Asymptotic expansion of a nonlinear oscillatorwith a jump-diffusion process　　　　　　　　　　　　　　　
Yasushi Ishikawa, Takanobu Yamanobe
Japan J. Induct. Appl. Math., 35, 969, 1004, 2018年, ［査読有り］
英語, 研究論文（学術雑誌）

Global dynamics of a stochastic neuronal oscillator
Takanobu Yamanobe
PHYSICAL REVIEW E, 88, 5, 052709, AMER PHYSICAL SOC, 2013年11月, ［査読有り］
英語, 研究論文（学術雑誌）, Nonlinear oscillators have been used to model neurons that fire periodically in the absence of input. These oscillators, which are called neuronal oscillators, share some common response structures with other biological oscillations such as cardiac cells. In this study, we analyze the dependence of the global dynamics of an impulse-driven stochastic neuronal oscillator on the relaxation rate to the limit cycle, the strength of the intrinsic noise, and the impulsive input parameters. To do this, we use a Markov operator that both reflects the density evolution of the oscillator and is an extension of the phase transition curve, which describes the phase shift due to a single isolated impulse. Previously, we derived the Markov operator for the finite relaxation rate that describes the dynamics of the entire phase plane. Here, we construct a Markov operator for the infinite relaxation rate that describes the stochastic dynamics restricted to the limit cycle. In both cases, the response of the stochastic neuronal oscillator to time-varying impulses is described by a product of Markov operators. Furthermore, we calculate the number of spikes between two consecutive impulses to relate the dynamics of the oscillator to the number of spikes per unit time and the interspike interval density. Specifically, we analyze the dynamics of the number of spikes per unit time based on the properties of the Markov operators. Each Markov operator can be decomposed into stationary and transient components based on the properties of the eigenvalues and eigenfunctions. This allows us to evaluate the difference in the number of spikes per unit time between the stationary and transient responses of the oscillator, which we show to be based on the dependence of the oscillator on past activity. Our analysis shows how the duration of the past neuronal activity depends on the relaxation rate, the noise strength, and the impulsive input parameters.

Stochastic phase transition operator
Takanobu Yamanobe
PHYSICAL REVIEW E, 84, 1, 011924, AMER PHYSICAL SOC, 2011年07月, ［査読有り］
英語, 研究論文（学術雑誌）, In this study a Markov operator is introduced that represents the density evolution of an impulse-driven stochastic biological oscillator. The operator's stochastic kernel is constructed using the asymptotic expansion of stochastic processes instead of solving the Fokker-Planck equation. The Markov operator is shown to successfully approximate the density evolution of the biological oscillator considered. The response of the oscillator to both periodic and time-varying impulses can be analyzed using the operator's transient and stationary properties. Furthermore, an unreported stochastic dynamic bifurcation for the biological oscillator is obtained by using the eigenvalues of the product of the Markov operators.

Role of the frontal eye fields in smooth-gaze tracking
K Fukushima, T Yamanobe, Y Shinmei, J Fukushima, S Kurkin
BRAIN MECHANISMS FOR THE INTEGRATION OF POSTURE AND MOVEMENT, 143, 391, 401, ELSEVIER SCIENCE BV, 2004年, ［査読有り］
英語, 研究論文（学術雑誌）, Visual and vestibular senses are essential for appropriate motor behavior in three-dimensional (3D) space. Discovery of relevant specific subdivisions in sensory and motor pathways in recent decades has considerably advanced our understanding of the overall neural control of movement. Such subdivisions must eventually be further delineated into functional neural circuits for purposeful motor acts. Two critical questions are where in the brain do such circuits operate, and by what means. In this chapter, these issues are addressed for smooth tracking eye-movement systems in the simian. These results show that contrary to current understanding, synthesis of the functionally similar eye-movement systems, smooth-pursuit and vergence, takes place in the frontal cortex. This processing, which is of higher order than previously supposed, enables primates to track and manipulate objects moving in 3D space with the utmost of efficiency.

Directional asymmetry in smooth ocular tracking in the presence of visual background in young and adult primates
N Takeichi, J Fukushima, S Kurkin, T Yamanobe, Y Shinmei, K Fukushima
EXPERIMENTAL BRAIN RESEARCH, 149, 3, 380, 390, SPRINGER-VERLAG, 2003年04月, ［査読有り］
英語, 研究論文（学術雑誌）, The smooth pursuit system moves the eyes in space accurately while compensating for visual inputs from the moving background and/or vestibular inputs during head movements. To understand the mechanisms underlying such interactions, we examined the influence of a stationary textured visual background on smooth pursuit tracking and compared the results in young and adult humans and monkeys. Six humans (three children, three adults) and six macaque monkeys (five young, one adult) were used. Human eye movements were recorded using infrared oculography and evoked by a sinusoidally moving target presented on a computer monitor. Scleral search coils were used for monkeys while they tracked a target presented on a tangent screen. The target moved in a sinusoidal or trapezoidal fashion with or without whole body rotation in the same plane. Two kinds of backgrounds, homogeneous and stationary textured, were used. Eye velocity gains (eye velocity/target velocity) were calculated in each condition to compare the influence of the textured background. Children showed asymmetric eye movements during vertical pursuit across the textured (but not the homogeneous) background; upward pursuit was severely impaired, and consisted mostly of catch-up saccades. In contrast, adults showed no asymmetry during pursuit across the different backgrounds. Monkeys behaved similarly; only slight effects were observed with the textured background in a mature monkey, whereas upward pursuit was severely impaired in young monkeys. In addition, VOR cancellation was severely impaired during upward eye and head movements, resulting in residual downward VOR in young monkeys. From these results, we conclude that the directional asymmetry observed in young primates may reflect a different neural organization of the vertical, particularly upward, pursuit system in the face of conflicting visual and vestibular inputs that can be associated with pursuit eye movements. Apparently, proper compensation matures later.

Coding of smooth eye movements in three-dimensional space by frontal cortex
K Fukushima, T Yamanobe, Y Shinmei, J Fukushima, S Kurkin, BW Peterson
NATURE, 419, 6903, 157, 162, NATURE PUBLISHING GROUP, 2002年09月, ［査読有り］
英語, 研究論文（学術雑誌）, Through the development of a high-acuity fovea, primates with frontal eyes have acquired the ability to use binocular eye movements to track small objects moving in space(1). The smooth-pursuit system moves both eyes in the same direction to track movement in the frontal plane (frontal pursuit), whereas the vergence system moves left and right eyes in opposite directions to track targets moving towards or away from the observer (vergence tracking). In the cerebral cortex and brainstem, signals related to vergence eye movements-and the retinal disparity and blur signals that elicit them-are coded independently of signals related to frontal pursuit(2-6). Here we show that these types of signal are represented in a completely different way in the smooth-pursuit region of the frontal eye fields(7-11). Neurons of the frontal eye field modulate strongly during both frontal pursuit and vergence tracking, which results in three-dimensional cartesian representations of eye movements. We propose that the brain creates this distinctly different intermediate representation to allow these neurons to function as part of a system that enables primates to track and manipulate objects moving in three-dimensional space.

Predictive responses of periarcuate pursuit neurons to visual target motion
K Fukushima, T Yamanobe, Y Shinmei, J Fukushima
EXPERIMENTAL BRAIN RESEARCH, 145, 1, 104, 120, SPRINGER-VERLAG, 2002年07月, ［査読有り］
英語, 研究論文（学術雑誌）, The smooth pursuit eye movement system uses retinal information about the image-slip-velocity of the target in order to match the eye-velocity-in-space (i.e., gaze-velocity) to the actual target velocity. To maintain the target image on the fovea during smooth gaze tracking, and to compensate for the long delays involved in processing visual motion information and/or eye velocity commands, the pursuit system must use prediction. We have shown recently that both retinal image-slip-velocity and gaze-velocity signals are coded in the discharge of single pursuit-related neurons in the simian periarcuate cortex. To understand how periarcuate pursuit neurons are involved in predictive smooth pursuit, we examined the discharge characteristics of these neurons in trained Japanese macaques. When a stationary target abruptly moved sinusoidally along the preferred direction at 0.5 Hz, the response delays of pursuit cells seen at the onset of target motion were compensated in succeeding cycles. The monkeys were also required to continue smooth pursuit of a sinusoidally moving target while it was blanked for about half of a cycle at 0.5 Hz. This blanking was applied before cell activity normally increased and before the target changed direction. Normalized mean gain of The cells' responses (re control value without blanking) decreased to 0.81(+/-0.67 SD), whereas normalized mean gain of the eye movement (eye gain) decreased to 0.65 (+/-0.16 SD). A majority (75%) of pursuit neurons discharged appropriately up to 500 ms after target blanking even though eye velocity decreased sharply, suggesting a dissociation of the activity of those pursuit neurons and eye velocity. To examine whether pursuit cell responses contain a predictive component that anticipates visual input, the monkeys were required to fixate a stationary target while a second test laser spot was moved sinusoidally. A majority (68%) of pursuit cells tested responded to the second target motion. When the second spot moved abruptly along the preferred direction, the response delays clearly seen at the onset of sinusoidal target motion were compensated in succeeding cycles. Blanking (400-600 ms) was also applied during sinusoidal motion at 1 Hz before the test spot changed its direction and before pursuit neurons normally increased their activity. Preferred directions were similar to those calculated for target motion (normalized mean gain=0.72). Similar responses were also evoked even if the second spot was flashed as it moved. Since the monkeys fixated the stationary spot well, such flashed stimuli should not induce significant retinal slip. These results taken together suggest that the prediction-related activity of periarcuate pursuit neurons contains extracted visual components that reflect direction and speed of the reconstructed target image, signals sufficient for estimating target motion. We suggest that many periarcuate pursuit neurons convey this information to generate appropriate smooth pursuit eye movements.

Purkinje cells of the cerebellar dorsal vermis: Simple-spike activity during pursuit and passive whole-body rotation
Y Shinmei, T Yamanobe, J Fukushima, K Fukushima
JOURNAL OF NEUROPHYSIOLOGY, 87, 4, 1836, 1849, AMER PHYSIOLOGICAL SOC, 2002年04月, ［査読有り］
英語, 研究論文（学術雑誌）, To track a slowly moving object during whole body rotation, smooth-pursuit and vestibularly induced eye movements must interact to maintain the accuracy of eye movements in space (i. e., gaze), and gaze movement signals must eventually be converted into eye movement signals in the orbit. To understand the role played by the cerebellar vermis in pursuit-vestibular interactions, in particular whether the output of the vermis codes gaze-velocity or eye-velocity, we examined simple-spike activity of 58 Purkinje (P-)cells in lobules VI-VII of head-stabilized Japanese monkeys that were trained to elicit smooth-pursuit eye movements and cancel their vestibuloocular reflex (VOR) during passive whole body rotation around horizontal, vertical, or oblique axes. All pursuit-sensitive vermal P- cells also responded during VOR cancellation, and the majority of them had peak modulation near peak stimulus velocity. The directions of maximum modulation during these two tasks were distributed in all directions with a downward preponderance. Using standard criteria, 40% of pursuit-sensitive vermal P- cells were classified as gaze-velocity. Other P- cells were classified either as eye/head-velocity group I (36%) that had similar preferred directions during pursuit and VOR cancellation but that had larger responses during VOR x1 when gaze remained stationary, or as eye/head-velocity group II (24%) that had oppositely directed or orthogonal eye and head movement sensitivity during pursuit and VOR cancellation. Eye/head-velocity group I P- cells contained cells whose activity was correlated with eye velocity. Modulation of many P- cells of the three groups during VOR x1 could be accounted for by the linear addition of their modulations during pursuit and VOR cancellation. When monkeys fixated a stationary target, over half of the P- cells tested, including gaze-velocity P- cells, discharged in proportion to the velocity of retinal motion of a second spot. These observations are in a striking contrast to our previous results for floccular vertical P- cells. Because we used identical tasks, these differences suggest that the two cerebellar regions are involved in very different kinds of processing of pursuit-vestibular interactions.

Response of a pacemaker neuron model to stochastic pulse trains
T Yamanobe, K Pakdaman
BIOLOGICAL CYBERNETICS, 86, 2, 155, 166, SPRINGER-VERLAG, 2002年02月, ［査読有り］
英語, 研究論文（学術雑誌）, We investigated the response of a pacemaker neuron model to trains of inhibitory stochastic impulsive perturbations. The model captures the essential aspect of the dynamics of pacemaker neurons. Especially, the model reproduces linearization by stochastic pulse trains, that is, the disappearance of the paradoxical segments in which the output firing rate of pacemaker neurons increases with inhibition rate, as the coefficient of variation of the input pulse train increases. To study the response of the model to stochastic pulse trains, we use a Markov operator governing the phase transition. We show how linearization occurs based on the spectral analysis of the Markov operator. Moreover, using Lyapunov exponents, we show that variable inputs evoke reliable firing, even in situations where periodic stimulation with the same mean rate does not.

Response of a pacemaker neuron model to transient pulse trains
Takanobu Yamanobe, Taishin Nomura, Khashayar Pakdaman, Shunsuke Sato
Systems and Computers in Japan, 33, 3, 63, 73, 2002年, ［査読有り］
英語, 研究論文（学術雑誌）, In this study, the response of the pacemaker neuron model to transient pulse inputs (input sequence composed of a finite number of pulses with interval variations) is examined. The shift of the firing phase of the pacemaker neuron generated by a single pulse stimulus is represented by the phase transition curve. The dynamics of the pacemaker neuron receiving pacemaker pulse stimuli has been analyzed in terms of the one-dimensional discrete dynamical system derived from the phase transition curve. This paper shows that the dynamics of the model for the transient pulse input can be described by a finite set of phase transition curves. The constructed pacemaker neuron model can reproduce the response of the slowly adapting stretch receptor organ (SAO) of the crayfish to the transient pulse inputs observed in the experiment. It is observed in the experiment that the qualitative property of the response pattern of the SAO to the transient pulse inputs changes suddenly while the input is applied. In order to analyze the generation mechanism underlying the response to the transient pulse inputs, the response of the model is analyzed in detail for inputs with increasing rate, that is, pulse input trains in which the inverse of the input pulse interval monotonically increases. In particular, the mechanism of generation of the paradoxical response, in which the output rate increases monotonously in response to the inhibitory input with increasing rate, is described. © 2002 Scripta Technica, Syst. Comp. Jpn.

3J0945 神経情報コーディングにおける確率的入力の効果(16.神経回路・脳の情報処理,一般講演,日本生物物理学会第40回年会)
山野辺 貴信, Pakdaman Khashayar
生物物理, 42, 2, S177, 一般社団法人 日本生物物理学会, 2002年
日本語

Adaptive changes in smooth pursuit eye movements induced by cross-axis pursuit-vestibular interaction training in monkeys
K Fukushima, SG Wells, T Yamanobe, N Takeichi, Y Shinmei, J Fukushima
EXPERIMENTAL BRAIN RESEARCH, 139, 4, 473, 481, SPRINGER-VERLAG, 2001年08月, ［査読有り］
英語, 研究論文（学術雑誌）, The smooth pursuit system interacts with the vestibular system to maintain the accuracy of eye movements in space. To understand neural mechanisms of short-term modifications of the vestibulo-ocular reflex (VOR) induced by pursuit-vestibular interactions, we used a cross-axis procedure in trained monkeys. We showed earlier that pursuit training in the plane orthogonal to the rotation plane induces adaptive cross-axis VOR in complete darkness. To further study the properties of adaptive responses, we examined here the initial eye movements during tracking of a target while being rotated with a trapezoidal waveform. (peak velocity 30 or 40 degrees /s). Subjects were head-stabilized Japanese monkeys that were rewarded for accurate pursuit. Whole body rotation was applied either in the yaw or pitch plane while presenting a target moving in-phase with the chair with the same trajectory but in the orthogonal plane. Eye movements induced by equivalent chair rotation with or without the target were examined before and after training. Before training, chair rotation alone resulted only in the collinear VOR, and smooth eye movement-tracking of orthogonal target motion during rotation had a normal smooth pursuit latency (ca 100 ms). With training, the latency of orthogonal smooth tracking eye movements shortened, and the mean latency after 1 h of training was 42 ins with a mean gain, at 100 ms after stimulus onset, of 0.4. The cross-axis VOR induced by chair rotation in complete darkness had identical latencies with the orthogonal smooth tracking eye movements, but its gains were < 0.2. After cross-axis pursuit training, target movement alone without chair rotation induced smooth pursuit eye movements with latencies ca 100 ins. Pursuit training alone for 1 h using the same trajectory but without chair rotation did not result in any clear change in pursuit latency (ca 100 ms) or initial eye velocity. When a new target velocity was presented during identical chair rotation after training, eye velocity was correspondingly modulated by just 80 ms after rotation onset, which was shorter than the expected latency of pursuit (ca 100 ms). These results indicate that adaptive changes were induced in the smooth pursuit system by pursuit-vestibular interaction training. We suggest that this training facilitates the response of pursuit-related neurons in the cortical smooth pursuit pathways to vestibular inputs in the orthogonal plane, thus enabling smooth eye movements to be executed with shorter latencies and larger eye velocities than in normal smooth pursuit driven only by visual feedback.

Analysis of models for crustacean stretch receptors
E Takeuchi, T Yamanobe, K Pakdaman, S Sato
BIOLOGICAL CYBERNETICS, 84, 5, 349, 363, SPRINGER-VERLAG, 2001年05月, ［査読有り］
英語, 研究論文（学術雑誌）, The mechanisms underlying the diverse responses to step current stimuli of models [Edman et al. (1987)J Physiol (Lond) 384: 649-669] of lobster slowly adapting stretch receptor organs (SAO) and fast-adapting stretch receptor organs (FAO) are analyzed. In response to a step current, the models display three distinct types of firing reflecting the level of adaptation to the stimulation. Low-amplitude currents evoke transient firing containing one to several action potentials before the system stabilizes to a resting state. Conversely, high-amplitude stimulations induce a high frequency transient burst that can last several seconds before the model returns to its quiescent state. In the SAO model, the transition between the two regimes is characterized by a sustained pacemaker firing at an intermediate stimulation amplitude. The FAO model does not exhibit such a maintained firing; rather, the duration of the transient firing increases at first with the stimulus intensity, goes through a maximum and then decreases at larger intensities. Both models comprise seven variables representing the membrane potential, the sodium fast activation, fast inactivation, slow inactivation, the potassium fast activation, slow inactivation gating variables, and the intra cellular sodium concentration. To elucidate the mechanisms of the firing adaptations, the seven-variable model for the lobster stretch receptor neuron is first reduced to a three-dimensional system by regrouping variables with similar time scales. More precisely, we substituted the membrane potential V for the sodium fast activation equivalent potential V-m, the potassium fast inactivation V-n for the sodium fast inactivation V-h, and the sodium slow inactivation V-l for the potassium slow inactivation V-r. Comparison of the responses of the reduced models to those of the original models revealed that the main behaviors of the system were preserved in the reduction process. We classified the different types of responses of the reduced SAO and FAO models to constant current stimulation. We analyzed the transient and stationary responses of the reduced models by constructing bifurcation diagrams representing the qualitatively distinct dynamics of the models and the transitions between them. These revealed that (1) the transient firings prior to reaching the stationary state can be accounted for by the sodium slow inactivation evolving more slowly than the other two variables, so that the changes during the transient firings reflect the bifurcations that the two-dimensional system undergoes when the sodium slow inactivation, considered as a parameter, is varied; and (2) the stationary behaviors of the models are captured by the standard bifurcations of a two-dimensional system formed by the membrane potential and the potassium fast inactivation. We found that each type of firing and the transitions between them is due to the interplay between essentially three variables: two fast ones accounting for the action potential generation and the post-discharge refractoriness, and a third slow one representing the adaptation.

Adaptive eye movements induced by cross-axis pursuit - vestibular interactions in trained monkeys
K Fukushima, J Fukushima, T Yamanobe, Y Shinmei, S Kurkin
ACTA OTO-LARYNGOLOGICA, 121, 73, 79, TAYLOR & FRANCIS AS, 2001年, ［査読有り］
英語, 研究論文（学術雑誌）, We showed previously that smooth pursuit training combined with whole-body rotation in the orthogonal plane induces adaptive cross-axis vestibulo-ocular reflex (VOR). To gain an insight into the possible pathways and the nature of error signals for cross-axis VOR adaptation, we examined further properties of adaptive responses. In the first series, we trained monkeys for vertical pursuit during sinusoidal yaw rotation at 0.5 Hz ( +/- 10 degrees) by presenting a target spot either in phase with, or with phase shifts (lead or lag) of 90 degrees to, the chair for I h. After training, sinusoidal or trapezoidal yaw rotation was tested in complete darkness without a target. Different training conditions resulted in different amounts of phase shift in cross-axis VOR. Trapezoidal yaw rotation (peak acceleration, approximate to 780 degrees /s(2)) revealed further differences in the direction, latency and time course of the adaptive responses depending on the conditions of the pursuit task. At least two (fast and slow) components with different latencies were induced in the cross-axis VOR by trapezoidal rotation after in-phase and phase-shift training. Adaptive responses were accurately simulated by the weighted sum of these two components. In the second series, we examined the effects of sequentially flashed (10 mus) targets in the horizontal plane during pitch rotation. The monkeys learned to track such targets by smooth pursuit, and cross-axis VOR was also induced after such apparent motion stimuli without retinal slip of the target image. These results indicate the importance of eye velocity for cross-axis VOR and suggest that this adaptation occurs most probably in the smooth pursuit pathways.

サル前頭眼野の化学的不活性化--精神分裂病患者の滑動性眼球運動障害に対する前頭眼野の関与--　　　　　　　　　　　　　　　
福島順子, 山野辺貴信, 新明康弘, 福島菊郎
脳と精神の医学, 12, 53, 62, 2001年, ［査読有り］
日本語, 研究論文（学術雑誌）

過渡的パルス入力に対するペースメーカ細胞モデルの応答
山野辺 貴信, 野村 泰伸, PAKDAMAN Khashayar, 佐藤 俊輔
電子情報通信学会論文誌. D-2, 情報・システム 2-パターン処理, 83, 8, 1811, 1821, 一般社団法人電子情報通信学会, 2000年08月20日, ［査読有り］
日本語, 研究論文（学術雑誌）, 過渡的パルス入力(有限個の間隔変動パルス列入力)に対するペースメーカ細胞モデルの応答を調べた.単一パルス刺激によって発生するペースメーカ細胞の発火位相の変化は位相遷移曲線で表される.周期パルス刺激を受けるペースメーカ細胞のダイナミックスは位相遷移曲線から導出される1次元離散力学系で解析されてきた.我々は過渡的パルス入力に対するモデルのダイナミックスが位相遷移曲線の有限個の集合で記述されることを示す.ペースメーカ細胞モデルは過渡的パルス入力に対するザリガニの筋伸張受容器(Slowly Adapting stretch receptor Organ:SAO)の実験で観察される応答を再現する.そこでは, 過渡的入力に対するSAOの応答パターンが入力が加えられている途中で急激にその定性的性質が変化する.我々は過渡的パルス入力に対する応答生成の背後にあるメカニズムを明らかにするために周波数増加入力, すなわち, 入力パルス間隔の逆数が単調に増加するパルス列入力に対するモデルの応答を詳細に解析する.特に, 抑制性の周波数増加入力に対し出力周波数が単調に増加する逆説的応答の生成メカニズムを明らかにする.

Activity of frontal eye movement-related neurons during pursuit-vestibular interactions
K Fukushima, T Sato, T Yamanobe, Y Shinmei, J Fukushima
ELECTROPHYSIOLOGY AND KINESIOLOGY, 247, 251, MEDIMOND S R L, 2000年, ［査読有り］
英語, 研究論文（国際会議プロシーディングス）, Pursuit-related neurons in the periarcuate cortex carry various signals, particularly velocity, for eye, head (vestibular) and retinal slip of target image. The majority of them carry gaze-velocity signals during pursuit-vestibular interaction conditions. Retinal image-velocity response can be induced by apparent motion stimuli without retinal slip of target image. Pursuit-, vestibular and gaze- related activity is also seen in the supplementary eye fields.

Rate coding in a chain of pulse-coupled oscillators
T Yamanobe, K Pakdaman, S Sato
PHYSICAL REVIEW E, 60, 4, 4564, 4570, AMERICAN PHYSICAL SOC, 1999年10月, ［査読有り］
英語, 研究論文（学術雑誌）, The input-output relation of a chain of pulse-coupled oscillators is examined. The oscillators capture the essential aspect of the dynamics of pacemaker neurons. Inputs consist of pacemaker, and noisy trains impinging upon the first unit in the chain. The response of the chain is defined as the spike train emitted by the last unit. We observe two important phenomena in the response of the chain for a given input train, whether pacemaker or noisy. First, the mean output rate of the chain is equal to he mean input race in the range of input rate in which one input pulse corresponds to one:output spike without phase locking (1:1 alternation). Second, for the same input range, the output interspike intervals tend to the average of the input interpulse intervals in a long chain of oscillators. This behavior contrasts with the fact that the response of a single unit depends on both input rate and pattern. We show that the response of the chain is reproduced by the phase transition curve which represents the phase shift due to a single isolated pulse stimulus. This analysis reveals that the averaging of the output interspike intervals is due to the geometrical aspect of the phase transition curve. This geometrical aspect causes the dependence of the response of a single unit on input pattern. [S1063-651X(99)11009-2].

Analysis of the response of a pacemaker neuron model to transient inputs
T Yamanobe, K Pakdaman, T Nomura, S Sato
BIOSYSTEMS, 48, 1-3, 287, 295, ELSEVIER SCI IRELAND LTD, 1998年09月, ［査読有り］
英語, 研究論文（学術雑誌）, The response of a pacemaker neuron model to a train of transient inhibitory impulsive perturbations is examined. The model reproduces the heterogeneous discharge forms and abrupt switchings displayed by the crayfish slowly adapting stretch receptor organ (Segundo et al., 1994, Neuroscience 62(2), pp. 459-480). The non-monotonous aspect of the instantaneous firing rate of the model reflects the fact that in some regimes input and output rates are both increasing, despite the inhibitory effect of the former. We determine how such paradoxical acceleration takes place by analyzing the response of the model using its phase transition curve. We show that paradoxical acceleration results from the fact that the phase transition curve exhibits a large slowly increasing, almost linear section similar to that of living preparations. (C) 1998 Elsevier Science Ireland Ltd. All rights reserved.

A mathematical aspect of neural coding
S Sato, T Nomura, K Pakdaman, Y Maeda, T Yamanobe, H Fukai
ADVANCED TOPICS IN BIOMATHEMATICS, 229, 238, WORLD SCIENTIFIC PUBL CO PTE LTD, 1998年, ［査読有り］
英語, 研究論文（国際会議プロシーディングス）, In this paper, we show bifurcation diagrams of various models of single neuron to direct current stimuli and to periodic pulse trains. We introduce a simple mathematical model of a. living pacemaker neuron and show that the phase transition curve is a useful tool to investigate the neuron's response to periodic pulse trains. We also mention a model for bursting oscillation and reduction of its dynamics.

The response of lobster stretch receptor models to single pulses and step currents
T Yamanobe, K Pakdaman, T Nomura, S Sato
ICONIP'98: THE FIFTH INTERNATIONAL CONFERENCE ON NEURAL INFORMATION PROCESSING JOINTLY WITH JNNS'98: THE 1998 ANNUAL CONFERENCE OF THE JAPANESE NEURAL NETWORK SOCIETY - PROCEEDINGS, VOLS 1-3, 1252, 1255, OHMSHA LTD, 1998年, ［査読有り］
英語, 研究論文（国際会議プロシーディングス）, The response of lobster slowly and fast adapting stretch receptor organ models to single pulses and step currents are investigated. The comparison of the two models clarifies the differences between their discharge adaptation. To clarify the difference, we analyze the discharge adaptation from three points of view which are frequency adaptation, adaptation of membrane potential amplitude and duration of firing.

On the behavior of mRIC - A simple model of living pacemakers driven by periodic pulse trains
S Sato, T Nomura, S Doi, T Yamanobe
BIOSYSTEMS, 40, 1-2, 169, 176, ELSEVIER SCI IRELAND LTD, 1997年, ［査読有り］
英語, 研究論文（学術雑誌）, The main feature separating a living pacemaker from other oscillators is the fact that the former has not only the oscillatory property but also slow and fast changes of the membrane potential corresponding to the sub- and suprathreshold regions. We propose a simple mathematical model called mRIC and show that the model exhibited the essential feature of pacemakers generating spikes at constant time intervals. The behavior of the model driven by periodic pulse trains is analysed using the phase transition curve.

Stochastic phase transition operator (vol 84, 011924, 2011)
Takanobu Yamanobe, PHYSICAL REVIEW E, 88, 1, 2013年07月
AMER PHYSICAL SOC, 英語, その他

Dynamics of oscillating squid giant axons in response to periodically modulating impulses and modeling analysis
Takanobu Yamanobe, JOURNAL OF PHYSIOLOGICAL SCIENCES, 63, S189, S189, 2013年
SPRINGER JAPAN KK, 英語, 研究発表ペーパー・要旨（国際会議）

Relation Between the Information Carrier in Nervous Systems and the Dependence of a Neuron Model Behavior on the Past Activity
Takanobu Yamanobe, BIOPHYSICAL JOURNAL, 102, 3, 546A, 546A, 2012年01月
CELL PRESS, 英語, 研究発表ペーパー・要旨（国際会議）

甲殻類伸張受容器の数理モデル
竹内 英二, 山野辺 貴信, PAKDAMAN Khashayar, 野村 泰伸, 佐藤 俊輔, 電子情報通信学会技術研究報告. MBE, MEとバイオサイバネティックス, 98, 94, 85, 92, 1998年05月29日
伸張受容器は受容器筋肉繊維に伸張刺激が加わると, 樹状突起に受容器電位が発生し, それが軸索初筋に伝わって活動電位が発生する.本研究では独立に提案された甲殻類の受容器電位モデル(Swerupら, 1996)と活動電位モデル(Edmanら, 1987)を用い, その2つのモデルを結合することにより新たに結合モデルを構築した.この結合モデルを用いて, ザリガニの遅順応性伸張受容器が伸張刺激を受けた時に生じる活動電位に関する生理学実験結果(Vibertら, 1979)を説明する., 一般社団法人電子情報通信学会, 日本語

甲殻類伸長受容器の非線形ダイナミクス
山野辺 貴信, PAKDAMAN K., 野村 泰伸, 佐藤 俊輔, 電子情報通信学会技術研究報告. MBE, MEとバイオサイバネティックス, 98, 94, 93, 100, 1998年05月29日
遅順応性伸張受容器(Sloly Adapting stretch receptor Organ; SAO), 速順応性伸長受容器(Fast Adapting stretch receptoro Organ; FAO)モデルの非線形ダイナミクスについて報告する.伸長受容器モデルはイオンの透過率に基づき, 7つの変数から構成される.まず, 伸長受容器モデルが単一パルス入力, ステップ入力, 一定電流入力に対するザリガニ伸長受容器の発火パターンを再現することを示す.次に, このモデルが3変数まで簡約化できることを示し, さらに, この簡約化した3変数モデルのダイナミクスを分岐理論を用いて解析する.最後にこの解析に基づき, SAOとFAOのダイナミクスを比較する., 一般社団法人電子情報通信学会, 英語

過渡的パルス入力に対するペースメーカ細胞モデルの応答
山野辺 貴信, PAKDAMAN Khashayar, 野村 泰伸, 佐藤 俊輔, 生体・生理工学シンポジウム論文集, 12, 45, 48, 1997年09月04日
日本語

ペースメーカ細胞モデルの情報コーディング様式について
山野辺貴信, 野村泰伸, 土居伸二, 佐藤俊輔, 生体・生理工学シンポジウム論文集, 11th, 77-80, 80, 1996年11月
日本語

間隔変動パルス列入力に対するmRICの応答特性について
山野辺 貴信, 野村 泰伸, 土居 伸二, 佐藤 俊輔, 電子情報通信学会技術研究報告. MBE, MEとバイオサイバネティックス, 96, 75, 127, 134, 1996年05月24日
自発的に一定の時間間隔で反復興奮する神経細胞はペースメーカ細胞と呼ばれる. mRICはこの振舞いを模倣するモデルである. このモデルに, 刺激強度が一定で, 刺激間隔が適当な規則に従い時間変化するパルス入力を加えたときの応答特性を1次元写像(PTC)を用いて解析する. 特に, 入力パルス列と出力パルス列の瞬時周波数の関係について考察する., 一般社団法人電子情報通信学会, 日本語

簡約化された Hodgkin-Huxley 方程式の解析
山野辺, 土居 伸二, 佐藤 俊輔, 信学技報, 94, 41, 48, 1994年
Keplerらによって提出された簡約化法を用い,Hodgkin-Huxley(H-H)方程式を簡約化する.簡約化された方程化の相平面上での振る舞いを詳しく調べ,彼らの簡約化法を検討する.とりわけ,簡約化法における重み係数の決め方について考察する.さらに簡約化されたH-H方程式の周期パルス刺激に対する応答特性を調べる., 一般社団法人電子情報通信学会, 日本語

Reduction of a Markov operator representing the dynamics of stochastic neuronal model by sparse discrete cosine transform　　　　　　　　　　　　　　　
山野辺貴信
第５６回日本生物物理学会年会, 2018年09月17日, 英語, ポスター発表
［国内会議］

Reduction of the dynamics of stochastic neuronal models by sparse discrete cosine transform　　　　　　　　　　　　　　　
山野辺貴信
11th FENS Forum of Neuroscience, 2018年07月10日, 英語, ポスター発表
［国内会議］

確率過程の漸近展開理論による振動子モデルの解析　　　　　　　　　　　　　　　
山野辺貴信
Perspectives of Nonlinear Phenomena in Random and Non-autonomous Dynamics, 2017年09月29日, 日本語
［招待講演］, ［国内会議］

次元の呪いを克服した固有値問題数値解法による確率的神経細胞モデルの解析　　　　　　　　　　　　　　　
科学研究費補助金（基盤研究（C））
2018年04月 - 2021年03月
山野辺貴信
文部科学省, 研究代表者, 競争的資金

スパースモデリングによる確率的神経細胞モデルダイナミクスの縮約
科学研究費助成事業
2016年04月01日 - 2018年03月31日
山野辺 貴信
これまでの研究で、我々は、確率微分方程式で表される神経細胞モデルに、時間変化するパルス列入力が入るときの統計的大域挙動を記述する線形作用素を構築した。この線形作用素は有限次元の行列で近似されることが理論的に示されるが、線形作用素の単なる離散近似では近似行列の要素数が多くなりすぎ、与えられたモデルの統計的大域挙動を解析するのが困難となる。本研究では、我々が提案した線形作用素の積分核が、良く用いられるパラメータの範囲でスパース性を持つことに着目し、線形作用素をある基底で展開し、この困難を緩和することにした。構築した線形作用素は確率的神経細胞モデルのパラメータや入力パラメータに依存し、そのスペクトル特性が変わる。入力は時間変化するため、線形作用素を縮約する問題は画像圧縮とほぼ同じ問題となる。したがって、パラメータごとに基底を用意するのではなく、同じ基底を用い変換した方が応用上適している。そこで離散コサイン変換（DCT-II）のFFT の部分にsparse FFT を用い、線形作用素を少ない要素数の行列で近似することを試みた。sparse FFT には大きく分けて確率的sparse FFT と決定論的sparse FFT の２つのアプローチがある。ここでは決定論的sparse FFT を用いた。これによりスパースなフーリエ係数を決定論的に計算可能となり、FFT を用いたDCT-II を用いるときより、sparse FFT を用いたDCT-IIの方が効率的に線形作用素を縮約できることを示した。
日本学術振興会, 新学術領域研究(研究領域提案型), 北海道大学, 16H01527