arXiv subjects

Rundong Zhao

Publications and source records attributed to Rundong Zhao.

8 recordsLinked to original sources

arXiv2026

A Large-scale Parallel Implementation of Quasi-Four-Component Relativistic Density Functional Theory with Numeric Atom-centered Orbitals

We present a large-scale parallel implementation of fully relativistic density functional theory (DFT) for both molecules and periodic solids, using the quasi-four-component (Q4C) method and numeric atom-centered orbital basis sets. Our approach employs a domain decomposition method on nonuniform real-space integration grids, which enables order-N integration of the Q4C Hamiltonian matrix elements using efficient, distributed-memory and compute-parallel real-space operations. Next, we build the Hamiltonian and overlap matrices in a two-dimensional block-cyclic distribution layout. The resulting generalized eigenvalue problems are solved with the massively parallel ELPA eigenvalue solver library. We benchmark memory usage, parallel efficiency, and scalability across multiple MPI tasks and compute nodes. This algorithm extends the reach of fully relativistic DFT simulations for periodic solids, tested up to 3,383 atoms per unit cell (216,628 basis functions) and likely still well below the true reach of the implementation. As a demonstration, we calculate the fully relativistic band structure for a 3,383 atom-per-unit-cell doped hybrid organic-inorganic perovskite, (PEA)2(Pb1-xBix)I4 (PEA=phenethylammonium), showing nearly ideal scalability between 336 and 672 physical CPU cores.

cond-mat.mtrl-sci↗

arXiv2026

CogniFold: Always-On Proactive Memory via Cognitive Folding

Existing agent memory remains predominantly reactive and retrieval-based, lacking the capacity to autonomously organize experience into persistent cognitive structure. Toward genuinely autonomous agents, we introduce CogniFold, a brain-inspired "always-on" agent memory designed for the next generation of proactive assistants. CogniFold continuously folds fragmented event streams into self-emerging cognitive structures, bootstrapping progressively higher-level cognition from incoming events and accumulated knowledge. We ground this by extending Complementary Learning Systems (CLS) theory from two layers (hippocampus, neocortex) to three, adding a prefrontal intent layer. Emulating the prefrontal cortex as the locus of intentional control and decision-making, CogniFold achieves this through graph-topology self-organization: cognitive structures proactively assemble under the stream, merge when semantically similar, decay when stale, relink through associative recall, and surface intents when concept-cluster density crosses a threshold. We evaluate structural formation using CogEval-Bench, demonstrating that CogniFold uniquely produces memory structures that match cognitive expectations and concept emergence. Furthermore, across eight downstream benchmarks -- two probing long-term conversational memory (LoCoMo, LongMemEval) and six spanning other cognitive domains -- we validate that CogniFold simultaneously performs robustly on conventional memory tasks. Our code is available at https://github.com/OpenNorve/CogniFold.

cs.AI↗

arXiv2026

Robust quantized thermal conductance of Majorana floating edge bands in d-wave superconductors

We propose and characterize a new class of Majorana boundary states, i.e., floating Majorana edge bands (FMEBs), which emerge in two-dimensional (2D) superconductors that break time-reversal symmetry yet host helical-like transport. In contrast to conventional chiral or helical edge modes, FMEBs form isolated, momentum-separated counterpropagating Majorana modes detached from the bulk continuum. We identify a minimal mechanism for their emergence via anisotropic Wilson masses in a two-band Bogoliubov-de Gennes (BdG) model, and demonstrate their microscopic realization in a quantum anomalous Hall (QAH) insulator proximitized by a $d$-wave superconductor. Using nonequilibrium Green's function (NEGF) simulations, we uncover clear transport fingerprints: a quantized total thermal conductance in two-terminal devices, and a robust half-quantized plateau in four-terminal geometries that cleanly distinguishes FMEBs from chiral $\mathcal{N}= \pm 2$ QAH phases. This thermal response remains remarkably stable under finite temperature, moderate long-range disorder, and finite chemical potential. Our findings establish FMEBs as an experimentally accessible route toward helical-like Majorana transport in systems without time-reversal symmetry, with direct implications for topological quantum computation.

cond-mat.mes-hall↗

arXiv2020

HERMES: Persistent spectral graph software

Persistent homology (PH) is one of the most popular tools in topological data analysis (TDA), while graph theory has had a significant impact on data science. Our earlier work introduced the persistent spectral graph (PSG) theory as a unified multiscale paradigm to encompass TDA and geometric analysis. In PSG theory, families of persistent Laplacians (PLs) corresponding to various topological dimensions are constructed via a filtration to sample a given dataset at multiple scales. The harmonic spectra from the null spaces of PLs offer the same topological invariants, namely persistent Betti numbers, at various dimensions as those provided by PH, while the non-harmonic spectra of PLs give rise to additional geometric analysis of the shape of the data. In this work, we develop an open-source software package, called highly efficient robust multidimensional evolutionary spectra (HERMES), to enable broad applications of PSGs in science, engineering, and technology. To ensure the reliability and robustness of HERMES, we have validated the software with simple geometric shapes and complex datasets from three-dimensional (3D) protein structures. We found that the smallest non-zero eigenvalues are very sensitive to data abnormality.

math.AT↗

arXiv2019

Evolutionary de Rham-Hodge method

The de Rham-Hodge theory is a landmark of the 20$^\text{th}$ Century's mathematics and has had a great impact on mathematics, physics, computer science, and engineering. This work introduces an evolutionary de Rham-Hodge method to provide a unified paradigm for the multiscale geometric and topological analysis of evolving manifolds constructed from a filtration, which induces a family of evolutionary de Rham complexes. While the present method can be easily applied to close manifolds, the emphasis is given to more challenging compact manifolds with 2-manifold boundaries, which require appropriate analysis and treatment of boundary conditions on differential forms to maintain proper topological properties. Three sets of unique evolutionary Hodge Laplacian operators are proposed to generate three sets of topology-preserving singular spectra, for which the multiplicities of zero eigenvalues correspond to exactly the persistent Betti numbers of dimensions 0, 1, and 2. Additionally, three sets of non-zero eigenvalues further reveal both topological persistence and geometric progression during the manifold evolution. Extensive numerical experiments are carried out via the discrete exterior calculus to demonstrate the utility and usefulness of the proposed method for data representation and shape analysis.

math.DG↗

arXiv2019

The de Rham-Hodge analysis and modeling of biomolecules

Recent years have witnessed a trend that advanced mathematical tools, such as algebraic topology, differential geometry, graph theory, and partial differential equations, have been developed for describing biological macromolecules. These tools have considerably strengthened our ability to understand the molecular mechanism of macromolecular function, dynamics and transport from their structures. However, currently, there is no unified mathematical theory to analyze, describe and characterize biological macromolecular geometry, topology, flexibility and natural mode at a variety of scales. We introduce the de Rham-Hodge theory, a landmark of 20th Century's mathematics, as a unified paradigm for analyzing biological macromolecular geometry and algebraic topology, for predicting macromolecular flexibility, and for modeling macromolecular natural modes at a variety of scales. In this paradigm, macromolecular geometric characteristic and topological invariants are revealed by de Rham-Hodge spectral analysis. By using the Helmholtz-Hodge decomposition, every macromolecular vector field is split into orthogonal divergence-free, curl-free, and harmonic components with a distinct physical interpretation. We organize the eigenvalues and eigenvectors of the 0-form Laplace-de Rham operator into one of the most accurate protein B-factor predictors. By combining the 1-form Laplace-de Rham operator and the Helfrich-type curvature energy, we predict the natural modes of both X-ray protein structures and cryo-EM maps. We construct accurate and efficient three-dimensional discrete exterior calculus algorithms for the aforementioned modeling and analysis of biological macromolecules. Using extensive experiments, we validate that the proposed paradigm is one of the most versatile and powerful tools for biological macromolecular studies.

q-bio.BM↗

arXiv2018

Divide-and-Conquer Strategy for Large-Scale Eulerian Solvent Excluded Surface

Motivation: Surface generation and visualization are some of the most important tasks in biomolecular modeling and computation. Eulerian solvent excluded surface (ESES) software provides analytical solvent excluded surface (SES) in the Cartesian grid, which is necessary for simulating many biomolecular electrostatic and ion channel models. However, large biomolecules and/or fine grid resolutions give rise to excessively large memory requirements in ESES construction. We introduce an out-of-core and parallel algorithm to improve the ESES software. Results: The present approach drastically improves the spatial and temporal efficiency of ESES. The memory footprint and time complexity are analyzed and empirically verified through extensive tests with a large collection of biomolecule examples. Our results show that our algorithm can successfully reduce memory footprint through a straightforward divide-and-conquer strategy to perform the calculation of arbitrarily large proteins on a typical commodity personal computer. On multi-core computers or clusters, our algorithm can reduce the execution time by parallelizing most of the calculation as disjoint subproblems. Various comparisons with the state-of-the-art Cartesian grid based SES calculation were done to validate the present method and show the improved efficiency. This approach makes ESES a robust software for the construction of analytical solvent excluded surfaces. Availability and implementation: http://weilab.math.msu.edu/ESES.

q-bio.QM↗

arXiv2018

Interlocking mechanism between molecular gears attached to surfaces

While molecular machines play an increasingly significant role in nanoscience research and applications, there remains a shortage of investigations and understanding of the molecular gear (cogwheel), which is an indispensable and fundamental component to drive a larger correlated molecular machine system. Employing ab initio calculations, we investigate model systems consisting of molecules adsorbed on metal or graphene surfaces, ranging from very simple triple-arm gears such as PF3 and NH3 to larger multi-arm gears based on carbon rings. We explore in detail the transmission of slow rotational motion from one gear to the next by these relatively simple molecules, so as to isolate and reveal the mechanisms of the relevant intermolecular interactions. Several characteristics of molecular gears are discussed, in particular the flexibility of the arms and the slipping and skipping between interlocking arms of adjacent gears, which differ from familiar macroscopic rigid gears. The underlying theoretical concepts suggest strongly that other analogous structures may also exhibit similar behavior which may inspire future exploration in designing large correlated molecular machines.

physics.chem-ph↗