The phase oscillator model can succinctly describe the periodic oscillation observed in many real-world biological systems. In this phase description, the phase response curve (PRC) plays a crucial role in determining the dynamical properties of synchronization. Therefore, it is very important to correctly estimate the PRC in general situations. However, we find that known methods, including the recently proposed WSTA method, often give incorrect PRCs under plausible conditions. To overcome this difficulty, here we propose an improved WSTA method using the multicycle data. As a result, we can obtain the correct PRCs of the oscillatory systems to which the conventional methods are inapplicable. Furthermore, by applying this method to a chaotic system with strong periodicity, we demonstrate that the method provides results effective in predicting the synchronization properties of chaotic systems. These results support the applicability to biological systems frequently exhibiting noisy chaotic behavior with some periodicity.
To investigate the structural dynamics of the homology pairing of polymers, we modeled the scenario of homologous chromosome pairings during meiosis in Schizosaccharomyces pombe, one of the simplest model organisms of eukaryotes. We consider a simple model consisting of pairs of homologous polymers with the same structures that are confined in a cylindrical container, which represents the local parts of chromosomes contained in an elongated nucleus of S. pombe. Brownian dynamics simulations of this model showed that the excluded volume effects among non-homological chromosomes and the transitional dynamics of nuclear shape serve to enhance the pairing of homologous chromosomes.
Axons are computational units in neuronal networks. Little is known about relationships between firing frequency and the extent of changes in axonal conduction velocity. Therefore, we stimulated axons extending through microtunnels with various stimulation frequencies, and recorded axonal conduction delays. Additionally, ZD7288, an h-current blocker, was added during stimulation to elucidate the mechanism underlying the change. Changes observed in the first 75 stimuli with a frequency of 20 Hz were smaller than those observed with lower frequencies, a tendency that was abolished by ZD7288. These results suggest that our method is capable of detecting activity-dependent changes in axonal conduction property.
This paper presents a simplistic dynamic circuit analogue for an adaptive transport network model in true slime mold by Tero et al. This circuit analogue model is derived from Tero's model through nontrivial simplification under certain assumptions, and it realizes less computational complexity through a reduction of the number of variables. Despite of its simplicity, systematic simulations confirm that the shortest path search task is efficiently accomplished with this model; (i) the shortest path is always identified, for various random networks; (ii) if there are multiple, competing shortest paths in the network, they are simultaneously identified; and (iii) for random deletions of a link in the shortest path, a new shortest path is quickly identified accordingly. The model proposed here is easily implemented on the circuit simulator SPICE for instance, and hence the path search time will be further reduced with certain numerical devices including automatic adaptive numerical integration schemes as well as an acceleration method proposed in the end of the paper.
In biologically-inspired, neuromorphic engineering, it is important to design silicon neurons (SiNs) with desirable functions in a systematic way. However, the conventional design methods such as phenomenological design and the conductance-based design relied on the hand-tuned parameters. Thus a more systematic design principle, that considers mathematical structures in the dynamical systems, is needed for efficiency and robustness. In this work, we present the phase response curve (PRC)-based design for SiNs as a dynamical systems design for SiNs to enhance synchronization in an ensemble of SiNs on the basis of the phase reduction theory. By analyzing various circuit models of the previous SiNs, we explore key criteria to realize transitions between two typical PRCs, Type I and Type II. As a case study, we focus on the hybrid type SiNs for tractability and demonstrate how to tune circuit parameters of a resonate-and-fire neuron (RFN) circuit to control the peak location of phase coupling functions resulting from PRCs, which matters for phase locking.
This study investigates the influence of lattice structure in evolutionary games. The snowdrift game and the prisoner's dilemma game are considered in networks with high clustering coefficients, that use four different strategy-updating. Analytical conjectures using pair approximation were compared with the numerical results. Results indicate that the clustering coefficient does not influence the evolution of cooperation in the prisoner's dilemma game, while it does in the snow-drift game. Lattice structure yields high ‘effective’ clustering coefficient and enhances the frequency of the majority rather than cooperators.
Information flow in adaptively interacting stochastic processes is studied. We give an extended form of game dynamics for interacting Markovian processes and compute a measure of causal information flow, which is different from the transfer entropy. In the game theoretic situation, causal information flow can show oscillatory behavior through reward-maximizing adaptation of two players. The adaptive dynamics for the coin-tossing game is exemplified and the causal information flow therein is investigated.
We examined the indirect positive effect of one plant on the growth of another via growth suppression of a shared competing plant as an indirect facilitation between plants. We simulated the dynamics of populations of 3600 competing plants and used absolute interaction intensity (AIIi,j), the causal effect of plant j on plant i. The positive effect due to indirect facilitation between two plants occurs at a short distance apart and increases with increasing average density. The indirect facilitation between plants becomes increasingly important with increasing average density to explain the dynamics of size structure in plant populations.
Bayesian estimation theory has been expected to explain how the brain deals with uncertainty. Several previous studies have implied that cortical network models could implement Bayesian computation. However, the feasibility of the required computational procedures is still unclear under the physiological and anatomical constraints of neural systems. Here, we propose a neural network model that implements the algorithm in a biologically realizable manner, incorporating discrete choice theory. Our model successfully demonstrates an orientation discrimination task with significantly noisy visual images and the relation between the stimulus intensity and the reaction time known as Piéron’s law.
Investigation of synaptic connectivity between neurons is essential for understanding information processing mechanisms in the brain because this connectivity determines how spikes propagate in a neural circuit. Recent advances in experimental technology have enabled simultaneous recording of the spiking activity from hundreds of neurons. In this study, we propose a method for estimating synaptic connectivity using the spike data from multiple neurons. We first demonstrated that this method can perfectly estimate synaptic connectivity using synthetic spike data in an ideal condition. Subsequently, this method is applied to more realistic spike data generated by a large-scale network of Hodgkin-Huxley neurons. The results suggest that our estimation method is superior to a conventional method in identifying synaptic connectivity when the spiking activity from a large number of neurons is available for the analysis.
Stochastic resonance (SR) is a phenomenon in which dynamic noise is effectively used to drive a system with subthreshold input signals. In the classical model of SR induced in a network, each constituting unit must be delivered noise from independent external sources. Recently, a new model of SR has been proposed, where internal noise is exploited as the solution to avoid the burden of generating independent external noise for each unit. In this study, we employ a network of FitzHugh-Nagumo neurons as a candidate of the new model of SR system using internal noise. The network is formed as a circular system where all connections between neurons strictly consist of self-connections or connections propagating into a unique direction. Hence, each neuron receives stimuli from its four predecessors within the circular arrangement, from its own output, as well as from a unique input node. An input signal of an amplitude that is smaller than the threshold of individual neurons is provided to the network. Owing to a process of SR that occurs within the network and that is sustained by internally generated noise, the subthreshold signal is detected and amplified and delivered to the network output node. The frequency characteristics of the network in terms of its operational bandwidth is established.
A biological pacemaker, which is a pacemaker cell created from normally quiescent non-pacemaking cells, is expected to be an alternative to electronic pacemakers. Recent studies on biological pacemaker engineering have revealed that a modification of ionic currents across the cell membrane elicits the pacemaking ability of a ventricular myocyte. We perform bifurcation analyses using an elaborate mathematical cell model to investigate an efficient way to create biological pacemakers from human ventricular myocytes. Pacemaker activity appears during the suppression of IK1. Furthermore, we show that an additional increment of ICaL, INaCa, or If facilitates the generation of pacemaker activity under IK1-reduced conditions.
Owing to recent progress in structural biology, the structures of a number of proteins have been resolved and deposited into databases such as the Protein Data Bank (PDB). Many proteins function as molecular machines or show allosteric effects, which require integrated communication between different parts of the protein structure;however, the general principles underlying such communication are not yet clear. All-atom molecular dynamics simulation is a powerful tool for tracking molecular motion, but is still far too computationally costly to be applied widely. In this paper, we present a simple method for assessing the properties of mechanical communications using coarse-grained steered molecular dynamics simulations with elastic network models. The method was tested by screening for a certain mechanical property among protein structures in the PDB.
Biological networks, such as that of the human brain, show a remarkable ability to adapt to changing environments by long-term evolution and short-term adaptations. This is facilitated by the core-periphery structure of the network, where a core of densely connected network nodes provides long-term functionality and robustness, while the periphery is responsible for adaptation on short time scales to changing conditions in the environment. In this paper, we discuss the characteristics of the core-periphery network structure and its relation with adaptability and evolvability, which we also illustrate with own experimental data from the brain's functional network. Based on this concept, we propose a mechanism for the adaptive placement of network functions to virtual servers in network function virtualization (NFV) under time-varying user requests. Our simulation results show that the number of server manipulations (migrations, merges, and replications of virtual machines) necessary to accommodate changes in network function requests can be greatly reduced compared to the conventional placement method.
Pancreatic β-cells exhibit bursting electrical activity, which is correlated with insulin secretion. It has been reported that several ionic channels may contribute to the characteristic electrical activities of these cells but their mechanisms are still unclear. In this study, we examined how the characteristic electrical activity of isolated β-cells occurs. Using a simple mathematical model of pancreatic β-cells, we found that conductances of the voltage-sensitive mixed ion channel and voltage-sensitive potassium channel contribute to such electrical activity. In addition, we found that noise can play a key role in this activity. These results imply that the bursting electrical activity of pancreatic β-cells can be controlled by ionic conductances or noise. Such control enables medical application of β-cells in type II diabetes, wherein insulin secretion is difficult to control. Our findings may contribute to a novel treatment for type II diabetes.
We propose an extended framework of two dimensional neural field with network between distant cortical areas as a model of global brain dynamics, and the models whose geometry of the neural field changes depending on the field dynamics as a model for growing brains. As a characteristic pattern with non-local and network interactions in neural field, pulser and memory are constructed. Possible applications to quantitative measurements of cortical activities of mouse and human brain development are briefly discussed.
In this contribution we review progress on the problem of forecasting chaotic dynamical systems. The nature of chaos was initially illusive, having escaped discovery by several great minds who were in a position to find it. Once the essential features of chaos were uncovered, the concept greatly influenced the thinking of physicists and forecasters, in particular, it brought into focus the limitation of forecasting nonlinear dynamical systems. This resulted in a dichotomy between prediction methods for (nearly) linear systems and nonlinear systems; the important features and distinctions of these two approaches are reviewed. An important issue that arises is the role of model error in forecasting; many methods either ignore or over-simplify the nature of model error, largely because this allows adaption of existing techniques. Finally it is argued that the Isis Programme(Imperfect-model Shadowing and Indistinguishable States) provides a theoretical and practical basis for dealing with all sources of uncertainty, including observational noise and model error.
This paper investigates and proposes one advantageous function of a power packet dispatching system, which has been proposed by authors' group with being apart from the conventional power distribution system. Here is focused on the feature on safety of power packet dispatching which covers two aspects: information safety (protect the information of packet from attackers) and power safety (keep loads safe regarding supplied power from packet). For the purpose of achieving the information safety and the power safety, we introduce simple modulations of power packets before sending them. In particular, in order to protect the information of packets, partial packet modulation is proposed first, i.e., modulating partial information tags of packets. Modulation scheme based on chaotic signal is one possibility for this purpose and we adopt the differential chaos shift keying (DCSK) scheme in this paper. Next, the power safety can be achieved by applying pulse width modulation (PWM) to the payload of packets. Meanwhile, considering the effect of the noise on the packet dispatching, further modulation of the payload using the DCSK scheme is proposed, which can spread the spectrum of the noise. Consequently, we introduce the concept of whole packet modulation, in which PWM is applied to the payload of packets first, and then modulation using the DCSK scheme is applied throughout the whole packet. In this manner, both the information safety and the power safety can be achieved and the spectrum of noise is spread as well. Additionally, it is worth mentioning that the rigorous examination of the modulation method is not the target in this moment.
A complex-valued Hopfield neural network is a useful model for processing multi-level data. A rotor Hopfield network is an extension of a complex-valued Hopfield neural network but much more flexible. In addition, a rotor Hopfield neural network has excellent storage capacity and noise robustness characteristics. In the present work, we investigate the rotor Boltzmann machine (RoBM), a stochastic model of a rotor Hopfield neural network, through information geometry, which is a useful tool for analyzing stochastic models. We discuss RoBM through concepts of information geometry, such as the Fisher metric, parameters and potential functions. Moreover, we provide natural gradient descent learning and em-algorithms for RoBM as applications of information geometry.
Recurrence plots are useful tools for visualizing the inner structure of a time series, and they have been applied to physiological data to examine brain activity. However, these studies have focused on qualitative analysis of the data. In this study, we used unthresholded recurrence plots of near-infrared spectroscopy (NIRS) data to detect the difference in brain activity between task periods and non-task periods. Histograms derived from the recurrence plots showed a statistical difference between the periods. Throughout the pre-task period, task period, and post-task period, the histogram kept its shape statistically and shifted horizontally according to the period. Therefore, the changes in dynamical systems describing brain activity were observed as changes in histograms derived from NIRS data.
In this paper, for contributing to solve the problems of one-sided, or two-sided approximation, a constructive enclosure approximation (having representable lower and upper bounds) of a continuous function of many variables by piecewise linear functions is provided. A theorem of a representation like Kolmogorov's superposition theorem of continuous functions of many variables is provided, and a theorem of a constructive piecewise linear enclosure of a continuous function of many variables is also provided. By using an implementation of the theorems on Maple, the examples of piecewise linear enclosures of a polynomial and a transcendental function of three variables are obtained.