8,854 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
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
Dose-dense paclitaxel/carboplatin as neo-adjuvant chemotherapy followed by radical surgery in locally advanced cervical cancer: a prospective phase II study
No full textPURPOSE:
The role of dose-dense schedules in the neo-adjuvant treatment (NACT) of locally advanced cervical cancer (LACC) has been reported. This phase II study investigated activity of dose-dense paclitaxel/platinum before radical surgery (RS) in LACC patients.
METHODS:
The primary end-point was the rate of optimal pathological response (OPR: pathological complete/microscopic response). NACT (paclitaxel: 80 mg/m2) and carboplatin (AUC 2) were administered for 6 weeks. Overall response rate (ORR) to NACT was assessed by the RECIST criteria. Patients amenable to surgery were triaged to RS. The null hypothesis was that the OPR rate would improve from 30.0 to 45.0% (α error: 0.05, β error: 0.2). The regimen would be considered active if > 25 OPRs were found.
RESULTS:
36 patients were enrolled; 19 patients were stage IIB (52.8%) and 16 (44.4%) patients had pelvic lymph-node involvement at imaging. All patients completed neo-adjuvant chemotherapy; ORR was of 75.0%. RS was performed in 29 (93.5%) patients. Since the OPR was 16.1%, we evaluated the real chances to achieve the number of OPR required by the Simon design and decided to close the study. Grade 3/4 hematological toxicity occurred in 5 patients; surgical morbidity occurred in 14 patients. The 2-year PFS rate was 69.0%.
CONCLUSION:
Dose-dense neo-adjuvant paclitaxel/carboplatin is feasible and safe in LACC patients; however, failure to achieve the primary end-point has to be recognized. Given the heterogeneity of the available studies, robust data from an adequately sized prospective study focused on more homogeneous series are require
Data adjuvant therapy dose schedules
No full textData file of simulated dose schedules that prevent the recurrence of colon cancer by apoptotic adjuvant therapy. Includes numerical data in columns for Interval, Duration, Treatment, and 50-year dose sum, ranked by 50-year dose sum. Supplementary file for article tentatively titled “Prevention of Colon Cancer Recurrence from Minimal Residual Disease: Computer Optimized Dose Schedule of Intermittent Apoptotic Adjuvant Therapy.”No restriction on public acces
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