in
routing games has been studied as a function of the traffic demand, providing
asymptotic results in light and heavy traffic. The aim of this paper is to
study the price of anarchy in nonatomic routing games in the intermediate
region of the demand. To achieve this goal, we begin by establishing some
smoothness properties of Wardrop equilibria and social optima for general
smooth costs. In the case of affine costs we show that the equilibrium is
piecewise linear, with break points at the demand levels at which the set of
active paths changes. We prove that the number of such break points is finite,
although it can be exponential in the size of the network. Exploiting a scaling
law between the equilibrium and the social optimum, we derive a similar
behavior for the optimal flows. We then prove that in any interval between
break points the price of anarchy is smooth and it is either monotone
(decreasing or increasing) over the full interval, or it decreases up to a
certain minimum point in the interior of the interval and increases afterwards.
We deduce that for affine costs the maximum of the price of anarchy can only
occur at the break points. For general costs we provide counterexamples showing
that the set of break points is not always finite.Comment: 22 pages, 7 figure
Automorphisms of Cartan modular curves of prime and composite level
Get PDFWe study the automorphisms of modular curves associated to Cartan subgroups
of and certain subgroups of their
normalizers. We prove that if is large enough, all the automorphisms are
induced by the ramified covering of the complex upper half-plane. We get new
results for non-split curves of prime level : the curve
has no non-trivial automorphisms, whereas the curve
has exactly one non-trivial automorphism. Moreover, as an
immediate consequence of our results we compute the automorphism group of
, where is the group generated by the Atkin-Lehner
involutions of and is a large enough square.Comment: 36 pages, 4 tables. Some proofs rely on MAGMA scripts available at
https://github.com/guidoshore/automorphisms_of_Cartan_modular_curve
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Variations on the Author
Get PDF“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
Get PDFWe 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
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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