1,233 research outputs found
Monotonicity of equilibria in nonatomic congestion games
No full textThis 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
No full textWe 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
ON THE AUTOMORPHISMS OF THE NONSPLIT CARTAN MODULAR CURVES OF PRIME LEVEL
No full textWe study the automorphisms of the nonsplit Cartan modular curves Xns(p) of prime level p. We prove that if p ≥ 29 all the automorphisms preserve the cusps. Furthermore, if p ≡ 1 mod 12 and p ≠13 , the automorphism group is generated by the modular involution given by the normalizer of a nonsplit Cartan subgroup of GL2(Fp). We also prove that for every p ≥ 29 the existence of an exceptional rational automorphism would give rise to an exceptional rational point on the modular curve X+ns(p) associated to the normalizer of a nonsplit Cartan subgroup of GL2(Fp)
Automorphisms of Cartan modular curves of prime and composite level
No full textWe 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
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Fantastic Architecture and the Building of Europe in Valerio Evangelisti's Eymerich Fiction
No full textConcomitant with the horizontal expansion of EU territory through physical and political enlargement is a genealogy narrative, which emphasizes the ostensible roots of Europeanness in classical antiquity and Christianity. In the face of this sanitized genealogy, which lies at the heart of the European constitutional project, a range of alternative and more inclusive narratives circulate in contemporary European popular fiction. This paper focuses on a series of fantasy novels by the Italian author Valerio Evangelisti, featuring Inquisitor Eymerich as hero-investigator. In his highly popular novels, Evangelisti seeks to uncover layers of shared historical memory untainted with post-Enlightenment rhetoric.
The central architectural tropes of Evangelisti’s imaginary world are those of a castle and a convent, epitomizing the temporal and sacral power in European history. Each isolated from its outside environment and built on layer upon layer of subterranean chambers and corridors, the castle and the convent conceal a past quite different from the one championed in the official European genealogy. Memories of pagan worship and Islamic or Judaic learning – banished from the official rhetoric – continue to thrive, dark and threatening, in the subterranean strata of Evangelisti’s European edifice. Evangelisti thus provides an incisive critique of the official European story of origin, which threatens to suppress any alternative visions of European history or unorthodox avenues for European identity formation
The Price of Anarchy in Routing Games as a Function of the Demand
No full textThe 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
Modular Curves with many Points over Finite Fields
No full textWe 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
Hermann Kant. Ein bio- bibliografisches Profil
No full textThe proximity to the power apparatus has cast dark shadows on the literary work of Hermann Kant, who is regarded as one of the most read authors of the GDR. Valerio Furneri embeds Kant's life and work in the all-German context of the 20th century and reinterprets his classics such as Die Aula or Der Aufenthalt. The author does not pursue the claim to rehabilitate the GDR, nor to trivialise Kant's role in it. Instead, the attempt is made to look at Kant's entire work from a temporal distance and to re-evaluate it. Through his works, Kant was able to accompany and depict not only the German-German history, but also European history.Die Nähe zum Machtapparat hat dunkle Schatten auf das literarische Werk von Hermann Kant, der als meistgelesener Schriftsteller der DDR gilt, geworfen. Valerio Furneri bettet Kants Leben und Werk in den gesamtdeutschen Kontext des 20. Jahrhunderts ein und interpretiert vor diesem Hintergrund Klassiker wie Die Aula oder Der Aufenthalt neu. Der Autor verfolgt dabei weder den Anspruch, die DDR zu rehabilitieren, noch Kants Rolle darin kleinzureden. Stattdessen wird der Versuch unternommen, Kants Gesamtwerk aus zeitlicher Distanz zu betrachten und neu zu bewerten. Durch seine Werke gelang es Kant nämlich nicht nur die deutsch-deutsche, sondern auch die europäische Geschichte zu begleiten und abzubilden
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