Hidden Markov models revealing the stress field underlying the earthquake generation

The application of the hidden Markov models (HMMs) is attempted for revealing key features for the earthquake generation which are not accessible to direct observation. Considering that the states of the HMM correspond to levels of the stress field, our objective is to identify these states. The observations are considered after grouping earthquake magnitudes and the cases of different number of states are examined. The problems of HMMs theory are solved and the ensuing HMMs are compared on the basis of Akaike and Bayesian information criteria. A new insight on the evaluation of future seismic hazard is given by calculating the mean number of steps for the first visit to a particular state, along with the respective variance. We further calculate an estimator of the mean number of steps for the first visit to a particular state and we construct its confidence interval. Additionally, a second approach to the problem is followed by assuming a different determination of observations. The HMMs applied to both approaches, contribute significantly to seismic hazard assessment via revealing the number of the stress levels as well as the way in which these levels are associated with certain earthquake occurrence.     

非线性互补约束规划问题的一个新的QP-free算法

本文研究了非线性互补约束均衡问题.利用互补函数以及光滑近似法,把非线性互补约束均衡问题转化为一个光滑非线性规划问题,得到了超线性收敛速度,数值实验结果表明本文提出的算法是可行的.     

High‐ and low‐temperature phases in isostructural 4‐chloro‐3‐nitroaniline and 4‐iodo‐3‐nitroaniline

The structures of 4‐chloro‐3‐nitroaniline, C₆H₅ClN₂O₂, (I), and 4‐iodo‐3‐nitroaniline, C₆H₅IN₂O₂, (II), are isomorphs and both undergo continuous (second order) phase transitions at 237 and 200 K, respectively. The structures, as well as their phase transitions, have been studied by single‐crystal X‐ray diffraction, Raman spectroscopy and difference scanning calorimetry experiments. Both high‐temperature phases (293 K) show disorder of the nitro substituents, which are inclined towards the benzene‐ring planes at two different orientations. In the low‐temperature phases (120 K), both inclination angles are well maintained, while the disorder is removed. Concomitantly, the b axis doubles with respect to the room‐temperature cell. Each of the low‐temperature phases of (I) and (II) contains two pairs of independent molecules, where the molecules in each pair are related by noncrystallographic inversion centres. The molecules within each pair have the same absolute value of the inclination angle. The Flack parameter of the low‐temperature phases is very close to 0.5, indicating inversion twinning. This can be envisaged as stacking faults in the low‐temperature phases. It seems that competition between the primary amine–nitro N—H...O hydrogen bonds which form three‐centred hydrogen bonds is the reason for the disorder of the nitro groups, as well as for the phase transition in both (I) and (II). The backbones of the structures are formed by N—H...N hydrogen bonding of moderate strength which results in the graph‐set motif C(3). This graph‐set motif forms a zigzag chain parallel to the monoclinic b axis and is maintained in both the high‐ and the low‐temperature structures. The primary amine groups are pyramidal, with similar geometric values in all four determinations. The high‐temperature phase of (II) has been described previously [Garden et al. (2004). Acta Cryst. C 60 , o328–o330].     

动态环境约束下企业的资本积累

本文讨论动态环境约束下企业的动态投资行为,拓广了文献[4]的结果.为了使讨论的问题更符合实际情况,本文假设政府设定的污染排放上限是与企业的规模大小有关,即假设污染排放上限是生产资本的函数,讨论动态环境约束下企业的最佳动态投资行为,并为政府制定污染排放政策提供依据.     

基于相场描述的拉压不对称强度结构拓扑优化

运用了基于相场描述的拓扑优化方法,来寻找在拉伸和压缩中表现出不对称强度行为的连续体结构的最优布局。依据Drucker-Prager屈服准则和幂率插值方案,优化问题可以描述为在局部应力约束下的最小化结构的体积。用qp放松法来解决应力约束的奇异性,并采用基于P-norm函数的聚合方法对应力约束进行凝聚,该方法实现了约束个数的降低,同时引入了稳定转化法来处理大量的局部应力约束和高度非线性的应力行为,以修正应力,提高优化收敛的稳定性。在优化问题求解时,使用拉格朗日乘子法对目标函数和应力约束进行处理。利用伴随变量法进行灵敏度分析,并通过求解Allen-Cahn方程更新相场函数设计变量。数值算例证明了该优化模型和相应数值技术的有效性,相关算例还揭示了考虑拉压不同强度和考虑同拉压强度约束时得到的结构优化拓扑构型具有显著的差异。     

On the Nature of Functional Differentiation: The Role of Self-Organization with Constraints

The focus of this article is the self-organization of neural systems under constraints. In 2016, we proposed a theory for self-organization with constraints to clarify the neural mechanism of functional differentiation. As a typical application of the theory, we developed evolutionary reservoir computers that exhibit functional differentiation of neurons. Regarding the self-organized structure of neural systems, Warren McCulloch described the neural networks of the brain as being “heterarchical”, rather than hierarchical, in structure. Unlike the fixed boundary conditions in conventional self-organization theory, where stationary phenomena are the target for study, the neural networks of the brain change their functional structure via synaptic learning and neural differentiation to exhibit specific functions, thereby adapting to nonstationary environmental changes. Thus, the neural network structure is altered dynamically among possible network structures. We refer to such changes as a dynamic heterarchy. Through the dynamic changes of the network structure under constraints, such as physical, chemical, and informational factors, which act on the whole system, neural systems realize functional differentiation or functional parcellation. Based on the computation results of our model for functional differentiation, we propose hypotheses on the neuronal mechanism of functional differentiation. Finally, using the Kolmogorov–Arnold–Sprecher superposition theorem, which can be realized by a layered deep neural network, we propose a possible scenario of functional (including cell) differentiation.     

遗传算法求解约束非线性规划及Matlab实现

对于约束非线性规划问题,传统的方法:可行方向法、惩罚函数法计算烦琐且精度不高.用新兴的遗传算法来解决约束非线性规划,核心是惩罚函数的构造.以前的惩罚函数遗传算法有的精度较低,有的过于复杂.本文在两个定义的基础上构造了新的惩罚函数,并在新的惩罚函数的基础上,提出了一种解决约束非线性最优化问题的方法.通过两个例子应用Matlab说明了这个算法的可行性.     

工件的释放时间和加工时间具有一致性的单机在线排序问题研究

工件的释放时间和加工时间具有一致性, 是指释放时间大的工件其加工时间不小于释放时间小的工件的加工时间, 即若$r_{i}\geq r_{j}$, 则$p_{i}\geq p_{j}$。本文在该一致性约束下, 研究最小化最大加权完工时间单机在线排序问题, 和最小化总加权完工时间单机在线排序问题, 并分别设计出$\frac{\sqrt{5}+1}{2}$-竞争的最好可能在线算法。     

Modified sub-population teaching-learning-based optimization for design of truss structures with natural frequency constraints

In this paper, a modified sub-population teaching-learning-based optimization (MS-TLBO) algorithm is proposed to improve the exploration and exploitation capacities by including the concept of number of teachers, adaptive teaching factor, learning through tutorial, and self-motivated learning in the basic TLBO algorithm. The multiple frequency responses to the structural optimization problems are challenging due to its search space, which is implicit, nonconvex, nonlinear, and often leading to divergence. The viability and efficiency of the proposed method are tested by five structural benchmark problems of shape and size optimization with multiple natural frequency constraints on the planar and space trusses. The results reveal that MS-TLBO is more effective as compared to the original TLBO and other state-of-the-art algorithms.