Reduced Dimension, Biophysical Neuron Models Constructed From Observed Data

Using methods from nonlinear dynamics and interpolation techniques from applied mathematics, we show how to use data alone to construct discrete time dynamical rules that forecast observed neuron properties. These data may come from from simulations of a Hodgkin-Huxley (HH) neuron model or from laboratory current clamp experiments. In each case the reduced dimension data driven forecasting (DDF) models are shown to predict accurately for times after the training period.When the available observations for neuron preparations are, for example, membrane voltage V(t) only, we use the technique of time delay embedding from nonlinear dynamics to generate an appropriate space in which the full dynamics can be realized.The DDF constructions are reduced dimension models relative to HH models as they are built on and forecast only observables such as V(t). They do not require detailed specification of ion channels, their gating variables, and the many parameters that accompany an HH model for laboratory measurements, yet all of this important information is encoded in the DDF model.As the DDF models use only voltage data and forecast only voltage data they can be used in building networks with biophysical connections. Both gap junction connections and ligand gated synaptic connections among neurons involve presynaptic voltages and induce postsynaptic voltage response. Biophysically based DDF neuron models can replace other reduced dimension neuron models, say of the integrate-and-fire type, in developing and analyzing large networks of neurons.When one does have detailed HH model neurons for network components, a reduced dimension DDF realization of the HH voltage dynamics may be used in network computations to achieve computational efficiency and the exploration of larger biological networks.

Observation of anyonic Bloch oscillations

Bloch oscillations are exotic phenomena describing the periodic motion of a wave packet subjected to the external force in a lattice, where the system possessing single- or multiple-particles could exhibit distinct oscillation behaviors. In particular, it has been pointed out that quantum statistics could dramatically affected the Bloch oscillation even in the absence of particle interactions, where the oscillation frequency of two pseudofermions with the anyonic statistical angle being π becomes half of that for two bosons. However, these statistic-dependent Bloch oscillations have never been observed in experiments up to now. Here, we report the first experimental simulation of anyonic Bloch oscillations using electric circuits. By mapping eigenstates of two anyons to modes of designed circuit simulators, the Bloch oscillation of two bosons and two pseudofermions are verified by measuring the voltage dynamics. It is found that the oscillation period in the two-boson simulator is almost twice of that in the two-pseudofermion simulator, which is consistent with the theoretical prediction. Our proposal provides a flexible platform to investigate and visualize many interesting phenomena related to particle statistics, and could have potential applications in the field of the novelty signal control.

Dynamics-Based Piecewise Constant Control of Omni-Vehicle

In this paper, we consider the dynamics of a mobile vehicle moving under control on a perfectly rough horizontal plane. The vehicle consists of a horizontal platform and three omni-wheels that can rotate independently. An omni-wheel has freely rotating rollers on its rim [1]. We use its simplest model: an omni-wheel on a perfectly rough plane is modelled as a rigid disk with a constraint that its contact point velocity directed perpendicular to the disk's plane. The vehicle is controlled by three direct current motors in wheels' axes. Two terms model torques generated by motors: the rst one is proportional to the voltage, the second one is proportional to the value of the angular velocity of a wheel (counter-electromotive force). We study constant voltage dynamics and boundary-value problems for arbitrary initial and nal mass center coordinates, course angles and their derivatives using a piecewise constant control with one switching point. This problem is reduced to a system of algebraic equations for some specific (symmetric) vehicle model. We numerically model the system and analyze the possibility of optimization. For another vehicle configuration, we get the solution as numerical parametric continuation starting from the solution for the symmetric vehicle.

Impedance Modeling and Stability Analysis of DFIG-Based Wind Energy Conversion System Considering Frequency Coupling

Impedance-based stability analysis is an effective method for addressing a new type of SSO accidents that have occurred in recent years, especially those caused by the control interaction between a DFIG and the power grid. However, the existing impedance modeling of DFIGs is mostly focused on a single converter, such as the GSC or RSC, and the influence between the RSC and GSC, as well as the frequency coupling effect inside the converter are usually overlooked, reducing the accuracy of DFIG stability analysis. Hence, the entire impedance is proposed in this paper for the DFIG-based WECS, taking coupling factors into account (e.g., DC bus voltage dynamics, asymmetric current regulation in the dq frame, and PLL). Numerical calculations and HIL simulations on RT-Lab were used to validate the proposed model. The results indicate that the entire impedance model with frequency coupling is more accurate, and it is capable of accurately predicting the system’s possible resonance points.

Activity-mediated accumulation of potassium induces a switch in firing pattern and neuronal excitability type

During normal neuronal activity, ionic concentration gradients across a neuron’s membrane are often assumed to be stable. Prolonged spiking activity, however, can reduce transmembrane gradients and affect voltage dynamics. Based on mathematical modeling, we investigated the impact of neuronal activity on ionic concentrations and, consequently, the dynamics of action potential generation. We find that intense spiking activity on the order of a second suffices to induce changes in ionic reversal potentials and to consistently induce a switch from a regular to an intermittent firing mode. This transition is caused by a qualitative alteration in the system’s voltage dynamics, mathematically corresponding to a co-dimension-two bifurcation from a saddle-node on invariant cycle (SNIC) to a homoclinic orbit bifurcation (HOM). Our electrophysiological recordings in mouse cortical pyramidal neurons confirm the changes in action potential dynamics predicted by the models: (i) activity-dependent increases in intracellular sodium concentration directly reduce action potential amplitudes, an effect typically attributed solely to sodium channel inactivation; (ii) extracellular potassium accumulation switches action potential generation from tonic firing to intermittently interrupted output. Thus, individual neurons may respond very differently to the same input stimuli, depending on their recent patterns of activity and/or the current brain-state.

Analysis of an Electrical Circuit Using Two-Parameter Conformable Operator in the Caputo Sense

The problem of voltage dynamics description in a circuit containing resistors, and at least two fractional order elements such as supercapacitors, supplied with constant voltage is addressed. A new operator called Conformable Derivative in the Caputo sense is used. A state solution is proposed. The considered operator is a generalization of three derivative definitions: classical definition (integer order), Caputo fractional definition and the so-called Conformable Derivative (CFD) definition. The proposed solution based on a two-parameter Conformable Derivative in the Caputo sense is proven to be better than the classical approach or the one-parameter fractional definition. Theoretical considerations are verified experimentally. The cumulated matching error function is given and it reveals that the proposed CFD–Caputo method generates an almost two times lower error compared to the classical method.

Activity-mediated accumulation of potassium induces a switch in firing pattern and neuronal excitability type

During normal neuronal activity, ionic concentration gradients across a neuron’s membrane are often assumed to be stable. Prolonged spiking activity, however, can reduce transmembrane gradients and affect voltage dynamics. Based on mathematical modeling, we here investigate the impact of neuronal activity on ionic concentrations and, consequently, the dynamics of action potential generation. We find that intense spiking activity on the order of a second suffices to induce changes in ionic reversal potentials and to consistently induce a switch from a regular to an intermittent firing mode. This transition is caused by a qualitative alteration in the system’s voltage dynamics, mathematically corresponding to a co-dimension-two bifurcation from a saddle-node on invariant cycle (SNIC) to a homoclinic orbit bifurcation (HOM). Our electrophysiological recordings in mouse cortical pyramidal neurons confirm the changes in action potential dynamics predicted by the models: (i) activity-dependent increases in intracellular sodium concentration directly reduce action potential amplitudes, an effect that previously had been attributed soley to sodium channel inactivation; (ii) extracellular potassium accumulation switches action potential generation from tonic firing to intermittently interrupted output. Individual neurons thus may respond very differently to the same input stimuli, depending on their recent patterns of activity or the current brain-state.Author summaryIonic concentrations in the brain are not constant. We show that during intense neuronal activity, they can change on the order of seconds and even switch neuronal spiking patterns under identical stimulation from a regular firing mode to an intermittently interrupted one. Triggered by an accumulation of extracellular potassium, such a transition is caused by a specific, qualitative change in of the neuronal voltage dynamics – a so-called bifurcation – which affects crucial features of action-potential generation and bears consequences for how information is encoded and how neurons behave together in the network. Also changes in intracellular sodium can induce measurable effects, like a shrinkage of spike amplitude that occurs independently of the fast amplitude-effects attributed to sodium channel inactivation. Taken together, our results demonstrate that a neuron can respond very differently to the same stimulus, depending on its previous activity or the current brain state. The finding is particularly relevant when other regulatory mechanisms of ionic homeostasis are challenged, for example, during pathological states of glial impairment or oxygen deprivation. Categorization of cortical neurons as intrinsically bursting or regular spiking may be biased by the ionic concentrations at the time of the observation, highlighting the non-static nature of neuronal dynamics.