About

Gabriel Ocker is an Assistant Professor in the Department of Mathematics & Statistics at Boston University. He is a member of the Applied Mathematics and Dynamical Systems research groups. For more information about Professor Ocker, please see his personal webpage.

Research topics

• Computer Science
• Neuroscience
• Artificial Intelligence
• Biology
• Psychology
• Medicine
• Cognitive science

Selected publications

• Field-Theoretic Approach to Compartmental Neuronal Networks: Impact of Dendritic Calcium Spike-Dependent Bursting

  PRX Life · 2026-01-05

  articleOpen accessSenior author

  Neurons are spatially extended cells. Different parts of a neuron have specific voltage dynamics. Important types of neurons even generate different spikes in different parts of the cell. Neurons' inputs are also often spatially compartmentalized, with different sources targeting different locations on the cell. Classic mean-field theories for neural population activity, however, rely on point-neuron models with at most one type of spike, the sodium-potassium action potential. Here, we develop a statistical field-theoretic approach to understanding collective activity in networks of compartmental neurons, including those generating multiple types of spikes. We use this to examine simple models of cortical networks with pyramidal cells that generate dendritic calcium spikes. In the weakly coupled regime, we uncover an exact mean-field limit for these networks that maps them to a marked point process. We use this mean-field limit to compare the impact of compartmentalized recurrent excitatory and inhibitory connectivity on the equilibrium phase diagram. This exposes regions of metastability between various activity states, including activity with silent vs active dendrites, with and without inhibitory activity, and oscillations.

  PublisherDOI

• Metastability in networks of stochastic integrate-and-fire neurons

  Physical review. E · 2025-06-02

  article

  Neurons in the brain continuously process the barrage of sensory inputs they receive from the environment. A wide array of experimental work has shown that the collective activity of neural populations encodes and processes this constant bombardment of information. How these collective patterns of activity depend on single-neuron properties is often unclear. Single-neuron recordings have shown that individual neurons' responses to inputs are nonlinear, which prevents a straightforward extrapolation from single-neuron features to emergent collective states. Here, we use a field-theoretic formulation of a stochastic leaky integrate-and-fire model to study the impact of single-neuron nonlinearities on macroscopic network activity. In this model, a neuron integrates spiking output from other neurons in its membrane voltage and emits spikes stochastically with an intensity depending on the membrane voltage, after which the voltage resets. We show that the interplay between nonlinear spike intensity functions and membrane potential resets can (i) give rise to metastable active firing rate states in recurrent networks, and (ii) can enhance or suppress mean firing rates and membrane potentials in the same or paradoxically opposite directions.

  PublisherDOI

• Coherent dynamics in soft-threshold integrate-and-fire networks

  ArXiv.org · 2025-08-28

  preprintOpen accessSenior author

  We study bifurcations in networks of integrate-and-fire neurons with stochastic spike emission, focusing on the effects of the spatial and temporal structure of the synaptic interactions. Using a deterministic mean-field approximation of the population dynamics, we characterize spatial, temporal, and spatiotemporal patterns of macroscopic activity. In the mean-field theory, synaptic delays give rise to uniform oscillations across the population through a subcritical Hopf bifurcation of the stationary uniform equilibrium. With local excitation and long-range inhibition the network undergoes a Turing bifurcation, resulting in a localized area of sustained activity, or stationary bump. When the coupling has both delays, local inhibition, and long range excitation, the network undergoes a Turing-Hopf bifurcation leading to spatiotemporal dynamics, such as standing and traveling waves. When multiple instabilities are excited, we observe other complex spatiotemporal dynamics. We confirm all these predictions of the mean-field theory in simulations of the underlying stochastic model.

  PublisherOA PDFDOI

• When non-canonical olfaction is optimal

  bioRxiv (Cold Spring Harbor Laboratory) · 2025-03-04 · 1 citations

  preprintOpen accessSenior authorCorresponding

  Abstract The early olfactory system is canonically described by a “one-receptor-to-one-neuron” model: each olfactory sensory neuron (OSN) expresses a single type of olfactory receptor. Although the olfactory systems of many model organisms approximately follow this canonical organization, a number of exceptions are known. In particular, Aedes aegypti mosquitoes co-express multiple types of olfactory receptors in many OSNs. Why do some olfactory systems follow the canonical organization while others violate it? We approach this question from the normative perspective of efficient coding. We find that the canonical and non-canonical organizations optimally encode odor signals in different types of olfactory environment. Non-canonical olfaction is beneficial when relevant sources emit correlated odorants and the environment contains odorants from ethologically irrelevant odor sources. Our theory explains previous observations of receptor co-expression and provides a framework from which to understand the structure of early olfactory systems.

  PublisherOA PDFDOI

• Diverse Mean-Field Dynamics of Clustered, Inhibition-Stabilized Hawkes Networks via Combinatorial Threshold-Linear Networks

  PRX Life · 2025-09-03 · 1 citations

  articleOpen accessSenior author

  Networks of interconnected neurons display diverse patterns of collective activity. Relating this collective activity to the network's connectivity structure is a key goal of computational neuroscience. We approach this question for clustered networks, which can form via biologically realistic learning rules and allow for the reactivation of learned patterns. Previous studies of clustered networks have focused on metastabilty between fixed points, leaving open the question of whether clustered spiking networks can display richer dynamics—and if so, whether these can be predicted from their connectivity. Here we show that in the limits of large population size and fast inhibition, the combinatorial threshold linear network (CTLN) model is a mean-field theory for inhibition-stabilized nonlinear Hawkes networks with clustered connectivity. The CTLN has a large body of “graph rules” relating network structure to dynamics. By applying these, we can predict the dynamic attractors of our clustered spiking networks from the structure of between-cluster connectivity. This allows us to construct networks displaying a diverse array of nonlinear cluster dynamics, including metastable periodic orbits and chaotic attractors. Relaxing the assumption that inhibition is fast, we see that the CTLN model is still able to predict the activity of clustered spiking networks with reasonable inhibitory timescales. For slow enough inhibition, we observe bifurcations between CTLN-like dynamics and global excitatory/inhibitory oscillations.

  PublisherDOI

• Diverse mean-field dynamics of clustered, inhibition-stabilized Hawkes networks via combinatorial threshold-linear networks

  ArXiv.org · 2025-06-06

  preprintOpen accessSenior author

  Networks of interconnected neurons display diverse patterns of collective activity. Relating this collective activity to the network's connectivity structure is a key goal of computational neuroscience. We approach this question for clustered networks, which can form via biologically realistic learning rules and allow for the re-activation of learned patterns. Previous studies of clustered networks have focused on metastabilty between fixed points, leaving open the question of whether clustered spiking networks can display more rich dynamics--and if so, whether these can be predicted from their connectivity. Here, we show that in the limits of large population size and fast inhibition, the combinatorial threshold linear network (CTLN) model is a mean-field theory for inhibition-stabilized nonlinear Hawkes networks with clustered connectivity. The CTLN has a large body of ``graph rules'' relating network structure to dynamics. By applying these, we can predict the dynamic attractors of our clustered spiking networks from the structure of between-cluster connectivity. This allows us to construct networks displaying a diverse array of nonlinear cluster dynamics, including metastable periodic orbits and chaotic attractors. Relaxing the assumption that inhibition is fast, we see that the CTLN model is still able to predict the activity of clustered spiking networks with reasonable inhibitory timescales. For slow enough inhibition, we observe bifurcations between CTLN-like dynamics and global excitatory/inhibitory oscillations.

  PublisherOA PDFDOI

• When noncanonical olfaction is optimal

  Proceedings of the National Academy of Sciences · 2025-10-07 · 1 citations

  articleOpen accessSenior authorCorresponding

  The early olfactory system is canonically described by a "one-receptor-to-one-neuron" model: each olfactory sensory neuron (OSN) expresses a single type of olfactory receptor (OR). Although the olfactory systems of many model organisms approximately follow this canonical organization, a number of exceptions are known. In particular, Aedes aegypti mosquitoes coexpress multiple types of ORs in many OSNs. Why do some olfactory systems follow the canonical organization while others violate it? We approach this question from the normative perspective of efficient coding. We find that the canonical and noncanonical organizations optimally encode odor signals in different types of olfactory environment. Noncanonical olfaction is beneficial when relevant sources emit correlated odorants and the environment contains odorants from ethologically irrelevant odor sources. Our theory explains previous observations of receptor coexpression and provides a framework from which to understand the structure of early olfactory systems.

  PublisherDOI

• CA1 Engram Cell Dynamics Before and After Learning

  bioRxiv (Cold Spring Harbor Laboratory) · 2024 · 16 citations

  • Computer Science
  • Artificial Intelligence
  • Neuroscience

  Summary A fundamental question in neuroscience is how memory formation shapes brain activity at the level of neuronal populations. Recent studies of hippocampal ‘engram’ cells—neurons identified by learning-induced immediate early gene (IEG) expression—propose that these populations form the cellular substrate for memory. Previous experimental work suggests that cells are recruited into engrams via elevated intrinsic excitability and that learning drives coactivity among these cells to support retrieval. Despite this, an understanding of how engram dynamics evolve across learning and recall remains incomplete. Here, we combined activity-dependent genetic tagging with longitudinal two-photon calcium imaging to track CA1 engram population dynamics before and after fear conditioning. Our results reveal that engram activity is modulated by intrinsic dynamics, behavioral state, and stimulus-cued reactivation. First, spontaneous activity during quiet rest–up to two days before Fos expression–predicted future engram membership, consistent with the idea that intrinsic dynamics bias engram allocation. In parallel, we found sequential activity during locomotion recruited both engram and non-engram cells, but that engram cells were less modulated by velocity after contextual fear conditioning. Surprisingly, after fear conditioning, we didn’t find changes in the average spontaneous activity rates or correlations of CA1 engram cells. However, within the engram population, we identified a subset of cells that increased their spontaneous correlations after fear learning, specifically during quiet rest. Furthermore, we used a trace fear conditioning paradigm to show that CS presentation drove elevated activity and increased correlations amongst engram cells, demonstrating learning-dependent reactivation. Finally, computational modeling of CA3-CA1 circuit dynamics demonstrated that a network with strong excitatory-inhibitory balance, capable of CA3-driven reactivation, is consistent with our experimental results. Together, these results show that memory formation reshapes engram population dynamics across spontaneous states, behavior, and recall.

  PublisherOA PDFDOI

• CA1 Engram Cell Dynamics Before and After Learning

  Research Square · 2024-06-24

  preprintOpen access
  PublisherOA PDFDOI

• Prospects on non-canonical olfaction in the mosquito and other organisms: why co-express?

  Current Opinion in Insect Science · 2024-10-29 · 8 citations

  reviewOpen access

  The Aedes aegypti mosquito utilizes olfaction during the search for humans to bite. The attraction to human body odor is an innate behavior for this disease-vector mosquito. Many well-studied model species have olfactory systems that conform to a particular organization that is sometimes referred to as the 'one-receptor-to-one-neuron' organization because each sensory neuron expresses only a single type of olfactory receptor that imparts the neuron's chemical selectivity. This sensory architecture has become the canon in the field. This review will focus on the recent finding that the olfactory system of Ae. aegypti has a different organization, with multiple olfactory receptors co-expressed in many of its olfactory sensory neurons. We will discuss the canonical organization and how this differs from the non-canonical organization, examine examples of non-canonical olfactory systems in other species, and discuss the possible roles of receptor co-expression in odor coding in the mosquito and other organisms.

  PublisherDOI

Frequent coauthors

• Michael A. Buice

  Allen Institute

  110 shared

• Brent Doiron

  University of Chicago

  87 shared

• Eric Shea‐Brown

  75 shared

• Saskia de Vries

  Allen Institute for Neural Dynamics

  39 shared

• Jérôme Lecoq

  Allen Institute

  39 shared

• Christof Koch

  31 shared

• Shawn R. Olsen

  Allen Institute for Neural Dynamics

  31 shared

• Shiella Caldejon

  Allen Institute

  31 shared