Retinothalamic and thalamocortical synapses are efficient in the sense that each synapse conveys as many bits per Joule as possible, but efficiency falls rapidly if synaptic conductance deviates from its natural value Harris et al. (2015, 2019). However, the manner in which efficiency falls with conductance remains unexplained. Recently, Malkin et al. (2026) showed that synaptic noise is minimised given the available energy, consistent with a minimal energy boundary. Here, this boundary is expressed in terms of Shannon’s information theory Shannon and Weaver (1949), which yields a model that predicts the efficiency values observed in Harris et al. (2015) across a 120-fold change in synaptic conductance ( R^2= 0.769 , p<0.001 ). This model also predicts that, for a synapse at its natural conductance, each pre-synaptic spike provides an average of 3.58 bits to its post-synaptic neuron, which is consistent with physiological values. Crucially, given the biophysical constraints that, a) synaptic efficiency is maximised at the natural conductance, and, b) synaptic noise variance is minimised in accordance with the minimal energy boundary, the proposed model contains no free parameters, so it is predictive rather than descriptive. The results presented here are consistent with the general principle that CNS neurons maximise information efficiency (bits per Joule), rather than information rate (bits per second).
The neural correlates of consciousness have been characterized primarily through temporal EEG features, while the spatial dynamics of cortical activity across consciousness states remain poorly understood. Here, we analyze the spatial mode structure of the Robinson corticothalamic neural field model (CTM) across five consciousness states: healthy wakefulness, emergence from minimally conscious state (eMCS), minimally conscious state (MCS), deep sleep (N3), and unresponsive wakefulness syndrome (UWS). We compute the noise-amplified spatial spectrum, which quantifies how the CTM filters spatiotemporal noise across spatial wavenumbers. We find systematic spectral narrowing with decreasing consciousness: the spectral centroid decreases by 48
Finite-dimensional Koopman MPC for nonlinear controlled systems requires care when a learned LTI lift is used as a finite-horizon surrogate. We recast the memristive Hindmarsh–Rose benchmark through an input-exact Lie-lifting certificate. Because the stimulation vector field is g=e_1 , the augmented polynomial dictionary is closed under ℒ_g ; the pure stimulation flow is represented exactly by a nilpotent matrix exponential. Moreover, the drift–input commutator cascade terminates after three input commutators, so the controlled Koopman error can be written as a finite shifted-drift defect rather than an uncontrolled truncation heuristic. The resulting theory supports a bilinear, stimulation-aligned surrogate and places the affine EDMDc-MPC implementation in a conservative finite-horizon deterministic setting. Paired comparisons with Hermite and SINDy polynomial baselines, controlled-pulse prediction, measurement-noise stress tests, and affine-versus-bilinear Lie-MPC evaluations show that the bilinear Lie model gives the lowest controlled-prediction error, closed-loop RMSE, and control energy in the deterministic benchmark.
It is not easy to measure the amount of information within an object that is capable of leading to aesthetics-based feelings in a viewer, especially because of a subjective variability of human perception. Cybernetic aesthetics, for its part, might provide a rational way for understanding such a human phenomenon at least in special cases. Now, cyclic human movements — not only gait cycles, but also swimming strokes and tennis forehand strokes — were found, with their given internal sub-phases, to be characterized, from a temporal point of view, by the existence of coordinatively mechanized and self-similar harmonic fractal patterns. Such harmonic patterns were specifically found to be symmetrized in time so as to compose a generalized Fibonacci sequence and then implicitly dictated by the golden ratio, when it occurs as the ratio of the resulting sub-phases durations. The lowest amount of information for the movement temporal design (Shannon entropy minimization, SEM) makes one sub-phase duration of the movement temporally generate an entire sequence of sub-phase durations of the same movement. However, different spatial profiles can correspond to identical temporal partitions, suggesting the presence of an additional optimization principle that acts within the spatial domain. The original contribution of this paper consists of unveiling what is beyond the aforementioned temporal characterization, revealing the existence of a possible cyclic movement attractor, named golden faux sinus, which is based on a spatial smooth sewing of zero-jerk portions. This might suggest how the neuromuscular system organizes complex repetitive movements and how information processing is exploited into a sub-movement generation architecture. The resulting hidden patterns are the ones that might be caught by a viewer, who is able to concentrate separately on different categories of meaning. Experiments concerning young healthy walking subjects, as well as ATP-WTA top-level tennis players during some of the latest strongest moments of their career, illustrate the effectiveness of the presented derivations.
Most studies of motor learning focus on adaptation, which can be described as recalibration within an existing controller following changes in dynamics, kinematics, or sensory feedback. In these paradigms, control variables, coordinate representations, and feedback organization are treated as available a priori, and learning as parameter tuning within a specified controller architecture. However, de novo motor-learning tasks require learners to establish novel relationships between intention, sensory feedback, and action, rather than merely recalibrating a familiar control organization. These tasks often show slow or variable acquisition, selective and task-dependent generalization, strong context dependence, and dissociations between learning rate and final performance. Such features are difficult to explain solely as parameter tuning within a fixed controller architecture. Here we propose that de novo motor learning is better understood as controller synthesis, rather than only as parameter adaptation. On this view, learning involves forming and stabilizing content-addressable, plant-state-addressed controller memories: local sensorimotor control organizations that specify where a controller applies, which task-relevant signals are selected and routed, how state and progress are estimated, how control is computed, how internal control signals map onto action, and when and how the controller is expressed. This framework interprets slow or variable acquisition, structured generalization, context dependence, and learning-rate/outcome dissociations as possible consequences of controller-memory formation, stabilization, retrieval, and expression, rather than of slow parameter convergence within an established controller. It also suggests tests for distinguishing controller synthesis from fixed-structure alternatives based on adaptation, contextual inference, or policy learning.
Quantifying consciousness from brain activity remains a major challenge in neuroscience and clinical practice. Many existing EEG measures focus on a single feature of neural activity, such as complexity, synchrony, or spectral structure, but no single feature appears sufficient across different brain states. We introduce a composite dynamical framework that combines three complementary properties of brain activity, i.e., scale-free temporal organisation, cross-frequency organisation, and metastable flexibility in large-scale synchronisation. These components are normalised and combined into a single index designed to capture organised dynamical complexity rather than raw signal complexity alone. We test the framework in both synthetic and empirical settings. In a generative model of nine EEG-like brain states, including wakefulness, dreaming, anaesthesia, non-conscious states, and seizure states, the index separates the synthetic conscious and non-conscious classes without overlap and remains stable across ablation, sensitivity, and Monte Carlo analyses. We then apply the framework to two-channel Sleep-EDF recordings from 30 healthy adults, where it provides a proof-of-principle subject-level separation of wakefulness from N2 and REM sleep. The framework is dynamical-systems-inspired and is not committed to any single theory of consciousness, making it compatible with a range of theoretical perspectives. With further validation, the framework may be applicable across multichannel brain recordings, including anaesthesia, disorders of consciousness, and basic consciousness-research settings.
The previously proposed Neural Mode (J. Kanev, A. Koutsou, C. Christodoulou, K. Obermayer; 2016; Neural Computation, 28(10):2091-2128) quantifies to what extent spiking neurons use temporal integration or coincidence detection to calculate their output from their input. While the Neural Mode is easy to measure, parameterising a neuron model to show a certain level of coincidence detection or integration is not straightforward. We propose a new spiking neuron model – the Difference Neuron – that integrates or detects coincidences according to a predefined value of the Neural Mode. The Difference Neuron is a simple model without hidden states that depend on infinite input. It receives one or several input spike trains, and it can be configured to detect simple coincidences, gaps, or more complex patterns. It can exhibit spike bursting, and it covers areas of mathematical operation a biological neuron does not - it can spike without stimulus, it can operate purely on inhibition, and it can show inhibition and coincidence detection combinations that are unavailable to other neuron models. Sparsely connected networks of Difference Neurons can show different levels of regular and irregular synchronisation, depending on the Neural Mode of their neurons. We explore several single-neuron examples and investigate the neuron’s behaviour. Because this new model does not include differential equations describing membrane potentials or ion concentrations, but computes its output spike times from simple time comparisons, we believe the Difference Neuron will simplify investigations into dynamics of spiking neurons and networks, and into spike patterns and the mechanisms of the neural code.
An array of inertial phasor units coupled through a common substrate can exhibit stable collective phase patterns. This paper explores this phenomenon by investigating a closed array–interface–substrate feedback structure. Each array unit has a device-level angular coordinate θ _n and produces a phasor output e^iθ _n . The interface forms products and combinations of these phasor outputs, producing harmonics indexed by integer mode vectors. The substrate processes these harmonic components and returns a modulatory signal to the array. In the case studied here, the returned feedback has gradient form and is generated by a harmonic potential V(θ ) . This structure leads to a geometric theory of harmonic memory. Memories appear as stable phase-locked periodic solutions, or memory loops, selected by the resonant harmonic structure of V . Memory recall occurs when the drive parameters, interpreted as attentional control variables, tune the system toward a harmonic channel: resonance selects a latent coherent loop, and the closed dynamics relax toward recurrent activity in the array.
Despite the growing prevalence of network models in biological and medical research, the philosophical foundations of these constructs remain elusive and insufficiently examined. Building on data-driven insights in systems biology and teleological models of integrative physiology, we have criticised agentless theory, relational ontologies, and cybernetic perspectives in biological contexts. We have posited the necessity for a philosophical advocacy of a holistic approach to biology alongside a relational epistemology. A foundational issue in network models in biology and physiology is recognising the network as the predominant meme of contemporary society, which has permeated all aspects of human life and has been cultivated within biology and physiology through modern theoretical constructs and practical applications. By discussing minimal cognition, tinkering, and stigmergy, we argued for a philosophical advocacy of the person as a relational cybernetic organism. Philosophical arguments concerning graph and relational models in biology can be resolved by embracing epistemic humility.
Intelligent behavior across motor control, speech production, learning, and social cognition operates under uncertainty: sensory feedback is noisy and delayed, actions are imprecise, and observable outcomes often have ambiguous causes. When multiple latent states generate identical or sufficiently similar observations, regulation, learning, and evaluation based on behavior alone become underdetermined. We argue that inference over latent state is therefore a feasibility condition for cognition under partial observability, rather than merely a modeling convenience. Observable signals—movements, sensory inputs, speech outputs, and social actions—should be understood as noisy evidence about hidden causes, including motor state, articulatory configuration, task context, and intentions. This perspective suggests that separate psychological literatures share a common control-theoretic structure: regulation under noise, delay, ambiguity, and partial observability. It also helps explain why diverse domains exhibit robustness, tolerance of variability, context sensitivity, and structured credit assignment. These properties arise from regulation of inferred, task-relevant state, rather than precise control of observable behavior. The account is not proposed as a replacement for belief-state, internal-model, predictive-coding, or active-inference approaches, but as a cross-domain feasibility argument: latent-state representations support control, learning, and evaluation only when task-relevant hidden distinctions are detectable from observations and stabilizable or actionable. Cognition, from this view, depends on latent state estimates that render behavior, learning, and evaluation well-defined under uncertainty.
Recently a method has been put forward to connect the measures of spontaneous neuronal activity and the measures of the average single-neuron response to stimuli via fluctuation-response relations (FRRs) for some integrate-and-fire (IF) type neuron models. In this work we expand this method to populations of neurons, relating their spontaneous correlation and linear-response statistics. To this end, we analyze the simple case of uncoupled cells modeled by IF neurons (first stage of processing) which receive common stochastic input and project their output spike trains onto a readout neuron (second stage of processing). We derive and verify FRRs connecting the single neuron response to cross-correlations among neurons and the response of the full system to cross-stage correlations. Furthermore, we utilize these FRRs to derive approximations of all cross-stage cross-spectra for a relevant model of a second-stage cell, the partial synchronous output (PSO). We conclude with a discussion of how our results can be expanded to more involved network settings and neuron models.
The publication of Mainen and Sejnowski’s 1995 seminal paper strongly renewed interest in how spike timing contributes to the neural code. In the 3 decades since then, considerable experimental and theoretical research has investigated the timescales at which spike timing contributes to the neural code. Here we review theoretical and experimental research of the last 30 years aimed at defining conceptually and measuring operationally these timescales. By a critical review of the literature, we individuate six broad classes of timescales that have been conceptualized and operationalized: the maximal temporal precision of spiking that a neuron can achieve, the encoding time window (the time window containing the information-bearing spike times), the encoding timescale (the coarsest time resolution for measuring spikes without losing information), the maximal discrimination precision timescale (the smallest spike time difference that can be discriminated behaviorally), the encoding-readout intersection timescale (the maximal timing precision at which stimulus information encoded in neural activity is also actually read out to inform behavior), and the information consistency timescale (measuring the stability of information encoding over time). Together, this work has revealed short and long timescales that influence information coding and affect behavior. Short encoding timescales, from milliseconds to tens of milliseconds, are useful for sensory information encoding and perception. Long consistency timescales, ranging from hundreds of milliseconds to seconds, are useful for accumulating evidence and stabilizing decisions.
The reconstruction of complex networks from time series data has become a common practice in neuroscience and dynamical systems, particularly using synchronization-based measures such as phase locking value (PLV) or correlation. However, the validity of such reconstructions-especially the assumption that synchronization implies direct coupling-remains questionable. In this work, we critically investigate the relationship between structural connectivity and functional synchronization in networks of coupled FitzHugh-Nagumo (FHN) neurons. We generate synthetic networks with known topologies (regular, small-world, and scale-free) and compute pairwise synchronization from the resulting time series. A functional network is then reconstructed based on synchronization strength, and its adjacency matrix is compared with the original structural network using the Root Mean Square Error (RMSE). Our results demonstrate that high synchronization between nodes does not necessarily indicate a direct structural link, and conversely, structurally coupled nodes may remain desynchronized. These findings challenge the reliability of synchronization-based network inference methods and call for caution in interpreting functional connectivity as structural connectivity, particularly in brain network studies.
We propose a novel computational model incorporating simplified representations of the basal ganglia, cortex, and thalamus (SGGCT network), and systematically investigate the regulatory and control mechanisms underlying typical absence seizures in the cortex under memristive electromagnetic induction. Spike-and-wave discharges (SWDs, 2-4 Hz), a hallmark of absence epilepsy, are successfully reproduced in the SGGCT model by modulating the coupling strengths of two excitatory output projections to the thalamic specific relay nuclei (SRN). Our findings highlight the critical role of both the direct glutamatergic cortico-pallidal and cortico-nigral pathways in seizure regulation, acting through distinct inhibitory routes: the globus pallidus interna (GPi)-SRN pathway and the GPi-thalamic reticular nucleus (TRN) pathway, respectively. The cortex emerges as a promising target for electrical stimulation to suppress SWDs. We observe that applying memristive electromagnetic induction to the cortex significantly reduces the parameter space conducive to SWDs generation. Furthermore, electromagnetic induction enhances the ability of basal ganglia pathways to inhibit SWDs. Specifically, electromagnetic induction can transform previously unsuppressible SWDs regimes into suppressible ones. It also alters the operational mode of basal ganglia pathways in controlling seizure dynamics. Notably, the suppression efficacy can be optimized by tuning the memristor's control parameters. These results provide computational evidence supporting the potential of electromagnetic induction as a neuromodulatory strategy, which might offer testable hypotheses for future clinical interventions in epilepsy treatment.
We propose Waves as Space-Time (WST) as a conceptual framework for understanding how the brain may utilize subthreshold travelling waves of the membrane potential to flexibly link spatial and temporal dimensions of neural activity. Rather than presenting a complete biological model, WST is intended to serve as a simplified lens for investigating how wave dynamics can enrich neural coding. The core proposition is that subthreshold membrane potential oscillations constitute a substrate capable of transforming as well as transmitting neural activity, enabling temporal spike patterns to be recast as spatially differentiated signatures and spatial patterns to be unfolded into temporally structured sequences. This perspective highlights how such bidirectional transformations offer the brain a versatile encoding strategy that can support functions such as memory, propagation, and dynamic reconfiguration of information. By considering WST travelling waves as a powerful mechanism for neural computation, it encourages further theoretical, computational and experimental work on their potential role in complex cognitive processes.
Proprioception is key to all behaviours that involve the control of force, posture or movement. Computationally, many proprioceptive afferents share three features: First, their strictly local encoding of stimulus magnitudes causes range fractionation in sensory arrays. As a result, encoding of large joint angle ranges requires convergence of afferent information onto first-order interneurons. Second, their phasic-tonic response properties lead to fractional encoding of the fundamental sensory magnitude and its derivatives (e.g., joint angle and angular velocity). Third, the distribution of disjunct sensory arrays across the body implies that complex movements involve information from multiple joints or limbs. The present study proposes a multi-layer spiking neural network for distributed computation of whole-body posture and movement. The first part of the study models strictly local, phasic-tonic encoding of joint angle by proprioceptive hair field afferents by use of Adaptive Exponential Integrate-and-Fire neurons. Fractionally encoded afferent information about single-joint posture and movement converges on two types of first-order interneurons, tuned to encode either joint angle or velocity across the entire working range with high accuracy. In velocity-encoding interneurons, spike rate increases linearly with angular velocity. The companion paper exploits this distributed position/velocity encoding in second- and third-order interneurons, using combinations of two or three position/velocity inputs from disjunct arrays. The encoding properties of all interneuron layers are evaluated with experimental data on whole-body kinematics of unrestrained stick insect locomotion, comprising concurrent joint angle time courses of 6× 3 leg joints. The hierarchical model allows increasingly complex encoding of posture and movement, from angular velocity of a single joint, to movement cycle phases of an entire limb, to parameters of overall body posture.
Since the advent of widely accessible AI tools, AI technology has been in high demand by businesses, academic researchers and individuals. Technology companies are building AI infrastructure at a rapid pace, and these facilities consume vast and growing resources, particularly electricity and water, with significant real and projected climate impacts. There is a need for new research initiatives to support long time horizon efforts to develop energy efficient computing capabilities to support the continued growth of AI infrastructure in a sustainable fashion. Such efficiency is required at both the hardware and software levels. Where can industry turn for examples of ultra-low power, energy efficient computing? We argue here that neurobiological principles offer rich and under-exploited sources of inspiration for energy efficient NeuroAI, and that new partnerships between industry and academia should be developed in this direction.
We propose a quality measure for spatio-temporal spike patterns (STPs) in multiple-neuron recordings. In such recordings, repeating STPs or pattern repetitions (PRs) are often found, with many of these generated by chance. To rule those out, statistical tests have been developed to discriminate the unlikely from the more likely PRs. This statistical problem is complicated by the fact that there are several obvious quality criteria for a PR, such as the size (the number of spikes) of the pattern and the number of its occurrences. Here, we propose a canonical way of combining several criteria (which we collect in the so-called signature of the pattern) into a single quality measure, based on the ’unlikeliness’ of the pattern. This measure is defined mathematically, and a formula for its computation is derived for stationary spike trains. It can be used to compare PRs. Since spike trains are not stationary in practice, we discuss, for two experimental data sets, how well the stationary formula correlates with the defined quality measure as determined from simulations. Sometimes the calculated values are far off, but one can still use the stationary formula or also some simpler, related formulas as ’proxies’ for the quality, to compare PRs and also for statistical tests that avoid the multiple testing problem incurred by using several quality criteria. Based on our results, we propose a few test statistics, i.e., random variables on the space of multi-unit spike trains with an appropriate null-hypothesis distribution, to evaluate STPs with less computational and sampling efforts.
In the last century, most sensorimotor studies of cortical neurons relied on average firing rates. Rate coding is efficient for fast sensorimotor processing that occurs within a few seconds. Much less is known about the neural mechanisms underlying long-term working memory with a time scale of hours (Ericsson and Kintsch in Psychol Rev 102(2):211, 1995). Cognitive states may not have sensory or motor correlates. For example, you can sit in a quiet room making plan without moving or sensory processing. You can also make plans while out walking. This suggests that the neural substrate for cognitive states neither depends on nor interferes with ongoing sensorimotor brain activity. In this perspective, I make the case for a possible second tier of neural activity that coexists with the well-established sensorimotor tier. The prominent physiological feature of the second tier is coordinated spike timing activity. The interplay of data supporting this hypothesis involves three puzzling yet highly intriguing experimental observations, without any obvious indication that they might actually represent different aspects of a single functional organization. First, consider the precision of spiking in individual neurons. The discovery of millisecond-precision spike initiation in cortical neurons was unexpected (Mainen and Sejnowski in Science 268:1503-1506, 1995). Even more striking was the precision of spiking in vivo, in response to rapidly fluctuating sensory inputs. Second, high temporal resolution can also mediate spike timing-dependent plasticity (STDP) by controlling the relative timing of presynaptic and postsynaptic spikes at the millisecond scale. Third, we observe waves across many frequency bands traveling across the cortex. Strikingly, their timing is highly precise. Gamma waves, for example, which are triggered by attention, can plausibly trigger STDP that lasts for hours in cortical neurons. This temporary cortical network, ostensibly a second tier of functionality, rides astride the long-term sensorimotor network and could support cognitive processing and long-term working memory.
