Self-orthogonal codes from pp-divisible codes

Self-orthogonal codes are an important subclass of linear codes which have nice applications in quantum codes and lattices. It is known that a binary linear code is self-orthogonal if its every codeword has weight divisible by four, and a ternary linear code is self-orthogonal if and only if its every codeword has weight divisible by three. It remains open for a long time to establish the relationship between the self-orthogonality of a general $q$-ary linear code and the divisibility of its weights, where $q=p^m$ for a prime $p$. In this paper, we mainly prove that any $p$-divisible code containing the all-1 vector over the finite field $\mathbb{F}_q$ is self-orthogonal for odd prime $p$, which solves this open problem under certain conditions. Thanks to this result, we characterize that any projective two-weight code containing the all-1 codeword over $\mathbb{F}_q$ is self-orthogonal. Furthermore, by the extending and augmentation techniques, we construct six new families of self-orthogonal divisible codes from known cyclic codes. Finally, we construct two more families of self-orthogonal divisible codes with locality 2 which have nice application in distributed storage systems.Comment: 61 page

Modeling and Dynamic Characteristic Analysis of a Ball Screw Feed Drive System Based on Receptance Coupling

Modeling and modal analysis method based on receptance coupling are proposed for a vibration mode of a ball screw feed drive system, which cannot be determined by axial and torsional modal shape curves through a traditional method. In this study, the mathematical model for ball screw feed drive system is obtained by improved receptance coupling. The natural frequencies of different assembly states are calculated in the modeling process. The vibration modes of the feed drive system are determined by comparing the natural frequency distributions of different assembly states for a detailed analysis of the dynamic characteristics of the feed drive system. In the proposed method, a self-developed ball screw feed drive system is selected to study the influence of worktable position, worktable mass, and screw lead on the dynamic characteristics of the ball screw feed drive system. A change in the worktable position mainly affects the vibration of the ball screw itself. A change in the worktable mass mainly affects the coupling vibration between the ball screw and the rotor or bearing. The screw lead has an opposite influence on axial and torsional vibrations of the feed drive system, and the stability of the feed drive system improves with the screw lead. The validity of the proposed method is verified by the case study

How does working time impact perceived mental disorders? New insights into the U-shaped relationship

Based on a large-scale nationally representative survey in China, this paper uses the exogenous impact of automation on working hours as the instrumental variable to examine working time’s impact on perceived mental disorders, on the basis of dealing with endogeneity. Different from existing literature, it is found that the impact of working time on perceived mental disorders is U-shaped, rather than linear. Mental disorders firstly decrease with working hours. After working more than 48.688 h per week, further increases in working time carry notable mental health costs, leading to a positive relationship between working hours and depression. The turning point of this U-shaped relationship is almost in line with the International Labor Organization’s 48 working hours/week standard, justifying it from a mental health perspective. In addition, we further exclude the possibility of more complex nonlinear relationships between working time and perceived mental disorders. Furthermore, heterogeneities are found in the effects of working hours on mental disorders across different subgroups. Males are more depressed when working overtime. Older workers have a lower tolerance for overwork stress. The turning point is smaller for the highly educated group and they are more sensitive to working longer. Those with higher socioeconomic status are less depressed after exceeding the optimal hours of work. The increase in depression among rural workers faced with overwork is not prominent. Perceived mental disorders are lower among immigrants and those with higher health status. In addition, labor protection and social security help to weaken mental disorders caused by overtime work. In conclusion, this paper demonstrates that working time has a U-shaped impact on perceived mental disorders and highlights the vulnerability of certain groups, providing a reference for setting optimal working hours from a mental health perspective

Multi-Position Identification of Joint Parameters in Ball Screw Feed System Based on Response Coupling

Existing methods of parameters identification do not consider the torsion characteristics of a ball screw and the worktable position simultaneously. Therefore, this paper proposes a multi-position identification method based on receptance coupling. Firstly, the mathematical model of the feed drive system is established by the improved receptance coupling, and this model considers both axial and torsional vibration of the ball screw. Secondly, the identification equation is established by minimum error of the modal parameters of multiple worktable position, and differential evolution algorithm is used to calculate the stiffness and damping of the joint. Finally, the self-developed ball screw feed drive system is used for experimental study. The maximum error of the first four orders of natural frequencies predicted through multi-position identification results is 2.95%, and the multi-position method is more robust than the common method identification at one position. The experiment study showed that the proposed method is accuracy and necessity

Formal Analysis of Fairness for Optimistic Multiparty Contract Signing Protocol

Optimistic multiparty contract signing (OMPCS) protocols are proposed for exchanging multiparty digital signatures in a contract. Compared with general two-party exchanging protocols, such protocols are more complicated, because the number of protocol messages and states increases considerably when signatories increase. Moreover, fairness property in such protocols requires protection from each signatory rather than from an external hostile agent. It thus presents a challenge for formal verification. In our analysis, we employ and combine the strength of extended modeling language CSP# and linear temporal logic (LTL) to verify the fairness of OMPCS protocols. Furthermore, for solving or mitigating the state space explosion problem, we set a state reduction algorithm which can decrease the redundant states properly and reduce the time and space complexity greatly. Finally, this paper illustrates the feasibility of our approach by analyzing the GM and CKS protocols, and several fairness flaws have been found in certain computation times

Two families of linear codes with desirable properties from some functions over finite fields

Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic. In this paper, based on the augmentation technique, we present two families of linear codes from some functions over finite fields. The first family of linear codes is constructed from monomial functions over finite fields. The locality of them is determined and the weight distributions of two subfamilies of the codes are also given. An infinite family of locally recoverable codes which are at least almost optimal and some optimal recoverable codes are obtained from the linear codes. In particular, the two subfamilies of the codes are proved to be both optimally or almost optimally extendable and self-orthogonal. The second family of linear codes is constructed from weakly regular bent functions over finite fields and their weight distribution is determined. This family of codes is proved to have locality 3 for some cases and is conjectured to have locality 2 for other cases. Particularly, two families of optimal locally recoverable codes are derived from the linear codes. Besides, this family of codes is also proved to be both optimally or almost optimally extendable and self-orthogonal.Comment: 44 page

Pre-IdentifyNet: An Improved Neural Network for Image Recognition

With the rise and development of artificial intelligence, image recognition and classification technology has received more and more attention as an important branch of its research field. Among them, the introduction of deep learning networks and the construction of neural network structures not only avoid a lot of the tedious work of manual extraction, but also improve the accuracy of image recognition. Convolutional neural networks have many advantages that conventional neural networks do not have. Therefore, image classification systems based on convolutional neural networks emerge in endlessly, but there is still much room for improvement in terms of recognition accuracy and recognition speed. Based on this, this paper proposes an improved deep convolutional neural network to improve the accuracy of the network by changing a series of parameters such as the number of channels of the convolution layer, the size of the convolution kernel, the learning rate, the number of iterations, and the size of the small batch with speed. In this paper, three data sets were selected, namely sewage, animals and the Simpson Family. Comparing the improved convolutional neural network network with the existing SqueezeNet and GoogleNet. It is found that the accuracy of the network is maintained while maintaining a similar speed. Both F1-score and F1-score have been improved with a higher recognition rate and better recognition effect in image recognition classification