Leg compliance is required to explain the ground reaction force patterns and speed ranges in different gaits.

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 legs are compliant while walking. Despite this agreement, stiff legs continue to be employed to model walking.

Geometric framework to predict structure from function in neural networks.

Neural computation in biological and artificial networks relies on the nonlinear summation of many inputs. The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function, but quantitative links between neural network structure and function are complex and subtle. For example, many networks can give rise to similar functional responses, and the same network can function differently depending on context.

uses a tripod gait across all walking speeds, and the geometry of the tripod is important for speed control.

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 . We measured the fly's center of mass movement with high spatial resolution and the position of its footprints.

Theoretical principles for illuminating sensorimotor processing with brain-wide neuronal recordings.

Modern recording techniques now permit brain-wide sensorimotor circuits to be observed at single neuron resolution in small animals. Extracting theoretical understanding from these recordings requires principles that organize findings and guide future experiments. Here we review theoretical principles that shed light onto brain-wide sensorimotor processing.

Spring-loaded inverted pendulum goes through two contraction-extension cycles during the single-support phase of walking.

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.

A simple extension of inverted pendulum template to explain features of slow walking.

Locomotion involves complex interactions between an organism and its environment. Despite these complex interactions, many characteristics of the motion of an animal's center of mass (COM) can be modeled using simple mechanical models such as inverted pendulum (IP) and spring-loaded inverted pendulum (SLIP) which employ a single effective leg to model an animal's COM. However, because these models are simple, they also have many limitations.

Visual Motion: Cellular Implementation of a Hybrid Motion Detector.

Visual motion detection in insects is mediated by three-input detectors that compare inputs of different spatiotemporal properties. A new modeling study shows that only a small subset of possible arrangements of the input elements provides high direction-selectivity.

Towards singularity- and ghost-free theories of gravity.

We present the most general covariant ghost-free gravitational action in a Minkowski vacuum. Apart from the much studied f(R) models, this includes a large class of nonlocal actions with improved UV behavior, which nevertheless recover Einstein's general relativity in the IR.

Thermal duality and Hagedorn transition from p-adic strings.

We develop the finite temperature theory of p-adic string models. We find that the thermal properties of these nonlocal field theories can be interpreted either as contributions of standard thermal modes with energies proportional to the temperature, or inverse thermal modes with energies proportional to the inverse of the temperature, leading to a thermal duality at leading order (genus one) analogous to the well-known T duality of string theory. The p-adic strings also recover the asymptotic limits (high and low temperature) for arbitrary genus that purely stringy calculations have yielded.