A generalization of the predictable degree property to rational convolutional encoding matrices

The predictable degree property was introduced by Forney (1970) for polynomial convolutional encoding matrices. In this paper two generalizations to rational convolutional encoding matrices are discusse

Quasi-analytical solutions for APSIDAL motion in the three-body problem: Sun - minor planet - Jupiter

This paper deals with the effect of a third body on the apsidal motion of two bodies. The specific case involves a third body-planet Jupiter and the apsidal line motion of a minor planet that orbits the Sun and has its apsidal line go through the major axis of an ellipse. The third body (Jupiter) which satisfies the Langrangian solution will affect the apsidal line motion and therefore affects the ascending and descending motions of the minor planet. In this case no analytical solutions can be obtained, and therefore specific assumptions are made along with numerical solutions. For convenience, we adopt the Lagrangian solution in the three-body problem and obtain quasi-analytical results, which are used to evaluate the effect of the planet on the d Omega/dt (Omega ascending node) of each minor planet. This method is beneficial for improving our knowledge of the orbital elements of the asteroids, and perhaps even much smaller effects such as the effects of the planets on the interplanetary dust complex. Information on the latter may be provided by using this method to investigate Jupiter\u27s effect on the inclination of the symmetry surface of the zodiacal dust cloud

Some structural properties of convolutional codes over rings

Convolutional codes over rings have been motivated by phase-modulated signals. Some structural properties of the generator matrices of such codes are presented. Successively stronger notions of the invertibility of generator matrices are studied, and a new condition for a convolutional code over a ring to be systematic is given and shown to be equivalent to a condition given by Massey and Mittelholzer (1990). It is shown that a generator matrix that can be decomposed into a direct sum is basic, minimal, and noncatastrophic if and only if all generator matrices for the constituent codes are basic, minimal, and noncatastrophic, respectively. It is also shown that if a systematic generator matrix can be decomposed into a direct sum, then all generator matrices of the constituent codes are systematic, but that the converse does not hold. Some results on convolutional codes over Z(pe) are obtaine

Surveying the sense of urgency of the tactical-level management to adopt industry 4.0 technologies: Ranking of three sister plants based on BWM-CRITIC-TOPSIS

Purpose:Although the decision to adopt Industry 4.0 technologies is commonly strategical, the selection and implementation of technology are the responsibilities of the tactical level management. The tactical level management will also directly experience the impact of adopting the technology towards the organizational performances in their functional areas. The comparative survey study aims to measure the tactical level management’s sense of urgency of the nine pillars in three plants of a single manufacturing organization. Design/methodology/approach: The research methodology starts with a literature review to collect the criteria appertaining to the pillars. Based on the 95 constituting criteria, the second step prepares and conducts a questionnaire survey with 32 participants on three sister plants. Next, rough BWM-CRITIC-TOPSIS ranks these plants at the pillar and criteria levels. The ranking method integrates Best-Worst Method (BWM), Criteria Importance Through Intercriteria Correlation (CRITIC), and technique for order performance by similarity to ideal solution (TOPSIS). The top management discussed and rendered insights into the results. Findings: Results show that the high-mix and labor-intensive plant (Plant 1) has the highest urgency, whereas the largely automated plant (Plant 3) has the lowest urgency to adopt the nine pillars. The findings provide empirical evidence of the effect of the recent Industry 4.0 awareness programs in Plant 1 and advanced infrastructure would lead to organization inertia (Plant 3) to aggressively pursue technological change. The most urgent pillar is cybersecurity, and the least urgent pillar is additive manufacturing (AM), outlining the concern over cyber threats when product information is increasingly integrated into the supply chain and technology immaturity of AM in production. Research limitations/implications: A limitation of this study is that the comparative survey only focused on three plants and the tactical level management of an organization. Originality/value: This study contributes to the knowledge of Industry 4.0 readiness by being the first to show different levels in the sense of urgency of the tactical level managements on the relevant technologies, which potentially affect the direction and the pace of Industry 4.0 adoptionPeer Reviewe

Curvature-based Transformer for Molecular Property Prediction

The prediction of molecular properties is one of the most important and challenging tasks in the field of artificial intelligence-based drug design. Among the current mainstream methods, the most commonly used feature representation for training DNN models is based on SMILES and molecular graphs, although these methods are concise and effective, they also limit the ability to capture spatial information. In this work, we propose Curvature-based Transformer to improve the ability of Graph Transformer neural network models to extract structural information on molecular graph data by introducing Discretization of Ricci Curvature. To embed the curvature in the model, we add the curvature information of the graph as positional Encoding to the node features during the attention-score calculation. This method can introduce curvature information from graph data without changing the original network architecture, and it has the potential to be extended to other models. We performed experiments on chemical molecular datasets including PCQM4M-LST, MoleculeNet and compared with models such as Uni-Mol, Graphormer, and the results show that this method can achieve the state-of-the-art results. It is proved that the discretized Ricci curvature also reflects the structural and functional relationship while describing the local geometry of the graph molecular data