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Graphical abstract, We here introduce the third major release of the SIMPLE (Single-particle IMage Processing Linux Engine) open-source software package for analysis of cryogenic transmission electron microscopy (cryo-EM) movies of single-particles (Single-Particle Analysis, SPA). Development of SIMPLE 3.0 has been focused on real-time data processing using minimal CPU computing resources to allow easy and cost-efficient scaling of processing as data rates escalate. Our stream SPA tool implements the steps of anisotropic motion correction and CTF estimation, rapid template-based particle identification and 2D clustering with automatic class rejection. SIMPLE 3.0 additionally features an easy-to-use web-based graphical user interface (GUI) that can be run on any device (workstation, laptop, tablet or phone) and supports a remote multi-user environment over the network. The new project-based execution model automatically records the executed workflow and represents it as a flow diagram in the GUI. This facilitates meta-data handling and greatly simplifies usage. Using SIMPLE 3.0, it is possible to automatically obtain a clean SP data set amenable to high-resolution 3D reconstruction directly upon completion of the data acquisition, without the need for extensive image processing post collection. Only minimal standard CPU computing resources are required to keep up with a rate of ∼300 Gatan K3 direct electron detector movies per hour. SIMPLE 3.0 is available for download from simplecryoem.com.

Algorithms for atomic-resolution 3D reconstruction of nanocrystals imaged in solution with electron microscopy are introduced., Analysis of the three-dimensional (3D) structures of nanocrystals with solution-phase transmission electron microscopy is beginning to reveal their unique physiochemical properties. We developed a “one-particle Brownian 3D reconstruction method” based on imaging of ensembles of colloidal nanocrystals using graphene liquid cell electron microscopy. Projection images of differently rotated nanocrystals are acquired using a direct electron detector with high temporal (

We analyze a method for the creation, storage, and retrieval of optomechanical Schr\"odinger cat states, in which there is a quantum superposition of two distinct macroscopic states of a mechanical oscillator. In the quantum memory protocol, an optical cat state is first prepared in an optical cavity, then transferred to the mechanical mode, where it is stored and later retrieved using control fields. We carry out numerical simulations for the quantum memory protocol for optomechanical cat states using the positive-P phase space representation. This has a compact, positive representation for a cat state, thus allowing a probabilistic simulation of this highly nonclassical quantum system. It is essential to use importance sampling to carry out the simulation effectively. To verify the effectiveness of the cat-state quantum memory, we consider several cat-state signatures and show how they can be computed. We also investigate the effects of decoherence on a cat state by solving the standard master equation for a simplified model analytically, allowing us to compare with the numerical results. Focusing on the negativity of the Wigner function as a signature of the cat state, we evaluate analytically an upper bound on the time taken for the negativity to vanish, for a given temperature of the environment of the mechanical oscillator. We show consistency with the numerical methods. These provide exact solutions, allowing a full treatment of decoherence in an experiment that involves creating, storing, and retrieving mechanical cat states using temporally mode-matched input and output pulses. Our analysis treats the internal optical and mechanical modes of an optomechanical oscillator, and the complete set of input and output field modes which become entangled with the internal modes. The model includes decoherence due to thermal effects in the mechanical reservoirs, as well as optical and mechanical losses.

Cryogenic electron microscopy (cryo-EM) and single-particle analysis enables determination of near-atomic resolution structures of biological molecules. However, large computational requirements limit throughput and rapid testing of new image processing tools. We developed PRIME, an algorithm part of the SIMPLE software suite, for determination of the relative 3D orientations of single-particle projection images. PRIME has primarily found use for generation of an initial ab initio 3D reconstruction. Here we show that the strategy behind PRIME, iterative estimation of per-particle orientation distributions with stochastic hill climbing, provides a competitive approach to near-atomic resolution single-particle 3D reconstruction. A number of mathematical techniques for accelerating the convergence rate are introduced, leading to a speedup of nearly two orders of magnitude. We benchmarked our developments on numerous publicly available data sets and conclude that near-atomic resolution ab initio 3D reconstructions can be obtained with SIMPLE in a matter of hours, using standard over-the-counter CPU workstations.

Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales proportionate to 1/N_S for N_S samples. In this paper, we obtain a new class of variance reduction methods for treating stochastic equations, called parallel optimized sampling. The objective of parallel optimized sampling is to reduce the sampling variance in the observables of an ensemble of stochastic trajectories. This is achieved through calculating a finite set of observables - typically statistical moments - in parallel, and minimizing the errors compared to known values. The algorithm is both numerically efficient and unbiased. Importantly, it does not increase the errors in higher order moments, and generally reduces such errors as well. The same procedure is applied both to initial ensembles and to changes in a finite time-step. Results of these methods show that errors in initially optimized moments can be reduced to the machine precision level, typically around 10^(-16) in current hardware. For nonlinear stochastic equations, sampled moment errors during time-evolution are larger than this, due to error propagation effects. Even so, we provide evidence for error reductions of up to two orders of magnitude in a nonlinear equation example, for low order moments, which is a large practical benefit. The sampling variance typically scales as 1/N_S, but with the advantage of a very much smaller prefactor than for standard, non-optimized methods., Comment: 32 pages

A strategy for generating entanglement between two separated optomechanical oscillators is analyzed, using entangled radiation produced from down-conversion and stored in an initiating cavity. We show that the use of pulsed entanglement with optimally shaped temporal modes can efficiently transfer quantum entanglement into a mechanical mode, then remove it after a fixed waiting time for measurement. This protocol could provide new avenues for testing for bounds on decoherence in massive systems that are spatially separated, as originally suggested by Furry not long after the discussion by Einstein-Podolsky-Rosen and Schr\"odinger of entanglement.

We examine the $N$-partite quaternion and octonion dichotomic Bell inequalities derived by Vogel and Shchukin utilizing the square identities of Euler and Degen, which apply to experiments with $M$ settings at each spatially separated site. We reveal these inequalities to be violated by the Greenberger-Horne-Zeilinger state, for $N\ensuremath{\ge}3$ and $2\ensuremath{\le}M\ensuremath{\le}8$. Violations are robust with respect to loss, the threshold detection efficiency being $\ensuremath{\eta}g{2}^{\frac{2}{N}\ensuremath{-}1}$ for all $M$, implying violations for efficiencies as low as $\ensuremath{\eta}\ensuremath{\sim}50%$ at each site, as $N\ensuremath{\rightarrow}\ensuremath{\infty}$.

We demonstrate a complete, probabilistic quantum dynamical simulation of the standard nonlinear Hamiltonian of optomechanics, including decoherence at finite temperatures. Robust entanglement of a photonic pulse with a mechanical oscillator is predicted. Our exact quantum simulations use the positive-$P$ technique, are scalable to large Hilbert spaces, and give excellent agreement with recent experiments. We predict the required conditions for the next stage in this research. Strong quantum steering between the photonic and mechanical systems is possible, depending on thermal occupation. This is more viable in optical than in electromechanical experiments.

We have revisited glueball mixing with the pseudoscalar mesons in the MIT bag model scheme. The calculation has been performed in the spherical cavity approximation to the bag using two different fermion propagators, the cavity and the free propagators. We obtain probabilities of mixing for the $\ensuremath{\eta}$ at the level of 0.006%--2.0%, while for the ${\ensuremath{\eta}}^{\ensuremath{'}}$ one at the level of 0.6%--40%, depending on the choice of bag radius and, therefore, of the strong coupling constant. Our results differ from previous calculations. The origin of our difference stems from the treatment of the time integrations. The comparison of our calculation with experimental data, which is consistent with small $\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{-}G$ mixing, implies that the pseudoscalar glueball is small, $R\ensuremath{\sim}0.5--0.6\text{ }\text{ }\mathrm{fm}$ and has a large mass, ${M}_{G}\ensuremath{\sim}2000--2500\text{ }\text{ }\mathrm{MeV}$.

We give a brief history of probabilistic quantum simulations of Einstein–Podolsky–Rosen paradoxes. This treats the early origins of the modern proposals using continuous variables, simulation methods using the positive-P representation, and current developments. Recent simulations treated include the behavior of parametric downconversion near the critical point, the simulation of parametric Bell violations, quantum entanglement, and correlations in optomechanics, as well as extensions to quantum field systems with planar interferometers.