Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2111.10719

Mathematical representation of the structure of neuron-glia networks

Marco Peña-Garcia·Francesco Peña-Garcia·Nelson Castro·Walter Cabrera-Febola
View original source ↗Read source document ↗Export metadata ↓

Abstract

Network representations of the nervous system have been useful for the understanding of brain phenomena such as perception, motor coordination, and memory. Although brains are composed of both neurons and glial cells, neuron-glial networks have been little studied so far. Given the emergent role of glial cells in information transmission in the brain, we developed a mathematical representation for neuron-glial networks ($Υ$-graph). We also defined the concepts of isomorphisms, unnested form (multidigraph) and matrix equation for $Υ$-graphs. Although we found several network motives where the isomorphism between unnested forms does not guarantees the isomorphism between their respective $Υ$-graphs, we found that if the matrix equations satisfy some conditions, the unnested forms isomorphism guarantees the isomorphism between $Υ$-graphs. Finally, we introduced a novel approach to modeling the network shape. Our work presents a mathematical framework for working with neuron-glia networks.

Explore related subjects

q-bio.NC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Marco Peña-Garcia, Francesco Peña-Garcia, Nelson Castro, Walter Cabrera-Febola. 2024-11-12. Mathematical representation of the structure of neuron-glia networks. https://arxiv.org/abs/2111.10719

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Improving the adaptive and continuous learning capabilities of artificial neural networks: Lessons from multi-neuromodulatory dynamics

Continuous adaptive learning, the ability to adapt to the environment and keep improving performance, is a hallmark of natural intelligence. Biological organisms excel in acquiring, transferring, and retaining knowledge while adapting to volatile environments, making them a source of inspiration for artificial neural networks (ANNs). This study explores how neuromodulation, a building block of learning in biological systems, can help address catastrophic forgetting and enhance the robustness of ANNs in continual learning. Driven by neuromodulators including dopamine (DA), acetylcholine (ACh), serotonin (5-HT) and noradrenaline (NA), neuromodulatory processes in the brain operate at multiple scales, facilitating dynamic responses to environmental changes through mechanisms ranging from local synaptic plasticity to global network-wide adaptability. Importantly, the relationship between neuromodulators and their interplay in modulating sensory and cognitive processes is more complex than previously expected, demonstrating a "many-to-many" neuromodulator-to-task mapping. To inspire neuromodulation-aware learning rules, we highlight (i) how multi-neuromodulatory interactions enrich single-neuromodulator-driven learning, (ii) the impact of neuromodulators across multiple spatio-temporal scales, and correspondingly, (iii) strategies for approximating and integrating neuromodulated learning processes in ANNs, and (iv) an architectural-general formulation of multi-neuromodulatory dynamics. We also present a conceptual study to showcase how neuromodulation-inspired mechanisms, such as DA-driven reward processing and NA-based cognitive flexibility, can enhance ANN performance in a Go/No-Go task. Though multi-scale neuromodulation, we aim to bridge the gap between biological and artificial learning, paving the way for ANNs with greater flexibility, robustness, and adaptability.

q-bio.NC↗
arXiv2026

Axonal delay dispersion decides whether a neuron detects an event or a sequence, and predicts cortical column diameter

Cortical neurons fire sparsely -- often fewer than one spike per sensory window -- making rate coding insufficient and temporal coding a necessity. That conduction delays convert firing order into synchrony is long established. What governs which class of temporal feature a neuron detects -- one volley of coincident input, or two in a particular order -- has not been examined. We propose a delay-signature framework in which the axonal conduction delays converging on a dendritic branch constitute a physical key: only input sequences whose spike-time differences the delays compensate arrive synchronously, and coincidence detection, via calcium plateau thresholds, converts that synchrony into an all-or-none output. In simulations of an integrator-neuron model we report three results. First, a single physical scalar -- the dispersion of the delay set -- moves a population from event detection to order-selective sequence detection. The transition is emergent under random delays and connectivity: at narrow dispersion sequence detectors do not exist, and the dispersion at which they overtake event detectors tracks the inter-event interval with a slope statistically indistinguishable from one. This maps a computational distinction onto the anatomical one between myelinated and unmyelinated projections, making myelination a switch on what a neuron computes, not only a regulator of speed. Second, the same dispersion sets the code's limits: it bounds the longest codable interval and fixes an absolute timing tolerance of about a millisecond, with slowing better tolerated than speeding. Third, that millisecond window and horizontal conduction velocity together predict cortical column diameter, and the two areas with direct measurements fall where the relation puts them. One anatomically measurable parameter thus sets what a neuron detects and the limits of what it can represent.

q-bio.NC↗
arXiv2026

A Roadmap for MEG Foundation Models

Foundation models are beginning to reshape brain-signal analysis by moving the field beyond task-specific decoding pipelines toward reusable models pretrained on broad neural datasets. Magnetoencephalography (MEG) is a compelling but still underdeveloped target for this shift: it captures human cortical dynamics at millisecond resolution while offering stronger spatial interpretability than EEG, making it especially valuable for source-resolved studies of perception, language, cognition, and clinical brain function. Yet MEG foundation models remain at an early stage, with only a small number of MEG-specific and MEG-inclusive multi-modal models, modest pretraining corpora, and emerging but still limited benchmarks. This perspective lays down the basic concepts needed to understand MEG foundation models and provides a didactic overview of the field's key design choices, including tokenization, sensor- versus source-space representations, sensor-geometry encoding, backbone architectures, self-supervised objectives, and pretraining data. We then offer a roadmap for future development, organized around native MEG pretraining, adaptation of EEG foundation models, transfer from generic time-series models, and multi-modal integration with EEG, fMRI, MRI, behaviour, and stimulus features. We highlight the need for coordinated infrastructure, including diverse and reusable MEG datasets, rigorous evaluation across subjects, sites, tasks, and clinical settings, and responsible data-sharing practices that address consent, privacy, access, and governance.

q-bio.NC↗