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Research Square 2022年

作者： Sevinç, Volkan Kırca, Meryem Merve Muğla Sıtkı Koçman University Faculty of Science Department of Statistics Turkey Muğla Sıtkı Koçman University Graduate School of Natural and Applied Sciences Statistics Program Turkey

One of the most important problems occurring in ceramic tile industry is defective product problem. Defective ceramics leads to loss of income and waste of resources in enterprises. However, it is generally unknown which factors and production stages cause what kinds of defects. On the other hand, in the literature, the existing modeling studies usually consider the defects seen on industrial ceramics. The defect types of industrial ceramics and those of ceramic tiles are different. Moreover, the classification types encountered in both kinds of ceramics also differ from each other. This article investigates the reasons behind the defect occurrences on ceramic tiles, along with a comparison between a logistic regression model and a Bayesian network model. In the study, the model validation results of the logistic regression model and the Bayesian network model show that the Bayesian network model is more successful in estimating the defect types. Thus, the constructed Bayesian network model indicates that in general, the high speeds of the production band significantly increase the probabilities of all kinds of defects except the deformation defect. Additionally, the high densities of the glaze also increase the occurrence levels of the defects, except the deformation defect. Similarly, the high levels of the engobe weight and the engobe density are also among the factors increasing the defect occurrences. © 2022, CC BY.

关键词： Bayesian networks

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Goodness-of-fit tests for multivariate skewed distributions based on the characteristic function

arXiv

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arXiv 2023年

作者： Karling, Maicon J. Genton, Marc G. Meintanis, Simos G. Statistics Program King Abdullah University of Science and Technology Thuwal Saudi Arabia Department of Economics National and Kapodistrian University of Athens Athens Greece Pure and Applied Analytics North-West University Potchefstroom South Africa

We employ a general Monte Carlo method to test composite hypotheses of goodness-of-fit for several popular multivariate models that can accommodate both asymmetry and heavy tails. Specifically, we consider weighted L2-type tests based on a discrepancy measure involving the distance between empirical characteristic functions and thus avoid the need for employing corresponding population quantities which may be unknown or complicated to work with. The only requirements of our tests are that we should be able to draw samples from the distribution under test and possess a reasonable method of estimation of the unknown distributional parameters. Monte Carlo studies are conducted to investigate the performance of the test criteria in finite samples for several families of skewed distributions. Real-data examples are also included to illustrate our *** Codes 62F03, 62H12, 62H15 © 2023, CC BY.

关键词： Monte Carlo methods

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A novel application of finite Gaussian mixture model (GMM) using real and simulated biomarkers of cardiovascular disease to distinguish adolescents with and without obesity

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Communications in statistics Case Studies Data Analysis and Applications 2023年第1期9卷 106-120页

作者： Hossain, Md Jobayer Balagopal, P. Babu Biostatistics Program Biomedical Research A. I. Dupont Hospital for Children Nemours Children’s Health System Wilmington DE United States Applied Economics and Statistics University of Delaware Newark DE United States Biomedical Research Nemours Children’s Health System Jacksonville FL United States Division of Pediatrics Mayo Clinic College of Medicine Rochester MN United States Division of Pediatrics Mayo Clinic College of Medicine Jacksonville FL United States

Obesity-induced derangements in adipose tissue and other organs lead to the development of cardiovascular disease (CVD). The loss of CV-health in children is a continuum, and the manifestation of overt CVD takes several years. Therefore, robust biomarkers are crucial for its early prediction, prevention, and management. Biomarkers of CVD are highly mutually correlated, and typical regression approaches do not precisely appraise the obesity-induced summative alterations of these overlapping variables. This study examines if the confluence of biomarkers of CVD can distinguish adolescents with obesity from their normal-weight counterparts to illustrate obesity as a strong risk factor of CVD. The biomarkers were measured in a well-controlled study in 21 adolescents. Application of the Gaussian mixture model to these biomarkers identified two distinct groups that matched with the obesity status of participants, which was further confirmed using supervised learning methods. Classification of biomarkers from a simulation study of 1,000 data points, each comprising a vector of five biomarkers and the classification identifier, resulted in two groups that matched with the classification in the simulated dataset. The precise identification of obesity by the pattern of concurring CVD biomarkers in real and simulated datasets confirms obesity as a strong risk factor of CVD. © 2023 Taylor & Francis Group, LLC.

关键词： biomarker cardiovascular disease Classification Gaussian mixture models principal component analysis

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Exploring Multiscale Quantum Media: High-Precision Efficient Numerical Solution of the Fractional Schrödinger equation, Eigenfunctions with Physical Potentials, and Fractionally-Enhanced Quantum Tunneling

arXiv

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arXiv 2024年

作者： Lewis, Joshua M. Carr, Lincoln D. 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

Fractional evolution equations lack generally accessible and well-converged codes excepting anomalous diffusion. A particular equation of strong interest to the growing intersection of applied mathematics and quantum information science and technology is the fractional Schrödinger equation, which describes sub-and super-dispersive behavior of quantum wavefunctions induced by multiscale media. We derive a computationally efficient sixth-order split-step numerical method to converge the eigenfunctions of the FSE to arbitrary numerical precision for arbitrary fractional order derivative. We demonstrate applications of this code to machine precision for classic quantum problems such as the finite well and harmonic oscillator, which take surprising twists due to the non-local nature of the fractional derivative. For example, the evanescent wave tails in the finite well take a Mittag-Leffer-like form which decay much slower than the well-known exponential from integer-order derivative wave theories, enhancing penetration into the barrier and therefore quantum tunneling rates. We call this effect fractionally enhanced quantum tunneling. This work includes an open source code for communities from quantum experimentalists to applied mathematicians to easily and efficiently explore the solutions of the fractional Schrödinger equation in a wide variety of practical potentials for potential realization in quantum tunneling enhancement and other quantum applications. © 2024, CC BY.

关键词： Eigenvalues and eigenfunctions

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Generalized Multiquadric Neural Networks in Image Reconstruction 4

Generalized Multiquadric Neural Networks in Image Reconstruc...

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4th International Conference on Machine Learning and Intelligent Systems, MLIS 2022

作者： Pongchalee, Pornthip Inthapong, Pirapong Chanthawara, Krittidej Paewpolsong, Pichapop Kaennakham, Sayan Department of Applied Mathematics and Statistics Faculty of Science and Liberal Arts Rajamangala University of Technology Isan Nakhon Ratchasima30000 Thailand School of Mathematics Institute of Science Suranaree University of Technology Nakhon Ratchasima30000 Thailand Program of Mathematics Faculty of Science Ubon Ratchathani Rajabhat University Ubon Ratchathani34000 Thailand

ISBN: (纸本)9781643683560

This work aims to numerically investigate the performance of the multiquadric (MQ) radial basis function in more general formats for image reconstruction applications. Desired features, i.e., accuracy and shape parameter sensitivity, of each form is numerically compared and explored. The famous Lena image is damaged using two levels of damage: 20% and 40%, in a Salt-and-Pepper manner. It has been discovered in this work that β=3/2 produces reasonably good accuracy and is least affected by the change in shape parameter while keeping both the CPU time and the condition number reasonably acceptable. This finding is promising and useful for further applications of MQ in more complex contexts. © 2022 The authors and IOS Press.

关键词： Image reconstruction

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Drought propagation in an Andean basin in South America: a spatio-temporal analysis approach with monitoring indices

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Arabian Journal of Geosciences 2025年第3期18卷 1-21页

作者： Ocampo-Marulanda, Camilo Mera-Franco, Julián David Lizcano, Víctor Augusto Carvajal-Escobar, Yesid Canchala, Teresita Zorrilla-Millan, Daniel Felipe Caicedo-Bravo, Eduardo Water Resources Engineering and Soil Research Group (IREHISA) School of Natural Resources and Environmental Engineering Universidad del Valle Cali Colombia Graduate Program in Biometrics and Applied Statistics Department of Statistics and Informatics Federal Rural University of Pernambuco Recife Brazil School of Exact Sciences and Engineering Universidad Sergio Arboleda Bogotá Colombia Programa de Ingeniería Ambiental Facultad de Ingeniería Universidad Mariana Pasto Colombia School of Electrical and Electronic Engineering Universidad del Valle Cali Colombia

Drought is a climatic phenomenon that has increased in severity over time. This study analyzed drought spread in the Alto Patía basin (13,047 km2) in South America, applying the Standardized Precipitation Index (SPI), Vegetation Health Index (VHI), and Streamflow Drought Index (SDI) to assess meteorological, agricultural, and hydrological drought, respectively. Synchronous and asynchronous correlations were estimated, and Wavelet analysis was conducted to verify relationships among drought types. Results show that the lag between drought types varies based on the intensity, temporal continuity, and spatial extent of meteorological drought. A lag of zero months (1–2 months) was observed between meteorological and hydrological drought when moderate (severe) meteorological drought partially (fully) covers the basin. Agricultural drought, however, does not always correspond to meteorological drought during isolated rainfall events. As the first study in Colombia to systematically connect these drought types, this research addresses a gap in understanding how drought impacts progress across systems in regions with complex rainfall patterns. These findings offer critical insights into the interdependencies among drought types, supporting enhanced drought monitoring and early warning systems in similar climatic regions. By identifying specific lags between meteorological and hydrological droughts, this study provides practical guidance for land management, water conservation, and crop planning, offering a foundation for future research on drought resilience strategies.

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Early-Stage Detection of Cognitive Impairment by Hybrid Quantum-Classical Algorithm Using Resting-State Functional MRI Time-Series

SSRN

引用

SSRN 2024年

作者： Choi, Junggu Hur, Tak Park, Daniel Kyungdeock Shin, Na-Young Lee, Seung-Koo Lee, Hakbae Han, Sanghoon Yonsei Graduate Program in Cognitive Science Yonsei University Seoul Korea Republic of Department of Statistics and Data Science Yonsei University Seoul Korea Republic of Department of Applied Statistics Yonsei University Seoul Korea Republic of Department of Radiology College of Medicine Yonsei University Seoul Korea Republic of Department of Psychology Yonsei University Seoul Korea Republic of Cleveland Clinic United States

Following recent developments in quantum machine learning techniques, several algorithms have been developed for disease detection. This study explored the application of a hybrid quantum-classical algorithm for classifying region-of-interest time-series data obtained from resting-state functional magnetic resonance imaging (FMRI) in patients with early-stage cognitive impairment. Classical one-dimensional convolutional layers were used in conjunction with quantum convolutional neural networks in our hybrid algorithm. In a classical simulation, the proposed hybrid algorithms in our study exhibited higher balanced accuracies than classical convolutional neural networks under similar training conditions. In addition, in our study, among the 116 brain regions, two brain regions (the right hippocampus and left parahippocampus) were found to be relatively effective for classification based on the model performance. The associations of the two selected regions with cognitive decline, as found in previous studies, were validated using seed-based functional connectivity analysis. Thus, we confirmed both improvement in model performance with the quantum convolutional neural network and neuroscientific validity of brain regions from our hybrid quantum-classical model. © 2024, The Authors. All rights reserved.

关键词： Convolutional neural networks

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

arXiv

引用

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

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Fractional Integrable Nonlinear Soliton Equations

引用

Physical Review Letters 2022年第18期128卷 184101-184101页

作者： Mark J. Ablowitz Joel B. Been Lincoln D. Carr Department of Applied Mathematics University of Colorado Boulder Colorado 80309 USA Department of Applied Mathematics and Statistics Colorado School of Mines Golden Colorado 80401 USA Department of Physics Colorado School of Mines Golden Colorado 80401 USA Quantum Engineering Program Colorado School of Mines Golden Colorado 80401 USA

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 superdispersive transport of nondissipative solitons in fractional media.

关键词： Solitons

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A Flow Artist for High-Dimensional Cellular Data

A Flow Artist for High-Dimensional Cellular Data

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IEEE Workshop on Machine Learning for Signal Processing

作者： Kincaid MacDonald Dhananjay Bhaskar Guy Thampakkul Nhi Nguyen Joia Zhang Michael Perlmutter Ian Adelstein Smita Krishnaswamy Department of Mathematics Yale University Department of Genetics Yale School of Medicine Department of Computer Science Yale University Department of Mathematics Pomona College Applied Mathematics Program Yale University Department of Statistics University of Washington Department of Mathematics Boise State University Computational Biology and Bioinformatics Program Yale University

We consider the problem of embedding point cloud data sampled from an underlying manifold with an associated flow or velocity. Such data arises in many contexts where static snapshots of dynamic entities are measured, including in high-throughput biology such as single-cell transcriptomics. Existing embedding techniques either do not utilize velocity information or embed the coordinates and velocities independently, i.e., they either impose velocities on top of an existing point embedding or embed points within a prescribed vector field. Here we present FlowArtist, a neural network that embeds points while jointly learning a vector field around the points. The combination allows FlowArtist to better separate and visualize velocity-informed structures. Our results, on toy datasets and single-cell RNA velocity data, illustrate the value of utilizing coordinate and velocity information in tandem for embedding and visualizing high-dimensional data.

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