Solar flares, email exchanges, and many natural or social systems exhibit bursty dynamics, with periods of intense activity separated by long inactivity. These patterns often follow power- law distributions in inter-event intervals or event rates. Existing models typically capture only one of these features and rely on non-local memory, which complicates analysis and mechanistic interpretation. We introduce a novel self-reinforcing point process whose event rates are governed by local, Markovian nonlinear dynamics and post-event resets. The model generates power-law tails for both inter-event intervals and event rates over a broad range of exponents observed empirically across natural and human phenomena. Compared to non-local models such as Hawkes processes, our approach is mechanistically simpler, highly analytically tractable, and also easier to simulate. We provide methods for model fitting and validation, establishing this framework as a versatile foundation for the study of bursty phenomena.

Power-law scaling in coarse-grained data suggests critical dynamics, but the true source of this scaling often remains unclear. Here, we analyze neural activity recorded during spatial navigation, reproducing power-law scaling under a phenomenological renormalization group (PRG) procedure that clusters units by activity similarity. Such scaling was previously linked to criticality. Here, we show that the iterative nature of the procedure itself leads to the emergence of power laws when applied to heterogeneous, non-interacting units obeying spatially structured activity without requiring critical interactions. Furthermore, the scaling exponents produced by heteregeneous non-interacting units match the observed exponents in recorded neural data. A simplified version of the PRG further reveals how heterogeneity smooths transitions across scales, mimicking critical behavior. The resulting exponents depend systematically on system and population size, predictions confirmed by subsampling the data.

Two simple models—vaulting over stiff legs and rebounding over compliant legs—are employed to describe the mechanics of legged locomotion. It is agreed that compliant legs are necessary for describing running, and that leg compliance is also present during walking. Stiff legs continue to be employed to model walking under the assumption that the compliance of the leg during walking is low enough to be considered stiff. Here we study gait choice and walk-to-run transition in a biped with compliance and show that the principles underlying gait choice and transition are completely different from stiff legs. Two findings underpin our conclusions: First, at the same speed, step length and stance duration, multiple gaits that differ in the number of times the leg expands and contracts during a single stance are possible. Among them, humans and other animals choose the (normal) gait with M-shaped vertical ground reaction forces (vGRF) not just because of energy considerations but also constraints from forces. Second, the transition from walking to running occurs because of three factors: vGRF minimum at mid-stance characteristic of normal walking, synchronization of horizontal and vertical motions during single support, and velocity redirection during the double support. The insight above required an analytical approximation of the double spring-loaded pendulum (DSLIP) model describing the intricate oscillatory dynamics that relate single and double support phases. Additionally, we also examined DSLIP as a quantitative model for locomotion and conclude that DSLIP speed range is limited. However, insights gleaned from the analytical treatment of DSLIP are general and will inform the construction of more accurate models of walking.

bioRxiv preprint: https://doi.org/10.1101/2024.09.23.612940

Sex differences in behaviour exist across the animal kingdom, typically under strong genetic regulation. In Drosophila, previous work has shown that fruitless and doublesex transcription factors identify neurons driving sexually dimorphic behaviour. However, the organisation of dimorphic neurons into functional circuits remains unclear.We now present the connectome of the entire Drosophila male central nervous system. This contains 166,691 neurons spanning the brain and ventral nerve cord, fully proofread and comprehensively annotated including fruitless and doublesex expression and 11,691 cell types. By comparison with a previous female brain connectome, we provide the first comprehensive description of the differences between male and female brains to synaptic resolution. Of 7,319 cross-matched cell types in the central brain, 114 are dimorphic with an additional 262 male- and 69 female-specific (totalling 4.8% of neurons in males and 2.4% in females).This resource enables analysis of full sensory-to-motor circuits underlying complex behaviours as well as the impact of dimorphic elements. Sex-specific and dimorphic neurons are concentrated in higher brain centres while the sensory and motor periphery are largely isomorphic. Within higher centres, male-specific connections are organised into hotspots defined by male-specific neurons or the presence of male-specific arbours on neurons that are otherwise similar between sexes. Numerous circuit switches reroute sensory information to form conserved, antagonistic circuits controlling opposing behaviours.

Complete synaptic wiring diagrams, or connectomes, of whole brains open new opportunities for studying the structure-function relationship of neural circuits. However, the large number of nodes and edges in the graphs makes the analysis challenging. Here, we present the Connectome Interpreter (https://github.com/YijieYin/connectome_interpreter), an open-source software toolkit for efficient graph traversal to find polysynaptic pathways, compute the effective connectivity and receptive fields for arbitrarily deep neurons, slice out subcircuits, and non-linear but differentiable circuit modeling, implemented using efficient approaches tailored to the high density and size of connectomes such as that of the fruit fly Drosophila melanogaster. Our approach delivers results orders of magnitude faster than conventional methods in consumer computer hardware. We demonstrate the capabilities of our toolkit with select applications, including quantifying the density of polysynaptic connections in the whole adult fruit fly brain, exploring the necessity for non-linearities in circuit modeling, and combining known function of neurons with the connectome to aid in formulating hypotheses of circuit function.

A cognitive compass enabling spatial navigation requires neural representation of heading direction (HD), yet the neural circuit architecture enabling this representation remains unclear. While various network models have been proposed to explain HD systems, these models rely on simplified circuit architectures that are incompatible with empirical observations from connectomes. Here we construct a novel network model for the fruit fly HD system that satisfies both connectome-derived architectural constraints and the functional requirement of continuous heading representation. We characterize an ensemble of continuous attractor networks where compass neurons providing local mutual excitation are coupled to inhibitory neurons. We discover a new mechanism where continuous heading representation emerges from combining symmetric and anti-symmetric activity patterns. Our analysis reveals three distinct realizations of these networks that all match observed compass neuron activity but differ in their predictions for inhibitory neuron activation patterns. Further, we found that deviations from these realizations can be compensated by cell-type-specific rescaling of synaptic weights, which could be potentially achieved through neuromodulation. This framework can be extended to incorporate the complete fly central complex connectome and could reveal principles of neural circuits representing other continuous quantities, such as spatial location, across insects and vertebrates.

Hippocampal CA3 is central to memory formation and retrieval. Although various network mechanisms have been proposed, direct evidence is lacking. Using intracellular Vm recordings and optogenetic manipulations in behaving mice, we found that CA3 place-field activity is produced by a symmetric form of behavioral timescale synaptic plasticity (BTSP) at recurrent synapses among CA3 pyramidal neurons but not at synapses from the dentate gyrus (DG). Additional manipulations revealed that excitatory input from the entorhinal cortex (EC) but not the DG was required to update place cell activity based on the animal's movement. These data were captured by a computational model that used BTSP and an external updating input to produce attractor dynamics under online learning conditions. Theoretical analyses further highlight the superior memory storage capacity of such networks, especially when dealing with correlated input patterns. This evidence elucidates the cellular and circuit mechanisms of learning and memory formation in the hippocampus.

Many animals rely on persistent internal representations of continuous variables for working memory, navigation, and motor control. Existing theories typically assume that large networks of neurons are required to maintain such representations accurately; networks with few neurons are thought to generate discrete representations. However, analysis of two-photon calcium imaging data from tethered flies walking in darkness suggests that their small head-direction system can maintain a surprisingly continuous and accurate representation. We thus ask whether it is possible for a small network to generate a continuous, rather than discrete, representation of such a variable. We show analytically that even very small networks can be tuned to maintain continuous internal representations, but this comes at the cost of sensitivity to noise and variations in tuning. This work expands the computational repertoire of small networks, and raises the possibility that larger networks could represent more and higher-dimensional variables than previously thought.

As we move through the world, we see the same visual scenes from different perspectives. Although we experience perspective deformations, our perception of a scene remains stable. This raises the question of which neuronal representations in visual brain areas are perspective-tuned and which are invariant. Focusing on planar rotations, we introduce a mathematical framework based on the principle of equivariance, which asserts that an image rotation results in a corresponding rotation of neuronal representations, to explain how the same representation can range from being fully tuned to fully invariant. We applied this framework to large-scale simultaneous neuronal recordings from four visual cortical areas in mice, where we found that representations are both tuned and invariant but become more invariant across higher-order areas. While common deep convolutional neural networks show similar trends in orientation-invariance across layers, they are not rotation-equivariant. We propose that equivariance is a prevalent computation of populations of biological neurons to gradually achieve invariance through structured tuning.

Flying insects exhibit remarkable navigational abilities controlled by their compact nervous systems. Optic flow, the pattern of changes in the visual scene induced by locomotion, is a crucial sensory cue for robust self-motion estimation, especially during rapid flight. Neurons that respond to specific, large-field optic flow patterns have been studied for decades, primarily in large flies, such as houseflies, blowflies, and hover flies. The best-known optic-flow sensitive neurons are the large tangential cells of the dipteran lobula plate, whose visual-motion responses, and to a lesser extent, their morphology, have been explored using single-neuron neurophysiology. Most of these studies have focused on the large, Horizontal and Vertical System neurons, yet the lobula plate houses a much larger set of 'optic-flow' sensitive neurons, many of which have been challenging to unambiguously identify or to reliably target for functional studies. Here we report the comprehensive reconstruction and identification of the Lobula Plate Tangential Neurons in an Electron Microscopy (EM) volume of a whole Drosophila brain. This catalog of 58 LPT neurons (per brain hemisphere) contains many neurons that are described here for the first time and provides a basis for systematic investigation of the circuitry linking self-motion to locomotion control. Leveraging computational anatomy methods, we estimated the visual motion receptive fields of these neurons and compared their tuning to the visual consequence of body rotations and translational movements. We also matched these neurons, in most cases on a one-for-one basis, to stochastically labeled cells in genetic driver lines, to the mirror-symmetric neurons in the same EM brain volume, and to neurons in an additional EM data set. Using cell matches across data sets, we analyzed the integration of optic flow patterns by neurons downstream of the LPTs and find that most central brain neurons establish sharper selectivity for global optic flow patterns than their input neurons. Furthermore, we found that self-motion information extracted from optic flow is processed in distinct regions of the central brain, pointing to diverse foci for the generation of visual behaviors.