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An ensemble technique of SmoteENN and random forest for classification of the cardiotocography data

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An ensemble technique of SmoteENN and random forest for clas...

International Conference on Computer Vision and Internet of Things 2023 (ICCVIoT'23)

作者： R. Hephzibah A. H. Christinal R. Jayanthi D. A. Chandy C. Bajaj Department of Mathematics Karunya University Coimbatore India Department of Electronics and Communication Engineering Karunya University Coimbatore India Computational applied Mathematics chair in visualization Institute for Computational Engineering and Sciences University of Texas Austin India

Fetal heart rate monitoring is very important to check the status of the fetal heart during pregnancy. Cardiotocography is the most extensively used technique for the surveillance of the fetal heart rate signal and uterine activity of the mother. It helps in monitoring the health of the fetus in pregnant women at high risk. The various Machine Learning classifiers play a vital role in the classification of the CTG data. The CTG data is the publicly available data with 2126 instances and 21 features which consists of 8 continuous and 13 discrete values. It consists of 1655 normal, 295 suspect, and 176 pathology classes which represents a clear imbalance in the dataset. In this paper, we proposed a novel ensemble method of sampling technique combined with a Random Forest classifier for the classification of the CTG data. There are two sampling techniques such as the oversampling technique to increase the samples in the minority class and the undersampling technique to decrease the samples in the majority class. Here we combined both the techniques such as the SMOTE (Synthetic Minority Oversampling Technique) from the oversampling technique and ENN (Edited Nearest Neighbor) from the undersampling technique and implemented it in the Random Forest classifier for classification. As there is an imbalance in the data, the sampling techniques help to balance the data. This proposed technique achieves the best accuracy of 93% in the classification of the normal, suspect, and pathology data. It also provides better results in terms of other metrics such as sensitivity and specificity. This method is also compared with other competent classifiers and is found to be an effective method for the classification of the CTG data.

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Statistical mechanics and pressure of composite multimoded weakly nonlinear optical systems

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arXiv 2024年

作者： Efremidis, Nikolaos K. Christodoulides, Demetrios N. Department of Applied Mathematics University of Crete Heraklion71409 Greece Institute of Applied and Computational Mathematics FORTH Crete Heraklion70013 Greece Ming Hsieh Department of Electrical and Computer Engineering University of Southern California Los AngelesCA90089 United States

Statistical mechanics can provide a versatile theoretical framework for investigating the collective dynamics of weakly nonlinear waves-settings that can be utterly complex to describe otherwise. In optics, composite systems arise due to interactions between different frequencies and/or polarizations. The purpose of this work is to develop a thermodynamic theory that takes into account the synergistic action of multiple components. We find that the type of the nonlinearity involved can have important implications in the thermalization process and, hence, can lead to different thermal equilibrium conditions. Importantly, we derive closed-form expressions for the actual optomechanical pressure that is exerted on the system. In particular, the total optomechanical pressure is the sum of the partial pressures due to each component. Our results can be applied to a variety of weakly nonlinear optical settings such as multimode fibers, bulk waveguides, photonic lattices, and coupled microresonators. We present two specific examples, where two colors interact in a waveguide array with either a cubic or quadratic nonlinearity. Copyright © 2024, The Authors. All rights reserved.

关键词： Statistical mechanics

Quasi-Lindblad pseudomode theory for open quantum systems

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Physical Review B 2024年第19期110卷 195148-195148页

作者： Gunhee Park (박건희) Zhen Huang Yuanran Zhu Chao Yang Garnet Kin-Lic Chan Lin Lin Division of Engineering and Applied Science California Institute of Technology Pasadena California 91125 USA Department of Mathematics University of California Berkeley California 94720 USA Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA Division of Chemistry and Chemical Engineering California Institute of Technology Pasadena California 91125 USA

We introduce a new framework to study the dynamics of open quantum systems with linearly coupled Gaussian baths. Our approach replaces the continuous bath with an auxiliary discrete set of pseudomodes with dissipative dynamics, but we further relax the complete positivity requirement in the Lindblad master equation and formulate a quasi-Lindblad pseudomode theory. We show that this quasi-Lindblad pseudomode formulation directly leads to a representation of the bath correlation function in terms of a complex weighted sum of complex exponentials, an expansion that is known to be rapidly convergent in practice and thus leads to a compact set of pseudomodes. The pseudomode representation is not unique and can differ by a gauge choice. When the global dynamics can be simulated exactly, the system dynamics is unique and independent of the specific pseudomode representation. However, the gauge choice may affect the stability of the global dynamics, and we provide an analysis of why and when the global dynamics can retain stability despite losing positivity. We showcase the performance of this formulation across various spectral densities in both bosonic and fermionic problems, finding significant improvements over conventional pseudomode formulations.

关键词： Open quantum systems Open quantum systems & decoherence Strongly correlated systems Anderson impurity model Lindblad equation Non-Markovian processes Nonperturbative methods Spin-boson model

GLOBAL WELL-POSEDNESS OF THE ENERGY-CRITICAL COMPLEX GINZBURG-LANDAU EQUATION IN EXTERIOR DOMAINS

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arXiv 2024年

作者： Cheng, Xing Guo, Chang-Yu Zheng, Jiqiang Zheng, Yunrui School of mathematics Hohai University Jiangsu Nanjing210098 China Research Center for Mathematics and Interdisciplinary Sciences Shandong University Qingdao266237 China Department of Physics and Mathematics University of Eastern Finland Joensuu80101 Finland Institute of Applied Physics and Computational Mathematics Beijing100088 China National Key Laboratory of Computational Physics Beijing100088 China School of Mathematics Shandong University Jinan Shandong250100 China

In this article, we consider an energy-critical complex Ginzburg-Landau equation in the exterior of a smooth compact strictly convex obstacle. We prove the global well-posedness of energy-critical complex Ginzburg-Landau equation in an exterior domain by the concentration-compactness/rigidity theorem method. As corollaries of our main result, we establish both the existence of global weak solutions to energy-critical defocusing nonlinear Schrödinger equations and the global well-posedness theory for energy-critical semi-linear heat equation in exterior domains. © 2024, CC BY-NC-SA.

关键词： Schrodinger equation

DEGREE OF THE GRASSMANNIAN AS AN AFFINE VARIETY

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arXiv 2024年

作者： Lim, Lek-Heng Ye, Ke Computational and Applied Mathematics Initiative Department of Statistics University of Chicago ChicagoIL60637-1514 United States KLMM Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

The degree of the Grassmannian with respect to the Plücker embedding is well-known. However, the Plücker embedding, while ubiquitous in pure mathematics, is almost never used in applied mathematics. In applied mathematics, the Grassmannian is usually embedded as projection matrices Gr(k, Rn) ∼= {P ∈ Rn×n : P T = P = P 2, tr(P) = k} or as involution matrices Gr(k, Rn) ∼= {X ∈ Rn×n : XT = X, X2 = I, tr(X) = 2k − n}. We will determine an explicit expression for the degree of the Grassmannian with respect to these embeddings. In so doing, we resolved a conjecture of Devriendt–Friedman–Sturmfels about the degree of Gr(2, Rn) and in fact generalized it to Gr(k, Rn). We also proved a set theoretic variant of another conjecture of Devriendt–Friedman–Sturmfels about the limit of Gr(k, Rn) in the sense of Gröbner *** Codes 14E25, 14F45 © 2024, CC BY.

关键词： Embeddings

Local Sequential MCMC for Data Assimilation with Applications in Geoscience

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arXiv 2024年

作者： Ruzayqat, Hamza Knio, Omar Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

This paper presents a new data assimilation (DA) scheme based on a sequential Markov Chain Monte Carlo (SMCMC) DA technique [36] which is provably convergent and has been recently used for filtering, particularly for high-dimensional non-linear, and potentially, non-Gaussian state-space models. Unlike particle filters, which can be considered exact methods and can be used for filtering non-linear, non-Gaussian models, SMCMC does not assign weights to the samples/particles, and therefore, the method does not suffer from the issue of weight-degeneracy when a relatively small number of samples is used. We design a localization approach within the SMCMC framework that focuses on regions where observations are located and restricts the transition densities included in the filtering distribution of the state to these regions. This results in immensely reducing the effective degrees of freedom and thus improving the efficiency. We test the new technique on high-dimensional (d ∼ 104 − 105) linear Gaussian model and non-linear shallow water models with Gaussian noise with real and synthetic observations. For two of the numerical examples, the observations mimic the data generated by the Surface Water and Ocean Topography (SWOT) mission led by NASA, which is a swath of ocean height observations that changes location at every assimilation time step. We also use a set of ocean drifters' real observations in which the drifters are moving according the ocean kinematics and assumed to have uncertain locations at the time of assimilation. We show that when higher accuracy is required, the proposed algorithm is superior in terms of efficiency and accuracy over competing ensemble methods and the original SMCMC *** Codes 62M20, 60G35, 60J20, 94A12, 93E11, 65C40 © 2024, CC BY.

关键词： Markov chains

FEDERATED LEARNING on RIEMANNIAN MANIFOLDS

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Applied Set-Valued Analysis and Optimization

applied Set-Valued Analysis and Optimization 2023年第2期5卷 213-232页

作者： Li, Jiaxiang Ma, Shiqian Department of Mathematic University of California Davis United States Computational Applied Mathematics and Operations Research Rice University Houston United States

Federated learning (FL) has found many important applications in smart-phone-APP based machine learning applications. Although many algorithms have been studied for FL, to the best of our knowledge, algorithms for FL with nonconvex constraints have not been studied. This paper studies FL over Riemannian manifolds, which finds important applications such as federated PCA and federated kPCA. We propose a Riemannian federated SVRG (RFedSVRG) method to solve federated optimization over Riemannian manifolds. We analyze its convergence rate under different scenarios. Numerical experiments are conducted to compare RFedSVRG with the Riemannian counterparts of FedAvg and FedProx. We observed from the numerical experiments that the advantages of RFedSVRG are significant. © 2023 applied Set-Valued Analysis and Optimization.

关键词： Machine learning

Inferring the Parameters of Ultrafast Lasers from Images with Surface Patterns 13

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Inferring the Parameters of Ultrafast Lasers from Images wit...

13th International Symposium on Image and Signal Processing and Analysis, ISPA 2023

作者： Litsas, Anastasis Fraggelakis, Fotis Tsibidis, George D. Stratakis, Emmanuel Pantazis, Yannis University of Crete Computer Science Department Heraklion Crete Greece Institute of Electronic Structure and Laser Foundation for Research and Technology - Hellas Heraklion Crete Greece Institute of Applied and Computational Mathematics Foundation for Research and Technology - Hellas Heraklion Crete Greece

ISBN: (纸本)9798350315363

In this paper, we explore the potential of deep learning techniques in the field of ultra-fast laser processing. More specifically, we trained convolutional neural networks on an in-house dataset with the aim of predicting the laser parameters from images which capture the morphological characteristics of the material surface after being laser fabricated. There are several challenges related with the collected dataset stemming from stochastic variations of the material and the laser, the sampling scheme and the overall low sample size. Therefore, to further test our models we additionally construct a synthetic dataset. The results on the synthetic dataset are almost perfect showing that the proposed predictive models have the capacity to learn the assigned tasks. As expected, the predictive performance decreases when the real dataset is utilized. Nevertheless, we show that both the accuracy in the classification task and the mean square error in the majority of the regression tasks are satisfactory (e.g., classification accuracy drops from 99.9% to 94.8%). © 2023 IEEE.

关键词： Convolutional neural networks

Cryptography: Recent research trends of encrypting mathematics

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Materials Today: Proceedings 2022年 56卷 3247-3253页

作者： Kikani, Ria Jatin Verma, Kirti Navalakhe, Rachna Shrivastava, Gourav Shrivastava, Vineeta Department of Information Technology Silver Oak College of Engineering and Technology GTU Gujarat India Department of Engineering Mathematics Lakshmi Narain College of Technology MP Bhopal India Department of Applied Mathematics and Computational Science Shri G.S. Institute of Technology and Science MP Indore India Department of Computer Science and Engineering SAGE University MP Bhopal India Department of Computer Science and Engineering Lakshmi Narain College of Technology MP Bhopal India

In today's world where technology and mathematics are progressing hand in hand there are so many things to be considered and thought of when it comes to network security. Cryptography plays a prominent and an important role when it comes to securing the system from unwanted hazardous attacks. As the Internet has made great strides in different domains it has impacted the human life in several ways and hence data security has become the question of the hour. In such a scenario cryptography plays a big role as it ensures that the data transmitted is received as it is without any alteration or modification. However, we have discussed the algorithms and various methods required in order to maintain the security. In the subsequent sections we shall be discussing about theoretical computer science, cryptography attacks, algorithms and its application in everyday life. © 2021

关键词： Cryptography