An Improved Modification of Accelerated Double Direction and Double Step-Size Optimization Schemes

We propose an improved variant of the accelerated gradient optimization models for solving unconstrained minimization problems. Merging the positive features of either double direction, as well as double step size accelerated gradient models, we define an iterative method of a simpler form which is generally more effective. Performed convergence analysis shows that the defined iterative method is at least linearly convergent for uniformly convex and strictly convex functions. Numerical test results confirm the efficiency of the developed model regarding the CPU time, the number of iterations and the number of function evaluations metrics.

Assembly variation analysis of the non-rigid assembly with a deformation gradient model

Purpose This paper aims to develop a mathematical method to analyze the assembly variation of the non-rigid assembly, considering the manufacturing variations and the deformation variations of the non-rigid parts during the assembly process. Design/methodology/approach First, this paper proposes a deformation gradient model, which represents the deformation variations during the assembly process by considering the forces and the self-weight of the non-rigid parts. Second, the developed deformation gradient models from the assembly process are integrated into the homogenous transformation matrix to model the deformation variations and manufacturing variations of the deformed non-rigid part. Finally, a mathematical model to analyze the assembly variation propagation is developed to predict the dimensional and geometrical variations due to the manufacturing variations and the deformation variations during the assembly process. Findings Through the case study with a crosshead non-rigid assembly, the results indicate that during the assembly process, the individual deformation values of the non-rigid parts are small. However, the cumulative deformation variations of all the non-rigid parts and the manufacturing variations present a target value (w) of −0.2837 mm as compared to a target value of −0.3995 mm when the assembly is assumed to be rigid. The difference in the target values indicates that the influence of the non-rigid part deformation variations during the assembly process on the mechanical assembly accuracy cannot be ignored. Originality/value In this paper, a deformation gradient model is proposed to obtain the deformation variations of non-rigid parts during the assembly process. The small deformation variation, which is often modeled using a finite-element method in the existing works, is modeled using the proposed deformation gradient model and integrated into the nominal dimensions. Using the deformation gradient models, the non-rigid part deformation variations can be computed and the accumulated deformation variation can be easily obtained. The assembly variation propagation model is developed to predict the accuracy of the non-rigid assembly by integrating the deformation gradient models into the homogeneous transformation matrix.

Housing Market in the Time of Pandemic: A Price Gradient Analysis from the COVID-19 Epicentre in China

While the outbreak of the COVID-19 disease has caused asset markets to experience an unprecedented spike of risk and uncertainty worldwide, the real estate market in many global cities appears to be immune to the adverse effects. How does COVID-19 affect urban housing markets? This study is a first attempt to identify the pandemic’s impact on house prices by applying a price gradient analysis to the COVID-19 epicentre in China. Considering microlevel housing transaction data in 62 areas from nine districts in Wuhan City from January 2019 to July 2020, the hedonic pricing and the price gradient models suggest that there was, respectively, a 4.8% and a 5.0–7.0% year-on-year fall in house prices immediately after the pandemic outbreak. Although house prices rebounded after the lockdown period, the gradient models show that the price gradients were flattened from the epicentre to the urban peripherals. The price premiums in high-density areas were also substantially discounted after the city’s lockdown. Our findings are robust to different model specifications. The implication is that the risk associated with the pandemic is localised and transitory in nature. People may be able to internalise the risk by residing in low-density residential areas.

Value-free reinforcement learning: Policy optimization as a minimal model of operant behavior

Reinforcement learning is a powerful framework for modelling the cognitive and neural substrates of learning and decision making. Contemporary research in cognitive neuroscience and neuroeconomics typically uses value-based reinforcement-learning models, which assume that decision-makers choose by comparing learned values for different actions. However, another possibility is suggested by a simpler family of models, called policy-gradient reinforcement learning. Policy-gradient models learn by optimizing a behavioral policy directly, without the intermediate step of value-learning. Here we review recent behavioral and neural findings that are more parsimoniously explained by policy-gradient models than by value-based models. We conclude that, despite the ubiquity of `value' in reinforcement-learning models of decision making, policy-gradient models provide a lightweight and compelling alternative model of operant behavior.

Homogenization of an elastic material reinforced by very strong fibres arranged along a periodic lattice

We provide in this paper homogenization results for the L 2 -topology leading to complete strain-gradient models and generalized continua. Actually, we extend to the L 2 -topology the results obtained in (Abdoul-Anziz & Seppecher, 2018 Homogenization of periodic graph-based elastic structures. Journal de l’Ecole polytechnique–Mathématiques 5 , 259–288) using a topology adapted to minimization problems set in varying domains. Contrary to (Abdoul-Anziz & Seppecher, 2018 Homogenization of periodic graph-based elastic structures. Journal de l’Ecole polytechnique–Mathématiques 5 , 259–288) we consider elastic lattices embedded in a soft elastic matrix. Thus our study is placed in the usual framework of homogenization. The contrast between the elastic stiffnesses of the matrix and the reinforcement zone is assumed to be very large. We prove that a suitable choice of the stiffness on the weak part ensures the compactness of minimizing sequences while the energy contained in the matrix disappears at the limit: the Γ-limit energies we obtain are identical to those obtained in (Abdoul-Anziz & Seppecher, 2018 Homogenization of periodic graph-based elastic structures. Journal de l’Ecole polytechnique–Mathématiques 5 , 259–288).