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Bragg coherent X‐ray diffraction imaging (BCDI) has emerged as a powerful technique for strain imaging and morphology reconstruction of nanometre‐scale crystals. However, BCDI often suffers from angular distortions that appear during data acquisition, caused by radiation pressure, heating or imperfect scanning stages. This limits the applicability of BCDI, in particular for small crystals and high‐flux X‐ray beams. Here, we present a pre‐processing algorithm that recovers the 3D datasets from the BCDI dataset measured under the impact of large angular distortions. We systematically investigate the performance of this method for different levels of distortion and find that the algorithm recovers the correct angles for distortions up to 16.4× (1640%) the angular step size dθ = 0.004°. We also show that the angles in a continuous scan can be recovered with high accuracy. As expected, the correction provides marked improvements in the subsequent phase retrieval. An algorithm has been developed that effectively corrects and tracks angular distortions, enabling BCDI to work much more robustly and accurately in a wider range of challenging experimental scenarios.

Since free-space optical links (especially fully photonic ones) are very challenging to accurately align; scanning algorithms are used for the initial search and alignment of the transceivers. The initial alignment aims to intercept the optical beam so that it hits a position-sensitive detector. However, this operation can be very time-consuming (depending on the system parameters, such as transceiver parameters, distance between transceivers, divergence of the transmitter, angle of view of the receiver, etc.). A spiral scan is used as the most widespread pattern for scanning. This article examines the effects of system parameters (e.g., global navigation satellite systems and compass accuracy) on the angular area of uncertainty that must be scanned to find the optical beam. Furthermore, several types of spiral pattern are compared depending on the time of the scan execution and the required number of points for scanning the given uncertainty area. The cut hexagonal spiral scan achieved the best results as it required 18.1% less time than the common spiral scan for the presented transceiver.

Entanglement of the properties of two separated particles constitutes a fundamental signature of quantum mechanics and is a key resource for quantum information science. We demonstrate strong Einstein, Podolsky, and Rosen correlations between the angular position and orbital angular momentum of two photons created by the nonlinear optical process of spontaneous parametric down-conversion. The discrete nature of orbital angular momentum and the continuous but periodic nature of angular position give rise to a special sort of entanglement between these two variables. The resulting correlations are found to be an order of magnitude stronger than those allowed by the uncertainty principle for independent (nonentangled) particles. Our results suggest that angular position and orbital angular momentum may find important applications in quantum information science.

In this work we study various notions of uncertainty for angular momentum in the spin-s representation of SU(2). We characterize the 'uncertainty regions' given by all vectors, whose components are specified by the variances of the three angular momentum components. A basic feature of this set is a lower bound for the sum of the three variances. We give a method for obtaining optimal lower bounds for uncertainty regions for general operator triples, and evaluate these for small s. Further lower bounds are derived by generalizing the technique by which Robertson obtained his state-dependent lower bound. These are optimal for large s, since they are saturated by states taken from the Holstein-Primakoff approximation. We show that, for all s, all variances are consistent with the so-called vector model, i.e., they can also be realized by a classical probability measure on a sphere of radius Entropic uncertainty relations can be discussed similarly, but are minimized by different states than those minimizing the variances for small s. For large s the Maassen-Uffink bound becomes sharp and we explicitly describe the extremalizing states. Measurement uncertainty, as recently discussed by Busch, Lahti and Werner for position and momentum, is introduced and a generalized observable (POVM) which minimizes the worst case measurement uncertainty of all angular momentum components is explicitly determined, along with the minimal uncertainty. The output vectors for the optimal measurement all have the same length where as

Some of the important geodetic time series used in various Earth science disciplines are provided without uncertainty estimates. This can affect the validity of conclusions based on such data. However, an efficient uncertainty quantification algorithm to tackle this problem is currently not available. Here we present a methodology to approximate the aleatoric uncertainty in time series, called Bayesian Hamiltonian Monte Carlo Autoencoders (BaHaMAs). BaHaMAs is based on three elements: (1) self-supervised autoencoders that learn the underlying structure of the time series, (2) Bayesian machine learning that accurately quantifies the data uncertainty, and (3) Monte Carlo sampling that follows the Hamiltonian dynamics. The method can be applied in various fields in the Earth sciences. As an example, we focus on Atmospheric and Oceanic Angular Momentum time series (AAM and OAM, respectively), which are typically provided without uncertainty information. We apply our methodology to 3-hourly AAM and OAM time series and quantify the uncertainty in the data from 1976 up to the end of 2022. Furthermore, since Length of Day (LOD) is a geodetic time series that is closely connected to AAM and OAM and its short-term prediction is important for various space-geodetic applications, we show that the use of the derived uncertainties alongside the time series of AAM and OAM improves the prediction performance of LOD on average by 17% for different time spans. Finally, a comparison with alternative uncertainty quantification baseline methods, i.e., variational autoencoders and deep ensembles, reveals that BaHaMAs is more accurate in quantifying uncertainty. Graphical Abstract

This paper presents updated estimates of source parameters for GW150914, a binary black-hole coalescence event detected by the Laser Interferometer Gravitational-wave Observatory (LIGO) in 2015 [Abbott et al. Phys. Rev. Lett. 116, 061102 (2016).]. Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016).] presented parameter estimation of the source using a 13-dimensional, phenomenological precessing-spin model (precessing IMRPhenom) and an 11-dimensional nonprecessing effective-one-body (EOB) model calibrated to numerical-relativity simulations, which forces spin alignment (nonprecessing EOBNR). Here, we present new results that include a 15-dimensional precessing-spin waveform model (precessing EOBNR) developed within the EOB formalism. We find good agreement with the parameters estimated previously [Abbott et al. Phys. Rev. Lett. 116, 241102 (2016).], and we quote updated component masses of 35(+5)(-3) solar M; and 30(+3)(-4) solar M; (where errors correspond to 90 symmetric credible intervals). We also present slightly tighter constraints on the dimensionless spin magnitudes of the two black holes, with a primary spin estimate is less than 0.65 and a secondary spin estimate is less than 0.75 at 90% probability. Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016).] estimated the systematic parameter-extraction errors due to waveform-model uncertainty by combining the posterior probability densities of precessing IMRPhenom and nonprecessing EOBNR. Here, we find that the two precessing-spin models are in closer agreement, suggesting that these systematic errors are smaller than previously quoted.

The ramming coordination mechanism is a critical component of the artillery automatic loading system. Its primary function is to receive projectiles from the manipulator and align them parallel to the bore axis, facilitating subsequent chambering of the projectiles. The reliability of the ramming coordination mechanism directly influences the subsequent precision of chambering. Therefore, analysing the boundary response of this mechanism is crucial for subsequent reliability assessments. In response to the issue of interval uncertainty response for the ramming coordination mechanism, this paper proposes a method that combines sequential simulation strategy with rigid-flexible coupled dynamic analysis. First, a ramming coordination mechanism rigid-flexible coupled controlled dynamic model considering clearances is constructed based on its motion principle. Subsequently, the sequential method is employed to solve the boundary response, resulting in the boundary response curve of angular displacement for the ramming coordination mechanism. The results indicate that the method combining sequential simulation with rigid-flexible coupled dynamic analysis can more efficiently solve the boundary response of the mechanism. Moreover, the uncertainty factors present during the initial coordination and velocity mutation moments significantly impact the motion precision of the mechanism, potentially leading to motion failure in severe cases. This provides a reference for the subsequent reliability analysis of the mechanism.

This study presents a novel uncertainty estimation algorithm that aims to enhance the accuracy of a reduced-order dynamic model for a flexible-joint lever arm (FJLA). The model uncertainties are compensated by adding a complementary term to the reduced-order model, upgrading it to the real model. The gyroscope bias in measuring the angular velocity is corrected by fusing the information of encoder/gyroscope. The effective data fusion is provided by adaptive adjustment of the estimator coefficient. The constructed model, with low order but rich content, is reliable for use in the position controller of FJLA, developed by a continuous predictive method. The control system adapts itself to real conditions and is cost-effective due to the use of fewer sensors. The saturation of motor torque, as the control input, is modeled within the structure of a constrained optimization problem solved by Karush–Kuhn–Tucker Theorem. The boundedness of the mean and covariance of tracking error and its derivative are demonstrated by stochastic analysis. The results of simulations and experimental implementations demonstrate the high efficiency of the proposed system in controlling the position of the FJLA under different trajectories. Moreover, the comparative results with the other methods show a great performance for the suggested control system in rejecting disturbances and other uncertainties under saturated control input.

State‐of‐the‐art navigated transcranial magnetic stimulation (nTMS) systems can display the TMS coil position relative to the structural magnetic resonance image (MRI) of the subject's brain and calculate the induced electric field. However, the local effect of TMS propagates via the white‐matter network to different areas of the brain, and currently there is no commercial or research neuronavigation system that can highlight in real time the brain's structural connections during TMS. This lack of real‐time visualization may overlook critical inter‐individual differences in brain connectivity and does not provide the opportunity to target brain networks. In contrast, real‐time tractography enables on‐the‐fly parameter tuning and detailed exploration of connections, which is computationally inefficient and limited with offline methods. To target structural brain connections, particularly in network‐based treatments like major depressive disorder, a real‐time tractography‐based neuronavigation solution is needed to account for each individual's unique brain connectivity. The objective of this work is to develop a real‐time tractography‐assisted TMS neuronavigation system and investigate its feasibility. We propose a modular framework that seamlessly integrates offline (preparatory) analysis of diffusion MRI data with online (real‐time) probabilistic tractography using the parallel transport approach. For tractography and neuronavigation, we combine our open source software Trekker and InVesalius, respectively. We evaluate our system using synthetic data and MRI scans of four healthy volunteers obtained using a multi‐shell high‐angular resolution diffusion imaging protocol. The feasibility of our online approach is assessed by studying four major TMS targets via comparing streamline count and overlap against offline tractography results based on filtering of one hundred million streamlines. Our development of a real‐time tractography‐assisted TMS neuronavigation system showcases advanced tractography techniques, with interactive parameter tuning and real‐time visualization of thousands of streamlines via an innovative uncertainty visualization method. Our analysis reveals considerable variability among subjects and TMS targets in the streamline count, for example, while 15,000 streamlines were observed for the TMS target on the visual cortex (V1) of subject #4, in the case of subject #3's V1, no streamlines were obtained. Overlap analysis against offline tractograms demonstrated that real‐time tractography can quickly cover a substantial part of the target areas' connectivity, often surpassing the coverage of offline approaches within seconds. For instance, significant portions of Broca's area and the primary motor cortex were effectively visualized after generating tens of thousands of streamlines, highlighting the system's efficiency and feasibility in capturing brain connectivity in real‐time. Overall, our work shows that real‐time tractography‐assisted TMS neuronavigation is feasible. With our system, it is possible to target specific brain regions based on their structural connectivity, and to aim for the fiber tracts that make up the brain's networks. Real‐time tractography provides new opportunities for TMS targeting through novel visualization techniques without compromising structural connectivity estimates when compared to the offline approach. We developed a real‐time tractography‐assisted transcranial magnetic stimulation (TMS) neuronavigation system capable of showing structural brain networks during TMS applications using novel visualization techniques. Our system enables targeting of neuronal networks and brain regions based on their connectivity. Our research demonstrates the feasibility of real‐time tractography‐assisted neuronavigation, expanding the possibilities for TMS‐based brain stimulation. Furthermore, we shared our tools as open‐source software to accelerate progress in this research domain.

A bstract A new phase for the measurements of radiative decay modes in b → s transitions has started with new measurements of exclusive modes by LHCb and with Belle-II showing distinctive promises in both inclusive and exclusive channels. After critically reviewing the hadronic uncertainties in exclusive radiative decays, we analyze the impact of recent measurements of the branching ratio and mass-eigenstate rate asymmetry in B s → ϕγ and of the angular distribution of B → K ∗ e + e − at low q 2 on new physics in the b → s γ transition.