Journal of Physics A: Mathematical and Theoretical
We consider a system of clusters of various sizes or masses, subject to aggregation and fragmenta... more We consider a system of clusters of various sizes or masses, subject to aggregation and fragmentation by collision with monomers or by self-disintegration. The aggregation rate for the cluster of size or mass k is given by a kernel proportional to k a , whereas the collision and disintegration kernels are given by λ k b and μ k a , respectively, with 0 ⩽ a , b ⩽ 1 and positive factors λ and µ. We study the emergence of oscillations in the phase diagram ( μ , λ ) for two models: ( a , b ) = ( 1 , 0 ) and ( 1 , 1 ) . It is shown that the monomer population satisfies a class of integral equations possessing oscillatory solutions in a finite domain in the plane ( μ , λ ) . We evaluate analytically this domain and give an estimate of the oscillation frequency. In particular, these oscillations are found to occur generally for small but nonzero values of the parameter µ, far smaller than λ.
Journal of Physics A: Mathematical and Theoretical, 2021
The integrate-and-fire (IF) model is the most widely used simple spiking neuron model in neuromor... more The integrate-and-fire (IF) model is the most widely used simple spiking neuron model in neuromorphic computing as well as in artificial neural network algorithms. Here, we characterize the dynamics and information processing of IF models using computer simulations and information-theoretic approaches. Neural dynamics is analysed by means of the time evolution of axonal spikes and the phase-plane portrait, and the coding efficiency of a neuron is estimated by the ratio of mutual information of input and output spikes for the binary hidden neural state. The exponential IF model exhibits higher similarity to the biophysical model in both neural dynamics and coding, compared to other IF type models. Electronic circuit simulations based on the simulation programme with integrated circuit emphasis reveal the nonlinear current–voltage characteristics of the IF neuron models and criticalities in the neural networks. Relevant information-theoretic measures indicate that the computational capabilities of neuromorphic devices largely depend on the neuron models. Such an approach combined with the analysis of neural dynamics provides a useful tool to investigate underlying dynamics of mathematical neuron models; it is applicable to the design and evaluation of neuromorphic models.
This study examines the human behavioral dynamics of pedestrians crossing a street with vehicular... more This study examines the human behavioral dynamics of pedestrians crossing a street with vehicular traffic. To this end, an experiment was constructed in which human participants cross a road between two moving vehicles in a virtual reality setting. A mathematical model is developed in which the position is given by a simple function. The model is used to extract information on each crossing by performing root-mean-square deviation (RMSD) minimization of the function from the data. By isolating the parameter adjusted to gap features, we find that the subjects primarily changed the timing of the acceleration to adjust to changing gap conditions, rather than walking speed or duration of acceleration. Moreover, this parameter was also adjusted to the vehicle speed and vehicle type, even when the gap size and timing were not changed. The model is found to provide a description of gap affordance via a simple inequality of the fitting parameters. In addition, the model turns out to predict...
The principle of least effort has been widely used to explain phenomena related to human behavior... more The principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.
Background Autophagy is an evolutionarily conserved intracellular process that is used for delive... more Background Autophagy is an evolutionarily conserved intracellular process that is used for delivering proteins and organelles to the lysosome for degradation. For decades, autophagy has been speculated to regulate amyloid-β peptide (Aβ) accumulation, which is involved in Alzheimer’s disease (AD); however, specific autophagic effects on the Aβ kinetics only have begun to be explored. Results We develop a mathematical model for autophagy with respect to Aβ kinetics and perform simulations to understand the quantitative relationship between Aβ levels and autophagy activity. In the case of an abnormal increase in the Aβ generation, the degradation, secretion, and clearance rates of Aβ are significantly changed, leading to increased levels of Aβ. When the autophagic Aβ degradation is defective in addition to the increased Aβ generation, the Aβ-regulation failure is accompanied by elevated concentrations of autophagosome and autolysosome, which may further clog neurons. Conclusions The mo...
Journal of Physics A: Mathematical and Theoretical
We consider a system of clusters of various sizes or masses, subject to aggregation and fragmenta... more We consider a system of clusters of various sizes or masses, subject to aggregation and fragmentation by collision with monomers or by self-disintegration. The aggregation rate for the cluster of size or mass k is given by a kernel proportional to k a , whereas the collision and disintegration kernels are given by λ k b and μ k a , respectively, with 0 ⩽ a , b ⩽ 1 and positive factors λ and µ. We study the emergence of oscillations in the phase diagram ( μ , λ ) for two models: ( a , b ) = ( 1 , 0 ) and ( 1 , 1 ) . It is shown that the monomer population satisfies a class of integral equations possessing oscillatory solutions in a finite domain in the plane ( μ , λ ) . We evaluate analytically this domain and give an estimate of the oscillation frequency. In particular, these oscillations are found to occur generally for small but nonzero values of the parameter µ, far smaller than λ.
Journal of Physics A: Mathematical and Theoretical, 2021
The integrate-and-fire (IF) model is the most widely used simple spiking neuron model in neuromor... more The integrate-and-fire (IF) model is the most widely used simple spiking neuron model in neuromorphic computing as well as in artificial neural network algorithms. Here, we characterize the dynamics and information processing of IF models using computer simulations and information-theoretic approaches. Neural dynamics is analysed by means of the time evolution of axonal spikes and the phase-plane portrait, and the coding efficiency of a neuron is estimated by the ratio of mutual information of input and output spikes for the binary hidden neural state. The exponential IF model exhibits higher similarity to the biophysical model in both neural dynamics and coding, compared to other IF type models. Electronic circuit simulations based on the simulation programme with integrated circuit emphasis reveal the nonlinear current–voltage characteristics of the IF neuron models and criticalities in the neural networks. Relevant information-theoretic measures indicate that the computational capabilities of neuromorphic devices largely depend on the neuron models. Such an approach combined with the analysis of neural dynamics provides a useful tool to investigate underlying dynamics of mathematical neuron models; it is applicable to the design and evaluation of neuromorphic models.
This study examines the human behavioral dynamics of pedestrians crossing a street with vehicular... more This study examines the human behavioral dynamics of pedestrians crossing a street with vehicular traffic. To this end, an experiment was constructed in which human participants cross a road between two moving vehicles in a virtual reality setting. A mathematical model is developed in which the position is given by a simple function. The model is used to extract information on each crossing by performing root-mean-square deviation (RMSD) minimization of the function from the data. By isolating the parameter adjusted to gap features, we find that the subjects primarily changed the timing of the acceleration to adjust to changing gap conditions, rather than walking speed or duration of acceleration. Moreover, this parameter was also adjusted to the vehicle speed and vehicle type, even when the gap size and timing were not changed. The model is found to provide a description of gap affordance via a simple inequality of the fitting parameters. In addition, the model turns out to predict...
The principle of least effort has been widely used to explain phenomena related to human behavior... more The principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.
Background Autophagy is an evolutionarily conserved intracellular process that is used for delive... more Background Autophagy is an evolutionarily conserved intracellular process that is used for delivering proteins and organelles to the lysosome for degradation. For decades, autophagy has been speculated to regulate amyloid-β peptide (Aβ) accumulation, which is involved in Alzheimer’s disease (AD); however, specific autophagic effects on the Aβ kinetics only have begun to be explored. Results We develop a mathematical model for autophagy with respect to Aβ kinetics and perform simulations to understand the quantitative relationship between Aβ levels and autophagy activity. In the case of an abnormal increase in the Aβ generation, the degradation, secretion, and clearance rates of Aβ are significantly changed, leading to increased levels of Aβ. When the autophagic Aβ degradation is defective in addition to the increased Aβ generation, the Aβ-regulation failure is accompanied by elevated concentrations of autophagosome and autolysosome, which may further clog neurons. Conclusions The mo...
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Papers by MooYoung Choi