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In interacting dynamical systems, specific local interaction rules for system components give rise to diverse and complex global dynamics. Long dynamical cycles are a key feature of many natural interacting systems, especially in biology. Examples of dynamical cycles range from circadian rhythms regulating sleep to cell cycles regulating reproductive behavior. Despite the crucial role of cycles in nature, the properties of network structure that give rise to cycles still need to be better understood. Here, we use a Boolean interaction network model to study the relationships between network structure and cyclic dynamics. We identify particular structural motifs that support cycles, and other motifs that suppress them. More generally, we show that the presence ofdynamical reflection symmetryin the interaction network enhances cyclic behavior. In simulating an artificial evolutionary process, we find that motifs that break reflection symmetry are discarded. We further show that dynamical reflection symmetries are over-represented in Boolean models of natural biological systems. Altogether, our results demonstrate a link between symmetry and functionality for interacting dynamical systems, and they provide evidence for symmetry’s causal role in evolving dynamical functionality.

 

Quantum information processing and quantum sensing is a central topic for researchers who are part of the Materials Research Society and the Quantum Staging Group is providing leadership and guidance in this context. We convened a workshop before the 2022 MRS Spring Meeting and covered four topics to explore challenges that need to be addressed to further promote and accelerate the development of materials with applications in quantum technologies. This article captures the discussions at this workshop and refers to the pertinent literature.

 

Abstract A safety-critical measure of legged locomotion performance is a robot's ability to track its desired time-varying position trajectory in an environment, which is herein termed as “global-position tracking.” This paper introduces a nonlinear control approach that achieves asymptotic global-position tracking for three-dimensional (3D) bipedal robots. Designing a global-position tracking controller presents a challenging problem due to the complex hybrid robot model and the time-varying desired global-position trajectory. Toward tackling this problem, the first main contribution is the construction of impact invariance to ensure all desired trajectories respect the foot-landing impact dynamics, which is a necessary condition for realizing asymptotic tracking of hybrid walking systems. Thanks to their independence of the desired global position, these conditions can be exploited to decouple the higher-level planning of the global position and the lower-level planning of the remaining trajectories, thereby greatly alleviating the computational burden of motion planning. The second main contribution is the Lyapunov-based stability analysis of the hybrid closed-loop system, which produces sufficient conditions to guide the controller design for achieving asymptotic global-position tracking during fully actuated walking. Simulations and experiments on a 3D bipedal robot with twenty revolute joints confirm the validity of the proposed control approach in guaranteeing accurate tracking. 

This study evidences that the particle surface-area-to-volume ratio (A/V) and the particle volume (V) have the key information of particle geometry and the ‘signature’ is realized by a power-law relationship between A/V and V in a form of V = (A/V)^α × β. We find that the power value α is influenced by the shape-size relationship while the β* term (β evaluated with a fixed value of α = -3) informs the average particle shape of a granular material regarding the overall angularity. This study also discusses how the particle shape can be retrieved in terms of Wadell’s true sphericity using the A/V and V. This concept is linked to another shape index M that interprets the particle shape as a function of surface area A, volume V, and size L. This paper explains the analytical aspects of geometric ‘signature’ and examines the idea using the example particles to address the DEM modelling-related questions.