Sampling Function Research Articles

Spike Estimation from Fluorescence Signals Using High-Resolution Property of Group Delay.

Spike estimation from calcium (Ca2+) fluorescence signals is a fundamental and challenging problem in neuroscience. Several models and algorithms have been proposed for this task over the past decade. Nevertheless, it is still hard to achieve accurate spike positions from the Ca2+ fluorescence signals. While existing methods rely on data-driven methods and the physiology of neurons for modelling the spiking process, this work exploits the nature of the fluorescence responses to spikes using signal processing. We first motivate the problem by a novel analysis of the high-resolution property of minimum-phase group delay (GD) functions for multi-pole resonators. The resonators could be connected either in series or in parallel. The Ca2+ indicator responds to a spike with a sudden rise, that is followed by an exponential decay. We interpret the Ca2+ signal as the response of an impulse train to the change in Ca2+ concentration, where the Ca2+ response corresponds to a resonator. We perform minimum-phase group delay-based filtering of the Ca2+ signal for resolving spike locations. The performance of the proposed algorithm is evaluated on nine datasets spanning various indicators, sampling rates and, mouse brain regions. The proposed approach: GDspike, is compared with other spike estimation methods including MLspike, Vogelstein de-convolution algorithm, and data-driven Spike Triggered Mixture (STM) model. The performance of GDSpike is superior to that of the Vogelstein algorithm and is comparable to that of MLSpike. It can also be used to post-process the output of MLSpike, which further enhances the performance.

Cohen’s Class Time-Frequency Distributions for Measurement Signals as a Means of Monitoring Technological Processes

The article presents and describes Cohen’s class time-frequency distributions which are expedient to use as a mathematical tool that allows you to create a convenient—in terms of information content and semantic clarity—visual-graphical representation of the operating modes of various technological processes including ferrous metallurgy processes. It was noted that a controlling process is usually implemented without simultaneous visual monitoring of each scalar (one-dimensional) coordinate that is under control, but the presence of such monitoring is an important condition for computer-aided controlling the dynamics of non-stationary technological processes. To eliminate this drawback, it was proposed to perform synchronous monitoring using the multidimensional Cohen’s class time-frequency distributions, when each measurement scalar signal is specifically represented through one of these distributions, for example, the Wigner–Ville distribution. An expression is given for the generalized distribution of Cohen’s class with a distribution kernel and an ambiguity function available. The latter allows you to receive distributions of various types from the maternal function. The most typical representatives of time-frequency distributions forming this class, with their kernels available, are given. The possibility of the appearance of interference elements on a signal distribution map, which ones make it difficult to identify controlled modes, is proved. The case of the formation of virtual elements within the Wigner–Ville distribution, which represents a two-component one-dimensional signal, is considered. The conditions are explained for the emergence of parasitic elements on the distribution map, obtained, for example, during realizing the process of multi-component feeding the bulk blast furnace charge materials in the production of sintering mixture. An analytical expression is obtained for the Wigner distribution, which displays a multi-component scalar signal and contains the information (useful) and virtual (parasitic) parts of the time-frequency distribution. A link is made known between the number of bulk material feeders available in the feeding devices unit and the number of parasitic (virtual) elements in the Wigner distribution. Using the feeding process as an example, the effect of the noise components propagation in the Wigner distribution is demonstrated. An example is given to illustrate the penetration of noise into the Wigner distribution and the appearance of a virtual concentration in it when displaying a signal waveform with a noisy pause and two sections with different frequencies. An expression for the Wigner distribution in the form of a comb function is obtained. The conclusion was made about the parameters of the distribution periodicity and the required sampling frequency of measurement signals.

On weakly almost periodic measures

We study the diffraction and dynamical properties of translation bounded weakly almost periodic measures. We prove that the dynamical hull of a weakly almost periodic measure is a weakly almost periodic dynamical system with unique minimal component given by the hull of the strongly almost periodic component of the measure. In particular the hull is minimal if and only if the measure is strongly almost periodic and the hull is always measurably conjugate to a torus and has pure point spectrum with continuous eigenfunctions. As an application we show the stability of the class of weighted Dirac combs with Meyer set or FLC support and deduce that such measures have either trivial or large pure point respectively continuous spectrum. We complement these results by investigating the Eberlein convolution of two weakly almost periodic measures. Here, we show that it is unique and a strongly almost periodic measure. We conclude by studying the Fourier-Bohr coefficients of weakly almost periodic measures.

Nonstationary model of oblique x-ray incidence in amorphous selenium detectors: II. Transfer functions.

One limitation of experimental techniques for quantifying resolution and noise in detectors is that the measurement is made in a region-of-interest (ROI). With theoretical modeling, these properties can be measured at a point, allowing for quantification of spatial anisotropy. This paper calculates nonstationary transfer functions for amorphous selenium (a-Se) detectors in breast imaging. We use this model to demonstrate the performance advantage of a "next-generation" tomosynthesis (NGT) system, which is capable of x-ray source motion with more degrees of freedom than a clinical tomosynthesis system. Using Swank's formulation, the optical transfer function (OTF) and presampled noise power spectra (NPS) are determined based on the point spread function derived in Part 1. The modulation transfer function (MTF) is found from the normalized modulus of the OTF. To take into account the presence of digitization, the presampled NPS is convolved with a two-dimensional comb function, for which the period along each direction is the reciprocal of the detector element size. The detective quantum efficiency (DQE) is then determined from combined knowledge of the OTF and NPS. First, the model is used to demonstrate the loss of image quality due to oblique x-ray incidence. The MTF is calculated along various polar angles, corresponding to different orientations of the input frequency. The MTF is independent of the incidence angle if the polar angle is perpendicular to the ray incidence direction. However, along other polar angles, oblique incidence results in MTF degradation at high frequencies. The MTF degradation is most substantial along the ray incidence direction. Unlike the MTF, the normalized NPS (NNPS) is independent of the incidence angle. To measure the relative signal-to-noise, the DQE is also calculated. Oblique incidence yields high-frequency DQE degradation, which is more pronounced than the MTF degradation. This arises because the DQE is proportionate with the square of the MTF. Ultimately, this model is used to evaluate how the image quality varies over the detector area. For various projection images, we calculate the variation in the incidence angle over this area. With the NGT system, the source can be positioned in such a way that this variation is minimized, and hence the DQE exhibits less anisotropy. To achieve this improvement in the image quality, the source needs to have a component of motion in the posteroanterior (PA) direction, which is perpendicular to the conventional direction of source motion in tomosynthesis. In a-Se detectors, the DQE at high frequencies is degraded due to oblique incidence. The DQE degradation is more pronounced than the MTF degradation. This model is used to quantify the spatial variation in DQE over the detector area. The use of PA source motion is a strategy for minimizing this variation and thus improving the image quality.

Diffraction of Return Time Measures

Letting $T$ denote an ergodic transformation of the unit interval and letting $f \colon [0,1)\to \mathbb{R}$ denote an observable, we construct the $f$-weighted return time measure $\mu_y$ for a reference point $y\in[0,1)$ as the weighted Dirac comb with support in $\mathbb{Z}$ and weights $f \circ T^z(y)$ at $z\in\mathbb{Z}$, and if $T$ is non-invertible, then we set the weights equal to zero for all $z < 0$. Given such a Dirac comb, we are interested in its diffraction spectrum which emerges from the Fourier transform of its autocorrelation and analyse it for the dependence on the underlying transformation. For certain rapidly mixing transformations and observables of bounded variation, we show that the diffraction of $\mu_{y}$ consists of a trivial atom and an absolutely continuous part, almost surely with respect to $y$. This contrasts what occurs in the setting of regular model sets arising from cut and project schemes and deterministic incommensurate structures. As a prominent example of non-mixing transformations, we consider the family of rigid rotations $T_{\alpha} \colon x \to x + \alpha \bmod{1}$ with rotation number $\alpha \in \mathbb{R}^+$. In contrast to when $T$ is mixing, we observe that the diffraction of $\mu_{y}$ is pure point, almost surely with respect to $y$. Moreover, if $\alpha$ is irrational and the observable $f$ is Riemann integrable, then the diffraction of $\mu_{y}$ is independent of $y$. Finally, for a converging sequence $(\alpha_{i})_{i \in \mathbb{N}}$ of rotation numbers, we provide new results concerning the limiting behaviour of the associated diffractions.

Berry phase oscillations in a simple model

While the Berry phase is often introduced in a variety of contexts, it is generally neglected in solid state courses due to a lack of simple models and the difficulty of the required mathematical techniques. In this paper, we calculate the Berry phase for a simple model, a one-dimensional Dirac comb with a secondary peak treated as a perturbation, using relatively straightforward techniques. Interestingly, we find that for this specific model the phase exhibits a band-dependent beat-like phenomenon as the secondary peak sweeps across the unit cell. Using perturbation theory we obtain an explicit expression for these oscillations, in excellent agreement with numerical results.

Distributional Behavior of Convolution Sum System Representations

In this paper, we study the validity of the usual convolution sum sampling representation of linear time-invariant (LTI) systems. We consider continuous input signals with finite energy that are absolutely integrable and vanish at infinity. Even for these benign signals, the convolution sum does not always converge. There exist LTI systems and signals such that the convolution sum diverges even in a distributional sense. This result shows that the practice of multiplying a signal with a Dirac comb and convolving subsequently with the impulse response of the LTI system is not valid for this signal space. We further fully characterize the LTI systems for which we have convergence for all signals in the space, and establish a connection between the pointwise, uniform, and distributional convergence. In particular, we show that the convolution sum converges in a distributional sense if and only it converges in a classical pointwise sense. Hence, for this signal space, nothing can be gained by treating the convergence in a distributional sense.

Glottal inverse filtering by combining a constrained LP and an HMM-based generative model of glottal flow derivative

Glottal flow is expected to convey useful information that can be effectively used in several speech applications, such as speech synthesis, expressive speech processing, speaker recognition, and voice-based biomedical engineering. Glottal inverse filtering (GIF) estimates the glottal flow that cannot be directly measured from a speech signal without any prior knowledge. Thus far, although many GIF methods have been proposed, several studies have concluded that conventional GIFs tend to degrade in estimation accuracy, especially in analyses of speech signals of high fundamental frequencies. A method based on the auto-regressive hidden Markov model (AR-HMM) was introduced to improve the estimation accuracy of the AR filter representing the vocal tract from such high fundamental frequency speech signals. In the previous AR-HMM analysis, the HMM represented a generative model of an excitation source as an impulse train that might have little information related to any physically observable signal. Therefore, the learned HMM was not expected to convey essential information of the glottal flow. The main goal of the present study is to realize an HMM-based generative model of the glottal flow derivative by imposing constraints on AR filter optimization. The proposed AR-HMM analysis is expected to realize a robust GIF for high fundamental frequency speech signals. We evaluated the proposed method by using two test sets generated by a linear source-filter model and a physiological speech synthesizer. The results indicate that the AR-HMM analysis tends to outperform the closed phase covariance analysis on constrained linear prediction in the evaluation of the linear source-filter model-based test set.

Microneurography: how it started and how it works.

In the first section, this historical review describes endeavors to develop the method for recording normal nerve impulse traffic in humans, designated microneurography. The method was developed at the Department of Clinical Neurophysiology of the Academic Hospital in Uppsala, Sweden. Microneurography involves the impalement of a peripheral nerve with a tungsten needle electrode. Electrode position is adjusted by hand until the activity of interest is discriminated. Nothing similar had previously been tried in animal preparations, and thus the large number of preceding studies that recorded afferent activity in other mammals did not offer pertinent methodological guidance. For 2 years, the two scientists involved in the research impaled their own nerves with electrodes to test various kinds of needles and explore different neural systems, all the while carefully watching for signs of nerve damage. Temporary paresthesiae were common, whereas enduring sequelae never followed. Single-unit impulse trains could be discriminated, even those originating from unmyelinated fibers. An explanation for the discrimination of unitary impulses using a coarse electrode is inferred based on the electrical characteristics of the electrode placed in the flesh and the impulse shapes, as discussed in the second section of this paper. Microneurography and the microstimulation of single afferents, combined with psychophysical methods and behavioral tests, have generated new knowledge particularly regarding four neural systems, namely the proprioceptive system, the cutaneous mechanoreceptive system, the cutaneous nociceptive system, and the sympathetic efferent system to skin structures and muscular blood vessels. Examples of achievements based on microneurography are presented in the final section.

Anesthesia modifies subthreshold critical slowing down in a stochastic Hodgkin-Huxley-like model with inhibitory synaptic input.

The dynamics of a stochastic type-I Hodgkin-Huxley-like point neuron model exposed to inhibitory synaptic noise are investigated as a function of distance from spiking threshold and the inhibitory influence of the general anesthetic agent propofol. The model is biologically motivated and includes the effects of intrinsic ion-channel noise via a stochastic differential equation description as well as inhibitory synaptic noise modeled as multiple Poisson-distributed impulse trains with saturating response functions. The effect of propofol on these synapses is incorporated through this drug's principal influence on fast inhibitory neurotransmission mediated by γ-aminobutyric acid (GABA) type-A receptors via reduction of the synaptic response decay rate. As the neuron model approaches spiking threshold from below, we track membrane voltage fluctuation statistics of numerically simulated stochastic trajectories. We find that for a given distance from spiking threshold, increasing the magnitude of anesthetic-induced inhibition is associated with augmented signatures of critical slowing: fluctuation amplitudes and correlation times grow as spectral power is increasingly focused at 0 Hz. Furthermore, as a function of distance from threshold, anesthesia significantly modifies the power-law exponents for variance and correlation time divergences observable in stochastic trajectories. Compared to the inverse square root power-law scaling of these quantities anticipated for the saddle-node bifurcation of type-I neurons in the absence of anesthesia, increasing anesthetic-induced inhibition results in an observable exponent <-0.5 for variance and >-0.5 for correlation time divergences. However, these behaviors eventually break down as distance from threshold goes to zero with both the variance and correlation time converging to common values independent of anesthesia. Compared to the case of no synaptic input, linearization of an approximating multivariate Ornstein-Uhlenbeck model reveals these effects to be the consequence of an additional slow eigenvalue associated with synaptic activity that competes with those of the underlying point neuron in a manner that depends on distance from spiking threshold.

Periodically kicked network of RLC oscillators to produce ECG signals

We propose a simple model of the electrical activity of the heart that reproduces realistic healthy electrocardiogram (ECG) signals. The model consists of two RLC linear oscillators periodically kicked by impulses of the main pacemaker with the frequency rate of a real heart. In the proposed model, one oscillator represents the atria, another represents the ventricles, and an electrical cardiac conduction system is included using a coupling capacitor, which can be either unidirectional or bidirectional. The network of the two capacitively coupled oscillators is periodically kicked by the main pacemaker to introduce the periodic forcing of limit cycles into the system; a time delay is introduced to represent the electrical transport delay from atria to ventricles. In this manner, healthy synthetic ECG signals are obtained by combining the signals of the currents of the oscillators. We show that an analytical solution of the model can be obtained when a single impulse is applied. From this, by the superposition principle, a solution with an impulse train is obtained. Note that analytical treatment is a feature not available in current cardiac oscillator models.

Oxygen Consumption and Acoustic Activity of Adult Callosobruchus maculatus (F.) (Coleoptera: Chrysomelidae: Bruchinae) during Hermetic Storage.

Acoustic monitoring was applied to consider hermetic exposure durations and oxygen levels required to stop adult Callosobruchus maculatus activity and economic damage on cowpea. A 15-d study was conducted with six treatments of 25, 50, and 100 C. maculatus adults in 500 and 1000 mL jars using acoustic probes inserted through stoppers sealing the jars. Acoustic activity as a result of locomotion, mating, and egg-laying was measured by identifying sound impulses with frequency spectra representative of known insect sounds, and counting trains (bursts) of impulses separated by intervals of <200 ms, that typically are produced only by insects. By the end of the first week of storage in all treatments, oxygen levels declined to levels below 4%, which has been demonstrated to cause mortality in previous studies. Concomitantly, insect sound burst rates dropped below an acoustic detection threshold of 0.02 bursts s−1, indicating that the insects had ceased feeding. Statistically significant relationships were obtained between two different measures of the acoustic activity and the residual oxygen level. Based on the experimental results, a simple equation can be used to estimate the time needed for oxygen to decline to levels that limit insect feeding damage and thus grain losses in hermetic storage containers of different insect population levels and various volumes.

Dissipative Mayer’s waves in fluid-filled viscoelastic tubes

Wave propagation in a viscoelastic tube filled with viscous fluid is addressed. We show that the dissipative Navier–Stokes equations can asymptotically be reduced to a pair of nonlinearly coupled complex Ginzburg–Landau equations. Modulational instability is then investigated analytically and numerically. The instability domain, using the growth rate, is shown to be importantly dependent on the vessel relative stiffness and fluid viscosity. A comprehensive analysis is proposed to that effect, which is confirmed by direct numerical simulations. Dissipative trains of impulses are found as the main manifestation of modulational instability and results are recorded for some hemodynamic factors such as the pressure, velocity and vessel cross-section.

Motor Unit Action Potential Clustering-Theoretical Consideration for Muscle Activation during a Motor Task.

During dynamic or sustained isometric contractions, bursts of muscle activity appear in the electromyography (EMG) signal. Theoretically, these bursts of activity likely occur because motor units are constrained to fire temporally close to one another and thus the impulses are “clustered” with short delays to elicit bursts of muscle activity. The purpose of this study was to investigate whether a sequence comprised of “clustered” motor unit action potentials (MUAP) can explain spectral and amplitude changes of the EMG during a simulated motor task. This question would be difficult to answer experimentally and thus, required a model to study this type of muscle activation pattern. To this end, we modeled two EMG signals, whereby a single MUAP was either convolved with a randomly distributed impulse train (EMG-rand) or a “clustered” sequence of impulses (EMG-clust). The clustering occurred in windows lasting 5–100 ms. A final mixed signal of EMG-clust and EMG-rand, with ratios (1:1–1:10), was also modeled. A ratio of 1:1 would indicate that 50% of MUAP were randomly distributed, while 50% of “clustered” MUAP occurred in a given time window (5–100 ms). The results of the model showed that clustering MUAP caused a downshift in the mean power frequency (i.e., ~30 Hz) with the largest shift occurring with a cluster window of 10 ms. The mean frequency shift was largest when the ratio of EMG-clust to EMG-rand was high. Further, the clustering of MUAP also caused a substantial increase in the amplitude of the EMG signal. This model potentially explains an activation pattern that changes the EMG spectra during a motor task and thus, a potential activation pattern of muscles observed experimentally. Changes in EMG measurements during fatiguing conditions are typically attributed to slowing of conduction velocity but could, per this model, also result from changes of the clustering of MUAP. From a clinical standpoint, this type of muscle activation pattern might help describe the pathological movement issues in people with Parkinson’s disease or essential tremor. Based on our model, researchers moving forward should consider how MUAP clustering influences EMG spectral and amplitude measurements and how these changes influence movements.

Lack of BV bounds for impulsive control systems

For a nonlinear impulsive control system, we extend the so-called graph completion approach and introduce a notion of generalized solution x associated to a control u whose total variation is bounded on [0,t] for every t<T, but possibly unbounded on [0,T]. We prove existence, consistency with classical solutions and well-posedness of this solution. In particular, we characterize it as a pointwise limit of certain regular solutions. The notion that we consider provides the natural setting for controllability questions and for some non-coercive optimal control problems, where chattering phenomena at the final time are expected. More in general, it is well suited to describe the evolution of control systems subject to a train of impulses where no a-priori bounds on the number and the amplitude of the impulses are imposed.

Deconvolution of blast vibration signals by wiener filtering

Ground vibration is one of the environmental concerns caused by mine blasts. The signature-hole technique, essentially the convolution of a single-hole signature with an impulse train function representing the timing of the blast, is one method used to predict and control ground vibrations. This method requires measuring a signature waveform from a singular blasting hole, which may be a limitation. Deconvolution of vibration signals, the inverse problem of signature-hole method, is still a frontier issue to solve that limitation in mining engineering. Wiener filtering deconvolution is used to compress the impulse train into a time-lagged spike, so that a normalized single-hole signature can be extracted from the full blast vibration waveform. The proposed methodology gives good results for a case study of mining blast using electronic detonators. Successful deconvolution will eliminate the need for measuring signatures by using all the seismograph information collected routinely in mine operations.

Structure of the transmission peaks in bands generated by attractive Dirac comb potentials

We study the pattern of bands generated by the transmission coefficient for transmission across N equispaced attractive Dirac comb potentials each having strength parameter V. The nature of the first band is found to be different from all higher bands and requires careful analysis. The number of peaks in the first band is found to depend on the bound states generated by N attractive delta potential, whereas in all other higher bands the number of peak is found to depend on the number of gaps between the adjacent delta terms. We illustrate these results for various values of N and V.

Effects of Hermetic Storage on Adult Sitophilus oryzae L. (Coleoptera: Curculionidae) Acoustic Activity Patterns and Mortality.

Hermetic storage is of interest to farmers and warehouse managers as a method to control insect pests in small storage facilities. To develop improved understanding of effects of hermetic storage on insect pest activity and mortality over time, oxygen levels, acoustic signals, and observations of visual movement were recorded from replicates of 25, 50, and 100 adult Sitophilus oryzae (L.) (Coleoptera: Curculionidae) hermetically sealed in 500- and 1,000-ml glass jars. Recordings were done for 28 d; twice daily for the first 6 d and twice weekly thereafter. Insect sounds were analyzed as short bursts (trains) of impulses with spectra that matched average spectra (profiles) of previously verified insect sound impulses. Oxygen consumption was highest in treatments of 100 insects/500-ml jar and lowest in 25/1000-ml jars. The rates of bursts per insect, number of impulses per burst, and rates of burst impulses per insect decreased as the residual oxygen levels decreased in each treatment. Activity rates <0.02 bursts s−1, the acoustic detection threshold, typically occurred as oxygen fell below 5%. Mortality was observed at 2% levels. The time to obtain these levels of insect activity and oxygen depletion ranged from 3–14 d depending on initial infestation levels. Acoustic detection made it possible to estimate the duration required for reduction of insect activity to levels resulting in negligible damage to the stored product under hermetic conditions. Such information is of value to farmers and warehouse managers attempting to reduce pest damage in stored crops.

In vivo assessment of muscle membrane properties in the sodium channel myotonias.

The gain-of-function mutations that underlie sodium channel myotonia (SCM) and paramyotonia congenital (PMC) produce differing clinical phenotypes. We used muscle velocity recovery cycles (MVRCs) to investigate membrane properties. MVRCs and responses to trains of stimuli were compared in patients with SCM (n = 9), PMC (n = 8), and normal controls (n = 26). The muscle relative refractory period was reduced in SCM, consistent with faster recovery of the mutant sodium channels from inactivation. Both SCM and PMC showed an increased early supernormality and increased mean supernormality following multiple conditioning stimuli, consistent with slowed sodium channel inactivation. Trains of fast impulses caused a loss of amplitude in PMC, after which only half of the muscle fibers recovered, suggesting that the remainder stayed depolarized by persistent sodium currents. The differing effects of mutations on sodium channel function can be demonstrated in human subjects in vivo using this technique. Muscle Nerve 57: 586-594, 2018.

Metabotropic Glutamate Receptor 7 (mGluR7) as a Target for Modulating Pain-evoked Activities of Neurons in the Hippocampal CA3 Region of Rats.

Metabotropic glutamate could contribute to the development of neuropathic pain-related behaviors. Previously, we have confirmed that the glutamic acid and dizocilpine maleate in the hippocampal CA3 region are involved in the modulation of noxious stimulation. However, whether the metabotropic glutamate receptor 7 (mGluR7) can modulate the pain-evoked electrical activities of pain-excited neurons and pain-inhibited neurons in the hippocampal CA3 region is not clear. The study aimed to examine the effects of mGluR7 allosteric agonist N,N'-dibenzhydrylethane- 1,2-diamine dihydrochloride (AMN082) and antagonist 6-(4-methoxyphenyl)-5-methyl-3- pyridin-4-ylisoxazolo[4,5-c]pyridin-4(5H)-one (MMPIP) on the pain-evoked electrical activities of pain-excited neurons and pain-inhibited neurons in the CA3 region of rats. A train of electric impulses applied to the sciatic nerve were used for noxious stimulation. The bio-electrical activities of pain-excited neuron or pain-inhibited neuron in the CA3 region were recorded by a glass microelectrode. Our results exhibited that intra-CA3 region administration of the glutamic acid or AMN082 increased the pain-evoked discharged frequency and shortened the latency of pain-excited neuron, while decreased the pain-evoked discharged frequency and prolonged the inhibitory duration of paininhibited neuron in the CA3 region. The intra-CA3 region microinjection of MMPIP produced the opposite response. These findings demonstrated that the glutamic acid and mGluR7 in hippocampal CA3 region are involved in the modulation of nociceptive information transmission by regulating pain-evoked electric activities of pain-excited neurons and pain-inhibited neurons.