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Abstract In this work we examine synthetic antiferromagnetic structures consisting of two, three, and four antiferromagnetic coupled layers, i.e. bilayers, trilayers, and tetralayers. We vary the thickness of the ferromagnetic layers across all structures and, using a macrospin formalism, find that the nearest neighbor exchange interaction between layers is consistent across all structures for a given thickness of the ferromagnetic layer. Our model and experimental results demonstrate significant differences in how the static equilibrium states of even and odd-layered structures evolve as a function of the external field. Even layered structures continuously evolve from a collinear antiferromagnetic state to a spin canted non-collinear magnetic configuration that is mirror-symmetric about the external field. In contrast, odd-layered structures begin with a ferrimagnetic ground state; at a critical field, the ferrimagnetic ground state evolves into a non-collinear state with broken symmetry. Specifically, the magnetic moments found in the odd-layered samples possess stable static equilibrium states that are no longer mirror-symmetric about the external field after a critical field is reached. 

This study introduces a novel neuromechanical model of rat hindlimbs with biarticular muscles producing walking movements without ground contact. The design of the control network is informed by the findings from our previous investigations into two-layer central pattern generators (CPGs). Specifically, we examined one plausible synthetic nervous system (SNS) designed to actuate 3 biarticular muscles, including the Biceps femoris posterior (BFP) and Rectus femoris (RF), both of which provide torque about the hip and knee joints. We conducted multiple perturbation tests on the simulation model to investigate the contribution of these two biarticular muscles in stabilizing perturbed hindlimb walking movements. We tested the BFP and RF muscles under three conditions: active, only passive tension, and fully disabled. Our results show that when these two biarticular muscles were active, they not only reduced the impact of external torques, but also facilitated rapid coordination of motion phases. As a result, the hindlimb model with biarticular muscles demonstrated faster recovery compared to our previous monoarticular muscle model. 

Summary Sequential Monte Carlo algorithms are widely accepted as powerful computational tools for making inference with dynamical systems. A key step in sequential Monte Carlo is resampling, which plays the role of steering the algorithm towards the future dynamics. Several strategies have been used in practice, including multinomial resampling, residual resampling, optimal resampling, stratified resampling and optimal transport resampling. In one-dimensional cases, we show that optimal transport resampling is equivalent to stratified resampling on the sorted particles, and both strategies minimize the resampling variance as well as the expected squared energy distance between the original and resampled empirical distributions. For general $$d$$-dimensional cases, we show that if the particles are first sorted using the Hilbert curve, the variance of stratified resampling is $$O(m^{-(1+2/d)})$$, an improvement over the best previously known rate of $$O(m^{-(1+1/d)})$$, where $$m$$ is the number of resampled particles. We show that this improved rate is optimal for ordered stratified resampling schemes, as conjectured in Gerber et al. (2019). We also present an almost-sure bound on the Wasserstein distance between the original and Hilbert-curve-resampled empirical distributions. In light of these results, we show that for dimension $d>1$ the mean square error of sequential quasi-Monte Carlo with $$n$$ particles can be $$O(n^{-1-4/\{d(d+4)\}})$$ if Hilbert curve resampling is used and a specific low-discrepancy set is chosen. To our knowledge, this is the first known convergence rate lower than $$o(n^{-1})$$.