This paper is concerned with (3,n) and (4,n) regular quasi-cyclic Low Density Parity Check (LDPC) code constructions from elementary number theory.Given the column weight,we determine the shift values of the circulant...This paper is concerned with (3,n) and (4,n) regular quasi-cyclic Low Density Parity Check (LDPC) code constructions from elementary number theory.Given the column weight,we determine the shift values of the circulant permutation matrices via arithmetic analysis.The proposed constructions of quasi-cyclic LDPC codes achieve the following main advantages simultaneously:1) our methods are constructive in the sense that we avoid any searching process;2) our methods ensure no four or six cycles in the bipartite graphs corresponding to the LDPC codes;3) our methods are direct constructions of quasi-cyclic LDPC codes which do not use any other quasi-cyclic LDPC codes of small length like component codes or any other algorithms/cyclic codes like building block;4)the computations of the parameters involved are based on elementary number theory,thus very simple and fast.Simulation results show that the constructed regular codes of high rates perform almost 1.25 dB above Shannon limit and have no error floor down to the bit-error rate of 10-6.展开更多
Digital Number(DN)是信息科学关于信息采集的术语,需要界定和理顺DN各方面的关系,解决DN在遥感技术、数学、计算机科学的表达问题。阐述DN基本认识及其应有常态,给出DN名称和DN含义,梳理DN来源及其演变,明确DN与模拟量关系、DN与数值...Digital Number(DN)是信息科学关于信息采集的术语,需要界定和理顺DN各方面的关系,解决DN在遥感技术、数学、计算机科学的表达问题。阐述DN基本认识及其应有常态,给出DN名称和DN含义,梳理DN来源及其演变,明确DN与模拟量关系、DN与数值关系及DN与非DN界限,陈述数字结构、数字标识及不同系统层面DN,形成10方面正面共识,供分析对照。对DN表达问题归纳为DN代表关系、技术关系、数学关系、数值关系、标识关系5种类型,分析这些相应关系的表达缺陷,对DN有关方面做表达示范。创新成果:界定DN与模拟量关系;归纳DN的感性错误与其错误导向关系;重新解释数值及数值类型,对数值做定义,数值类型应包括DN分支,数值应包括DN来源成员;完善DN、数值及非数值式中参数的相应描述;规范数字术语在数字技术及数学的使用。达到提高DN及其关联的认识,促进数学的发展,利于消除遥感技术、数学、计算机科学出现的DN各种表达问题。展开更多
By combination of finite number theory and quantum information, the complete quantum information in the <em>DNA</em> genetic code has been made likely by <em>Planat et al</em>. (2020). In the p...By combination of finite number theory and quantum information, the complete quantum information in the <em>DNA</em> genetic code has been made likely by <em>Planat et al</em>. (2020). In the present contribution a varied quartic polynomial contrasting the polynomial used by <em>Planat et al</em>. is proposed that considered apart from the golden mean also the fifth power of this dominant number of nature to adapt the code information. The suggested polynomial is denoted as <em>g</em>(<em>x</em>) = <em>x</em><sup>4</sup> - <em>x</em><sup>3</sup> - (4 - <em><i style="white-space:normal;">ϕ</i></em><sup>2</sup> )<em>x</em><sup>2</sup> + (4 – <i>ϕ</i><sup>2</sup>)x + 1, where <img src="Edit_40efe764-d690-499f-8424-129f9ca46f78.bmp" alt="" /> is the golden mean. Its roots are changed to more golden mean based ones in comparison to the <em>Planat</em> polynomial. The new coefficients 4 – <em>ϕ</em><sup>2</sup> instead of 4 would implement the fifth power of the golden mean indirectly applying <img src="Edit_5b44b644-3f59-4fad-a586-ec5345ba6be4.bmp" alt="" />. As an outlook, it should be emphesized that the connection between genetic code and resonance code of the <em>DNA</em> may lead us to a full understanding of how nature stores and processes compacted information and what indeed is consciousness linking everything with each other suggestedly mediated by all-pervasive dark constituents of matter respectively energy. The number-theoretical approach to <em>DNA</em> coding leads to the question about the helical structure of the electron.展开更多
Recently,both the importance and awareness relating to food safety relating to agrochemicals,chemical fertilizers,the pollution of ecosystem and unwholesome foods are growing rapidly.For the same reason,the purchaser&...Recently,both the importance and awareness relating to food safety relating to agrochemicals,chemical fertilizers,the pollution of ecosystem and unwholesome foods are growing rapidly.For the same reason,the purchaser's curiosity increases to know about the production process which can be accomplished by production traceability system.The traceability system can store and superintend the specific attribute information about products regarding the productive centre,producer and production finish data.The products undergo various circulation processes and they are being managed by individually constructed traceability system.Thus,it is difficult for the producer and the consumer to guarantee the safety from transpirable issues about the falsification of production traceability because the traceability information can be re-produced by forging through various ways.So in this paper,we proposed a system for integrated management of agro-fishery products based on quick response code(QR-code)for forgery prevention which may help to solve these issues.The proposed system makes QR-code using production information provided by producer.And then it is provided to the distributor and the consumer through integrated service model using the QR-code.Therefore,this system make sure to provide the same production traceability about the products to the distributor and the consumer and always keeps both updated with the same information.展开更多
Let G =( V,E) be a connected graph and W = { w_1,w_2,…,w_k} be an ordered subset of V( G).For any vertex v ∈V,the locating code of v with respect to W is the k-vector CW( v) = { d( v,w_1),d( v,w_2),…,d( v,w_k) },W ...Let G =( V,E) be a connected graph and W = { w_1,w_2,…,w_k} be an ordered subset of V( G).For any vertex v ∈V,the locating code of v with respect to W is the k-vector CW( v) = { d( v,w_1),d( v,w_2),…,d( v,w_k) },W is said to be a locating set of G if distinct vertices have the distinct locating code,and the locating number of G is defined as: Loc( G) = min{ | W| : W is a locating set of G}.We study the locating set and locating number of a graph G,obtain some bounds for the locating numbers of graphs,and determine the exact value of Loc( G) for some special classes of graphs,such as cycles,wheels,complete t-partite graph and some Cartesian products of paths and cycles. In addition,we also prove that Loc( T) ≥Δ-1 holds for all trees T with maximum degree Δ,and shows a tree T with Loc( T) = Δ-1.展开更多
The plasma shape and other paremeters such as /3P, li is important for the tokamak deveice where the plasma has a non-circular cross-section of sufficient elongation. The measuered signals of magnetic probes and flux ...The plasma shape and other paremeters such as /3P, li is important for the tokamak deveice where the plasma has a non-circular cross-section of sufficient elongation. The measuered signals of magnetic probes and flux loops are used to reconstruct the plasma shape and the current profile in device operation and plasma shape feed back control system. So the number and positions of magnetic probes and flux loops provides the basis of the plasma reconstruction. This paper instroduce how to use EFIT code (equilibrium fitting code) to determine the number and positions of the magnetic probes and flux loops. The simulation result is given also.展开更多
With the challenge of quantum computing ahead, an analysis of number and representation adequate to the task is needed. Some clarifications on the combinatorial nature of representation are presented here;this is rela...With the challenge of quantum computing ahead, an analysis of number and representation adequate to the task is needed. Some clarifications on the combinatorial nature of representation are presented here;this is related to the foundations of digital representations of integers, and is thus also of interest in clarifying what numbers are and how they are used in pure and applied mathematics. The author hopes this work will help mathematicians and computer scientists better understand the nature of the Generalized Knapsack Code, a lattice-based code which the author believes to be particularly promising, and the use of number in computing in general.展开更多
ABSTRACT． Led。 be the n^(th) Lucas number， n＞0． Let p be an odd prime． In this paperwe prove a general theorem． According to the theorem we give an algorithm by using whichthe equationl-(n)＝px^(2) can be ...ABSTRACT． Led。 be the n^(th) Lucas number， n＞0． Let p be an odd prime． In this paperwe prove a general theorem． According to the theorem we give an algorithm by using whichthe equationl-(n)＝px^(2) can be solved for arbitrary given p．Por example，we find its all solutionsfor 1000＜p＜40000． By the end of the paper an Interestingconjecture Is presented．展开更多
This article proves the existence of a hyper-precise global numerical meta-architecture unifying, structuring, binding and controlling the billion triplet codons constituting the sequence of single-stranded DNA of the...This article proves the existence of a hyper-precise global numerical meta-architecture unifying, structuring, binding and controlling the billion triplet codons constituting the sequence of single-stranded DNA of the entire human genome. Beyond the evolution and erratic mutations like transposons within the genome, it’s as if the memory of a fossil genome with multiple symmetries persists. This recalls the “intermingling” of information characterizing the fractal universe of chaos theory. The result leads to a balanced and perfect tuning between the masses of the two strands of the huge DNA molecule that constitute our genome. We show here how codon populations forming the single-stranded DNA sequences can constitute a critical approach to the understanding of junk DNA function. Then, we suggest revisiting certain methods published in our 2009 book “Codex Biogenesis”. In fact, we demonstrate here how the universal genetic code table is a powerful analytical filter to characterize single-stranded DNA sequences constituting chromosomes and genomes. We can then show that any genomic DNA sequence is featured by three numbers, which characterize it and its 64 codon populations with correlations greater than 99%. The number “1” is common to all sequences, expressing the second law of Chargaff. The other 2 numbers are related to each specific DNA sequence case characterizing life species. For example, the entire human genome is characterized by three remarkable numbers 1, 2, and Phi = 1.618 the golden ratio. Associated with each of these three numbers, we can match three axes of symmetry, then “imagine” a kind of hyperspace formed by these codon populations. Then we revisit the value (3-Phi)/2 which is probably universal and common to both the scale of quarks and atomic levels, balancing and tuning the whole human genome codon population. Finally, we demonstrate a new kind of duality between “form and substance” overlapping the whole human genome: we will show that—simultaneously with the duality between genes and junk DNA—there is a second layer of embedded hidden structure overlapping all the DNA of the whole human genome, dividing it into a second type of duality information/redundancy involving golden ratio proportions.展开更多
A novel drop unit for the optical code-division multiple access(OCDMA) based on fiber Bragg gratings and two-dimensional wavelength-time code is studied.The simple OCDMA drop unit can drop a code channel without distu...A novel drop unit for the optical code-division multiple access(OCDMA) based on fiber Bragg gratings and two-dimensional wavelength-time code is studied.The simple OCDMA drop unit can drop a code channel without disturbing the rest code channels.A similar unit for dropping a group of code channels is also proposed.Numerical simulation is given.The system delay can decrease by substituting the electrieal driving optical switch with a specific optical driving.The single channel drop unit can also be the basis for multiple channels drop.展开更多
A low-complexity algorithm is proposed in this paper in order to optimize irregular low-density parity-check （LDPC） codes.The algorithm proposed can calculate the noise threshold by means of a one-dimensional densit...A low-complexity algorithm is proposed in this paper in order to optimize irregular low-density parity-check （LDPC） codes.The algorithm proposed can calculate the noise threshold by means of a one-dimensional density evolution and search the optimal degree profiles with fast-convergence differential evolution,so that it has a lower complexity and a faster convergence speed.Simulation resuits show that the irregular LDPC codes optimized by the presented algorithm can also perform better than Turbo codes at moderate block length even with less computation cost.展开更多
By exploiting the structural features of L1C messages,a novel Early Termination( ET) strategy is proposed to speed up the decoding of low-density parity-check( LDPC) codes in the GPS system. The proposed strategy is b...By exploiting the structural features of L1C messages,a novel Early Termination( ET) strategy is proposed to speed up the decoding of low-density parity-check( LDPC) codes in the GPS system. The proposed strategy is based on the cyclic redundancy check( CRC) of the messages in the subframes 2 and 3. The simulation results show that average number of iterations of the proposed strategy is less than that of the standard ET strategy,with nearly no degradation in decoding performance. Besides,the proposed ET strategy can be efficiently implemented in a sequential or parallel manner. Thus,the proposed ET strategy is attractive for practical purposes.展开更多
为解析柠檬草[Cymbopogon citratus(DC.)Stapf]叶绿体基因组密码子使用偏好及其进化驱动因素,通过系统分析其密码子模式,为后续基因组功能研究与种质资源开发提供依据。基于美国国家生物技术信息中心(national center for biotechnology...为解析柠檬草[Cymbopogon citratus(DC.)Stapf]叶绿体基因组密码子使用偏好及其进化驱动因素,通过系统分析其密码子模式,为后续基因组功能研究与种质资源开发提供依据。基于美国国家生物技术信息中心(national center for biotechnology information,NCBI)数据库获取柠檬草叶绿体基因组完整序列,筛选50条蛋白质编码序列(protein-coding sequences,CDS)。结合有效密码子数量绘图(effective number of codons plot,ENC-plot)、奇偶规则2绘图(parity rule 2 plot,PR2-plot)和中性绘图等方法,探究密码子使用偏好性及影响因素。柠檬草叶绿体基因组整体鸟嘌呤和胞嘧啶(guanine and cytosine,GC)含量为38.70%,第3位GC含量(GC_(3))均值为29.60%,均低于其他同科物种。密码子适应指数(codon adaptation index,CAI)均值为0.17,有效密码子数量(effective number of codons,ENC)均值为48.62,表明密码子偏好性较弱。筛选出30个高频使用密码子,其中26个为高表达密码子;进一步确定12个兼具高频率与高表达密度的最优密码子,如亮氨酸和丙氨酸等。该研究表明,自然选择是柠檬草叶绿体基因组密码子偏好性形成的主要驱动力。展开更多
基金supported by the National Natural Science Foundation of China under Grants No.61172085,No.61103221,No.61133014,No.11061130539 and No.61021004
文摘This paper is concerned with (3,n) and (4,n) regular quasi-cyclic Low Density Parity Check (LDPC) code constructions from elementary number theory.Given the column weight,we determine the shift values of the circulant permutation matrices via arithmetic analysis.The proposed constructions of quasi-cyclic LDPC codes achieve the following main advantages simultaneously:1) our methods are constructive in the sense that we avoid any searching process;2) our methods ensure no four or six cycles in the bipartite graphs corresponding to the LDPC codes;3) our methods are direct constructions of quasi-cyclic LDPC codes which do not use any other quasi-cyclic LDPC codes of small length like component codes or any other algorithms/cyclic codes like building block;4)the computations of the parameters involved are based on elementary number theory,thus very simple and fast.Simulation results show that the constructed regular codes of high rates perform almost 1.25 dB above Shannon limit and have no error floor down to the bit-error rate of 10-6.
文摘By combination of finite number theory and quantum information, the complete quantum information in the <em>DNA</em> genetic code has been made likely by <em>Planat et al</em>. (2020). In the present contribution a varied quartic polynomial contrasting the polynomial used by <em>Planat et al</em>. is proposed that considered apart from the golden mean also the fifth power of this dominant number of nature to adapt the code information. The suggested polynomial is denoted as <em>g</em>(<em>x</em>) = <em>x</em><sup>4</sup> - <em>x</em><sup>3</sup> - (4 - <em><i style="white-space:normal;">ϕ</i></em><sup>2</sup> )<em>x</em><sup>2</sup> + (4 – <i>ϕ</i><sup>2</sup>)x + 1, where <img src="Edit_40efe764-d690-499f-8424-129f9ca46f78.bmp" alt="" /> is the golden mean. Its roots are changed to more golden mean based ones in comparison to the <em>Planat</em> polynomial. The new coefficients 4 – <em>ϕ</em><sup>2</sup> instead of 4 would implement the fifth power of the golden mean indirectly applying <img src="Edit_5b44b644-3f59-4fad-a586-ec5345ba6be4.bmp" alt="" />. As an outlook, it should be emphesized that the connection between genetic code and resonance code of the <em>DNA</em> may lead us to a full understanding of how nature stores and processes compacted information and what indeed is consciousness linking everything with each other suggestedly mediated by all-pervasive dark constituents of matter respectively energy. The number-theoretical approach to <em>DNA</em> coding leads to the question about the helical structure of the electron.
基金The MSIP(Ministry of Science,ICT&Future Planning),Korea,under the ITRC(Information Technology Research Center)support program(NIPA-2013-H0301-13-2006)supervised by the NIPA(National IT Industry Promotion Agency)
文摘Recently,both the importance and awareness relating to food safety relating to agrochemicals,chemical fertilizers,the pollution of ecosystem and unwholesome foods are growing rapidly.For the same reason,the purchaser's curiosity increases to know about the production process which can be accomplished by production traceability system.The traceability system can store and superintend the specific attribute information about products regarding the productive centre,producer and production finish data.The products undergo various circulation processes and they are being managed by individually constructed traceability system.Thus,it is difficult for the producer and the consumer to guarantee the safety from transpirable issues about the falsification of production traceability because the traceability information can be re-produced by forging through various ways.So in this paper,we proposed a system for integrated management of agro-fishery products based on quick response code(QR-code)for forgery prevention which may help to solve these issues.The proposed system makes QR-code using production information provided by producer.And then it is provided to the distributor and the consumer through integrated service model using the QR-code.Therefore,this system make sure to provide the same production traceability about the products to the distributor and the consumer and always keeps both updated with the same information.
基金Sponsored by the National Natural Science Foundation of China(Grant Nos.11361024,61472138)the Provincial Natural Science Foundation(Grant Nos.20171BAB201009,20161BAB202066)the Jiangxi Provincial Science and Technology Project(Grant No.KJLD12067)
文摘Let G =( V,E) be a connected graph and W = { w_1,w_2,…,w_k} be an ordered subset of V( G).For any vertex v ∈V,the locating code of v with respect to W is the k-vector CW( v) = { d( v,w_1),d( v,w_2),…,d( v,w_k) },W is said to be a locating set of G if distinct vertices have the distinct locating code,and the locating number of G is defined as: Loc( G) = min{ | W| : W is a locating set of G}.We study the locating set and locating number of a graph G,obtain some bounds for the locating numbers of graphs,and determine the exact value of Loc( G) for some special classes of graphs,such as cycles,wheels,complete t-partite graph and some Cartesian products of paths and cycles. In addition,we also prove that Loc( T) ≥Δ-1 holds for all trees T with maximum degree Δ,and shows a tree T with Loc( T) = Δ-1.
基金The project supported by the National Meg-Science Engineering Project of the Chinese Government
文摘The plasma shape and other paremeters such as /3P, li is important for the tokamak deveice where the plasma has a non-circular cross-section of sufficient elongation. The measuered signals of magnetic probes and flux loops are used to reconstruct the plasma shape and the current profile in device operation and plasma shape feed back control system. So the number and positions of magnetic probes and flux loops provides the basis of the plasma reconstruction. This paper instroduce how to use EFIT code (equilibrium fitting code) to determine the number and positions of the magnetic probes and flux loops. The simulation result is given also.
文摘With the challenge of quantum computing ahead, an analysis of number and representation adequate to the task is needed. Some clarifications on the combinatorial nature of representation are presented here;this is related to the foundations of digital representations of integers, and is thus also of interest in clarifying what numbers are and how they are used in pure and applied mathematics. The author hopes this work will help mathematicians and computer scientists better understand the nature of the Generalized Knapsack Code, a lattice-based code which the author believes to be particularly promising, and the use of number in computing in general.
文摘ABSTRACT． Led。 be the n^(th) Lucas number， n＞0． Let p be an odd prime． In this paperwe prove a general theorem． According to the theorem we give an algorithm by using whichthe equationl-(n)＝px^(2) can be solved for arbitrary given p．Por example，we find its all solutionsfor 1000＜p＜40000． By the end of the paper an Interestingconjecture Is presented．
文摘This article proves the existence of a hyper-precise global numerical meta-architecture unifying, structuring, binding and controlling the billion triplet codons constituting the sequence of single-stranded DNA of the entire human genome. Beyond the evolution and erratic mutations like transposons within the genome, it’s as if the memory of a fossil genome with multiple symmetries persists. This recalls the “intermingling” of information characterizing the fractal universe of chaos theory. The result leads to a balanced and perfect tuning between the masses of the two strands of the huge DNA molecule that constitute our genome. We show here how codon populations forming the single-stranded DNA sequences can constitute a critical approach to the understanding of junk DNA function. Then, we suggest revisiting certain methods published in our 2009 book “Codex Biogenesis”. In fact, we demonstrate here how the universal genetic code table is a powerful analytical filter to characterize single-stranded DNA sequences constituting chromosomes and genomes. We can then show that any genomic DNA sequence is featured by three numbers, which characterize it and its 64 codon populations with correlations greater than 99%. The number “1” is common to all sequences, expressing the second law of Chargaff. The other 2 numbers are related to each specific DNA sequence case characterizing life species. For example, the entire human genome is characterized by three remarkable numbers 1, 2, and Phi = 1.618 the golden ratio. Associated with each of these three numbers, we can match three axes of symmetry, then “imagine” a kind of hyperspace formed by these codon populations. Then we revisit the value (3-Phi)/2 which is probably universal and common to both the scale of quarks and atomic levels, balancing and tuning the whole human genome codon population. Finally, we demonstrate a new kind of duality between “form and substance” overlapping the whole human genome: we will show that—simultaneously with the duality between genes and junk DNA—there is a second layer of embedded hidden structure overlapping all the DNA of the whole human genome, dividing it into a second type of duality information/redundancy involving golden ratio proportions.
基金Supported by National Hi-tech863 project(No.2002 AA 311141)
文摘A novel drop unit for the optical code-division multiple access(OCDMA) based on fiber Bragg gratings and two-dimensional wavelength-time code is studied.The simple OCDMA drop unit can drop a code channel without disturbing the rest code channels.A similar unit for dropping a group of code channels is also proposed.Numerical simulation is given.The system delay can decrease by substituting the electrieal driving optical switch with a specific optical driving.The single channel drop unit can also be the basis for multiple channels drop.
基金Leading Academic Discipline Project of Shanghai Municipal Education Commission,China(No.J51801)Shanghai Second Polytechnic University Foundation,China(No.QD209008)Leading Academic Discipline Project of Shanghai Second Polytechnic University,China(No.XXKZD1302)
文摘A low-complexity algorithm is proposed in this paper in order to optimize irregular low-density parity-check （LDPC） codes.The algorithm proposed can calculate the noise threshold by means of a one-dimensional density evolution and search the optimal degree profiles with fast-convergence differential evolution,so that it has a lower complexity and a faster convergence speed.Simulation resuits show that the irregular LDPC codes optimized by the presented algorithm can also perform better than Turbo codes at moderate block length even with less computation cost.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61271423)
文摘By exploiting the structural features of L1C messages,a novel Early Termination( ET) strategy is proposed to speed up the decoding of low-density parity-check( LDPC) codes in the GPS system. The proposed strategy is based on the cyclic redundancy check( CRC) of the messages in the subframes 2 and 3. The simulation results show that average number of iterations of the proposed strategy is less than that of the standard ET strategy,with nearly no degradation in decoding performance. Besides,the proposed ET strategy can be efficiently implemented in a sequential or parallel manner. Thus,the proposed ET strategy is attractive for practical purposes.
文摘为解析柠檬草[Cymbopogon citratus(DC.)Stapf]叶绿体基因组密码子使用偏好及其进化驱动因素,通过系统分析其密码子模式,为后续基因组功能研究与种质资源开发提供依据。基于美国国家生物技术信息中心(national center for biotechnology information,NCBI)数据库获取柠檬草叶绿体基因组完整序列,筛选50条蛋白质编码序列(protein-coding sequences,CDS)。结合有效密码子数量绘图(effective number of codons plot,ENC-plot)、奇偶规则2绘图(parity rule 2 plot,PR2-plot)和中性绘图等方法,探究密码子使用偏好性及影响因素。柠檬草叶绿体基因组整体鸟嘌呤和胞嘧啶(guanine and cytosine,GC)含量为38.70%,第3位GC含量(GC_(3))均值为29.60%,均低于其他同科物种。密码子适应指数(codon adaptation index,CAI)均值为0.17,有效密码子数量(effective number of codons,ENC)均值为48.62,表明密码子偏好性较弱。筛选出30个高频使用密码子,其中26个为高表达密码子;进一步确定12个兼具高频率与高表达密度的最优密码子,如亮氨酸和丙氨酸等。该研究表明,自然选择是柠檬草叶绿体基因组密码子偏好性形成的主要驱动力。
