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
The probability hypothesis density （PHD） propagates the posterior intensity in place of the poste- rior probability density of the multi-target state. The cardinalized PHD （CPHD） recursion is a generalization of P...The probability hypothesis density （PHD） propagates the posterior intensity in place of the poste- rior probability density of the multi-target state. The cardinalized PHD （CPHD） recursion is a generalization of PHD recursion, which jointly propagates the posterior intensity function and posterior cardinality distribution. A number of sequential Monte Carlo （SMC） implementations of PHD and CPHD filters （also known as SMC- PHD and SMC-CPHD filters, respectively） for general non-linear non-Gaussian models have been proposed. However, these approaches encounter the limitations when the observation variable is analytically unknown or the observation noise is null or too small. In this paper, we propose a convolution kernel approach in the SMC-CPHD filter. The simuIation results show the performance of the proposed filter on several simulated case studies when compared to the SMC-CPHD filter.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
The purpose of this study is to reduce the uncertainty in the calculation process on hesitant fuzzy sets(HFSs).The innovation of this study is to unify the cardinal numbers of hesitant fuzzy elements(HFEs)in a special...The purpose of this study is to reduce the uncertainty in the calculation process on hesitant fuzzy sets(HFSs).The innovation of this study is to unify the cardinal numbers of hesitant fuzzy elements(HFEs)in a special way.Firstly,a probability density function is assigned for any given HFE.Thereafter,equal-probability transformation is introduced to transform HFEs with different cardinal numbers on the condition into the same probability density function.The characteristic of this transformation is that the higher the consistency of the membership degrees in HFEs,the higher the credibility of the mentioned membership degrees is,then,the bigger the probability density values for them are.According to this transformation technique,a set of novel distance measures on HFSs is provided.Finally,an illustrative example of intersection traffic control is introduced to show the usefulness of the given distance measures.The example also shows that this study is a good complement to operation theories on HFSs.展开更多
The Gibbs-like variational methodology is applied to the heterogeneous systems with rigid pyroelectric or pyromagnetic domains. The processes of depolarization/demagnetization are taken into account by assuming the sp...The Gibbs-like variational methodology is applied to the heterogeneous systems with rigid pyroelectric or pyromagnetic domains. The processes of depolarization/demagnetization are taken into account by assuming the spatial mobility of the interfaces. The simplest configuration of flat interface separating rigid pyroelectric half-spaces permits explicit analysis of morphological stability.展开更多
In the 19th century, Cantor created the infinite cardinal number theory based on the “1-1 correspondence” principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it th...In the 19th century, Cantor created the infinite cardinal number theory based on the “1-1 correspondence” principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it the first problem in his famous speech on mathematical problems, which shows the importance of this question. We know that the infinitesimal problem triggered the second mathematical crisis in the 17-18th centuries. The Infinity problem is no less important than the infinitesimal problem. In the 21st century, Sergeyev introduced the Grossone method from the principle of “whole is greater than part”, and created another ruler for measuring infinite sets. The discussion in this paper shows that, compared with the cardinal number method, the Grossone method enables infinity calculation to achieve a leap from qualitative calculation to quantitative calculation. According to Grossone theory, there is neither the largest infinity and infinitesimal, nor the smallest infinity and infinitesimal. Hilbert’s first problem was caused by the immaturity of the infinity theory.展开更多
In multiple extended targets tracking, replacing traditional multiple measurements with a rectangular region of the nonzero volume in the state space inspired by the box-particle idea is exactly suitable to deal with ...In multiple extended targets tracking, replacing traditional multiple measurements with a rectangular region of the nonzero volume in the state space inspired by the box-particle idea is exactly suitable to deal with extended targets, without distinguishing the measurements originating from the true targets or clutter.Based on our recent work on extended box-particle probability hypothesis density(ET-BP-PHD) filter, we propose the extended labeled box-particle cardinalized probability hypothesis density(ET-LBP-CPHD) filter, which relaxes the Poisson assumptions of the extended target probability hypothesis density(PHD) filter in target numbers, and propagates not only the intensity function but also cardinality distribution. Moreover, it provides the identity of individual target by adding labels to box-particles. The proposed filter can improve the precision of estimating target number meanwhile achieve targets' tracks. The effectiveness and reliability of the proposed algorithm are verified by the simulation results.展开更多
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.
基金Supported in Part by the Foundation of the Excellent State Key Laboratory under Grant 40523005,and the Ministry of Education of China
文摘The probability hypothesis density （PHD） propagates the posterior intensity in place of the poste- rior probability density of the multi-target state. The cardinalized PHD （CPHD） recursion is a generalization of PHD recursion, which jointly propagates the posterior intensity function and posterior cardinality distribution. A number of sequential Monte Carlo （SMC） implementations of PHD and CPHD filters （also known as SMC- PHD and SMC-CPHD filters, respectively） for general non-linear non-Gaussian models have been proposed. However, these approaches encounter the limitations when the observation variable is analytically unknown or the observation noise is null or too small. In this paper, we propose a convolution kernel approach in the SMC-CPHD filter. The simuIation results show the performance of the proposed filter on several simulated case studies when compared to the SMC-CPHD filter.
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.
基金supported by Shanghai Pujiang Program (No.2019PJC062)the Natural Science Foundation of Shandong Province (No.ZR2021MG003)the Research Project on Undergraduate Teaching Reform of Higher Education in Shandong Province (No.Z2021046).
文摘The purpose of this study is to reduce the uncertainty in the calculation process on hesitant fuzzy sets(HFSs).The innovation of this study is to unify the cardinal numbers of hesitant fuzzy elements(HFEs)in a special way.Firstly,a probability density function is assigned for any given HFE.Thereafter,equal-probability transformation is introduced to transform HFEs with different cardinal numbers on the condition into the same probability density function.The characteristic of this transformation is that the higher the consistency of the membership degrees in HFEs,the higher the credibility of the mentioned membership degrees is,then,the bigger the probability density values for them are.According to this transformation technique,a set of novel distance measures on HFSs is provided.Finally,an illustrative example of intersection traffic control is introduced to show the usefulness of the given distance measures.The example also shows that this study is a good complement to operation theories on HFSs.
文摘The Gibbs-like variational methodology is applied to the heterogeneous systems with rigid pyroelectric or pyromagnetic domains. The processes of depolarization/demagnetization are taken into account by assuming the spatial mobility of the interfaces. The simplest configuration of flat interface separating rigid pyroelectric half-spaces permits explicit analysis of morphological stability.
文摘In the 19th century, Cantor created the infinite cardinal number theory based on the “1-1 correspondence” principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it the first problem in his famous speech on mathematical problems, which shows the importance of this question. We know that the infinitesimal problem triggered the second mathematical crisis in the 17-18th centuries. The Infinity problem is no less important than the infinitesimal problem. In the 21st century, Sergeyev introduced the Grossone method from the principle of “whole is greater than part”, and created another ruler for measuring infinite sets. The discussion in this paper shows that, compared with the cardinal number method, the Grossone method enables infinity calculation to achieve a leap from qualitative calculation to quantitative calculation. According to Grossone theory, there is neither the largest infinity and infinitesimal, nor the smallest infinity and infinitesimal. Hilbert’s first problem was caused by the immaturity of the infinity theory.
文摘In multiple extended targets tracking, replacing traditional multiple measurements with a rectangular region of the nonzero volume in the state space inspired by the box-particle idea is exactly suitable to deal with extended targets, without distinguishing the measurements originating from the true targets or clutter.Based on our recent work on extended box-particle probability hypothesis density(ET-BP-PHD) filter, we propose the extended labeled box-particle cardinalized probability hypothesis density(ET-LBP-CPHD) filter, which relaxes the Poisson assumptions of the extended target probability hypothesis density(PHD) filter in target numbers, and propagates not only the intensity function but also cardinality distribution. Moreover, it provides the identity of individual target by adding labels to box-particles. The proposed filter can improve the precision of estimating target number meanwhile achieve targets' tracks. The effectiveness and reliability of the proposed algorithm are verified by the simulation results.
