In the age of connectomics, it is increasingly important to understand how the nodes and edges of a brain's anatomical network, or "connectome," gives rise to neural signaling and neural function. I will present the first comprehensive brain-wide cell-resolved causal measurements of how neurons signal to one another in response to stimulation in the nematode C. elegans. I will compare this signal propagation atlas to the worm's known connectome to address fundamental questions of structure and function in the brain.

Changes in the geometry and topology of self-assembled membranes underlie diverse processes across cellular biology and engineering. Similar to lipid bilayers, monolayer colloidal membranes studied by the Sharma (IISc Bangalore) and Dogic (UCSB) Labs have in-plane fluid-like dynamics and out-of-plane bending elasticity, but their open edges and micron length scale provide a tractable system to study the equilibrium energetics and dynamic pathways of membrane assembly and reconfiguration. First, we discuss how doping colloidal membranes with short miscible rods transforms disk-shaped membranes into saddle-shaped minimal surfaces with complex edge structures. Theoretical modeling demonstrates that their formation is driven by increasing positive Gaussian modulus, which in turn is controlled by the fraction of short rods. Further coalescence of saddle-shaped surfaces leads to exotic topologically distinct structures, including shapes similar to catenoids, tri-noids, four-noids, and higher order structures. We then mathematically explore the mechanics of these catenoid-like structures subject to an external axial force and elucidate their intimate connection to two problems whose solutions date back to Euler: the shape of an area-minimizing soap film and the buckling of a slender rod under compression. A perturbation theory argument directly relates the tensions of membranes to the stability properties of minimal surfaces. We also investigate the effects of including a Gaussian curvature modulus, which, for small enough membranes, causes the axial force to diverge as the ring separation approaches its maximal value.

The challenges of problem solving do not exclusively lie in how to perform heuristic search, but they begin with how we understand a given task: How to cognitively represent the task domain and its components can determine how quickly someone is able to progress towards a solution, whether advanced strategies can be discovered, or even whether a solution is found at all. While this challenge of constructing and changing representations has been acknowledged early on in problem solving research, for the most part it has been sidestepped by focussing on simple, well-defined problems whose representation is almost fully determined by the task instructions. Thus, the established theory of problem solving as heuristic search in problem spaces has little to say on this. In this talk, I will present a study designed to explore this issue, by virtue of finding and refining an adequate problem representation being its main challenge. In this exploratory case study, it was investigated how pairs of participants acquaint themselves with a complex spatial transformation task in the domain of iterated mental paper folding over the course of several days. Participants have to understand the geometry of edges which occurs when repeatedly mentally folding a sheet of paper in alternating directions without the use of external aids. Faced with the difficulty of handling increasingly complex folds in light of limited cognitive capacity, participants are forced to look for ways in which to represent folds more efficiently. In a qualitative analysis of video recordings of the participants' behaviour, the development of their conceptualisation of the task domain was traced over the course of the study, focussing especially on their use of gesture and the spontaneous occurrence and use of metaphors in the construction of new representations. Based on these observations, I will conclude the talk with several theoretical speculations regarding the roles of metaphor and cognitive capacity in representational change.

A rich data representation that finds wide application in industry and research is the so-called knowledge graph - a graph-based structure where entities are depicted as nodes and relations between them as edges. Complex systems like molecules, social networks and industrial factory systems can be described using the common language of knowledge graphs, allowing the usage of graph embedding algorithms to make context-aware predictions in these information-packed environments.

Goal-directed navigation requires precise estimates of spatial relationships between current position and future goal, as well as planning of an associated route or action. While neurons in the hippocampal formation can represent the animal’s position and nearby trajectories, their role in determining the animal’s destination or action has been questioned. We thus hypothesize that brain regions outside the hippocampal formation may play complementary roles in navigation, particularly for guiding goal-directed behaviours based on the brain’s internal cognitive map. In this seminar, I will first describe a subpopulation of neurons in the retrosplenial cortex (RSC) that increase their firing when the animal approaches environmental boundaries, such as walls or edges. This boundary coding is independent of direct visual or tactile sensation but instead depends on inputs from the medial entorhinal cortex (MEC) that contains spatial tuning cells, such as grid cells or border cells. However, unlike MEC border cells, we found that RSC border cells encode environmental boundaries in a self-centred egocentric coordinate frame, which may allow an animal for efficient avoidance from approaching walls or edges during navigation. I will then discuss whether the brain can possess a precise estimate of remote target location during active environmental exploration. Such a spatial code has not been described in the hippocampal formation. However, we found that neurons in the rat orbitofrontal cortex (OFC) form spatial representations that persistently point to the animal’s subsequent goal destination throughout navigation. This destination coding emerges before navigation onset without direct sensory access to a distal goal, and are maintained via destination-specific neural ensemble dynamics. These findings together suggest key roles for extra-hippocampal regions in spatial navigation, enabling animals to choose appropriate actions toward a desired destination by avoiding possible dangers.

In the past several years, I have been involved in building a biologically realistic model of the monkey visual cortex. Work on one of the input layers (4Ca) of the primary visual cortex (V1) is now nearly complete, and I would like to share some of what I have learned with the community. After a brief overview of the model and its capabilities, I would like to focus on three sets of results that represent three different aspects of the modeling. They are: (i) emergent E-I dynamics in local circuits; (ii) how visual cortical neurons acquire their ability to detect edges and directions of motion, and (iii) a view across the cortical surface: nonequilibrium steady states (in analogy with statistical mechanics) and beyond.

Figure-ground organisation and perceptual grouping are classic topics in Gestalt and perceptual psychology. They often appear alongside one another in introductory textbook chapters on perception and have a long history of investigation. However, they are typically discussed as separate processes of perceptual organisation with their own distinct phenomena and mechanisms. Here, I will propose that perceptual grouping and figure-ground organisation are strongly linked. In particular, perceptual grouping can provide a basis for, and may share mechanisms with, a wide range of figure-ground principles. To support this claim, I will describe a new class of figure-ground principles based on perceptual grouping between edges and demonstrate that this inter-edge grouping (IEG) is a powerful influence on figure-ground organisation. I will also draw support from our other results showing that grouping between edges and regions (i.e., edge-region grouping) can affect figure-ground organisation (Palmer & Brooks, 2008) and that contextual influences in figure-ground organisation can be gated by perceptual grouping between edges (Brooks & Driver, 2010). In addition to these modern observations, I will also argue that we can describe some classic figure-ground principles (e.g., symmetry, convexity, etc.) using perceptual grouping mechanisms. These results suggest that figure-ground organisation and perceptual grouping have more than a mere association under the umbrella topics of Gestalt psychology and perceptual organisation. Instead, perceptual grouping may provide a mechanism underlying a broad class of new and extant figure-ground principles.