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ROBUST PARAMETER ESTIMATION FOR RATIONAL ORDINARY DIFFERENTIAL EQUATIONS

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arXiv 2023年

作者： Bassik, Oren Berman, Yosef Go, Soo Hong, Hoon Ilmer, Ilia Ovchinnikov, Alexey Rackauckas, Chris Soto, Pedro Yap, Chee Ph.D. Program in Mathematics CUNY Graduate Center New YorkNY United States Ph.D. Program in Computer Science CUNY Graduate Center New YorkNY United States Department of Mathematics North Carolina State University RaleighNC United States Department of Mathematics CUNY Queens College United States Ph.D. Programs in Mathematics and Computer Science CUNY Graduate Center New YorkNY United States Department of Mathematics Massachusetts Institute of Technology CambridgeMA United States Mathematical Institute University of Oxford Oxford United Kingdom Department of Computer Science Courant Institute of Mathematical Science New York University New YorkNY United States

We present a new approach for estimating parameters in rational ODE models from given (measured) time series data. In typical existing approaches, an initial guess for the parameter values is made from a given search interval. Then, in a loop, the corresponding outputs are computed by solving the ODE numerically, followed by computing the error from the given time series data. If the error is small, the loop terminates and the parameter values are returned. Otherwise, heuristics/theories are used to possibly improve the guess and continue the loop. These approaches tend to be non-robust in the sense that their accuracy depend on the search interval and the true parameter values;furthermore, they cannot handle the case where the parameters are locally identifiable. In this paper, we propose a new approach, which does not suffer from the above non-robustness. In particular, it does not require making good initial guesses for the parameter values or specifying search intervals. Instead, it uses differential algebra, interpolation of the data using rational functions, and multivariate polynomial system solving. We also compare the performance of the resulting software with several other estimation software packages. © 2023, CC BY-NC-SA.

关键词： Parameter estimation

ProtSCAPE: Mapping the landscape of protein conformations in molecular dynamics

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arXiv 2024年

作者： Viswanath, Siddharth Bhaskar, Dhananjay Johnson, David R. Rocha, João Felipe Castro, Egbert Grady, Jackson D. Grigas, Alex T. Perlmutter, Michael A. O’Hern, Corey S. Krishnaswamy, Smita Department of Computer Science Yale University United States Department of Genetics Yale University United States Program in Computing Boise State University United States Computational Biology and Bioinformatics Program Yale University United States Department of Mathematics Boise State University United States

Understanding the dynamic nature of protein structures is essential for comprehending their biological functions. While significant progress has been made in predicting static folded structures, modeling protein motions on microsecond to millisecond scales remains challenging. To address these challenges, we introduce a novel deep learning architecture, Protein Transformer with Scattering, Attention, and Positional Embedding (ProtSCAPE), which leverages the geometric scattering transform alongside transformer-based attention mechanisms to capture protein dynamics from molecular dynamics (MD) simulations. ProtSCAPE utilizes the multi-scale nature of the geometric scattering transform to extract features from protein structures conceptualized as graphs and integrates these features with dual attention structures that focus on residues and amino acid signals, generating latent representations of protein trajectories. Furthermore, ProtSCAPE incorporates a regression head to enforce temporally coherent latent representations. Importantly, we demonstrate that ProtSCAPE generalizes effectively from short to long trajectories and from wild-type to mutant proteins, surpassing traditional approaches by delivering more precise and interpretable upsampling of dynamics. © 2024, CC BY.

关键词： Molecular docking

Parallel Approximations for High-Dimensional Multivariate Normal Probability Computation in Confidence Region Detection Applications

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Parallel Approximations for High-Dimensional Multivariate No...

International Symposium on Parallel and Distributed Processing (IPDPS)

作者： Xiran Zhang Sameh Abdulah Jian Cao Hatem Ltaief Ying Sun Marc G. Genton David E. Keyes Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Statistics Program King Abdullah University of Science and Technology Extreme Computing Research Center King Abdullah University of Science and Technology Thuwal Saudi Arabia Department of Mathematics The University of Houston Houston Texas USA

ISBN: (数字)9798350387117

ISBN: (纸本)9798350387124

Addressing the statistical challenge of computing the multivariate normal (MVN) probability in high dimensions holds significant potential for enhancing various applications. For example, the critical task of detecting confidence regions where a process probability surpasses a specific threshold is essential in diverse applications, such as pinpointing tumor locations in magnetic resonance imaging (MRI) scan images, determining hydraulic parameters in groundwater flow issues, and forecasting regional wind power to optimize wind turbine placement, among numerous others. One common way to compute high-dimensional MVN probabilities is the Separation-of-Variables (SOV) algorithm. This algorithm is known for its high computational complexity of O(n 3 ) and space complexity of O(n 2 ), mainly due to a Cholesky factorization operation for an n×n covariance matrix, where n represents the dimensionality of the MVN problem. This work proposes a high-performance computing framework that allows scaling the SOV algorithm and, subsequently, the confidence region detection algorithm. The framework leverages parallel linear algebra algorithms with a task-based programming model to achieve performance scalability in computing process probabilities, especially on large-scale systems. In addition, we enhance our implementation by incorporating Tile Low-Rank (TLR) approximation techniques to reduce algorithmic complexity without compromising the necessary accuracy. To evaluate the performance and accuracy of our framework, we conduct assessments using simulated data and a wind speed dataset. Our proposed implementation effectively handles high-dimensional multivariate normal (MVN) probability computations on shared and distributed-memory systems using finite precision arithmetics and TLR approximation computation. Performance results show a significant speedup of up to 20X in solving the MVN problem using TLR approximation compared to the reference dense solution without sacrificin

关键词： Accuracy Tensors Wind speed Magnetic resonance imaging Linear algebra Wind power generation Approximation algorithms

Accelerating Real-Time Imaging for Radiotherapy: Leveraging Multi-GPU Training with PyTorch 22

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Accelerating Real-Time Imaging for Radiotherapy: Leveraging ...

22nd IEEE International Conference on Machine Learning and Applications, ICMLA 2023

作者： Obe, Ruth Kaufmann, Brandt Baird, Kaelen Kadel, Sam Soltani, Yasmin Cham, Mostafa Gobbert, Matthias K. Barajas, Carlos A. Jiang, Zhuoran Sharma, Vijay R. Ren, Lei Peterson, Stephen W. Poif, Jerimy C. U. of Houston-Clear Lake Dept. of Computer Science and of Software Engineering United States U. of San Francisco Dept. of Mathematics and Statistics United States Skidmore College Dept. of Computer Science and of Mathematics United States Mount Holyoke College Dept. of Computer Science and of Psychology United States U. of Houston Dept. of Biomedical Engineering United States U. of Maryland Dept. of Information Systems Baltimore County United States U. of Maryland Dept. of Mathematics and Statistics Baltimore County United States Medical Physics Graduate Program Duke University United States U. of Maryland School of Medicine Dept. of Radiation Oncology United States U. of Maryland School of Medicine Department of Radiation Oncology United States U. of Cape Town Dept. of Physics South Africa H3D Inc. United States

ISBN: (纸本)9798350345346

Proton beam therapy is an advanced form of cancer radiotherapy that uses high-energy proton beams to deliver precise and targeted radiation to tumors. This helps to mit-igate unnecessary radiation exposure in healthy tissues. Real-time imaging of prompt gamma rays with Compton cameras has been suggested to improve therapy efficacy. However, the camera's non-zero time resolution leads to incorrect interaction classifications and noisy images that are insufficient for accurately assessing proton delivery in patients. To address the challenges posed by the Compton camera's image quality, machine learning techniques are employed to classify and refine the generated data. These machine-learning techniques include recurrent and feedforward neural networks. A PyTorch model was designed to improve the data captured by the Compton camera. This decision was driven by PyTorch's flexibility, powerful capabilities in handling sequential data, and enhanced G PU usage. This accelerates the model's computations on large-scale radiotherapy data. Through hyperparameter tuning, the validation accuracy of our PyTorch model has been improved from an initial 7 % to over 60 %. Moreover, the PyTorch Distributed Data Parallelism strategy was used to train the RNN models on multiple G PU s, which significantly reduced the training time with a minor impact on model accuracy. © 2023 IEEE.

关键词： Clas-sification Compton camera Distributed Data Parallelism Proton beam therapy PyTorch Recurrent neural network

Contributions to the Theory of Large Cardinals through the Method of Forcing

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Bulletin of Symbolic Logic 2021年第2期27卷 221-222页

作者： Alejandro Poveda Doctorate program in Mathematics and Computer Science—Universitat de Barcelona Barcelona Spain 2020

The dissertation under comment is a contribution to the area of Set Theory concerned with the interactions between the method of Forcing and the so-called Large Cardinal *** dissertation is divided into two thematic blocks. In Block I we analyze the large-cardinal hierarchy between the first supercompact cardinal and Vopěnka’s Principle (Part I). In turn, Block II is devoted to the investigation of some problems arising from Singular Cardinal Combinatorics (Part II and Part III).We commence Part I by investigating the Identity Crisis phenomenon in the region comprised between the first supercompact cardinal and Vopěnka’s Principle. As a result, we generalize Magidor’s classical theorems [2] to this higher region of the large-cardinal hierarchy. Also, our analysis allows to settle all the questions that were left open in [1]. Finally, we conclude Part I by presenting a general theory of preservation of $C^{(n)}$ -extendible cardinals under class forcing iterations. From this analysis we derive several applications. For instance, our arguments are used to show that an extendible cardinal is consistent with “ $(\lambda ^{+\omega })^{\mathrm {HOD}}<\lambda ^+$ , for every regular cardinal $\lambda $ .” In particular, if Woodin’s HOD Conjecture holds, and therefore it is provable in ZFC + “There exists an extendible cardinal” that above the first extendible cardinal every singular cardinal $\lambda $ is singular in HOD and $(\lambda ^+)^{\textrm {{HOD}}}=\lambda ^+$ , there may still be no agreement at all between V and HOD about successors of regular *** Part II and Part III we analyse the relationship between the Singular Cardinal Hypothesis (SCH) with other relevant combinatorial principles at the level of successors of singular cardinals. Two of these are the Tree Property and the Reflection of Stationary sets, which are central in Infinite ***, Part II is devoted to prove the consistency of the Tree Property at both $\kap

关键词： Large Cardinals Forcing Prikry-type forcings Singular Cardinal Combinatorics

Data Mining and Bioinformatics Approaches to Elucidate Bacterial Communities in the Extreme Environment

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Data Mining and Bioinformatics Approaches to Elucidate Bacte...

International Conference on Informatics, Multimedia, Cyber and Information System (ICIMCIS)

作者： Joko Pebrianto Trinugroho Alam Ahmad Hidayat Rudi Nirwantono Faisal Asadi Bens Pardamean Bioinformatics and Data Science Research Center Bina Nusantara University Jakarta Indonesia Mathematics Department School of Computer Science Bioinformatics and Data Science Research Center Bina Nusantara University Jakarta Indonesia Biotechnology Department Faculty of Engineering Bioinformatics and Data Science Research Center Bina Nusantara University Jakarta Indonesia Computer Science Department School of Computer Science Bioinformatics and Data Science Research Center Bina Nusantara University Jakarta Indonesia Computer Science Department BINUS Graduate Program Master of Computer Science Bina Nusantara University Jakarta Indonesia

Bacteria are microscopic organisms that can be found in many environments. They are abundant and have many roles in our life. Studying bacteria is essential so that we can identify the bacteria that are needed for many industrial applications. However, the main problem is that majority of the bacteria are unculturable, hampering the exploration of bacteria from different environments. Metagenomics approach which employs Next Generation Sequencing technology could help study bacteria by utilizing 16S rRNA marker gene. This study aims to demonstrate data mining and bioinformatics approaches to analyze 16S rRNA sequencing data. The raw sequencing data of 16S rRNA was collected from biological database. Then, the data were trimmed, denoised, and clustered to generate Amplicon Sequence Variants (ASVs). Diversity (alpha and beta) and taxonomic analyses were then conducted to elucidate the bacterial diversity and taxonomic profile of ASVs. The results of this work showed that Shannon and PD indices in China's hot spring were higher than Singapore and the USA. Furthermore, a significant difference was observed in the PD index. The unweighted UniFrac distance also showed there was a significant difference of the bacterial communities between the three locations. In addition, the taxonomic investigation unveiled prevalent bacterial groups in the ecosystem, namely Proteobacteria, Chloroflexi, Cyanobacteria, and Crenarchaeota. The research outcomes have the potential to serve as a foundational resource for subsequent bacterial metagenomic research, particularly the hot spring environment.

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An Assessment of the Supremizer and Aggregation Methods of Stabilization for Reduced-Order Models

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arXiv 2023年

作者： Davie, Kayla D. Elman, Howard C. Applied Mathematics & Statistics Scientific Computation Program University of Maryland College ParkMD20742 United States Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States

MSC Codes 65N22, 65K10, 65F45We explore the features of two methods of stabilization, aggregation and supremizer methods, for reduced-order modeling of parametrized optimal control problems. In both methods, the reduced basis spaces are augmented to guarantee stability. For the aggregation method, the reduced basis approximation spaces for the state and adjoint variables are augmented in such a way that the spaces are identical. For the supremizer method, the reduced basis approximation space for the state-control product space is augmented with the solutions of a supremizer equation. We implement both of these methods for solving several parametrized control problems and assess their performance. Results indicate that the number of reduced basis vectors needed to approximate the solution space to some tolerance with the supremizer method is much larger, possibly double, that for aggregation. There are also some cases where the supremizer method fails to produce a converged solution. We present results to compare the accuracy, efficiency, and computational costs associated with both methods of stabilization which suggest that stabilization by aggregation is a superior stabilization method for control problems. © 2023, CC BY.

关键词： Stabilization

COVID-19 Infected Lung Computed Tomography Segmentation and Supervised Classification Approach

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computers, Materials & Continua 2021年第7期68卷 391-407页

作者： Aqib Ali Wali Khan Mashwani Samreen Naeem Muhammad Irfan Uddin Wiyada Kumam Poom Kumam Hussam Alrabaiah Farrukh Jamal Christophe Chesneau Department of Computer Science Concordia College BahawalpurBahawalpur63100Pakistan Department of Computer Science&IT Glim Institute of Modern StudiesBahawalpur63100Pakistan Institute of Numerical Sciences Kohat University of Science&TechnologyKohat26000Pakistan Institute of Computing Kohat University of Science and TechnologyKohat26000Pakistan Program in Applied Statistics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology ThanyaburiThanyaburi12110Thailand Departments of Mathematics Faculty of ScienceCenter of Excellence in Theoretical and Computational Science(TaCS-CoE)&KMUTT Fixed Point Research LaboratoryRoom SCL 802 Fixed Point LaboratoryScience Laboratory BuildingKing Mongkut’s University of Technology Thonburi(KMUTT)Bangkok10140Thailand Department of Medical Research China Medical University HospitalTaichung40402Taiwan College of Engineering Al Ain UniversityAl Ain64141United Arab Emirates Department of Mathematics Tafila Technical UniversityTafila66110Jordan Department of Statistics The Islamia University of BahawalpurBahawalpur63100Pakistan 11Department of MathematicsUniversitéde CaenLMNOCaen14032France

The purpose of this research is the segmentation of lungs computed tomography(CT)scan for the diagnosis of COVID-19 by using machine learning *** dataset contains data from patients who are prone to the *** contains three types of lungs CT images(Normal,Pneumonia,and COVID-19)collected from two different sources;the first one is the Radiology Department of Nishtar Hospital Multan and Civil Hospital Bahawalpur,Pakistan,and the second one is a publicly free available medical imaging database known as *** the preprocessing,a novel fuzzy c-mean automated region-growing segmentation approach is deployed to take an automated region of interest(ROIs)and acquire 52 hybrid statistical features for each ***,12 optimized statistical features are selected via the chi-square feature reduction *** the classification,five machine learning classifiers named as deep learning J4,multilayer perceptron,support vector machine,random forest,and naive Bayes are deployed to optimize the hybrid statistical features *** is observed that the deep learning J4 has promising results(sensitivity and specificity:0.987;accuracy:98.67%)among all the deployed *** a complementary study,a statistical work is devoted to the use of a new statistical model to fit the main datasets of COVID-19 collected in Pakistan.

关键词： COVID-19 machine learning fuzzy c-mean deep learning J4

OSM: Leveraging model checking for observing dynamic 1 behaviors in aspect-oriented applications

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arXiv 2024年

作者： AlSobeh, Anas Mohammad Ramadan Department of Information Systems Faculty of Information Technology and Computer Science Yarmouk University Irbid Jordan Program of Information Technology School of Computing College of Engineering Computing Technology and Mathematics Southern Illinois University CarbondaleIL United States

In the intricate domain of software systems verification, dynamically model checking multifaceted system characteristics remains paramount, yet challenging. This research proposes the advanced observe-based statistical model-checking (OSM) framework, devised to craft executable formal models directly from foundational system code. Leveraging model checking predicates, the framework melds seamlessly with aspect-oriented programming paradigms, yielding a potent method for the analytical verification of varied behavioral attributes. Exploiting the transformative capacity of OSM framework, primary system code undergoes a systematic metamorphosis into multifaceted analysis constructs. This not only simplifies the model verification process but also orchestrates feature interactions using an innovative observing join point abstraction mechanism. Within this framework, components encompassing parsing, formal verification, computational analytics, and rigorous validation are intrinsically interwoven. Marrying the principles of model checking with aspect-oriented (AO) modularization, OSM framework stands as a paragon, proficiently scrutinizing and affirming system specifications. This ensures the unyielding performance of electronic health record systems amidst shifting preconditions. OSM framework offers runtime verification of both object-oriented and AO deployments, positioning itself as an indispensable open-source resource, poised to automate the enhancement of system performance and scalability. Copyright © 2024, The Authors. All rights reserved.

关键词： Aspect oriented programming