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It has been hypothesized that during a motion task the central nervous system controls the skeletal muscles partitioning them into synergetic groups, hence effectively reducing the dimensionality of the control problem. The identification of muscle groups that are co-activated remains an open problem: its solution could have important implications in the design of training or rehabilitation protocols. In this article, we combine Bayesian inverse problem techniques and data science algorithms to identify muscle synergies in human motion from the motion tracker time series of positions of fiducial markers on the body during the task. The inverse problem of estimating the muscle activation patterns from the motion tracking data is cast in the Bayesian framework, and the posterior distribution of muscle activations is explored using Myobolica, a Gibbs-sampler-based Markov chain Monte Carlo sampler. A low-rank approximation of the muscle activation patterns is then obtained via a sparsity promoting Bayesian non-negative matrix factorization of the sample mean, where the sparse coefficient vectors correspond to groups of muscles that show co-activation over the sample. This article is part of the theme issue ‘Frontiers of applied inverse problems in science and engineering’. 

A single particle representation of a self-propelled microorganism in a viscous incompressible fluid is derived based on regularised Stokeslets in three dimensions. The formulation is developed from a limiting process in which two regularised Stokeslets of equal and opposite strength but with different size regularisation parameters approach each other. A parameter that captures the size difference in regularisation provides the asymmetry needed for propulsion. We show that the resulting limit is the superposition of a regularised stresslet and a potential dipole. The model framework is then explored relative to the model parameters to provide insight into their selection. The particular case of two identical particles swimming next to each other is presented and their stability is investigated. Additional flow characteristics are incorporated into the modelling framework with in the addition of a rotlet double to characterise rotational flows present during swimming. Lastly, we show the versatility of deriving the model in the method of regularised Stokeslets framework to model wall effects of an infinite plane wall using the method of images. 

Upside-down jellyfish, Cassiopea , are prevalent in warm and shallow parts of the oceans throughout the world. They are unique among jellyfish in that they rest upside down against the substrate and extend their oral arms upwards. This configuration allows them to continually pull water along the substrate, through their oral arms, and up into the water column for feeding, nutrient and gas exchange, and waste removal. Although the hydrodynamics of the pulsation of jellyfish bells has been studied in many contexts, it is not clear how the presence or absence of the substrate alters the bulk flow patterns generated by Cassiopea medusae. In this paper, we use three-dimensional (3D) particle tracking velocimetry and 3D immersed boundary simulations to characterize the flow generated by upside-down jellyfish. In both cases, the oral arms are removed, which allows us to isolate the effect of the substrate. The experimental results are used to validate numerical simulations, and the numerical simulations show that the presence of the substrate enhances the generation of vortices, which in turn augments the upward velocities of the resulting jets. Furthermore, the presence of the substrate creates a flow pattern where the water volume within the bell is ejected with each pulse cycle. These results suggest that the positioning of the upside-down jellyfish such that its bell is pressed against the ocean floor is beneficial for augmenting vertical flow and increasing the volume of water sampled during each pulse. 

Understanding the dynamics of the spread of COVID-19 between connected communities is fundamental in planning appropriate mitigation measures. To that end, we propose and analyze a novel metapopulation network model, particularly suitable for modeling commuter traffic patterns, that takes into account the connectivity between a heterogeneous set of communities, each with its own infection dynamics. In the novel metapopulation model that we propose here, transport schemes developed in optimal transport theory provide an efficient and easily implementable way of describing the temporary population redistribution due to traffic, such as the daily commuter traffic between work and residence. Locally, infection dynamics in individual communities are described in terms of a susceptible-exposed-infected-recovered (SEIR) compartment model, modified to account for the specific features of COVID-19, most notably its spread by asymptomatic and presymptomatic infected individuals. The mathematical foundation of our metapopulation network model is akin to a transport scheme between two population distributions, namely the residential distribution and the workplace distribution, whose interface can be inferred from commuter mobility data made available by the US Census Bureau. We use the proposed metapopulation model to test the dynamics of the spread of COVID-19 on two networks, a smaller one comprising 7 counties in the Greater Cleveland area in Ohio, and a larger one consisting of 74 counties in the Pittsburgh–Cleveland–Detroit corridor following the Lake Erie’s American coastline. The model simulations indicate that densely populated regions effectively act as amplifiers of the infection for the surrounding, less densely populated areas, in agreement with the pattern of infections observed in the course of the COVID-19 pandemic. Computed examples show that the model can be used also to test different mitigation strategies, including one based on state-level travel restrictions, another on county level triggered social distancing, as well as a combination of the two. 

As fish swim through a fluid environment, they must actively use their fins in concert to stabilize their motion and have a robust form of locomotion. However, there is little knowledge of how these forces act on the fish body. In this study, we employ a 3D immersed boundary model to decode the relationship between roll, pitch, and yaw of the fish body and the driving forces acting on flexible fish bodies. Using bluegill sunfish as our representative geometry, we first examine the role of an actuating torque on the stability of the fish model, with a torque applied at the head of the unconstrained fish body. The resulting kinematics is a product of the passive elasticity, fluid forces, and driving torque. We then examine a constrained model to understand the role that fin geometry, body elasticity, and frequency play on the range of corrective forces acting on the fish. We find non-monotonic behavior with respect to frequency, suggesting that the effective flexibility of the fins play an important role in the swimming performance. 

We initiate a fine-grained study of the round complexity of Oblivious RAM (ORAM). We prove that any one-round balls-in-bins ORAM that does not duplicate balls must have either 𝛺(𝑁‾‾√) bandwidth or 𝛺(𝑁‾‾√) client memory, where N is the number of memory slots being simulated. This shows that such schemes are strictly weaker than general (multi-round) ORAMs or those with server computation, and in particular implies that a one-round version of the original square-root ORAM of Goldreich and Ostrovksy (J. ACM 1996) is optimal. We prove this bound via new techniques that differ from those of Goldreich and Ostrovksy, and of Larsen and Nielsen (CRYPTO 2018), which achieved an 𝛺(log𝑁) bound for balls-in-bins and general multi-round ORAMs respectively. Finally we give a weaker extension of our bound that allows for limited duplication of balls, and also show that our bound extends to multiple-round ORAMs of a restricted form that include the best known constructions. 

Current quantum computer designs will not scale. To scale beyond small prototypes, quantum architectures will likely adopt a modular approach with clusters of tightly connected quantum bits and sparser connections between clusters. We exploit this clustering and the statically-known control flow of quantum programs to create tractable partitioning heuristics which map quantum circuits to modular physical machines one time slice at a time. Specifically, we create optimized mappings for each time slice, accounting for the cost to move data from the previous time slice and using a tunable lookahead scheme to reduce the cost to move to future time slices. We compare our approach to a traditional statically-mapped, owner-computes model. Our results show strict improvement over the static mapping baseline. We reduce the non-local communication overhead by 89.8% in the best case and by 60.9% on average. Our techniques, unlike many exact solver methods, are computationally tractable.