In this article, a control strategy is proposed to control the energy level and firing modes in a memristive neuron with hybrid ion channel, in which this branch circuit connects a memristor in series with an inductor. Energy and current are shunted from the hybrid ion channel for further saving in the external applied control device. Another memristor connects a constant voltage source for producing memristive current as external excitation and this design generates forcing currents within finite frequency band like realistic stimuli applied to biological neurons. A sub-branch circuit containing a capacitor is intervened into the hybrid ion channel (combining memristor and inductor), and the shunting current is changed when the capacitor parameter in the control branch circuit is tamed following continuous energy shunting from the neural circuit, as a result, the energy level in the neuron is modified to support appropriate firing patterns. In presence of noisy disturbance, coherence resonance is induced and affected by the parameter setting in the sub-branch circuit. Our results provide a feasible strategy for controlling electrical activities in neurons and their equivalent neural circuits, and also offer guidance for further local pacing in neural networks by injecting or shunting energy flow.

Effort-based decision making evaluates rewards relative to the effort required to obtain it, an important process of healthy goal-directed motivation and behavior. Computational models provide mechanistic insights underlying choice behavior and potential alterations in neuropsychiatric disorders, including substance use disorders. We applied computational models to effort-based choice behavior to characterize underlying decision processes and if these mechanisms differ by substance use status. Participants completed the Effort Expenditure for Rewards Task, choosing between low- and high-effort options for monetary rewards varying in magnitude and probability. Participants met criteria for no tobacco use (n = 23), current tobacco use disorder (n = 26), former tobacco use disorder (n = 22), and tobacco and opioid use disorder (n = 29). Computational models from two families, Subjective Value and Reinforcement Learning, were fit and compared. Parameters from the best-fitting model underwent principal components analysis and linear discriminant analysis. Temporal difference reinforcement learning model demonstrated greater model evidence and predictive accuracy, indicating better fit to effort-based choice behavior. Principal components analysis revealed meaningful multivariate distinctions: PC1 differentiated all groups except individuals without tobacco use versus individuals with current tobacco use disorder; PC3 distinguished tobacco and opioid use disorder from all other groups. Linear discriminant analysis demonstrated group separation with 84% classification accuracy. A reinforcement learning framework better explained participants' effort-based choice behavior. Substance use status relates to dynamic behavioral changes (i.e. learning) as measured by the multivariate combination of learning rate, future discounting, and choice temperature.

Parkinson's disease is characterized by pathological beta-band oscillations ([Formula: see text]) arising from dopamine-depletion-induced instability in the basal ganglia-thalamocortical network. Although deep brain stimulation of the subthalamic nucleus is the most effective therapy for advanced Parkinson's disease, the mechanistic relationship between stimulation amplitude and network-state transitions remains poorly delineated, limiting the rational design of adaptive closed-loop protocols. We addressed this gap using a seven-population Wilson-Cowan mean-field model in which the Parkinsonian state was induced by reducing the STN→ GPe coupling weight from 19 to 5 and the DCN→ Th(Vim) cerebellar drive from 25 to 20. Six complementary analyses were applied across a continuous deep brain stimulation amplitude sweep of [Formula: see text]-15 a.u.: time-domain dynamics, Welch power spectral density, steady-state population profiling, Dose-response characterization using three validated metrics, phase-portrait geometry and bifurcation analysis. Three novel Dose-response metrics were introduced and supports: beta-band power suppression [Formula: see text], thalamic relay preservation and STN oscillation amplitude reduction. The Parkinson's disease network produced sustained [Formula: see text] beta oscillations, a multi-harmonic spectral profile and a large-amplitude STN→ GPe limit cycle. Sub-therapeutic stimulation ([Formula: see text]) left pathological dynamics unchanged; intermediate stimulation ([Formula: see text]) partially disrupted the oscillatory cycle; and high-amplitude stimulation ([Formula: see text]) abolished both beta oscillations and thalamic relay function via the GPi inhibitory cascade, constituting a model of functional thalamotomy. A transitional therapeutic window [Formula: see text] was identified in which beta suppression and thalamic preservation coexist, corroborated across all six analytical perspectives. Bifurcation analysis confirmed that reduced STN→ GPe gain is the primary instability mechanism, with cerebellar drive as a modulatory parameter. These findings provide mechanistically rigorous explanations of amplitude-dependent network state changes and offer a quantitative framework for adaptive closed-loop deep brain stimulation design.

How do recurrent neural networks (RNNs) internally represent elapsed time to initiate responses after learned delays? To address this question, we trained RNNs on delayed decision-making tasks with progressively increasing temporal demands, including binary decisions, context-dependent decisions, and perceptual integration. We analyzed trained networks using connectivity statistics, eigenvalue spectra, readout alignment, and low-dimensional population trajectories. Across tasks, networks converged to qualitatively distinct but behaviourally comparable dynamical solutions, including oscillatory and non-oscillatory (ramping/decaying) regimes, consistent with solution degeneracy. Population activity was well approximated by a low-dimensional subspace and distributed across recurrent units rather than localized to individual neurons. Readout alignment was strongly epoch-dependent: as required by the near-zero target output during that epoch, activity evolved largely in the readout-null subspace prior to response generation, and became increasingly aligned with the output dimension near decision time. In sign-symmetric tasks, trained networks preserved exact sign-flip equivariance inherited from architecture and training symmetry. Together, these results show that temporal and decision-related computations can emerge through multiple dynamical regimes, while maintaining structured low-dimensional representations and comparable behavioural performance, mirroring biological principles of degeneracy and functional redundancy.

Neural population activity in sensory cortex is organized on low-dimensional manifolds, but it is unclear why such manifolds should arise and what determines their geometry. We address this sensory representation problem by modeling cortical populations as recurrent circuits driven by low-dimensional, regular sensory dynamics (e.g. motion on a circle, head direction, multi-frequency tones on tori). By combining tools from generalized synchronization and delay-embedding theory, specialized to this quasiperiodic regime, we show that contracting recurrent networks generically develop smooth internal manifolds that embed the sensory dynamics. The dimensional requirement is modest and depends only on the intrinsic dimension [Formula: see text] of the effective sensory manifold, not on the complexity of the external world: a hidden dimension [Formula: see text] generically suffices (e.g. [Formula: see text] for a circle, [Formula: see text] for a two-frequency torus; bounds compatible with Whitney and Takens' embedding theorems). We then prove a prediction-separation result that links representational geometry directly to predictive performance, without assuming knowledge of contraction rates: if the circuit can predict future sensory inputs with small error, then states with different futures must be separated in neural state space, up to a resolution set by the prediction error. The resulting scale-limited embeddings naturally give rise to categorical boundaries, metameric equivalence of distinct stimuli, and discrimination thresholds. Numerical experiments with trained [Formula: see text] recurrent networks driven by head-direction-like and multi-frequency signals recover ring- and torus-shaped hidden manifolds with the expected topology; state separation improves most rapidly near the [Formula: see text] threshold. Training typically pushes the networks beyond the strict contraction regime where the theory guarantees faithful embedding, yet convergence consistent with generalized synchronization and manifold recovery persist, indicating that our conditions are sufficient but not necessary. Together, these results provide a mechanistic account of why low-dimensional sensory manifolds emerge in recurrent circuits and how prediction constrains their resolution, grounded in dynamical systems embedding theory and consistent with empirical findings on cortical population dynamics.

The dynamical behaviour of a population-based rate model with firing adaptation is studied. An excitatory and inhibitory population of neurons is recurrently coupled and a negative feedback term is added to the excitatory population as firing adaptation. In several studies of these models, the UP-DOWN transitions are in focus, which are also exhibited by the investigated model. In this paper we provide a full characterization of equilibrium points with the precise conditions for their existence and stability. Calculations can be performed analytically and explicit formulas can be provided due to the fact that the activation function is a threshold linear function. We use bifurcation analysis to detect significant changes in the phase space. Complete list of bifurcation diagrams is provided with respect to the number of steady states. Oscillatory dynamics of neurobiological relevance are examined through local bifurcation analysis. The study demonstrates that sharp wave-ripple oscillations may emerge in certain regions of the parameter space.

The brain operates across multiple spatial and temporal scales, necessitating computationally efficient models that link micro-scale mechanisms to meso- and macro-scale dynamics. Here, we introduce a novel convolutional neural mass model (CNMM) that computes the meso-scale activity of spatially discretized neural populations ("neural masses") in the rat hippocampal CA3 subregion. The CNMM employs a kernel-based architecture, leveraging first-order Volterra expansions with Laguerre (temporal) and Chebyshev (spatial) basis functions to transform input spike densities from entorhinal cortex (EC), dentate gyrus (DG), and neighboring CA3 masses into output CA3 spike density. The model was trained and validated using data from a biophysically detailed large-scale mechanistic model (LSM) simulating exploratory behavior. The CNMM achieved high predictive accuracy for spike density across 32 neural masses spanning the entire extent of CA3 (mean correlation coefficient [Formula: see text]) and replicated theta and beta oscillations consistent with experimental findings. When extended for forward modeling, the CNMM accurately predicted local field potentials (LFPs) at a single neural mass ([Formula: see text]), demonstrating feasibility of this approach. Kernel analysis revealed topographic gradients in afferent integration, with DG inputs dominating proximally (CA3c) and associational connections distally (CA3a), aligning with anatomical gradients. Compared to the LSM, the CNMM provided a 658-fold speedup in simulation time, 322-fold reduction in memory usage, and 183-fold less disk space for LFP predictions. This framework offers a scalable, efficient approach for meso-scale modeling of neural tissue, bridging detailed simulations with empirical data and laying groundwork for future investigations into both normal and pathological brain function.

Understanding complex neuronal behavior in our brain requires accurate estimation of neuronal models from observed time-series data. In this study, we propose a data-driven sparse modeling method to estimate multi-dimensional latent variables and electrical properties while extracting essential membrane currents from partially observable time series data. First, we derive a nonlinear state space model from a conductance-based neuron model that couples membrane potential and calcium concentration including a set of candidate membrane currents. Then, we derive a sparse modeling-based expectation-maximization (EM) algorithm. In the expectation step, the expectation of the log-likelihood with Laplace prior distribution is evaluated using the posterior distribution of latent states, which is approximated by a sequential Monte Carlo (SMC) method under one-dimensional noisy observations. In the maximization step, the conductances are estimated as zero value for unnecessary currents whereas those are estimated as non-zero value for necessary currents. We show using simulation with conductance-based neuron model that the proposed method can extract the latent nonlinear neuronal dynamics from partially observable data by estimating latent variables and biophysical parameters and extracting only necessary membrane currents.

We propose two experiments for identifying quantum markers in neural data based on quantum variants of well-known equations for neural activity that describe electrical signal propagation on axonal arbors and dendrites. These include (i) testing if power spectra from subthreshold oscillations in neuronal cultures follow the classical Fitzgugh-Nagumo equations or a recently introduced quantum variant of them and (ii) testing if propagation statistics of electrical activity in axons follow the classical diffusive cable equation or a quantum variant of it.

The spindle refractory period refers to the interval following a spindle during which another spindle does not occur. Lengthening of the spindle refractory period (SRPL) is commonly observed in EEG recordings of patients with neuropsychiatric disorders (NPDs) and may contribute to cognitive impairments. Histamine (HA), a key neuromodulator of thalamic oscillations, has been implicated in spindle refractoriness. However, the pathways through which HA influences SRPL remain poorly understood. To address this issue, we extended the thalamic modeling framework to construct an HA-based thalamic neural mass model (HA-TNMM) incorporating HA-related neurophysiological mechanisms within a circuit composed of thalamocortical relay population (TCR) and thalamic reticular nucleus (TRN). In particular, we propose a mathematical expression to characterize the effects of HA on two critical currents: the calcium-activated K[+] current [Formula: see text] blocked by HA, and the anomalous rectifier current [Formula: see text] activated by HA. The HA-TNMM is further formulated by adding [Formula: see text] and [Formula: see text] into Costa model. Subsequently, we investigated the model's capability to elucidate HA's effects on SRPL. Simulation results demonstrated that: (1) A decrease in HA concentration weakens HA-mediated blockade of [Formula: see text], allowing [Formula: see text] to increase; the enhanc [Formula: see text] prolongs afterhyperpolarization and thereby delays the initiation of subsequent TRN bursts, extending the inter-spindle interval and leading to SRPL; (2) An increase in HA concentration enhances [Formula: see text], raising membrane potentials, slowing spindle waning, and thus extending SRPL. Furthermore, our results were validated from a theoretical perspective. These modeling findings provide insights into the mechanisms underlying spindle refractory period modulation and offer a theoretical basis for future experimental and clinical studies.

We present a novel astro-neural-field population model with application to migraine-related cortical spreading depolarization. The model is composed of four spatio-temporal state variables: excitatory and inhibitory membrane potentials, astrocytic potassium uptake recruitment, and extracellular potassium concentration. Extending a previous neural field model, we incorporate activity-dependent astrocytic potassium clearance via a nonlinear term coupled to astrocyte dynamics. The astrocyte transfer function, like its neural counterpart, exhibits three regimes governed by extracellular potassium, capturing its effect on clearance. This yields a more comprehensive framework, better fits experimental data, and provides new insights into the mechanisms of cortical spreading depolarization.

Neural information flow describes the movement of activity between neurons or brain areas. Advances in experimental methods have allowed production of large amounts of observational data related to neuronal activity from the single-neuron to population level. Most current methods for analysing these data are based on pairwise comparison of activity, and fall short of reliably extracting neural information flow network structure. Dynamic Bayesian networks may overcome some of these limitations. Here we evaluate the performance of a range of Bayesian network scoring metrics against the performance of multivariate Granger causality and LASSO regression for their ability to learn the connectivity underlying simulated single-neuron and neuronal population data. We find that discrete dynamic Bayesian networks are the best performing method for single-neuron data, and perform consistently for neural-population data. Continuous dynamic Bayesian networks have a tendency to learn overly dense structures for both data types, but may have utility in scoping studies on single-neuron data. Multivariate Granger causality is the most robust method for learning structure of neural information flow between neural-populations, but performs poorly on single-neuron data. Significance testing within multivariate Granger causality produces variable results between data types. Overall, this work highlights how the analysis of neural information flow can vary depending on the type and structure of underlying data, and promotes discrete dynamic Bayesian networks as a useful and consistent tool for neural information flow analysis.

Altered connectivity in the prefrontal cortex-amygdala circuit in Major Depressive Disorder is associated with abnormal circuit states. Although substantial evidence from neuroimaging studies has demonstrated that changes in functional connectivity within this circuit during depressive states are commonly reported as a key feature, little is known about how these changes may relate to circuit functioning. In this study, we propose a biophysical computational model that incorporates an improved Jansen-Rit neural mass model to construct the circuit. Resting-state functional magnetic resonance imaging is used to calculate the functional connectivity of the circuit and simulate brain signals. The aim is to investigate how abnormalities in functional connectivity may contribute to or be associated with the underlying mechanisms of circuit dysfunction. The numerical simulation results indicate that under normal conditions, the amygdala plays a key regulatory role in this circuit. When the amygdala is strongly activated in the model, it suppresses the ventromedial prefrontal cortex and activates the rostral anterior cingulate cortex, leading to an abnormal circuit state. In a healthy state, the amygdala maintains activation through bottom-up regulation, supporting emotional regulation and network stability. The amygdala plays a key regulatory role in this circuit, and changes in functional connectivity are a potential factor that may contribute to the imbalance between cognitive control and emotional regulation. We also show within the modeling framework that alterations in functional connectivity are associated with an abnormal circuit state, which may be an important mechanism underlying the expression of depressive symptoms. This study combines data and theoretical modeling techniques, providing a computational perspective on the potential pathological mechanisms of depression and suggests potential therapeutic targets.

Chronic stress is associated with persistent alterations in neural circuit function, yet how these changes are expressed across multiple descriptive levels remains unclear. Here, we re-analyzed in vivo GCaMP8s recordings from BLA-DMS and CeA-DMS projection pathways using complementary distributional, dynamical, and computational approaches. Distributional analyses based on Kullback-Leibler (KL) divergence revealed stress-associated changes in the temporal organization of neural activity patterns, particularly following acute aversive perturbations where stressed animals exhibited prolonged deviations from baseline distributions. Dynamical analyses using phenomenological second-order regression models revealed corresponding alterations in recovery-related properties. Following footshock, stress was associated with shifts in principal eigenvalue distributions and reconstructed quasi-potential profiles, whereas learned lever press-reward behaviors exhibited broadly similar local stability despite differences in coefficient structure. Notably, stress-related differences in reconstructed dynamics were detectable during task acquisition even when overt behavioral performance remained comparable between groups. To examine whether these qualitative signatures could arise from simple computational principles, we implemented a minimal artificial neural network (ANN) framework as a hypothesis-generating sufficiency test. Models incorporating asymmetric optimization objectives reproduced selected experimental signatures, whereas symmetric objectives did not. Together, these findings suggest that chronic stress is associated with a reorganization of neural activity patterns across multiple descriptive levels, altering responses to perturbations and producing detectable changes in neural activity organization before overt behavioral divergence emerges.

Cognitive neural circuits must balance the plasticity needed for continual learning with the stability needed to preserve an underlying reasoning framework, called a schema. How circuit learning rules form and protect such schemata from being continually overwritten during learning remains unknown. On a visual boundary detection task, we show that a hierarchical learning algorithm creates an invariant schema circuit whose weights remain fixed following sparse initial training, with additional data serving to refine the upstream representation. In contrast, the end-to-end backpropagation algorithm used to train nearly all current artificial neural networks comprehensively changes its weights throughout training. We show that the hierarchical schema makes an independent mechanistic hypothesis about circuit computation that is consistent with experimental ordering observed in single-neuron measurements in humans. These results suggest that hierarchical learning is sufficient to encode biologically consistent persistent cognitive models within otherwise malleable neural networks.