New methods for quantifying rapidity of action potential onset differentiate neuron types

Two new methods for quantifying the rapidity of action potential onset have lower relative standard deviations and better distinguish neuron cell types than current methods. Action potentials (APs) in most central mammalian neurons exhibit sharp onset dynamics. The main views explaining such an abrupt onset differ. Some studies suggest sharp onsets reflect cooperative sodium channels activation, while others suggest they reflect AP backpropagation from the axon initial segment. However, AP onset rapidity is defined subjectively in these studies, often using the slope at an arbitrary value on the phase plot. Thus, we proposed more systematic methods using the membrane potential’s second-time derivative (V¨m) peak width. Here, the AP rapidity was measured for four different cortical and hippocampal neuron types using four quantification methods: the inverse of full-width at the half maximum of the V¨m peak (IFWd2), the inverse of half-width at the half maximum of the V¨m peak (IHWd2), the phase plot slope, and the error ratio method. The IFWd2 and IHWd2 methods show the smallest variation among neurons of the same type. Furthermore, the AP rapidity, using the V¨m peak width methods, significantly differentiates between different types of neurons, indicating that AP rapidity can be used to classify neuron types. The AP rapidity measured using the IFWd2 method was able to differentiate between all four neuron types analyzed. Therefore, the V¨m peak width methods provide another sensitive tool to investigate the mechanisms impacting the AP onset dynamics.

Simultaneous Compensation of the Gain, Phase, and Phase-Slope

This paper deals with the problem of simultaneous compensation of the gain, phase, and phase-slope at an arbitrary frequency by using a fractional-order lead/lag compensator. The necessary and sufficient conditions for feasibility of the problem are derived. Also, the number of existing solutions (i.e., the number of distinct fractional-order lead/lag compensators satisfying the considered compensation requirements) is analytically found. Moreover, as a sample application, it is shown that the obtained results for the considered compensation problem are helpful in tuning fractional-order lead/lag compensators for simultaneously achieving desired phase margin, desired gain cross frequency, and flatness of the Bode phase plot of the loop transfer function at this frequency.

Using Swarm Intelligence for Optimization of Parameters in Approximations of Fractional-Order Operators

This chapter applies Particle Swarm Optimization (PSO) to rational approximation of fractional order differential or integral operators. These operators are the building blocks of Fractional Order Controllers, that often can improve performance and robustness of control loops. However, the implementation of fractional order operators requires a rational approximation specified by a transfer function, i.e. by a set of zeros and poles. Since the quality of the approximation in the frequency domain can be measured by the linearity of the Bode magnitude plot and by the “flatness” of the Bode phase plot in a given frequency range, the zeros and poles must be properly set. Namely, they must guarantee stability and minimum-phase properties, while enforcing zero-pole interlacing. Hence, the PSO must satisfy these requirements in optimizing the zero-pole location. Finally, to enlighten the crucial role of the zero-pole distribution, the outputs of the PSO optimization are compared with the results of classical schemes. The comparison shows that the PSO algorithm improves the quality of the approximation, especially in the Bode phase plot.

THE CONTROL OF STOCHASTIC COMPLEX DAMPED NONLINEAR SYSTEMS

The aim of this paper is to continue our investigations by studying complex damped nonlinear systems with random noise. The effect of random phase for these systems is examined. The interested system demonstrates unstable periodic attractors when the intensity of random noise equals zero, and we show that the unstable dynamical behavior will be stabilized as the intensity of random noise properly increases. The phase plot and the time evolution are carried out to confirm the obtained results of Poincaré map analysis and top Lyapunov exponent on the dynamical behavior of stability. Excellent agreement is found between these results.

A Phase-Plot Method for Diagnosing Vorticity Concentration Mechanisms in Mesoscale Convective Vortices

Mesoscale convective vortex (MCV) analysis results show that these vortices form by way of different evolutionary paths. Rewriting the traditional form of the relative vertical vorticity equation in terms of momentum advection curl produces an alternative form of the equation containing two terms. When the terms are normalized and plotted on orthogonal axes, a phase-plot path depicting MCV evolutionary growth is created. Thermodynamics is included in the phase plot by correlating the path to the heating characteristics of the troposphere. The application of the phase-plot scheme to several cases shows that for MCV formation events, there are two interconnected regions that combine to produce the vortex. The upper-middle- and upper-troposphere vorticity growth is governed primarily by vertical motion, with heating driving the vorticity growth in the upper-middle region. The lower-middle and lower-troposphere vorticity growth is governed primarily by horizontal motion, with the vertical heating gradient driving the vorticity growth in the lower-middle region. Which regime leads the vorticity growth is found to be case dependent. In the middle troposphere, evolutionary paths are governed by the relative strengths of heating and heating gradient. Additional phase-plot and mesoscale analyses clarify the characteristics of two MCV formation modes. In some cases, heating drives the complete formation of the MCV, whereas in cases with lesser heating, tipping is vital to the MCV formation process. In total, these results help synthesize many of the various discoveries regarding the origin and formation of the MCV.