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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Malicious Cyber Activity Detection using Zigzag Persistence

In this study we synthesize zigzag persistence from topological data analysis with autoencoder-based approaches to detect malicious cyber activity, and derive analytic insights. Cybersecurity aims to safeguard computers, networks, and servers from various forms of malicious attacks, including network damage, data theft, and activity monitoring. We focus on the cybersecurity domain and investigate the detection of malicious activity using log data. We consider the dynamics of the log data and explore the changing topology of a hypergraph representation of this data to gain insights into the underlying activity. These hypergraphs capture complex interactions between processes, together with their temporal information. To study the changing topology we use zigzag persistence, which captures how topological features persist at multiple dimensions over time. We observe that this detects malicious activity in a cyber data set. To automate this detection we implement an autoencoder trained on a vectorization of the resulting zigzag persistence barcodes. Our experimental results demonstrate the effectiveness of the autoencoder in detecting malicious activity. Overall, this study highlights the potential of zigzag persistence and its combination with temporal hypergraphs for analyzing cybersecurity log data and detecting malicious behavior.

hypergraphs, temporal hypergraph, topological data↗
DOE OSTI2019

Parametrized homology via zigzag persistence

This paper introduces parametrized homology, a continuous-parameter generalization of levelset zigzag persistent homology that captures the behavior of the homology of the fibers of a real-valued function on a topological space. This information is encoded as a “barcode” of real intervals, each corresponding to a homological feature supported over that interval; or, equivalently, as a persistence diagram. Points in the persistence diagram are classified algebraically into four classes; geometrically, the classes identify the distinct ways in which homological features perish at the boundaries of their interval of persistence. We study the conditions under which spaces fibered over the real line have a well-defined parametrized homology; here, we establish the stability of these invariants and we show how the four classes of persistence diagram correspond to the four diagrams that appear in the theory of extended persistence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Topological Analysis of Temporal Hypergraphs

In this work we study the topological properties of temporal hypergraphs. Hypergraphs provide a higher dimensional generalization of a graph that is capable of capturing multi-way connections. As such, they have become an integral part of network science. A common use of hypergraphs is to model events as hyperedges in which the event can involve many elements as nodes. This provides a more complete picture of the event in comparison to the standard dyadic connection limitation of a graph. However, a common attribution to events is temporal information as an interval for when the event occurred. Consequently, a temporal hypergraph is born which accurately captures both the temporal information of events as well as their multi-way connections. Common tools for studying these temporal hypergraphs typically use summary statistics of snapshots from a sliding window procedure to capture changes in the underlying dynamics. However, these do not provide insight into how the changing structure of the hypergraph evolves and which components of the temporal hypergraph persist and are influential to the underlying system. To alleviate this need we leverage zigzag persistence from the field of Topological Data Analysis (TDA) to study the change in topological structure of time-evolving hypergraphs. We apply our pipeline to both a cyber security and social network dataset and show how the topological structure of their temporal hypergraphs change and can be used to understand the underlying dynamics.

hypergraphs, topological data analysis, zigzag per↗
NASA NTRS2022

A Survey of Mathematical Structures for Lunar Networks

To sustain the current and increasing accessibility of space, a scalable communications infrastructure (i.e. the Solar System Internet, SSI) is necessary. The goal of this paper is to begin the discovery of the fundamental underlying mathematical structure of space networks to help the research community harness these structures for algorithm development and optimization. To ensure the applicability of the research, the approaches are considered through the lens of simulated scenarios inspired by the Artemis Back-to-the-Moon mission set for 2024. We note that any approach to an SSI must fit under the umbrella of Delay Tolerant Networking (DTN), due to celestial mobility, high link latencies, high variance in link latencies, disconnections, lack of end-to-end paths, and so on. These difficulties are exacerbated by the fact that the underlying structure of a space network is a time-evolving network and may experience multiple discontinuities in its topology. In this paper we propose several novel approaches to a mathematical foundation for Delay Tolerant Networking Theory that fall outside the traditional scope of temporal network theory. These techniques include methods from Topological Data Analysis, Dynamic Graph Analysis, Applied Algebraic Geometry, Probability Theory, and Game Theory. Some of these methods include tools adapted to the study of dynamic metric spaces, such as zigzag persistent homology and their higher parameter analogs. We find that several of these methods target desired engineering outcomes such as discovery and automatic sub-netting. While each approach is theoretical, they are also algorithmic in nature and offer immediate practical applications. The paper concludes with comparisons of the various methods along with suggestions for future work.

Delay tolerant networking↗
DOE OSTI2022

Local Versus Global Distances for Zigzag and Multi-Parameter Persistence Modules

In this paper, we establish explicit and broadly applicable relationships between persistence-based distances computed locally and globally. In particular, we show that the bottleneck distance and the Wasserstein distance between two zigzag persistence modules restricted to an interval is always bounded above by the distance between the unrestricted versions. While this result is not surprising, it could have potential practical implications. We give two related applications for metric graph distances, as well as an extension for the matching distance between multi-parameter persistence modules.

persistent homology, metric graph, inequality↗
DOE OSTI2026

Ultrafast One-Dimensional Peierls-Distortion Dynamics in 1⁢T′−Re⁢S 2 Revealed by 4D Electron Microscopy

Rhenium disulfide (ReS 2 ), a prototypical 2D semiconductor with an anisotropic 1⁢T′ structure due to the pronounced Peierls distortion, has demonstrated great potential for polarization-dependent optoelectronics and photonics. Here, we report an ultrafast phase transition occurring within 1 ps, accompanied by a one-dimensional Peierls-distortion relaxation in 1⁢T′−ReS 2 revealed with combined 4D electron microscopy and time-dependent density functional theory calculations. Upon femtosecond laser pulse excitation, the Re-Re dimerization morphology rapidly transforms from a diamond cluster to zigzag chains and persists for several nanoseconds. Here, this ultrafast Peierls-distortion relaxation is further verified by transient changes in optical anisotropy via polarization-dependent transient absorption spectroscopy. Time-dependent density functional theory calculations attribute this novel phase transition to strong correlation between Peierls distortion and impulsive photoexcited carrier doping, predicting a transient band-gap collapse. This Letter opens up an exciting avenue for ultrafast control of Peierls-distortion-induced anisotropy and the metal-insulator transition in 1⁢T′−ReS 2 .

1T’-ReS2↗
DOE OSTI2026

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 $O(m^ω)$ in time, where $ω < 2.373$ 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 $O(m^ω)$. However, no known algorithm for zigzag filtrations computes the representatives with the $O(m^3)$ time bound. We present an $O(m^3 n)$ time algorithm for this problem, where $n ≤ m$ is the size of the largest complex in the filtration.

Persistent homology↗
DOE OSTI2025

Domain Nucleation and Growth in an Epitaxially Grown Wurtzite Ferroelectric

Ferroelectric domain nucleation and growth in epitaxial (Al, B, Sc)N films grown on n-GaN substrates are explored using a combination of ferroelectric property measurements and scanning transmission electron microscopy, including novel in situ switching studies. The films are electrically switched to nitrogen-polar (N-polar) and metal-polar (M-polar) configurations, attaining a remanent polarization of 120 µC cm −2 with coercive fields of ≈6 MV cm −1 . In the initial switching cycle, the ferroelectric domains nucleate near the bottom n-GaN electrode and develop domain walls with zigzag morphologies, while residual “dead layers” that do not switch from the as-deposited orientation persist at the top and bottom electrodes. The in situ microscopy experiments reveal that domain walls propagate fastest in the lateral direction, parallel to the electrode/film interface. These findings provide insights into the domain dynamics and structural evolution of wurtzite ferroelectrics, offering implications for next-generation electronic devices.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Dual Orbital Degeneracy Lifting in a Strongly Correlated Electron System

The local structure of NaTiSi 2 O 6 is examined across its Ti-dimerization orbital-assisted Peierls transition at 210 K. An atomic pair distribution function approach evidences local symmetry breaking preexisting far above the transition. The analysis unravels that, on warming, the dimers evolve into a short range orbital degeneracy lifted (ODL) state of dual orbital character, persisting up to at least 490 K. The ODL state is correlated over the length scale spanning ~ 6 sites of the Ti zigzag chains. Results imply that the ODL phenomenology extends to strongly correlated electron systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Visualizing topological edge states of single and double bilayer Bi supported on multibilayer Bi(111) films

Freestanding single bilayer Bi(111) is a two-dimensional topological insulator with edge states propagating along its perimeter. Given the interlayer coupling experimentally, the topological nature of Bi(111) thin films and the impact of the supporting substrate on the topmost Bi bilayer are still under debate. Combined with scanning tunneling microscopy and first-principles calculations, we systematically study the electronic properties of Bi(111) thin films grown on a $\mathrm{NbS}{\mathrm{e}}_{2}$ substrate. Two types of nonmagnetic edge structures, i.e., a conventional zigzag edge and a 2 x 1 reconstructed edge, coexist alternately at the boundaries of single bilayer islands, the topological edge states of which exhibit remarkably different energy and spatial distributions. Prominent edge states are persistently visualized at the edges of both single and double bilayer Bi islands, regardless of the underlying thickness of Bi(111) thin films. We provide an explanation for the topological origin of the observed edge states that is verified with first-principles calculations. Our paper clarifies the long-standing controversy regarding the topology of Bi(111) thin films and reveals the tunability of topological edge states via edge modifications.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Thickness dependence of electronic structure and optical properties of a correlated van der Waals antiferromagnetic NiPS 3 thin film

In this work, we study the thickness dependence of the electronic, magnetic, and optical properties of a NiPS 3 thin film, which is an antiferromagnetic charge-transfer insulator. Utilizing state-of-the-art advanced density functionals, we find the antiferromagnetic zigzag order, the band gap, and the main peaks in the dielectric tensor are all in good agreement with the corresponding experimental values. Upon thinning, the zigzag antiferromagnetic order becomes virtually degenerate with a competing Néel order, consistent with the suppression of long-range order observed by Raman spectroscopy due to strong magnetic fluctuations. Additionally, due to the robustness of the electronic band gap observed by spectroscopic ellipsometry measurements above T N , we suggest that the persistence of the band gap is driven by strong electronic correlations. Other systematic changes in electronic dispersion, effective mass, and Kerr angle with thickness are also discussed. Finally, an applied external electric field is found to suppress the band gap by up to 13%, until precipitating an insulator-metal transition at a critical field value of 0.7 eV/Å.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Carbon-carbon interactions in warm dense titanium carbide

Encouraged by experimental reports of diamond precipitation in carbon-containing materials under warm dense matter conditions and in shock compression experiments, we examine the behavior of carbon in TiC using density functional theory-molecular dynamics simulations. Two polymorphs of TiC are considered, the ambient-pressure B1 ($Fm$$\overline{3}$$m$) structure in which C-C interactions are prevented by geometric constraints, and a high-pressure Cmcm structure in which C atoms condense into zigzag chains. Chemistry-inspired bonding analyses confirm the covalently bound nature of these chains and further illuminate important interatomic interactions in both structures. Upon melting of B1 TiC, new short-range C-C interactions develop in the liquid, while the pre-existing C-C interactions in Cmcm TiC persist in the liquid. Here, the resulting carbon networks in the melt provide a promising environment for eventual diamond nucleation.

Ab initio molecular dynamics↗
DOE OSTI2019

Ground state in the novel dimer iridate Ba 13 Ir 6 O 30 with Ir 6+ (5$d^3$) ions

We have synthesized and studied an iridate, Ba 13 Ir 6 O 30 , with unusual Ir oxidation states: 2/3 Ir 6+ (5$d^3$) ions and 1/3 Ir 5+ (5$d^4$) ions. Its crystal structure features dimers of face-sharing IrO 6 octahedra, and IrO 6 monomers that are linked via long, zigzag Ir-O-Ba-O-Ir pathways. Nevertheless, Ba 13 Ir 6 O 30 exhibits two transitions at $T_{\text{N}1}$ = 4.7K and $T_{\text{N}2}$ = 1.6 K. This magnetic order is accompanied by a huge Sommerfeld coefficient 200 mJ/mole K 2 below $T_{\text{N}2}$, signaling a coexisting frustrated/disordered state persisting down to at least 0.05 K. This iridate hosts unusually large $J_{\text{eff}}$ = 3/2 degrees of freedom, which is enabled by strong spin-orbit interactions (SOI) in the monomers with Ir 6+ ions and a joint effect of molecular orbitals and SOI in the dimers occupied by Ir 5+ and Ir 6+ ions. Features displayed by the magnetization and heat capacity suggest that the combination of covalency, SOI, and large effective spins leads to highly frustrated ferrimagnetic ordering, an interesting feature of this high-spin iridate.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Ferromagnetism and Persistent Currents in Finely Dispersed Highly Oriented Pyrolytic Graphite Samples

Synthesis of finely dispersed graphite powders is described and results of their investigations by the methods of electron microscopy and magnetometry are presented. The samples have been prepared from crystal highly oriented pyrolytic graphite by grinding in an inert atmosphere for a long time with subsequent annealing at 400°C for 24 h in air or in vacuum. It is demonstrated that annealing of the powder in vacuum leads to a considerable increase in the ferromagnetic component associated with the formation of edge defects of zigzag type. The phenomenon of magnetic flux trapping is manifested in the samples annealed both in air and in vacuum upon cooling down to 10 K in a magnetic field that is indicative of the formation of superconducting regions in the samples.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Long-range magnetic order with disordered spin orientations in a high-entropy antiferromagnet

Disorder in magnetic systems typically suppresses long-range order, promoting short-range states such as spin glasses and magnetic clusters. This is particularly prominent in high-entropy materials, characterized by the random distributions of local magnetic entities and exchange interactions. However, in rare exceptions, long-range magnetic order can persist in high-entropy systems, while the microscopic characters and underlying mechanisms remain elusive, especially the magnetic behaviors of individual elements. Here, combining neutron diffraction and resonant soft x-ray scattering, we have conducted an element-specific investigation into the magnetic order of a high-entropy honeycomb-lattice van der Waals material (Mn 1/4 Fe 1/4 Co 1/4 Ni 1/4 )PS 3 . Despite significant atomic disorder, long-range zigzag antiferromagnetic order is observed below 72 K, with all four transition-metal elements participating in a unified phase transition. However, the spin orientations of various elements are distinct, attributed to the competition between single-ion anisotropies and exchange interactions. Our findings showcase a novel form of long-range magnetic order with disordered spin orientations, which is synergically stabilized by distinct magnetic elements in a high entropy magnet, offering a new paradigm for understanding complex magnetic systems.

Shen, Yao [Chinese Academy of Sciences (CAS), Beij↗
DOE OSTI2025

Magnetic properties of metastable honeycomb KCoAsO 4

We present comprehensive neutron scattering data on polycrystalline samples of a new metastable honeycomb material KCoAsO 4 . Below 𝑇 𝑁 = 14 K, the system orders into a zigzag antiferromagnetic state, with spins ordered into alternating ferromagnetic chains similar to the isostructural sister compound KNiAsO 4 . In the case of KCoAsO 4 , we find the moments are robustly canted out of plane closer to the crystallographic 𝑐 axis. A combination of weak interlayer coupling, lattice strain, and inhomogeneities lead to the coexistence of two magnetic ordering wave vectors 𝑘 1 = (1.5 0 0) and 𝑘 2 = (0.5 0 0.5), where the two structures differ only in their layer stacking. Inelastic data show the presence of a spin orbital mode at 24 meV, supporting a pseudospin $\tilde{𝑆}$ = 1/2 Kramer's doublet ground state of the Co 2+ ions. We model the low energy excitations using both a conventional XXZ Hamiltonian and generalized Kitaev Heisenberg Hamiltonian within a linear spin wave limit. While either model can qualitatively reproduce the observed spectra, the lack of fine features and observation of disorder prevent a clear-cut determination of the low energy Hamiltonian. In the case of an XXZ-type model, a large easy-axis anisotropy is necessary to reproduce the gapped spectra and canting of the magnetic moments. For the generalized Kitaev model, despite the large canting of the moments away from the honeycomb layers, we find a noticeable if nondominant Kitaev term persists. In conclusion, the contrast of the magnetic properties of KCoAsO 4 to other cobalt honeycombs highlights the sensitivity of the low energy magnetic properties of Co 2+ to fine details of its crystalline environment.

Honeycomb lattice↗