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arXiv 2021年

作者： Landa, Boris Zhang, Thomas T.C.K. Kluger, Yuval Program in Applied Mathematics Yale University United States Department of Electrical and Systems Engineering University of Pennsylvania United States Interdepartmental Program in Computational Biology and Bioinformatics Yale University United States Department of Pathology Yale University School of Medicine United States

Estimating the rank of a corrupted data matrix is an important task in data analysis, most notably for choosing the number of components in PCA. Significant progress on this task was achieved using random matrix theory by characterizing the spectral properties of large noise matrices. However, utilizing such tools is not straightforward when the data matrix consists of count random variables, e.g., Poisson, in which case the noise can be heteroskedastic with an unknown variance in each entry. In this work, we consider a Poisson random matrix with independent entries, and propose a simple procedure termed biwhitening for estimating the rank of the underlying signal matrix (i.e., the Poisson parameter matrix) without any prior knowledge. Our approach is based on the key observation that one can scale the rows and columns of the data matrix simultaneously so that the spectrum of the corresponding noise agrees with the standard Marchenko-Pastur (MP) law, justifying the use of the MP upper edge as a threshold for rank selection. Importantly, the required scaling factors can be estimated directly from the observations by solving a matrix scaling problem via the Sinkhorn-Knopp algorithm. Aside from the Poisson, our approach is extended to families of distributions that satisfy a quadratic relation between the mean and the variance, such as the generalized Poisson, binomial, negative binomial, gamma, and many others. This quadratic relation can also account for missing entries in the data. We conduct numerical experiments that corroborate our theoretical findings, and showcase the advantage of our approach for rank estimation in challenging regimes. Furthermore, we demonstrate the favorable performance of our approach on several real datasets of single-cell RNA sequencing (scRNA-seq), High-Throughput Chromosome Conformation Capture (Hi-C), and document topic *** Codes 62H12, 62H25. Copyright © 2021, The Authors. All rights reserved.

关键词： Random variables

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Integrability of Goldilocks quantum cellular automata

arXiv

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arXiv 2024年

作者： Hillberry, Logan E. Piroli, Lorenzo Vernier, Eric Halpern, Nicole Yunger Prosen, Tomaž Carr, Lincoln D. Department of Physics The University of Texas at Austin AustinTX78712 United States Dipartimento di Fisica e Astronomia Università di Bologna INFN Sezione di Bologna via Irnerio 46 BolognaI-40126 Italy Laboratoire de Probabilités Statistique et Modélisation CNRS Université Paris Cité Sorbonne Université Paris France Joint Center for Quantum Information and Computer Science NIST University of Maryland College ParkMD20742 United States Institute for Physical Science and Technology University of Maryland College ParkMD20742 United States Faculty of Mathematics and Physics University of Ljubljana Jadranska 19 LjubljanaSI-1000 Slovenia Institute of Mathematics Physics and Mechanics Jadranska 19 LjubljanaSI-1000 Slovenia Quantum Engineering Program Colorado School of Mines GoldenCO80401 United States Department of Physics Colorado School of Mines GoldenCO80401 United States Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401 United States

Goldilocks quantum cellular automata (QCA) have been simulated on quantum hardware and produce emergent small-world correlation networks. In Goldilocks QCA, a single-qubit unitary is applied to each qubit in a one-dimensional chain subject to a balance constraint: a qubit is updated if its neighbors are in opposite basis states. Here, we prove that a subclass of Goldilocks QCA—including the one implemented experimentally—map onto free fermions and therefore can be classically simulated efficiently. We support this claim with two independent proofs, one involving a Jordan–Wigner transformation and one mapping the integrable six-vertex model to QCA. We compute local conserved quantities of these QCA and predict experimentally measurable expectation values. These calculations can be applied to test large digital quantum computers against known solutions. In contrast, typical Goldilocks QCA have equilibration properties and quasienergy-level statistics that suggest nonintegrability. Still, the latter QCA conserve one quantity useful for error mitigation. Our work provides a parametric quantum circuit with tunable integrability properties with which to test quantum hardware. © 2024, CC BY.

关键词： Qubits

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Constraining f(R) models with cosmic chronometers and the HII galaxy Hubble diagram

arXiv

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arXiv 2022年

作者： Sultana, Joseph Yennapureddy, Manoj K. Melia, Fulvio Kazanas, Demosthenes Department of Mathematics Faculty of Science University of Malta MSD Msida2080 Malta Department of Physics The University of Arizona TucsonAZ85721 United States Department of Physics The Applied Math Program Department of Astronomy The University of Arizona TucsonAZ85721 United States Astrophysics Science Division NASA/Goddard Space Flight Center GreenbeltMD20771 United States

We consider several well-known f(R) cosmological models and constrain their parameters, namely the deviation parameter b and the cosmological parameters Ωm and h. We first obtain analytical approximations for the Hubble rate H(z) and the luminosity distance dL(z) in terms of these parameters, and then test these against the observational expansion rate derived from cosmic chronometers and the distance modulus in the HII galaxy Hubble diagram, obtained in a model-independent way using Gaussian Processes (GP). We first optimize the models based solely on the cosmic chronometers and then repeat this process with a joint analysis using both the cosmic chronometers and HII galaxies. Copyright © 2022, The Authors. All rights reserved.

关键词： Chronometers

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Algebraic constraints and algorithms for common lines in cryo-EM

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Biological imaging 2024年 4卷 e9页

作者： Tommi Muller Adriana L Duncan Eric J Verbeke Joe Kileel Mathematical Institute University of Oxford Oxford UK. Department of Mathematics University of Texas at Austin Austin TX USA. Program in Applied and Computational Mathematics Princeton University Princeton NJ USA. Oden Institute University of Texas at Austin Austin TX USA.

We revisit the topic of common lines between projection images in single-particle cryo-electron microscopy (cryo-EM). We derive a novel low-rank constraint on a certain 2 × matrix storing properly scaled basis vectors for the common lines between projection images of one molecular conformation. Using this algebraic constraint and others, we give optimization algorithms to denoise common lines and recover the unknown 3D rotations associated with the images. As an application, we develop a clustering algorithm to partition a set of noisy images into homogeneous communities using common lines, in the case of discrete heterogeneity in cryo-EM. We demonstrate the methods on synthetic and experimental datasets.

关键词： ADMM common lines cryo-electron microscopy discrete heterogeneity group synchronization low-rank matrix

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Human-induced carbon stress power upon earth: integrated data set, rheological findings and consequences

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Science of The Total Environment 2025年 992卷

作者： Matthias Jonas Rostyslav Bun Iryna Ryzha Piotr Żebrowski Advancing Systems Analysis Program International Institute for Applied Systems Analysis 2361 Laxenburg Austria Department of Applied Mathematics Lviv Polytechnic National University 79013 Lviv Ukraine Department of Transport and Computer Sciences WSB University 41300 Dąbrowa Górnicza Poland

In this study we take the position of an outer-space observer to understand Earth's planetary carbon-climate response to stress from a rheological perspective; with stress upon the Earth atmosphere–land and ocean system given by the uninterrupted increase in cumulative CO 2 emissions caused by humankind between 1850 and 2021. This perspective complements the global carbon mass balance perspective applied by the carbon community. It gives reason to suspect that Earth is in an even worse environmental condition than commonly believed. We apply a rheological (stress–strain) analogue model, a Maxwell body, consisting of elastic and damping (viscous) elements to reflect the overall behavior of the atmosphere–land and ocean system under the influence of global warming. For an observer it is the overall strain response of that system – expansion of the atmosphere by volume and uptake of CO 2 by sinks – that is unknown. Our rheological study addresses two important issues that had neither been mentioned previously nor elsewhere. Firstly, we quantify stress power exerted by humans upon Earth and its two subsystems, atmosphere and land-ocean, for 1850–2021. Secondly, we compute the second derivative by time of the system's delay time, which indicates that Earth experienced a major change in its dynamics in the past by exhibiting a turning point which is when the deacceleration rate of the system's delay time goes through a maximum, some time between 1925 and 1945. After passing through the maximum, Earth's land-ocean subsystem does not respond characteristically to stress anymore; that is, outside its natural regime. This finding suggests that the Earth system is on a slow end-of-life path since then, not necessarily collapsing as a whole; but, nonetheless, that it is becoming increasingly vulnerable to sub-global, threshold-transgressing incidents acting bottom-up which may cause the entire atmosphere–land and ocean system to ultimately collapse.

关键词： System Earth Atmosphere and land-ocean carbon system Human-induced carbon emissions Stress power upon Earth Earth's strain response Earth's rheological parameters

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Autonomous Electron Tomography Reconstruction with Machine Learning

arXiv

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arXiv 2023年

作者： Millsaps, William Schwartz, Jonathan Di, Zichao Wendy Jiang, Yi Hovden, Robert Department of Nuclear Engineering & Radiological Sciences University of Michigan Ann ArborMI United States Department of Materials Science and Engineering University of Michigan Ann ArborMI United States Mathematics and Computer Science Division Argonne National Laboratory LemontIL United States Advanced Photon Source Facility Argonne National Laboratory LemontIL United States Applied Physics Program University of Michigan Ann ArborMI United States

This manuscript is published in Microscopy and Microanalysis (DOI: 10.1093/micmic/ozad083). Modern electron tomography has progressed to higher resolution at lower doses by leveraging compressed sensing methods that minimize total variation (TV). However, these sparsity-emphasized reconstruction algorithms introduce tunable parameters that greatly influence the reconstruction quality. Here, Pareto front analysis shows that high-quality tomograms are reproducibly achieved when TV minimization is heavily weighted. However, in excess, compressed sensing tomography creates overly smoothed 3D reconstructions. Adding momentum to the gradient descent during reconstruction reduces the risk of over-smoothing and better ensures that compressed sensing is well behaved. For simulated data, the tedious process of tomography parameter selection is efficiently solved using Bayesian optimization with Gaussian processes. In combination, Bayesian optimization with momentum-based compressed sensing greatly reduces the required compute time-an 80% reduction was observed for the 3D reconstruction of SrTiO3 nanocubes. Automated parameter selection is necessary for large scale tomographic simulations that enable the 3D characterization of a wider range of inorganic and biological materials. © 2023, CC BY.

关键词： Compressed sensing

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ReLSO: A Transformer-based Model for Latent Space Optimization and Generation of Proteins

arXiv

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arXiv 2022年

作者： Castro, Egbert Godavarthi, Abhinav Rubinfien, Julian Givechian, Kevin Bhaskar, Dhananjay Krishnaswamy, Smita Computational Biology and Bioinformatics Program Yale University New HavenCT06511 United States Department of Applied Mathematics Yale University New HavenCT06511 United States Department of Genetics Yale University New HavenCT06511 United States Department of Computer Science Yale University New HavenCT06511 United States

The development of powerful natural language models have increased the ability to learn meaningful representations of protein sequences. In addition, advances in high-throughput mutagenesis, directed evolution, and next-generation sequencing have allowed for the accumulation of large amounts of labeled fitness data. Leveraging these two trends, we introduce Regularized Latent Space Optimization (ReLSO), a deep transformer-based autoencoder which features a highly structured latent space that is trained to jointly generate sequences as well as predict fitness. Through regularized prediction heads, ReLSO introduces a powerful protein sequence encoder and novel approach for efficient fitness landscape traversal. Using ReLSO, we explicitly model the sequence-function landscape of large labeled datasets and generate new molecules by optimizing within the latent space using gradient-based methods. We evaluate this approach on several publicly-available protein datasets, including variant sets of anti-ranibizumab and GFP. We observe a greater sequence optimization efficiency (increase in fitness per optimization step) by ReLSO compared to other approaches, where ReLSO more robustly generates high-fitness sequences. Furthermore, the attention-based relationships learned by the jointly-trained ReLSO models provides a potential avenue towards sequence-level fitness attribution information. © 2022, CC BY-NC-ND.

关键词： Proteins

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Machine learning based non-Newtonian fluid model with molecular fidelity

arXiv

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arXiv 2020年

作者： Lei, Huan Wu, Lei Weinan, E. Department of Computational Mathematics Science & Engineering Department of Statistics & Probability Michigan State University MI48824 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University NJ08544 United States

We introduce a machine-learning-based framework for constructing continuum non-Newtonian fluid dynamics model directly from a micro-scale description. Polymer solution is used as an example to demonstrate the essential ideas. To faithfully retain molecular fidelity, we establish a micro-macro correspondence via a set of encoders for the micro-scale polymer configurations and their macro-scale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from the micro-scale model and the relevant terms can be parametrized using machine learning. The final model, named the deep non-Newtonian model (DeePN2), takes the form of conventional non-Newtonian fluid dynamics models, with a new form of the objective tensor derivative. Numerical results demonstrate the accuracy of DeePN2. Copyright © 2020, The Authors. All rights reserved.

关键词： Viscous flow

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3D imaging lipidometry in single cell by in-flow holographic tomography

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Opto-Electronic Advances 2023年第1期6卷 10-25页

作者： Daniele Pirone Daniele Sirico Lisa Miccio Vittorio Bianco Martina Mugnano Danila del Giudice Gianandrea Pasquinelli Sabrina Valente Silvia Lemma Luisa Iommarini Ivana Kurelac Pasquale Memmolo Pietro Ferraro CNR-ISASI Institute of Applied Sciences and Intelligent Systems“E.Caianiello”Via Campi Flegrei 34PozzuoliNapoli 80078Italy Department of Electrical Engineering and Information Technologies University of Naples“FedericoⅡ”via Claudio 21Napoli 80125Italy Department of Chemical Materials and Production Engineering of the University of Naples FedericoⅡPiazzale Tecchio 80Napoli 80125Italy Department of Mathematics and Physics University of Campania“Luigi Vanvitelli”Caserta 81100Italy Biotechnology and Methods in Laboratory Medicine Department of ExperimentalDiagnostic and Specialty Medicine(DIMES)University of BolognaBologna 40126Italy Subcellular Nephro-Vascular Diagnostic Program Pathology Unit S.Orsola IRCCSUniversity of BolognaBologna 40126Italy Unit of Medical Genetics Department of Medical and Surgical Sciences(DIMEC)University of BolognaVia Massarenti 9Bologna 40138Italy Study and Research Center on Gynecological Neoplasias Department of Medical and Surgical Sciences(DIMEC)University of BolognaVia Massarenti 9Bologna 40138Italy Center for Applied Biomedical Research(CRBA) University of BolognaBologna 40138Italy Department of Pharmacy and Biotechnology(FABIT) University of BolognaBologna 40126Italy

The most recent discoveries in the biochemical field are highlighting the increasingly important role of lipid droplets(LDs)in several regulatory mechanisms in living *** are dynamic organelles and therefore their complete characterization in terms of number,size,spatial positioning and relative distribution in the cell volume can shed light on the roles played by *** now,fluorescence microscopy and transmission electron microscopy are assessed as the gold standard methods for identifying LDs due to their high sensitivity and ***,such methods generally only provide 2D assays and partial ***,both can be destructive and with low productivity,thus limiting analysis of large cell numbers in a *** we demonstrate for the first time the capability of 3D visualization and the full LD characterization in high-throughput with a tomographic phase-contrast flow-cytometer,by using ovarian cancer cells and monocyte cell lines as models.A strategy for retrieving significant parameters on spatial correlations and LD 3D positioning inside each cell volume is *** information gathered by this new method could allow more in depth understanding and lead to new discoveries on how LDs are correlated to cellular functions.

关键词： lipid droplets label-free phase-contrast imaging in-flow tomography 3D imaging

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Isotope effects in x-ray absorption spectra of liquid water

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Physical Review B 2020年第11期102卷 115155-115155页

作者： Chunyi Zhang Linfeng Zhang Jianhang Xu Fujie Tang Biswajit Santra Xifan Wu Department of Physics Temple University Philadelphia Pennsylvania 19122 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The isotope effects in x-ray absorption spectra of liquid water are studied by a many-body approach within electron-hole excitation theory. The molecular structures of both light and heavy water are modeled by path-integral molecular dynamics based on the advanced deep-learning technique. The neural network is trained on ab initio data obtained with SCAN density functional theory. The experimentally observed isotope effect in x-ray absorption spectra is reproduced semiquantitatively in theory. Compared to the spectrum in normal water, the blueshifted and less pronounced pre- and main-edge in heavy water reflect that the heavy water is more structured at short- and intermediate-range of the hydrogen-bond network. In contrast, the isotope effect on the spectrum is negligible at post-edge, which is consistent with the identical long-range ordering in both liquids as observed in the diffraction experiment.

关键词： Atomic & molecular structure Electronic excitation & ionization Water Density functional calculations Electronic structure First-principles calculations Machine learning Molecular dynamics X-ray absorption spectroscopy

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