Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1602.03764

Theoretical connections between mathematical neuronal models corresponding to different expressions of noise

Grégory Dumont·Jacques Henry·Carmen Oana Tarniceriu
View original source ↗Read source document ↗Export metadata ↓

Abstract

Identifying the right tools to express the stochastic aspects of neural activity has proven to be one of the biggest challenges in computational neuroscience. Even if there is no definitive answer to this issue, the most common procedure to express this randomness is the use of stochastic models. In accordance with the origin of variability, the sources of randomness are classified as intrinsic or extrinsic and give rise to distinct mathematical frameworks to track down the dynamics of the cell. While the external variability is generally treated by the use of a Wiener process in models such as the Integrate-and-Fire model, the internal variability is mostly expressed via a random firing process. In this paper, we investigate how those distinct expressions of variability can be related. To do so, we examine the probability density functions to the corresponding stochastic models and investigate in what way they can be mapped one to another via integral transforms. Our theoretical findings offer a new insight view into the particular categories of variability and it confirms that, despite their contrasting nature, the mathematical formalization of internal and external variability are strikingly similar.

Explore related subjects

q-bio.NC

Keep this discovery

BibTeXRIS

Grégory Dumont, Jacques Henry, Carmen Oana Tarniceriu. 2016-02-10. Theoretical connections between mathematical neuronal models corresponding to different expressions of noise. https://arxiv.org/abs/1602.03764

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

KEEP EXPLORING

Related papers

arXiv2026

The Platonic brain bridge hypothesis: human brain networks as an architectural prior for omni models

We propose the Platonic brain bridge hypothesis: omni models, which process video, audio and text jointly like the brain, converge on brain-like representations, and the correspondence is bidirectional. From model to brain, brain-likeness of seven omni models is stable across participants, and our encoding models on their internal hidden states rank first on the Algonauts 2025 out-of-distribution leaderboard. From brain to model, three contributions follow. Brain-MoE gives seven cortical networks one brain-pretrained expert each and raises held-out accuracy in all 15 model-benchmark pairs by 6.42 percentage points on average. Brain-AVQA builds questions from video clips labelled by the most responsive brain network; the real network-to-expert map exceeds shuffled maps in-domain on all three models. Brain-Scope uses sparse autoencoders to localize the correspondence to a small subset whose removal weakens brain prediction in all three bases tested. Human brain networks are therefore a usable architectural prior for omni models.

q-bio.NC↗
arXiv2026

Degeneracy along the sensorimotor hierarchy: motor control within a framework larger than redundancy

Motor control has described the surplus of solutions available to the nervous system as redundancy, a term that names duplication: interchangeable elements, robust to loss but incapable of differential adaptation. Biology has had a second term for twenty-five years. Degeneracy names elements that are not interchangeable and are nonetheless isofunctional with respect to a given output, and it supports adaptability, since non-identical elements necessarily diverge in some context. Circuit neuroscience has relabeled its own results accordingly, while motor control has kept the older vocabulary. Neuromechanical models, by placing a spinal circuit in the loop with a musculoskeletal apparatus, bring the two traditions onto the same class of objects. We restate the Edelman and Tononi distinction for sensorimotor systems and derive an operational requirement: not the existence of multiple solutions, but their divergence in contexts they were not selected for. Three influential studies each meet part of that requirement and none meets all. We then argue that degeneracy and redundancy coexist along the sensorimotor hierarchy in a proportion that varies continuously, and that this proportion is measurable: computing degeneracy twice for the same configuration, once with muscle activation as the output and once with the movement produced, isolates what the musculoskeletal apparatus contributes. Five predictions follow, with the single outcome that would refute the proposal. We set out the adaptations the measurement requires in a nonlinear, non-stationary, closed-loop system, and what changes for motor control once solutions are no longer assumed equivalent: the question shifts from which rule selects a command to what the repertoire of the system still allows.

q-bio.NC↗
arXiv2026

pyAvalanches: A Python Package for Analyzing Spatiotemporal Propagation in Neuronal Avalanches

The analysis of neuronal avalanches offers insights into brain dynamics utilizing the framework of criticality, but the reproducibility and comparability of studies are limited by the use of fragmented, lab-specific scripts. To address this issue, we introduce pyAvalanches, an open-source Python package providing a standardized, end-to-end pipeline for avalanche analysis from electrophysiological recordings (e.g., electroencephalography-EEG). Starting from the detection of neuronal avalanches the package provides their core statistical characterization, including size and duration distributions. Beyond this, the main aim of pyAvalanches is to characterize the spatiotemporal organization of activity propagation during avalanches. To this end, the core innovation of pyAvalanches is the compuation of Avalanche Transition Matrices (ATMs) to map spatiotemporal propagation patterns. Building on this, the package derives network-based metrics from the ATMs, bridging the study of the topology and organization of the underlying dynamical interactions with network neuroscience adopting the framework of neuronal avalanches. The entire workflow is encapsulated in a modular and scikit-learn compatible architecture. We demonstrate the utility of pyAvalanches through an illustrative group-level analysis on a public resting-state EEG dataset, comparing propagation patterns across different clinical populations. By providing a user-friendly, tested, and extensible tool, pyAvalanches facilitates reproducible research, enables the development of novel avalanche-based biomarkers, and makes complex avalanche analysis accessible to a broader scientific community. The package is fully documented and distributed via the Python Package Index (PyPI).

q-bio.NC↗