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Emulating complex synapses using interlinked proton conductors

Physical Review applied 2025年第1期23卷 014027-014027页

作者： Lifu Zhang Ji-An Li Yang Hu Jie Jiang Rongjie Lai Marcus K. Benna Jian Shi Department of Materials Science and Engineering Rensselaer Polytechnic Institute Troy New York 12180 USA Neurosciences Graduate Program University of California San Diego La Jolla California 92093 USA Department of Mathematics Purdue University West Lafayette Indiana 47907 USA Department of Neurobiology School of Biological Sciences University of California at San Diego La Jolla California 92093 USA Department of Physics Applied Physics and Astronomy Rensselaer Polytechnic Institute Troy New York 12180 USA

In terms of energy efficiency and computational speed, neuromorphic electronics based on nonvolatile memory devices are expected to be one of most promising hardware candidates for future artificial intelligence (AI). However, catastrophic forgetting, networks rapidly overwriting previously learned weights when learning new tasks, remains a pivotal obstacle in either digital or analog AI chips for unleashing the true power of brainlike computing. To address catastrophic forgetting in the context of online memory storage, a complex synapse model (the Benna-Fusi model) was proposed recently [M. K. Benna and S. Fusi, Nat. Neurosci. 19, 1697 (2016)], the synaptic weight and internal variables of which evolve following diffusion dynamics. In this work, by designing a proton transistor with a series of charge-diffusion-controlled storage components, we have experimentally realized the Benna-Fusi artificial complex synapse. Memory consolidation from coupled storage components is revealed by both numerical simulations and experimental observations. Different memory timescales for the complex synapse are engineered by the diffusion length of charge carriers and the capacity and number of coupled storage components. The advantages of the demonstrated complex synapse for both memory capacity and memory consolidation are revealed by neural network simulations of face-familiarity detection. Our experimental realization of the complex synapse suggests a promising approach to enhance memory capacity and to enable continual learning.

关键词： Nonvolatile storage

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Ab Initio Generalized Langevin Equation

arXiv

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arXiv 2022年

作者： Xie, Pinchen Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States AI for Science Institute Beijing China Center for Machine Learning Research School of Mathematical Sciences Peking University Beijing China

We introduce a machine learning-based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori-Zwanzig formalism, under the constraint of the fluctuation-dissipation theorem. Combined with deep potential molecular dynamics and electronic density functional theory, this approach opens the way to multi-scale modeling in a variety of situations. Here, we demonstrate this capability with a study of two mesoscale processes in crystalline lead titanate, namely the field-driven dynamics of a planar ferroelectric domain wall, and the dynamics of an extensive lattice of coarse-grained electric dipoles. In the first case, AIGLE extends the reach of ab initio simulations to a regime of noise-driven motions not accessible to molecular dynamics. In the second case, AIGLE deals with an extensive set of collective variables by adopting a local approximation for the memory kernel and retaining only short-range noise correlations. The scheme is computationally more efficient than molecular dynamics by several orders of magnitude, and mimics the microscopic dynamics at low frequencies where it reproduces accurately the dominant far-infrared absorption frequency. © 2022, CC BY.

关键词： Molecular dynamics

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Fractional Integrable Nonlinear Soliton Equations

arXiv

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arXiv 2022年

作者： Ablowitz, Mark J. Been, Joel B. Carr, Lincoln D. Department of Applied Mathematics University of Colorado BoulderCO80309 United States Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401 United States Department of Physics Colorado School of Mines GoldenCO80401 United States Quantum Engineering Program Colorado School of Mines GoldenCO80401 United States

Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional equations are well known in anomalous diffusion. We connect these two fields by presenting the discovery of a new class of integrable fractional nonlinear evolution equations describing dispersive transport in fractional media. These equations can be constructed from nonlinear integrable equations using a widely generalizable mathematical process utilizing completeness relations, dispersion relations, and inverse scattering transform techniques. As examples, this general method is used to characterize fractional extensions to two physically relevant, pervasive integrable nonlinear equations: the Korteweg–deVries and nonlinear Schrödinger equations. These equations are shown to predict super-dispersive transport of non-dissipative solitons in fractional media. © 2022, CC BY.

关键词： Nonlinear equations

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Fractional Integrable and Related Discrete Nonlinear Schrödinger Equations

arXiv

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arXiv 2022年

Integrable fractional equations such as the fractional Korteweg-deVries and nonlinear Schrödinger equations are key to the intersection of nonlinear dynamics and fractional calculus. In this manuscript, the first discrete/differential difference equation of this type is found, the fractional integrable discrete nonlinear Schrödinger equation. This equation is linearized;special soliton solutions are found whose peak velocities exhibit more complicated behavior than other previously obtained fractional integrable equations. This equation is compared with the closely related fractional averaged discrete nonlinear Schrödinger equation which has simpler structure than the integrable case. For positive fractional parameter and small amplitude waves, the soliton solutions of the integrable and averaged equations have similar behavior. © 2022, CC BY.

关键词： Nonlinear equations

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QCD-based charge symmetry breaking interaction and the Okamoto-Nolen-Schiffer anomaly

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Physical Review C 2024年第1期109卷 L011302-L011302页

作者： Hiroyuki Sagawa (佐川弘幸) Tomoya Naito (内藤智也) Xavier Roca-Maza Tetsuo Hatsuda (初田哲男) RIKEN Nishina Center for Accelerator-based Science Wako 351-0198 Japan Center for Mathematics and Physics University of Aizu Aizu-Wakamatsu Fukushima 965-8560 Japan RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) Wako 351-0198 Japan Department of Physics Graduate School of Science The University of Tokyo Tokyo 113-0033 Japan Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos Universitat de Barcelona Martí i Franqués 1 08028 Barcelona Spain Dipartimento di Fisica Università degli Studi di Milano Via Celoria 16 20133 Milano Italy INFN Sezione di Milano Via Celoria 16 20133 Milano Italy

An approach is proposed to link the charge symmetry breaking (CSB) nuclear interaction and the low-energy constants in quantum chromodynamics (QCD) by matching the CSB effect in nuclear matter. The resulting CSB interaction is applied to study the Okamoto-Nolen-Schiffer anomaly, still lacking a satisfactory microscopic understanding, on the energy differences of mirror nuclei by taking F17−O17, O15−N15, Sc41−Ca41, and Ca39−K39 as typical examples. The magnitude and sign of the QCD-based CSB interactions are found to resolve the anomaly successfully within theoretical uncertainties.

关键词： Coulomb energies & analogue states Nuclear forces Nuclear many-body theory Nucleon-nucleon interactions Quantum chromodynamics Sum rules Chiral symmetry Nuclear density functional theory

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Exploring Barriers to the Use of Evidence-Based Instructional Practices

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Journal of College Science Teaching 2021年第2期51卷 56-66页

作者： Gardner, Grant E. Brown, Evelyn Grimes, Zachary Bishara, Gina Department of Biology and doctoral faculty in the Interdisciplinary Mathematics and Sciences Education Research PhD program at Middle Tennessee State University United States North Carolina State University United States Crowley’s Ridge College United States Department of Biology at Middle Tennessee State University United States

Recent reform documents in postsecondary science, technology, engineering, and mathematics (STEM) fields recommend the use of evidence-based instructional practices (EBIPs) in the classroom. National surveys in the United States suggest a continued reliance on instructorcentered practices that have little evidentiary support for long-term impacts on student learning. This study utilized a cross-sectional survey research design to explore the awareness and use of EBIPs by STEM instructors at two large universities (n = 104) in the southeastern United States. Participants’ perceived individual and situational barriers impaired their use of EBIPs. We also examined how these barriers may be related to faculty use of these instructional practices. Results indicate high awareness of many EBIPs but with little subsequent classroom use. Results also suggest that STEM faculty’s gender and pedagogical beliefs may mediate what they perceive as significant barriers to EBIP implementation. © 2021 National Science Teaching Association.

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Transductive and inductive outlier detection with robust autoencoders 24

Transductive and inductive outlier detection with robust aut...

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Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence

作者： Ofir Lindenbaum Yariv Aizenbud Yuval Kluger Faculty of Engineering Bar-Ilan University Ramat Gan Israel School of Mathematical Sciences Tel Aviv University Tel Aviv Israel Program in Applied Mathematics Yale University New Haven CT and Department of Pathology Yale University School of Medicine New Haven CT and Computational Biology & Bioinformatics Program Yale University New Haven CT

Accurate detection of outliers is crucial for the success of numerous data analysis tasks. In this context, we propose the Probabilistic Robust AutoEncoder (PRAE) that can simultaneously remove outliers during training (transductive) and learn a mapping that can be used to detect outliers in new data (inductive). We first present the Robust AutoEncoder (RAE) objective that excludes outliers while including a subset of samples (inliers) that can be effectively reconstructed using an AutoEncoder (AE). RAE minimizes the autoencoder's reconstruction error while incorporating as many samples as possible. This could be formulated via regularization by subtracting an ℓ0 norm, counting the number of selected samples from the reconstruction term. As this leads to an intractable combinatorial problem, we propose two probabilistic relaxations of RAE, which are differentiable and alleviate the need for a combinatorial search. We prove that the solution to the PRAE problem is equivalent to the solution of RAE. We then use synthetic data to demonstrate that PRAE can accurately remove outliers in various contamination levels. Finally, we show that using PRAE for outlier detection leads to state-of-the-art results for inductive and transductive outlier detection.

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A Molecular Prior Distribution for Bayesian Inference Based on Wilson Statistics

arXiv

引用

arXiv 2022年

作者： Gilles, Marc Aurèle Singer, Amit Program in Applied and Computational Mathematics Princeton University Fine Hall Washington Road Princeton NJ08544-1000 United States Department of Mathematics and PACM Princeton University Fine Hall Washington Road Princeton NJ08544-1000 United States

Background and Objective: Wilson statistics describe well the power spectrum of proteins at high frequencies. Therefore, it has found several applications in structural biology, e.g., it is the basis for sharpening steps used in cryogenic electron microscopy (cryo-EM). A recent paper gave the first rigorous proof of Wilson statistics based on a formalism of Wilson's original argument. This new analysis also leads to statistical estimates of the scattering potential of proteins that reveal a correlation between neighboring Fourier coefficients. Here we exploit these estimates to craft a novel prior that can be used for Bayesian inference of molecular structures. Methods: We describe the properties of the prior and the computation of its hyperparameters. We then evaluate the prior on two synthetic linear inverse problems, and compare against a popular prior in cryo-EM reconstruction at a range of SNRs. Results: We show that the new prior effectively suppresses noise and fills-in low SNR regions in the spectral domain. Furthermore, it improves the resolution of estimates on the problems considered for a wide range of SNR and produces Fourier Shell Correlation curves that are insensitive to masking effects. Conclusions: We analyze the assumptions in the model, discuss relations to other regularization strategies, and postulate on potential implications for structure determination in cryo-EM. Copyright © 2022, The Authors. All rights reserved.

关键词： Proteins

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Ground state phases of the two-dimension electron gas with a unified variational approach

arXiv

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arXiv 2024年

作者： Smith, Conor Chen, Yixiao Levy, Ryan Yang, Yubo Morales, Miguel A. Zhang, Shiwei Center for Computational Quantum Physics Flatiron Institute New YorkNY10010 United States Department of Electrical and Computer Engineering University of New Mexico AlbuquerqueNM87131 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The two-dimensional electron gas (2DEG) is a fundamental model, which is drawing increasing interest because of recent advances in experimental and theoretical studies of 2D materials. Current understanding of the ground state of the 2DEG relies on quantum Monte Carlo calculations, based on variational comparisons of different ansatze for different phases. We use a single variational ansatz, a general backflow-type wave function using a message-passing neural quantum state architecture, for a unified description across the entire density range. The variational optimization consistently leads to lower ground-state energies than previous best results. Transition into a Wigner crystal (WC) phase occurs automatically at rs = 37±1, a density lower than currently believed. Between the liquid and WC phases, the same ansatz and variational search strongly suggest the existence of intermediate states in a broad range of densities, with enhanced short-range nematic spin correlations. Copyright © 2024, The Authors. All rights reserved.

关键词： Message passing

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Engaging Engineering mathematics students online: Tutoring using MS Teams

Engaging Engineering Mathematics students online: Tutoring u...

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World Engineering Education Forum - Global Engineering Deans Council (WEEF-GEDC)

作者： Pragashni Padayachee Anita Campbell Ebrahim Fredericks Academic Support Program in Engineering University of Cape Town Cape Town South Africa Academic Support Program in Engineering Centre for Research in Engineering Education University of Cape Town Cape Town South Africa Department of Mathematics and Applied Mathematics University of Cape Town Cape Town South Africa

ISBN: (数字)9781665475280

ISBN: (纸本)9781665475297

Uncommon in the South African higher education landscape, online learning came to the fore during the global pandemic. We present an account of the use of Microsoft Teams for hybrid mathematics tutorials in a one-semester Vector Calculus course at a South African university in 2022. Interviews with the lecturer, analysed through a Community of Inquiry lens, showed the lecturer's perspective of the design and experience for tutors and students. Our aim is to improve the design of future hybrid tutorials to ensure engineering students' capacity in mathematics is well developed, their communication skills are improved, and that they experience working in a team. Future research will evaluate students' and tutors' accounts of their experiences. Our findings raise awareness of the possibilities and potential difficulties when using Microsoft Teams for communication, teaching and learning mathematics.

关键词： Visualization Pandemics Navigation Tutorials mathematics Reflection Calculus

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