On the basis of information theory and statistical methods, we use mutual information, n- tuple entropy and conditional entropy, combined with biological characteristics, to analyze the long range correlation and shor...On the basis of information theory and statistical methods, we use mutual information, n- tuple entropy and conditional entropy, combined with biological characteristics, to analyze the long range correlation and short range correlation in human Y chromosome palindromes. The magnitude distribution of the long range correlation which can be reflected by the mutual information is PS〉PSa〉PSb （P5a and P5b are the sequences that replace solely Alu repeats and all interspersed repeats with random uneorrelated sequences in human Y chromosome palindrome 5, respectively）; and the magnitude distribution of the short range correlation which can be reflected by the n-tuple entropy and the conditional entropy is PS〉P5a〉PSb〉random uncorrelated sequence. In other words, when the Alu repeats and all interspersed repeats replace with random uneorrelated sequence, the long range and short range correlation decrease gradually. However, the random nncorrelated sequence has no correlation. This research indicates that more repeat sequences result in stronger correlation between bases in human Y chromosome. The analyses may be helpful to understand the special structures of human Y chromosome palindromes profoundly.展开更多
We analyze for the first time the rules of breaking in an X-palindrome between human and chimpanzee. Results indicate that although the overall changes that occurred in the human X-palindrome are fewer than in the chi...We analyze for the first time the rules of breaking in an X-palindrome between human and chimpanzee. Results indicate that although the overall changes that occurred in the human X-palindrome are fewer than in the chimpanzee, mutations occurring between the left arm and right arm were nearly equivalent both in human and chimpanzee when compared with orangutan, which implies evolutionary synchronization. However, there are many more A/T→G/C changes than G/C→A/T in a single arm, which would lead to an increasing trend in GC content and suggest that the composition is not at equilibrium. In addition, it is remarkable to find that there are much more asymmetrical nucleotide changes between the two arms of the human palindrome than that of the chimpanzee palindrome, and these mutations are prone to occur between bases with similar chemical structures. The symmetry seems higher in the chimpanzee palindrome than in the human X-palindrome.展开更多
Palindrome number conjecture: Take any non-palindromic natural number with two or more digits, add its inverse ordinal number, continue to use the inverted number of sum plus sum, repeat this process continuously. Aft...Palindrome number conjecture: Take any non-palindromic natural number with two or more digits, add its inverse ordinal number, continue to use the inverted number of sum plus sum, repeat this process continuously. After a finite number of operations, a palindrome number must be obtained. We firstly give out several definitions: The pure-single-digit-of-sum is the number of single digits that only count the sum of two numbers of the same digit in the vertical operation of addition, which is referred to as pure single digit for short, denoted by g. The pure-carry-digit-of-sum is the carry digit that only counts the sum of two numbers in the same bit in the vertical operation of addition. It is a special number composed of only 1 and 0, which is represented by j'. The complement-0-carry-digit-of-sum is to supplement a 0 on the last side of j' according to the rule of adding bits, which is denoted by j. Therefore, in the addition operation, the sum of any natural number and its inverse ordinal number is divided into two parts: g and j. Then, the characteristics of g and j are characterized by the following two theorems: Theorem 1: As all the numbers in j are 0, j is the palindrome number;As the numbers in j are not all 0, j is not a palindrome number. Theorem 2: The sum of any palindrome number H and any non-palindrome j number must be a non-palindrome number. Then we proved the palindrome number conjecture is not correct by using the above two theorems.展开更多
This paper presents a novel approach to improve aliasing rejection in comb-based decimation filters. The method is established on certain palindromic polynomials with all zeros on the unit circle and the sharpening te...This paper presents a novel approach to improve aliasing rejection in comb-based decimation filters. The method is established on certain palindromic polynomials with all zeros on the unit circle and the sharpening technique. As a result, aliasing rejection and the passband characteristic are improved. The method is illustrated with various examples and compared with the methods from the literature. .展开更多
基金This work was supported by the National Natu- ral Science Foundation of China （No.20173023 and No.90203012） and the Specialized Research Fund for the Doctoral Program of Higher Education of China （No.20020730006）.
文摘On the basis of information theory and statistical methods, we use mutual information, n- tuple entropy and conditional entropy, combined with biological characteristics, to analyze the long range correlation and short range correlation in human Y chromosome palindromes. The magnitude distribution of the long range correlation which can be reflected by the mutual information is PS〉PSa〉PSb （P5a and P5b are the sequences that replace solely Alu repeats and all interspersed repeats with random uneorrelated sequences in human Y chromosome palindrome 5, respectively）; and the magnitude distribution of the short range correlation which can be reflected by the n-tuple entropy and the conditional entropy is PS〉P5a〉PSb〉random uncorrelated sequence. In other words, when the Alu repeats and all interspersed repeats replace with random uneorrelated sequence, the long range and short range correlation decrease gradually. However, the random nncorrelated sequence has no correlation. This research indicates that more repeat sequences result in stronger correlation between bases in human Y chromosome. The analyses may be helpful to understand the special structures of human Y chromosome palindromes profoundly.
基金ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China （No.20173023 and No.90203012） and the Specialized Research Fund for the Doctoral Program of Higher Education of China （No.20020730006）.
文摘We analyze for the first time the rules of breaking in an X-palindrome between human and chimpanzee. Results indicate that although the overall changes that occurred in the human X-palindrome are fewer than in the chimpanzee, mutations occurring between the left arm and right arm were nearly equivalent both in human and chimpanzee when compared with orangutan, which implies evolutionary synchronization. However, there are many more A/T→G/C changes than G/C→A/T in a single arm, which would lead to an increasing trend in GC content and suggest that the composition is not at equilibrium. In addition, it is remarkable to find that there are much more asymmetrical nucleotide changes between the two arms of the human palindrome than that of the chimpanzee palindrome, and these mutations are prone to occur between bases with similar chemical structures. The symmetry seems higher in the chimpanzee palindrome than in the human X-palindrome.
文摘Palindrome number conjecture: Take any non-palindromic natural number with two or more digits, add its inverse ordinal number, continue to use the inverted number of sum plus sum, repeat this process continuously. After a finite number of operations, a palindrome number must be obtained. We firstly give out several definitions: The pure-single-digit-of-sum is the number of single digits that only count the sum of two numbers of the same digit in the vertical operation of addition, which is referred to as pure single digit for short, denoted by g. The pure-carry-digit-of-sum is the carry digit that only counts the sum of two numbers in the same bit in the vertical operation of addition. It is a special number composed of only 1 and 0, which is represented by j'. The complement-0-carry-digit-of-sum is to supplement a 0 on the last side of j' according to the rule of adding bits, which is denoted by j. Therefore, in the addition operation, the sum of any natural number and its inverse ordinal number is divided into two parts: g and j. Then, the characteristics of g and j are characterized by the following two theorems: Theorem 1: As all the numbers in j are 0, j is the palindrome number;As the numbers in j are not all 0, j is not a palindrome number. Theorem 2: The sum of any palindrome number H and any non-palindrome j number must be a non-palindrome number. Then we proved the palindrome number conjecture is not correct by using the above two theorems.
文摘This paper presents a novel approach to improve aliasing rejection in comb-based decimation filters. The method is established on certain palindromic polynomials with all zeros on the unit circle and the sharpening technique. As a result, aliasing rejection and the passband characteristic are improved. The method is illustrated with various examples and compared with the methods from the literature. .
