In this paper, we introduce and study differential graded(DG for short) polynomial algebras. In brief, a DG polynomial algebra A is a connected cochain DG algebra such that its underlying graded algebra A~# is a polyn...In this paper, we introduce and study differential graded(DG for short) polynomial algebras. In brief, a DG polynomial algebra A is a connected cochain DG algebra such that its underlying graded algebra A~# is a polynomial algebra K[x_1, x_2,..., x_n] with |xi| = 1 for any i ∈ {1, 2,..., n}. We describe all possible differential structures on DG polynomial algebras, compute their DG automorphism groups, study their isomorphism problems, and show that they are all homologically smooth and Gorenstein DG algebras. Furthermore, it is proved that the DG polynomial algebra A is a Calabi-Yau DG algebra when its differential ?_A≠ 0 and the trivial DG polynomial algebra(A, 0) is Calabi-Yau if and only if n is an odd integer.展开更多
With the prevalence of various sensors and smart devices in people’s daily lives,numerous types of information are being sensed.While using such information provides critical and convenient services,we are gradually ...With the prevalence of various sensors and smart devices in people’s daily lives,numerous types of information are being sensed.While using such information provides critical and convenient services,we are gradually exposing every piece of our behavior and activities.Researchers are aware of the privacy risks and have been working on preserving privacy while sensing human activities.This survey reviews existing studies on privacy-preserving human activity sensing.We first introduce the sensors and captured private information related to human activities.We then propose a taxonomy to structure the methods for preserving private information from two aspects:individual and collaborative activity sensing.For each of the two aspects,the methods are classified into three levels:signal,algorithm,and system.Finally,we discuss the open challenges and provide future directions.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11001056)the China Postdoctoral Science Foundation (Grant Nos. 20090450066 and 201003244)+1 种基金the Key Disciplines of Shanghai Municipality (Grant No. S30104)the Innovation Program of Shanghai Municipal Education Commission (Grant No. 12YZ031)
文摘In this paper, we introduce and study differential graded(DG for short) polynomial algebras. In brief, a DG polynomial algebra A is a connected cochain DG algebra such that its underlying graded algebra A~# is a polynomial algebra K[x_1, x_2,..., x_n] with |xi| = 1 for any i ∈ {1, 2,..., n}. We describe all possible differential structures on DG polynomial algebras, compute their DG automorphism groups, study their isomorphism problems, and show that they are all homologically smooth and Gorenstein DG algebras. Furthermore, it is proved that the DG polynomial algebra A is a Calabi-Yau DG algebra when its differential ?_A≠ 0 and the trivial DG polynomial algebra(A, 0) is Calabi-Yau if and only if n is an odd integer.
基金supported by the National Key Research and Development Program of China(2021YFB3100400)National Natural Science Foundation of China(62302274,62202276 and 62232010)+3 种基金Shandong Science Fund for Excellent Young Scholars,China(2022HWYQ-038)Natural Science Foundation of Shandong,China(ZR2023QF113)financial support of Lingnan University(LU),China(DB23A4)Lam Woo Research Fund at LU,China(871236)。
文摘With the prevalence of various sensors and smart devices in people’s daily lives,numerous types of information are being sensed.While using such information provides critical and convenient services,we are gradually exposing every piece of our behavior and activities.Researchers are aware of the privacy risks and have been working on preserving privacy while sensing human activities.This survey reviews existing studies on privacy-preserving human activity sensing.We first introduce the sensors and captured private information related to human activities.We then propose a taxonomy to structure the methods for preserving private information from two aspects:individual and collaborative activity sensing.For each of the two aspects,the methods are classified into three levels:signal,algorithm,and system.Finally,we discuss the open challenges and provide future directions.
