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arXiv 2019年

作者： Pinilla, Samuel Bendory, Tamir Eldar, Yonina C. Arguello, Henry Department of Electrical Engineering Universidad Industrial de Santander BucaramangaSantander680002 Colombia Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Weizmann Institute of Science Rehovot7610001 Israel Department of Computer Science Universidad Industrial de Santander BucaramangaSantander680002 Colombia

Frequency-resolved optical gating (FROG) is a popular technique for complete characterization of ultrashort laser pulses. The acquired data in FROG, called FROG trace, is the Fourier magnitude of the product of the unknown pulse with a time-shifted version of itself, for several different shifts. To estimate the pulse from the FROG trace, we propose an algorithm that minimizes a smoothed non-convex least-squares objective function. The method consists of two steps. First, we approximate the pulse by an iterative spectral algorithm. Then, the attained initialization is refined based upon a sequence of block stochastic gradient iterations. The algorithm is theoretically simple, numerically scalable, and easy-to-implement. Empirically, our approach outperforms the state-of-the-art when the FROG trace is incomplete, that is, when only few shifts are recorded. Simulations also suggest that the proposed algorithm exhibits similar computational cost compared to a state-of-the-art technique for both complete and incomplete data. In addition, we prove that in the vicinity of the true solution, the algorithm converges to a critical point. A Matlab implementation is publicly available at https://***/samuelpinilla/FROG. Copyright © 2019, The Authors. All rights reserved.

关键词： Ultrashort pulses

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Geometry based data generation 32

Geometry based data generation

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32nd Conference on Neural Information Processing Systems, NeurIPS 2018

作者： Lindenbaum, Ofir Wolf, Guy Stanley, Jay S. Krishnaswamy, Smita Applied Mathematics Program Yale University New HavenCT06511 United States Computational Biology and Bioinformatics Program Yale University New HavenCT06510 United States Departments of Genetics and Computer Science Yale University New HavenCT06510 United States

We propose a new type of generative model for high-dimensional data that learns a manifold geometry of the data, rather than density, and can generate points evenly along this manifold. This is in contrast to existing generative models that represent data density, and are strongly affected by noise and other artifacts of data collection. We demonstrate how this approach corrects sampling biases and artifacts, thus improves several downstream data analysis tasks, such as clustering and classification. Finally, we demonstrate that this approach is especially useful in biology where, despite the advent of single-cell technologies, rare subpopulations and gene-interaction relationships are affected by biased sampling. We show that SUGAR can generate hypothetical populations, and it is able to reveal intrinsic patterns and mutual-information relationships between genes on a single-cell RNA sequencing dataset of hematopoiesis. © 2018 Curran Associates Inc..All rights reserved.

关键词： Genes

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End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems 18

End-to-end symmetry preserving inter-atomic potential energy...

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Proceedings of the 32nd International Conference on Neural Information Processing Systems

作者： Linfeng Zhang Jiequn Han Han Wang Wissam A. Saidi Roberto Car E. Weinan Program in Applied and Computational Mathematics Princeton University Institute of Applied Physics and Computational Mathematics China and CAEP Software Center for High Performance Numerical Simulation China Department of Mechanical Engineering and Materials Science University of Pittsburgh Program in Applied and Computational Mathematics Princeton University and Department of Chemistry and Department of Physics Princeton University and Princeton Institute for the Science and Technology of Materials Princeton University Program in Applied and Computational Mathematics Princeton University and Department of Mathematics Princeton University and Beijing Institute of Big Data Research China

Machine learning models are changing the paradigm of molecular modeling, which is a fundamental tool for material science, chemistry, and computational biology. Of particular interest is the inter-atomic potential energy surface (PES). Here we develop Deep Potential - Smooth Edition (DeepPot-SE), an end-to-end machine learning-based PES model, which is able to efficiently represent the PES of a wide variety of systems with the accuracy of ab initio quantum mechanics models. By construction, DeepPot-SE is extensive and continuously differentiable, scales linearly with system size, and preserves all the natural symmetries of the system. Further, we show that DeepPot-SE describes finite and extended systems including organic molecules, metals, semiconductors, and insulators with high fidelity.

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Manifold learning-based methods for analyzing single-cell RNA-sequencing data

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Current Opinion in Systems Biology 2018年 7卷 36-46页

作者： Moon, Kevin R. Stanley, Jay S. Burkhardt, Daniel van Dijk, David Wolf, Guy Krishnaswamy, Smita Department of Genetics Yale University New Haven CT United States Applied Mathematics Program Yale University New Haven CT United States Computational Biology and Bioinformatics Program Yale University New Haven CT United States Department of Computer Science Yale University New Haven CT United States

Recent advances in single-cell RNA sequencing technologies enable deep insights into cellular development, gene regulation, and phenotypic diversity by measuring gene expression for thousands of cells in a single experiment. While these technologies hold great potential for improving our understanding of cellular states and progression, they also pose new challenges and require advanced mathematical and algorithmic tools to extract underlying biological signals. In this review, we cover one of the most promising avenues of research into unlocking the potential of scRNA-seq data: the field of manifold learning, and the related manifold assumption in data analysis. Manifold learning provides a powerful structure for algorithmic approaches to process the data, extract its dynamics, and infer patterns in it. In particular, we cover manifold learning-based methods for denoising the data, revealing gene interactions, extracting pseudotime progressions with model fitting, visualizing the cellular state space via dimensionality reduction, and clustering the data. © 2017 Published by Elsevier Ltd.

关键词： Data mining Gene regulatory networks Imputation Manifold learning Pseudotime trends Single cell RNA sequencing

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Fulde-Ferrell-Like Molecular States in Spin-Orbit Coupled Ultracold Fermi Gases

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Communications in Theoretical Physics 2017年第8期67卷 255-258页

作者：叶冲傅立斌 National Laboratory of Science and Technology on Computational Physics Institute of Applied Physics and Computational Mathematics Graduate School China Academy of Engineering Physics HEDPS CAPTand CICIFSA MoEPeking University

We study the molecular state in three-component Fermi gases with a single impurity of ~6Li immersing in a no-interacting Fermi sea of ^(40)K in the presence of an equal weight combination of Rashba-type and Dresselhaustype spin-orbit coupling. In the region where the Fermi sea has two disjointed Fermi surfaces, we find that there are two Fulde–Ferrell-like molecular states with dominating contributions from the lower helicity branch. Decreasing the scattering length or the spin-orbit coupled Fermi energy, we find the Fulde–Ferrell-like molecular state with small center-of-mass momentum is always energy favored and the other one will suddenly disappear.

关键词： spin-orbit coupling

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Identification of fishing ground hotspot of traditional purse seine fisher at northern waters of Aceh – A community-based data collection approach

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IOP Conference Series: Earth and Environmental science 2021年第1期674卷

作者： H A Haridhi S Rizal M Nanda Muhammad C R Wilson Department of Marine Sciences Faculty of Marine and Fisheries Syiah Kuala University Banda Aceh Indonesia Marine and Fisheries Research Center Syiah Kuala University Banda Aceh Indonesia Doctoral Program of Mathematics and Applied Science Graduate School Syiah Kuala University Banda Aceh Indonesia Asian Development Bank Mandaluyong Phillippines

Fishing grounds are among the most important key of information kept by the fishermen. Understanding the fishing ground locations are considered important as an evaluation of the fishing effort being reached by the fishermen as well as understanding the pressure being received to the fish stock at the surrounding water. The recent study has shown that a community-based data collection approach was found successful in recording and analyzing the fishing ground locations and its properties. One of the few projects implementing this concept is the Community-Based Bathymetric Survey (CBBS), which was realized by the Body of Rehabilitation and Reconstruction (BRR) Nanggroe Aceh Darussalam (NAD) – Nias with funding from the Asian Development Bank (ADB). As many as 151 GPS-transducer recording devices were installed to the fishermen boats along the coast of Aceh, with 45 devices were installed to the traditional purse seine fisher at the northern water of Aceh. These devices were configured to automatically record locations each time the boat moved 30 m. Other important information, such as water depth, time, speed, and sea surface temperature (SST) were recorded as well. This study aims to examine the fishing ground and its fishing hotspot of the traditional purse seine fisher in the northern waters of Aceh. The data collection was performed between June 2007 and May 2009 and gathered as many as 922 data sets consist of 6,170,648 data points, from the 45 purse seine boats. Trough the data, we are able to identify the typical fishing activities of purse seiner and as many as 1,619 data points were being detected. The results indicate that there are five main regions of the fishing ground hotspot in the northern waters of Aceh, i.e. 1. Western offshore of Lhok Nga, 2. Northern offshore of Ulee Lheue, 3. Western offshore of Aceh Islands, 4. Eastern offshore of Aceh Island, and 5. Northern offshore of Krueng Raya. Among the fishing ground hotspot analyzed, the Western offshor

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The bulk van der Waals layered magnet CrSBr is a quasi-1D material

arXiv

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arXiv 2022年

作者： Klein, Julian Pingault, Benjamin Florian, Matthias Heißenbüttel, Marie-Christin Steinhoff, Alexander Song, Zhigang Torres, Kierstin Dirnberger, Florian Curtis, Jonathan B. Weile, Mads Penn, Aubrey Deilmann, Thorsten Dana, Rami Bushati, Rezlind Quan, Jiamin Luxa, Jan Sofer, Zdenek Alù, Andrea Menon, Vinod M. Wurstbauer, Ursula Rohlfing, Michael Narang, Prineha Lončar, Marko Ross, Frances M. Department of Materials Science and Engineering Massachusetts Institute of Technology CambridgeMA02139 United States John A. Paulson School of Engineering and Applied Sciences Harvard University CambridgeMA02138 United States QuTech Delft University of Technology Delft2600 GA Netherlands Department of Electrical and Computer Engineering Department of Physics University of Michigan Ann ArborMI48109 United States Institut für Festkörpertheorie Westfälische Wilhelms-Universität Münster Münster48149 Germany Institut für Theoretische Physik Universität Bremen P.O. Box 330 440 Bremen28334 Germany Bremen Center for Computational Materials Science University of Bremen Bremen28359 Germany Department of Physics City College of New York New YorkNY10031 United States College of Letters and Science UCLA Los AngelesCA90095 United States Department of Physics Technical University of Denmark Kgs. LyngbyDK-2800 Denmark MIT.nano Massachusetts Institute of Technology CambridgeMA02139 United States Department of Physics The Graduate Center City University of New York New YorkNY10016 United States Photonics Initiative CUNY Advanced Science Research Center New YorkNY10031 United States Physics Program Graduate Center City University of New York New YorkNY10026 United States Department of Inorganic Chemistry University of Chemistry and Technology Prague Technická 5 Prague 6166 28 Czech Republic Institute of Physics Center for Nanotechnology University of Münster Münster48149 Germany

Correlated quantum phenomena in one-dimensional (1D) systems that exhibit competing electronic and magnetic order are of strong interest for studying fundamental interactions and excitations, such as Tomonaga-Luttinger liquids and topological orders and defects with properties completely different from the quasiparticles expected in their higher-dimensional counterparts. However, clean 1D electronic systems are difficult to realize experimentally, particularly magnetically ordered systems. Here, we show that the van der Waals layered magnetic semiconductor CrSBr behaves like a quasi-1D material embedded in a magnetically ordered environment. The strong 1D electronic character originates from the Cr-S chains and the combination of weak interlayer hybridization and anisotropy in effective mass and dielectric screening with an effective electron mass ratio of meX/meY ∼ 50. This extreme anisotropy experimentally manifests in strong electron-phonon and exciton-phonon interactions, a Peierls-like structural instability and a Fano resonance from a van Hove singularity of similar strength of metallic carbon nanotubes. Moreover, due to the reduced dimensionality and interlayer coupling, CrSBr hosts spectrally narrow (1 meV) excitons of high binding energy and oscillator strength that inherit the 1D character. Overall, CrSBr is best understood as a stack of weakly hybridized monolayers and appears to be an experimentally attractive candidate for the study of exotic exciton and 1D correlated many-body physics in the presence of magnetic order. Copyright © 2022, The Authors. All rights reserved.

关键词： Excitons

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Retraction notice to "Hydrological and climate impacts on river characteristics of Pahang River Basin, Malaysia" [ Heliyon 9 2023 e21573]

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Heliyon 2025年第1期11卷 e41351页

作者： Mohd Khairul Amri Kamarudin Mohd Ekhwan Toriman Noorjima Abd Wahab Mohd Armi Abu Samah Khairul Nizam Abdul Maulud Firdaus Mohamad Hamzah Ahmad Shakir Mohd Saudi Sunardi Sunardi Faculty of Applied Social Science University Sultan Zainal Abidin Gong Badak Campus 21300 Terengganu Malaysia. East Coast Environmental Research Institute (ESERI) University Sultan Zainal Abidin Gong Badak Campus Nerus 21300 Kuala Malaysia. Faculty of Social Sciences and Humanities National University of Malaysia 43600 Bangi Selangor Malaysia. Kulliyyah of Science International Islamic University Malaysia 25200 Kuantan Pahang Malaysia. Earth Observation Center Institute of Climate Change National University of Malaysia 43600 Bangi Selangor Malaysia. Department of Mathematics Defense Base Center National Defence University of Malaysia Sungai Besi Camp 57000 Kuala Lumpur Malaysia. Department of Environmental Health Institute of Medical Science Technology Universiti Kuala Lumpur Kajang Selangor Malaysia. Graduate Program on Environmental Studies Postgraduate School Universitas Padjadjaran Jl. Dipati Ukur No. 35 Bandung 40132 Indonesia.

[This retracts the article DOI: 10.1016/***.2023.e21573.].

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Isotope effects in liquid water via deep potential molecular dynamics

arXiv

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arXiv 2019年

作者： Ko, Hsin-Yu Zhang, Linfeng Santra, Biswajit Wang, Han Weinan, E. DiStasio, Robert A. Cara, Roberto Department of Chemistry Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Physics Temple University PhiladelphiaPA19122 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China Department of Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry and Chemical Biology Cornell University IthacaNY14853 United States Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States

A comprehensive microscopic understanding of ambient liquid water is a major challenge for ab initio simulations as it simultaneously requires an accurate quantum mechanical description of the underlying potential energy surface (PES) as well as extensive sampling of configuration space. Due to the presence of light atoms (e.g., H or D), nuclear quantum fluctuations lead to observable changes in the structural properties of liquid water (e.g., isotope effects), and therefore provide yet another challenge for ab initio approaches. In this work, we demonstrate that the combination of dispersion-inclusive hybrid density functional theory (DFT), the Feynman discretized path-integral (PI) approach, and machine learning (ML) constitutes a versatile ab initio based framework that enables extensive sampling of both thermal and nuclear quantum fluctuations on a quite accurate underlying PES. In particular, we employ the recently developed deep potential molecular dynamics (DPMD) model - a neural-network representation of the ab initio PES - in conjunction with a PI approach based on the generalized Langevin equation (PIGLET) to investigate how isotope effects influence the structural properties of ambient liquid H2O and D2O. Through a detailed analysis of the interference differential cross sections as well as several radial and angular distribution functions, we demonstrate that this approach can furnish a semi-quantitative prediction of these subtle isotope effects. Copyright © 2019, The Authors. All rights reserved.

关键词： Deep neural networks

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Deterministic guarantees for Burer–Monteiro factorizations of smooth semidefinite programs

arXiv

引用

arXiv 2018年

作者： Boumal, Nicolas Voroninski, Vladislav Bandeira, Afonso S. Mathematics Department Program in Applied and Computational Mathematics Princeton University Department of Mathematics Center for Data Science Courant Institute of Mathematical Sciences New York University

We consider semidefinite programs (SDPs) with equality constraints. The variable to be optimized is a positive semidefinite matrix X of size n. Following the Burer–Monteiro approach, we optimize a factor Y of size n× p instead, such that X = YY. This ensures positive semidefiniteness at no cost and can reduce the dimension of the problem if p is small, but results in a non-convex optimization problem with a quadratic cost function and quadratic equality constraints in Y. In this paper, we show that if the set of constraints on Y regularly defines a smooth manifold, then, despite non-convexity, first- and second-order necessary optimality conditions are also sufficient, provided p is large enough. For smaller values of p, we show a similar result holds for almost all (linear) cost functions. Under those conditions, a global optimum Y maps to a global optimum X = YY of the SDP. We deduce old and new consequences for SDP relaxations of the generalized eigenvector problem, the trust-region subproblem and quadratic optimization over several spheres, as well as for the Max-Cut and Orthogonal-Cut SDPs which are common relaxations in stochastic block modeling and synchronization of rotations. Copyright © 2018, The Authors. All rights reserved.

关键词： Stochastic systems

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