Optical conductivity of the Majorana mode at the s- and d-wave topological superconductor edge.

The Majorana fermion offers fascinating possibilities such as non-Abelian statistics and nonlocal robust qubits, and hunting it is one of the most important topics in current condensed matter physics. Most of the efforts have been focused on the Majorana bound state at zero energy in terms of scanning tunneling spectroscopy searching for the quantized conductance. On the other hand, a chiral Majorana edge channel appears at the surface of a three-dimensional topological insulator when engineering an interface between proximity-induced superconductivity and ferromagnetism. Recent advances in microwave spectroscopy of topological edge states open a new avenue for observing signatures of such Majorana edge states through the local optical conductivity. As a guide to future experiments, we show how the local optical conductivity and density of states present distinct qualitative features depending on the symmetry of the superconductivity, that can be tuned via the magnetization and temperature. In particular, the presence of the Majorana edge state leads to a characteristic nonmonotonic temperature dependence achieved by tuning the magnetization.

Meandering conduction channels and the tunable nature of quantized charge transport.

The discovery of the quantum Hall effect has established the foundation of the field of topological condensed matter physics. An amazingly accurate quantization of the Hall conductance, now enshrined in quantum metrology, is stable against any reasonable perturbation due to its topological protection. Conversely, the latter implies a form of censorship by concealing any local information from the observer. The spatial distribution of the current in a quantum Hall system is such a piece of information, which, thanks to spectacular recent advances, has now become accessible to experimental probes. It is an old question whether the original and intuitively compelling theoretical picture of the current, flowing in a narrow channel along the sample edge, is the physically correct one. Motivated by recent experiments locally imaging quantized current in a Chern insulator (Bi, Sb)[Formula: see text]Te[Formula: see text] heterostructure [Rosen et al., Phys. Rev. Lett. 129, 246602 (2022); Ferguson et al., Nat. Mater. 22, 1100-1105 (2023)], we theoretically demonstrate the possibility of a broad "edge state" generically meandering away from the sample boundary deep into the bulk. Further, we show that by varying experimental parameters one can continuously tune between the regimes with narrow edge states and meandering channels, all the way to the charge transport occurring primarily within the bulk. This accounts for various features observed in, and differing between, experiments. Overall, our findings underscore the robustness of topological condensed matter physics, but also unveil the phenomenological richness, hidden until recently by the topological censorship-most of which, we believe, remains to be discovered.

Urbanization and edge effects interact to drive mutualism breakdown and the rise of unstable pathogenic communities in forest soil.

Temperate forests are threatened by urbanization and fragmentation, with over 20% (118,300 km2) of U.S. forest land projected to be subsumed by urban land development. We leveraged a unique, well-characterized urban-to-rural and forest edge-to-interior gradient to identify the combined impact of these two land use changes-urbanization and forest edge creation-on the soil microbial community in native remnant forests. We found evidence of mutualism breakdown between trees and their fungal root mutualists [ectomycorrhizal (ECM) fungi] with urbanization, where ECM fungi colonized fewer tree roots and had less connectivity in soil microbiome networks in urban forests compared to rural forests. However, urbanization did not reduce the relative abundance of ECM fungi in forest soils; instead, forest edges alone led to strong reductions in ECM fungal abundance. At forest edges, ECM fungi were replaced by plant and animal pathogens, as well as copiotrophic, xenobiotic-degrading, and nitrogen-cycling bacteria, including nitrifiers and denitrifiers. Urbanization and forest edges interacted to generate new "suites" of microbes, with urban interior forests harboring highly homogenized microbiomes, while edge forest microbiomes were more heterogeneous and less stable, showing increased vulnerability to low soil moisture. When scaled to the regional level, we found that forest soils are projected to harbor high abundances of fungal pathogens and denitrifying bacteria, even in rural areas, due to the widespread existence of forest edges. Our results highlight the potential for soil microbiome dysfunction-including increased greenhouse gas production-in temperate forest regions that are subsumed by urban expansion, both now and in the future.

A green edge-hosted zinc single-site heterogeneous catalyst for superior Fenton-like activity.

Developing green heterogeneous catalysts with excellent Fenton-like activity is critical for water remediation technologies. However, current catalysts often rely on toxic transitional metals, and their catalytic performance is far from satisfactory as alternatives of homogeneous Fenton-like catalysts. In this study, a green catalyst based on Zn single-atom was prepared in an ammonium atmosphere using ZIF-8 as a precursor. Multiple characterization analyses provided evidence that abundant intrinsic defects due to the edge sites were created, leading to the formation of a thermally stable edge-hosted Zn-N4 single-atom catalyst (ZnN4-Edge). Density functional theory calculations revealed that the edge sites equipped the single-atom Zn with a super catalytic performance, which not only promoted decomposition of peroxide molecule (HSO5-) but also greatly lowered the activation barrier for •OH generation. Consequently, the as-prepared ZnN4-Edge exhibited extremely high Fenton-like performance in oxidation and mineralization of phenol as a representative organic contaminant in a wide range of pH, realizing its quick detoxification. The atom-utilization efficiency of the ZnN4-Edge was ~104 higher than an equivalent amount of the control sample without edge sites (ZnN4), and the turnover frequency was ~103 times of the typical benchmark of homogeneous catalyst (Co2+). This study opens up a revolutionary way to rationally design and optimize heterogeneous catalysts to homogeneous catalytic performance for Fenton-like application.

Edge-Based General Linear Models Capture Moment-to-Moment Fluctuations in Attention.

Although we must prioritize the processing of task-relevant information to navigate life, our ability to do so fluctuates across time. Previous work has identified fMRI functional connectivity (FC) networks that predict an individual's ability to sustain attention and vary with attentional state from 1 min to the next. However, traditional dynamic FC approaches typically lack the temporal precision to capture moment-to-moment network fluctuations. Recently, researchers have "unfurled" traditional FC matrices in "edge cofluctuation time series" which measure timepoint-by-timepoint cofluctuations between regions. Here we apply event-based and parametric fMRI analyses to edge time series to capture moment-to-moment fluctuations in networks related to attention. In two independent fMRI datasets examining young adults of both sexes in which participants performed a sustained attention task, we identified a reliable set of edges that rapidly deflects in response to rare task events. Another set of edges varies with continuous fluctuations in attention and overlaps with a previously defined set of edges associated with individual differences in sustained attention. Demonstrating that edge-based analyses are not simply redundant with traditional regions-of-interest-based approaches, up to one-third of reliably deflected edges were not predicted from univariate activity patterns alone. These results reveal the large potential in combining traditional fMRI analyses with edge time series to identify rapid reconfigurations in networks across the brain.

Identifying covariate-related subnetworks for whole-brain connectome analysis.

Whole-brain connectome data characterize the connections among distributed neural populations as a set of edges in a large network, and neuroscience research aims to systematically investigate associations between brain connectome and clinical or experimental conditions as covariates. A covariate is often related to a number of edges connecting multiple brain areas in an organized structure. However, in practice, neither the covariate-related edges nor the structure is known. Therefore, the understanding of underlying neural mechanisms relies on statistical methods that are capable of simultaneously identifying covariate-related connections and recognizing their network topological structures. The task can be challenging because of false-positive noise and almost infinite possibilities of edges combining into subnetworks. To address these challenges, we propose a new statistical approach to handle multivariate edge variables as outcomes and output covariate-related subnetworks. We first study the graph properties of covariate-related subnetworks from a graph and combinatorics perspective and accordingly bridge the inference for individual connectome edges and covariate-related subnetworks. Next, we develop efficient algorithms to exact covariate-related subnetworks from the whole-brain connectome data with an $\ell_0$ norm penalty. We validate the proposed methods based on an extensive simulation study, and we benchmark our performance against existing methods. Using our proposed method, we analyze two separate resting-state functional magnetic resonance imaging data sets for schizophrenia research and obtain highly replicable disease-related subnetworks.

Latent space search based multimodal optimization with personalized edge-network biomarker for multi-purpose early disease prediction.

Considering that cancer is resulting from the comutation of several essential genes of individual patients, researchers have begun to focus on identifying personalized edge-network biomarkers (PEBs) using personalized edge-network analysis for clinical practice. However, most of existing methods ignored the optimization of PEBs when multimodal biomarkers exist in multi-purpose early disease prediction (MPEDP). To solve this problem, this study proposes a novel model (MMPDENB-RBM) that combines personalized dynamic edge-network biomarkers (PDENB) theory, multimodal optimization strategy and latent space search scheme to identify biomarkers with different configurations of PDENB modules (i.e. to effectively identify multimodal PDENBs). The application to the three largest cancer omics datasets from The Cancer Genome Atlas database (i.e. breast invasive carcinoma, lung squamous cell carcinoma and lung adenocarcinoma) showed that the MMPDENB-RBM model could more effectively predict critical cancer state compared with other advanced methods. And, our model had better convergence, diversity and multimodal property as well as effective optimization ability compared with the other state-of-art methods. Particularly, multimodal PDENBs identified were more enriched with different functional biomarkers simultaneously, such as tissue-specific synthetic lethality edge-biomarkers including cancer driver genes and disease marker genes. Importantly, as our aim, these multimodal biomarkers can perform diverse biological and biomedical significances for drug target screen, survival risk assessment and novel biomedical sight as the expected multi-purpose of personalized early disease prediction. In summary, the present study provides multimodal property of PDENBs, especially the therapeutic biomarkers with more biological significances, which can help with MPEDP of individual cancer patients.

Improving the performance of single-cell RNA-seq data mining based on relative expression orderings.

The advent of single-cell RNA-sequencing (scRNA-seq) provides an unprecedented opportunity to explore gene expression profiles at the single-cell level. However, gene expression values vary over time and under different conditions even within the same cell. There is an urgent need for more stable and reliable feature variables at the single-cell level to depict cell heterogeneity. Thus, we construct a new feature matrix called the delta rank matrix (DRM) from scRNA-seq data by integrating an a priori gene interaction network, which transforms the unreliable gene expression value into a stable gene interaction/edge value on a single-cell basis. This is the first time that a gene-level feature has been transformed into an interaction/edge-level for scRNA-seq data analysis based on relative expression orderings. Experiments on various scRNA-seq datasets have demonstrated that DRM performs better than the original gene expression matrix in cell clustering, cell identification and pseudo-trajectory reconstruction. More importantly, the DRM really achieves the fusion of gene expressions and gene interactions and provides a method of measuring gene interactions at the single-cell level. Thus, the DRM can be used to find changes in gene interactions among different cell types, which may open up a new way to analyze scRNA-seq data from an interaction perspective. In addition, DRM provides a new method to construct a cell-specific network for each single cell instead of a group of cells as in traditional network construction methods. DRM's exceptional performance is due to its extraction of rich gene-association information on biological systems and stable characterization of cells.

Predicting Drug-drug Interaction with Graph Mutual Interaction Attention Mechanism.

Effective representation of molecules is a crucial step in AI-driven drug design and drug discovery, especially for drug-drug interaction (DDIs) prediction. Previous work usually models the drug information from the drug-related knowledge graph or the single drug molecules, but the interaction information between molecular substructures of drug pair is seldom considered, thus often ignoring the influence of bond information on atom node representation, leading to insufficient drug representation. Moreover, key molecular substructures have significant contribution to the DDIs prediction results. Therefore, in this work, we propose a novel Graph learning framework of Mutual Interaction Attention mechanism (called GMIA) to predict DDIs by effectively representing the drug molecules. Specifically, we build the node-edge message communication encoder to aggregate atom node and the incoming edge information for atom node representation and design the mutual interaction attention decoder to capture the mutual interaction context between molecular graphs of drug pairs. GMIA can bridge the gap between two encoders for the single drug molecules by attention mechanism. We also design a co-attention matrix to analyze the significance of different-size substructures obtained from the encoder-decoder layer and provide interpretability. In comparison with other recent state-of-the-art methods, our GMIA achieves the best results in terms of area under the precision-recall-curve (AUPR), area under the ROC curve (AUC), and F1 score on two different scale datasets. The case study indicates that our GMIA can detect the key substructure for potential DDIs, demonstrating the enhanced performance and interpretation ability of GMIA.

Hybrid multimodal fusion for graph learning in disease prediction.

Graph neural networks (GNNs) have gained significant attention in disease prediction where the latent embeddings of patients are modeled as nodes and the similarities among patients are represented through edges. The graph structure, which determines how information is aggregated and propagated, plays a crucial role in graph learning. Recent approaches typically create graphs based on patients' latent embeddings, which may not accurately reflect their real-world closeness. Our analysis reveals that raw data, such as demographic attributes and laboratory results, offers a wealth of information for assessing patient similarities and can serve as a compensatory measure for graphs constructed exclusively from latent embeddings. In this study, we first construct adaptive graphs from both latent representations and raw data respectively, and then merge these graphs via weighted summation. Given that the graphs may contain extraneous and noisy connections, we apply degree-sensitive edge pruning and kNN sparsification techniques to selectively sparsify and prune these edges. We conducted intensive experiments on two diagnostic prediction datasets, and the results demonstrate that our proposed method surpasses current state-of-the-art techniques.

Edge states in rationally terminated honeycomb structures.

Consider the tight binding model of graphene, sharply terminated along an edge l parallel to a direction of translational symmetry of the underlying period lattice. We classify such edges l into those of "zigzag type" and those of "armchair type," generalizing the classical zigzag and armchair edges. We prove that zero-energy/flat-band edge states arise for edges of zigzag type, but never for those of armchair type. We exhibit explicit formulae for flat-band edge states when they exist. We produce strong evidence for the existence of dispersive (nonflat) edge state curves of nonzero energy for most l.

Artificial intelligence-derived risk score for mortality in secondary mitral regurgitation treated by transcatheter edge-to-edge repair: the EuroSMR risk score.

BACKGROUND AND AIMS: Risk stratification for mitral valve transcatheter edge-to-edge repair (M-TEER) is paramount in the decision-making process to appropriately select patients with severe secondary mitral regurgitation (SMR). This study sought to develop and validate an artificial intelligence-derived risk score (EuroSMR score) to predict 1-year outcomes (survival or survival + clinical improvement) in patients with SMR undergoing M-TEER. METHODS: An artificial intelligence-derived risk score was developed from the EuroSMR cohort (4172 and 428 patients treated with M-TEER in the derivation and validation cohorts, respectively). The EuroSMR score was validated and compared with established risk models. RESULTS: The EuroSMR risk score, which is based on 18 clinical, echocardiographic, laboratory, and medication parameters, allowed for an improved discrimination of surviving and non-surviving patients (hazard ratio 4.3, 95% confidence interval 3.7-5.0; P < .001), and outperformed established risk scores in the validation cohort. Prediction for 1-year mortality (area under the curve: 0.789, 95% confidence interval 0.737-0.842) ranged from <5% to >70%, including the identification of an extreme-risk population (2.6% of the entire cohort), which had a very high probability for not surviving beyond 1 year (hazard ratio 6.5, 95% confidence interval 3.0-14; P < .001). The top 5% of patients with the highest EuroSMR risk scores showed event rates of 72.7% for mortality and 83.2% for mortality or lack of clinical improvement at 1-year follow-up. CONCLUSIONS: The EuroSMR risk score may allow for improved prognostication in heart failure patients with severe SMR, who are considered for a M-TEER procedure. The score is expected to facilitate the shared decision-making process with heart team members and patients.

Metalens for Accelerated Optoelectronic Edge Detection under Ambient Illumination.

Analog systems may allow image processing, such as edge detection, with low computational power. However, most demonstrated analog systems, based on either conventional 4-f imaging systems or nanophotonic structures, rely on coherent laser sources for illumination, which significantly restricts their use in routine imaging tasks with ambient, incoherent illumination. Here, we demonstrated a metalens-assisted imaging system that can allow optoelectronic edge detection under ambient illumination conditions. The metalens was designed to generate polarization-dependent optical transfer functions (OTFs), resulting in a synthetic OTF with an isotropic high-pass frequency response after digital subtraction. We integrated the polarization-multiplexed metalens with a polarization camera and experimentally demonstrated single-shot edge detection of indoor and outdoor scenes, including a flying airplane, under ambient sunlight illumination. The proposed system showcased the potential of using polarization multiplexing for the construction of complex optical convolution kernels toward accelerated machine vision tasks such as object detection and classification under ambient illumination.

Engineering Gapless Edge States from Antiferromagnetic Chern Homobilayer.

We put forward that stacked Chern insulators with opposite chiralities offer a strategy to achieve gapless helical edge states in two dimensions. We employ the square lattice as an example and elucidate that the gapless chiral and helical edge states emerge in the monolayer and antiferromagnetically stacked bilayer, characterized by Chern number C=-1 and spin Chern number CS=-1, respectively. Particularly, for a topological phase transition to the normal insulator in the stacked bilayer, a band gap closing and reopening procedure takes place accompanied by helical edge states disappearing, where the Chern insulating phase in the monolayer vanishes at the same time. Moreover, EuO is revealed as a suitable candidate for material realization. This work is not only valuable to the research of the quantum anomalous Hall effect but also offers a favorable platform to realize magnetic topologically insulating materials for spintronics applications.

Edge-by-Edge Lateral Heterostructure through Interfacial Sliding.

van der Waals heterostructures (vdWHs) based on two-dimensional (2D) semiconductors have attracted considerable attention. However, the reported vdWHs are largely based on vertical device structure with large overlapping area, while the realization of lateral heterostructures contacted through 2D edges remains challenging and is majorly limited by the difficulties of manipulating the lateral distance of 2D materials at nanometer scale (during transfer process). Here, we demonstrate a simple interfacial sliding approach for realizing an edge-by-edge lateral contact. By stretching a vertical vdWH, two 2D flakes could gradually slide apart or toward each other. Therefore, by applying proper strain, the initial vertical vdWH could be converted into a lateral heterojunction with intimately contacted 2D edges. The lateral contact structure is supported by both microscope characterization and in situ electrical measurements, exhibiting carrier tunneling behavior. Finally, this approach can be extended to 3D thin films, as demonstrated by the lateral 2D/3D and 3D/3D Schottky junction.

Robust Edge States of Quasi-1D Material Ta2NiSe7 and Applications in Saturable Absorbers.

The helical edge states (ESs) protected by underlying Z2 topology in two-dimensional topological insulators (TIs) arouse upsurges in saturable absorptions thanks to the strong photon-electron coupling in ESs. However, limited TIs demonstrate clear signatures of topological ESs at liquid nitrogen temperatures, hindering the applications of such exotic quantum states. Here, we demonstrate the existence of one-dimensional (1D) ESs at the step edge of the quasi-1D material Ta2NiSe7 at 78 K by scanning tunneling microscopy. Such ESs are rather robust against the irregularity of the edges, suggesting a possible topological origin. The exfoliated Ta2NiSe7 flakes were used as saturable absorbers (SAs) in an Er-doped fiber laser, hosting a mode-locked pulse with a modulation depth of up to 52.6% and a short pulse duration of 225 fs, far outstripping existing TI-based SAs. This work demonstrates the existence of robust 1D ESs and the superior SA performance of Ta2NiSe7.

Engineering Three-Dimensional Interconnected Pores with Plentiful Edge Sites via a Confined Space for Enhanced Oxygen Reduction.

N-Doped carbon sheets based on edge engineering provide more opportunities for improving oxygen reduction reaction (ORR) active sites. However, with regard to the correlation between porous structural configurations and performances, it remains underexplored. Herein, a silica-assisted localized etching method was employed to create two-dimensional mesoporous carbon materials with customizable pore structures, abundant edge sites, and nitrogen functionalities. The mesoporous carbon exhibited superior electrocatalytic performance for the ORR compared to that of a 20 wt % Pt/C catalyst, achieving a half-wave potential of 0.88 V versus RHE, situating them in the leading level of the reported carbon electrocatalysts. Experimental data suggest that the edge graphitic nitrogen sites played a crucial role in the ORR process. The three-dimensional interconnected pores provided a high density of active sites for the ORR and facilitated the efficient transport of electrons. These unique properties make the carbon sheets a promising candidate for highly efficient air cathodes in rechargeable Zn-air batteries.

Polychromatic Dual-Mode Imaging with Structured Chiral Photonic Crystals.

Optical spatial differentiation is a typical operation of optical analog computing and can single out the edge to accelerate the subsequent image processing, but in some cases, overall information about the object needs to be presented synchronously. Here, we propose a multifunctional optical device based on structured chiral photonic crystals for the simultaneous realization of real-time dual-mode imaging. This optical differentiator is realized by self-organized large-birefringence cholesteric liquid crystals, which are photopatterned to encode with a special integrated geometric phase. Two highly spin-selective modes of second-order spatial differentiation and bright-field imaging are exhibited in the reflected and transmitted directions, respectively. Two-dimensional edges of both amplitude and phase objects have been efficiently enhanced in high contrast and the broadband spectrum. This work extends the ingenious building of hierarchical chiral nanostructures, enriches their applications in the emerging frontiers of optical computing, and boasts considerable potential in machine vision and microscopy.

Atomic Evolution Mechanism and Suppression of Edge Threading Dislocations in Nitride Remote Heteroepitaxy.

The majority of dislocations in nitride epilayers are edge threading dislocations (TDs), which diminish the performance of nitride devices. However, it is extremely difficult to reduce the edge TDs due to the lack of available slip systems. Here, we systematically investigate the formation mechanism of edge TDs and find that besides originating at the coalescence boundaries, these dislocations are also closely related to geometrical misfit dislocations at the interface. Based on this understanding, we propose a novel strategy to reduce the edge TD density of the GaN epilayer by nearly 1 order of magnitude via graphene-assisted remote heteroepitaxy. The first-principles calculations confirm that the insertion of graphene dramatically reduces the energy barrier required for interfacial sliding, which promotes a new strain release channel. This work provides a unique approach to directly suppress the formation of edge TDs at the source, thereby facilitating the enhanced performance of photoelectronic and electronic devices.

Topological Nodal-Point Superconductivity in Two-Dimensional Ferroelectric Hybrid Perovskites.

Two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs) with enhanced stability, high tunability, and strong spin-orbit coupling have shown great potential in vast applications. Here, we extend the already rich functionality of 2D HOIPs to a new territory, realizing topological superconductivity and Majorana modes for fault-tolerant quantum computation. Especially, we predict that room-temperature ferroelectric BA2PbCl4 (BA for benzylammonium) exhibits topological nodal-point superconductivity (NSC) and gapless Majorana modes on selected edges and ferroelectric domain walls when proximity-coupled to an s-wave superconductor and an in-plane Zeeman field, attractive for experimental verification and application. Since NSC is protected by spatial symmetry of 2D HOIPs, we envision more exotic topological superconducting states to be found in this class of materials due to their diverse noncentrosymmetric space groups, which may open a new avenue in the fields of HOIPs and topological superconductivity.