Living systems exhibit various robust dynamics during system regulation, growth, and motility. However, how robustness emerges from stochastic components remains unclear. Towards understanding this, I develop topological theories that support robust edge currents and localization, effectively reducing the system function to a lower-dimensional subspace. I will introduce stochastic networks in molecular reaction space that model long and stable time scales, such as the circadian rhythm. More generally, we prove that unlike their quantum counterparts, stochastic topological systems require non-Hermiticity for edge states and strong localization. I will close by discussing experimental platforms for the detection and use of edge currents for self-assembly and replication in living systems.

Neural responses in association brain areas during cognitive tasks are heterogeneous, and the widespread assumption is that this heterogeneity reflects complex dynamics involved in cognition. However, the complexity may arise from a fundamentally different coding principle: the collective dynamics of a neural population encode simple cognitive variables, while individual neurons have diverse tuning to the cognitive variable, similar to tuning curves of sensory neurons to external stimuli. We developed an approach to simultaneously infer neural population dynamics and tuning functions of single neurons to the latent population state. Applied to spike data recorded from primate premotor cortex during decision-making, our model revealed that populations of neurons encoded the same dynamic variable predicting choices, and heterogeneous firing rates resulted from the diverse tuning of single neurons to this decision variable. The inferred dynamics indicated an attractor mechanism for decision computation. Our results reveal a unifying geometric principle for neural encoding of sensory and dynamic cognitive variables.

Connections between neurons can be mapped by acquiring and analyzing electron microscopic (EM) brain images. In recent years, this approach has been applied to chunks of brains to reconstruct local connectivity maps that are highly informative yet inadequate for understanding brain function more globally. We reconstructed the first neuronal wiring diagram of a whole adult brain, containing >50 million chemical synapses between 139,255 neurons reconstructed from a female Drosophila melanogaster. In this talk, I will highlight the technological progress leading up to the creation of this resource. Further, I will discuss how the connectome can be used to study the global organization of the brain and facilitate the tracing of synaptic pathways from the inputs (e.g., sensory neurons) to outputs (e.g., descending neurons). The technologies and open ecosystem developed for the fly brain connectome set the stage for future large-scale connectome projects in other species. I will give an outlook on connectomes for large mammalian brains.

Shear thickening in concentrated suspensions occurs when the imposed stress drives particles together to form a frictional contact network. This implies a balancing resisting force, whose magnitude sets the threshold for the imposed stress to induce contacts. Using an established simulation technique [1] and motivated by recent work showing the rapid onset of system-spanning rigid structures (identified by a pebble game algorithm) with increase of volume fraction [2], we show for a two-dimensional (monolayer) suspension that the number of contacts in the network is an increasing function of stress, but it also fluctuates during flow. We go on to explore the development of minimally rigid structures in the shear-thickened suspension as it approaches jamming at high stress, and show that the onset of large rigid clusters exhibits critical behavior. The possible relationship of this behavior to other work showing critical scaling in this system will be discussed.

[1] R. Mari, R. Seto, J. F. Morris & M. M. Denn 2014 Shear thickening, frictionless and frictional rheologies. J. Rheol. 58, 1693.

[2] M. van der Naald, A. Singh, T.T. Eid, K. Tang, J. J. de Pablo & H. M. Jaeger, H.M. 2024. Minimally rigid clusters in dense suspension flow. Nature Physics 20, 653–659.

In this talk, I will share two stories. First, I will share our discoveries on why aquatic worms braid, tangle, and knot with their neighbors to form extraordinary living “blobs”. These soft, squishy “living polymers” shape-morph, crawl, float, and untangle – the stuff of science fiction. Through mathematical models and robotic analogs, I will explain how these worms solve Gordian knot problems, inspiring active, topological tunable robotic swarms.

Second, I will explore the century-old practice of sheepdog trials to uncover strategies for controlling noisy, indecisive herds of sheep. In these competitions, sheep stochastically switch between following and ignoring control signals, yet skilled dog-handler teams excel at herding and splitting them on demand. Using simulations and temporal network theory, I will demonstrate how stochastic indecisiveness—a behavior often seen as a challenge—can instead be harnessed to efficiently control noisy swarms, with applications in swarm robotics, opinion dynamics, and adaptive networks.

Mass loss from the Antarctic Ice Sheet occurs due to the viscous ice flow of glaciers from the interior of ice sheets towards the ocean, along with brittle fracture of ice into icebergs. Viscous flow and brittle fracture of ice are governed by microphysical processes that occur on scales of ice crystals or smaller. However, incorporating physics on these small spatial and temporal scales into ice sheet models is made difficult by gaps in our physical understanding of these microphysical processes and by the computational cost of models that resolve them. Here, we propose a framework for incorporating small-scale processes governing ice deformation into large-scale ice sheet models. In particular, we present a bulk parameterization method for incorporating ice crystal-scale processes into models of viscous ice flow, and we show that this parameterization provides a way of representing the effect of varying flow conditions on future ice sheet behavior. Our results help to explain the range of ice deformation processes previously inferred in laboratory and field studies and allow for the future development of a microphysics-driven ice flow model.