The construction and properties of interval minimum-energy wavelet frame are systematically studied in this paper. They are as follows: 1) give the definition of interval minimum-energy wavelet frame; 2) give the n...The construction and properties of interval minimum-energy wavelet frame are systematically studied in this paper. They are as follows: 1) give the definition of interval minimum-energy wavelet frame; 2) give the necessary and sufficient conditions for the minimum-energy frames for L^2[0,1]; 3) present the construction algorithm for minimum-energy wavelet frame associated with refinable functions on the interval with any support y; 4) give the decomposition and reconstruction formulas of the minimum-energy frame on the interval [0,1],展开更多
According to the description effect range, the method of scaling system in cartography is with the precision of four grades: nominal scaling, ordinal scaling, interval scaling and ratio scaling. The authors have rese...According to the description effect range, the method of scaling system in cartography is with the precision of four grades: nominal scaling, ordinal scaling, interval scaling and ratio scaling. The authors have researched their innate character and inherent relations. The essence of evaluation partialordering set (A ,≤) is the mapping of evaluation object (X, ≤) under fixed condition. The collection and classification of xi ∈ X corresponds how to express Aj ∈ A, i.e. , V xi ∈ X→f(xi ) = Aj → A, Aj is the image of xi under mapping f. The function relation between evaluation partial-ordering set (A, ≤) and evaluation object (X, ≤) is decided by the space character and the way of collection and classification. The different space character and way of collection and classification will produce the different express method and evaluation result, accordingly the authors give out the mathematical definitions for nominal scaling, ordinal scaling, interval scaling and ratio scaling respectively. These results have been proved through the examples.展开更多
Interval timing is involved in a variety of cognitive behaviors such as associative learning and decision-making.While it has been shown that time estimation is adaptive to the temporal context,it remains unclear how ...Interval timing is involved in a variety of cognitive behaviors such as associative learning and decision-making.While it has been shown that time estimation is adaptive to the temporal context,it remains unclear how interval timing behavior is influenced by recent trial history.Here we found that,in mice trained to perform a licking-based interval timing task,a decrease of inter-reinforcement interval in the previous trial rapidly shifted the time of anticipatory licking earlier.Optogenetic inactivation of the anterior lateral motor cortex(ALM),but not the medial prefrontal cortex,for a short time before reward delivery caused a decrease in the peak time of anticipatory licking in the next trial.Electrophysiological recordings from the ALM showed that the response profiles preceded by short and long inter-reinforcement intervals exhibited task-engagement-dependent temporal scaling.Thus,interval timing is adaptive to recent experience of the temporal interval,and ALM activity during time estimation reflects recent experience of interval.展开更多
针对流水线型坐标旋转数字计算机(coordinate rotation digital computer,CORDIC)算法的输出精度低、输出时延长、硬件资源消耗大的问题,提出一种双向预判免缩放因子CORDIC算法.该算法首先将[0,π/4)内的输入角度通过角度二进制编码后...针对流水线型坐标旋转数字计算机(coordinate rotation digital computer,CORDIC)算法的输出精度低、输出时延长、硬件资源消耗大的问题,提出一种双向预判免缩放因子CORDIC算法.该算法首先将[0,π/4)内的输入角度通过角度二进制编码后按位值i分解为2-i的较小角度,然后使用设立的查找表在初始角度的基础上进行双向免缩放因子旋转,无需根据中间迭代结果判断下次的旋转方向,避免了迭代方向的不确定性,减少了迭代单元级数和迭代次数,同时提高了运算精度;最后将[π/4,2π)内的输入角度通过角度区间折叠技术变换到[0,π/4),使计算区间扩展到整个圆周[0,2π),保证了运算范围,且只需要使用移位和加减运算即可实现,避免了进行乘法运算.在MATLAB和Vivado软件平台上进行算法仿真与验证,结果表明:在输出位宽均为14位时,与流水线型和单向免缩放因子型CORDIC算法相比,输出精度分别提高了47.5%、18.8%,最大输出时延分别降低了53.8%、40.0%,硬件资源消耗也有一定的改善.本文提出的CORDIC算法具有输出精度高、输出时延短等特点,其综合性能具有较大的提升.展开更多
Biorthogonal multiwavelets are generated from related scaling function vectors via multiresolution analysis. In this paper, we first show how to derive even-length biorthogonal lowpass filter pair from odd-length bior...Biorthogonal multiwavelets are generated from related scaling function vectors via multiresolution analysis. In this paper, we first show how to derive even-length biorthogonal lowpass filter pair from odd-length biorthogonal multiwavelet system with such properties as symmetry-antisymmetry and compactly support. So based on this, odd-length biorthogonal multiwavelet system can be constructed.展开更多
基金the National Natural Science Foundation of China (Grant No.60375021)the Natural Science Foundation of Hunan Province,China (Grant No.05JJ10011)the Scientific Research Fund of Hunan Provincial Education Department of China (Grant Nos.04A056 and 06C836)
文摘The construction and properties of interval minimum-energy wavelet frame are systematically studied in this paper. They are as follows: 1) give the definition of interval minimum-energy wavelet frame; 2) give the necessary and sufficient conditions for the minimum-energy frames for L^2[0,1]; 3) present the construction algorithm for minimum-energy wavelet frame associated with refinable functions on the interval with any support y; 4) give the decomposition and reconstruction formulas of the minimum-energy frame on the interval [0,1],
文摘According to the description effect range, the method of scaling system in cartography is with the precision of four grades: nominal scaling, ordinal scaling, interval scaling and ratio scaling. The authors have researched their innate character and inherent relations. The essence of evaluation partialordering set (A ,≤) is the mapping of evaluation object (X, ≤) under fixed condition. The collection and classification of xi ∈ X corresponds how to express Aj ∈ A, i.e. , V xi ∈ X→f(xi ) = Aj → A, Aj is the image of xi under mapping f. The function relation between evaluation partial-ordering set (A, ≤) and evaluation object (X, ≤) is decided by the space character and the way of collection and classification. The different space character and way of collection and classification will produce the different express method and evaluation result, accordingly the authors give out the mathematical definitions for nominal scaling, ordinal scaling, interval scaling and ratio scaling respectively. These results have been proved through the examples.
基金supported by the National Science and Technology Innovation 2030 Major Program of China(2021ZD0203700/2021ZD0203703)the National Natural Science Foundation of China(31771151 and 32171030)+2 种基金Lingang Lab(LG202104-01-03)a Shanghai Municipal Science and Technology Major Project(2018SHZDZX05)the Strategic Priority Research Program of the Chinese Academy of Sciences(XDB32010200)。
文摘Interval timing is involved in a variety of cognitive behaviors such as associative learning and decision-making.While it has been shown that time estimation is adaptive to the temporal context,it remains unclear how interval timing behavior is influenced by recent trial history.Here we found that,in mice trained to perform a licking-based interval timing task,a decrease of inter-reinforcement interval in the previous trial rapidly shifted the time of anticipatory licking earlier.Optogenetic inactivation of the anterior lateral motor cortex(ALM),but not the medial prefrontal cortex,for a short time before reward delivery caused a decrease in the peak time of anticipatory licking in the next trial.Electrophysiological recordings from the ALM showed that the response profiles preceded by short and long inter-reinforcement intervals exhibited task-engagement-dependent temporal scaling.Thus,interval timing is adaptive to recent experience of the temporal interval,and ALM activity during time estimation reflects recent experience of interval.
文摘针对流水线型坐标旋转数字计算机(coordinate rotation digital computer,CORDIC)算法的输出精度低、输出时延长、硬件资源消耗大的问题,提出一种双向预判免缩放因子CORDIC算法.该算法首先将[0,π/4)内的输入角度通过角度二进制编码后按位值i分解为2-i的较小角度,然后使用设立的查找表在初始角度的基础上进行双向免缩放因子旋转,无需根据中间迭代结果判断下次的旋转方向,避免了迭代方向的不确定性,减少了迭代单元级数和迭代次数,同时提高了运算精度;最后将[π/4,2π)内的输入角度通过角度区间折叠技术变换到[0,π/4),使计算区间扩展到整个圆周[0,2π),保证了运算范围,且只需要使用移位和加减运算即可实现,避免了进行乘法运算.在MATLAB和Vivado软件平台上进行算法仿真与验证,结果表明:在输出位宽均为14位时,与流水线型和单向免缩放因子型CORDIC算法相比,输出精度分别提高了47.5%、18.8%,最大输出时延分别降低了53.8%、40.0%,硬件资源消耗也有一定的改善.本文提出的CORDIC算法具有输出精度高、输出时延短等特点,其综合性能具有较大的提升.
文摘Biorthogonal multiwavelets are generated from related scaling function vectors via multiresolution analysis. In this paper, we first show how to derive even-length biorthogonal lowpass filter pair from odd-length biorthogonal multiwavelet system with such properties as symmetry-antisymmetry and compactly support. So based on this, odd-length biorthogonal multiwavelet system can be constructed.