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Molten salts-assisted synthesis is widely used in the construction of high efficiency graphitic carbon nitride (g-C3N4) photocatalysts, and two isotypes of g-C3N4 have been synthesized by such method, namely poly (heptazine imide) (PHI) and poly (triazine imide) (PTI). However, the understanding of the structural changes taking place during the molten salt process and the structure–activity relationship of g-C3N4 polymorphs remain blurred. Herein, by regulating the treatment duration of g-C3N4 nanosheets (melon) in molten salts, we successfully synthesized g-C3N4 with phases of PHI, PHI/PTI and PTI. A continuous structural transformation induced by ions, in which melon transforms to a stable phase PTI via PHI, an intermediate state, was unveiled for the first time. In addition, results reveal that atomic configurations play a vital role in photo absorption, and charge carrier transfer and surface reaction, leading to significant differences in photocatalytic degradation. Among them, PHI with K+ and cyan groups modification, as well as high crystallinity, exhibits remarkable degradation efficiency, with 90% removal of tetracycline in 10 min and 80% removal of phenol in 60 min. This study sheds light on a deeper understanding for the molten salt-assisted synthesis and provides new ideas for preparing efficient organic semiconductor photocatalysts.

This article discusses how to create an interactive virtual training program at the intersection of neuroscience, robotics, and computer science for high school students. A four-day microseminar, titled Swarming Powered by Neuroscience (SPN), was conducted virtually through a combination of presentations and interactive computer game simulations, delivered by subject matter experts in neuroscience, mathematics, multi-agent swarm robotics, and education. The objective of this research was to determine if taking an interdisciplinary approach to high school education would enhance the students learning experiences in fields such as neuroscience, robotics, or computer science. This study found an improvement in student engagement for neuroscience by 16.6%, while interest in robotics and computer science improved respectively by 2.7% and 1.8%. The curriculum materials, developed for the SPN microseminar, can be used by high school teachers to further evaluate interdisciplinary instructions across life and physical sciences and computer science.

Insect neural systems are a promising source of inspiration for new algorithms for navigation, especially on low size, weight, and power platforms. There have been unprecedented recent neuroscience breakthroughs with Drosophila in behavioral and neural imaging experiments as well as the mapping of detailed connectivity of neural structures. General mechanisms for learning orientation in the central complex (CX) of Drosophila have been investigated previously; however, it is unclear how these underlying mechanisms extend to cases where there is translation through an environment (beyond only rotation), which is critical for navigation in robotic systems. Here, we develop a CX neural connectivity-constrained model that performs sensor fusion, as well as unsupervised learning of visual features for path integration; we demonstrate the viability of this circuit for use in robotic systems in simulated and physical environments. Furthermore, we propose a theoretical understanding of how distributed online unsupervised network weight modification can be leveraged for learning in a trajectory through an environment by minimizing of orientation estimation error. Overall, our results here may enable a new class of CX-derived low power robotic navigation algorithms and lead to testable predictions to inform future neuroscience experiments.SummaryAn insect neural connectivity-constrained model performs sensor fusion and online learning for orientation estimation.

We present a theoretical study aiming at model fitting for sensory neurons. Conventional neural network training approaches are not applicable to this problem due to lack of continuous data. Although the stimulus can be considered as a smooth time-dependent variable, the associated response will be a set of neural spike timings (roughly the instants of successive action potential peaks) that have no amplitude information. A recurrent neural network model can be fitted to such a stimulus-response data pair by using the maximum likelihood estimation method where the likelihood function is derived from Poisson statistics of neural spiking. The universal approximation feature of the recurrent dynamical neuron network models allows us to describe excitatory-inhibitory characteristics of an actual sensory neural network with any desired number of neurons. The stimulus data are generated by a phased cosine Fourier series having a fixed amplitude and frequency but a randomly shot phase. Various values of amplitude, stimulus component size, and sample size are applied in order to examine the effect of the stimulus to the identification process. Results are presented in tabular and graphical forms at the end of this text. In addition, to demonstrate the success of this research, a study involving the same model, nominal parameters and stimulus structure, and another study that works on different models are compared to that of this research.

Head-direction cells have been found in several areas in the mammalian brains. The firing rate of an ideal head-direction cell reaches its peak value only when the animal's head points in a specific direction, and this preferred direction stays the same regardless of spatial location. In this paper we combine mathematical analytical techniques and numerical simulations to fully analyze the equilibrium states of a generic ring attractor network, which is a widely used modeling framework for the head-direction system. Under specific conditions, all solutions of the ring network are bounded, and there exists a Lyapunov function that guarantees the stability of the network for any given inputs, which may come from multiple sources in the biological system, including self-motion information for inertially based updating and landmark information for calibration. We focus on the first few terms of the Fourier series of the ring network to explicitly solve for all possible equilibrium states, followed by a stability analysis based on small perturbations. In particular, these equilibrium states include the standard single-peaked activity pattern as well as double-peaked activity pattern, whose existence is unknown but has testable experimental implications. To our surprise, we have also found an asymmetric equilibrium activity profile even when the network connectivity is strictly symmetric. Finally we examine how these different equilibrium solutions depend on the network parameters and obtain the phase diagrams in the parameter space of the ring network.

During spatial navigation, the frequency and timing of spikes from spatial neurons including place cells in hippocampus and grid cells in medial entorhinal cortex are temporally organized by continuous theta oscillations (6–11 Hz). The theta rhythm is regulated by subcortical structures including the medial septum, but it is unclear how spatial information from place cells may reciprocally organize subcortical theta-rhythmic activity. Here we recorded single-unit spiking from a constellation of subcortical and hippocampal sites to study spatial modulation of rhythmic spike timing in rats freely exploring an open environment. Our analysis revealed a novel class of neurons that we termed ‘phaser cells,’ characterized by a symmetric coupling between firing rate and spike theta-phase. Phaser cells encoded space by assigning distinct phases to allocentric isocontour levels of each cell’s spatial firing pattern. In our dataset, phaser cells were predominantly located in the lateral septum, but also the hippocampus, anteroventral thalamus, lateral hypothalamus, and nucleus accumbens. Unlike the unidirectional late-to-early phase precession of place cells, bidirectional phase modulation acted to return phaser cells to the same theta-phase along a given spatial isocontour, including cells that characteristically shifted to later phases at higher firing rates. Our dynamical models of intrinsic theta-bursting neurons demonstrated that experience-independent temporal coding mechanisms can qualitatively explain (1) the spatial rate-phase relationships of phaser cells and (2) the observed temporal segregation of phaser cells according to phase-shift direction. In open-field phaser cell simulations, competitive learning embedded phase-code entrainment maps into the weights of downstream targets, including path integration networks. Bayesian phase decoding revealed error correction capable of resetting path integration at subsecond timescales. Our findings suggest that phaser cells may instantiate a subcortical theta-rhythmic loop of spatial feedback. We outline a framework in which location-dependent synchrony reconciles internal idiothetic processes with the allothetic reference points of sensory experience., Author summary Spatial cognition in mammals depends on position-related activity in the hippocampus and entorhinal cortex. Hippocampal place cells and entorhinal grid cells carry distinct maps as rodents move around. The grid cell map is thought to measure angles and distances from previous locations using path integration, a strategy of internally tracking self motion. However, path integration accumulates errors and must be ‘reset’ by external sensory cues. Allowing rats to explore an open arena, we recorded spiking neurons from areas interconnected with the entorhinal cortex, including subcortical structures and the hippocampus. Many of these subcortical regions help coordinate the hippocampal theta rhythm. Thus, we looked for spatial information in theta-rhythmic spiking and discovered ‘phaser cells’ in the lateral septum, which receives dense hippocampal input. Phaser cells encoded the rat’s position by shifting spike timing in symmetry with spatial changes in firing rate. We theorized that symmetric rate-phase coupling allows downstream networks to flexibly learn spatial patterns of synchrony. Using dynamical models and simulations, we showed that phaser cells may collectively transmit a fast, oscillatory reset signal. Our findings develop a new perspective on the temporal coding of space that may help disentangle competing models of path integration and cross-species differences in navigation.

A simulation based study on model fitting for sensory neurons from stimulus/response data is presented. The employed model is a continuous time recurrent neural network (CTRNN) which is a member of models with known universal approximation features. This feature of the recurrent dynamical neuron network models allow us to describe excitatory-inhibitory characteristics of an actual sensory neural network with any desired number of neurons. This work will be a continuation of a previous study where the parameters associated with the sigmoidal gain functions are not taken into account. In this work, we will construct a similar framework but all parameters associated with the model are estimated. The stimulus data is generated by a Phased Cosine Fourier series having fixed amplitude and frequency but a randomly shot phase. Various values of amplitude, stimulus component size and sample size are applied in order to examine the effect of stimulus to the identification process. Results are presented in tabular and graphical forms at the end of this text. In addition a comparison of the results with previous researches including will be presented.

The theory of attractor neural networks has been influential in our understanding of the neural processes underlying spatial, declarative, and episodic memory. Many theoretical studies focus on the inherent properties of an attractor, such as its structure and capacity. Relatively little is known about how an attractor neural network responds to external inputs, which often carry conflicting information about a stimulus. In this paper we analyze the behavior of an attractor neural network driven by two conflicting external inputs. Our focus is on analyzing the emergent properties of the megamap model, a quasi-continuous attractor network in which place cells are flexibly recombined to represent a large spatial environment. In this model, the system shows a sharp transition from the winner-take-all mode, which is characteristic of standard continuous attractor neural networks, to a combinatorial mode in which the equilibrium activity pattern combines embedded attractor states in response to conflicting external inputs. We derive a numerical test for determining the operational mode of the system a priori. We then derive a linear transformation from the full megamap model with thousands of neurons to a reduced 2-unit model that has similar qualitative behavior. Our analysis of the reduced model and explicit expressions relating the parameters of the reduced model to the megamap elucidate the conditions under which the combinatorial mode emerges and the dynamics in each mode given the relative strength of the attractor network and the relative strength of the two conflicting inputs. Although we focus on a particular attractor network model, we describe a set of conditions under which our analysis can be applied to more general attractor neural networks.

Neurons use two main schemes to encode information: rate coding (frequency of firing) and temporal coding (timing or pattern of firing). While the importance of rate coding is well-established, it remains controversial whether temporal codes alone are sufficient for controlling behavior. Moreover, the molecular mechanisms underlying the generation of specific temporal codes are enigmatic. Here, we show in Drosophila clock neurons that distinct temporal spike patterns, dissociated from changes in firing rate, encode time-dependent arousal and regulate sleep. From a large-scale genetic screen, we identify the molecular pathways mediating the circadian-dependent changes in ionic flux and spike morphology that rhythmically modulate spike timing. Remarkably, the daytime spiking pattern alone is sufficient to drive plasticity in downstream arousal neurons, leading to increased firing of these cells. These findings demonstrate a causal role for temporal coding in behavior and define a form of synaptic plasticity triggered solely by temporal spike patterns.

© 2018 The Author(s). Analysis of chromatin accessibility can reveal transcriptional regulatory sequences, but heterogeneity of primary tissues poses a significant challenge in mapping the precise chromatin landscape in specific cell types. Here we report single-nucleus ATAC-seq, a combinatorial barcoding-assisted single-cell assay for transposase-accessible chromatin that is optimized for use on flash-frozen primary tissue samples. We apply this technique to the mouse forebrain through eight developmental stages. Through analysis of more than 15,000 nuclei, we identify 20 distinct cell populations corresponding to major neuronal and non-neuronal cell types. We further define cell-type-specific transcriptional regulatory sequences, infer potential master transcriptional regulators and delineate developmental changes in forebrain cellular composition. Our results provide insight into the molecular and cellular dynamics that underlie forebrain development in the mouse and establish technical and analytical frameworks that are broadly applicable to other heterogeneous tissues.

Temporal analysis of sound is fundamental to auditory processing throughout the animal kingdom. Echolocating bats are powerful models for investigating the underlying mechanisms of auditory temporal processing, as they show microsecond precision in discriminating the timing of acoustic events. However, the neural basis for microsecond auditory discrimination in bats has eluded researchers for decades. Combining extracellular recordings in the midbrain inferior colliculus (IC) and mathematical modeling, we show that microsecond precision in registering stimulus events emerges from synchronous neural firing, revealed through low-latency variability of stimulus-evoked extracellular field potentials (EFPs, 200–600 Hz). The temporal precision of the EFP increases with the number of neurons firing in synchrony. Moreover, there is a functional relationship between the temporal precision of the EFP and the spectrotemporal features of the echolocation calls. In addition, EFP can measure the time difference of simulated echolocation call–echo pairs with microsecond precision. We propose that synchronous firing of populations of neurons operates in diverse species to support temporal analysis for auditory localization and complex sound processing., Author summary We routinely rely on a stopwatch to precisely measure the time it takes for an athlete to reach the finish line. Without the assistance of such a timing device, our measurement of elapsed time becomes imprecise. By contrast, some animals, such as echolocating bats, naturally perform timing tasks with remarkable precision. Behavioral research has shown that echolocating bats can estimate the elapsed time between sonar cries and echo returns with a precision in the range of microseconds. However, the neural basis for such microsecond precision has remained a puzzle to scientists. Combining extracellular recordings in the bat’s inferior colliculus (IC)—a midbrain nucleus of the auditory pathway—and mathematical modeling, we show that microsecond precision in registering stimulus events emerges from synchronous neural firing. Our recordings revealed a low-latency variability of stimulus-evoked extracellular field potentials (EFPs), which, according to our mathematical modeling, was determined by the number of firing neurons and their synchrony. Moreover, the acoustic features of echolocation calls, such as signal duration and bandwidth, which the bat dynamically modulates during prey capture, also modulate the precision of EFPs. These findings have broad implications for understanding temporal analysis of acoustic signals in a wide range of auditory behaviors across the animal kingdom.

Spatial cells of the hippocampal formation are embedded in networks of theta cells. The septal theta rhythm (6–10 Hz) organizes the spatial activity of place and grid cells in time, but it remains unclear how spatial reference points organize the temporal activity of theta cells in space. We study spatial theta cells in simulations and single-unit recordings from exploring rats to ask whether temporal phase codes may anchor spatial representations to the outside world. We theorize that an experience-independent mechanism for temporal coding may combine with burst synchronization to continuously calibrate self-motion to allocentric reference frames. Subcortical recordings revealed spatial theta cells with strong rate-phase correlations related to distinct theta phases. Simulations of bursting neurons and networks explained that relationship and, with competitive learning, demonstrated flexible spatial synchronization patterns when driven by low-dimensional spatial components from the recording data. Thus temporal coding synchrony may reconcile extrinsic and intrinsic neural codes.

Genome-wide analysis of chromatin accessibility in primary tissues has uncovered millions of candidate regulatory sequences in the human and mouse genomes1–4. However, the heterogeneity of biological samples used in previous studies has prevented a precise understanding of the dynamic chromatin landscape in specific cell types. Here, we show that analysis of the transposase-accessible-chromatin in single nuclei isolated from frozen tissue samples can resolve cellular heterogeneity and delineate transcriptional regulatory sequences in the constituent cell types. Our strategy is based on a combinatorial barcoding assisted single cell assay for transposase-accessible chromatin5 and is optimized for nuclei from flash-frozen primary tissue samples (snATAC-seq). We used this method to examine the mouse forebrain at seven development stages and in adults. From snATAC-seq profiles of more than 15,000 high quality nuclei, we identify 20 distinct cell populations corresponding to major neuronal and non-neuronal cell-types in foetal and adult forebrains. We further define cell-type specific cis regulatory sequences and infer potential master transcriptional regulators of each cell population. Our results demonstrate the feasibility of a general approach for identifying cell-type-specific cis regulatory sequences in heterogeneous tissue samples, and provide a rich resource for understanding forebrain development in mammals.

We have developed an efficient information-maximization method for computing the optimal shapes of tuning curves of sensory neurons by optimizing the parameters of the underlying feedforward network model. When applied to the problem of population coding of visual motion with multiple directions, our method yields several types of tuning curves with both symmetric and asymmetric shapes that resemble what have been found in the visual cortex. Our result suggests that the diversity or heterogeneity of tuning curve shapes as observed in neurophysiological experiment might actually constitute an optimal population representation of visual motions with multiple components., Comment: The 51st Annual Conference on Information Sciences and Systems (CISS), 2017

The problem of how the hippocampus encodes both spatial and nonspatial information at the cellular network level remains largely unresolved. Spatial memory is widely modeled through the theoretical framework of attractor networks, but standard computational models can only represent spaces that are much smaller than the natural habitat of an animal. We propose that hippocampal networks are built on a basic unit called a “megamap,” or a cognitive attractor map in which place cells are flexibly recombined to represent a large space. Its inherent flexibility gives the megamap a huge representational capacity and enables the hippocampus to simultaneously represent multiple learned memories and naturally carry nonspatial information at no additional cost. On the other hand, the megamap is dynamically stable, because the underlying network of place cells robustly encodes any location in a large environment given a weak or incomplete input signal from the upstream entorhinal cortex. Our results suggest a general computational strategy by which a hippocampal network enjoys the stability of attractor dynamics without sacrificing the flexibility needed to represent a complex, changing world.

Animals are capable of navigation even in the absence of prominent landmark cues. This behavioral demonstration of path integration is supported by the discovery of place cells and other neurons that show path-invariant response properties even in the dark. That is, under suitable conditions, the activity of these neurons depends primarily on the spatial location of the animal regardless of which trajectory it followed to reach that position. Although many models of path integration have been proposed, no known single theoretical framework can formally accommodate their diverse computational mechanisms. Here we derive a set of necessary and sufficient conditions for a general class of systems that performs exact path integration. These conditions include multiplicative modulation by velocity inputs and a path-invariance condition that limits the structure of connections in the underlying neural network. In particular, for a linear system to satisfy the path-invariance condition, the effective synaptic weight matrices under different velocities must commute. Our theory subsumes several existing exact path integration models as special cases. We use entorhinal grid cells as an example to demonstrate that our framework can provide useful guidance for finding unexpected solutions to the path integration problem. This framework may help constrain future experimental and modeling studies pertaining to a broad class of neural integration systems.

While Shannon's mutual information has widespread applications in many disciplines, for practical applications it is often difficult to calculate its value accurately for high-dimensional variables because of the curse of dimensionality. This article focuses on effective approximation methods for evaluating mutual information in the context of neural population coding. For large but finite neural populations, we derive several information-theoretic asymptotic bounds and approximation formulas that remain valid in high-dimensional spaces. We prove that optimizing the population density distribution based on these approximation formulas is a convex optimization problem that allows efficient numerical solutions. Numerical simulation results confirmed that our asymptotic formulas were highly accurate for approximating mutual information for large neural populations. In special cases, the approximation formulas are exactly equal to the true mutual information. We also discuss techniques of variable transformation and dimensionality reduction to facilitate computation of the approximations.

The dorsomedial entorhinal cortex (dMEC) of the rat brain contains a remarkable population of spatially tuned neurons called grid cells (Hafting et al., 2005). Each grid cell fires selectively at multiple spatial locations, which are geometrically arranged to form a hexagonal lattice that tiles the surface of the rat's environment. Here, we show that grid fields can combine with one another to form moiré interference patterns, referred to as “moiré grids,” that replicate the hexagonal lattice over an infinite range of spatial scales. We propose that dMEC grids are actually moiré grids formed by interference between much smaller “theta grids,” which are hypothesized to be the primary source of movement-related theta rhythm in the rat brain. The formation of moiré grids from theta grids obeys two scaling laws, referred to as the length and rotational scaling rules. The length scaling rule appears to account for firing properties of grid cells in layer II of dMEC, whereas the rotational scaling rule can better explain properties of layer III grid cells. Moiré grids built from theta grids can be combined to form yet larger grids and can also be used as basis functions to construct memory representations of spatial locations (place cells) or visual images. Memory representations built from moiré grids are automatically endowed with size invariance by the scaling properties of the moiré grids. We therefore propose that moiré interference between grid fields may constitute an important principle of neural computation underlying the construction of scale-invariant memory representations.

Neocortex, a new and rapidly evolving brain structure in mammals, has a similar layered architecture in species over a wide range of brain sizes. Larger brains require longer fibers to communicate between distant cortical areas; the volume of the white matter that contains long axons increases disproportionally faster than the volume of the gray matter that contains cell bodies, dendrites, and axons for local information processing, according to a power law. The theoretical analysis presented here shows how this remarkable anatomical regularity might arise naturally as a consequence of the local uniformity of the cortex and the requirement for compact arrangement of long axonal fibers. The predicted power law with an exponent of 4/3 minus a small correction for the thickness of the cortex accurately accounts for empirical data spanning several orders of magnitude in brain sizes for various mammalian species, including human and nonhuman primates.

Although the orientation of an arm in space or the static view of an object may be represented by a population of neurons in complex ways, how these variables change with movement often follows simple linear rules, reflecting the underlying geometric constraints in the physical world. A theoretical analysis is presented for how such constraints affect the average firing rates of sensory and motor neurons during natural movements with low degrees of freedom, such as a limb movement and rigid object motion. When applied to nonrigid reaching arm movements, the linear theory accounts for cosine directional tuning with linear speed modulation, predicts a curl-free spatial distribution of preferred directions, and also explains why the instantaneous motion of the hand can be recovered from the neural population activity. For three-dimensional motion of a rigid object, the theory predicts that, to a first approximation, the response of a sensory neuron should have a preferred translational direction and a preferred rotation axis in space, both with cosine tuning functions modulated multiplicatively by speed and angular speed, respectively. Some known tuning properties of motion-sensitive neurons follow as special cases. Acceleration tuning and nonlinear speed modulation are considered in an extension of the linear theory. This general approach provides a principled method to derive mechanism-insensitive neuronal properties by exploiting the inherently low dimensionality of natural movements.