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In this paper, a nonparametric method for reliability of the stress-strength model is proposed when the dependent stress variable and strength variable are subject to right censoring. The dependence between variables is measured by the common Farlie-Gumbel-Morgenstern copula function and Clayton copula function. Using the empirical process theory, consistency and asymptotic normality of the proposed estimator is established in this paper. The results of numerical simulation show that the proposed method performs well in the case of finite sample. The method proposed in this paper has a wide application prospect in practice.     

Transferred multipolar atom model for 10β,17β‐dihydroxy‐17α‐methylestr‐4‐en‐3‐one dihydrate obtained from the biotransformation of methyloestrenolone

Biotransformation is the structural modification of compounds using enzymes as the catalysts and it plays a key role in the synthesis of pharmaceutically important compounds. 10β,17β‐Dihydroxy‐17α‐methylestr‐4‐en‐3‐one dihydrate, C₁₉H₂₈O₃·2H₂O, was obtained from the fungal biotransformation of methyloestrenolone. The structure was refined using the classical independent atom model (IAM) and a transferred multipolar atom model using the ELMAM2 database. The results from the two refinements have been compared. The ELMAM2 refinement has been found to be superior in terms of the refinement statistics. It has been shown that certain electron‐density‐derived properties can be calculated on the basis of the transferred parameters for crystals which diffract to ordinary resolution.     

Spin frustration-related behavior of mixed spin diamond chain

The magnetization of mixed spin-1/2, 1 Ising diamond chain with antiferromagnetic spin exchange interaction has been investigated by using the Monte Carlo simulation. Magnetization behaviors with different antiferromagnetic interactions are simulated under magnetic field at low temperature. The behaviors are studied in two different cases. In one case the absolute value of the interaction between two spin-1/2 atoms is the largest and in the other case it is not the largest. Multiple plateaus of magnetization M, such as plateaus at M=±1, M=0 and M=±0.566 are obtained. The plateaus at M=±0.566 correspond to two metastable states. The M=0 plateau may disappear at some specific values of spin exchange interactions. The spin configurations were checked when the plateaus appear. The dimmer and trimmer states are found.     

Historical data learning based dynamic LSP routing for overlay IP/MPLS over WDM networks

Overlay IP/MPLS over WDM network is a promising network architecture starting to gain wide deployments recently. A desirable feature of such a network is to achieve efficient routing with limited information exchanges between the IP/MPLS and the WDM layers. This paper studies dynamic label switched path (LSP) routing in the overlay IP/MPLS over WDM networks. To enhance network performance while maintaining its simplicity, we propose to learn from the historical data of lightpath setup costs maintained by the IP-layer integrated service provider (ISP) when making routing decisions. Using a novel historical data learning scheme for logical link cost estimation, we develop a new dynamic LSP routing method named Existing Link First (ELF) algorithm. Simulation results show that the proposed algorithm significantly outperforms the existing ones under different traffic loads, with either limited or unlimited numbers of optical ports. Effects of the number of candidate routes, add/drop ratio and the amount of historical data are also evaluated.     

Flocking and asymptotic velocity of the Cucker–Smale model with processing delay

The processing delay is incorporated into the influence function of the well-known Cucker–Smale model for self-organized systems with multiple agents. Both symmetric and non-symmetric pairwise influence functions are considered, and a Lyapunov functional approach is developed to establish the existence of flocking solutions for the proposed delayed Cucker–Smale model. An analytic formula is given to calculate the asymptotic flocking velocity in terms of model parameters and the variation of the position during the initial time interval.     

Understanding convolutional neural networks with a mathematical model

This work attempts to address two fundamental questions about the structure of the convolutional neural networks (CNN): (1) why a nonlinear activation function is essential at the filter output of all intermediate layers? (2) what is the advantage of the two-layer cascade system over the one-layer system? A mathematical model called the “REctified-COrrelations on a Sphere” (RECOS) is proposed to answer these two questions. After the CNN training process, the converged filter weights define a set of anchor vectors in the RECOS model. Anchor vectors represent the frequently occurring patterns (or the spectral components). The necessity of rectification is explained using the RECOS model. Then, the behavior of a two-layer RECOS system is analyzed and compared with its one-layer counterpart. The LeNet-5 and the MNIST dataset are used to illustrate discussion points. Finally, the RECOS model is generalized to a multilayer system with the AlexNet as an example.     

Degradation performance of polyglutamic acid and its application of calcium supplement

Degradable biopolymers with functional groups play a crucial role in the biomedical field. In this case, the influences of temperature and pH values on the degradation performance of poly (γ‐glutamic acid) (γ‐PGA) were fully explored by gel permeation chromatography. Further, γ‐PGA‐Ca was prepared by using calcium chloride to react with the low molecular weight γ‐PGA and characterized by Fourier transform infrared, differential scanning calorimetry test, gel permeation chromatography, atomic absorption spectrophotometric, Ca²⁺ release in vivo, and cytotoxicity experiments. Furthermore, Caco‐2 cell model was constructed to study the mechanism of γ‐PGA‐Ca intestinal absorption. Results indicated that low pH value and high temperature are the suitable conditions for the degradation of γ‐PGA. It also suggested that γ‐PGA‐Ca can be used as calcium supplements due to its high rate of absorption.     

Like‐Charge Attraction: A Combined Electrostatic–Hydrodynamic Approach

Abstract

This article discusses the like‐charge attraction of colloidal spheres close to a charged plate and compares results produced by an electrostatic and a hydrodynamic model with experimental data. Hydrodynamic coupling is shown to be the dominating effect, while the electrostatic influence may often be neglected. Some observations, however, can be explained only by means of a combined electrostatic–hydrodynamic model, which is derived in this work. The combined model is able to predict not only the attractive force between particles of similar charge close to a charged plate but also the change to a purely repulsive force once the sphere‐plate distance is further reduced. This prediction matches qualitatively results of experiments reported in the literature.     

Existence and uniqueness of maximal strong solution of a 1D blood flow in a network of vessels

We study the well-posedness of a system of one-dimensional partial differential equations modeling blood flows in a network of vessels with viscoelastic walls. We prove the existence and uniqueness of maximal strong solution for this type of hyperbolic/parabolic model. We also prove a stability estimate under suitable nonlinear Robin boundary conditions.