检索结果-内蒙古大学图书馆

HiPoNet: A Topology-Preserving Multi-View Neural Network For High Dimensional Point Cloud and Single-Cell Data

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Viswanath, Siddharth Madhu, Hiren Bhaskar, Dhananjay Kovalic, Jake Johnson, Dave Ying, Rex Tape, Christopher Adelstein, Ian Perlmutter, Michael Krishnaswamy, Smita Department of Computer Science Yale University New Haven United States Department of Genetics Yale University New Haven United States Department of Applied Physics Yale University New Haven United States Program in Computing Boise State University Idaho United States Cell Communication Lab Department of Oncology University College London Cancer Institute London United Kingdom Department of Mathematics Yale University New Haven United States Department of Mathematics Boise State University Idaho United States Computational Biology and Bioinformatics Program Yale University New Haven United States Wu-Tsai Institute Yale University New Haven United States Program for Applied Math Yale University New Haven United States

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Single-cell data can have high dimensionality exceeding the capabilities of existing methods for point clouds which are tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e. one on every patient), necessitating models that can process large, high-dimensional point clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric information. In contrast, HiPoNet forms higher-order simplicial complexes through learnable feature reweighting, generating multiple data views that disentangle distinct biological processes. It then employs simplicial wavelet transforms to extract multiscale features—capturing both local and global topology. We empirically show that these components preserve topological information in the learned representations, and that HiPoNet significantly outperforms state-of-the-art point-cloud and graph-based models on single cell. We also show an application of HiPoNet on spatial transcriptomics datasets using spatial co-ordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis. © 2025, CC BY.

关键词： Network topology

Machine Learning for Climate Physics and Simulations

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Lai, Ching-Yao Hassanzadeh, Pedram Sheshadri, Aditi Sonnewald, Maike Ferrari, Raffaele Balaji, Venkatramani Department of Geophysics Stanford University StanfordCA94305 United States Department of Geophysical Sciences and Commitee on Computational and Applied Mathematics University of Chicago ChicagoIL60637 United States Department of Earth System Sciences Stanford University StanfordCA94305 United States Department of Computer Science University of California Davis DavisCA95616 United States Department of Earth Atmospheric and Planetary Sciences Massachusetts Institute of Technology CambridgeMA02139 United States Schmidt Sciences United States

We discuss the emerging advances and opportunities at the intersection of machine learning (ML) and climate physics, highlighting the use of ML techniques, including supervised, unsupervised, and equation discovery, to accelerate climate knowledge discoveries and simulations. We delineate two distinct yet complementary aspects: (1) ML for climate physics and (2) ML for climate simulations. While physics-free ML-based models, such as ML-based weather forecasting, have demonstrated success when data is abundant and stationary, the physics knowledge and interpretability of ML models become crucial in the small-data/non-stationary regime to ensure generalizability. Given the absence of observations, the long-term future climate falls into the small-data regime. Therefore, ML for climate physics holds a critical role in addressing the challenges of ML for climate simulations. We emphasize the need for collaboration among climate physics, ML theory, and numerical analysis to achieve reliable ML-based models for climate applications. © 2024, CC BY.

关键词： Adversarial machine learning

Certified randomness using a trapped-ion quantum processor

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Liu, Minzhao Shaydulin, Ruslan Niroula, Pradeep DeCross, Matthew Hung, Shih-Han Kon, Wen Yu Cervero-Martín, Enrique Chakraborty, Kaushik Amer, Omar Aaronson, Scott Acharya, Atithi Alexeev, Yuri Berg, K. Jordan Chakrabarti, Shouvanik Curchod, Florian J. Dreiling, Joan M. Erickson, Neal Foltz, Cameron Foss-Feig, Michael Hayes, David Humble, Travis S. Kumar, Niraj Larson, Jeffrey Lykov, Danylo Mills, Michael Moses, Steven A. Neyenhuis, Brian Eloul, Shaltiel Siegfried, Peter Walker, James Lim, Charles Pistoia, Marco Global Technology Applied Research JPMorganChase New YorkNY10017 United States Quantinuum BroomfieldCO80021 United States Computational Science Division Argonne National Laboratory LemontIL60439 United States Department of Physics The University of Chicago ChicagoIL60637 United States Department of Computer Science The University of Texas at Austin AustinTX78712 United States Department of Electrical Engineering National Taiwan University Taipei City10617 Taiwan Quantinuum Terrington House 13–15 Hills Road CambridgeCB2 1NL United Kingdom Quantum Science Center Oak Ridge National Laboratory Oak RidgeTN37831 United States Mathematics and Computer Science Division Argonne National Laboratory LemontIL60439 United States

While quantum computers have the potential to perform a wide range of practically important tasks beyond the capabilities of classical computers [1, 2], realizing this potential remains a challenge. One such task is to use an untrusted remote device to generate random bits that can be certified to contain a certain amount of entropy [3]. Certified randomness has many applications [4] but is fundamentally impossible to achieve solely by classical computation. In this work, we demonstrate the generation of certifiably random bits using the 56-qubit Quantinuum H2-1 trapped-ion quantum computer accessed over the internet. Our protocol leverages the classical hardness of recent random circuit sampling demonstrations [5, 6]: a client generates quantum "challenge" circuits using a small randomness seed, sends them to an untrusted quantum server to execute, and verifies the server’s results. We analyze the security of our protocol against a restricted class of realistic near-term adversaries. Using classical verification with measured combined sustained performance of 1.1 × 1018 floating-point operations per second across multiple supercomputers, we certify 71, 313 bits of entropy under this restricted adversary and additional assumptions. Our results demonstrate a step towards the practical applicability of today’s quantum computers. Copyright © 2025, The Authors. All rights reserved.

关键词： Quantum computers

Color-avoiding percolation in edge-colored Erdős–Rényi graphs

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Ráth, Balázs Varga, Kitti Fekete, Panna Tímea Molontay, Roland Afréd Rényi Institute of Mathematics Hungary Department of Stochastics Institute of Mathematics Budapest University of Technology and Economics Hungary ELKH-BME Stochastics Research Group Chile Department of Computer Science and Information Theory Faculty of Electrical Engineering and Informatics Budapest University of Technology and Economics Hungary ELKH-ELTE Egerváry Research Group Hungary Department of Applied Analysis and Computational Mathematics Eötvös Loránd University Hungary

We study a variant of the color-avoiding percolation model introduced by Krause et al., namely we investigate the color-avoiding bond percolation setup on (not necessarily properly) edge-colored Erd̋ os–Rényi random graphs. We say that two vertices are color-avoiding connected in an edge-colored graph if after the removal of the edges of any color, they are in the same component in the remaining graph. The color-avoiding connected components of an edge-colored graph are maximal sets of vertices such that any two of them are color-avoiding connected. We consider the fraction of vertices contained in color-avoiding connected components of a given size as well as the fraction of vertices contained in the giant color-avoiding connected component. Under some mild assumptions on the color-densities, we prove that these quantities converge and the limits can be expressed in terms of probabilities associated to edge-colored branching process trees. We provide explicit formulas for the limit of the normalized size of the giant color-avoiding connected component, and in the two-colored case we also provide explicit formulas for the limit of the fraction of vertices contained in color-avoiding connected components of a given size. Copyright © 2022, The Authors. All rights reserved.

关键词： Color

Efficient Combinatorial Optimization via Heat Diffusion

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Ma, Hengyuan Lu, Wenlian Feng, Jianfeng Institute of Science and Technology for Brain-inspired Intelligence Fudan University Shanghai200433 China Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence Fudan University Ministry of Education China School of Mathematical Sciences Fudan University No. 220 Handan Road Shanghai Shanghai200433 China Shanghai Center for Mathematical Sciences No. 220 Handan Road Shanghai Shanghai200433 China Shanghai Key Laboratory for Contemporary Applied Mathematics No. 220 Handan Road Shanghai Shanghai200433 China Key Laboratory of Mathematics for Nonlinear Science No. 220 Handan Road Shanghai Shanghai200433 China Department of Computer Science University of Warwick CoventryCV4 7AL United Kingdom

Combinatorial optimization problems are widespread but inherently challenging due to their discrete nature. The primary limitation of existing methods is that they can only access a small fraction of the solution space at each iteration, resulting in limited efficiency for searching the global optimal. To overcome this challenge, diverging from conventional efforts of expanding the solver’s search scope, we focus on enabling information to actively propagate to the solver through heat diffusion. By transforming the target function while preserving its optima, heat diffusion facilitates information flow from distant regions to the solver, providing more efficient navigation. Utilizing heat diffusion, we propose a framework for solving general combinatorial optimization problems. The proposed methodology demonstrates superior performance across a range of the most challenging and widely encountered combinatorial optimizations. Echoing recent advancements in harnessing thermodynamics for generative artificial intelligence, our study further reveals its significant potential in advancing combinatorial optimization. The codebase of our study is available in https://***/AwakerMhy/HeO. © 2024, CC BY.

关键词： Combinatorial optimization

Effect of matrix sparsity and quantum noise on quantum random walk linear solvers

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Wu, Benjamin Patil, Hrushikesh Krstic, Predrag Department of Applied Mathematics and Statistics Stony Brook University Stony Brook NY11794 United States Department of Electrical and Computer Engineering North Carolina State University RaleighNC27606 United States Institute for Advanced Computational Science Stony Brook University Stony Brook NY11794-5250 United States

We study the effects of quantum noise in hybrid quantum-classical solver for sparse systems of linear equations using quantum random walks, applied to stoquastic Hamiltonian matrices. In an ideal noiseless quantum computer, sparse matrices achieve solution vectors with lower relative error than dense matrices. However, we find quantum noise reverses this effect, with overall error increasing as sparsity increases. We identify invalid quantum random walks as the cause of this increased error and propose a revised linear solver algorithm which improves accuracy by mitigating these invalid walks. © 2022, CC BY.

关键词： Hamiltonians

Coulomb-corrected quantum-trajectories method for recollision-impact double ionization in an intense laser field

学校读者我要写书评

暂无评论

Physical Review A 2023年第1期108卷 013115-013115页

作者： Yuxing Bai Xiaolei Hao Weidong Li Weifeng Yang Jing Chen Institute of Theoretical Physics and Department of Physics State Key Laboratory of Quantum Optics and Quantum Optics Devices Collaborative Innovation Center of Extreme Optics Shanxi University Taiyuan 030006 China Department of Computer Science and Technology Taiyuan University Taiyuan 237016 China Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology Center for Advanced Material Diagnostic Technology and College of Engineering Physics Shenzhen Technology University Shenzhen 518118 China Department of Physics School of Science Hainan University Haikou 570228 China Institute of Applied Physics and Computational Mathematics P. O. Box 8009 Beijing 100088 China

By incorporating the quantum effects and the Coulomb interaction between the first ionized electron and the residual ion in a uniform theory, the Coulomb-corrected quantum-trajectories (CCQT) method is developed to describe the recollision-impact ionization (RII) process in nonsequential double ionization of atoms in intense laser field. The results simulated by CCQT are found to be in better agreement with the experimental results, compared with those calculated by the classical-trajectory Monte Carlo (CTMC) and strong-field approximation (SFA) methods. Considering its advantage of small computational cost and back-trajectory analysis, the CCQT method will be an efficient theoretical tool to quantitatively investigate the underlying physics of the complex and coherent multielectron dynamics in intense laser field.

关键词： Atomic & molecular processes in external fields Electronic excitation & ionization Strong field excitation Atomic systems Electronic structure High-harmonic generation Optical techniques Quantum Monte Carlo Semiclassical methods

The $\gamma$γ-OMP Algorithm for Feature Selection With Application to Gene Expression Data

学校读者我要写书评

暂无评论

IEEE/ACM Transactions on computational Biology and Bioinformatics 2020年第2期19卷 1214-1224页

作者： Michail Tsagris Zacharias Papadovasilakis Kleanthi Lakiotaki Ioannis Tsamardinos Department of Economics University of Crete Rethymnon Greece Department of Computer Science University of Crete Herakleion Greece Department of Computer Science Institute of Applied and Computational Mathematics FORTH University of Crete Herakleion Greece

Feature selection for predictive analytics is the problem of identifying a minimal-size subset of features that is maximally predictive of an outcome of interest. To apply to molecular data, feature selection algorithms need to be scalable to tens of thousands of features. In this paper, we propose $\gamma$ -OMP, a generalisation of the highly-scalable Orthogonal Matching Pursuit feature selection algorithm. $\gamma$ -OMP can handle (a)various types of outcomes, such as continuous, binary, nominal, time-to-event, (b)discrete (categorical)features, (c)different statistical-based stopping criteria, (d)several predictive models (e.g., linear or logistic regression), (e)various types of residuals, and (f)different types of association. We compare $\gamma$ -OMP against LASSO, a prototypical, widely used algorithm for high-dimensional data. On both simulated data and several real gene expression datasets, $\gamma$ -OMP is on par, or outperforms LASSO in binary classification (case-control data), regression (quantified outcomes), and time-to-event data (censored survival times). $\gamma$ -OMP is based on simple statistical ideas, it is easy to implement and to extend, and our extensive evaluation shows that it is also effective in bioinformatics analysis settings.

关键词： Matching pursuit algorithms Prediction algorithms Feature extraction Gene expression Signal processing algorithms Bioinformatics computational modeling

Subdiffusive wave transport and weak localization transition in three-dimensional stealthy hyperuniform disordered systems

学校读者我要写书评

暂无评论

Physical Review B 2022年第6期105卷 064204-064204页

作者： F. Sgrignuoli S. Torquato L. Dal Negro Department of Electrical and Computer Engineering & Photonics Center Boston University 8 Saint Mary's Street Boston Massachusetts 02215 USA Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA Division of Material Science and Engineering Boston University 15 Saint Mary's Street Brookline Massachusetts 02446 USA Department of Physics Boston University 590 Commonwealth Avenue Boston Massachusetts 02215 USA

The purpose of this work is to understand the fundamental connection between structural correlations and light localization in three-dimensional (3D) open scattering systems of finite size. We numerically investigate the transport of vector electromagnetic waves scattered by resonant electric dipoles spatially arranged in 3D space by stealthy hyperuniform disordered point patterns. Three-dimensional stealthy hyperuniform disordered systems are engineered with different structural correlation properties determined by their degree of stealthiness χ. Such fine control of exotic states of amorphous matter enables the systematic design of optical media that interpolate in a tunable fashion between uncorrelated random structures and crystalline materials. By solving the electromagnetic multiple scattering problem using Green's matrix spectral method, we establish a transport phase diagram that demonstrates a distinctive transition from a diffusive to a weak localization regime beyond a critical scattering density that depends on χ. The transition is characterized by studying the Thouless number and the spectral statistics of the scattering resonances. In particular, by tuning the χ parameter, we demonstrate large spectral gaps and suppressed subradiant proximity resonances, facilitating light localization. Moreover, consistently with previous studies, our results show a region of the transport phase diagram where the investigated scattering systems become transparent. Our work provides a systematic description of the transport and weak localization properties of light in stealthy hyperuniform structures and motivates the engineering of photonic systems with enhanced light-matter interactions for applications to both classical and quantum devices.

关键词： Anderson localization Light-matter interaction Mesoscopics Photonics Scattering theory Weak localization Metamaterials