•A novel boosting-based algorithm is proposed for numerically solving nonlinear high-dimensional backward stochastic differential equations (BSDEs) and PDEs.•A rigorous analysis of the convergence ...and time complexity is provided.•Several numerical examples with very high space dimensions are provided to demonstrate the accuracy and performance.
In this work we propose new algorithms for solving high-dimensional backward stochastic differential equations (BSDEs). Based on the general theta-discretization for the time-integrands, we show how to efficiently use eXtreme Gradient Boosting (XGBoost) regression to approximate the resulting conditional expectations in a quite high dimension. A rigorous analysis of the convergence and time complexity is provided. Numerical results illustrate the efficiency and accuracy of our proposed algorithms for solving very high-dimensional (up to 10,000 dimensions) nonlinear BSDEs. Notably, our new algorithms works also quite well on the problems with highly complex structure in high dimension, which cannot be tackled with most of the state-of-art numerical methods.
An enantioselective C−H addition to a C=C bond represents the most atom‐efficient route for the construction of chiral carbon–carbon skeletons, a central research topic in organic synthesis. We ...herein report the enantioselective yttrium‐catalyzed C(sp3)−H bond addition of 2‐methyl azaarenes, such as 2‐methyl pyridines, to various substituted cyclopropenes and norbornenes. This process efficiently afforded a new family of chiral pyridylmethyl‐functionalized cyclopropane and norbornane derivatives in high yields and high enantioselectivities (up to 97 % ee).
Enantioselective C(sp3)−H bond additions of 2‐methyl azaarenes, such as 2‐methylpyridines, to substituted cyclopropenes and norbornenes have been achieved by using a chiral half‐sandwich yttrium catalyst. This process afforded a series of chiral pyridylmethyl‐functionalized cyclopropane and norbornane derivatives in good yields, high enantioselectivity, and 100 % atom efficiency.
It is difficult to track the posture of players in the course, mainly because of the changing environment and players. In this paper, the improved neural network is used to extract the trajectory ...characteristics of the athletes in the football player’s game video, and the network is trained on a large number of data objects containing similarity objects, which improves the ability of the algorithm to distinguish the athlete’s trajectory. A scheme of soccer attitude tracking based on twin neural network. The experimental results show that the algorithm has a good effect in the field of football and the accuracy is over 90% and the Siamese neural network is better than a traditional convolutional neural network.
The catalytic asymmetric construction of silicon‐stereogenic silanes is of great interest and significance, but has met with only limited success to date. We herein report the enantioselective ...hydrosilylation of alkenes with dihydrosilanes by a chiral half‐sandwich scandium catalyst, which constitutes an efficient and general route for the synthesis of a wide range of enantioenriched silicon‐stereogenic silanes from easily accessible starting materials. This reaction features a broad substrate scope, high yields, and high enantioselectivity. Some of the chiral tertiary silane products were also converted into valuable derivatives, such as chiral silanol, quaternary silane, and benzosilole compounds.
A chiral half‐sandwich scandium catalyst enables the highly enantioselective hydrosilylation of alkenes with dihydrosilanes. This process constitutes an efficient and general route for the synthesis of a wide range of enantioenriched silicon‐stereogenic silanes from easily accessible starting materials.
Robust fuzzy model predictive control of discrete nonlinear systems is investigated in this paper. A recently developed Takagi-Sugeno (T-S) fuzzy approach which uses nonlinear local models is adopted ...to approximate the nonlinear systems. A critical issue that restricts the practical application of classical model predictive control is the online computational cost. For model predictive control of T-S fuzzy systems, the online computational burden is even worse. Especially for complex systems with severe nonlinearities, parametric uncertainties, and disturbances, existing model predictive control of T-S fuzzy systems usually leads to a very conservative solution or even no solution in some occasions. However, more relaxed results can be achieved by the proposed fuzzy model predictive control approach which adopts T-S systems with nonlinear local models. Another advantage is that online computational cost of the optimization problem through solving matrix inequalities can be significantly reduced at the same time. Simulations on a numerical example and a two-tank system are presented to verify the effectiveness and advantages of the proposed method. Comparisons among several T-S fuzzy approaches are illustrated and show that the best settling time is achieved via the proposed method.
The search for efficient and selective routes for the synthesis of chiral aminocyclopropane derivatives is of great interest and importance as these structures are important components of ...biologically active natural products and pharmaceuticals. We herein report the enantioselective intermolecular hydroamination of substituted cyclopropenes with various amines catalyzed by chiral half‐sandwich rare‐earth‐metal complexes. This method constitutes a 100 % atom‐efficient route for the synthesis of a variety of chiral α‐aminocyclopropane derivatives in high yields (up to 96 %) and excellent stereoselectivity (up to >20:1 d.r. and 99 % ee) under mild reaction conditions (25 °C).
A rare reaction: The enantioselective intermolecular hydroamination of cyclopropenes with amines was achieved by using chiral half‐sandwich rare‐earth‐metal catalysts. A range of chiral aminocyclopropane derivatives were thus obtained in high yields and with excellent stereoselectivity under mild conditions.
Transient electronics, arising electronic devices with dissolvable or degradable features on demand, is still at an early stage of development due to the limited choices of materials and strategies. ...Herein, a facile fabrication method for transient circuits by the combination of room‐temperature liquid metals (RTLMs) as the electronic circuit and water‐soluble poly(vinyl alcohol) (PVA) as the packaging material is reported. The as‐made transient circuits exhibit remarkable durability and stable electric performance upon bending and twisting, while possessing short transience times, owing to the excellent solubility of PVA substrates and the intrinsic flexibility of RTLM patterns. Moreover, the RTLM‐based transient circuit shows an extremely high recycling efficiency, up to 96% of the employed RTLM can be recovered. As such, the economic and environmental viability of transient electronics increases substantially. To validate this concept, the surface patterning of RTLMs with complicated shapes is demonstrated, and a transient antenna is subsequently applied for passive near‐field communication tag and a transient capacitive touch sensor. The application of the RTLM‐based transient circuit for sequentially turning off an array of light‐emitting‐diode lamps is also demonstrated. The present RTLM‐based PVA‐encapsulated circuits substantially expand the scope of transient electronics toward flexible and recyclable transient systems.
Flexible and recyclable transient circuits are fabricated by employing room‐temperature liquid metals as the electronic circuit and water‐soluble poly(vinyl alcohol) as the packaging material. The as‐made transient circuits are successfully applied to various electronic devices, including near‐field communication, capacitive touch sensors, and transient circuits to allow sequentially turning off an array of light‐emitting‐diode lamps.
The single-mode Dicke model is well known to undergo a quantum phase transition from the so-called normal phase to the superradiant phase (hereinafter called the 'superradiant quantum phase ...transition'). Normally, quantum phase transitions can be identified by the critical behavior of quantities such as entanglement, quantum fluctuations, and fidelity. In this paper, we study the role of the quantum Fisher information (QFI) of both the field mode and the atoms in the ground state of the Dicke Hamiltonian. For a finite but large number of atoms, our numerical results show that near the critical atom-field coupling, the QFI of the atomic and the field subsystems can surpass their classical limits, due to the appearance of nonclassical quadrature squeezing. As the coupling increases far beyond the critical point, each subsystem becomes a highly mixed state, which degrades the QFI and hence the ultimate phase sensitivity. In the thermodynamic limit, we present the analytical results of the QFI and their relationship with the reduced variances of the field mode and the atoms. For each subsystem, we find that there is a singularity in the derivative of the QFI at the critical point, a clear signature of the quantum criticality in the Dicke model.
In this paper, two efficient robust fuzzy model predictive control algorithms are investigated for discrete nonlinear systems with multiple time delays and bounded disturbances. The famous ...Takagi-Sugeno (T-S) fuzzy systems are utilized to represent nonlinear systems. Instead of the Lyapunov-Krasovskii functional, the Lyapunov-Razumikhin function is adopted to deal with time delays because it involves invariant sets in the original state space of the system. A sequence of explicit control laws corresponding to a sequence of constraint sets are computed offline so that the online computational burden associated with the classical model predictive control algorithms is significantly reduced. In particular, the set invariance theory behind the Razumikhin approach, which is more complicated than the one for nondelayed systems, is directly observed. Additionally, it is proved that all (delayed) states can enter the terminal set in finite time. Moreover, robust positive invariance and input-to-state stability for time-delay systems concerning disturbances are realized. Additionally, an online optimization algorithm is also provided based on the offline computed ellipsoidal sets. Therefore, the conservatism induced by the Razumikhin approach is relaxed, while the computational cost is not significantly increased.
Wheelchair upper-limb exoskeletons can offer a new paradigm to assist people with neuromuscular dysfunction in their activities of daily living such as eating and drinking. A key challenge in their ...control is to ensure safe and comfortable interaction between the human upper limb and exoskeleton. Compared with industrial manipulators, exoskeletons suffer severe kinematic and dynamic uncertainties and external disturbances. Therefore, the selection of optimal control methods that can address the aforementioned challenge is required. In this article, a method combining proportional-derivative (PD) control, sliding mode control, and fuzzy logic control, i.e., PD-based fuzzy sliding mode control, is developed to deal with unmodeled dynamics and external disturbances in the human-exoskeleton system. The sliding mode control can be generally divided by the equivalent control law and the switching control law. For the basic equivalent control part, it adopts the PD controller due to its simplicity in controller design and parameter tuning. For the switching control part, it is replaced by fuzzy logic control to eliminate the chattering of control input such that the smooth motion of the system is achieved. Simulation and experiment results are provided to show the effectiveness of the proposed control method.
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