According to the chemical kinetic model of lysogeny/lysis switch in Escherichia coli （E. coil） infected by bacteriophage A, the entropy production rates of steady states are calculated. The resuits show that the lys...According to the chemical kinetic model of lysogeny/lysis switch in Escherichia coli （E. coil） infected by bacteriophage A, the entropy production rates of steady states are calculated. The resuits show that the lysogenic state has lower entropy production rate than lyric state, which provides an explanation on why the lysogenic state of A phage is so stable. We a/so notice that the entropy production rates of both lysogenic state and lyric state are lower than that of saddle-point and bifurcation state, which is consistent with the principle of minimum entropy production for living organism in nonequilibrium stationary state. Subsequently, the relations between CI and Cro degradation rates at two bifurcations and the changes of entropy production rate with CI and Cro degradation are deduced. The theory and method can be used to calculate entropy change in other molecular network.展开更多
This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent innovations. Let {Xt} be a linear process defined by Xt =∑k=0^∞ψ kεt-k, where {ψk, k ≥...This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent innovations. Let {Xt} be a linear process defined by Xt =∑k=0^∞ψ kεt-k, where {ψk, k ≥ 0} is a sequence of real numbers and {εk, k = 0, ±1, ±2,...} is a sequence of random variables. Two results are proved in this paper. In the first result, assuming that {εk, k ≥ 1} is a sequence of asymptotically linear negative quadrant dependent （ALNQD） random variables, the authors find the limiting distributions of the least squares estimator and the associated regression t statistic. It is interesting that the limiting distributions are similar to the one found in earlier work under the assumption of i.i.d, innovations. In the second result the authors prove that the least squares estimator is not a strong consistency estimator of the autoregressive parameter a when {εk, k ≥ 1} is a sequence of negatively associated （NA） random variables, and ψ0 = 1, ψk = 0, k ≥ 1.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.11047180,90403010,and 200408020102Scientific Research Startup Foundation of University of Electronic Science and Technology of China
文摘According to the chemical kinetic model of lysogeny/lysis switch in Escherichia coli （E. coil） infected by bacteriophage A, the entropy production rates of steady states are calculated. The resuits show that the lysogenic state has lower entropy production rate than lyric state, which provides an explanation on why the lysogenic state of A phage is so stable. We a/so notice that the entropy production rates of both lysogenic state and lyric state are lower than that of saddle-point and bifurcation state, which is consistent with the principle of minimum entropy production for living organism in nonequilibrium stationary state. Subsequently, the relations between CI and Cro degradation rates at two bifurcations and the changes of entropy production rate with CI and Cro degradation are deduced. The theory and method can be used to calculate entropy change in other molecular network.
基金supported by the National Natural Science Foundation of China under Grant Nos.10971081 and 11001104985 Project of Jilin University
文摘This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent innovations. Let {Xt} be a linear process defined by Xt =∑k=0^∞ψ kεt-k, where {ψk, k ≥ 0} is a sequence of real numbers and {εk, k = 0, ±1, ±2,...} is a sequence of random variables. Two results are proved in this paper. In the first result, assuming that {εk, k ≥ 1} is a sequence of asymptotically linear negative quadrant dependent （ALNQD） random variables, the authors find the limiting distributions of the least squares estimator and the associated regression t statistic. It is interesting that the limiting distributions are similar to the one found in earlier work under the assumption of i.i.d, innovations. In the second result the authors prove that the least squares estimator is not a strong consistency estimator of the autoregressive parameter a when {εk, k ≥ 1} is a sequence of negatively associated （NA） random variables, and ψ0 = 1, ψk = 0, k ≥ 1.
