Despite the overall complexity of legged locomotion, the motion of the center of mass (COM) itself is relatively simple, and can be qualitatively described by simple mechanical models. In particular, walking can be qualitatively modeled by a simple model in which each leg is described by a spring-loaded inverted pendulum (SLIP). However, SLIP has many limitations and is unlikely to serve as a quantitative model. As a first step to obtaining a quantitative model for walking, we explored the ability of SLIP to model the single-support phase of walking, and found that SLIP has two limitations. First, it predicts larger horizontal ground reaction forces (GRFs) than empirically observed. A new model – angular and radial spring-loaded inverted pendulum (ARSLIP) – can overcome this deficit. Second, although the leg spring (surprisingly) goes through contraction-extension-contraction-extensions (CECEs) during the single-support phase of walking and can produce the characteristic M-shaped vertical GRFs, modeling the single-support phase requires active elements. Despite these limitations, SLIP as a model provides important insights. It shows that the CECE cycling lengthens the stance duration allowing the COM to travel passively for longer, and decreases the velocity redirection between the beginning and end of a step.

Changes in walking speed are characterized by changes in both the animal's gait and the mechanics of its interaction with the ground. Here we study these changes in walking Drosophila. We measured the fly's center of mass (CoM) movement with high spatial resolution and the position of its footprints. Flies predominantly employ a modified tripod gait that only changes marginally with speed. The mechanics of a tripod gait can be approximated with a simple model – angular and radial spring-loaded inverted pendulum (ARSLIP) – which is characterized by two springs of an effective leg that become stiffer as the speed increases. Surprisingly, the change in the stiffness of the spring is mediated by the change in tripod shape rather than a change in stiffness of the individual leg. The effect of tripod shape on mechanics can also explain the large variation in kinematics among insects, and ARSLIP can model these variations.

Seizures are thought to arise from an imbalance of excitatory and inhibitory neuronal activity. While most classical studies suggest excessive excitatory neural activity plays a generative role, some recent findings challenge this view and instead argue that excessive activity in inhibitory neurons initiates seizures. We investigated this question of imbalance in a zebrafish seizure model with two-photon imaging of excitatory and inhibitory neuronal activity throughout the brain using a nuclear-localized calcium sensor. We found that seizures consistently initiated in circumscribed zones of the midbrain before propagating to other brain regions. Excitatory neurons were both more prevalent and more likely to be recruited than inhibitory neurons in initiation as compared with propagation zones. These findings support a mechanistic picture whereby seizures initiate in a region of hyper-excitation, then propagate more broadly once inhibitory restraint in the surround is overcome.

Despite the overall complexity of legged locomotion, the motion of the center of mass (COM) itself is relatively simple, and can be qualitatively described by simple mechanical models. The spring-loaded inverted pendulum (SLIP) is one such model, and describes both the COM motion and the ground reaction forces (GRFs) during running. Similarly, walking can be modeled by two SLIPlike legs (double SLIP or DSLIP). However, DSLIP has many limitations and is unlikely to serve as a quantitative model for walking. As a first step to obtaining a quantitative model for walking, we explored the ability of SLIP to model the single stance phase of walking across the entire range of walking speeds. We show that SLIP can be employed to quantitatively model the single stance phase except for two exceptions: first, it predicts larger horizontal GRFs than empirically observed. A new model -angular and radial spring-loaded inverted pendulum (ARSLIP) can overcome this deficit. Second, even the single stance phase has active elements, and therefore a quantitative model of locomotion would require active elements. Surprisingly, the leg spring undergoes a contraction-extension-contraction-extension (CECE) during walking; this cycling is partly responsible for the M-shaped GRFs produced during walking. The CECE cycle also lengthens the stance duration allowing the COM to travel passively for a longer time, and decreases the velocity redirection between the beginning and end of a step. A combination of ARSLIP along with active mechanisms during transition from one step to the next is necessary to describe walking.

Perception is an outcome of neuronal computations. Our perception changes only when the underlying neuronal responses change. Because visual neurons preferentially respond to adjustments in some pixel values of an image more than others, our perception has greater sensitivity in detecting change to some pixel combinations more than others. Here, we examined how perceptual discriminability varies to arbitrary image perturbations assuming different models of neuronal responses. In particular, we investigated that under the assumption of different neuronal computations, how perceptual discriminability relates to neuronal receptive fields - the change in pixel combinations that invokes the largest increase in neuronal responses. We assumed that perceptual discriminability reflects the magnitude of change (the L2 norm) in neuronal responses, and the L2 norm assumption gained empirical support. We examined how perceptual discriminability relates to deterministic and stochastic neuronal computations. In the case of deterministic neuronal computations, perceptual discriminability is completely determined by neuronal receptive fields. For multiple layers of canonical linear-nonlinear (LN) computations in particular (which is a feed-forward neural network), neuronal receptive fields are linear transforms of the first-layer neurons' image filters. When one image is presented to the neural network, the first layer neurons' filters and the linear transform completely determine neuronal receptive fields across all layers, and perceptual discriminability to arbitrary distortions to the image. We expanded our analysis to examine stochastic neuronal computations, in which case perceptual discriminability can be summarized as the magnitude of change in stochastic neuronal responses, with the L2 norm being replaced by a Fisher-information computation. Using a practical lower bound on Fisher information, we showed that for stochastic neuronal computations, perceptual discriminability is completely determined by neuronal receptive fields, together with how responses co-variate across neurons.