A hierarchical zeolitic imidazole framework (ZIF) combining a micropore with a mesoporous structure is desirable to enhance mass transport and gives rise to novel applications. Here, hierarchically porous graphene/ZIF-8 hybrid aerogel (GZAn) materials were successfully prepared by a two-step reduction strategy and a layer-by-layer assembly method. To avoid a tedious dry step and the use of an energy-consuming freeze-drying technology, a reduced graphene oxide hydrogel with different reduction degrees was chosen as a template to grow ZIF-8 crystals in situ. The parameter of density and elemental analysis was adopted to calculate the amount of ZIF-8 in GZAn materials for different assembly cycles. The distribution of micropores and mesopores of GZAn materials was controlled by changing the loading of ZIFs in GZAn materials. Furthermore, GZA8 materials showed enhanced CO uptake capacity (0.99 mmol g, 298 K, 1 bar) than pure ZIF-s crystals and pure graphene aerogels, showing an excellent synergistic effect of hierarchical pore structures. Meanwhile, with the increase of ZIF-8 loading, the mechanical robustness of GZAn was uplifted obviously. This work provides an efficient method to prepare hierarchically porous ZIFs-based materials with good CO uptake capacity and tunable mechanical robustness.

This project investigates numerical methods for solving fully coupled forward-backward stochastic differential equations (FBSDEs) of McKean-Vlasov type. Having numerical solvers for such mean field FBSDEs is of interest because of the potential application of these equations to optimization problems over a large population, say for instance mean field games (MFG) and optimal mean field control problems. Theory for this kind of problems has met with great success since the early works on mean field games by Lasry and Lions, see [27], and by Huang, Caines, and Malhamé, see [24]. Generally speaking, the purpose is to understand the continuum limit of optimizers or of equilibria (say in Nash sense) as the number of underlying players tends to infinity. When approached from the probabilistic viewpoint, solutions to these control problems (or games) can be described by coupled mean field FBSDEs, meaning that the coefficients depend upon the own marginal laws of the solution. In this note, we detail two methods for solving such FBSDEs which we implement and apply to five benchmark problems. The first method uses a tree structure to represent the pathwise laws of the solution, whereas the second method uses a grid discretization to represent the time marginal laws of the solutions. Both are based on a Picard scheme; importantly, we combine each of them with a generic continuation method that permits to extend the time horizon (or equivalently the coupling strength between the two equations) for which the Picard iteration converges.

The research on driver fatigue detection is of great significance to improve driving safety. This paper proposes a real-time comprehensive driver fatigue detection algorithm based on facial landmarks to improve the detection accuracy, which detects the driver’s fatigue status by using facial video sequences without equipping their bodies with other intelligent devices. A tasks-constrained deep convolutional network is constructed to detect the face region based on 68 key points, which can solve the optimization problem caused by the different convergence speeds of each task. According to the real-time facial video images, the eye feature of the eye aspect ratio (EAR), mouth aspect ratio (MAR) and percentage of eye closure time (PERCLOS) are calculated based on facial landmarks. A comprehensive driver fatigue assessment model is established to assess the fatigue status of drivers through eye/mouth feature selection. After a series of comparative experiments, the results show that this proposed algorithm achieves good performance in both accuracy and speed for driver fatigue detection.

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Abstract. In this paper, we establish a probabilistic representation as well as some integration by parts formulae for the marginal law at a given time maturity of some stochastic volatility model with unbounded drift. Relying on a perturbation technique for Markov semigroups, our formulae are based on a simple Markov chain evolving on a random time grid for which we develop a tailor-made Malliavin calculus. Among other applications, an unbiased Monte Carlo path simulation method stems from our formulas so that it can be used in order to numerically compute with optimal complexity option prices as well as their sensitivities with respect to the initial values or Greeks in finance, namely the Delta and Vega , for a large class of non-smooth European payoff. Numerical results are proposed to illustrate the efficiency of the method.

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