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SSRN 2023年

作者： Skolnick, Murray Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States School of Natural Sciences The Institute for Advanced Study PrincetonNJ08540 United States

Time-dependent diffusion processes between phases are ubiquitous in physical, chemical, and biological materials. Examples of such materials include composite materials, porous materials, cellular solids, polymer blends, colloids, gels, and biological materials. The recently developeddiffusion spreadability, S(t), provides a direct link between time-dependent interphase diffusive transport and the microstructure of two-phase materials across length scales [Torquato, S., Phys. Rev. E., 104 054102 (2021)];thus making S(t) a powerful dynamic means for classifying all statistically homogeneous microstructures, spanning from anti-hyperuniform to hyperuniform. It was shown that the small-, intermediate-, and long-time behaviors of S(t) are directly determined by the small-, intermediate-, and large-scale structural features of the material. Moreover, the spreadability can be applied as a physical-property based tool for microstructural characterization in the absence of or as supplement to scattering information. In this work, we develop a computationally efficient algorithm for ascertaining s(t) directly from digitized representations of material microstructures via random-walk techniques. Our algorithm computes the time-dependent local walker concentration field c(x, t), a quantity not previously examined in the context of the spreadability, enabling us to compute the entropy production rate s(t) of the associated diffusion process which is a quantity related to the rate of dissipation. We also derive exact analytical expressions for s(t), and find that hyperuniform materials have smaller dissipation than any nonhyperuniform materials. Lastly, we use our algorithm to compute, for the first time, the more general case of the spreadability in which the phase diffusion coefficients are distinct and provide a method for extracting the effective diffusion coefficient of the two-phase material from such data. We apply our algorithm to a variety of two- and three-dimensional s

关键词： Microstructure

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Consensus dynamics and coherence in hierarchical small-world networks

arXiv

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arXiv 2023年

作者： Liao, Yunhua Maama, Mohamed Aziz-Alaoui, M.A. Department of Mathematics Hunan University of Technology and Business Hunan Changsha410205 China Key Laboratory of Hunan Province for Statistical Learning and Intelligent Computation Hunan Changsha410205 China Applied Mathematics and Computational Science Program KAUST Thuwal23955-6900 Saudi Arabia Normandie Univ UNIHAVRE LMAH FR-CNRS-3335 ISCN Le Havre76600 France

The hierarchical small-world network is a real-world network. It models well the benefit transmission web of the pyramid selling in China and many other countries. In this paper, by applying the spectral graph theory, we study three important aspects of the consensus problem in the hierarchical small-world network: convergence speed, communication time-delay robustness, and network coherence. Firstly, we explicitly determine the Laplacian eigenvalues of the hierarchical small-world network by making use of its treelike structure. Secondly, we find that the consensus algorithm on the hierarchical small-world network converges faster than that on some well-studied sparse networks, but is less robust to time delay. The closed-form of the first-order and the second-order network coherence are also derived. Our result shows that the hierarchical small-world network has an optimal structure of noisy consensus dynamics. Therefore, we provide a positive answer to two open questions of Yi et al. Finally, we argue that some network structure characteristics, such as large maximum degree, small average path length, and large vertex and edge connectivity, are responsible for the strong robustness with respect to external perturbations. Copyright © 2023, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

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Integrating Chain-of-Thought and Retrieval Augmented Generation Enhances Rare Disease Diagnosis from Clinical Notes

arXiv

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arXiv 2025年

作者： Wu, Da Wang, Zhanliang Nguyen, Quan Wang, Kai Raymond G. Perelman Center for Cellular and Molecular Therapeutics Children's Hospital of Philadelphia PhiladelphiaPA19104 United States Applied Mathematics and Computational Science Graduate Program University of Pennsylvania PhiladelphiaPA19104 United States Bioengineering Graduate Program University of Pennsylvania PhiladelphiaPA19104 United States Department of Pathology and Laboratory Medicine Perelman School of Medicine University of Pennsylvania PhiladelphiaPA19104 United States

Background: Several studies show that large language models (LLMs) struggle with phenotype-driven gene prioritization for rare diseases. These studies typically use Human Phenotype Ontology (HPO) terms to prompt foundation models like GPT and LLaMA to predict candidate genes. However, in real-world settings, foundation models are not optimized for domain-specific tasks like clinical diagnosis, yet inputs are unstructured clinical notes rather than standardized terms. How LLMs can be instructed to predict candidate genes or disease diagnosis from unstructured clinical notes remains a major challenge. Methods: We introduce RAG-driven CoT and CoT-driven RAG, two methods that combine Chain-of-Thought (CoT) and Retrieval Augmented Generation (RAG) to analyze clinical notes. A five-question CoT protocol mimics expert reasoning, while RAG retrieves data from sources like HPO and OMIM (Online Mendelian Inheritance in Man). We evaluated these approaches on rare disease datasets, including 5,980 Phenopacket-derived notes, 255 literature-based narratives, and 220 in-house clinical notes from Children’s Hospital of Philadelphia. Results: We found that recent foundations models, including Llama 3.3-70B-Instruct and DeepSeek-R1-Distill-Llama-70B, outperformed earlier versions such as Llama 2 and GPT-3.5. We also showed that RAG-driven CoT and CoT-driven RAG both outperform foundation models in candidate gene prioritization from clinical notes;in particular, both methods with DeepSeek backbone resulted in a top-10 gene accuracy of over 40% on Phenopacket-derived clinical notes. RAG-driven CoT works better for high-quality notes, where early retrieval can anchor the subsequent reasoning steps in domain-specific evidence, while CoT-driven RAG has advantage when processing lengthy and noisy notes. Conclusions: Integrating CoT and RAG enhances LLMs’ understanding of clinical notes in the context of rare disease diagnosis, and can facilitate various downstream medical tasks. © 2025, CC

关键词： Chains

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Protein folding as a jamming transition

arXiv

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arXiv 2024年

作者： Grigas, Alex T. Liu, Zhuoyi Logan, Jack A. Shattuck, Mark D. O’Hern, Corey S. Graduate Program in Computational Biology and Bioinformatics Yale University New HavenCT06520 United States Integrated Graduate Program in Physical and Engineering Biology Yale University New HavenCT06520 United States Department of Mechanical Engineering and Materials Science Yale University New HavenCT06520 United States Benjamin Levich Institute and Physics Department The City College of New York New YorkNY10031 United States Department of Physics Yale University New HavenCT06520 United States Department of Applied Physics Yale University New HavenCT06520 United States

Proteins fold to a specific functional conformation with a densely packed hydrophobic core that controls their stability. We develop a geometric, yet all-atom model for proteins that explains the universal core packing fraction of φc = 0.55 found in experimental measurements. We show that as the hydrophobic interactions increase relative to the temperature, a novel jamming transition occurs when the core packing fraction exceeds φc. The model also recapitulates the global structure of proteins since it can accurately refold to native-like structures from partially unfolded states. © 2024, CC BY.

关键词： Proteins

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Ultradense Sphere Packings Derived From Disordered Stealthy Hyperuniform Ground States

arXiv

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arXiv 2025年

作者： Kim, Jaeuk Torquato, Salvatore Princeton Materials Institute Department of Physics Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Materials Institute Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Disordered stealthy hyperuniform (SHU) packings are an emerging class of exotic amorphous two-phase materials endowed with novel optical, transport, and mechanical properties. Such packings of identical spheres have been created from SHU ground-state point patterns via a modified collective-coordinate optimization scheme that includes a soft-core repulsion, besides the standard "stealthy" pair potential. To explore maximal ranges of the packing fraction , we investigate the distributions of minimum pair distances as well as nearest-neighbor distances of ensembles of SHU point patterns without and with soft-core repulsions in the first three space dimensions as a function of the stealthiness parameter χ and number of particles N within a hypercubic simulation box under periodic boundary conditions. Within the disordered regime (χ max(χ, d), decrease to zero on average as N increases if there are no soft-core repulsions. By contrast, the inclusion of soft-core repulsions results in very large max(χ, d) independent of N, reaching up to max(χ, d) = 1.0, 0.86, 0.63 in the zero-χ limit and decreasing to max(χ, d) = 1.0, 0.67, 0.47 at χ = 0.45 for d = 1, 2, 3, respectively. We obtain explicit formulas for max(χ, d) as functions of χ and N for a given value of d in both cases with and without soft-core repulsions. In two and three dimensions, our soft-core SHU ground-state packings for small χ become configurationally very close to the corresponding jammed hard-particle packings created by fast compression algorithms, as measured by their pair statistics. As χ increases beyond 0.20, the packings form fewer contacts and linear polymer-like chains as χ tends to 1/2. The resulting structure factors S(k) and pair correlation functions g2(r) reveal that soft-core repulsions significantly alter the short- and intermediate-range correlations in the SHU ground states. We show that the degree of large-scale order of the soft-core SHU ground states increases as χ increases from 0 to

关键词： Digital arithmetic

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From Dyson models to many-body quantum chaos

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Physical Review B 2025年第3期111卷 035147-035147页

作者： Alexei Andreanov Matteo Carrega Jeff Murugan Jan Olle Dario Rosa Ruth Shir Center for Theoretical Physics of Complex Systems Institute for Basic Science (IBS) Daejeon 34126 Korea Basic Science Program Korea University of Science and Technology (UST) Daejeon 34113 Korea CNR-SPIN Via Dodecaneso 33 16146 Genova Italy The Laboratory for Quantum Gravity & Strings Department of Mathematics and Applied Mathematics University of Cape Town Cape Town 7701 South Africa The National Institute for Theoretical and Computational Sciences Private Bag X1 Matieland 7602 South Africa Max Planck Institute for the Science of Light 91058 Erlangen Germany ICTP South American Institute for Fundamental Research Instituto de Física Teórica UNESP—University of Estadual Paulista Rua Dr. Bento Teobaldo Ferraz 271 01140-070 São Paulo SP Brazil Department of Physics and Materials Science University of Luxembourg L-1511 Luxembourg Luxembourg

A deep understanding of the mechanisms underlying many-body quantum chaos is one of the big challenges in contemporary theoretical physics. We tackle this problem in the context of a set of perturbed quadratic Sachdev-Ye-Kitaev (SYK) Hamiltonians defined on graphs. This allows us to disentangle the geometrical properties of the underlying single-particle problem and the importance of the interaction terms, showing that the former is the dominant feature ensuring the single-particle to many-body chaotic transition. Our results are verified numerically with state-of-the-art numerical techniques, capable of extracting eigenvalues in a desired energy window of very large Hamiltonians. Our approach essentially provides a new way of viewing many-body chaos from a single-particle perspective.

关键词： Quantum chaos

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Numerical analysis of growth-mediated autochemotactic pattern formation in self-propelling bacteria

arXiv

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arXiv 2022年

作者： Zhang, Jiansong Jiang, Maosheng Zhu, Jiang Yu, Xijun Bevilacqua, Luiz Department of Applied Mathematics China University of Petroleum Qingdao266580 China School of Mathematics and Statistics Qingdao University Qingdao266071 China Laboratório Nacional de Computação Científica MCTI Avenida Getúlio Vargas 333 RJ Petrópolis25651-075 Brazil Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China A.L. Coimbra Institute COPPE Federal University of Rio de Janeiro Rio de Janeiro Brazil

In this paper, a decoupled characteristic Galerkin finite element procedure is provided for simulating growth-mediated autochemotactic pattern formation in self-propelling bacteria. In this procedure, a modified characteristic Galerkin method is established to solve the bacterial density equation, while the classical finite element procedure is considered for the self-secreted chemical density and polarization dynamics equations system. The convergence of this proposed method is considered under some regularity assumptions and the corresponding error estimate is derived. Numerical experiments are carried out to support the theoretical analysis. Furthermore, several new wave type pattern formations are found. © 2022, CC BY.

关键词： Bacteria

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Cluster decay half-lives of Ba112–122 isotopes from the ground state and intrinsic excited state using the relativistic mean-field formalism within the preformed-cluster-decay model

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Physical Review C 2022年第4期105卷 044617-044617页

作者： Joshua T. Majekodunmi M. Bhuyan D. Jain K. Anwar N. Abdullah Raj Kumar Institute of Engineering Mathematics Faculty of Applied and Human Sciences Universiti Malaysia Perlis Arau 02600 Perlis Malaysia Center for Theoretical and Computational Physics Department of Physics Faculty of Science University of Malaya Kuala Lumpur 50603 Malaysia Department of Physics Mata Gujri College Fatehgarh Punjab 140407 India School of Physics and Science Thapar Institute of Engineering and Technology Patiala Punjab 147004 India

Background: The cluster radioactivity from the neutron-deficient trans-tin region of the nuclear landscape has given immediate attention in the nuclear structure studies. Recent prediction of the emitting clusters from the ground and intrinsic excited states of proton-rich Ba isotopes opens the direction to explore the corresponding decay characteristics. A theoretical probe is necessary for understanding the cluster decays of Ba isotopes.

关键词： Nuclear reactions Nuclear structure & decays

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核心坍缩超新星中辐射冲击波的实验室模拟及首次量化校验（英文）

引用

Science Bulletin 2024年第20期 3188-3191页

作者：张璐郑建华杨正华宋天明张帅刘彤韦云锋况龙钰景龙飞林雉伟李丽灵黎航郑金华杨品张玉雪张志宇赵阳何智兵李平杨冬杨家敏赵宗清丁永坤 Research Center of Laser Fusion China Academy of Engineering Physics Department of Astronomy Xiamen University Institute of Applied Physics and Computational Mathematics

A radiative shock(RS) is one in which the density and temperature structures are affected by radiation from the shock-heated matter. RS plays a special role in astrophysics as it nontrivially combines both hydrodynamics and radiation physics. In most astrophysical shocks, the temperature and density conditions lead to strong emission, with radiation thus playing a major role therein. Various RS structures can be implied for numerous astrophysical objects, such as supernova explosions, stellar interiors [1],stellar winds, star formation, black hole accretion disks [2], accreting neutron stars [3], and gamma-ray bursts [4]. In particular, RS exists in the blast waves of core-collapse supernovae(CCSNe),where the radiation pressure in matter is larger than the thermal one. On the basis of multi-messenger supernova observations, their explosion model and particle acceleration mechanisms have been built, and the characteristics of progenitor stars can be further constrained. However, entire supernova explosions are very difficult to model numerically because of the different spatial and temporal length scales involved and the controversial neutrino-driven mechanism [5].

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Generalized nonbacktracking bounds on the influence in independent cascade models

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2020年第1期21卷 1112-1147页

作者： Emmanuel Abbe Sanjeev Kulkarni Eun Jee Lee Program in Applied and Computational Mathematics and Department of Electrical Engineering Princeton University Princeton NJ Department of Electrical Engineering Princeton University Princeton NJ Program in Applied and Computational Mathematics Princeton University Princeton NJ

This paper develops deterministic upper and lower bounds on the influence measure in a network, more precisely, the expected number of nodes that a seed set can influence in the independent cascade model. In particular, our bounds exploit r-nonbacktracking walks and Fortuin--Kasteleyn--Ginibre (FKG) type inequalities, and are computed by message passing algorithms. Further, we provide parameterized versions of the bounds that control the trade-off between efficiency and accuracy. Finally, the tightness of the bounds is illustrated on various network models.

关键词： influence estimation nonbacktracking walk message passing social networks independent cascade model

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