Recent zbMATH articles in MSC 92C20
https://zbmath.org/atom/cc/92C20
2021-06-15T18:09:00+00:00
Werkzeug
Visibility-graphlet approach to the output series of a Hodgkin-Huxley neuron.
https://zbmath.org/1460.92040
2021-06-15T18:09:00+00:00
"Zhao, Yuanying"
https://zbmath.org/authors/?q=ai:zhao.yuanying
"Gu, Changgui"
https://zbmath.org/authors/?q=ai:gu.changgui
"Yang, Huijie"
https://zbmath.org/authors/?q=ai:yang.huijie
Summary: The output signals of neurons that are exposed to external stimuli are of great importance for brain functionality. Traditional time-series analysis methods have provided encouraging results; however, the associated patterns and their correlations in the output signals of neurons are masked by statistical procedures. Here, graphlets are employed to extract the local temporal patterns and the transitions between them from the output signals when neurons are exposed to external stimuli with selected stimulating periods. A transition network is defined where the node is the graphlet and the direct link is the transition between two successive graphlets. The transition-network structure is affected by the simulating periods. When the stimulating period moves close to an integer multiple of the neuronal intrinsic period, only the backbone or core survives, while the other linkages disappear. Interestingly, the size of the backbone (number of nodes) equals the multiple. The transition-network structure is conservative within each stimulating region, which is defined as the range between two successive integer multiples. Nevertheless, the backbone or detailed structure is significantly altered between different stimulating regions. This alternation is induced primarily from a total of 12 active linkages. Hence, the transition network shows the structure of cross correlations in the output time-series for a single neuron.
{\copyright 2021 American Institute of Physics}
Reviewer: Reviewer (Berlin)
Deep learning of biological models from data: applications to ODE models.
https://zbmath.org/1460.92014
2021-06-15T18:09:00+00:00
"Su, Wei-Hung"
https://zbmath.org/authors/?q=ai:su.wei-hung
"Chou, Ching-Shan"
https://zbmath.org/authors/?q=ai:chou.ching-shan
"Xiu, Dongbin"
https://zbmath.org/authors/?q=ai:xiu.dongbin
Summary: Mathematical equations are often used to model biological processes. However, for many systems, determining analytically the underlying equations is highly challenging due to the complexity and unknown factors involved in the biological processes. In this work, we present a numerical procedure to discover dynamical physical laws behind biological data. The method utilizes deep learning methods based on neural networks, particularly residual networks. It is also based on recently developed mathematical tools of flow-map learning for dynamical systems. We demonstrate that with the proposed method, one can accurately construct numerical biological models for unknown governing equations behind measurement data. Moreover, the deep learning model can also incorporate unknown parameters in the biological process. A successfully trained deep neural network model can then be used as a predictive tool to produce system predictions of different settings and allows one to conduct detailed analysis of the underlying biological process. In this paper, we use three biological models -- SEIR model, Morris-Lecar model and the Hodgkin-Huxley model -- to show the capability of our proposed method.
Reviewer: Reviewer (Berlin)
Synchronization and locking in oscillators with flexible periods.
https://zbmath.org/1460.92037
2021-06-15T18:09:00+00:00
"Savinov, Mariya"
https://zbmath.org/authors/?q=ai:savinov.mariya
"Swigon, David"
https://zbmath.org/authors/?q=ai:swigon.david
"Ermentrout, Bard"
https://zbmath.org/authors/?q=ai:ermentrout.bard-g
Summary: Entrainment of a nonlinear oscillator by a periodic external force is a much studied problem in nonlinear dynamics and characterized by the well-known Arnold tongues. The circle map is the simplest such system allowing for stable \(N\):\(M\) entrainment where the oscillator produces \(N\) cycles for every \(M\) stimulus cycles. There are a number of experiments that suggest that entrainment to external stimuli can involve both a shift in the phase and an adjustment of the intrinsic period of the oscillator. Motivated by a recent model of \textit{J. D. Loehr}, \textit{E. W. Large} and \textit{C. Palmer} [``Temporal coordination and adaptation to rate change in music performance'', J. Exp. Psychol.: Hum. Percept. Perform. 37, No. 4, 1292--1309 (2011; \url{doi:10.1037/a0023102})], we explore a two-dimensional map in which the phase and the period are allowed to update as a function of the phase of the stimulus. We characterize the number and stability of fixed points for different \(N\):\(M\)-locking regions, specifically, 1:1, 1:2, 2:3, and their reciprocals, as a function of the sensitivities of the phase and period to the stimulus as well as the degree that the oscillator has a preferred period. We find that even in the limited number of locking regimes explored, there is a great deal of multi-stability of locking modes, and the basins of attraction can be complex and riddled. We also show that when the forcing period changes between a starting and final period, the rate of this change determines, in a complex way, the final locking pattern.
{\copyright 2021 American Institute of Physics}
Reviewer: Reviewer (Berlin)
On the rate coding response of peripheral sensory neurons.
https://zbmath.org/1460.92039
2021-06-15T18:09:00+00:00
"Wong, Willy"
https://zbmath.org/authors/?q=ai:wong.willy
Summary: The rate coding response of a single peripheral sensory neuron in the asymptotic, near-equilibrium limit can be derived using information theory, asymptotic Bayesian statistics and a theory of complex systems. Almost no biological knowledge is required. The theoretical expression shows good agreement with spike-frequency adaptation data across different sensory modalities and animal species. The approach permits the discovery of a new neurophysiological equation and shares similarities with statistical physics.
Reviewer: Reviewer (Berlin)
Quasi-steady-state reduction of a model for cytoplasmic transport of secretory vesicles in stimulated chromaffin cells.
https://zbmath.org/1460.92067
2021-06-15T18:09:00+00:00
"Oelz, Dietmar B."
https://zbmath.org/authors/?q=ai:oelz.dietmar-b
Summary: Neurosecretory cells spatially redistribute their pool of secretory vesicles upon stimulation. Recent observations suggest that in chromaffin cells vesicles move either freely or in a directed fashion by what appears to be a conveyor belt mechanism. We suggest that this observation reflects the transient active transport through molecular motors along cytoskeleton fibres and quantify this effect using a 1D mathematical model that couples a diffusion equation to advection equations. In agreement with recent observations the model predicts that random motion dominates towards the cell centre whereas directed motion prevails in the region abutting the cortical membrane. Furthermore the model explains the observed bias of directed transport towards the periphery upon stimulation. Our model suggests that even if vesicle transport is indifferent with respect to direction, stimulation creates a gradient of free vesicles at first and this triggers the bias of transport in forward direction. Using matched asymptotic expansion we derive an approximate drift-diffusion type model that is capable of quantifying this effect. Based on this model we compute the characteristic time for the system to adapt to stimulation and we identify a Michaelis-Menten-type law describing the flux of vesicles entering the pathway to exocytosis.
Reviewer: Reviewer (Berlin)
The roles of ascending sensory signals and top-down central control in the entrainment of a locomotor CPG.
https://zbmath.org/1460.92035
2021-06-15T18:09:00+00:00
"Codianni, Marcello G."
https://zbmath.org/authors/?q=ai:codianni.marcello-g
"Daun, Silvia"
https://zbmath.org/authors/?q=ai:daun.silvia
"Rubin, Jonathan E."
https://zbmath.org/authors/?q=ai:rubin.jonathan-e
Summary: Previous authors have proposed two basic hypotheses about the factors that form the basis of locomotor rhythms in walking insects: sensory feedback only or sensory feedback together with rhythmic activity of small neural circuits called central pattern generators (CPGs). Here we focus on the latter. Following this concept, to generate functional outputs, locomotor control must feature both rhythm generation by CPGs at the level of individual joints and coordination of their rhythmic activities, so that all muscles are activated in an appropriate pattern. This work provides an in-depth analysis of an aspect of this coordination process based on an existing network model of stick insect locomotion. Specifically, we consider how the control system for a single joint in the stick insect leg may produce rhythmic output when subjected to ascending sensory signals from other joints in the leg. In this work, the core rhythm generating CPG component of the joint under study is represented by a classical half-center oscillator constrained by a basic set of experimental observations. While the dynamical features of this CPG, including phase transitions by escape and release, are well understood, we provide novel insights about how these transition mechanisms yield entrainment to the incoming sensory signal, how entrainment can be lost under variation of signal strength and period or other perturbations, how entrainment can be restored by modulation of tonic top-down drive levels, and how these factors impact the duty cycle of the motor output.
Reviewer: Reviewer (Berlin)
Stair-like frequency response of single neuron to external electromagnetic radiation and onset of chaotic behaviors.
https://zbmath.org/1460.92036
2021-06-15T18:09:00+00:00
"Feng, Peihua"
https://zbmath.org/authors/?q=ai:feng.peihua
"Zhang, Zhengyuan"
https://zbmath.org/authors/?q=ai:zhang.zhengyuan
"Wu, Ying"
https://zbmath.org/authors/?q=ai:wu.ying
This paper considers the equations \begin{align*} \frac{du}{dt} = & -ku(u-a)(u-1)-uv+I_0\sin{(\omega t)}+k_0(\alpha+3\beta\phi^2)u \\
\frac{dv}{dt} = & \left(\epsilon+\frac{\mu_1 v}{u+\mu_2}\right)[-v-ku(u-a-1)] \\
\frac{d\phi}{dt} = & k_1u-k_2\phi+A\cos{(2\pi ft)} \end{align*} meant to describe a FitzHugh-Nagumo neuron containing a memristor subject to time-periodic input current (amplitude \(I_0\)) and independent time-periodic external electromagnetic radiation (amplitude \(A\)). A ``winding number'' for solutions is numerically calculated as a function of \(\omega\) and \(I_0\) and some solutions on PoincarÃ© sections are plotted. The standard of English is poor.
Reviewer: Carlo Laing (Auckland)
Motor protein transport along inhomogeneous microtubules.
https://zbmath.org/1460.92068
2021-06-15T18:09:00+00:00
"Ryan, S. D."
https://zbmath.org/authors/?q=ai:ryan.shawn-d
"McCarthy, Z."
https://zbmath.org/authors/?q=ai:mccarthy.zachary
"Potomkin, M."
https://zbmath.org/authors/?q=ai:potomkin.mykhailo
Summary: Many cellular processes rely on the cell's ability to transport material to and from the nucleus. Networks consisting of many microtubules and actin filaments are key to this transport. Recently, the inhibition of intracellular transport has been implicated in neurodegenerative diseases such as Alzheimer's disease and amyotrophic lateral sclerosis (ALS). Furthermore, microtubules may contain so-called \textit{defective regions} where motor protein velocity is reduced due to accumulation of other motors and microtubule-associated proteins. In this work, we propose a new mathematical model describing the motion of motor proteins on microtubules which incorporate a defective region. We take a mean-field approach derived from a first principle lattice model to study motor protein dynamics and density profiles. In particular, given a set of model parameters we obtain a closed-form expression for the equilibrium density profile along a given microtubule. We then verify the analytic results using mathematical analysis on the discrete model and Monte Carlo simulations. This work will contribute to the fundamental understanding of inhomogeneous microtubules providing insight into microscopic interactions that may result in the onset of neurodegenerative diseases. Our results for inhomogeneous microtubules are consistent with prior work studying the homogeneous case.
Reviewer: Reviewer (Berlin)
Order in chaos: structure of chaotic invariant sets of square-wave neuron models.
https://zbmath.org/1460.92038
2021-06-15T18:09:00+00:00
"Serrano, Sergio"
https://zbmath.org/authors/?q=ai:serrano.sergio-e
"MartÃnez, M. Angeles"
https://zbmath.org/authors/?q=ai:martinez.m-angeles
"Barrio, Roberto"
https://zbmath.org/authors/?q=ai:barrio.roberto
Summary: Bursting phenomena and, in particular, square-wave or fold/hom bursting, are found in a wide variety of mathematical neuron models. These systems have different behavior regimes depending on the parameters, whether spiking, bursting, or chaotic. We study the topological structure of chaotic invariant sets present in square-wave bursting neuron models, first detailed using the Hindmarsh-Rose neuron model and later exemplary in the more realistic model of a leech heart neuron. We show that the unstable periodic orbits that form the skeleton of the chaotic invariant sets are deeply related to the spike-adding phenomena, typical from these models, and how there are specific symbolic sequences and a symbolic grammar that organize how and where the periodic orbits appear. Linking this information with the topological template analysis permits us to understand how the internal structure of the chaotic invariants is modified and how more symbolic sequences are allowed. Furthermore, the results allow us to conjecture that, for these systems, the limit template when the small parameter \(\varepsilon \), which controls the slow gating variable, tends to zero is the complete Smale topological template.
{\copyright 2021 American Institute of Physics}
Reviewer: Reviewer (Berlin)
Numerical solution of the neural field equation in the presence of random disturbance.
https://zbmath.org/1460.65008
2021-06-15T18:09:00+00:00
"Kulikov, G. Yu."
https://zbmath.org/authors/?q=ai:kulikov.gennady-yurevich
"Lima, Pedro M."
https://zbmath.org/authors/?q=ai:lima.pedro-miguel
"Kulikova, Maria V."
https://zbmath.org/authors/?q=ai:kulikova.maria-v
Summary: This paper aims at presenting an efficient and accurate numerical method for treating both deterministic- and stochastic-type \textit{neural field equations} (NFEs) in the presence of external stimuli input (or without it). The devised numerical integration means belongs to the class of Galerkin-type spectral approximations. The particular effort is focused on an efficient practical implementation of the solution technique because of the partial integro-differential fashion of the NFEs in use, which are to be integrated, numerically. Our method is implemented in Matlab. Its practical performance and efficiency are investigated on three variants of an NFE model with external stimuli inputs. We study both the deterministic case of the mentioned model and its stochastic counterpart to observe important differences in the solution behavior. First, we observe only stable one-bump solutions in the deterministic neural field scenario, which, in general, will be preserved in our stochastic NFE scenario if the level of random disturbance is sufficiently small. Second, if the area of the external stimuli is large enough and exceeds the size of the bump, considerably, the stochastic neural field solution's behavior may change dramatically and expose also two- and three-bump patterns. In addition, we show that strong random disturbances, which may occur in neural fields, fully alter the behavior of the deterministic NFE solution and allow for multi-bump (and even periodic-type) solutions to appear in all variants of the stochastic NFE model studied in this paper.
Reviewer: Reviewer (Berlin)
Exponential attractor for Hindmarsh-Rose equations in neurodynamics.
https://zbmath.org/1460.35049
2021-06-15T18:09:00+00:00
"Phan, Chi"
https://zbmath.org/authors/?q=ai:phan.chi
"You, Yuncheng"
https://zbmath.org/authors/?q=ai:you.yuncheng
Summary: The existence of exponential attractor for the diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain in the study of neurodynamics is proved through uniform estimates and a new theorem on the squeezing property of the abstract reaction-diffusion equation established in this paper. This result on the exponential attractor infers that the global attractor whose existence has been proved in [the authors and \textit{J. Su},``Global attractors for Hindmarsh-Rose equationsin neurodynamics'', Preprint, \url{arXiv:1907.13225}] for the diffusive Hindmarsh-Rose semiflow has a finite fractal dimension.
Reviewer: Reviewer (Berlin)