We review the constructions of two main kinds of generalized cyclotomic binary sequences with length pq （the product with two distinct primes）. One is the White-generalized cyclotomic sequences, the other is the Din...We review the constructions of two main kinds of generalized cyclotomic binary sequences with length pq （the product with two distinct primes）. One is the White-generalized cyclotomic sequences, the other is the Ding-Helleseth（DH, for short）-generalized cyclotomic sequences. We present some new pseudo-random properties of DH-generalized cyclotomic sequences using the theory of character sums instead of the theory of cyclotomy, which is a conventional method for investigating generalized cyclotomic sequences.展开更多
We present the basic idea of abstract principal component analysis(APCA)as a general approach that extends various popular data analysis techniques such as PCA and GPCA.We describe the mathematical theory behind APCA ...We present the basic idea of abstract principal component analysis(APCA)as a general approach that extends various popular data analysis techniques such as PCA and GPCA.We describe the mathematical theory behind APCA and focus on a particular application to mode extractions from a data set of mixed temporal and spatial signals.For illustration,algorithmic implementation details and numerical examples are presented for the extraction of a number of basic types of wave modes including,in particular,dynamic modes involving spatial shifts.展开更多
基金supported in part by the Open Funds of Key Lab of Fujian Province University Network Security and Cryptology(Grant No. 07B005)the Funds of the Education Department of Fujian Province (Grant No. JA07164) the Natural Science Foundation of Fujian Province of China (Grant No. 2007F3086).
文摘We review the constructions of two main kinds of generalized cyclotomic binary sequences with length pq （the product with two distinct primes）. One is the White-generalized cyclotomic sequences, the other is the Ding-Helleseth（DH, for short）-generalized cyclotomic sequences. We present some new pseudo-random properties of DH-generalized cyclotomic sequences using the theory of character sums instead of the theory of cyclotomy, which is a conventional method for investigating generalized cyclotomic sequences.
基金supported by National Science Foundation of USA(Grant No.DMS101607)
文摘We present the basic idea of abstract principal component analysis(APCA)as a general approach that extends various popular data analysis techniques such as PCA and GPCA.We describe the mathematical theory behind APCA and focus on a particular application to mode extractions from a data set of mixed temporal and spatial signals.For illustration,algorithmic implementation details and numerical examples are presented for the extraction of a number of basic types of wave modes including,in particular,dynamic modes involving spatial shifts.
