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Based on image moment theory, an approach for space-variant Shack-Hartmann wavefront reconstruction is presented in this article. The relation between the moment of a pair of subimages and the local transformation coefficients is derived. The square guide 'star' is used to obtain a special solution from this relation. The moment-based wavefront reconstruction has a reduced computational complexity compared to the iteration-based algorithm. Image restorations are executed by the tiling strategy with 5 $\times$ 5 PSFs as well as the conventional strategy with a global average PSF. Visual and quantitative evaluations support our approach., This paper has been accepted for publication in the journal Optics Communications on April 12th, 2023

Caenorhabditis elegans (C. elegans) is an ideal model organism for studying neuronal functions at the system level. This article develops a customized system for whole-body motor neuron calcium imaging of freely moving C. elegans without the coverslip pressed. Firstly, we proposed a fast centerline localization algorithm that could deal with most topology-variant cases costing only 6 ms for one frame, not only benefits for real-time localization but also for post-analysis. Secondly, we implemented a full-time two-axis synchronized motion strategy by adaptively adjusting the motion parameters of two motors in every short-term motion step (~50 ms). Following the above motion tracking configuration, the tracking performance of our system has been demonstrated to completely support the high spatiotemporal resolution calcium imaging on whole-body motor neurons of wild-type (N2) worms as well as two mutants (unc-2, unc-9), even the instantaneous speed of worm moving without coverslip pressed was extremely up to 400 μm/s.

Action potentials (APs) in neurons are generated at the axon initial segment (AIS). AP dynamics, including initiation and propagation, are intimately associated with neuronal excitability and neurotransmitter release kinetics. Most learning and memory studies at the single-neuron level have relied on the use of animal models, most notably rodents. Here, we studied AP initiation and propagation in cultured hippocampal neurons from Sprague-Dawley (SD) rats and C57BL/6 (C57) mice with genetically encoded voltage indicator (GEVI)-based voltage imaging. Our data showed that APs traveled bidirectionally in neurons from both species; forward-propagating APs (fpAPs) had a different speed than backpropagating APs (bpAPs). Additionally, we observed distinct AP propagation characteristics in AISs emerging from the somatic envelope compared to those originating from dendrites. Compared with rat neurons, mouse neurons exhibited higher bpAP speed and lower fpAP speed, more distally located ankyrin G (AnkG) in AISs, and longer Nav1.2 lengths in AISs. Moreover, during AIS plasticity, AnkG and Nav1.2 showed distal shifts in location and shorter lengths of labeled AISs in rat neurons; in mouse neurons, however, they showed a longer AnkG-labeled length and more distal Nav1.2 location. Our findings suggest that hippocampal neurons in SD rats and C57 mice may have different AP propagation speeds, different AnkG and Nav1.2 patterns in the AIS, and different AIS plasticity properties, indicating that comparisons between these species must be carefully considered.动作电位产生于神经元的轴突起始节（Axon initial segment , AIS），动作电位的爆发与传播，与神经元兴奋性以及神经递质释放密切相关。神经元水平的学习和记忆研究依赖于许多动物模型的使用，尤其是啮齿类动物。该文中，我们利用基于遗传编码电压指示器的电压成像技术，研究动作电位在Sprague-Dawley（SD）大鼠和C57BL/6（C57）小鼠海马神经元中的爆发和传播。我们的实验数据显示，在两种物种的神经元中动作电位都是双向传播的，其中，沿轴突向下传播动作电位与向胞体往回传播动作电位的速度不同，且树突起源和胞体起源的AIS上动作电位的传播有其独特的性质。与大鼠相比，小鼠神经元表现出较高的回传动作电位速度和较低的下传动作电位速度，锚蛋白G (AnkG)在小鼠神经元的AIS上偏向于远端定位，Nav1.2在小鼠神经元AIS上呈现出较长的分布。此外，AIS可塑性发生时，大鼠神经元AIS上AnkG和Nav1.2的位置都向远端偏移，且长度均变短；而小鼠神经元的AIS却呈现出变长的AnkG和向远端定位的Nav1.2。综上，我们的研究结果表明，大鼠和小鼠的海马神经元可能在动作电位传播速度、AIS上AnkG和Nav1.2分布的模式以及AIS可塑性特性等方面都存在差异，对这两个物种的实验结果进行比较时需要要考虑到上述情况。.

In the brain, coherent neuronal activities often appear simultaneously in multiple frequency bands, e.g., as combinations of alpha (8-12 Hz), beta (12.5-30 Hz), gamma (30-120 Hz) oscillations, among others. These rhythms are believed to underlie information processing and cognitive functions and have been subjected to intense experimental and theoretical scrutiny. Computational modeling has provided a framework for the emergence of network-level oscillatory behavior from the interaction of spiking neurons. However, due to the strong nonlinear interactions between highly recurrent spiking populations, the interplay between cortical rhythms in multiple frequency bands has rarely been theoretically investigated. Many studies invoke multiple physiological timescales or oscillatory inputs to produce rhythms in multi-bands. Here we demonstrate the emergence of multi-band oscillations in a simple network consisting of one excitatory and one inhibitory neuronal population driven by constant input. First, we construct a data-driven, Poincar\'e section theory for robust numerical observations of single-frequency oscillations bifurcating into multiple bands. Then we develop model reductions of the stochastic, nonlinear, high-dimensional neuronal network to capture the appearance of multi-band dynamics and the underlying bifurcations theoretically. Furthermore, when viewed within the reduced state space, our analysis reveals conserved geometrical features of the bifurcations on low-dimensional dynamical manifolds. These results suggest a simple geometric mechanism behind the emergence of multi-band oscillations without appealing to oscillatory inputs or multiple synaptic or neuronal timescales. Thus our work points to unexplored regimes of stochastic competition between excitation and inhibition behind the generation of dynamic, patterned neuronal activities., Comment: 18 pages, 8 figures

Orientation tuning is a fundamental response property of V1 neurons and has been extensively studied with single-/multiunit recording and intrinsic signal optical imaging. Long-term 2-photon calcium imaging allows simultaneous recording of hundreds of neurons at single neuron resolution over an extended time in awake macaques, which may help elucidate V1 orientation tuning properties in greater detail. We used this new technology to study the microstructures of orientation functional maps, as well as population tuning properties, in V1 superficial layers of 5 awake macaques. Cellular orientation maps displayed horizontal and vertical clustering of neurons according to orientation preferences, but not tuning bandwidths, as well as less frequent pinwheels than previous estimates. The orientation tuning bandwidths were narrower than previous layer-specific single-unit estimates, suggesting more precise orientation selectivity. Moreover, neurons tuned to cardinal and oblique orientations did not differ in quantities and bandwidths, likely indicating minimal V1 representation of the oblique effect. Our experimental design also permitted rough estimates of length tuning. The results revealed significantly more end-stopped cells at a more superficial 150 μm depth (vs. 300 μm), but unchanged orientation tuning bandwidth with different length tuning. These results will help construct more precise models of V1 orientation processing.

The back-propagating action potential (bpAP) is crucial for neuronal signal integration and synaptic plasticity in dendritic trees. Its properties (velocity and amplitude) can be affected by dendritic morphology. Due to limited spatial resolution, it has been difficult to explore the specific propagation process of bpAPs along dendrites and examine the influence of dendritic morphology, such as the dendrite diameter and branching pattern, using patch-clamp recording. By taking advantage of Optopatch, an all-optical electrophysiological method, we made detailed recordings of the real-time propagation of bpAPs in dendritic trees. We found that the velocity of bpAPs was not uniform in a single dendrite, and the bpAP velocity differed among distinct dendrites of the same neuron. The velocity of a bpAP was positively correlated with the diameter of the dendrite on which it propagated. In addition, when bpAPs passed through a dendritic branch point, their velocity decreased significantly. Similar to velocity, the amplitude of bpAPs was also positively correlated with dendritic diameter, and the attenuation patterns of bpAPs differed among different dendrites. Simulation results from neuron models with different dendritic morphology corresponded well with the experimental results. These findings indicate that the dendritic diameter and branching pattern significantly influence the properties of bpAPs. The diversity among the bpAPs recorded in different neurons was mainly due to differences in dendritic morphology. These results may inspire the construction of neuronal models to predict the propagation of bpAPs in dendrites with enormous variation in morphology, to further illuminate the role of bpAPs in neuronal communication.

Axonal pathology has been widely reported in Alzheimer’s disease (AD). As a highly structured region in the axon, axon initial segment (AIS) plays a vital role in action potential (AP) dynamics, including initiation and propagation, closely linked to neuronal excitability and neurotransmitter release kinetics. Previously, we showed that proteins localized in the AIS were remarkably changed in neurons from APPswe/PS1ΔE9 mice carrying familial AD mutations. However, whether the AIS defects in APP/PS1 mouse neurons affect AP dynamics is unknown. Using genetically-encoded voltage indicators (GEVIs)-based voltage imaging, we studied AP initiation and propagation in the APP/PS1 neurons. We found that APP/PS1 neurons were more sensitive to intensive stimulations. Our data suggested that AP velocities significantly decreased in neurons from APP/PS1 mice than the wild-type mice. The velocity of forward-propagating action potentials was lower when the AIS was located more distally from the soma or when the AIS had a shorter length. The velocity of back-propagating action potentials was not correlated with the location nor with the length of the AIS. These experimental results were reproduced in neuronal simulations using multi-compartment modeling, suggesting a correlation between AIS length/location change and AP propagation velocity due to the distribution of sodium channels. Taken together, Our findings provide a deep insight into the abnormality of neuronal function in AD.

The C. elegans nervous system was thought to be strictly analog, constituted solely by graded neurons. We recently discovered neuronal action potentials in the sensory neuron AWA; however, the extent to which the C. elegans nervous system relies on analog or digital neural signaling and coding is unclear. Here we report that the enteric motor neurons AVL and DVB fire all-or-none calcium-mediated action potentials that play essential roles in the rhythmic defecation behavior in C. elegans. Both AVL and DVB synchronously fire giant action potentials to faithfully execute all-or-none expulsion following the intestinal pacemaker. AVL fires unusual compound action potentials with each positive calcium-mediated spike followed by a potassium-mediated negative spike. The depolarizing calcium spikes in AVL are mediated by a CaV2 calcium channel UNC-2, while the negative potassium spikes are mediated by a repolarization-activated potassium channel EXP-2. Whole-body behavior tracking and simultaneous neural imaging in free-moving animals suggest that action potentials initiated in AVL in the head propagate along its axon to the tail and activate DVB through the INX-1 gap junction. Synchronized action potential spikes between AVL and DVB, as well as the negative spike and long-lasting afterhyperpolarization in AVL, play an important function in executing expulsion behavior. This work provides the first evidence that in addition to sensory coding, C. elegans motor neurons also use digital coding scheme to perform specific functions including long-distance communication and temporal synchronization, suggesting further, unforeseen electrophysiological diversity remains to be discovered in the C. elegans nervous system.

Escape is an evolutionarily conserved and essential avoidance response. Considered to be innate, most studies on escape responses focused on hard-wired circuits. We report here that peptidergic signaling is an integral and necessary component of the Caenorhabditis elegans escape circuit. Combining genetic screening, electrophysiology and calcium imaging, we reveal that a neuropeptide NLP-18 and its cholecystokinin receptor CKR-1 enable the escape circuit to execute a full omega (Ω) turn, the last motor step where the animal robustly steers away from its original trajectory. We demonstrate in vivo and in vitro that CKR-1 is a Gαq protein coupled receptor for NLP-18. in vivo, NLP-18 is mainly secreted by the gustatory sensory neuron (ASI) to activate CKR-1 in the head motor neuron (SMD) and the turn-initiating interneuron (AIB). Removal of NLP-18, removal of CKR-1, or specific knockdown of CKR-1 in SMD or AIB neurons lead to shallower turns hence less robust escape steering. Consistently, elevation of head motor neuron (SMD)’s Ca2+ transients during escape steering is attenuated upon the removal of NLP-18 or CKR-1. in vitro, synthetic NLP-18 directly evokes CKR-1-dependent currents in oocytes and CKR-1-dependent Ca2+ transients in SMD. Thus, cholecystokinin signaling modulates an escape circuit to generate robust escape steering.

Gamma frequency oscillations (25–140 Hz), observed in the neural activities within many brain regions, have long been regarded as a physiological basis underlying many brain functions, such as memory and attention. Among numerous theoretical and computational modeling studies, gamma oscillations have been found in biologically realistic spiking network models of the primary visual cortex. However, due to its high dimensionality and strong non-linearity, it is generally difficult to perform detailed theoretical analysis of the emergent gamma dynamics. Here we propose a suite of Markovian model reduction methods with varying levels of complexity and apply it to spiking network models exhibiting heterogeneous dynamical regimes, ranging from nearly homogeneous firing to strong synchrony in the gamma band. The reduced models not only successfully reproduce gamma oscillations in the full model, but also exhibit the same dynamical features as we vary parameters. Most remarkably, the invariant measure of the coarse-grained Markov process reveals a two-dimensional surface in state space upon which the gamma dynamics mainly resides. Our results suggest that the statistical features of gamma oscillations strongly depend on the subthreshold neuronal distributions. Because of the generality of the Markovian assumptions, our dimensional reduction methods offer a powerful toolbox for theoretical examinations of other complex cortical spatio-temporal behaviors observed in both neurophysiological experiments and numerical simulations.

V1 neurons are functionally organized in orientation columns in primates. Whether spatial frequency (SF) columns also exist is less clear because mixed results have been reported. A definitive solution would be SF functional maps at single-neuron resolution. Here we used two-photon calcium imaging to construct first cellular SF maps in V1 superficial layers of five awake fixating macaques, and studied SF functional organization properties and neuronal tuning characteristics. The SF maps (850 × 850 μm2) showed weak horizontal SF clustering (median clustering index = 1.43 vs. unity baseline), about one sixth as strong as orientation clustering in the same sets of neurons, which argues against a meaningful orthogonal relationship between orientation and SF functional maps. These maps also displayed nearly absent vertical SF clustering between two cortical depths (150 & 300 μm), indicating a lack of SF columnar structures within the superficial layers. The underlying causes might be that most neurons were tuned to a narrow two-octave range of medium frequencies, and many neurons with different SF preferences were often spatially mixed, which disallowed finer grouping of SF tuning. In addition, individual SF tuning functions were often asymmetric, having wider lower frequency branches, which may help encode low SF information for later decoding.

The capabilities of natural neural systems have inspired new generations of machine learning algorithms as well as neuromorphic very large-scale integrated (VLSI) circuits capable of fast, low-power information processing. However, it has been argued that most modern machine learning algorithms are not neurophysiologically plausible. In particular, the workhorse of modern deep learning, the backpropagation algorithm, has proven difficult to translate to neuromorphic hardware. In this study, we present a neuromorphic, spiking backpropagation algorithm based on synfire-gated dynamical information coordination and processing, implemented on Intel's Loihi neuromorphic research processor. We demonstrate a proof-of-principle three-layer circuit that learns to classify digits from the MNIST dataset. To our knowledge, this is the first work to show a Spiking Neural Network (SNN) implementation of the backpropagation algorithm that is fully on-chip, without a computer in the loop. It is competitive in accuracy with off-chip trained SNNs and achieves an energy-delay product suitable for edge computing. This implementation shows a path for using in-memory, massively parallel neuromorphic processors for low-power, low-latency implementation of modern deep learning applications., arXiv

An error-correction code (ECC) sequencing approach has recently been reported to effectively reduce sequencing errors by interrogating a DNA fragment with three orthogonal degenerate sequencing-by-synthesis (SBS) reactions. However, similar to other non-single-molecule SBS methods, the reaction will gradually lose its synchronization within a molecular colony in ECC sequencing. This phenomenon, called dephasing, causes sequencing error, and in ECC sequencing, induces distinctive dephasing patterns. To understand the characteristic dephasing patterns of the dual-base flowgram in ECC sequencing and to generate a correction algorithm, we built a virtual sequencer in silico. Starting from first principles and based on sequencing chemical reactions, we simulated ECC sequencing results, identified the key factors of dephasing in ECC sequencing chemistry and designed an effective dephasing algorithm. The results show that our dephasing algorithm is applicable to sequencing signals with at least 500 cycles, or 1000-bp average read length, with acceptably low error rate for further parity checks and ECC deduction. Our virtual sequencer with our dephasing algorithm can further be extended to a dichromatic form of ECC sequencing, allowing for a potentially much more accurate sequencing approach., A computational model reveals how DNA molecules get unsynchronized in error-correction code sequencing and leads to algorithms to correct the aberrant signals back.

The optogenetic neuron ablation approach enables noninvasive remote decoding of specific neuron function within a complex living organism in high spatiotemporal resolution. However, it suffers from shallow tissue penetration of visible light with low ablation efficiency. This study reports a upconversion nanoparticle (UCNP)-based multiplex proteins activation tool to ablate deep-tissue neurons for locomotion modulation. By optimizing the dopant contents and nanoarchitecure, over 300-fold enhancement of blue (450-470 nm) and red (590-610 nm) emissions from UCNPs is achieved upon 808 nm irradiation. Such emissions simultaneously activate mini singlet oxygen generator and Chrimson, leading to boosted near infrared (NIR) light-induced neuronal ablation efficiency due to the synergism between singlet oxygen generation and intracellular Ca2+ elevation. The loss of neurons severely inhibits reverse locomotion, revealing the instructive role of neurons in controlling motor activity. The deep penetrance NIR light makes the current system feasible for in vivo deep-tissue neuron elimination. The results not only provide a rapidly adoptable platform to efficient photoablate single- and multiple-cells, but also define the neural circuits underlying behavior, with potential for development of remote therapy in diseases.

Modern electrophysiological recordings and optical imaging techniques have revealed a diverse spectrum of spatiotemporal neural activities underlying fundamental cognitive processing. Oscillations, traveling waves and other complex population dynamical patterns are often concomitant with sensory processing, information transfer, decision making and memory consolidation. While neural population models such as neural mass, population density and kinetic theoretical models have been used to capture a wide range of the experimentally observed dynamics, a full account of how the multi-scale dynamics emerges from the detailed biophysical properties of individual neurons and the network architecture remains elusive. Here we apply a recently developed coarse-graining framework for reduced-dimensional descriptions of neuronal networks to model visual cortical dynamics. We show that, without introducing any new parameters, how a sequence of models culminating in an augmented system of spatially-coupled ODEs can effectively model a wide range of the observed cortical dynamics, ranging from visual stimulus orientation dynamics to traveling waves induced by visual illusory stimuli. In addition to an efficient simulation method, this framework also offers an analytic approach to studying large-scale network dynamics. As such, the dimensional reduction naturally leads to mesoscopic variables that capture the interplay between neuronal population stochasticity and network architecture that we believe to underlie many emergent cortical phenomena., Author summary Emergent nonlinear dynamics in the primary visual cortex (V1) may influence information processing in the early visual pathway and has been shown to affect visual perception. A major goal of systems neuroscience is to understand how complex brain functions can arise from the collective nonlinear dynamics of the underlying neuronal network. This challenge has been partly met through electrophysiological recordings, optical imaging and neural population models. However, a full account of how the multi-scale population dynamics emerges from the detailed biophysical properties of individual neurons and the network architecture remains elusive. Previously, working on a homogeneously-coupled network, we derived a series of population dynamics models, ranging from Master equations, to Fokker-Planck equations, and culminating in an augmented system of spatially-coupled ODEs. Here we present an application of this reduction method to a heterogeneously coupled neuronal network that models a spatially-extended portion of V1. We found that the temporal dynamics of individual V1 patches can be well captured by a low-dimensional set of voltage moments. At the same time, the spatially-coupled system can recapitulate the cortical wave generation and propagation induced by many visual stimuli, including those that induce motion illusions. Furthermore, this coarse-graining reveals the importance of the temporal differences between on-/off-pathways, that may account for the directional motion perception from darks to brights.

For some time, it has been thought that backpropagation of errors could not be implemented in biophysiologically realistic neural circuits. This belief was largely due to either 1) the need for symmetric replication of feedback and feedforward weights, 2) the need for differing forms of activation between forward and backward propagating sweeps, and 3) the need for a separate network for error gradient computation and storage, on the one hand, or 4) nonphysiological backpropagation through the forward propagating neurons themselves, on the other. In this paper, we present spiking neuron mechanisms for gating pulses to maintain short-term memories, controlling forward inference and backward error propagation, and coordinating learning of feedback and feedforward weights. These neural mechanisms are synthesized into a new backpropagation algorithm for neuromorphic circuits.

Due to its ability of optical sectioning and low phototoxicity, z -stacking light-sheet microscopy has been the tool of choice for in vivo imaging of the zebrafish brain. To image the zebrafish brain with a large field of view, the thickness of the Gaussian beam inevitably becomes several times greater than the system depth of field (DOF), where the fluorescence distributions outside the DOF will also be collected, blurring the image. In this paper, we propose a 3D deblurring method, aiming to redistribute the measured intensity of each pixel in a light-sheet image to in situ voxels by 3D deconvolution. By introducing a Hessian regularization term to maintain the continuity of the neuron distribution and using a modified stripe-removal algorithm, the reconstructed z -stack images exhibit high contrast and a high signal-to-noise ratio. These performance characteristics can facilitate subsequent processing, such as 3D neuron registration, segmentation, and recognition.

Large field of view (FOV) imaging with high spatial resolution has been increasingly required for numerous applications in recent years. Obviously, conventional photosensitive detector with tens of megapixels cannot satisfy the requirement. As a result, gigapixel cameras based on the multi-aperture imaging have become a possible solution to overcome the above limitation. In this paper, we developed an alternative gigapixel imaging system which implements the multiple CMOS chips mosaic in the external optical path and presented the computation methods for calibrating the vignetting distributions and other geometric parameters in the system. Consequently, our gigapixel imaging system has achieved the performance of 24 Hz, 0.2Giga, single-pixel resolution.

In order to maximize the spatio-temporal resolution of the scientific grade camera at width-limited ROI, this paper proposes a new hyper-frame-rate imaging method by temporal multiplexing the sub-region of the image sensor. In the system, a dual-axis scanning galvanometer is localized at the relay pupil plane and a high quality scan lens is utilized to form an image-side telecentric path. Following this path can overcome bandwidth waste in the conventional exposure and readout mode, and maintain other performances of image sensors. As a result, the sCMOS camera has performed 432fps over 820 × 700 pixel arrays to record the dynamic heartbeat of zebrafish larvae.

Homogeneously structured, fluctuation-driven networks of spiking neurons can exhibit a wide variety of dynamical behaviors, ranging from homogeneity to synchrony. We extend our partitioned-ensemble average (PEA) formalism proposed in Zhang et al. (Journal of Computational Neuroscience, 37(1), 81–104, 2014a) to systematically coarse grain the heterogeneous dynamics of strongly coupled, conductance-based integrate-and-fire neuronal networks. The population dynamics models derived here successfully capture the so-called multiple-firing events (MFEs), which emerge naturally in fluctuation-driven networks of strongly coupled neurons. Although these MFEs likely play a crucial role in the generation of the neuronal avalanches observed in vitro and in vivo, the mechanisms underlying these MFEs cannot easily be understood using standard population dynamic models. Using our PEA formalism, we systematically generate a sequence of model reductions, going from Master equations, to Fokker-Planck equations, and finally, to an augmented system of ordinary differential equations. Furthermore, we show that these reductions can faithfully describe the heterogeneous dynamic regimes underlying the generation of MFEs in strongly coupled conductance-based integrate-and-fire neuronal networks.

The brain has a central, short-term learning module, the hippocampus, which transfers what it has learned to long-term memory in cortex during non-REM sleep. The putative mechanism responsible for this type of memory consolidation invokes hierarchically nested hippocampal ripples (100-250 Hz), thalamo-cortical spindles (7-15 Hz), and cortical slow oscillations (< 1 Hz) to enable transfer. Suppression of, for instance, thalamic spindles has been shown to impair hippocampus-dependent memory consolidation. Cortical oscillations are central to information transfer in neural systems. Significant evidence supports the idea that coincident spike input can allow the neural threshold to be overcome, and spikes to be propagated downstream in a circuit. Thus, an observation of oscillations in neural circuits would be an indication that repeated synchronous spiking is enabling information transfer. However, for memory transfer, in which synaptic weights must be being transferred from one neural circuit (region) to another, what is the mechanism? Here, we present a synaptic transfer mechanism whose structure provides some understanding of the phenomena that have been implicated in memory transfer, including the nested oscillations at various frequencies. The circuit is based on the principle of pulse-gated, graded information transfer between neural populations.PACS numbers: 87.18.Sn,87.19.lj,87.19.lm,87.19.lq

Coherent neuronal activity is believed to underlie the transfer and processing of information in the brain. Coherent activity in the form of synchronous firing and oscillations has been measured in many brain regions and has been correlated with enhanced feature processing and other sensory and cognitive functions. In the theoretical context, synfire chains and the transfer of transient activity packets in feedforward networks have been appealed to in order to describe coherent spiking and information transfer. Recently, it has been demonstrated that the classical synfire chain architecture, with the addition of suitably timed gating currents, can support the graded transfer of mean firing rates in feedforward networks (called synfire-gated synfire chains-SGSCs). Here we study information propagation in SGSCs by examining mutual information as a function of layer number in a feedforward network. We explore the effects of gating and noise on information transfer in synfire chains and demonstrate that asymptotically, two main regions exist in parameter space where information may be propagated and its propagation is controlled by pulse-gating: a large region where binary codes may be propagated, and a smaller region near a cusp in parameter space that supports graded propagation across many layers.

Background Aging is characterized by a gradual breakdown of cellular structures. Nuclear abnormality is a hallmark of progeria in human. Analysis of age-dependent nuclear morphological changes in Caenorhabditis elegans is of great value to aging research, and this calls for an automatic image processing method that is suitable for both normal and abnormal structures. Results Our image processing method consists of nuclear segmentation, feature extraction and classification. First, taking up the challenges of defining individual nuclei with fuzzy boundaries or in a clump, we developed an accurate nuclear segmentation method using fused two-channel images with seed-based cluster splitting and k-means algorithm, and achieved a high precision against the manual segmentation results. Next, we extracted three groups of nuclear features, among which five features were selected by minimum Redundancy Maximum Relevance (mRMR) for classifiers. After comparing the classification performances of several popular techniques, we identified that Random Forest, which achieved a mean class accuracy (MCA) of 98.69%, was the best classifier for our data set. Lastly, we demonstrated the method with two quantitative analyses of C. elegans nuclei, which led to the discovery of two possible longevity indicators. Conclusions We produced an automatic image processing method for two-channel C. elegans nucleus-labeled fluorescence images. It frees biologists from segmenting and classifying the nuclei manually. Electronic supplementary material The online version of this article (doi:10.1186/s12859-017-1817-3) contains supplementary material, which is available to authorized users.

Recent evidence suggests that neural information is encoded in packets and may be flexibly routed from region to region. We have hypothesized that neural circuits are split into sub-circuits where one sub-circuit controls information propagation via pulse gating and a second sub-circuit processes graded information under the control of the first sub-circuit. Using an explicit pulse-gating mechanism, we have been able to show how information may be processed by such pulse-controlled circuits and also how, by allowing the information processing circuit to interact with the gating circuit, decisions can be made. Here, we demonstrate how Hebbian plasticity may be used to supplement our pulse-gated information processing framework by implementing a machine learning algorithm. The resulting neural circuit has a number of structures that are similar to biological neural systems, including a layered structure and information propagation driven by oscillatory gating with a complex frequency spectrum., This invited paper was presented at the 50th Asilomar Conference on Signals, Systems and Computers

Line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. In this paper, we make the connection between line attractors and pulse-gating in feedforward neuronal networks. In this context, because of their neutral stability along a one-dimensional manifold, line attractors are associated with a time-translational invariance that allows graded information to be propagated from one neuronal population to the next. To understand how pulse-gating manifests itself in a high-dimensional, non-linear, feedforward integrate-and-fire network, we use a Fokker-Planck approach to analyze system dynamics. We make a connection between pulse-gated propagation in the Fokker-Planck and population-averaged mean-field (firing rate) models, then identify an approximate line attractor in state space as the essential structure underlying graded information propagation. An analysis of the line attractor shows that it consists of three fixed points: a central saddle with an unstable manifold along the line and stable manifolds orthogonal to the line, which is surrounded on either side by stable fixed points. Along the manifold defined by the fixed points, slow dynamics give rise to a ghost. We show that this line attractor arises at a cusp catastrophe, where a fold bifurcation develops as a function of synaptic noise; and that the ghost dynamics near the fold of the cusp underly the robustness of the line attractor. Understanding the dynamical aspects of this cusp catastrophe allows us to show how line attractors can persist in biologically realistic neuronal networks and how the interplay of pulse gating, synaptic coupling and neuronal stochasticity can be used to enable attracting one-dimensional manifolds and thus, dynamically control the processing of graded information., Comment: 7 pages, 5 figures

This paper reviews our recent work addressing the role of both synaptic-input and connectivity-architecture fluctuations in coarse-grained descriptions of integrate-and-fire (I&F) point- neuron network models. Beginning with the most basic coarse-grained description, the all-to-all coupled, mean-field model, which ignores all fluctuations, we add the effects of the two types of fluctuations one at a time. To study the effects of synaptic-input fluctuations, we derive a kinetic- theoretic description, first in the form of a Boltzmann equation in (2+1) dimensions, simplifying that to an advection-diffusion equation, and finally reducing the dimension to a system of two (1+1)- dimensional kinetic equations via the maximum entropy principle. In the limit of an infinitely-fast conductance relaxation time, we derive a Fokker-Planck equation which captures the bifurcation between a bistable, hysteretic operating regime of the network when the amount of synaptic-input fluctuations is small, and a stable regime when the amount of fluctuations increases. To study the ef- fects of complex neuronal-network architecture, we incorporate the network connectivity statistics in the mean-field description, and investigate the dependence of these statistics on the statistical prop- erties of the neuronal firing rates for three network examples with increasingly complex connectivity architecture.

Luminance and contrast are two major attributes of objects in the visual scene. Luminance and contrast information received by visual neurons are often updated simultaneously. We examined the temporal response properties of neurons in the primary visual cortex (V1) to stimuli whose luminance and contrast were simultaneously changed by 50 Hz. We found that response tuning to luminance changes precedes tuning to contrast changes in V1. For most V1 neurons, the onset time of response tuning to luminance changes was shorter than that to contrast changes. Most neurons carried luminance information in the early response stage, while all neurons carried both contrast and luminance information in the late response stage. The early luminance response suggests that cortical processing for luminance is not as slow as previously thought.

In this paper, we extend our framework for constructing low-dimensional dynamical system models of large-scale neuronal networks of mammalian primary visual cortex. Our dimensional reduction procedure consists of performing a suitable linear change of variables and then systematically truncating the new set of equations. The extended framework includes modeling the effect of neglected modes as a stochastic process. By parametrizing and including stochasticity in one of two ways we show that we can improve the systems-level characterization of our dimensionally reduced neuronal network model. We examined orientation selectivity maps calculated from the firing rate distribution of large-scale simulations and stochastic dimensionally reduced models and found that by using stochastic processes to model the neglected modes, we were able to better reproduce the mean and variance of firing rates in the original large-scale simulations while still accurately predicting the orientation preference distribution.

To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [13, 12], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [13] to further simplify the kinetic theory.

The state-of-the-art commercial telephoto lens has already provided us almost one giga space-bandwidth product. Since the single-image sensor cannot take such sampling capacity, we implement a four-parallel-boresight imaging system by using four such lenses and use 64 image sensors to complete full field of view (FOV) imaging for achieving 0.8 gigapixel over 15.6°×10.5°. Multiple sensors mosaicking can make most online computation and data transfer in parallel, and help us to realize a gigapixel video camera. Meanwhile, according to the four-parallel-boresight configuration, the flat image plane simplifies the image registration and image stitching, and allows us to keep high imaging performance in full frame following geometric and optical calibration and correction. Furthermore, considering that working distance changes do bring additional x/y offsets between sensor arrays, we propose a computation-based method and introduce an eight-axis automatic motion mechanism into the system to perform the online active displacement. Our prototype camera using 16 sensors has been validated in 50 m indoor conditions and 145 m outdoor condition experiments, respectively. The effective angular resolution under the 0.2 giga 24 Hz video output is 18 μrad, which is two times the lens instantaneous FOV. Compared with other gigapixel cameras, it is superior in terms of optical system simplicity and cost efficiency, which would potentially benefit numerous unmanned aerial vehicle photogrammetric applications that pursue high angular resolution over moderate FOV.

Systems-level neurophysiological data reveal coherent activity that is distributed across large regions of cortex. This activity is often thought of as an emergent property of recurrently connected networks. The fact that this activity is coherent means that populations of neurons may be thought of as the carriers of information, not individual neurons. Therefore, systems-level descriptions of functional activity in the network often find their simplest form as combinations of the underlying neuronal variables. In this paper, we provide a general framework for constructing low-dimensional dynamical systems that capture the essential systems-level information contained in large-scale networks of neurons. We demonstrate that these dimensionally-reduced models are capable of predicting the response to previously un-encountered input and that the coupling between systems-level variables can be used to reconstruct cellular-level functional connectivities. Furthermore, we show that these models may be constructed even in the absence of complete information about the underlying network.

Unifying the results obtained from the large-scale, physiologically realistic, yet minimal computational primary visual cortex (V1) network models and identifying the single cortical operating state, namely, an intermittent desuppressed state (IDS) with fluctuation-controlled criticality are presented. The study suggests a possible operating state of V1 characterised by high total conductance with strong inhibition, large synaptic fluctuation, and the important role played by the N-methyl-D-aspartic acid conductance in long-range, orientation-specific interactions. The model cortex has the ability to quantitatively and qualitatively reproduce a host of dynamical phenomena exhibited by the real cortex, and the network mechanisms as revealed in the IDS state with fluctuation-controlled criticality in the model V1 dynamics offers suggestions for the physiological underpinnings of the neuronal dynamics in real V1.

Recently developed kinetic theory and related closures for neuronal network dynamics have been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The moment equations arising from the kinetic theory are a system of (1+1)-dimensional nonlinear partial differential equations (PDE) on a bounded domain with nonlinear boundary conditions. The PDEs themselves are self-consistently specified by parameters which are functions of the boundary values of the solution. The moment equations can be stiff in space and time. Numerical methods are presented here for efficiently and accurately solving these moment equations. The essential ingredients in our numerical methods include: (i) the system is discretized in time with an implicit Euler method within a spectral deferred correction framework, therefore, the PDEs of the kinetic theory are reduced to a sequence, in time, of boundary value problems (BVPs) with nonlinear boundary conditions; (ii) a set of auxiliary parameters is introduced to recast the original BVP with nonlinear boundary conditions as BVPs with linear boundary conditions - with additional algebraic constraints on the auxiliary parameters; (iii) a careful combination of two Newton's iterates for the nonlinear BVP with linear boundary condition, interlaced with a Newton's iterate for solving the associated algebraic constraints is constructed to achieve quadratic convergence for obtaining the solutions with self-consistent parameters. It is shown that a simple fixed-point iteration can only achieve a linear convergence for the self-consistent parameters. The practicability and efficiency of our numerical methods for solving the moment equations of the kinetic theory are illustrated with numerical examples. It is further demonstrated that the moment equations derived from the kinetic theory of neuronal network dynamics can very well capture the coarse-grained dynamical properties of integrate-and-fire neuronal networks.

Neural oscillations can enhance feature recognition (Azouz and Gray Proceedings of the National Academy of Sciences of the United States of America, 97, 8110---8115 2000), modulate interactions between neurons (Womelsdorf et al. Science, 316, 1609---01612 2007), and improve learning and memory (Markowska et al. The Journal of Neuroscience, 15, 2063---2073 1995). Numerical studies have shown that coherent spiking can give rise to windows in time during which information transfer can be enhanced in neuronal networks (Abeles Israel Journal of Medical Sciences, 18, 83---92 1982; Lisman and Idiart Science, 267, 1512---1515 1995, Salinas and Sejnowski Nature Reviews. Neuroscience, 2, 539---550 2001). Unanswered questions are: 1) What is the transfer mechanism? And 2) how well can a transfer be executed? Here, we present a pulse-based mechanism by which a graded current amplitude may be exactly propagated from one neuronal population to another. The mechanism relies on the downstream gating of mean synaptic current amplitude from one population of neurons to another via a pulse. Because transfer is pulse-based, information may be dynamically routed through a neural circuit with fixed connectivity. We demonstrate the transfer mechanism in a realistic network of spiking neurons and show that it is robust to noise in the form of pulse timing inaccuracies, random synaptic strengths and finite size effects. We also show that the mechanism is structurally robust in that it may be implemented using biologically realistic pulses. The transfer mechanism may be used as a building block for fast, complex information processing in neural circuits. We show that the mechanism naturally leads to a framework wherein neural information coding and processing can be considered as a product of linear maps under the active control of a pulse generator. Distinct control and processing components combine to form the basis for the binding, propagation, and processing of dynamically routed information within neural pathways. Using our framework, we construct example neural circuits to 1) maintain a short-term memory, 2) compute time-windowed Fourier transforms, and 3) perform spatial rotations. We postulate that such circuits, with automatic and stereotyped control and processing of information, are the neural correlates of Crick and Koch's zombie modes.

Within a large-scale neuronal network model of macaque primary visual cortex, we examined how intrinsic dynamic fluctuations in synaptic currents modify the effect of strong recurrent excitation on orientation selectivity. Previously, we showed that, using a strong network inhibition countered by feedforward and recurrent excitation, the cortical model reproduced many observed properties of simple and complex cells. However, that network’s complex cells were poorly selective for orientation, and increasing cortical self-excitation led to network instabilities and unrealistically high firing rates. Here, we show that a sparsity of connections in the network produces large, intrinsic fluctuations in the cortico-cortical conductances that can stabilize the network and that there is a critical level of fluctuations (controllable by sparsity) that allows strong cortical gain and the emergence of orientation-selective complex cells. The resultant sparse network also shows near contrast invariance in its selectivity and, in agreement with recent experiments, has extracellular tuning properties that are similar in pinwheel center and iso-orientation regions, whereas intracellular conductances show positional dependencies. Varying the strength of synaptic fluctuations by adjusting the sparsity of network connectivity, we identified a transition between the dynamics of bistability and without bistability. In a network with strong recurrent excitation, this transition is characterized by a near hysteretic behavior and a rapid rise of network firing rates as the synaptic drive or stimulus input is increased. We discuss the connection between this transition and orientation selectivity in our model of primary visual cortex.

To address computational “scale-up” issues in modeling large regions of the cortex, many coarse-graining procedures have been invoked to obtain effective descriptions of neuronal network dynamics. However, because of local averaging in space and time, these methods do not contain detailed spike information and, thus, cannot be used to investigate, e.g., cortical mechanisms that are encoded through detailed spike-timing statistics. To retain high-order statistical information of spikes, we develop a hybrid theoretical framework that embeds a subnetwork of point neurons within, and fully interacting with, a coarse-grained network of dynamical background. We use a newly developed kinetic theory for the description of the coarse-grained background, in combination with a Poisson spike reconstruction procedure to ensure that our method applies to the fluctuation-driven regime as well as to the mean-driven regime. This embedded-network approach is verified to be dynamically accurate and numerically efficient. As an example, we use this embedded representation to construct “reverse-time correlations” as spiked-triggered averages in a ring model of orientation-tuning dynamics.

To avoid the numerical errors associated with resetting the potential following a spike in simulations of integrate-and-fire neuronal networks, Hansel et al. and Shelley independently developed a modified time-stepping method. Their particular scheme consists of second-order Runge-Kutta time-stepping, a linear interpolant to find spike times, and a recalibration of postspike potential using the spike times. Here we show analytically that such a scheme is second order, discuss the conditions under which efficient, higher-order algorithms can be constructed to treat resets, and develop a modified fourth-order scheme. To support our analysis, we simulate a system of integrate- and-fire conductance-based point neurons with all-to-all coupling. For six-digit accuracy, our modified Runge-Kutta fourth-order scheme needs a time-step oft = 0.5 × 10 −3 seconds, whereas to achieve comparable accuracy using a recalibrated second-order or a first-order algorithm requires time-steps of 10 −5 seconds or 10 −9 seconds, respectively. Furthermore, since the cortico-cortical conductances in standard integrate-and-fire neuronal networks do not depend on the value of the membrane potential, we can attain fourth-order accuracy with computational costs normally associated with second-order schemes.

In this paper, we extend a framework for constructing low-dimensional dynamical systems models of mammalian primary visual cortex to a cortical network model that incorporates the full nonlinear effects of complex cells. The procedure consists of capturing the essential dynamics in a low-dimensional subspace using empirical methods, then recasting the equations in the reduced vector space. Previously, we considered visual cortical network models consisting of only simple cells with nearly linear responses to external stimuli. Here we show that fully nonlinear effects can be incorporated by examining the dimensional reduction of an idealized ring model of V1 with both simple and complex cells. We found it expedient to divide the subspace into four separate neuronal populations: excitatory simple, excitatory complex, inhibitory simple and inhibitory complex. In order to reproduce the fluctuation-driven dynamics in this reduced space, we incorporated (1) white noises with different intensities into individual neuronal populations, and (2) firing rate estimates to capture the probability of firing due to subthreshold fluctuations. With a more accurate, fitted connectivity, our modified dimensional reduced models can reproduce the firing rates, circular variances and modulation ratios observed in the original ring model.

RLEdb: a database of rate-limiting enzymes and their regulation in human, rat, mouse, yeast and E. coli

Beginning from a relatively simple set of dynamical equations for a fluid permeated by a radiative field strong enough to produce significant forces, we find the structure of plane-parallel equilibria and study their stability to small acoustic disturbances. In doing this, we neglect viscous effects and complications of nongreyness. We find that acoutic instabilities occur over a wide range of conditions below the Eddington limit. This result is in line with findings reported twenty years ago but it contradicts some more recent reports of the absence of instabilities. We briefly attempt to identify the causes of the discrepancies and then close with a discussion of the possible astrophysical interest of such instabilities., 10 pages, LaTeX, 5 postscript figures, to be published in Physics Reports

The ratio ${R}_{1}$ between the average magnetic energy and the square-averaged flux plays an important role in the study of nonlinear dynamos, as a measure of the efficiency of a dynamo at generating flux. For large values of ${R}_{m}$, ${R}_{1}$ displays a scaling behavior of the type ${R}_{1}\ensuremath{\sim}{R}_{m}^{n}$, where ${R}_{m}$ is the magnetic Reynolds number. We show by direct numerical evaluation that $n$ depends sensitively on the flow complexity for small-scale dynamos. Furthermore, by relating $n$ to the cancellation exponent and the correlation dimension of the magnetic field, we argue that $n$ is not likely to be close to zero in general.

Coherent neural spiking and local field potentials are believed to be signatures of the binding and transfer of information in the brain. Coherent activity has now been measured experimentally in many regions of mammalian cortex. Recently experimental evidence has been presented suggesting that neural information is encoded and transferred in packets, i.e., in stereotypical, correlated spiking patterns of neural activity. Due to their relevance to coherent spiking, synfire chains are one of the main theoretical constructs that have been appealed to in order to describe coherent spiking and information transfer phenomena. However, for some time, it has been known that synchronous activity in feedforward networks asymptotically either approaches an attractor with fixed waveform and amplitude, or fails to propagate. This has limited the classical synfire chain’s ability to explain graded neuronal responses. Recently, we have shown that pulse-gated synfire chains are capable of propagating graded information coded in mean population current or firing rate amplitudes. In particular, we showed that it is possible to use one synfire chain to provide gating pulses and a second, pulse-gated synfire chain to propagate graded information. We called these circuits synfire-gated synfire chains (SGSCs). Here, we present SGSCs in which graded information can rapidly cascade through a neural circuit, and show a correspondence between this type of transfer and a mean-field model in which gating pulses overlap in time. We show that SGSCs are robust in the presence of variability in population size, pulse timing and synaptic strength. Finally, we demonstrate the computational capabilities of SGSC-based information coding by implementing a self-contained, spike-based, modular neural circuit that is triggered by streaming input, processes the input, then makes a decision based on the processed information and shuts itself down., Author Summary Cognitive tasks are associated with the dynamic excitation of neural assemblies. When we consider how quickly and flexibly such collectives may be formed and incorporated in a task, a persistent question has been: how can the brain rapidly evoke and involve different neural assemblies in a computation, when synaptic coupling changes only slowly? Here, we demonstrate mechanisms whereby information may be rapidly and selectively routed through a neural circuit, and sub-circuits may be turned on and off. The resulting information processing framework achieves the goal that has been pursued, but until now largely not attained, of achieving faithful, flexible information transfer across many synapses and dynamic excitation of neural assemblies with fixed connectivities.

We review a statistical physics approach for reduced descriptions of neuronal network dynamics. From a network of all-to-all coupled, excitatory integrate-and-fire neurons, we derive a (2+1)-D advection-diffusion equation for a probability distribution function, which describes neuronal population dynamics. We further show how to derive a (1+1)-D kinetic equation, using a moment closure scheme, without introducing any new parameters to the system. We demonstrate the numerical accuracy of our kinetic theory by comparing its results to Monte Carlo simulations of the full integrate-and-fire neuronal network.

The ability to map functional connectivity is necessary for the study of the flow of activity in neuronal circuits. Optical imaging of calcium indicators, including FRET-based genetically encoded indicators and extrinsic dyes, is an important adjunct to electrophysiology and is widely used to visualize neuronal activity. However, techniques for mapping functional connectivities with calcium imaging data have been lacking. We present a procedure to compute reduced functional couplings between neuronal ensembles undergoing seizure activity from ratiometric calcium imaging data in three steps: (1) calculation of calcium concentrations and neuronal firing rates from ratiometric data; (2) identification of putative neuronal populations from spatio-temporal time-series of neural bursting activity; and then, (3) derivation of reduced connectivity matrices that represent neuronal population interactions. We apply our method to the larval zebrafish central nervous system undergoing chemoconvulsant-induced seizures. These seizures generate propagating, central nervous system-wide neural activity from which population connectivities may be calculated. This automatic functional connectivity mapping procedure provides a practical and user-independent means for summarizing the flow of activity between neuronal ensembles.

Steady dynamics of coupled conductance-based integrate-and-fire neuronal networks in the limit of small fluctuations is studied via the equilibrium states of a Fokker-Planck equation. An asymptotic approximation for the membrane-potential probability density function is derived and the corresponding gain curves are found. Validity conditions are discussed for the Fokker-Planck description and verified via direct numerical simulations.

Human herpesvirus miRNAs statistically preferentially target host genes involved in cell signaling and adhesion/junction pathways