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With the emergence of super-resolution lenses such as superlens and hyperlens, coupled with advancements in metamaterials, the diffraction limit of approximately half wavelength is no longer unbreakable. However, superlenses are easily affected by weak intrinsic losses and hyperlenses cannot achieve perfect imaging, significantly constraining their practical utility. To address these challenges, here we propose a perfect hyperlens based on the transformation optics. Importantly, perfect hyperlens is capable of self-focusing in geometrical optics while supporting propagating waves with exceptionally large wavenumbers, which endows it with key advantages such as ultra-high resolution, no aberration and strong robustness. Furthermore, we demonstrate the hyperbolic focusing performance in naturally in-plane hyperbolic polaritons of {\alpha}-MoO3 films numerically, which can be achieved by gradient thickness. The results greatly innovate the design principles of traditional imaging lens, providing many potentially significant applications for super-resolution real-time imaging, lithography, and sensing., Comment: 23 pages, 8 figures

Histopathological image classification constitutes a pivotal task in computer-aided diagnostics. The precise identification and categorization of histopathological images are of paramount significance for early disease detection and treatment. In the diagnostic process of pathologists, a multi-tiered approach is typically employed to assess abnormalities in cell regions at different magnifications. However, feature extraction is often performed at a single granularity, overlooking the multi-granular characteristics of cells. To address this issue, we propose the Fuzzy-guided Multi-granularity Deep Neural Network (FMDNN). Inspired by the multi-granular diagnostic approach of pathologists, we perform feature extraction on cell structures at coarse, medium, and fine granularity, enabling the model to fully harness the information in histopathological images. We incorporate the theory of fuzzy logic to address the challenge of redundant key information arising during multi-granular feature extraction. Cell features are described from different perspectives using multiple fuzzy membership functions, which are fused to create universal fuzzy features. A fuzzy-guided cross-attention module guides universal fuzzy features toward multi-granular features. We propagate these features through an encoder to all patch tokens, aiming to achieve enhanced classification accuracy and robustness. In experiments on multiple public datasets, our model exhibits a significant improvement in accuracy over commonly used classification methods for histopathological image classification and shows commendable interpretability., Comment: This paper has been accepted by IEEE Transactions on Fuzzy Systems for publication. Permission from IEEE must be obtained for all other uses, in any current or future media. The final version is available at [doi: 10.1109/TFUZZ.2024.3410929]

In this study, we conduct a comprehensive review of smart grid security, exploring system architectures, attack methodologies, defense strategies, and future research opportunities. We provide an in-depth analysis of various attack vectors, focusing on new attack surfaces introduced by advanced components in smart grids. The review particularly includes an extensive analysis of coordinated attacks that incorporate multiple attack strategies and exploit vulnerabilities across various smart grid components to increase their adverse impact, demonstrating the complexity and potential severity of these threats. Following this, we examine innovative detection and mitigation strategies, including game theory, graph theory, blockchain, and machine learning, discussing their advancements in counteracting evolving threats and associated research challenges. In particular, our review covers a thorough examination of widely used machine learning-based mitigation strategies, analyzing their applications and research challenges spanning across supervised, unsupervised, semi-supervised, ensemble, and reinforcement learning. Further, we outline future research directions and explore new techniques and concerns. We first discuss the research opportunities for existing and emerging strategies, and then explore the potential role of new techniques, such as large language models (LLMs), and the emerging threat of adversarial machine learning in the future of smart grid security.

Higher-order properties of functional magnetic resonance imaging (fMRI) induced connectivity have been shown to unravel many exclusive topological and dynamical insights beyond pairwise interactions. Nonetheless, whether these fMRI-induced higher-order properties play a role in disentangling other neuroimaging modalities' insights remains largely unexplored and poorly understood. In this work, by analyzing fMRI data from the Human Connectome Project Young Adult dataset using persistent homology, we discovered that the volume-optimal persistence homological scaffolds of fMRI-based functional connectomes exhibited conservative topological reconfigurations from the resting state to attentional task-positive state. Specifically, while reflecting the extent to which each cortical region contributed to functional cycles following different cognitive demands, these reconfigurations were constrained such that the spatial distribution of cavities in the connectome is relatively conserved. Most importantly, such level of contributions covaried with powers of aperiodic activities mostly within the theta-alpha (4-12 Hz) band measured by magnetoencephalography (MEG). This comprehensive result suggests that fMRI-induced hemodynamics and MEG theta-alpha aperiodic activities are governed by the same functional constraints specific to each cortical morpho-structure. Methodologically, our work paves the way toward an innovative computing paradigm in multimodal neuroimaging topological learning., Comment: The code for our analyses is provided in https://github.com/ngcaonghi/scaffold_noise

Topology and interactions are foundational concepts in the modern understanding of quantum matter. Their nexus yields three significant research directions: competition between distinct interactions, as in the multiple intertwined phases, interplay between interactions and topology that drives the phenomena in twisted layered materials and topological magnets, and the coalescence of multiple topological orders to generate distinct novel phases. The first two examples have grown into major areas of research, while the last example remains mostly untouched, mainly because of the lack of a material platform for experimental studies. Here, using tunneling microscopy, photoemission spectroscopy, and theoretical analysis, we unveil a "hybrid" and yet novel topological phase of matter in the simple elemental solid arsenic. Through a unique bulk-surface-edge correspondence, we uncover that arsenic features a conjoined strong and higher-order topology, stabilizing a hybrid topological phase. While momentum-space spectroscopy measurements show signs of topological surface states, real-space microscopy measurements unravel a unique geometry of topology-induced step edge conduction channels revealed on various forms of natural nanostructures on the surface. Using theoretical models, we show that the existence of gapless step edge states in arsenic relies on the simultaneous presence of both a nontrivial strong Z2 invariant and a nontrivial higher-order topological invariant, providing experimental evidence for hybrid topology and its realization in a single crystal. Our discovery highlights pathways to explore the interplay of different kinds of band topology and harness the associated topological conduction channels in future engineered quantum or nano-devices., Comment: Nature (2024); in press

As the digital world evolves, so do the threats to our security do too. Keyloggers were once a large threat to the cyber world. Though undergoing many transformations alongside the technological advancements of today, it is important to raise questions about the importance of Anti-Keyloggers in our current state of cyber security. This survey dives into the historical evolution of Keyloggers and investigates their current day forms. Within this inspection of Keyloggers, we must propose whether Anti-Keyloggers serve a purpose to this ever-changing landscape before us or if emerging strategies have rendered them obsolete.

The paper explains that post-quantum cryptography is necessary due to the introduction of quantum computing causing certain algorithms to be broken. We analyze the different types of post-quantum cryptography, quantum cryptography and quantum-resistant cryptography, to provide a thorough understanding of the current solutions to the problems and their limitations. We explain the current state of quantum computing and how it has changed over time while discussing possible attacks on both types of post-quantum cryptography. Next, current post-quantum algorithms are discussed, and implementations are demonstrated. Lastly, we conclude that due to quantum cryptography's present limitations it is not a viable solution like it is often presented to be and that it is currently better to use quantum-resistant cryptography.

Chirality, a fundamental structural property of crystals, can induce many unique topological quantum phenomena. In kagome lattice, unconventional transports have been reported under tantalizing chiral charge order. Here, we show how by deforming the kagome lattice to obtain a three-dimensional (3D) chiral kagome lattice in which the key band features of the non-chiral 2D kagome lattice - flat energy bands, van Hove singularities (VHSs), and degeneracies - remain robust in both the $k_z$ = 0 and $\pi$ planes in momentum space. Given the handedness of our kagome lattice, degenerate momentum points possess quantized Chern numbers, ushering in the realization of Weyl fermions. Our 3D chiral kagome lattice surprisingly exhibits 1D behavior on its surface, where topological surface Fermi arc states connecting Weyl fermions are dispersive in one momentum direction and flat in the other direction. These 1D Fermi arcs open up unique possibilities for generating unconventional non-local transport phenomena at the interfaces of domains with different handedness, and the associated enhanced conductance as the separation of the leads on the surface is increased. Employing first-principles calculations, we investigate in-depth the electronic and phononic structures of representative materials within the ten space groups that can support topological chiral kagome lattices. Our study opens a new research direction that integrates the advantages of structural chirality with those of a kagome lattice and thus provides a new materials platform for exploring unique aspects of correlated topological physics in chiral lattices., Comment: 7 pages, 4 figures

Vines and vineyard connecting a stack of persistence diagrams have been introduced in the non-zigzag setting by Cohen-Steiner et al. We consider computing these vines over changing filtrations for zigzag persistence while incorporating two more operations: expansions and contractions in addition to the transpositions considered in the non-zigzag setting. Although expansions and contractions can be implemented in quadratic time in the non-zigzag case by utilizing the linear-time transpositions, it is not obvious how they can be carried out under the zigzag framework with the same complexity. While transpositions alone can be easily conducted in linear time using the recent FastZigzag algorithm, expansions and contractions pose difficulty in breaking the barrier of cubic complexity. Our main result is that, the half-way constructed up-down filtration in the FastZigzag algorithm indeed can be used to achieve linear time complexity for transpositions and quadratic time complexity for expansions and contractions, matching the time complexity of all corresponding operations in the non-zigzag case., Comment: Updated funding information for one co-author

It is well known that ordinary persistence on graphs can be computed more efficiently than the general persistence. Recently, it has been shown that zigzag persistence on graphs also exhibits similar behavior. Motivated by these results, we revisit graph persistence and propose efficient algorithms especially for local updates on filtrations, similar to what is done in ordinary persistence for computing the vineyard. We show that, for a filtration of length $m$, (i) switches (transpositions) in ordinary graph persistence can be done in $O(\log m)$ time; (ii) zigzag persistence on graphs can be computed in $O(m\log m)$ time, which improves a recent $O(m\log^4n)$ time algorithm assuming $n$, the size of the union of all graphs in the filtration, satisfies $n\in\Omega({m^\varepsilon})$ for any fixed $0<\varepsilon<1$; (iii) open-closed, closed-open, and closed-closed bars in dimension $0$ for graph zigzag persistence can be updated in $O(\log m)$ time, whereas the open-open bars in dimension $0$ and closed-closed bars in dimension $1$ can be done in $O(\sqrt{m}\,\log m)$ time.

Hyperbolic shear polaritons (HShPs) emerge with widespread attention as a new class of polariton modes with broken symmetry due to shear lattices. In this letter, we find a new mechanism of generating HShPs. When utilizing vortex waves as excitation sources of hyperbolic materials without off-diagonal elements, HShPs will appear. In addition, this asymmetric HShPs can be recovered as symmetric modes away from the source, with a critical transition mode between the left-skewed and right-skewed HShPs, via tuning the magnitude of the off-diagonal imaginary component and controlling the topological charge of vortex source. It is worth mentioning that we explore the influence of parity of topological charges on the field distribution and demonstrate these exotic phenomena from numerical and analytical perspectives. Our results will promote new opportunities for both HShPs and vortex waves, widening the horizon for various hyperbolic materials based on vortex sources and offering a new degree of freedom to control various kinds of polaritons.

Recently, the magnetic domain walls have been experimentally observed in antiferromagnetic topological insulators MnBi$_2$Te$_4$, where we find that the topological zero-line modes (ZLMs) appear along the domain walls. Here, we theoretically demonstrate that these ZLMs are layer-dependent in MnBi$_2$Te$_4$ multilayers. For domain walls with out-of-plane ferromagnetism, we find that ZLMs are equally distributed in the odd-number layers. When domain walls possess in-plane magnetization, the ZLMs can also exist in even-number layers due to in-plane mirror-symmetry breaking. Moreover, the conductive channels are mainly distributed in the outermost layers with increasing layer thickness. Our findings lay out a strategy in manipulating ZLMs and also can be utilized to distinguish the corresponding magnetic structures.

Recent experiments report a charge density wave (CDW) in the antiferromagnet FeGe, but the nature of the charge ordering and the associated structural distortion remains elusive. We discuss the structural and electronic properties of FeGe. Our proposed ground state phase accurately captures atomic topographies acquired by scanning tunneling microscopy. We show that the 2$\times$2$\times$1 CDW likely results from the Fermi surface nesting of hexagonal-prism-shaped kagome states. FeGe is found to exhibit distortions in the positions of the Ge atoms instead of the Fe atoms in the kagome layers. Using in-depth first-principles calculations and analytical modeling, we demonstrate that this unconventional distortion is driven by the intertwining of magnetic exchange coupling and CDW interactions in this kagome material. Movement of Ge atoms from their pristine positions also enhances the magnetic moment of the Fe kagome layers. Our study indicates that magnetic kagome lattices provide a material candidate for exploring the effects of strong electronic correlations on the ground state and their implications for transport, magnetic, and optical responses in materials.

Zigzag persistence is a powerful extension of the standard persistence which allows deletions of simplices besides insertions. However, computing zigzag persistence usually takes considerably more time than the standard persistence. We propose an algorithm called FastZigzag which narrows this efficiency gap. Our main result is that an input simplex-wise zigzag filtration can be converted to a cell-wise non-zigzag filtration of a $\Delta$-complex with the same length, where the cells are copies of the input simplices. This conversion step in FastZigzag incurs very little cost. Furthermore, the barcode of the original filtration can be easily read from the barcode of the new cell-wise filtration because the conversion embodies a series of diamond switches known in topological data analysis. This seemingly simple observation opens up the vast possibilities for improving the computation of zigzag persistence because any efficient algorithm/software for standard persistence can now be applied to computing zigzag persistence. Our experiment shows that this indeed achieves substantial performance gain over the existing state-of-the-art softwares., Comment: arXiv admin note: substantial text overlap with arXiv:2110.06315

With the proliferation of IoT devices, researchers have developed a variety of IoT device identification methods with the assistance of machine learning. Nevertheless, the security of these identification methods mostly depends on collected training data. In this research, we propose a novel attack strategy named IoTGAN to manipulate an IoT device's traffic such that it can evade machine learning based IoT device identification. In the development of IoTGAN, we have two major technical challenges: (i) How to obtain the discriminative model in a black-box setting, and (ii) How to add perturbations to IoT traffic through the manipulative model, so as to evade the identification while not influencing the functionality of IoT devices. To address these challenges, a neural network based substitute model is used to fit the target model in black-box settings, it works as a discriminative model in IoTGAN. A manipulative model is trained to add adversarial perturbations into the IoT device's traffic to evade the substitute model. Experimental results show that IoTGAN can successfully achieve the attack goals. We also develop efficient countermeasures to protect machine learning based IoT device identification from been undermined by IoTGAN.

Computing persistence over changing filtrations give rise to a stack of 2D persistence diagrams where the birth-death points are connected by the so-called `vines'. We consider computing these vines over changing filtrations for zigzag persistence. We observe that eight atomic operations are sufficient for changing one zigzag filtration to another and provide update algorithms for each of them. Six of these operations that have some analogues to one or multiple transpositions in the non-zigzag case can be executed as efficiently as their non-zigzag counterparts. This approach takes advantage of a recently discovered algorithm for computing zigzag barcodes by converting a zigzag filtration to a non-zigzag one and then connecting barcodes of the two with a bijection. The remaining two atomic operations do not have a strict analogue in the non-zigzag case. For them, we propose algorithms based on explicit maintenance of representatives (homology cycles) which can be useful in their own rights for applications requiring explicit updates of representatives.

Duality results connecting persistence modules for absolute and relative homology provides a fundamental understanding into persistence theory. In this paper, we study similar associations in the context of zigzag persistence. Our main finding is a weak duality for the so-called non-repetitive zigzag filtrations in which a simplex is never added again after being deleted. The technique used to prove the duality for non-zigzag persistence does not extend straightforwardly to our case. Accordingly, taking a different route, we prove the weak duality by converting a non-repetitive filtration to an up-down filtration by a sequence of diamond switches. We then show an application of the weak duality result which gives a near-linear algorithm for computing the $p$-th and a subset of the $(p-1)$-th persistence for a non-repetitive zigzag filtration of a simplicial $p$-manifold. Utilizing the fact that a non-repetitive filtration admits an up-down filtration as its canonical form, we further reduce the problem of computing zigzag persistence for non-repetitive filtrations to the problem of computing standard persistence for which several efficient implementations exist. Our experiment shows that this achieves substantial performance gain. Our study also identifies repetitive filtrations as instances that fundamentally distinguish zigzag persistence from the standard persistence.

In standard persistent homology, a persistent cycle born and dying with a persistence interval (bar) associates the bar with a concrete topological representative, which provides means to effectively navigate back from the barcode to the topological space. Among the possibly many, optimal persistent cycles bring forth further information due to having guaranteed quality. However, topological features usually go through variations in the lifecycle of a bar which a single persistent cycle may not capture. Hence, for persistent homology induced from PL functions, we propose levelset persistent cycles consisting of a sequence of cycles that depict the evolution of homological features from birth to death. Our definition is based on levelset zigzag persistence which involves four types of persistence intervals as opposed to the two types in standard persistence. For each of the four types, we present a polynomial-time algorithm computing an optimal sequence of levelset persistent $p$-cycles for the so-called weak $(p+1)$-pseudomanifolds. Given that optimal cycle problems for homology are NP-hard in general, our results are useful in practice because weak pseudomanifolds do appear in applications. Our algorithms draw upon an idea of relating optimal cycles to min-cuts in a graph that we exploited earlier for standard persistent cycles. Note that levelset zigzag poses non-trivial challenges for the approach because a sequence of optimal cycles instead of a single one needs to be computed in this case.

Tomography is a widely used tool for analyzing microstructures in three dimensions (3D). The analysis, however, faces difficulty because the constituent materials produce similar grey-scale values. Sometimes, this prompts the image segmentation process to assign a pixel/voxel to the wrong phase (active material or pore). Consequently, errors are introduced in the microstructure characteristics calculation. In this work, we develop a filtering algorithm called PerSplat based on topological persistence (a technique used in topological data analysis) to improve segmentation quality. One problem faced when evaluating filtering algorithms is that real image data in general are not equipped with the `ground truth' for the microstructure characteristics. For this study, we construct synthetic images for which the ground-truth values are known. On the synthetic images, we compare the pore tortuosity and Minkowski functionals (volume and surface area) computed with our PerSplat filter and other methods such as total variation (TV) and non-local means (NL-means). Moreover, on a real 3D image, we visually compare the segmentation results provided by our filter against TV and NL-means. The experimental results indicate that PerSplat provides a significant improvement in segmentation quality.

In gated bilayer graphene, topological zero-line modes (ZLMs) appear along lines separating regions with opposite valley Hall topologies. Although it is experimentally difficult to design the electric gates to realize ZLMs due to the extremely challenging techniques, twisted bilayer graphene provides a natural platform to produce ZLMs in the presence of uniform electric field. In this Letter, we develop a set of wavepacket dynamics, which can be utilized to characterize various gapless edge modes and can quantitatively reproduce the electronic transport properties at topological intersections. To our surprise, in the minimally twisted bilayer graphene where a topological trifurcation intersection naturally arises, we show that the counterintuitive current partition (i.e., the direct transport propagation) originates from the microscopic mechanism "bypass jump". Our method can be applied to understand the microscopic pictures of the electronic transport features of all kinds of topological states.

Graphs model real-world circumstances in many applications where they may constantly change to capture the dynamic behavior of the phenomena. Topological persistence which provides a set of birth and death pairs for the topological features is one instrument for analyzing such changing graph data. However, standard persistent homology defined over a growing space cannot always capture such a dynamic process unless shrinking with deletions is also allowed. Hence, zigzag persistence which incorporates both insertions and deletions of simplices is more appropriate in such a setting. Unlike standard persistence which admits nearly linear-time algorithms for graphs, such results for the zigzag version improving the general $O(m^\omega)$ time complexity are not known, where $\omega< 2.37286$ is the matrix multiplication exponent. In this paper, we propose algorithms for zigzag persistence on graphs which run in near-linear time. Specifically, given a filtration with $m$ additions and deletions on a graph with $n$ vertices and edges, the algorithm for $0$-dimension runs in $O(m\log^2 n+m\log m)$ time and the algorithm for 1-dimension runs in $O(m\log^4 n)$ time. The algorithm for $0$-dimension draws upon another algorithm designed originally for pairing critical points of Morse functions on $2$-manifolds. The algorithm for $1$-dimension pairs a negative edge with the earliest positive edge so that a $1$-cycle containing both edges resides in all intermediate graphs. Both algorithms achieve the claimed time complexity via dynamic graph data structures proposed by Holm et al. In the end, using Alexander duality, we extend the algorithm for $0$-dimension to compute the $(p-1)$-dimensional zigzag persistence for $\mathbb{R}^p$-embedded complexes in $O(m\log^2 n+m\log m+n\log n)$ time., Comment: The full version of the paper

We study the electronic transport properties at the intersection of three topological zero-lines as the elementary current partition node that arises in minimally twisted bilayer graphene. Unlike the partition laws of two intersecting zero-lines, we find that (i) the incoming current can be partitioned into both left-right adjacent topological channels and that (ii) the forward-propagating current is nonzero. By tuning the Fermi energy from the charge-neutrality point to a band edge, the currents partitioned into the three outgoing channels become nearly equal. Moreover, we find that current partition node can be designed as a perfect valley filter and energy splitter controlled by electric gating. By changing the relative electric field magnitude, the intersection of three topological zero-lines can transform smoothly into a single zero line, and the current partition can be controlled precisely. We explore the available methods for modulating this device systematically by changing the Fermi energy, the energy gap size, and the size of central gapless region. The current partition is also influenced by magnetic fields and the system size. Our results provide a microscopic depiction of the electronic transport properties around a unit cell of minimally twisted bilayer graphene and have far-reaching implications in the design of electron-beam splitters and interferometer devices., Comment: arXiv admin note: substantial text overlap with arXiv:1904.12826

The discovery of quantum Hall effect in two-dimensional (2D) electronic systems inspired the topological classifications of electronic systems1,2. By stacking 2D quantum Hall effects with interlayer coupling much weaker than the Landau level spacing, quasi-2D quantum Hall effects have been experimentally observed3~7, due to the similar physical origin of the 2D counterpart. Recently, in a real 3D electronic gas system where the interlayer coupling is much stronger than the Landau level spacing, 3D quantum Hall effect has been observed in ZrTe58. In this Letter, we report the electronic transport features of its sister bulk material, i.e., HfTe5, under external magnetic field. We observe a series of plateaus in Hall resistance \r{ho}xy as magnetic field increases until it reaches the quantum limit at 1~2 Tesla. At the plateau regions, the longitudinal resistance \r{ho}xx exhibits local minima. Although \r{ho}xx is still nonzero, its value becomes much smaller than \r{ho}xy at the last few plateaus. By mapping the Fermi surface via measuring the Shubonikov-de Haas oscillation, we find that the strength of Hall plateau is proportional to the Fermi wavelength, suggesting that its formation may be attributed to the gap opening from the interaction driven Fermi surface instability. By comparing the bulk band structures of ZrTe5 and HfTe5, we find that there exists an extra pocket near the Fermi level of HfTe5, which may lead to the finite but nonzero longitudinal conductance.