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It has recently been realised that illumination by intensely powerful radiation is not the only path to a nonlinear optical response by a given material. As demonstrated for a layer of indium tin oxide (ITO), strong nonlinear effects can be observed in a material for illuminating fields of quite moderate strength in a neighbourhood of the wavelengths which render it an epsilon-near-zero (ENZ) material. Inspired by these observations we introduce, discuss and analyse a rather different formulation of the governing equations for the Capretti experiment with a view towards robust and highly accurate numerical simulation. By contrast to volumetric algorithms which are greatly disadvantaged for the piecewise homogeneous geometries we consider, surface methods provide optimal performance as they only consider interfacial unknowns. In this contribution, we study an interfacial approach which is based upon Dirichlet–Neumann operators (DNOs). We show that, for a layer of nonlinear Kerr medium, the DNO is not only well-defined, but also analytic with respect to all of its independent variables. Our method of proof is perturbative in nature and suggests several new avenues of investigation, including stable numerical simulation, and how one would include the effects of periodic deformations of the layer interfaces into both theory and numerical simulation of the resulting DNOs. This article is part of the theme issue ‘Analytically grounded full-wave methods for advances in computational electromagnetics’. 

As experiments advance to record from tens of thousands of neurons, statistical physics provides a framework for understanding how collective activity emerges from networks of fine-scale correlations. While modeling these populations is tractable in loop-free networks, neural circuitry inherently contains feedback loops of connectivity. Here, for a class of networks with loops, we present an exact solution to the maximum entropy problem that scales to very large systems. This solution provides direct access to information-theoretic measures like the entropy of the model and the information contained in correlations, which are usually inaccessible at large scales. In turn, this allows us to search for the optimal network of correlations that contains the maximum information about population activity. Applying these methods to 45 recordings of approximately 10,000 neurons in the mouse visual system, we demonstrate that our framework captures more information—providing a better description of the population—than existing methods without loops. For a given population, our models perform even better during visual stimulation than spontaneous activity; however, the inferred interactions overlap significantly, suggesting an underlying neural circuitry that remains consistent across stimuli. Generally, we construct an optimized framework for studying the statistical physics of large neural populations, with future applications extending to other biological networks. 

Abstract Seismic and magnetotelluric studies suggest hydrous silicate melts atop the 410 km discontinuity form 30–100 km thick layers. Importantly, in some regions, two layers are observed. These stagnant layers are related to their comparable density to the surrounding mantle, but their formation mechanisms and detailed structures remain unclear. Here we report a large decrease of silicate melt viscosity at ~14 GPa, from 96(5) to 11.7(6) mPa⋅s, as water content increases from 15.5 to 31.8 mol% H₂O. Such low viscosities facilitate rapid segregation of melt, which would typically prevent thick layer accumulation. Our 1D finite element simulations show that continuous dehydration melting of upwelling mantle material produces a primary melt layer above 410 km and a secondary layer at the depth of equal mantle-melt densities. These layers can merge into a single thick layer under low density contrasts or high upwelling rates, explaining both melt doublets and thick single layers. 

Developing microrobotic systems for accurate and fast manipulation of microobjects or living cells has the potential to significantly advance biomedical and microfabrication applications. Despite recent progress in this field, comprehensive multistimuli responsive, fast, and precisely controllable microrobots remain limited. In this study, automated position and speed control of acoustically powered, bubble‐based, magnetically steerable microrobots is demonstrated, along with micromanipulation of mammalian cells using these microswimmers. Enhanced control of the microswimmers is achieved by designing and implementing a closed‐loop control system that guides the microrobots along a predetermined path while modulating their speed by adjusting the acoustic frequency near the resonant value. The microrobots are guided to cells, enabling cell manipulation by pulling them with the microrobots. Overall, the results highlight the capability and controllability of these magnetically and acoustically responsive microrobots for future cell‐based applications, including manipulation, delivery, and microsurgery. 

In the maximum coverage problem we are given d subsets from a universe [n], and the goal is to output k subsets such that their union covers the largest possible number of distinct items. We present the first algorithm for maximum coverage in the turnstile streaming model, where updates which insert or delete an item from a subset come one-by-one. Notably our algorithm only uses polylogn update time. We also present turnstile streaming algorithms for targeted and general fingerprinting for risk management where the goal is to determine which features pose the greatest re-identification risk in a dataset. As part of our work, we give a result of independent interest: an algorithm to estimate the complement of the pth frequency moment of a vector for p ≥ 2. Empirical evaluation confirms the practicality of our fingerprinting algorithms demonstrating a speedup of up to 210x over prior work.