Real Space Research Articles

Fluorescence complementation-based FRET imaging reveals centromere assembly dynamics.

Visualization of specific molecules and their assembly in real time and space is essential to delineate how cellular dynamics and signaling circuit are orchestrated during cell division cycle. Our recent studies reveal structural insights into human centromere-kinetochore core CCAN complex. Here we introduce a method for optically imaging trimeric and tetrameric protein interactions at nanometer spatial resolution in live cells using fluorescence complementation-based Förster resonance energy transfer (FC-FRET). Complementary fluorescent protein molecules were first used to visualize dimerization followed by FRET measurements. Using FC-FRET, we visualized centromere CENP-SXTW tetramer assembly dynamics in live cells, and dimeric interactions between CENP-TW dimer and kinetochore protein Spc24/25 dimer in dividing cells. We further delineated the interactions of monomeric CENP-T with Spc24/25 dimer in dividing cells. Surprisingly, our analyses revealed critical role of CDK1 kinase activity in the initial recruitment of Spc24/25 by CENP-T. However, interactions between CENP-T and Spc24/25 during chromosome segregation is independent of CDK1. Thus, FC-FRET provides a unique approach to delineate spatiotemporal dynamics of trimerized and tetramerized proteins at nanometer scale and establishes a platform to report the precise regulation of multimeric protein interactions in space and time in live cells.

Double inertial Forward–Backward–Forward method with adaptive step-size for variational inequalities with quasi-monotonicity

The paper introduce a new inertial forward–backward–forward method with adaptive step size constructed by double inertial extrapolation steps and relaxations to solve variational inequalities with quasi-monotonicity in real Hilbert spaces. We obtain weak and strong convergence results for our propose inertial Forward–Backward–Forward method under some mild conditions. Linear convergence results under a special case of our proposed method are given. Preliminary numerical results show that our proposed method is competitive with other related methods in the literature.

Arbitrary coefficient assignment to the characteristic function of the scalar type for linear systems with state delays by linear static delayed output feedback

We consider a control system defined by a system of linear differential equations in real or complex space with multiple lumped and distributed delays in the state variable. For this system, we study the problem of arbitrary coefficient assignment for the characteristic function of the scalar type by linear static delayed output feedback with lumped and distributed delays. We obtain necessary and sufficient conditions for solvability of the arbitrary coefficient assignment problem by the static delayed output feedback controller when the system coefficients have a special form. Corollaries on arbitrary finite spectrum assignment and on stabilization of the system are obtained. We prove that the obtained results generalize the corresponding theorem proved earlier for a control system defined by a linear delay-differential equation of nth order. Examples are presented illustrating the results obtained.

Real space characterization of nonlinear hall effect in confined directions

The nonlinear Hall effect (NLHE) is a phenomenon which could produce a transverse Hall voltage in a time-reversal-invariant material. Here, we report the real space characterizations of NLHE evaluated through quantum transport in TaIrTe4 nanoribbon without the explicit Berry curvature dipole (BCD) information. We first characterize the NLHE in both transverse confined directions in global-level measurement. The impact of quantum confinement in NLHE is evaluated by adjusting the width of nanoribbons. Then, the probing area is trimmed to the atomic scale to evaluate the local texture, where we discover its patterns differ among the probed neighboring atomic groups. The analysis of charge distribution reveals the connections between NLHE’s local patterns and its non-centrosymmetric nature, rendering nearly an order of Hall voltage enhancement through probe positioning. Our work paves the way to expand the range of NLHE study and unveil its physics in more versatile material systems.

A Modified Form of Inertial Viscosity Projection Methods for Variational Inequality and Fixed Point Problems

This paper aims to introduce an iterative algorithm based on an inertial technique that uses the minimum number of projections onto a nonempty, closed, and convex set. We show that the algorithm generates a sequence that converges strongly to the common solution of a variational inequality involving inverse strongly monotone mapping and fixed point problems for a countable family of nonexpansive mappings in the setting of real Hilbert space. Numerical experiments are also presented to discuss the advantages of using our algorithm over earlier established algorithms. Moreover, we solve a real-life signal recovery problem via a minimization problem to demonstrate our algorithm’s practicality.

Direct Imaging of Atomic Rattling Motion in a Clathrate Compound

Controlling nanoscale heat generation, dissipation, and transport is crucial for miniaturizing electronic devices and for designing highly efficient thermoelectric materials. However, it has been challenging to directly measure thermal properties at individual atom level. Herein, direct atomic‐resolution column‐by‐column imaging of the rattling motion of Ba atoms in a clathrate compound Ba8Ga16Ge30 using atomic‐resolution scanning transmission electron microscopy with a segmented detector is shown. The directional anisotropy of the rattling motion is clearly visualized in real space and its amplitude and anisotropy are quantitatively evaluated by Bayesian analysis of the thermal diffuse scattering distribution. These results open a new possibility for directly characterizing nanoscale thermal properties in materials and devices, even those containing heavy elements such as thermoelectric materials.

Atomic Imaging of the Pb Precipitation in Lead-Halide Perovskites.

The lead iodide (PbI2 ) in lead-halide perovskite (LHP) is both a positive additive for material properties and a site for the formation of device defects. Therefore, atomic-level detection of PbI2 and its derivedPbstructures are crucial for understanding the performance and stability of the LHP material. In this work, the atomic imaging of the LHP, PbI2 , and Pb lattices is achieved using low-dose integrated differential phase contrast (iDPC) scanning transmission electron microscopy (STEM). Combining it with the traditional high-angle annular dark field (HAADF)-STEM, the Pb precipitation in different LHPs (CsPbI3 , CsPbBr3, and FAPbI3 ) and under different conditions (light, air, and heat) can be investigated in real space. Then, the features of Pb precipitation (positions and sizes) are visually revealed under different conditions and the stabilities of different LHPs. Meanwhile, the pathway of Pb precipitation is directly imaged and confirmed by the iDPC-STEM during an in situ heating process, supporting the detailed mechanism of Pb precipitation. These results provide the visual evidence for analyzing atomic Pb precipitation in LHPs, which helps better understand the structure-property relation induced by Pb impurity.

Hybrid bias and displacement emulators for field-level modelling of galaxy clustering in real and redshift space

ABSTRACT Recently, hybrid bias expansions have emerged as a powerful approach to modelling the way in which galaxies are distributed in the Universe. Similarly, field-level emulators have recently become possible, thanks to advances in machine learning and N-body simulations. In this paper, we explore whether both techniques can be combined to provide a field-level model for the clustering of galaxies in real and redshift space. Specifically, here we will demonstrate that field-level emulators are able to accurately predict all the operators of a second-order hybrid bias expansion. The precision achieved in real and redshift space is similar to that obtained for the non-linear matter power spectrum. This translates to roughly 1–2 per cent precision for the power spectrum of a BOSS (Baryon Oscillation Spectroscopic Survey) and a Euclid-like galaxy sample up to $k\sim 0.6\ h\, {\rm Mpc}^{-1}$. Remarkably, this combined approach also delivers precise predictions for field-level galaxy statistics. Despite all these promising results, we detect several areas where further improvements are required. Therefore, this work serves as a road map for the developments required for a more complete exploitation of upcoming large-scale structure surveys.

How to choose a proper representation of compositional data for mineral exploration?

Regional mineral exploration is based on geochemical data of which the nature is compositional and frequently involves a large number of components. Consequently, it mostly needs multivariate dimension reduction methods such as principal component analysis (PCA) and its various robust versions. The application of such methods, defined for real random variables, require the data to be represented in coordinates supported in the real space. However, a common problem in exploration geochemistry is to select the appropriate representation. Using centered (clr) and isometric (ilr) logratio coordinates to discriminate anomalous zones for orogeny gold exploration throughout Sweden revealed that there is, as expected, no difference between the two representation methods. The main difference affects the interpretation of the coordinates used. This is observed for regional scale exploration, while it is also needed to study different ways of representing geochemical data in local scale.

Using cell phone usage data to explore the spatial distribution of virtual leisure and the impact on reality leisure

ABSTRACT This study aimed to determine the geospatial distribution of Virtual Leisure (VL) users and the impact of VL on users’ reality leisure behaviours. The empirical analysis was conducted using cell phone usage data collected from the Unicom platform in Wuhan, China (N= 2.84 × 10 6 ). The study collected information on the duration of cell phone users’ virtual leisure APP usage, their place of residence, and the frequency and duration of their visits to reality leisure spaces. Our empirical research suggests that individuals residing in suburban areas, situated at a distance from urban centres, are more likely to use VL compared to those living in the central city, although VL usage levels remain high in the latter. Furthermore, our findings also indicate that the impact of VL on individual’s reality leisure behaviour of an individual varies according to the type of VL activity, which could either act as a substitute or a facilitator. This study can inform the discussion of information geography on the interaction of virtual and real spaces, and on the intervention of virtual and reality behaviours.

Human-in-the-Loop: The Future of Machine Learning in Automated Electron Microscopy

Abstract Machine learning (ML) methods are progressively gaining acceptance in the electron microscopy community for de-noising, semantic segmentation, and dimensionality reduction of data post-acquisition. The introduction of the application programming interfaces (APIs) by major instrument manufacturers now allows the deployment of ML workflows in microscopes, not only for data analytics but also for real-time decision-making and feedback for microscope operation. However, the number of use cases for real-time ML remains remarkably small. Here, we discuss some considerations in designing ML-based active experiments and pose that the likely strategy for the next several years will be human-in-the-loop automated experiments (hAE). In this paradigm, the ML learning agent directly controls beam position and image and spectroscopy acquisition functions, and a human operator monitors experiment progression in real and feature space of the system and tunes the policies of the ML agent to steer the experiment toward specific objectives.

Electrostatic Gating of Phosphorene Polymorphs.

The ability to directly monitor the states of electrons in modern field-effect transistors (FETs) could transform our understanding of the physics and improve the function of related devices. In particular, phosphorene allotropes present a fertile landscape for the development of high-performance FETs. Using density functional theory-based methods, we have systematically investigated the influence of electrostatic gating on the structures, stabilities, and fundamental electronic properties of pristine and carbon-doped monolayer (bilayer) phosphorene allotropes. The remarkable flexibility of phosphorene allotropes, arising from intra- and interlayer van der Waals interactions, causes a good resilience up to equivalent gate potential of two electrons per unit cell. The resilience depends on the stacking details in such a way that rotated bilayers show considerably higher thermodynamical stability than the unrotated ones, even at a high gate potential. In addition, a semiconductor to metal phase transition is observed in some of the rotated and carbon-doped structures with increased electronic transport relative to graphene in the context of real space Green's function formalism.

Interacting topological quantum chemistry in 2D with many-body real space invariants

The topological phases of non-interacting fermions have been classified by their symmetries, culminating in a modern electronic band theory where wavefunction topology can be obtained from momentum space. Recently, Real Space Invariants (RSIs) have provided a spatially local description of the global momentum space indices. The present work generalizes this real space classification to interacting 2D states. We construct many-body local RSIs as the quantum numbers of a set of symmetry operators on open boundaries, but which are independent of the choice of boundary. Using the U(1) particle number, they yield many-body fragile topological indices, which we use to identify which single-particle fragile states are many-body topological or trivial at weak coupling. To this end, we construct an exactly solvable Hamiltonian with single-particle fragile topology that is adiabatically connected to a trivial state through strong coupling. We then define global many-body RSIs on periodic boundary conditions. They reduce to Chern numbers in the band theory limit, but also identify strongly correlated stable topological phases with no single-particle counterpart. Finally, we show that the many-body local RSIs appear as quantized coefficients of Wen-Zee terms in the topological quantum field theory describing the phase.

Representative Functions, Variational Convergence and Almost Convexity

We develop a new epi-convergence based on the use of bounded convergent nets on the product topology of the strong topology on the primal space and weak star topology on the dual space of a general real Banach space. We study the propagation of the associated variational convergences through conjugation of convex functions defined on this product space. These results are then applied to the problem of construction of a bigger-conjugate representative function for the recession operator associated with a maximal monotone operator on this real Banach space. This is then used to study the relationship between the recession operator of a maximal monotone operator and the normal–cone operator associated with the closed, convex hull of the domain of that monotone operator. This allows us to show that the strong closure of the domain of any maximal monotone operator is convex in a general real Banach space.

Tracing Photoinduced Hydrogen Migration in Alcohol Dications from Time-Resolved Molecular-Frame Photoelectron Angular Distributions.

The recent implementation of attosecond and few-femtosecond X-ray pump/X-ray probe schemes in large-scale free-electron laser facilities has opened the way to visualize fast nuclear dynamics in molecules with unprecedented temporal and spatial resolution. Here, we present the results of theoretical calculations showing how polarization-averaged molecular-frame photoelectron angular distributions (PA-MFPADs) can be used to visualize the dynamics of hydrogen migration in methanol, ethanol, propanol, and isopropyl alcohol dications generated by X-ray irradiation of the corresponding neutral species. We show that changes in the PA-MFPADs with the pump-probe delay as a result of intramolecular photoelectron diffraction carry information on the dynamics of hydrogen migration in real space. Although visualization of this dynamics is more straightforward in the smaller systems, methanol and ethanol, one can still recognize the signature of that motion in propanol and isopropyl alcohol and assign a tentative path to it. A possible pathway for a corresponding experiment requires an angularly resolved detection of photoelectrons in coincidence with molecular fragment ions used to define a molecular frame of reference. Such studies have become, in principle, possible since the first XFELs with sufficiently high repetition rates have emerged. To further support our findings, we provide experimental evidence of H migration in ethanol-OD from ion-ion coincidence measurements performed with synchrotron radiation.

Geometric Aspects of Mixed Quantum States Inside the Bloch Sphere

When studying the geometry of quantum states, it is acknowledged that mixed states can be distinguished by infinitely many metrics. Unfortunately, this freedom causes metric-dependent interpretations of physically significant geometric quantities such as the complexity and volume of quantum states. In this paper, we present an insightful discussion on the differences between the Bures and the Sjöqvist metrics inside a Bloch sphere. First, we begin with a formal comparative analysis between the two metrics by critically discussing three alternative interpretations for each metric. Second, we explicitly illustrate the distinct behaviors of the geodesic paths on each one of the two metric manifolds. Third, we compare the finite distances between an initial state and the final mixed state when calculated with the two metrics. Interestingly, in analogy with what happens when studying the topological aspects of real Euclidean spaces equipped with distinct metric functions (for instance, the usual Euclidean metric and the taxicab metric), we observe that the relative ranking based on the concept of a finite distance between mixed quantum states is not preserved when comparing distances determined with the Bures and the Sjöqvist metrics. Finally, we conclude with a brief discussion on the consequences of this violation of a metric-based relative ranking on the concept of the complexity and volume of mixed quantum states.

Variation type characterization of product Hardy spaces

In the multidimensional Euclidean space, except the classical real Hardy space, there are numerous product ones. We associate with each of them a class of functions related to the known variations and new ones. Such a characterization is fulfilled by means of the integrability of the Fourier transform

The Point-to-Set Principle and the dimensions of Hamel bases

We prove that, for every 0 ⩽ s ⩽ 1, there is a Hamel basis of the vector space of reals over the field of rationals that has Hausdorff dimension s. The logic of our proof is of particular interest. The statement of our theorem is classical; it does not involve the theory of computing. However, our proof makes essential use of algorithmic fractal dimension–a computability-theoretic construct–and the point-to-set principle of J. Lutz and N. Lutz (2018).

Extended Reality Platform for Metaverse Exhibition

This paper proposes a web-based extended reality (XR) platform integrating exhibitions based on augmented reality (AR) and virtual reality (VR). The proposed platform includes an XR cloud for managing and sharing data in XR spaces, a VR client for users, and an AR client for real-world users. The XR cloud is a web-based VR service responsible for managing objects and spatial information related to real and virtual spaces while simultaneously facilitating real-time information sharing and synchronization between AR and VR users. The VR client offers a virtual exhibition environment based on the virtual space and information for VR users. The AR client overlays virtual information over objects in a real space, allowing for intuitive interaction with them. The proposed XR platform was implemented with Oculus Quest 2 for VR and HoloLens 2 for AR and was evaluated in a small exhibition environment. In this experimental environment, VR and AR users were able to participate in the same exhibition from different spaces and share their experiences in real time.

Three-operator reflected forward-backward splitting algorithm with double inertial effects

In this paper, we propose a reflected forward-backward splitting algorithm with two different inertial extrapolations to find a zero of the sum of three monotone operators consisting of the maximal monotone operator, Lipschitz continuous monotone operator, and a cocoercive operator in real Hilbert spaces. One of the interesting features of the proposed algorithm is that both the Lipschitz continuous monotone operator and the cocoercive operator are computed explicitly each with one evaluation per iteration. We then obtain weak and strong convergence results under some mild conditions. We finally give a numerical illustration to show that our proposed algorithm is effective and competitive with other related algorithms in the literature.