arXiv subjects

Tao Hou

Publications and source records attributed to Tao Hou.

At least 19 recordsLinked to original sources

arXiv2026

Linked Barcode for Persistence Induced by Filtrations

The well-known persistence algorithm summarizes the evolution of homological cycles into what is called a \emph{barcode} while scanning an input simplicial filtration. We show that this summarization process can be enriched by monitoring other algebraic structures that weave through different dimensions. In particular, we propose an algorithm to monitor the $(p+1)$-chains that make $p$-cycles to be $p$-boundaries and then morph into $(p+1)$-cycles. In effect, we get extra bars called \emph{links} connecting the bars in dimension $p$ with the bars in dimension $p+1$ in the persistence barcode. The links produce extra barcodes, which we call \emph{link barcodes} in addition to the usual ones obtained by standard persistence. The link barcodes, as such, are not stable. However, we can make them stable using a fixed ``reference'' filtration. We apply the link barcodes to the graph isomorphism problem and to the link prediction problem in temporal networks exhibiting its discriminating power through these experiments.

cs.CG↗

arXiv2026

Updating zigzag representatives efficiently

Computation of zigzag persistence has progressed in recent years, with results showing that complexities of many problems closely align with those in the non-zigzag setting. The major efficiency gap now lies in the updating of zigzag representatives. In this paper, we propose efficient algorithms for updating zigzag representatives based on a recent algorithm for extracting zigzag representatives from a $R=DV$ decomposition of a constructed non-zigzag. The main difficulty for designing our update algorithms lies in the adjacency change occurring in two operations that elongate or shorten a filtration. Despite the adjacency change, we find that the update can still be done efficiently in quadratic time.

cs.CG↗

arXiv2025

Hyperbolic Continuous Topological Transition in Real Space

Hyperbolic topological transitions refer to the transformation of is isofrequency contours in hyperbolic materials from one topology (e.g., hyperbolic) to another (e.g., elliptical or a different hyperbolic topology). However, current research remains limited to investigating topological transitions in momentum space, thereby hindering the simultaneous real-space observation of distinct hyperbolic states and their associated topological transitions within a single system. In this work, we investigate real-space hyperbolic continuous topological transitions using gradient-index (GRIN) lenses, exemplified by hyperbolic Luneburg lens. By introducing Wick rotations, we demonstrate how spatially modulated refractive indices, mediated by variations in out-of-plane permittivity, drive continuous transitions between hyperbolic Type I and Type II topologies. Furthermore, using a harmonic oscillator model, we uncover the intrinsic relationship between the parameter E of hyperbolic Luneburg lens and its predominant topological behavior, whether hyperbolic Type I or Type II, and extend this concept to a broader framework of Morse lenses. This work provides a theoretical foundation for designing materials with tunable topological properties, advancing applications in photonics, metamaterials, and beyond.

physics.optics↗

arXiv2025

Hyperbolic absolute instruments

As a lens capable of sending images of deep sub-wavelength objects to the far field, the hyperlens has garnered significant attention for its super-resolution and magnification capabilities. However, traditional hyperlenses require extreme permittivity ratios and fail to achieve geometrically perfect imaging, significantly constraining their practical applications. In this paper, we introduce the general versions of hyperbolic absolute instruments from the perspective of dispersion and fundamental optical principles. These instruments enable the formation of closed orbits in geometric optics, allowing hyperlenses to achieve aberration-free, perfect imaging. This development not only provides a flexible and practical tool for enhancing the performance of traditional hyperlens, but also opens new possibilities for new optoelectronics applications based on hyperbolic ray dynamics.

physics.optics↗

arXiv2025

Apex Representatives

Given a zigzag filtration, we want to find its barcode representatives, i.e., a compatible choice of bases for the homology groups that diagonalize the linear maps in the zigzag. To achieve this, we convert the input zigzag to a levelset zigzag of a real-valued function. This function generates a Mayer-Vietoris pyramid of spaces, which generates an infinite strip of homology groups. We call the origins of indecomposable (diamond) summands of this strip their apexes and give an algorithm to find representative cycles in these apexes from ordinary persistence computation. The resulting representatives map back to the levelset zigzag and thus yield barcode representatives for the input zigzag. Our algorithm for lifting a $p$-dimensional cycle from ordinary persistence to an apex representative takes $O(p \cdot m \log m)$ time. From this we can recover zigzag representatives in time $O(\log m + C)$, where $C$ is the size of the output.

cs.CG↗

arXiv2024

Tracking the Persistence of Harmonic Chains: Barcode and Stability

The persistence barcode is a topological descriptor of data that plays a fundamental role in topological data analysis. Given a filtration of data, the persistence barcode tracks the evolution of its homology groups. In this paper, we introduce a new type of barcode, called the harmonic chain barcode, which tracks the evolution of harmonic chains. In addition, we show that the harmonic chain barcode is stable. Given a filtration of a simplicial complex of size $m$, we present an algorithm to compute its harmonic chain barcode in $O(m^3)$ time. Consequently, the harmonic chain barcode can enrich the family of topological descriptors in applications where a persistence barcode is applicable, such as feature vectorization and machine learning.

cs.CG↗

arXiv2024

Interlayer Charge-density-wave Vector Phase Induced Structural Chirality

Chiral charge density waves (CDWs) have attracted intense interest due to their exotic quantum properties, yet the microscopic origin of structural chirality emerging from correlated charge order remains elusive. Here, we reveal that the interlayer phases of CDW wave vectors, an overlooked degree of freedom, play a crucial role in driving chiral structural displacements in layered CDW materials. By explicitly incorporating the interlayer phases in first-principles calculations, we successfully obtained the chiral structure of the CDW phases of AV$_3$Sb$_5$ (A= K, Rb, and Cs) and 1T-TiSe$_2$. The electronic and optical properties of the predicted chiral structures are consistent with experimental measurements of these materials in their CDW phases. We further predict that 1T-NbSe$_2$ is a promising material candidate for realizing chiral CDW order. Beyond materials prediction, our theory reveals that the chiral CDW can be manipulated by electron filling. Our study opens new avenues for discovering, designing, and engineering chiral CDW materials.

cond-mat.mtrl-sci↗

arXiv2024

A Fast Algorithm for Computing Zigzag Representatives

Zigzag filtrations of simplicial complexes generalize the usual filtrations by allowing simplex deletions in addition to simplex insertions. The barcodes computed from zigzag filtrations encode the evolution of homological features. Although one can locate a particular feature at any index in the filtration using existing algorithms, the resulting representatives may not be compatible with the zigzag: a representative cycle at one index may not map into a representative cycle at its neighbor. For this, one needs to compute compatible representative cycles along each bar in the barcode. It is known that the barcode for a zigzag filtration with $m$ insertions and deletions can be computed in $O(m^\omega)$ time, where $\omega< 2.373$ is the matrix multiplication exponent. However, it is not known how to compute the compatible representatives so efficiently. For a non-zigzag filtration, the classical matrix-based algorithm provides representatives in $O(m^3)$ time, which can be improved to $O(m^\omega)$. However, no known algorithm for zigzag filtrations computes the representatives with the $O(m^3)$ time bound. We present an $O(m^2n)$ time algorithm for this problem, where $n\leq m$ is the size of the largest complex in the filtration.

cs.CG↗

arXiv2024

Cosmology analogy for perfect hyperlens

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 metric of de Sitter spacetime in cosmology. 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 and mimic the de Sitter spacetime in naturally in-plane hyperbolic polaritons of {\alpha}-MoO3 films numerically, which can be achieved with a gradient thickness profile. Our work provides cosmological insights into the field regulation in hyperbolic materials, greatly innovates the design principles of traditional imaging lenses.

physics.optics↗

arXiv2024

Volume-optimal persistence homological scaffolds of hemodynamic networks covary with MEG theta-alpha aperiodic dynamics

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.

q-bio.NC↗

arXiv2024

FMDNN: A Fuzzy-guided Multi-granular Deep Neural Network for Histopathological Image Classification

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.

cs.CV↗

arXiv2024

A Comprehensive Survey on the Security of Smart Grid: Challenges, Mitigations, and Future Research Opportunities

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.

cs.CR↗

arXiv2024

Computing Zigzag Vineyard Efficiently Including Expansions and Contractions

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.

cs.CG↗

arXiv2024

Discovery of a hybrid topological quantum state in an elemental solid

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.

cond-mat.mes-hall↗

arXiv2023

IoTGAN: GAN Powered Camouflage Against Machine Learning Based IoT Device Identification

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.

cs.CR↗

arXiv2023

A Survey on Post-Quantum Cryptography: State-of-the-Art and Challenges

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.

cs.CR↗

arXiv2023

The Evolution of Keylogger Technologies: A Survey from Historical Origins to Emerging Opportunities

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.

cs.CR↗

arXiv2023

Topological chiral kagome lattice

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 $π$ 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.

cond-mat.mtrl-sci↗