Testing dynamic correlations and nonlinearity in bivariate time series through information measures and surrogate data analysis.

The increasing availability of time series data depicting the evolution of physical system properties has prompted the development of methods focused on extracting insights into the system behavior over time, discerning whether it stems from deterministic or stochastic dynamical systems. Surrogate data testing plays a crucial role in this process by facilitating robust statistical assessments. This ensures that the observed results are not mere occurrences by chance, but genuinely reflect the inherent characteristics of the underlying system. The initial process involves formulating a null hypothesis, which is tested using surrogate data in cases where assumptions about the underlying distributions are absent. A discriminating statistic is then computed for both the original data and each surrogate data set. Significantly deviating values between the original data and the surrogate data ensemble lead to the rejection of the null hypothesis. In this work, we present various surrogate methods designed to assess specific statistical properties in random processes. Specifically, we introduce methods for evaluating the presence of autodependencies and nonlinear dynamics within individual processes, using Information Storage as a discriminating statistic. Additionally, methods are introduced for detecting coupling and nonlinearities in bivariate processes, employing the Mutual Information Rate for this purpose. The surrogate methods introduced are first tested through simulations involving univariate and bivariate processes exhibiting both linear and nonlinear dynamics. Then, they are applied to physiological time series of Heart Period (RR intervals) and respiratory flow (RESP) variability measured during spontaneous and paced breathing. Simulations demonstrated that the proposed methods effectively identify essential dynamical features of stochastic systems. The real data application showed that paced breathing, at low breathing rate, increases the predictability of the individual dynamics of RR and RESP and dampens nonlinearity in their coupled dynamics.

Single-particle cryo-EM structures from iDPC-STEM at near-atomic resolution.

In electron cryomicroscopy (cryo-EM), molecular images of vitrified biological samples are obtained by conventional transmission microscopy (CTEM) using large underfocuses and subsequently computationally combined into a high-resolution three-dimensional structure. Here, we apply scanning transmission electron microscopy (STEM) using the integrated differential phase contrast mode also known as iDPC-STEM to two cryo-EM test specimens, keyhole limpet hemocyanin (KLH) and tobacco mosaic virus (TMV). The micrographs show complete contrast transfer to high resolution and enable the cryo-EM structure determination for KLH at 6.5 Å resolution, as well as for TMV at 3.5 Å resolution using single-particle reconstruction methods, which share identical features with maps obtained by CTEM of a previously acquired same-sized TMV data set. These data show that STEM imaging in general, and in particular the iDPC-STEM approach, can be applied to vitrified single-particle specimens to determine near-atomic resolution cryo-EM structures of biological macromolecules.

Atomic imaging of zeolite-confined single molecules by electron microscopy.

Single-molecule imaging with atomic resolution is a notable method to study various molecular behaviours and interactions1-5. Although low-dose electron microscopy has been proved effective in observing small molecules6-13, it has not yet helped us achieve an atomic understanding of the basic physics and chemistry of single molecules in porous materials, such as zeolites14-16. The configurations of small molecules interacting with acid sites determine the wide applications of zeolites in catalysis, adsorption, gas separation and energy storage17-21. Here we report the atomic imaging of single pyridine and thiophene confined in the channel of zeolite ZSM-5 (ref. 22). On the basis of integrated differential phase contrast scanning transmission electron microscopy (iDPC-STEM)23-25, we directly observe the adsorption and desorption behaviours of pyridines in ZSM-5 under the in situ atmosphere. The adsorption configuration of single pyridine is atomically resolved and the S atoms in thiophenes are located after comparing imaging results with calculations. The strong interactions between molecules and acid sites can be visually studied in real-space images. This work provides a general strategy to directly observe these molecular structures and interactions in both the static image and the in situ experiment, expanding the applications of electron microscopy to the further study of various single-molecule behaviours with high resolution.

Imaging biological samples by integrated differential phase contrast (iDPC) STEM technique.

Scanning transmission electron microscopy (STEM) is a powerful imaging technique and has been widely used in current material science research. The attempts of applying STEM (annual dark field (ADF)-STEM or annular bright field (ABF)-STEM) into biological research have been going on for decades while applications have still been limited because of the existing bottlenecks in dose efficiency and non-linearity in contrast. Recently, integrated differential phase contrast (iDPC) STEM technique emerged and achieved a linear phase contrast imaging condition, while resolving signals of light elements next to heavy ones even at low electron dose. This enables successful investigation of beam sensitive materials. Here, we investigate iDPC-STEM advantages in biology, in particular, chemically fixed and resin embedded biological tissues. By comparing results to the conventional TEM, we have found that iDPC-STEM not only shows better contrast but also resolves more structural details at molecular level, including conditions of extremely low dose and minimal heavy-atom staining. We also compare iDPC-STEM with ABF-STEM and found that contrast of iDPC-STEM is even further improved, moderately in lower frequency domains while highly with preserving high frequency biological structural details. For thick sample sections, iDPC-STEM is particularly advantageous. It avoids contrast inversion canceling effects, and by adjusting the depth of focus, fully preserves the contrast of structural details along with the sample. In addition, using depth-sectioning, iDPC-STEM enables resolving in-depth structural variation. Our results suggest that iDPC-STEM have the place and advantages within the future biological research.

Imaging atomic motion of light elements in 2D materials with 30 kV electron microscopy.

Scanning transmission electron microscopy (STEM) is the most widespread adopted tool for atomic scale characterization of two-dimensional (2D) materials. However, damage free imaging of 2D materials with electrons has remained problematic even with powerful low-voltage 60 kV-microscopes. An additional challenge is the observation of light elements in combination with heavy elements, particularly when recording fast dynamical phenomena. Here, we demonstrate that 2D WS2 suffers from electron radiation damage during 30 kV-STEM imaging, and we capture beam-induced defect dynamics in real-time by atomic electrostatic potential imaging using integrated differential phase contrast (iDPC)-STEM. The fast imaging of atomic electrostatic potentials with iDPC-STEM reveals the presence and motion of single sulfur atoms near defects and edges in WS2 that are otherwise invisible at the same imaging dose at 30 kV with conventional annular dark-field STEM, and has a vast speed and data processing advantage over electron detector camera based STEM techniques like electron ptychography.

Assessment of Cardiorespiratory Interactions during Apneic Events in Sleep via Fuzzy Kernel Measures of Information Dynamics.

Apnea and other breathing-related disorders have been linked to the development of hypertension or impairments of the cardiovascular, cognitive or metabolic systems. The combined assessment of multiple physiological signals acquired during sleep is of fundamental importance for providing additional insights about breathing disorder events and the associated impairments. In this work, we apply information-theoretic measures to describe the joint dynamics of cardiorespiratory physiological processes in a large group of patients reporting repeated episodes of hypopneas, apneas (central, obstructive, mixed) and respiratory effort related arousals (RERAs). We analyze the heart period as the target process and the airflow amplitude as the driver, computing the predictive information, the information storage, the information transfer, the internal information and the cross information, using a fuzzy kernel entropy estimator. The analyses were performed comparing the information measures among segments during, immediately before and after the respiratory event and with control segments. Results highlight a general tendency to decrease of predictive information and information storage of heart period, as well as of cross information and information transfer from respiration to heart period, during the breathing disordered events. The information-theoretic measures also vary according to the breathing disorder, and significant changes of information transfer can be detected during RERAs, suggesting that the latter could represent a risk factor for developing cardiovascular diseases. These findings reflect the impact of different sleep breathing disorders on respiratory sinus arrhythmia, suggesting overall higher complexity of the cardiac dynamics and weaker cardiorespiratory interactions which may have physiological and clinical relevance.

A single-molecule van der Waals compass.

Single-molecule imaging is challenging but highly beneficial for investigating intermolecular interactions at the molecular level1-6. Van der Waals interactions at the sub-nanometre scale strongly influence various molecular behaviours under confinement conditions7-11. Inspired by the traditional compass12, here we use a para-xylene molecule as a rotating pointer to detect the host-guest van der Waals interactions in the straight channel of the MFI-type zeolite framework. We use integrated differential phase contrast scanning transmission electron microscopy13-15 to achieve real-space imaging of a single para-xylene molecule in each channel. A good correlation between the orientation of the single-molecule pointer and the atomic structure of the channel is established by combining the results of calculations and imaging studies. The orientations of para-xylene help us to identify changes in the van der Waals interactions, which are related to the channel geometry in both spatial and temporal dimensions. This work not only provides a visible and sensitive means to investigate host-guest van der Waals interactions in porous materials at the molecular level, but also encourages the further study of other single-molecule behaviours using electron microscopy techniques.

Analysis of depth-sectioning STEM for thick samples and 3D imaging.

We derive a model that describes 3D volume imaging in depth-sectioning STEM that is valid for all STEM techniques under three well-defined conditions: linearity, undisturbed probe and elastic scattering. The resulting undisturbed probe model generalizes the widely used idea that the undisturbed probe intensity in three dimensions can be used as the point spread function for depth-sectioning ADF-STEM to all STEM techniques including (A)BF- and iDPC-STEM. The model provides closed expressions for depth-sectioning STEM, which follow directly from the 2D expressions for thin samples, and thereby enables analysis of the 3D resolution. Using the model we explore the consequences of the resulting 3D contrast transfer function (CTF) for the z-resolution at different length scales and illustrate this with experiments. We investigate the validity and limitations of the model using multi-slice simulations showing that it is valid and quantitatively accurate for relatively thick amorphous samples but not for crystalline samples in zone-axis due to channeling. We compare depth-sectioning in iDPC- and ADF-STEM and show that iDPC-STEM can extract information from deeper into the sample, all the way till the bottom of the sample, thereby effectively allowing a thickness measurement. Also the difference in optimal focus conditions between iDPC- and ADF-STEM is explained. Finally, we propose practical criteria for deciding whether a sample is thin or thick.

Phase contrast scanning transmission electron microscopy imaging of light and heavy atoms at the limit of contrast and resolution.

Using state of the art scanning transmission electron microscopy (STEM) it is nowadays possible to directly image single atomic columns at sub-Å resolution. In standard (high angle) annular dark field STEM ((HA)ADF-STEM), however, light elements are usually invisible when imaged together with heavier elements in one image. Here we demonstrate the capability of the recently introduced Integrated Differential Phase Contrast STEM (iDPC-STEM) technique to image both light and heavy atoms in a thin sample at sub-Å resolution. We use the technique to resolve both the Gallium and Nitrogen dumbbells in a GaN crystal in [[Formula: see text]] orientation, which each have a separation of only 63 pm. Reaching this ultimate resolution even for light elements is possible due to the fact that iDPC-STEM is a direct phase imaging technique that allows fine-tuning the microscope while imaging. Apart from this qualitative imaging result, we also demonstrate a quantitative match of ratios of the measured intensities with theoretical predictions based on simulations.

Phase contrast STEM for thin samples: Integrated differential phase contrast.

It has been known since the 1970s that the movement of the center of mass (COM) of a convergent beam electron diffraction (CBED) pattern is linearly related to the (projected) electrical field in the sample. We re-derive a contrast transfer function (CTF) for a scanning transmission electron microscopy (STEM) imaging technique based on this movement from the point of view of image formation and continue by performing a two-dimensional integration on the two images based on the two components of the COM movement. The resulting integrated COM (iCOM) STEM technique yields a scalar image that is linear in the phase shift caused by the sample and therefore also in the local (projected) electrostatic potential field of a thin sample. We confirm that the differential phase contrast (DPC) STEM technique using a segmented detector with 4 quadrants (4Q) yields a good approximation for the COM movement. Performing a two-dimensional integration, just as for the COM, we obtain an integrated DPC (iDPC) image which is approximately linear in the phase of the sample. Beside deriving the CTFs of iCOM and iDPC, we clearly point out the objects of the two corresponding imaging techniques, and highlight the differences to objects corresponding to COM-, DPC-, and (HA) ADF-STEM. The theory is validated with simulations and we present first experimental results of the iDPC-STEM technique showing its capability for imaging both light and heavy elements with atomic resolution and a good signal to noise ratio (SNR).

Analysis of HR-STEM theory for thin specimen.

A compact mathematical model of the STEM imaging process including bright field (BF) and dark field (DF) is derived. This description is valid for thin samples, does not rely on the weak phase approximation and does not require time-consuming simulation of the scanning process. It is well-known that STEM imaging is a nonlinear technique and therefore cannot be described in terms of a sample-independent linear contrast transfer function (CTF). In this work we derive a nonlinear description showing that a STEM image can in fact be described with two terms. Both terms are cross-correlations between a function that is independent of the sample and a function that depends only on the sample. The latter two can be seen as two different objects. These objects directly correspond to two specific cases: the weak phase approximation (WPA) and annular dark field (ADF) imaging, which are known from the literature. We clarify the need for recognizing and understanding what the object is of any particular STEM technique. The model was validated using simulated STEM images and an excellent agreement as well as a reduction in computation time of 3 orders of magnitude was found.

Revisiting the Al/Al2O3 interface: coherent interfaces and misfit accommodation.

We study the coherent and semi-coherent Al/α-Al2O3 interfaces using molecular dynamics simulations with a mixed, metallic-ionic atomistic model. For the coherent interfaces, both Al-terminated and O-terminated nonstoichiometric interfaces have been studied and their relative stability has been established. To understand the misfit accommodation at the semi-coherent interface, a 1-dimensional (1D) misfit dislocation model and a 2-dimensional (2D) dislocation network model have been studied. For the latter case, our analysis reveals an interface dislocation structure with a network of three sets of parallel dislocations, each with pure-edge character, giving rise to a pattern of coherent and stacking-fault-like regions at the interface. Structural relaxation at elevated temperatures leads to a further change of the dislocation pattern, which can be understood in terms of a competition between the stacking fault energy and the dislocation interaction energy at the interface. Our results are expected to serve as an input for the subsequent dislocation dynamics models to understand and predict the macroscopic mechanical behavior of Al/α-Al2O3 composite heterostructures.

Scanning electron microscopy of individual nanoparticle bio-markers in liquid.

We investigated SEM imaging of nanoparticle biomarkers suspended below a thin membrane, with the ultimate goal of integrating functional fluorescence and structural SEM measurements of samples kept at ambient or hydrated conditions. In particular, we investigated how resolving power in liquid SEM is affected by the interaction of the electron beam with the membrane. Simulations with the Geant4-based Monte Carlo scheme developed by Kieft and Bosch (2008) [1] are compared to experimental results with suspended nanoparticles. For 20 nm and 50 nm thin membranes, we found a beam broadening of 1.5 nm and 3 nm, respectively, with an excellent agreement between simulations and experiments. 15 nm Au nanoparticles and bio-functionalized core-shell quantum dots can be individually resolved in denser clusters. We demonstrated the imaging of single EGF-conjugated quantum dots docked at filopodia during cellular uptake with both fluorescence microscopy and SEM simultaneously. These results open novel opportunities for correlating live fluorescence microscopy with structural electron microscopy.

Image formation modeling in cryo-electron microscopy.

Accurate modeling of image formation in cryo-electron microscopy is an important requirement for quantitative image interpretation and optimization of the data acquisition strategy. Here we present a forward model that accounts for the specimen's scattering properties, microscope optics, and detector response. The specimen interaction potential is calculated with the isolated atom superposition approximation (IASA) and extended with the influences of solvent's dielectric and ionic properties as well as the molecular electrostatic distribution. We account for an effective charge redistribution via the Poisson-Boltzmann approach and find that the IASA-based potential forms the dominant part of the interaction potential, as the contribution of the redistribution is less than 10%. The electron wave is propagated through the specimen by a multislice approach and the influence of the optics is included via the contrast transfer function. We incorporate the detective quantum efficiency of the camera due to the difference between signal and noise transfer characteristics, instead of using only the modulation transfer function. The full model was validated against experimental images of 20S proteasome, hemoglobin, and GroEL. The simulations adequately predict the effects of phase contrast, changes due to the integrated electron flux, thickness, inelastic scattering, detective quantum efficiency and acceleration voltage. We suggest that beam-induced specimen movements are relevant in the experiments whereas the influence of the solvent amorphousness can be neglected. All simulation parameters are based on physical principles and, when necessary, experimentally determined.