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

Long memory and crude oil’s price predictability

This paper discusses the usefulness of the long term memory property in price prediction. In particular, the Hurst’s exponents related to a wide set of portfolios generated by three crude oils are estimated by using the detrended fluctuation analysis. To this aim, the daily empirical data on West Texas Intermediate, Brent crude oil and Dubai crude oil for a period of more than 10 years have been considered. It is shown that specific combinations are associated to persistence/antipersistence long-run behaviors, and this highlights the presence of statistical arbitrage opportunities. Such an outcome shows that long term memory can effectively serve as price predictor. This is a post-peer-review, pre-copyedit version of an article published in Annals of Operations Research. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10479-019-03376-y

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

When pressure does not mean volume? Body mass index may account for the dissociation

Low tidal volume (VT 6 ml/predicted body weight) pressure limited (plateau pressure <30 cmH2O) protective ventilation as proposed by the ARDS Network was associated with an improvement in mortality and is considered the gold standard for acute respiratory distress syndrome (ARDS) ventilation strategies. Limiting plateau pressure minimizes ventilator-induced lung injury by reducing the trans-pulmonary pressure, which is the real alveolar distending pressure. However, in the presence of chest wall elastance impairment, as observed in obese patients, plateau pressure underestimates the trans-pulmonary pressure and derecrutiment at low distending pressure could occur. Moreover, low tidal volume to keep plateau pressure <30 cmH2O could be associated with large differences compared to measured total lung capacity. Quantitative bedside techniques that are able to measure lung volumes together with trans-pulmonary pressure could expand our chances to tailor mechanical ventilation in ARDS patients

Feature Selection Based on a Genetic Algorithm for Optimizing Weaning Success

Finding the right time for weaning from ventilator is a difficult clinical decision. Several systems based on machine or deep learning are reported in literature. However, the results of these applications are not completely satisfactory and may be improved. An important aspect is represented by the features used as input of these systems. In this paper we present the results of the application of genetic algorithms to perform feature selection on a dataset containing 13688 patients under mechanical ventilation characterizing by 58 variables, extracted from the MIMIC III database. The results show that all features are important, but four of them are essential: 'Sedation_days', 'Mean_Airway_Pressure', 'PaO2', and 'Chloride'. This is only the initial step to obtain a tool to be added to the other clinical indices for minimize the risk of extubation failure

Multicast Network Design Game on a Ring

In this paper we study quality measures of different solution concepts for the multicast network design game on a ring topology. We recall from the literature a lower bound of 4/3 and prove a matching upper bound for the price of stability, which is the ratio of the social costs of a best Nash equilibrium and of a general optimum. Therefore, we answer an open question posed by Fanelli et al. in [12]. We prove an upper bound of 2 for the ratio of the costs of a potential optimizer and of an optimum, provide a construction of a lower bound, and give a computer-assisted argument that it reaches $2$ for any precision. We then turn our attention to players arriving one by one and playing myopically their best response. We provide matching lower and upper bounds of 2 for the myopic sequential price of anarchy (achieved for a worst-case order of the arrival of the players). We then initiate the study of myopic sequential price of stability and for the multicast game on the ring we construct a lower bound of 4/3, and provide an upper bound of 26/19. To the end, we conjecture and argue that the right answer is 4/3.Comment: 12 pages, 4 figure