Topological Features Research Articles

A five‐level nested neutral point‐clamped inverter topology

AbstractClassical five‐level nested neutral point‐clamped (5L NNPC) inverter‐leg is a hybrid of the flying‐capacitor and diode‐clamped 5‐L inverter‐leg configurations. Though uniform reduced voltage stress on the constituting switches is evident in 5L NNPC inverter‐leg, trails of the drawbacks of diode‐clamping concept still exist. Compared with the classical 5L NNPC inverter, the state‐of‐the‐art diode‐free 5L NNPC inverter involves no passive power switches and has low conduction losses. However, in this 5L NNPC inverter, two of the eight active switches have blocking voltage rating of 1/2 of the input voltage. Considering this limiting topological feature, an inverter‐leg for 5L NNPC inverter is presented in this paper. In the proposed 5L NNPC inverter‐leg, only one switch has voltage stress of 1/2 of the input voltage. This reduced voltage stress has inverter cost and loss implications. The performances and competitiveness of the 5L NNPC inverter were analysed in detail and demonstrated with a prototype. The blocking voltages of all the constituting power switches; profiles of the flying‐capacitor voltages; and FFT spectrum of line voltage waveform were experimentally obtained. Experimental deactivation and activation of the inverter's capacitor voltages balancing scheme were typified for varying modulation index values.

Improving Classification Performance of Spatial Filters in Mammographic Microcalcifications Images Using Persistent Homology

Noise and artefacts in mammogram images can obscure important indicators of microcalcifications, complicating accurate diagnosis. While traditional spatial filters can reduce noise and are effective to some extent, they often fail to enhance features crucial for classification. This study uses persistent homology (PH) to evaluate and improve the classification performance of various spatial filters on mammogram images. The evaluation process involves converting filtered images into persistence diagrams (PDs) to capture topological features. These diagrams are then vectorised into PH features for classification using a neural network classifier. This study also examines further filtering of PDs from filtered images to enhance classification performance. Using the Digital Database for Screening Mammography (DDSM) and Mammographic Image Analysis Society (MIAS) datasets, we evaluate Median, Wiener, Gaussian, and Bilateral filters alone and integrate them with PH-based filtering. Results show significant classification improvements, with Wiener filters achieving 96.33% accuracy on the DDSM dataset (up from 57.38%) and Gaussian filters reaching 85.33% on the MIAS dataset (up from 73.33%). These findings demonstrate the potential of PH-based filters to enhance diagnostic accuracy in breast cancer detection by refining topological features and effectively reducing noise.

Enabling Ultrafast Intramolecular Singlet Fission in Perylene Diimide Tetramer with Saddle-Shaped Linker.

Intramolecular singlet fission (SF) in multichromophore systems is of high interest for photovoltaic application. As an attractive candidate for SF-based devices, enabling efficient SF in covalent oligomers of perylene diimide (PDI) still remains challenging. In this work, inter-PDI SF with τSF = ∼150 ps and ∼150% triplet yield in a covalent tetramer COTh-FPDI was facilitated by employing a saddle-shaped cyclooctatetrathiophene (COTh) core and fused linking with PDIs. In comparison, ultrafast symmetry-breaking charge separation (τCS = ∼100 fs) was observed for the tetramer COTh-αPDI with flexible linking. Taking advantage of rigid linking and minimized excited-state structural relaxation, unique inter-PDI geometry in COTh-FPDI can be fully defined by the topological characteristic of COTh, which plays a key role for inter-PDI electronic coupling required by SF. Our work provides a new strategy for enabling intramolecular SF by predefining interchromophore geometry by a rigid structure, which might be inspired for future designing of multichromophore SF systems.

Constructing a Conductive Micro/Nano Network Within Interpenetrating Phase Composites for Triboelectric Nanogenerators.

Interpenetrating phase composites (IPCs) are gaining popularity because of their unique topological characteristics, which include their light weight and ability to conduct electricity. Herein, a novel metal‒polymer IPC composed mainly of a 3D nickel foam(NF) at the microscale and a polytetrafluoroethylene (PTFE) matrix are developed. Moreover, a nanonetwork composed of carbon nanotubes (CNTs) bridging the nickel skeleton and PTFE matrix is created within the IPC via a simple impregnation method. The construction of a micro/nano hybrid network not only enhances the tribological performance and friction heat dissipation but also increases the triboelectric output response, which is 30 and 7.5 times greater than that of pristine PTFE and binary NF-PTFE IPC, respectively. The fabricated IPC endures long-term tests after 36000 cycles without notable wear scarring, exhibiting great potential for future optimization of triboelectric nanogenerator(TENG) durability and potential application in a variety of fields, such as wear-resisting materials, high-performance energy absorption and heat management.

The studies of topological phases and energy braiding of non-Hermitian models using machine learning

Abstract Complex-energy bands in non-Hermitian systems can exhibit diverse topological braiding, yet identifying these braids remains challenging and has garnered limited attention in previous studies. In this work, we explore energy braiding in one-dimensional non-Hermitian systems through both unsupervised and supervised learning techniques. For unsupervised learning, we apply diffusion maps to effectively identify non-Bloch energy braiding without requiring prior knowledge and use k-means clustering to categorize different topological features, such as Unlink and Hopf link configurations. In the supervised learning phase, we train a Convolutional Neural Network (CNN) on Bloch energy data to predict both Bloch and non-Bloch energy braiding with nearly $100\%$ accuracy. Through an analysis of the CNN, we confirm that the model has successfully developed the capacity to recognize the braiding topology of the energy bands. Our findings reveal that unsupervised learning can rapidly detect phase transition points, while the CNN is capable of predicting braid degrees even for models not included in the training set.

Collinear Fractals and Bandt’s Conjecture

For a complex parameter c outside the unit disk and an integer n≥2, we examine the n-ary collinear fractal E(c,n), defined as the attractor of the iterated function system {fk:C⟶C}k=1n, where fk(z):=1+n−2k+c−1z. We investigate some topological features of the connectedness locus Mn defined as the set of those c for which E(c,n) is connected. In particular, we provide a detailed answer to an open question posed by Calegari, Koch, and Walker in 2017. We also extend and refine the technique of the “covering property” by Solomyak and Xu to any n≥2. We use it to show that a nontrivial portion of Mn is regular closed. When n≥21, we enhance this result by showing that in fact, the whole Mn∖R lies within the closure of its interior, thus proving that the generalized Bandt’s conjecture is true.

Analysis of type 2 diabetes mellitus-related genes by constructing the pathway-based weighted network.

Complex network is an effective approach to studying complex diseases, and provides another perspective for understanding their pathological mechanisms by illustrating the interactions between various factors of diseases. Type 2 diabetes mellitus (T2DM) is a complex polygenic metabolic disease involving genetic and environmental factors. By combining the complex network approach with biological data, this study constructs a pathway-based weighted network model of T2DM-related genes to explore the interrelationships between genes, here a weight is assigned to each edge in terms of the number of the same pathways in which the two nodes (genes) connected to the edge are involved. The edge weights can reflect differences in the strength of connections (interactions) between nodes (genes), which intuitively reflect the extent of biological correlations between genes and contribute to the importance of the nodes. Analysis of statistical and topological characteristics shows that the edge weights are correlated to the network topology, and the edge weight distribution decays as a power-law. The disparity of the weights indicates that the edge weight distribution for the nodes with the same degree is of approximately equal weights; and most edges with the higher weights tend to connect with the higher degree nodes. To determine the key hub genes of the weighted network, an integrated ranking index is used to comprehensively reflect the contribution of the three indices (strength, degree and number of pathways) of nodes; by taking the threshold of integrated ranking index greater than 0.56, 12 key hub genes are identified: MAPK1, PIK3CD, PIK3CA, PIK3R1, AKT2, AKT1, KRAS, TNF, MAPK8, PRKCA, IL6 and MTOR. These genes should play an important role in the occurrence and development of T2DM, and can be regarded as potential therapeutic targets for further biological and medical research on their functions in T2DM. It can be expected that combining complex network approach with other data analysis techniques can provide more clues for exploring the pathogenesis and treatment of T2DM and other complex diseases in the future.

Deconstructing the Mapper algorithm to extract richer topological and temporal features from functional neuroimaging data.

Capturing and tracking large-scale brain activity dynamics holds the potential to deepen our understanding of cognition. Previously, tools from topological data analysis, especially Mapper, have been successfully used to mine brain activity dynamics at the highest spatiotemporal resolutions. Even though it is a relatively established tool within the field of topological data analysis, Mapper results are highly impacted by parameter selection. Given that noninvasive human neuroimaging data (e.g., from fMRI) is typically fraught with artifacts and no gold standards exist regarding "true" state transitions, we argue for a thorough examination of Mapper parameter choices to better reveal their impact. Using synthetic data (with known transition structure) and real fMRI data, we explore a variety of parameter choices for each Mapper step, thereby providing guidance and heuristics for the field. We also release our parameter exploration toolbox as a software package to make it easier for scientists to investigate and apply Mapper to any dataset.

Triangular Mesh Surface Subdivision Based on Graph Neural Network

Mesh subdivision is a common mesh-processing algorithm used to improve model accuracy and surface smoothness. Its classical scheme adopts a fixed linear vertex update strategy and is implemented iteratively, which often results in excessive mesh smoothness. In recent years, a nonlinear subdivision method that uses neural network methods, called neural subdivision (NS), has been proposed. However, as a new scheme, its application scope and the effect of its algorithm need to be improved. To solve the above problems, a graph neural network method based on neural subdivision was used to realize mesh subdivision. Unlike fixed half-flap structures, the non-fixed mesh patches used in this paper naturally expressed the interior and boundary of a mesh and learned its spatial and topological features. The tensor voting strategy was used to replace the half-flap spatial transformation method of neural subdivision to ensure the translation, rotation, and scaling invariance of the algorithm. Dynamic graph convolution was introduced to learn the global features of the mesh in the way of stacking, so as to improve the subdivision effect of the network on the extreme input mesh. In addition, vertex neighborhood information was added to the training data to improve the robustness of the subdivision network. The experimental results show that the proposed algorithm achieved a good subdivision of both the general input mesh and extreme input mesh. In addition, it effectively subdivided mesh boundaries. In particular, using the general input mesh, the algorithm in this paper was compared to neural subdivision through quantitative experiments. The proposed method reduced the Hausdorff distance and the mean surface distance by 27.53% and 43.01%, respectively.

Resilience Analysis of Transportation System Based on Complex Network Theory

In order to ensure the important role of the transportation system in economic development, it is particularly important to evaluate the characteristics and resilience of the network. According to the complex network theory, the original mapping method is used to construct the complex network model, and the topological features node degree, average path length, clustering coefficient and intermediate are analyzed. The improved network efficiency and the maximum connectivity sub-graph size were selected as the resilience indicators, and the random attack and deliberate attack were used to simulate, and the changes of the resilience analysis index were calculated and compared, so as to complete the analysis of the resilience of the transportation system. The node degree, clustering coefficient and intermediate were selected as the evaluation indexes of key nodes, and the coefficient of variation method and TOPSIS algorithm were used to identify the key nodes, which were used as the basis for node selection in the simulation. Finally, taking Tianjin Shugang Highway as an example, an empirical analysis is carried out to verify the accuracy and applicability of the method.

TD-GCN: A novel fusion method for network topological and dynamical features

The topological and dynamical features of complex networks hold abundant information. How to fully utilize this information for more accurate network structure mining is a significant issue. In this paper, we propose a novel method that simultaneously takes into account both network topological and dynamical features via graph convolutional networks (TD-GCN). Specifically, we obtain the topological features of the network by using the second-order adjacency matrix of the complex network, which captures indirect connections between nodes, for a more detailed representation of network structure, and use the SIS model to generate node state data in the complex network as the dynamical features of the network. The network topological and dynamical features are fused through the graph convolutional neural network. To verify the effectiveness and applicability of our method, we conduct extensive experiments on both simulated networks and real-world networks with various network scales. We comprehensively compare the proposed method with other existing methods in the domains of network link prediction and network node ranking learning. The experimental results show that our method can better capture the characteristic information in complex networks and has better performance compared with other methods.

Magnon valley Hall effect and tunable chiral edge transport in AB-stacked kagome lattices

Our research investigates the magnon bands and their topological characteristics in a ferromagnetic pyrochlore lattice, with the Dzyaloshinskii–Moriya (DM) interaction playing a significant role. Given its kagome AB bilayer structure, the ferromagnetic exchange couplings, which may differ among the AB triangles, are further considered for their implications on the system’s magnetic properties. By employing the non-equilibrium Green’s function method, we explicitly demonstrate that the one-way chiral edge magnon transport is indeed regulated by the DM interaction direction (D→−D) and the exchange interaction of J1 and J2 (J1↔J2). Moreover, we demonstrate that the topological edge state predominantly resides along the edges and exhibits an oscillatory decay as it penetrates into the bulk in a non-equilibrium state. Although the chiral edge magnons and the corresponding energy current tend to travel along one edge from the hot region to the cold one, in the bulk, however, the energy current flows reversely from the cold to the hot region. The valley magnon Hall effects and chiral edge transport proposed here may be realized in the thin films of the insulating ferromagnet, such as Lu2V2O7. Thus, it will pave the way for a more extensive use of magnonics in future technologies.

Bound States in the Continuum in Photonics and Metasurfaces: From Phenomena to Applications

AbstractBound states in the continuum (BICs) refer to nonradiative eigenmodes located within the radiation continuum, possessing infinitely high Q‐factor and enabling exceptionally strong light–matter interactions. BICs have found applications across various domains in photonics and metasurfaces, including nonlinear optical enhancement, vortex beam generation, sensor technology, microlasers, and other related areas. This work starts by classifying the phenomena of BICs and introducing the theoretical formation mechanisms and topological characteristics. Then, the current and advanced applications based on BIC‐devices are highlighted. Lastly, this work discusses the current challenges in studies related to BICs, such as structural precision, material selection, and measurement difficulties, and prospect the possible potentials in future developments. This review provides a theoretical background and application prospects of BIC‐engineered devices in optical and photonics fields, laying a solid foundation for future industrial applications.

Two-Dimensional Rare-Earth Metal Phosphides: From Weyl Semimetal to Semiconductor.

Two-dimensional (2D) nanomaterials have garnered extensive attention owing to their unique properties and versatile application. Here, a family of 2D rare-earth metal phosphides (M2P, M = Sc, Y, La) and their derivatives M2POT (T = F, OH) is developed to find their topological and electronic properties on the basis of density functional theory simulations. We show that the 2D M2P compounds are most possibly obtained from thermodynamically stable M2InP by chemical exfoliation. The In with a substantial atomic radius of 156 pm exhibits weak polarization ability, resulting in homogeneity of the electron cloud and a weakening of the M-In bond relative to the M-P bond. Upon exfoliation of the In layer, the M22+P3-:e- emerges as an electride with surface electrons, which is attributed to the larger ion radius and lower electronegativity of M2+ ions in M2P. The metallic M2P is found to be a Weyl semimetal derived from the contribution of surface electrons. Further, by leveraging the high reactivity of surface electrons, surface functionalization can produce M2POT compounds with the increased valence state of M3+, which results in their semiconducting properties characterized by high carrier mobilities and strong built-in electronic fields. These distinct topological and electronic characteristics position the 2D M2P and M2POT as promising candidates for a wide range of applications.

Exploring the Influence of Approximations for Simulating Valence Excited X-ray Spectra.

First-principles simulations of excited-state X-ray spectra are becoming increasingly important to interpret the wealth of electronic and geometric information contained within femtosecond X-ray absorption spectra recorded at X-ray Free Electron Lasers (X-FELs). However, because the transition dipole matrix elements must be calculated between two excited states (i.e., the valence excited state and the final core excited state arising from the initial valence excited state) of very different energies, this can be challenging and time-consuming to compute. Herein using two molecules, protonated formaldimine and cyclobutanone, we assess the ability of n-electron valence-state perturbation theory (NEVPT2), equation-of-motion coupled-cluster theory (EOM-CCSD), linear-response time-dependent density functional theory (LR-TDDFT) and the maximum overlap method (MOM) to describe excited state X-ray spectra. Our study focuses in particular on the behavior of these methods away from the Franck-Condon geometry and in the vicinity of important topological features of excited-state potential energy surfaces, namely, conical intersections. We demonstrate that the primary feature of excited-state X-ray spectra is associated with the core electron filling the hole created by the initial valence excitation, a process that all of the methods can capture. Higher energy states are generally weaker, but importantly much more sensitive to the nature of the reference electronic wave function. As molecular structures evolve away from the Franck-Condon geometry, changes in the spectral shape closely follow the underlying valence excitation, highlighting the importance of accurately describing the initial valence excitation to simulate the excited-state X-ray absorption spectra.

Using parenclitic networks on phaeochromocytoma and paraganglioma tumours provides novel insights on global DNA methylation

Despite the prevalence of sequencing data in biomedical research, the methylome remains underrepresented. Given the importance of DNA methylation in gene regulation and disease, it is crucial to address the need for reliable differential methylation methods. This work presents a novel, transferable approach for extracting information from DNA methylation data. Our agnostic, graph-based pipeline overcomes the limitations of commonly used differential methylation techniques and addresses the “small n, big k” problem. Pheochromocytoma and Paraganglioma (PPGL) tumours with known genetic aetiologies experience extreme hypermethylation genome wide. To highlight the effectiveness of our method in candidate discovery, we present the first phenotypic classifier of PPGLs based on DNA methylation achieving 0.7 ROC-AUC. Each sample is represented by an optimised parenclitic network, a graph representing the deviation of the sample’s DNA methylation from the expected non-aggressive patterns. By extracting meaningful topological features, the dimensionality and, hence, the risk of overfitting is reduced, and the samples can be classified effectively. By using an explainable classification method, in this case logistic regression, the key CG loci influencing the decision can be identified. Our work provides insights into the molecular signature of aggressive PPGLs and we propose candidates for further research. Our optimised parenclitic network implementation improves the potential utility of DNA methylation data and offers an effective and complete pipeline for studying such datasets.

Topological features in continuum mechanics: from simple to complex bodies

Topological features have a ubiquitous influence on the behaviour of condensed matter, from the qualitative analysis of fluids flows to the classification of defects in simple and complex solids. We review results concerning the incidence of topological features on foundational aspects of the mechanics of simple and complex bodies, with particular emphasis on the mechanics of defects. Pertinent to this last issue, unusual concepts such as the relative power or the structure invariance of the Clausius–Duhem inequality under diffeomorphism-based observer changes are discussed.

Topological pumping in an inhomogeneous Aubry-André model

The Aubry-André model is a fundamental theoretical model that exhibits interesting topological features. In this paper, we examine topologically protected boundary states in the inhomogeneous off-diagonal Aubry-André model. In contrast to the homogeneous case, the inhomogeneity triggers boundary states at phase boundaries that separate two distinct non-trivial topological domains. Remarkably, the topological character of the boundary states is predicted through topological pumping, where a boundary state is transferred from one boundary across the bulk region to the other by adiabatically tuning the pump parameter. Moreover, the role of the off-diagonal modulation strength (λ) on the transfer efficiency of the topological pumping is addressed. To support our results, we investigate the time evolution of a continuous-time quantum walk and show that its spread rate and λ are inversely related. Our work provides a new avenue to harness topological features of the Aubry-André model, where topological pumping can be used for robust quantum transport.

Effect of brain network scale on Persistence Cycles: An ADNI comparative study

AbstractBackgroundOur study aims to understand how network resolution scale impacts the association between topological features in the brain network and Alzheimer’s disease (AD) outcomes. In particular, we examine persistence homological cycles, derived from DTI and fMRI neuroimaging. We study subjects in various stages of AD progression. We utilize structural and functional connectomes extracted from aforementioned modalities and assess between group differences in average persistence of homological cycles, across various scales.MethodThis study is conducted on data obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database and utilizes two different modalities, with two independent datasets. First dataset involves structural connectomes obtained from diffusion tensor imaging (DTI) based on Lausanne parcellation on five scales: 33, 60,125, 250 and 500. The second dataset consists of functional connectome obtain from fMRI scans, measuring Pearson correlations between BOLD signal fluctuations of various regions of interests in the brain, based on Shaefer atlas and ten scales, starting from 100 up to 1000. We use topological data analysis tools, specifically persistence homology and computational package ripser to compute birth and death time for homological cycles for the underlying topological network obtained from both structural and functional connectomes, for all scales. Life of a cycle is defined to be birth time subtracted from death time, also equal to the length of a bar in the persistence barcode. Average Persistence (AP) is average length of a bar in the persistence barcode for each subject’s brain network. We perform a comparative study among different stages of disease progression across all scales of resolution.ResultWe find that the t‐test for the means of average persistence for different stages of disease progression reveals statistically significant between‐group difference in scale‐33 (HC vs MCI and MCI vs AD) and in scale‐125 (MCI vs AD) for structural connectomes (Figure 1) and in scale‐100 (MCI vs AD and HC vs AD) for functional connectomes (Figure 2). We also note that average persistence tends to stabilize as we increase image resolution.ConclusionFrom topological point of view, lower resolution images surprisingly perform better at capturing between group differences in various degrees of disease progression.

Hybrid Network Using Dynamic Graph Convolution and Temporal Self-Attention for EEG-Based Emotion Recognition.

The electroencephalogram (EEG) signal has become a highly effective decoding target for emotion recognition and has garnered significant attention from researchers. Its spatial topological and time-dependent characteristics make it crucial to explore both spatial information and temporal information for accurate emotion recognition. However, existing studies often focus on either spatial or temporal aspects of EEG signals, neglecting the joint consideration of both perspectives. To this end, this article proposes a hybrid network consisting of a dynamic graph convolution (DGC) module and temporal self-attention representation (TSAR) module, which concurrently incorporates the representative knowledge of spatial topology and temporal context into the EEG emotion recognition task. Specifically, the DGC module is designed to capture the spatial functional relationships within the brain by dynamically updating the adjacency matrix during the model training process. Simultaneously, the TSAR module is introduced to emphasize more valuable time segments and extract global temporal features from EEG signals. To fully exploit the interactivity between spatial and temporal information, the hierarchical cross-attention fusion (H-CAF) module is incorporated to fuse the complementary information from spatial and temporal features. Extensive experimental results on the DEAP, SEED, and SEED-IV datasets demonstrate that the proposed method outperforms other state-of-the-art methods.