Mathematical Biology ePosters

Imagine predicting the precise responses to arbitrary sensory stimuli for a neuron probed deeply within a brain. We developed a robust characterization technique called spike-triggered descent (STD) which optimally recovers n-order kernels for the very general cumulative spike response model (CSRM). This works by…

A line or a ring attractor stores active memory of an analog quantity that outlasts a transient stimulus. Such continuous attractor states can be realized by a recurrent neural network, when the connection weights are finely tuned. However, a continuum of attractor states is vulnerable to parameter variations,…

A large part of mammalian brains is dedicated to sensory processing. Sensory receptors extract distinct but partly correlated features of the environment that vary at different timescales, and then transmit them through subcortical structures and a succession of recurrently connected cortical areas. A general theory…

Continuous attractors offer a unique class of dynamical systems solutions for storing continuous-valued variables in recurrent neural states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability in general---they are destroyed by most infinitesimal changes…

Activity-dependent structural plasticity plays a pivotal role in the self-organization of neuronal networks. Emerging activity continuously feeds back into the growth process, regulating connectivity and activity homeostatically towards an optimal functional dynamic range. Transferred into cell culture, neurons follow…

Most mammalian species present topological maps of preference for the ori- entation of edges in their early visual cortex. However, despite the evidence that evolution has favoured topological map organisation in most species, a clear explanation for the functional role of such maps is lacking. Traditional approaches…

Advancements in machine learning have drastically improved our ability to fit biophysical models of neural systems. We present here a fully-differentiable, biophysical model of the mouse retina that is primed for gradient-based optimization. Our model is based on the Jaxley software library (Deistler et al. 2024,…

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),…

Neural activity in the cortex exhibits a wide range of timescales, allowing animals to respond to rapidly changing sensory stimuli while maintaining information in working memory. The timescales of neural activity are not only affected by bottom-up sensory inputs, but also by top-down inputs originating from…

The hippocampus plays a central role in memory processing. In order to avoid deleterious interference between stored and ongoing experience, theoretical considerations require a separation between phases of memory encoding and recall within the same neural circuit, putatively controlled by hippocampal theta…

Synfire chains have been postulated as a model for stable propagation of synchronous spikes through the cortical networks [1,2,3]. Synfire-chain-like activity can also be found in spiking artificial neural networks trained for a classification task [4]. Understanding the mechanism for generating such activity would…

Increasing the strength of synaptic connections (synaptic upscaling) within networks of randomly connected neurons transitions the internal dynamics from stationary to a chaotic regime [1, 2]. Synaptic upscaling in neural networks improves learning speed, accuracy, and robustness [3] and enhances the dimensionality of…

Neuronal tuning changes over time, even in the absence of obvious signs of learning or changes in behaviour. This representational drift causes fixed readouts from a neural population to gradually deteriorate, suggesting that downstream populations adapt to these tuning changes. Many statistical distributions of…

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…

The vast majority of neurons in the vertebrate nervous systems transmits information in a digital manner via action potentials. Yet, a detailed understanding of the advantages of digital communication in the brain is still lacking. In our study, we investigate synaptic transmission in terms of an optimization problem,…

Energy efficiency and robustness to noise for long-distance communication are often cited as reasons to the question of why the brain uses digital communication in the form of spiking neurons [1,2]. However, a quantitative and systematic analysis of the advantages and disadvantages of spikes in terms of communication,…

Cortical neurons exhibit rich, time-dependent patterns of activity that are often selective to specific stimuli. From a dynamical systems perspective, such complex activity can be conceptualized as ON/OFF responses, or also as transient amplification. It is still unclear if transient amplification is an artifact of a…

Noisy and ambiguous environments require using the arising uncertainty strategically for efficient behavior. Recent behavioral evidence confirms such strategic use during spatial navigation. Despite this, leading neural models for navigation ignore such uncertainty. I will focus on two examples for revising these…

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…

Extensive experimental evidence shows that task-relevant neural population dynamics often evolve along trajectories constrained to low-dimensional subspaces [1, 2]. However, how these low-dimensional task representations emerge through learning, and how the neural activity interacts with synaptic plasticity is still…

Since decades ago, biologists have recognized the existence of tradeoffs in biological systems (e.g., [1]). Yet, the first study that borrowed the idea of Pareto-optimality to analyze tradeoffs in biological systems was published in 1995 [2]. In 2008, following [2], it was hypothesized in [3] that Pareto-optimality,…

For the olfactory associative learning to be specific, stimulus representation in the Kenyon cell (KC) population should be accurate with minimal activity overlap between different stimuli, which is achieved by the sparse and highly odor-specific KC response patterns. While a multitude of cellular and network…

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…

Neuroimaging recordings during resting state (but also in tasks) reveal that brain-wide functional connectivity networks are highly dynamic, undergoing a structured flow of stochastic-like reconfiguration, with events of transient stabilization of connectivity, intertwined with "leaps" with high and fast variability.…