Related papers: Geometrical Structure of Bifurcations during Spati…
The work reported here aims to address the effects of time-dependent parameters and stochasticity on decision-making in biological systems. We achieve this by extending previous studies that resorted to simple normal forms. Yet, we focus…
Place cells in the rat hippocampus play a key role in creating the animal's internal representation of the world. During active navigation, these cells spike only in discrete locations, together encoding a map of the environment.…
Current practice in parameter space exploration in euclidean space is dominated by randomized sampling or design of experiment methods. The biggest issue with these methods is not keeping track of what part of parameter space has been…
The aim of our work is to study the effect of geometry variation on nucleation times and to address its role in the context of eukaryotic chemotaxis (i.e. the process which allows cells to identify and follow a gradient of chemical…
Human movement prediction is difficult as humans naturally exhibit complex behaviors that can change drastically from one environment to the next. In order to alleviate this issue, we propose a prediction framework that decouples short-term…
We outline a possible theoretical framework for the quantitative modeling of networked embodied cognitive systems. We notice that: 1) information self structuring through sensory-motor coordination does not deterministically occur in Rn…
When choosing between options, we must associate their values with the action needed to select them. We hypothesize that the brain solves this binding problem through neural population subspaces. To test this hypothesis, we examined…
Nonlocal aggregation-diffusion models, when coupled with a spatial map, can capture cognitive and memory-based influences on animal movement and population-level patterns. In this work, we study a one-dimensional…
The functioning of an organ such as the brain emerges from interactions between its constituent parts. Further, this interaction is not immutable in time but rather unfolds in a succession of patterns, thereby allowing the brain to adapt to…
In this paper, we investigate saddle-node to saddle separatrix--loops that we term SNICeroclinic bifurcations. They are generic codimension-two bifurcations involving a heteroclinic loop between one non-hyperbolic and one hyperbolic saddle.…
We present results of numerical experiments for neural networks with stochastic gradient-based optimization with adaptive momentum. This widely applied optimization has proved convergence and practical efficiency, but for long-run training…
Animals use a combination of egocentric navigation driven by the internal integration of environmental cues, interspersed with geocentric course correction and reorientation, often with uncertainty in sensory acquisition of information,…
Robots often have to deal with the challenges of operating in dynamic and sometimes unpredictable environments. Although an occupancy map of the environment is sufficient for navigation of a mobile robot or manipulation tasks with a robotic…
Neural or cortical fields are continuous assemblies of mesoscopic models, also called neural masses, of neural populations that are fundamental in the modeling of macroscopic parts of the brain. Neural fields are described by nonlinear…
For a continuous map on the unit interval or circle, we define the bifurcation set to be the collection of those interval holes whose surviving set is sensitive to arbitrarily small changes of their position. By assuming a global…
The ability to accurately predict the surrounding environment is a foundational principle of intelligence in biological and artificial agents. In recent years, a variety of approaches have been proposed for learning to predict the physical…
Understanding the dynamics of large-scale brain models remains a central challenge due to the inherent complexity of these systems. In this work, we explore the emergence of complex spatiotemporal patterns in a large scale-brain model…
Analysing how neural networks represent data features in their activations can help interpret how they perform tasks. Hence, a long line of work has focused on mathematically characterising the geometry of such "neural representations." In…
A grand challenge in modern neuroscience is to bridge the gap between the detailed mapping of microscale neural circuits and mechanistic understanding of cognitive functions. While extensive knowledge exists about neuronal connectivity and…
Efficient path planning and navigation is critical for animals, robotics, logistics and transportation. We study a model in which spatial navigation problems can rapidly be solved in the brain by parallel mental exploration of alternative…