From the 1 of 514 papers with an AI index.
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20 papers · 1 filter
The origin of the Poisson distribution in stochastic dynamics of gene expression
Julian Lee
The Poisson distribution is the probability distribution of the number of independent events in a given period of time. Although the Poisson distribution appears ubiquitously in va…
Quantitative Analysis of a Transient Dynamics of a Gene Regulatory Network
JaeJun Lee, Julian Lee
In a stochastic process, noise often modifies the picture offered by the mean field dynamics. In particular, when there is an absorbing state, the noise erases a stable fixed point…
The derivation of Markov processes that violate detailed balance
Julian Lee
Time-reversal symmetry of microscopic laws dictates that the equilibrium distribution of a stochastic process must obey the detailed balance. On the other hand, cyclic Markov proce…
Transfer matrix algorithm for computing the exact partition function of a square lattice polymer
Julian Lee
I develop a transfer matrix algorithm for computing the exact partition function of a square lattice polymer with nearest-neighbor interaction, by extending a previous algorithm fo…
Microcanonical analysis of a nonequilibrium phase transition
Julian Lee
Microcanonical analysis is a powerful method for studying phase transitions of finite-size systems. This method has been used so far only for studying phase transitions of equilibr…
Quantum phase transition of the transverse-field quantum Ising model on scale-free networks
Hangmo Yi
I investigate the quantum phase transition of the transverse-field quantum Ising model in which nearest neighbors are defined according to the connectivity of scale-free networks.…