How neuronal spike trains encode external information is a hot topic in neurodynamics studies. In this paper, we investigate the dynamical states of the Hodgkin-Huxley neuron under periodic forcing. Depending on the p...How neuronal spike trains encode external information is a hot topic in neurodynamics studies. In this paper, we investigate the dynamical states of the Hodgkin-Huxley neuron under periodic forcing. Depending on the parameters of the stimulus, the neuron exhibits periodic, quasiperiodic and chaotic spike trains. In order to analyze these spike trains quantitatively, we use the phase return map to describe the dynamical behavior on a one-dimensional （1D） map. According to the monotonicity or discontinuous point of the 1D map, the spike trains are transformed into symbolic sequences by implementing a coarse-grained algorithm -- symbolic dynamics. Based on the ordering rules of symbolic dynamics, the parameters of the external stimulus can be measured in high resolution with finite length symbolic sequences. A reasonable explanation for why the nervous system can discriminate or cognize the small change of the external signals in a short time is also presented.展开更多
The symbolization of land polygon is an important part of cartography. In the mapping of traditional present land-use maps, the symbol of land polygons was usually filled by the method of filling or plotting, but thes...The symbolization of land polygon is an important part of cartography. In the mapping of traditional present land-use maps, the symbol of land polygons was usually filled by the method of filling or plotting, but these methods can't solve the spatial conflicts of the symbol. According to the principle of cartography, the rule of how to symbolize the land polygon was summarized, and a new method that can generate and deploy the land symbols was presented. By making use of C# programming language and Arc Engine developing components, the algorithm can generate land symbols presenting triangle and adjust the coordinate of the symbol. Through mapping the present land-use map of Honghe county, this algorithm can reduce 88.84% of the spatial conflicts error rate compared with the traditional methods. It improves the accuracy and efficiency of the map symbolic.展开更多
The symbolic dynamics of a Belykh-type map （a two-dimensional discon- tinuous piecewise linear map） is investigated. The admissibility condition for symbol sequences named the pruning front conjecture is proved unde...The symbolic dynamics of a Belykh-type map （a two-dimensional discon- tinuous piecewise linear map） is investigated. The admissibility condition for symbol sequences named the pruning front conjecture is proved under a hyperbolicity condition. Using this result, a symbolic dynamics model of the map is constructed according to its pruning front and primary pruned region. Moreover, the boundary of the parameter region in which the map is chaotic of a horseshoe type is given.展开更多
On the basis of analysis of various algorithms, an anti-aliasing algorithm called brush method was presented, which is suitable to map publishing symbol. Aftes introducing the basic principle and implementation of bru...On the basis of analysis of various algorithms, an anti-aliasing algorithm called brush method was presented, which is suitable to map publishing symbol. Aftes introducing the basic principle and implementation of brush method in detail, the result and efficiency were evaluated through experiments.展开更多
A novel computationally efficient algorithm in terms of the time-varying symbolic dynamic method is proposed to estimate the unknown initial conditions of coupled map lattices （CMLs）. The presented method combines s...A novel computationally efficient algorithm in terms of the time-varying symbolic dynamic method is proposed to estimate the unknown initial conditions of coupled map lattices （CMLs）. The presented method combines symbolic dynamics with time-varying control parameters to develop a time-varying scheme for estimating the initial condition of multi-dimensional spatiotemporal chaotic signals. The performances of the presented time-varying estimator in both noiseless and noisy environments are analysed and compared with the common time-invariant estimator. Simulations are carried out and the obtained results show that the proposed method provides an efficient estimation of the initial condition of each lattice in the coupled system. The algorithm cannot yield an asymptotically unbiased estimation due to the effect of the coupling term, but the estimation with the time-varying algorithm is closer to the Cramer-Rao lower bound （CRLB） than that with the time-invariant estimation method, especially at high signal-to-noise ratios （SNRs）.展开更多
Based on symbolic dynamics, a novel computationally efficient algorithm is proposed to estimate the unknown initial vectors of globally coupled map lattices （CMLs）. It is proved that not all inverse chaotic mapping ...Based on symbolic dynamics, a novel computationally efficient algorithm is proposed to estimate the unknown initial vectors of globally coupled map lattices （CMLs）. It is proved that not all inverse chaotic mapping functions are satisfied for contraction mapping. It is found that the values in phase space do not always converge on their initial values with respect to sufficient backward iteration of the symbolic vectors in terms of global convergence or divergence （CD）. Both CD property and the coupling strength are directly related to the mapping function of the existing CML. Furthermore, the CD properties of Logistic, Bernoulli, and Tent chaotic mapping functions are investigated and compared. Various simulation results and the performances of the initial vector estimation with different signal-to- noise ratios （SNRs） are also provided to confirm the proposed algorithm. Finally, based on the spatiotemporal chaotic characteristics of the CML, the conditions of estimating the initial vectors usiug symbolic dynamics are discussed. The presented method provides both theoretical and experimental results for better understanding and characterizing the behaviours of spatiotemporal chaotic systems.展开更多
A joint cooperation diversity and symbol mapping diversity (SMD) strategy is proposed for cooperative packet retransmission system with high-order modulation such as 16QAM. Substantial SER/BER (symbol error rate/bit e...A joint cooperation diversity and symbol mapping diversity (SMD) strategy is proposed for cooperative packet retransmission system with high-order modulation such as 16QAM. Substantial SER/BER (symbol error rate/bit error rate) gains result from multiple packet transmissions over independent paths and distinct bit-to-symbol mappings for each packet transmis-sion. The SER/BER performance of relay assisted retransmission system is analyzed. Simulation results show that the joint-diversity strategy can provide more BER gains than other relaying strategies (i.e., decode-and-forward and constellation rearrangement relaying strategies) when no relay makes a decision error; but if some relays make decision errors, the joint-di-versity strategy outperforms other relaying strategies only when the relays are closer to the source than to the destination.展开更多
A well known chaotic mapping in symbol space is a shift mapping.However,other chaotic mappings in symbol space exist too.The basic change is to consider the process not only at a set of times which are equally spaced,...A well known chaotic mapping in symbol space is a shift mapping.However,other chaotic mappings in symbol space exist too.The basic change is to consider the process not only at a set of times which are equally spaced,say at unit time apart（a shift mapping）,but at a set of times which are not equally spaced,say if the unit time can not be fixed.The increasing mapping as a generalization of the shift mapping and the k-switch mapping are introduced.The increasing and k-switch mappings are chaotic.展开更多
We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of ...We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero.Next,for bounded symbols,we construct a symbol map and exhibit a short exact sequence associated with the C^(*)-algebra generated by all dual Toeplitz operators with bounded symbols.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.60871085)the Natural Science Foundation of Zhejiang Province,China (Grant No.Y1100119)
文摘How neuronal spike trains encode external information is a hot topic in neurodynamics studies. In this paper, we investigate the dynamical states of the Hodgkin-Huxley neuron under periodic forcing. Depending on the parameters of the stimulus, the neuron exhibits periodic, quasiperiodic and chaotic spike trains. In order to analyze these spike trains quantitatively, we use the phase return map to describe the dynamical behavior on a one-dimensional （1D） map. According to the monotonicity or discontinuous point of the 1D map, the spike trains are transformed into symbolic sequences by implementing a coarse-grained algorithm -- symbolic dynamics. Based on the ordering rules of symbolic dynamics, the parameters of the external stimulus can be measured in high resolution with finite length symbolic sequences. A reasonable explanation for why the nervous system can discriminate or cognize the small change of the external signals in a short time is also presented.
基金Project(41061043)support by the National Natural Science Foundation of China
文摘The symbolization of land polygon is an important part of cartography. In the mapping of traditional present land-use maps, the symbol of land polygons was usually filled by the method of filling or plotting, but these methods can't solve the spatial conflicts of the symbol. According to the principle of cartography, the rule of how to symbolize the land polygon was summarized, and a new method that can generate and deploy the land symbols was presented. By making use of C# programming language and Arc Engine developing components, the algorithm can generate land symbols presenting triangle and adjust the coordinate of the symbol. Through mapping the present land-use map of Honghe county, this algorithm can reduce 88.84% of the spatial conflicts error rate compared with the traditional methods. It improves the accuracy and efficiency of the map symbolic.
基金Project supported by the National Natural Science Foundation of China(Nos.11172246 and 11572263)
文摘The symbolic dynamics of a Belykh-type map （a two-dimensional discon- tinuous piecewise linear map） is investigated. The admissibility condition for symbol sequences named the pruning front conjecture is proved under a hyperbolicity condition. Using this result, a symbolic dynamics model of the map is constructed according to its pruning front and primary pruned region. Moreover, the boundary of the parameter region in which the map is chaotic of a horseshoe type is given.
基金Supported by Internal Fund of Institute of Surveying and Mapping (No.Y0506) .
文摘On the basis of analysis of various algorithms, an anti-aliasing algorithm called brush method was presented, which is suitable to map publishing symbol. Aftes introducing the basic principle and implementation of brush method in detail, the result and efficiency were evaluated through experiments.
基金supported by the National Natural Science Foundation of China(Grant Nos 60271023 and 60571066)the Natural Science Foundation of Guangdong Province,China(Grant Nos 5008317 and 7118382)
文摘A novel computationally efficient algorithm in terms of the time-varying symbolic dynamic method is proposed to estimate the unknown initial conditions of coupled map lattices （CMLs）. The presented method combines symbolic dynamics with time-varying control parameters to develop a time-varying scheme for estimating the initial condition of multi-dimensional spatiotemporal chaotic signals. The performances of the presented time-varying estimator in both noiseless and noisy environments are analysed and compared with the common time-invariant estimator. Simulations are carried out and the obtained results show that the proposed method provides an efficient estimation of the initial condition of each lattice in the coupled system. The algorithm cannot yield an asymptotically unbiased estimation due to the effect of the coupling term, but the estimation with the time-varying algorithm is closer to the Cramer-Rao lower bound （CRLB） than that with the time-invariant estimation method, especially at high signal-to-noise ratios （SNRs）.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61072037 and 60271023)the Natural Science Foundation of Guangdong Province,China (Grant No. 10151503101000011)
文摘Based on symbolic dynamics, a novel computationally efficient algorithm is proposed to estimate the unknown initial vectors of globally coupled map lattices （CMLs）. It is proved that not all inverse chaotic mapping functions are satisfied for contraction mapping. It is found that the values in phase space do not always converge on their initial values with respect to sufficient backward iteration of the symbolic vectors in terms of global convergence or divergence （CD）. Both CD property and the coupling strength are directly related to the mapping function of the existing CML. Furthermore, the CD properties of Logistic, Bernoulli, and Tent chaotic mapping functions are investigated and compared. Various simulation results and the performances of the initial vector estimation with different signal-to- noise ratios （SNRs） are also provided to confirm the proposed algorithm. Finally, based on the spatiotemporal chaotic characteristics of the CML, the conditions of estimating the initial vectors usiug symbolic dynamics are discussed. The presented method provides both theoretical and experimental results for better understanding and characterizing the behaviours of spatiotemporal chaotic systems.
基金the National Natural Science Foundation of China (No. 60372107)the Natural Science Fund for Higher Educa-tion of Jiangsu Province, China (No. 06KJA51001)the Natural Science Fund of the Science and Technology Department of Jiangsu Province, China (No. BK2007729)
文摘A joint cooperation diversity and symbol mapping diversity (SMD) strategy is proposed for cooperative packet retransmission system with high-order modulation such as 16QAM. Substantial SER/BER (symbol error rate/bit error rate) gains result from multiple packet transmissions over independent paths and distinct bit-to-symbol mappings for each packet transmis-sion. The SER/BER performance of relay assisted retransmission system is analyzed. Simulation results show that the joint-diversity strategy can provide more BER gains than other relaying strategies (i.e., decode-and-forward and constellation rearrangement relaying strategies) when no relay makes a decision error; but if some relays make decision errors, the joint-di-versity strategy outperforms other relaying strategies only when the relays are closer to the source than to the destination.
基金supported by Latvian Scientific(09.1220)ESF Project(2009/0223/1DP/1.1.1.2.0/09APIA/VIAA/008)
文摘A well known chaotic mapping in symbol space is a shift mapping.However,other chaotic mappings in symbol space exist too.The basic change is to consider the process not only at a set of times which are equally spaced,say at unit time apart（a shift mapping）,but at a set of times which are not equally spaced,say if the unit time can not be fixed.The increasing mapping as a generalization of the shift mapping and the k-switch mapping are introduced.The increasing and k-switch mappings are chaotic.
基金supported by the NSFC(12271134,11771401)supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(NRF-2019R1I1A3A01041943)。
文摘We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero.Next,for bounded symbols,we construct a symbol map and exhibit a short exact sequence associated with the C^(*)-algebra generated by all dual Toeplitz operators with bounded symbols.
