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A field equation for induction-transduction of activation-deactivation probability on measurable space

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arXiv 2022年

作者： Bastian, Caleb Deen Rabitz, Herschel Program in Applied and Computational Mathematics Princeton University Princeton NJ08544 United States Department of Chemistry Princeton University Princeton NJ08544 United States

Induction-transduction of activating-deactivating points are fundamental mechanisms of action that underlie innumerable systems and phenomena, mathematical, natural, and anthropogenic, and can exhibit complex behaviors such as self-excitation, phase transitions, hysteresis, polarization, periodicity, chaos, wave behavior, geometry, and energy transfer. We describe a class of primitives for induction-transduction based on dynamics on images of marked random counting measures under graphical random transformations. We derive a field equation for the law of the activation-deactivation (Bernoulli) process on an arbitrary measurable space and describe some mechanisms of action on the unit *** Codes 37A50, 60G57, 60G60, 60G55 © 2022, CC BY-NC-SA.

关键词： Energy transfer

Machine Learning for Electricity Market Clearing

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arXiv 2022年

作者： Pagnier, Laurent Ferrando, Robert Dvorkin, Yury Chertkov, Michael Program in Applied Mathematics University of Arizona TucsonAZ United States Electrical and Computer Engineering New York University New YorkNY United States

This paper seeks to design a machine learning twin of the optimal power flow (OPF) optimization, which is used in market-clearing procedures by wholesale electricity markets. The motivation for the proposed approach stems from the need to obtain the digital twin, which is much faster than the original, while also being sufficiently accurate and producing consistent generation dispatches and locational marginal prices (LMPs), which are primal and dual solutions of the OPF optimization, respectively. Availability of market-clearing tools based on this approach will enable computationally tractable evaluation of multiple dispatch scenarios under a given unit commitment. Rather than direct solution of OPF, the Karush–Kuhn–Tucker (KKT) conditions for the OPF problem in question may be written, and in parallel the LMPs of generators and loads may be expressed in terms of the OPF Lagrangian multipliers. Also, taking advantage of the practical fact that many of the Lagrangian multipliers associated with lines will be zero (thermal limits are not binding), we build and train an ML scheme which maps flexible resources (loads and renewables) to the binding lines, and supplement it with an efficient power-grid aware linear map to optimal dispatch and LMPs. The scheme is validated and illustrated on IEEE models. We also report a trade of analysis between quality of the reconstruction and number of samples needed to train the model. © 2022, CC BY.

关键词： Acoustic generators

Principal Curvatures Estimation with Applications to Single Cell Data

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Principal Curvatures Estimation with Applications to Single ...

2025 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2025

作者： Zhang, Yanlei Mezrag, Lydia Sun, Xingzhi Xu, Charles Macdonald, Kincaid Bhaskar, Dhananjay Krishnaswamy, Smita Wolf, Guy Rieck, Bastian Université de Montréal Dept. of Math. & Stat Canada Mila - Quebec AI Institute MontréalQC Canada Yale University Dept. of Comp. Sci. United States Dept. of Genetics United States Applied Mathematics Program New HavenCT United States Université de Fribourg Department of Informatics FR Fribourg Switzerland Helmholtz Zentrum München Institute of AI for Health BY Munich Germany

ISBN: (纸本)9798350368741

The rapidly growing field of single-cell transcriptomic sequencing (scRNAseq) presents challenges for data analysis due to its massive datasets. A common method in manifold learning consists in hypothesizing that datasets lie on a lower dimensional manifold. This allows to study the geometry of point clouds by extracting meaningful descriptors like curvature. In this work, we will present Adaptive Local PCA (AdaL-PCA), a data-driven method for accurately estimating various notions of intrinsic curvature on data manifolds, in particular principal curvatures for surfaces. The model relies on local PCA to estimate the tangent spaces. The evaluation of AdaL-PCA on sampled surfaces shows state-of-the-art results. Combined with a PHATE embedding, the model applied to single-cell RNA sequencing data allows us to identify key variations in the cellular differentiation. © 2025 IEEE.

关键词： Gaussian curvature Principal curvature principal directions single-cell

A Molecular Prior Distribution for Bayesian Inference Based on Wilson Statistics

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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

Modeling High-Resolution Spatio-Temporal Wind with Deep Echo State Networks and Stochastic Partial Differential Equations

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arXiv 2024年

作者： Wang, Kesen Kim, Minwoo Castruccio, Stefano Genton, Marc G. Statistics Program King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Statistics Pusan National University Busan46241 Korea Republic of Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States

In the past decades, clean and renewable energy has gained increasing attention due to a global effort on carbon footprint reduction. In particular, Saudi Arabia is gradually shifting its energy portfolio from an exclusive use of oil to a reliance on renewable energy, and, in particular, wind. Modeling wind for assessing potential energy output in a country as large, geographically diverse and understudied as Saudi Arabia is a challenge which implies highly non-linear dynamic structures in both space and time. To address this, we propose a spatio-temporal model whose spatial information is first reduced via an energy distance-based approach and then its dynamical behavior is informed by a sparse and stochastic recurrent neural network (Echo State Network). Finally, the full spatial data is reconstructed by means of a non-stationary stochastic partial differential equation-based approach. Our model can capture the fine scale wind structure and produce more accurate forecasts of both wind speed and energy in lead times of interest for energy grid management and save annually as much as one million dollar against the closest competitive model. © 2024, CC BY.

关键词： Clean energy

Fast decisions reflect biases, slow decisions do not

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arXiv 2023年

作者： Linn, Samantha Lawley, Sean D. Karamched, Bhargav R. Kilpatrick, Zachary P. Josić, Krešimir Department of Mathematics University of Utah Salt Lake CityUT United States Department of Mathematics Florida State University TallahasseeFL32306 United States Institute of Molecular Biophysics Florida State University TallahasseeFL32306 United States Program in Neuroscience Florida State University TallahasseeFL32306 United States Department of Applied Mathematics University of Colorado Boulder BoulderCO80309 United States Department of Mathematics University of Houston HoustonTX77004 United States Department of Biology and Biochemistry University of Houston HoustonTX77004 United States

Decisions are often made by heterogeneous groups of individuals, each with distinct initial biases and access to information of different quality. We show that in large groups of independent agents who accumulate evidence the first to decide are those with the strongest initial biases. Their decisions align with their initial bias, regardless of the underlying truth. In contrast, agents who decide last make decisions as if they were initially unbiased, and hence make better choices. We obtain asymptotic expressions in the large population limit that quantify how agents’ initial inclinations shape early decisions. Our analysis shows how bias, information quality, and decision order interact in non-trivial ways to determine the reliability of decisions in a group. © 2023, CC BY.

关键词： Reliability analysis

Reconsider photoplethysmogram signal quality assessment in the free living environment

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Physiological Measurement 2024年第6期45卷 06NT01-06NT01页

作者： Su, Yan-Wei Hao, Chia-Cheng Liu, Gi-Ren Sheu, Yuan-Chung Wu, Hau-Tieng Department of Applied Mathematics National Yang Ming Chiao Tung University Hsinchu Taiwan Data Science Degree Program National Taiwan University Academia Sinica Taipei Taiwan Department of Mathematics National Cheng-Kung University Tainan Taiwan National Center for Theoretical Sciences National Taiwan University Taipei Taiwan Courant Institute of Mathematical Sciences New York University New YorkNY10012 United States

Objective. Assessing signal quality is crucial for biomedical signal processing, yet a precise mathematical model for defining signal quality is often lacking, posing challenges for experts in labeling signal qualities. The situation is even worse in the free living environment. Approach. We propose to model a PPG signal by the adaptive non-harmonic model (ANHM) and apply a decomposition algorithm to explore its structure, based on which we advocate a reconsideration of the concept of signal quality. Main results. We demonstrate the necessity of this reconsideration and highlight the relationship between signal quality and signal decomposition with examples recorded from the free living environment. We also demonstrate that relying on mean and instantaneous heart rates derived from PPG signals labeled as high quality by experts without proper reconsideration might be problematic. Significance. A new method, distinct from visually inspecting the raw PPG signal to assess its quality, is needed. Our proposed ANHM model, combined with advanced signal processing tools, shows potential for establishing a systematic signal decomposition based signal quality assessment model. © 2024 Institute of Physics and Engineering in Medicine.

关键词： free-living environment photoplethysmogram signal quality index synchrosqueezing transform

Chaotic dynamics of the sugarcane borer-two parasitoid agroecosystem with seasonality

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arXiv 2022年

作者： Rafikov, Marat Molter, Alexandre Bezerra, João Inácio Moreira Rafikova, Elvira Varriale, Maria Cristina Center for Engineering Modeling and Applied Social Sciences Federal University of the ABC Brazil Post Graduate Program in Mathematical Modeling Federal University of Pelotas Brazil Post Graduate Program in Applied Mathematics Federal University of Rio Grande do Sul Brazil

Sugarcane production is a significant and profitable agribusiness sector in many countries. Nevertheless, this industry suffers significant losses from the sugarcane pests, among which the most important one is the sugarcane borer (Diatraea saccharalis). This pest population is hard to be controlled due to its different life stages, thus biological control (with more than one predator species) can be applied. Therefore, in this work, we present and analyze a mathematical model that describes the dynamics of the sugarcane borer and its two different life stages parasitoids: eggs (Trichogramma galloi) and larval (Cotesia flavipes). First, a host-parasitoid model is used to obtain the population dynamics, which also considers the influence of seasonal variations. Then, system simulations and bifurcation diagrams show that the introduction of seasonality perturbations causes complex dynamics and results in limit cycles and strange attractors. © 2022, CC0.

关键词： Dynamics

Transductive and inductive outlier detection with robust autoencoders 24

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Transductive and inductive outlier detection with robust aut...

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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