On the Impact of Fair Best Response Dynamics

In this work we completely characterize how the frequency with which each player participates in the game dynamics affects the possibility of reaching efficient states, i.e., states with an approximation ratio within a constant factor from the price of anarchy, within a polynomially bounded number of best responses. We focus on the well known class of congestion games and we show that, if each player is allowed to play at least once and at most $\beta$ times any $T$ best responses, states with approximation ratio $O(\beta)$ times the price of anarchy are reached after $T \lceil \log \log n \rceil$ best responses, and that such a bound is essentially tight also after exponentially many ones. One important consequence of our result is that the fairness among players is a necessary and sufficient condition for guaranteeing a fast convergence to efficient states. This answers the important question of the maximum order of $\beta$ needed to fast obtain efficient states, left open by [9,10] and [3], in which fast convergence for constant $\beta$ and very slow convergence for $\beta=O(n)$ have been shown, respectively. Finally, we show that the structure of the game implicitly affects its performances. In particular, we show that in the symmetric setting, in which all players share the same set of strategies, the game always converges to an efficient state after a polynomial number of best responses, regardless of the frequency each player moves with

Time decay of scaling invariant Schroedinger equations on the plane

We prove the sharp L^1-L^{\infty} time-decay estimate for the 2D-Schroedinger equation with a general family of scaling critical electromagnetic potentials.Comment: 26 page

Sublingual sufentanil, a new opportunity for the improvement of postoperative pain management in Italy

Despite the availability of national and international guidelines, adequate postoperative pain (POP) management is still a challenge in Italy. One of the potential reasons for the high incidence of surgical patients complaining moderate to severe pain is the difficult application of the currently recommended analgesic techniques in clinical practice. In particular, morphine, the most commonly used systemic opioid in the POP treatment, has some unfavorable pharmacodynamic and pharmacokinetic characteristics for POP management, suggesting a potential relevant improvement by using different opioids. Many of sufentanil properties make it particularly suitable for POP control: a high affinity for the µ opioid receptor, the highest therapeutic index compared to any other opioid used in clinical practice and the absence of clinically relevant active metabolites. The elevated potency, together with the high lipophilicity of sufentanil, allow the preparation of a nanotablet, 3 mm of diameter and 0.75 mm of thickness, containing 15 µg of active drug. The sublingual route allows a longer time of drug plasmatic permanence in comparison to IV route, overcoming the need for continuous dosing. The patient-controlled system, considered in the present review, is preprogrammed to deliver one sublingual tablet of sufentanil with a 20-minute lockout period with a radiofrequency identification thumb tag allowing only the patient to activate the on demand button. Phase II and III studies have assessed the efficacy of this system in POP management, showing that it was considered more satisfactory than the IV PCA morphine system by both patients and nurses. The introduction of this simple and innovative system of patient-controlled analgesic administration could represent an opportunity for Italy to update the current practice in POP management

Summary of DSN (Deep Space Network) reimbursable launch support

The Deep Space Network is providing ground support to space agencies of foreign governments as well as to NASA and other agencies of the Federal government which are involved in space activities. DSN funding for support of missions other than NASA are on either a cooperative or a reimbursable basis. Cooperative funding and support are accomplished in the same manner as NASA sponsored missions. Reimbursable launch funding and support methods are described

Time decay of scaling critical electromagnetic Schr\"odinger flows

We obtain a representation formula for solutions to Schr\"odinger equations with a class of homogeneous, scaling-critical electromagnetic potentials. As a consequence, we prove the sharp $L^{1}\to L^{\infty}$ time decay estimate for the 3D-inverse square and the 2D-Aharonov-Bohm potentials.Comment: 32 pages, 1 figur

ICE Second Halley radial: TDA mission support and DSN operations

The article documents the operations encompassing the International Cometary Explorer (ICE) second Halley radial experiment centered around March 28, 1986. The support was provided by the Deep Space Network (DSN) 64-meter subnetwork. Near continuous support was provided the last two weeks of March and the first two weeks of April to insure the collection of adequate background data for the Halley radial experiment. During the last week of March, plasma wave measurements indicate that ICE was within the Halley heavy ion pick-up region