SOLOVARY proved that every regular uncountable κ is the union of κ disjoint stationary sets (ref. [1], Theorem 85). Let κ be an ineffable ordinal, and let A(?)κ. If A is an ineffable set, then A is a stationary se...SOLOVARY proved that every regular uncountable κ is the union of κ disjoint stationary sets (ref. [1], Theorem 85). Let κ be an ineffable ordinal, and let A(?)κ. If A is an ineffable set, then A is a stationary set and A is the union of κ disjoint stationary sets. We ask the following question: Is A the union of κ disjoint ineffable sets? We will give a positive answer for the question.展开更多
The emergence of digital networks and the wide adoption of information on internet platforms have given rise to threats against users’private information.Many intruders actively seek such private data either for sale...The emergence of digital networks and the wide adoption of information on internet platforms have given rise to threats against users’private information.Many intruders actively seek such private data either for sale or other inappropriate purposes.Similarly,national and international organizations have country-level and company-level private information that could be accessed by different network attacks.Therefore,the need for a Network Intruder Detection System(NIDS)becomes essential for protecting these networks and organizations.In the evolution of NIDS,Artificial Intelligence(AI)assisted tools and methods have been widely adopted to provide effective solutions.However,the development of NIDS still faces challenges at the dataset and machine learning levels,such as large deviations in numeric features,the presence of numerous irrelevant categorical features resulting in reduced cardinality,and class imbalance in multiclass-level data.To address these challenges and offer a unified solution to NIDS development,this study proposes a novel framework that preprocesses datasets and applies a box-cox transformation to linearly transform the numeric features and bring them into closer alignment.Cardinality reduction was applied to categorical features through the binning method.Subsequently,the class imbalance dataset was addressed using the adaptive synthetic sampling data generation method.Finally,the preprocessed,refined,and oversampled feature set was divided into training and test sets with an 80–20 ratio,and two experiments were conducted.In Experiment 1,the binary classification was executed using four machine learning classifiers,with the extra trees classifier achieving the highest accuracy of 97.23%and an AUC of 0.9961.In Experiment 2,multiclass classification was performed,and the extra trees classifier emerged as the most effective,achieving an accuracy of 81.27%and an AUC of 0.97.The results were evaluated based on training,testing,and total time,and a comparative analysis with state-of-the-art studies proved the robustness and significance of the applied methods in developing a timely and precision-efficient solution to NIDS.展开更多
An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is ...An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is denoted by . Erdös, Faber and Lovász proposed a famous conjecture that holds for any loopless linear hypergraph H with n vertices. In this paper, we show that is true for gap-restricted hypergraphs. Our result extends a result of Alesandroni in 2021.展开更多
Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable ...Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.展开更多
文摘SOLOVARY proved that every regular uncountable κ is the union of κ disjoint stationary sets (ref. [1], Theorem 85). Let κ be an ineffable ordinal, and let A(?)κ. If A is an ineffable set, then A is a stationary set and A is the union of κ disjoint stationary sets. We ask the following question: Is A the union of κ disjoint ineffable sets? We will give a positive answer for the question.
文摘The emergence of digital networks and the wide adoption of information on internet platforms have given rise to threats against users’private information.Many intruders actively seek such private data either for sale or other inappropriate purposes.Similarly,national and international organizations have country-level and company-level private information that could be accessed by different network attacks.Therefore,the need for a Network Intruder Detection System(NIDS)becomes essential for protecting these networks and organizations.In the evolution of NIDS,Artificial Intelligence(AI)assisted tools and methods have been widely adopted to provide effective solutions.However,the development of NIDS still faces challenges at the dataset and machine learning levels,such as large deviations in numeric features,the presence of numerous irrelevant categorical features resulting in reduced cardinality,and class imbalance in multiclass-level data.To address these challenges and offer a unified solution to NIDS development,this study proposes a novel framework that preprocesses datasets and applies a box-cox transformation to linearly transform the numeric features and bring them into closer alignment.Cardinality reduction was applied to categorical features through the binning method.Subsequently,the class imbalance dataset was addressed using the adaptive synthetic sampling data generation method.Finally,the preprocessed,refined,and oversampled feature set was divided into training and test sets with an 80–20 ratio,and two experiments were conducted.In Experiment 1,the binary classification was executed using four machine learning classifiers,with the extra trees classifier achieving the highest accuracy of 97.23%and an AUC of 0.9961.In Experiment 2,multiclass classification was performed,and the extra trees classifier emerged as the most effective,achieving an accuracy of 81.27%and an AUC of 0.97.The results were evaluated based on training,testing,and total time,and a comparative analysis with state-of-the-art studies proved the robustness and significance of the applied methods in developing a timely and precision-efficient solution to NIDS.
文摘An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is denoted by . Erdös, Faber and Lovász proposed a famous conjecture that holds for any loopless linear hypergraph H with n vertices. In this paper, we show that is true for gap-restricted hypergraphs. Our result extends a result of Alesandroni in 2021.
文摘Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.
