Differential Equations ePosters

Reconciling theoretical models with experimental data is a major challenge in neuroscience. We investigate how neurons that exhibit disorderly properties individually can produce orderly collective dynamics. Focusing on continuous-attractor networks, which model representations of continuous variables such as head…

Mean-field models of neuronal populations in the brain have proven extremely useful to understand network dynamics and response to stimuli, but these models generally lack a faithful description of the fluctuations in the biologically relevant case of finite network size and connection probabilities $p<1$ (non-full…

Animals constantly decide how to allocate mental resources to thrive in their environments. Managing learning is a key challenge, and recent experiments show that animals often incur attentional costs for the potential of greater future rewards, or disengage when a task appears unlearnable, exhibiting nuanced…

Interactions between spiking units grouped in distinct excitatory (E) and inhibitory (I) populations can result in a complex dynamical landscape. Part of this complexity, namely dynamics that depend on undelayed connectivities and external inputs, is retained by a simplified model, the threshold-linear network (TLN),…

From the periodic spiking of single neurons to brain rhythms, oscillations are a ubiquitous neural phenomenon. Phase reduction is a powerful way of analysing deterministic systems exhibiting such oscillatory behavior: the N-dimensional state of the system is encoded into a one dimensional phase variable via projection…

Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for arbitrarily long time intervals. Unfortunately, because continuous attractors are not structurally stable, they suffer from severe structural instability in general---they are destroyed by…

Interneurons, ubiquitous in the central nervous system, form networks connected through both inhibitory chemical synapses and gap junctions. These networks are essential for regulating neuronal activity notably by regulating temporally patterned dynamic states. We aim to understand the mechanisms that allow for…

The interplay of the calcium concentration and the anatomical structure at the presynaptic zone of presynaptic boutons is an important challenge of the relationship of form and function in (computational) neuroscience. A simple model system to study such basic effects is the neuromuscular junction of the Drosophila…

Neural mass models (NMM) seek to unveil the fundamental principles governing macroscopic neural activity, drawing insights from the brain's intricate and multi-scale structure. The advent of an exact mean-field theory for networks of quadratic integrate-and-fire (QIF) neurons represents a significant leap forward in…

Understanding the mechanisms regulating Ca2+ concentrations in the presynapse is crucial for synaptic function. The endoplasmic reticulum (ER) acts as a finite calcium store and can modulate calcium signals involved in presynaptic neurotransmitter release. While computational studies have shed light on the…

Slow brain rhythms, observed during slow-wave sleep or seizures, often coincide with oscillations in extracellular potassium levels. These rhythms have a lower frequency compared to a typical neuron’s tonic firing. Mechanisms organizing these rhythms are believed to rely on synaptic interactions within the network or…

Memory and learning are significantly influenced by long-term changes in synaptic strength, though the exact molecular mechanisms remain unclear. The postsynaptic density (PSD) is a critical component for storing and organizing synaptic long-term changes. The PSD itself is organized into complex nano-clusters, which…

Continual learning involves a network adapting to new data while retaining previously learned information. In Artificial Neural Networks , this process faces the challenge of catastrophic forgetting, where updating parameters with new data causes an exponential decline in accuracy over time for previously learned…

The ability of a brain or a neural network to efficiently learn depends crucially on both the task structure and the learning rule. Previous works have analyzed the dynamical equations describing learning in the relatively simplified context of the perceptron under assumptions of a student-teacher framework or a…

In neuroscience, ordinary differential equations (ODEs) are widely used to simulate the dynamics of neural systems, but identifying parameters that explain experimental measurements is challenging. In particular, while these models are differentiable and would allow for gradient-based parameter optimization, the…

Automated voltage-clamp recordings from 40 voltage-gated potassium (Kv) channels [1] revealed the inherent kinetic heterogeneity of some Kv types expressed in the brain (e.g. Kv1.3). A model capable of capturing the kinetic Kv heterogeneity requires both fixed model features shared between cells, and the ability to…

A long-standing premise in theoretical neuroscience holds that the complex interactions between neurons or, at a different systems level, between networks in the nervous system can be expressed in terms of an underlying system of nonlinear dynamics. A classical approach has been dynamical systems theory, whereby…

In order to analyse complex networks in the cerebral cortex, different approaches are used in computational neuroscience: microscopic network models that consider every single neuron in simulations aiming for a realistic biological description as well as heuristic firing rate or neural-mass models which deliver a…

A model for NMDA-receptor-mediated synaptic currents generating persistent activity proposed by Wang and Brunel [1–3] has been widely adopted in computational neuroscience, both for spiking-neuron and mean-field models [2, 4]. The model describes NMDA synaptic dynamics by a phenomenological two-dimensional nonlinear…

Unsupervised segmentation of behavior and neural activity into simpler alternating states is providing unprecedented insights onto the neural underpinnings of decision-making. Recurrent Switching Linear Dynamical Systems (rSLDS) models use observations or continuous latent activity to guide the switching in states,…

An emerging perspective in neuroscience connects neural dynamics, or the rules that govern how neural population activity develops over time, to functional computations performed by the brain [1]. Unfortunately, neural dynamics cannot be observed directly and must instead be inferred from neural recordings. One…

A common approach to analyzing spike train data in stimulus-response experiments is to estimate spike rates relative to the stimulus onset. These experiments typically involve collecting measurements from the same subject across several trials and sessions, and performing the same experiment across multiple subjects.…

In order to navigate the world in an efficient manner, the brain seamlessly integrates signals received across multiple sensory modalities (Butler et al., 2010, 2011, 2015). A number of mathematical models have been used to investigate unisensory decision and reaction tasks, but to date very few have been extended to…

Olfactory Receptor Neurons (ORNs) in insects are tightly packed into sensory hairs (sensilla), where they are electrically coupled. This organization is highly stereotyped and genetically determined. Electrical (`ephaptic') coupling between neurons within the same hair results in strong lateral inhibition, posing…