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Synaptic Plasticity in Correlated Balanced Networks

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arXiv 2020年

作者： Akil, Alan Eric Rosenbaum, Robert Josić, Krešimir Department of Mathematics University of Houston HoustonTX United States Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN United States Interdisciplinary Center for Network Science and Applications University of Notre Dame Notre DameIN United States Department of Biology and Biochemistry University of Houston HoustonTX United States

The dynamics of local cortical networks are irregular, but correlated. Dynamic excitatory–inhibitory balance is a plausible mechanism that generates such irregular activity, but it remains unclear how balance is achieved and maintained in plastic neural networks. In particular, it is not fully understood how plasticity induced changes in the network affect balance, and in turn, how correlated, balanced activity impacts learning. How does the dynamics of balanced networks change under different plasticity rules? How does correlated spiking activity in recurrent networks change the evolution of weights, their eventual magnitude, and structure across the network? To address these questions, we develop a general theory of plasticity in balanced networks. We show that balance can be attained and maintained under plasticity induced weight changes. We find that correlations in the input mildly, but significantly affect the evolution of synaptic weights. Under certain plasticity rules, we find an emergence of correlations between firing rates and synaptic weights. Under these rules, synaptic weights converge to a stable manifold in weight space with their final configuration dependent on the initial state of the network. Lastly, we show that our framework can also describe the dynamics of plastic balanced networks when subsets of neurons receive targeted optogenetic input. Copyright © 2020, The Authors. All rights reserved.

关键词： Dynamics

Extending discrete exterior calculus to a fractional derivative

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arXiv 2019年

作者： Crum, Justin Levine, Joshua A. Gillette, Andrew Program in Applied Mathematics University of Arizona Department of Computer Science University of Arizona Department of Mathematics University of Arizona

Fractional partial differential equations (FDEs) are used to describe phenomena that involve a "non-local" or "long-range" interaction of some kind. Accurate and practical numerical approximation of their solutions is challenging due to the dense matrices arising from standard discretization procedures. In this paper, we begin to extend the well-established computational toolkit of Discrete Exterior Calculus (DEC) to the fractional setting, focusing on proper discretization of the fractional derivative. We define a Caputo-like fractional discrete derivative, in terms of the standard discrete exterior derivative operator from DEC, weighted by a measure of distance between p-simplices in a simplicial complex. We discuss key theoretical properties of the fractional discrete derivative and compare it to the continuous fractional derivative via a series of numerical experiments. Copyright © 2019, The Authors. All rights reserved.

关键词： Calculations

Neural network representation of electronic structure from ab initio molecular dynamics

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arXiv 2020年

作者： Gu, Qiangqiang Zhang, Linfeng Feng, Ji International Center for Quantum Materials School of Physics Peking University Beijing100871 China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Collaborative Innovation Center of Quantum Matter Beijing100871 China

Despite their rich information content, electronic structure data amassed at high volumes in ab initio molecular dynamics simulations are generally under-utilized. We introduce a transferable high-fidelity neural network representation of such data in the form of tight-binding Hamiltonians for crystalline materials. This predictive representation of ab initio electronic structure, combined with machine-learning boosted molecular dynamics, enables efficient and accurate electronic evolution and sampling. When applied to a one-dimension charge-density wave material, carbyne, we are able to compute the spectral function and optical conductivity in the canonical ensemble. The spectral functions evaluated during soliton-antisoliton pair annihilation process reveal significant renormalization of low-energy edge modes due to retarded electron-lattice coupling beyond the Born-Oppenheimer limit. The availability of an efficient and reusable surrogate model for the electronic structure dynamical system will enable calculating many interesting physical properties, paving way to previously inaccessible or challenging avenues in materials modeling. © 2020, CC-BY.

关键词： Electronic structure

Matrix-Model Simulations Using Quantum Computing, Deep Learning, and Lattice Monte Carlo

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PRX Quantum 2022年第1期3卷 010324-010324页

作者： Enrico Rinaldi Xizhi Han Mohammad Hassan Yuan Feng Franco Nori Michael McGuigan Masanori Hanada Physics Department University of Michigan Ann Arbor Michigan 48109 USA Theoretical Quantum Physics Laboratory Cluster for Pioneering Research RIKEN Wako Saitama 351-0198 Japan Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) RIKEN Wako Saitama 351-0198 Japan Department of Physics Stanford University Stanford California 94305-4060 USA City College of New York New York New York 10031 USA Pasadena City College Pasadena California 91106 USA RIKEN Center for Quantum Computing (RQC) Wako Saitama 351-0198 Japan Brookhaven National Laboratory Upton New York 11973 USA Department of Mathematics University of Surrey Guildford GU2 7XH United Kingdom

Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes, and it underpins the only practical numerical approach to the study of complex high-dimensional supergravity theories. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount importance for the realization of a quantum theory of gravity. Moreover, a complete numerical understanding of the holographic duality and the emergence of geometric space-time features from microscopic degrees of freedom could pave the way for new discoveries in quantum information science. Euclidean lattice Monte Carlo simulations are the de facto numerical tool for understanding the spectrum of large matrix models and have been used to test the holographic duality. However, they are not tailored to extract dynamical properties or even the quantum wave function of the ground state of matrix models. Quantum computing and deep learning provide potentially useful approaches to study the dynamics of matrix quantum mechanics. If successful in the context of matrix models, these rapidly improving numerical techniques could become the new Swiss army knife of quantum gravity practitioners. In this paper, we perform the first systematic survey for quantum computing and deep-learning approaches to matrix quantum mechanics, comparing them to lattice Monte Carlo simulations. These provide baseline benchmarks before addressing more complicated problems. In particular, we test the performance of each method by calculating the low-energy spectrum.

关键词： Lattice gauge theory Machine learning Quantum algorithms Supersymmetric field theories Hybrid Monte Carlo algorithm Path-integral Monte Carlo

Prediction of methylene blue dye sorption to sulfonated date palm kernel biochar using statistical regression and machine learning methods and DFT studies

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Journal of Molecular Liquids 2025年 429卷

作者： Aigbe, Uyiosa Osagie Ukhurebor, Kingsley Eghonghon Onyancha, Robert Birundu Osibote, Adelaja Otolorin Hassaan, Mohamed A. ElKatory, Marwa R. Nemr, Ahmed El Center for Space Research North-West University Private Bag X6001 Potchefstroom2531 South Africa National Institute of Theoretical and Computational Science Johannesburg2000 South Africa School of Chemistry & Physics University of KwaZulu-Natal Pietermaritzburg Campus Private Bag X01 Scottsville3209 South Africa Department of Physics Faculty of Science Edo State University Uzairue Edo State Nigeria School of Physics and Earth Science Faculty of Applied Science and Technology Technical University of Kenya Nairobi Kenya College of Graduate Studies School of Interdisciplinary Research and Graduate Studies Muckleneuk Campus University of South Africa Pretoria0003 South Africa Department of Mathematics and Physics Cape Peninsula University of Technology Cape Town South Africa Kayet Bey Alexandria Elanfoushy Egypt Advanced Technology and New Materials Research Institute SRTA-City New Borg El-Arab City 21934 Alexandria Egypt

In this study, methylene blue (MB) dye adsorption to synthesised sulfonated date palm kernel biochar (SDPKB) was predicted and optimized using statistical-based regression approach (response surface methodology (RSM), machine-learning algorithms (artificial-neural-network (ANN), and adaptive-neuro-fuzzy-inference-system (ANFIS) models), and quantum chemistry calculations performed using density function theory (DFT) to link the electrical properties of the MB dye with the experimental findings. The percentage (%) of MB dye removed using SDPKB was found to be proportional to the biosorbent dosage and interaction time and inversely proportional to the solution pH and initial concentrations based on different used models results. It was observed that these models were accurate and comparable for the prediction of the removal of MB with coefficient of regression (R2) values of 0.9174, 0.9742, and 0.9999, mean square error (MSE) values of 181.71, 94.50, and 0.00000049, and root MSE (RMSE) values of 13.48, 9.72, and 0.0007 for the RSM, ANN, and ANFIS, respectively. The ANFIS model was found to be more effective in the prediction of MB sorption to SDPKB than the other models (ANFIS > ANN > RSM), and it was highly applicable in the sorption process. This study has revealed that the SDPKB can serve as a better biosorbent for MB adsorption. Therefore, this study will serve as a first reference point data that will be of great assistance in industrial effluent management as well as decision-making on the adoption of statistical and machine learning models for adsorption study. © 2025 Elsevier B.V.

关键词： Adversarial machine learning

Using Cluster Analysis and Dynamic programming for Demand Response applied to Electricity Load in Residential Homes

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Journal of Engineering for Sustainable Buildings and Cities 2020年第1期1卷 011006页

作者： Chanpiwat, Pattanun Gabriel, Steven A. Moglen, Rachel L. Siemann, Michael J. Department of Mechanical Engineering University of Maryland College Park 20742 MD United States Department of Mechanical Engineering and the Applied Mathematics Statistics and Scientific Computation Program University of Maryland College Park 20742 MD United States Department of Industrial Economics and Technology Management Norwegian University of Science and Technology Trondheim NO-7491 Norway Operations Research and Industrial Engineering The University of Texas at Austin Austin 78712 TX United States Resideo Technologies Austin 78702 TX United States

This paper develops means to analyze and cluster residential households into homogeneous groups based on the electricity load. Classifying customers by electricity load profiles is a top priority for retail electric providers (REPs), so they can plan and conduct demand response (DR) effectively. We present a practical method to identify the most DR-profitable customer groups as opposed to tailoring DR programs for each separate household, which may be computationally prohibitive. Electricity load data of 10,000 residential households from 2017 located in Texas was used. The study proposed the clustered load-profile method (CLPM) to classify residential customers based on their electricity load profiles in combination with a dynamic program for DR scheduling to optimize DR profits. The main conclusions are that the proposed approach has an average 2.3% profitability improvement over a business-as-usual heuristic. In addition, the proposed method on average is approximately 70 times faster than running the DR dynamic programming separately for each household. Thus, our method not only is an important application to provide computational business insights for REPs and other power market participants but also enhances resilience for power grid with an advanced DR scheduling tool. Copyright © 2020 by ASME.

关键词： cluster analysis customer classification demand response dynamic programming energy efficiency integrated systems occupant behavior optimization residential household

Raman spectrum and polarizability of liquid water from deep neural networks

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arXiv 2020年

作者： Sommers, Grace M. Calegari Andrade, Marcos F. Zhang, Linfeng Wang, Han Car, Roberto Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China

We introduce a scheme based on machine learning and deep neural networks to model the environmental dependence of the electronic polarizability in insulating materials. Application to liquid water shows that training the network with a relatively small number of molecular configurations is sufficient to predict the polarizability of arbitrary liquid configurations in close agreement with ab initio density functional theory calculations. In combination with a neural network representation of the interatomic potential energy surface, the scheme allows us to calculate the Raman spectra along 2-nanosecond classical trajectories at different temperatures for H2O and D2O. The vast gains in efficiency provided by the machine learning approach enable longer trajectories and larger system sizes relative to ab initio methods, reducing the statistical error and improving the resolution of the low-frequency Raman spectra. Decomposing the spectra into intramolecular and intermolecular contributions elucidates the mechanisms behind the temperature dependence of the low-frequency and stretch modes. Copyright © 2020, The Authors. All rights reserved.

关键词： Liquids

Multi-target detection with an arbitrary spacing distribution

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arXiv 2019年

作者： Lan, Ti-Yen Bendory, Tamir Boumal, Nicolas Singer, Amit Program in Applied and Computational Mathematics Mathematics Department Princeton University PrincetonNJ08544 United States

Motivated by the structure reconstruction problem in cryo-electron microscopy, we consider the multi-target detection model, where multiple copies of a target signal occur at unknown locations in a long measurement, further corrupted by additive Gaussian noise. At low noise levels, one can easily detect the signal occurrences and estimate the signal by averaging. However, in the presence of high noise, which is the focus of this paper, detection is impossible. Here, we propose two approaches—autocorrelation analysis and an approximate expectation maximization algorithm—to reconstruct the signal without the need to detect signal occurrences in the measurement. In particular, our methods apply to an arbitrary spacing distribution of signal occurrences. We demonstrate reconstructions with synthetic data and empirically show that the sample complexity of both methods scales as SNR−3 in the low SNR regime. Copyright © 2019, The Authors. All rights reserved.

关键词： Convolution

Quasi-Monte Carlo software

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arXiv 2021年

作者： Choi, Sou-Cheng T. Hickernell, Fred J. Jagadeeswaran, R. McCourt, Michael J. Sorokin, Aleksei G. Department of Applied Mathematics Illinois Institute of Technology 10W. 32nd St. ChicagoIL60616 United States Kamakura Corporation 2222 Kalakaua Ave HonoluluHI96815 United States Center for Interdisciplinary Scientific Computation Department of Applied Mathematics Illinois Institute of Technology 10 W. 32nd St. ChicagoIL60616 United States Wi-Tronix Llc 631 E Boughton Rd BolingbrookIL60440 United States SigOpt An Intel Company 100 Bush St. San FranciscoCA94104 United States

Practitioners wishing to experience the efficiency gains from using low discrepancy sequences need correct, robust, well-written software. This article, based on our MCQMC 2020 tutorial, describes some of the better quasi-Monte Carlo (QMC) software available. We highlight the key software components required by QMC to approximate multivariate integrals or expectations of functions of vector random variables. We have combined these components in QMCPy, a Python opensource library, which we hope will draw the support of the QMC community. Here we introduce QMCPy. Copyright © 2021, The Authors. All rights reserved.

关键词： Python