We studied the collective behaviors of the time-delayed Kuramoto model with frustration under general network topology. For the generalized Kuramoto model with the graph diameter no greater than two and under a sufficient regime in terms of small time delay and frustration and large coupling strength, we showed that the complete frequency synchronization occurs exponentially fast when the initial configuration is distributed in a half circle. We also studied a complete network, which is a small perturbation of all-to-all coupling, as well as presented sufficient frameworks leading to the exponential emergence of frequency synchronization for the initial data confined in a half circle.
Cardiovascular disease (CVD) has now become the disease with the highest mortality worldwide and coronary artery disease (CAD) is the most common form of CVD. This paper makes effective use of patients' condition information to identify the risk factors of CVD and predict the disease according to these risk factors in order to guide the treatment and life of patients according to these factors, effectively reduce the probability of disease and ensure that patients can carry out timely treatment. In this paper, a novel method based on a new classifier, named multi-agent Adaboost (MA_ADA), has been proposed to diagnose CVD. The proposed method consists of four steps: pre-processing, feature extraction, feature selection and classification. In this method, feature extraction is performed by principal component analysis (PCA). Then a subset of extracted features is selected by the genetics algorithm (GA). This method also uses the novel MA_ADA classifier to diagnose CVD in patients. This method uses a dataset containing information on 303 cardiovascular surgical patients. During the experiments, a four-stage multi-classification study on the prediction of coronary heart disease was conducted. The results show that the prediction model proposed in this paper can effectively identify CVDs using different groups of risk factors, and the highest diagnosis accuracy is obtained when 45 features are used for diagnosis. The results also show that the MA_ADA algorithm could achieve an accuracy of 98.67% in diagnosis, which is at least 1% higher than the compared methods.
Dynamic coloring has recently emerged as a valuable tool to optimize cryptographic protocols based on secret sharing, which enforce data security in communication networks and have significant importance in both online storage and cloud computing. This type of graph labeling enables the dealer to distribute secret shares among the nodes of a communication network so that everybody can recover the secret after a minimum number of rounds of communication. This paper delves into this topic by dealing with the dynamic coloring problem for degree splitting graphs. The topological structure of the latter enables the dealer to avoid dishonesty by adding control nodes that supervise all those participants with a similar influence in the network. More precisely, we solve the dynamic coloring problem for degree splitting graphs of any regular graph. The irregular case is partially solved by establishing a lower bound for the corresponding dynamic chromatic number. As illustrative examples, we solve the dynamic coloring problem for the degree splitting graphs of cycles, cocktail, book, comb, fan, jellyfish, windmill and barbell graphs.
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