Cortical variations in cytoarchitecture form a sensory-fugal axis that shapes regional profiles of extrinsic connectivity and is thought to guide signal propagation and integration across the cortical hierarchy. While neuroimaging work has shown that this axis constrains local properties of the human connectome, it remains unclear whether it also shapes the asymmetric signaling that arises from higher-order topology. Here, we used network control theory to examine the amount of energy required to propagate dynamics across the sensory-fugal axis. Our results revealed an asymmetry in this energy, indicating that bottom-up transitions were easier to complete compared to top-down. Supporting analyses demonstrated that asymmetries were underpinned by a connectome topology that is wired to support efficient bottom-up signaling. Lastly, we found that asymmetries correlated with differences in communicability and intrinsic neuronal time scales and lessened throughout youth. Our results show that cortical variation in cytoarchitecture may guide the formation of macroscopic connectome topology.

Neural activity in many sensory systems is organized on low-dimensional manifolds by means of convex receptive fields. Neural codes in these areas are constrained by this organization, as not every neural code is compatible with convex receptive fields. The same codes are also constrained by the structure of the underlying neural network. In my talk I will attempt to provide answers to the following natural questions: (i) How do recurrent circuits generate codes that are compatible with the convexity of receptive fields? (ii) How can we utilize the constraints imposed by the convex receptive field to understand the underlying stimulus space. To answer question (i), we describe the combinatorics of the steady states and fixed points of recurrent networks that satisfy the Dale’s law. It turns out the combinatorics of the fixed points are completely determined by two distinct conditions: (a) the connectivity graph of the network and (b) a spectral condition on the synaptic matrix. We give a characterization of exactly which features of connectivity determine the combinatorics of the fixed points. We also find that a generic recurrent network that satisfies Dale's law outputs convex combinatorial codes. To address question (ii), I will describe methods based on ideas from topology and geometry that take advantage of the convex receptive field properties to infer the dimension of (non-linear) neural representations. I will illustrate the first method by inferring basic features of the neural representations in the mouse olfactory bulb.

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.

In sexually reproducing species, males and females respond to environmental sensory cues and transform the input into sexually dimorphic traits. Yet, how sexually dimorphic behavior is encoded in the nervous system is poorly understood. We characterize the sexually dimorphic nociceptive behavior in C. elegans – hermaphrodites present a lower pain threshold than males in response to aversive stimuli, and study the underlying neuronal circuits, which are composed of the same neurons that are wired differently. By imaging receptor expression, calcium responses and glutamate secretion, we show that sensory transduction is similar in the two sexes, and therefore explore how downstream network topology shapes dimorphic behavior. We generated a computational model that replicates the observed dimorphic behavior, and used this model to predict simple network rewirings that would switch the behavior between the sexes. We then showed experimentally, using genetic manipulations, artificial gap junctions, automated tracking and optogenetics, that these subtle changes to male connectivity result in hermaphrodite-like aversive behavior in-vivo, while hermaphrodite behavior was more robust to perturbations. Strikingly, when presented with aversive cues, rewired males were compromised in finding mating partners, suggesting that the network topology that enables efficient avoidance of noxious cues would have a reproductive "cost". To summarize, we present a deconstruction of a sex-shared neural circuit that affects sexual behavior, and how to reprogram it. More broadly, our results are an example of how common neuronal circuits changed their function during evolution by subtle topological rewirings to account for different environmental and sexual needs.

The talk will detail work drawing on behavioural results, formal analysis, and computational modelling with agent-based simulations to unpack the scale of the challenge humans face when trying to work out and factor in the reliability of their sources. In particular, it is shown how and why this task admits of no easy solution in the context of wider communication networks, and how this will affect the accuracy of our beliefs. The implications of this for the shift in the size and topology of our communication networks through the uncontrolled rise of social media are discussed.

Self-organization is a universal concept spanning numerous disciplines including mathematics, physics and biology. Chromosomes are self-organizing polymers that fold into orderly, hierarchical and yet dynamic structures. In the past decade, advances in experimental biology have provided a means to reveal information about chromosome connectivity, allowing us to directly use this information from experiments to generate 3D models of individual genes, chromosomes and even genomes. In this talk I will present a novel data-driven modeling approach and discuss a number of possibilities that this method holds. I will discuss a detailed study of the time-evolution of X chromosome inactivation, highlighting both global and local properties of chromosomes that result in topology-driven dynamical arrest and present and characterize a novel type of motion we discovered in knots that may have applications to nanoscale materials and machines.

To understand brain function and develop artificial general intelligence it has become abundantly clear that there should be a close interaction among Neuroscience, machine learning and mathematics. There is a general hope that understanding the brain function will provide us with more powerful machine learning algorithms. On the other hand advances in machine learning are now providing the much needed tools to not only analyse brain activity data but also to design better experiments to expose brain function. Both neuroscience and machine learning explicitly or implicitly deal with high dimensional data and systems. Mathematics can provide powerful new tools to understand and quantify the dynamics of biological and artificial systems as they generate behavior that may be perceived as intelligent. In this meeting we bring together experts from Mathematics, Artificial Intelligence and Neuroscience for a three day long hybrid meeting. We will have talks on mathematical tools in particular Topology to understand high dimensional data, explainable AI, how AI can help neuroscience and to what extent the brain may be using algorithms similar to the ones used in modern machine learning. Finally we will wrap up with a discussion on some aspects of neural hardware that may not have been considered in machine learning.

In our everyday lives, we form connections and build up social networks that allow us to function successfully as individuals and as a society. Our social networks tend to include well-connected individuals who link us to other groups of people that we might otherwise have limited access to. In addition, we are more likely to befriend individuals who a) live nearby and b) have mutual friends. Interestingly, neurons tend to do the same…until development is perturbed. Just like social networks, neuronal networks require highly connected hubs to elicit efficient communication at minimal cost (you can’t befriend everybody you meet, nor can every neuron wire with every other!). This talk will cover some of Alex’s work showing that microscopic (cellular scale) brain networks inferred from spontaneous activity show similar complex topology to that previously described in macroscopic human brain scans. The talk will also discuss what happens when neurodevelopment is disrupted in the case of a monogenic disorder called Rett Syndrome. This will include simulations of neuronal activity and the effects of manipulation of model parameters as well as what happens when we manipulate real developing networks using optogenetics. If functional development can be restored in atypical networks, this may have implications for treatment of neurodevelopmental disorders like Rett Syndrome.

Filaments (slender, microscopic elastic bodies) are prevalent in biological and industrial settings. In the biological case, the filaments are often active, in that they are driven internally by motor proteins, with the prime examples being cilia and flagella. For cilia in particular, which can appear in dense arrays, their resulting motions are coupled through the surrounding fluid, as well as through surfaces to which they are attached. In this talk, I present numerical simulations exploring the coordinated motion of active filaments and how it depends on the driving force, density of filaments, as well as the attached surface. In particular, we find that when the surface is spherical, its topology introduces local defects in coordinated motion which can then feedback and alter the global state. This is particularly true when the surface is not held fixed and is free to move in the surrounding fluid. These simulations take advantage of a computational framework we developed for fully 3D filament motion that combines unit quaternions, implicit geometric time integration, quasi-Newton methods, and fast, matrix-free methods for hydrodynamic interactions and it will also be presented.

The human brain is a complex network of neuronal connections. The precise arrangement of these connections, otherwise known as the topology of the network, is crucial to its functioning. Recent efforts to understand how the complex topology of the brain has emerged have used generative mathematical models, which grow synthetic networks according to specific wiring rules. Evidence suggests that a wiring rule which emulates a trade-off between connection costs and functional benefits can produce networks that capture essential topological properties of brain networks. In this webinar, Professor Alex Fornito and Dr Stuart Oldham will discuss these previous findings, as well as their own efforts in creating more physiologically constrained generative models. Professor Alex Fornito is Head of the Brain Mapping and Modelling Research Program at the Turner Institute for Brain and Mental Health. His research focuses on developing new imaging techniques for mapping human brain connectivity and applying these methods to shed light on brain function in health and disease. Dr Stuart Oldham is a Research Fellow at the Turner Institute for Brain and Mental Health and a Research Officer at the Murdoch Children’s Research Institute. He is interested in characterising the organisation of human brain networks, with particular focus on how this organisation develops, using neuroimaging and computational tools.

The human brain network architecture can reveal crucial aspects of brain function and dysfunction. The topology of this network (known as the connectome) is shaped by a trade-off between wiring cost and network efficiency, and it has highly connected hub regions playing a prominent role in many brain disorders. By studying a landscape of plausible brain networks that preserve the wiring cost, fragile and resilient hubs can be identified. In this webinar, Dr Leonardo Gollo and Dr James Pang from Monash University will discuss this approach across the lifespan and some of its implications for neurodevelopmental and neurodegenerative diseases. Dr Leonardo Gollo is a Senior Research Fellow at the Turner Institute for Brain and Mental Health, School of Psychological Sciences, Monash University. He holds an ARC Future Fellowship and his research interests include brain modelling, systems neuroscience, and connectomics. Dr James Pang is a Research Fellow at the Turner Institute for Brain and Mental Health, School of Psychological Sciences, Monash University. His research interests are on combining neuroimaging and biophysical modelling to better understand the mechanisms of brain function in health and disease.

Rigidity is the ability of a system to resist imposed stresses before ultimately undergoing failure. However, disordered materials often contain both rigid and floppy subregions that complicate the utility of taking system-wide averages. I will talk about 3 frameworks capable of connecting the internal structure of disordered materials to their rigidity and/or failure under loading, and describe how my collaborators and I have applied these frameworks to laboratory data on laser-cut lattices and idealized granular materials. These are, in order of increasing physics content: (1) centrality within an adjacency matrix describing its connectivity, (2) Maxwell constraint counting on the full network of frictional contact forces, and (3) the vibrational modes of a synthetic dynamical matrix (Hessian). The first two rely primarily on topology, and the second two contrast the utility of considering interparticle forces (Coulomb failure) vs. the energy landscape. All three methods, while successfully elucidating the origins of rigidity and brittle vs. ductile failure, also provide interesting counterpoints regarding how much information is enough to make predictions.

The dream of programmable matter is to create materials whose physical properties (shape, moduli, response to perturbations, etc.) can be changed on the fly. For many years, my group has been thinking about how to program flat sheets that fold up into three dimensional shapes, most recently by exploiting the principles of origami design. Unfortunately, a combinatorial explosion of folding pathways makes robust folding particularly challenging. In this talk, I will discuss how this pluripotency arises from the topology of the configuration space. This suggests a broader understanding of a larger class of materials spanning from folding forms to spring networks to mechanical structures that perform computational logic.

Clock networks containing the same central architectures may vary drastically in their potential to oscillate, raising the question of what controls robustness, one of the essential functions of an oscillator. We computationally generate an atlas of oscillators and found that, while core topologies are critical for oscillations, local structures substantially modulate the degree of robustness. Strikingly, two local structures, incoherent and coherent inputs, can modify a core topology to promote and attenuate its robustness, additively. The findings underscore the importance of local modifications to the performance of the whole network. It may explain why auxiliary structures not required for oscillations are evolutionary conserved. We also extend this computational framework to search hidden network motifs for other clock functions, such as tunability that relates to the capabilities of a clock to adjust timing to external cues. Experimentally, we developed an artificial cell system in water-in-oil microemulsions, within which we reconstitute mitotic cell cycles that can perform self-sustained oscillations for 30 to 40 cycles over multiple days. The oscillation profiles, such as period, amplitude, and shape, can be quantitatively varied with the concentrations of clock regulators, energy levels, droplet sizes, and circuit design. Such innate flexibility makes it crucial to studying clock functions of tunability and stochasticity at the single-cell level. Combined with a pressure-driven multi-channel tuning setup and long-term time-lapse fluorescence microscopy, this system enables a high-throughput exploration in multi-dimension continuous parameter space and single-cell analysis of the clock dynamics and functions. We integrate this experimental platform with mathematical modeling to elucidate the topology-function relation of biological clocks. With FRET and optogenetics, we also investigate spatiotemporal cell-cycle dynamics in both homogeneous and heterogeneous microenvironments by reconstructing subcellular compartments.

Ants, bees and other insects have the ability to return to their nest or hive using a navigation strategy known as path integration. Similarly, fruit flies employ path integration to return to a previously visited food source. An important component of path integration is the ability of the insect to keep track of its heading relative to salient visual cues. A highly conserved brain region known as the central complex has been identified as being of key importance for the computations required for an insect to keep track of its heading. However, the similarities or differences of the underlying heading tracking circuit between species are not well understood. We sought to address this shortcoming by using reverse engineering techniques to derive the effective underlying neural circuits of two evolutionary distant species, the fruit fly and the locust. Our analysis revealed that regardless of the anatomical differences between the two species the essential circuit structure has not changed. Both effective neural circuits have the structural topology of a ring attractor with an eight-fold radial symmetry (Fig. 1). However, despite the strong similarities between the two ring attractors, there remain differences. Using computational modelling we found that two apparently small anatomical differences have significant functional effect on the ability of the two circuits to track fast rotational movements and to maintain a stable heading signal. In particular, the fruit fly circuit responds faster to abrupt heading changes of the animal while the locust circuit maintains a heading signal that is more robust to inhomogeneities in cell membrane properties and synaptic weights. We suggest that the effects of these differences are consistent with the behavioural ecology of the two species. On the one hand, the faster response of the ring attractor circuit in the fruit fly accommodates the fast body saccades that fruit flies are known to perform. On the other hand, the locust is a migratory species, so its behaviour demands maintenance of a defined heading for a long period of time. Our results highlight that even seemingly small differences in the distribution of dendritic fibres can have a significant effect on the dynamics of the effective ring attractor circuit with consequences for the behavioural capabilities of each species. These differences, emerging from morphologically distinct single neurons highlight the importance of a comparative approach to neuroscience.