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arXiv 2021年

作者： Ametova, Evelina Burca, Genoveva Chilingaryan, Suren Fardell, Gemma Jørgensen, Jakob S. Papoutsellis, Evangelos Pasca, Edoardo Warr, Ryan Turner, Martin Lionheart, William R.B. Withers, Philip J. Henry Royce Institute Department of Materials The University of Manchester M13 9PL United Kingdom Laboratory for Application of Synchrotron Radiation Karlsruhe Institute of Technology Germany ISIS Pulsed Neutron and Muon Source STFC UKRI Rutherford Appleton Laboratory United Kingdom Department of Mathematics The University of Manchester M13 9PL United Kingdom Institute for Data Processing and Electronics Karlsruhe Institute of Technology Germany Scientific Computing Department STFC UKRI Rutherford Appleton Laboratory United Kingdom Department of Applied Mathematics and Computer Science Technical University of Denmark Denmark Research IT Services The University of Manchester M13 9PL United Kingdom

Time-of-flight neutron imaging offers complementary attenuation contrast to X-ray computed tomography (CT), coupled with the ability to extract additional information from the variation in attenuation as a function of neutron energy (time of flight) at every point (voxel) in the image. In particular Bragg edge positions provide crystallographic information and therefore enable the identification of crystalline phases directly. Here we demonstrate Bragg edge tomography with high spatial and spectral resolution. We propose a new iterative tomographic reconstruction method with a tailored regularisation term to achieve high quality reconstruction from low-count data, where conventional filtered back-projection (FBP) fails. The regularisation acts in a separated mode for spatial and spectral dimensions and favours characteristic piece-wise constant and piecewise smooth behaviour in the respective dimensions. The proposed method is compared against FBP and a state-of-the-art regulariser for multi-channel tomography on a multi-material phantom. The proposed new regulariser which accommodates specific image properties outperforms both conventional and state-of-the-art methods and therefore facilitates Bragg edge fitting at the voxel level. The proposed method requires significantly shorter exposure to retrieve features of interest. This in turn facilitates more efficient usage of expensive neutron beamline time and enables the full utilisation of state-of-the-art high resolution detectors. © 2021, CC BY.

关键词： Iterative methods

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Dynamics of the competition between two languages

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SeMA Journal 2020年第4期77卷 351-373页

作者： Tchendjeu, A. E. Tchahou Bowong, S. Tchitnga, R. Fotsin, H.B. Department of Computer Engineering National Higher Polytechnic Institute University of Bamenda PO Box 39 Bambili Cameroon Laboratory of Condensed Matters Electronics and Signal Processing (LAMACETS) Department of Physics Faculty of Science University of Dschang PO Box 63 Dschang Cameroon Research Group on Experimental and Applied Physics for Sustainable Development (EAPhySuD) Department of Physics Faculty of Science University of Dschang PO Box 63 Dschang Cameroon Laboratory of Applied Mathematics Department of Mathematics and Computer Science Faculty of Science University of Douala PO Box 24157 Douala Cameroon UMI 209 IRD/UPMC UMMISCO Bondy France LIRIMA Project Team GRIMCAPE Yaounde Cameroon The African Center of Excellence in Information and Communication Technologies (CETIC) University of Yaounde 1 Yaounde Cameroon Institute of Surface Chemistry and Catalysis University of Ulm Albert-Einstein-Allee 47 Ulm 89081 Germany

This paper reports a new kind of mathematical model for language competition dynamics using compartmental epidemiological modeling approach. The model describes the competition between two languages, say the predominant one called language 1, and the less spoken language 2, both in the same community. We distinguish three groups of population building the concerned community: one majority speaking language 1, one minority speaking language 2 and a last minority speaking neither language 1 nor language 2. The study of the proposed model includes an analysis of the evolution of the number of speakers over time. This model predicts that language 2 can inevitably disappear if the threshold parameter R is less than one. We show that our model is well-posed mathematically and linguistically. We also show that the model has basically two linguistic equilibrium points. A monolingual equilibrium point that corresponds to the case where only one language is spoken: some individuals speak only the language 1 and some others do speak neither language 1, nor language 2. A bilingual equilibrium point which corresponds to the case where all the languages are spoken: some individuals speak both languages 1 and 2, some others speak only language 1, while a third group does speak only language 2, and the last group speaks none of the two languages. In this bilingual equilibrium point, both languages coexist. Depending on the threshold parameter, we demonstrate the stability of these equilibria. The model presents on one hand, a direct bifurcation phenomenon, in which we have a stable equilibrium point without bilingual speakers when the associated basic reproduction number is less than one. On the other hand, it presents a stable bilingual equilibrium point when the number of associated basic reproductions is greater than one. The analysis of the overall sensitivity of the model is performed and the impact of the system parameters on the basic reproduction number was performed using

关键词： Bilingualism Compartmental modeling Dynamical system Language competition Stability

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Converting Neural Networks to Rule Foam

Converting Neural Networks to Rule Foam

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International Conference on Computational Science and Computational Intelligence (CSCI)

作者： Akash Kumar Panda Bart Kosko Department of Electrical and Computer Engineering Signal and Image Processing Institute University of Southern California Los Angeles California

ISBN: (数字)9781728155845

ISBN: (纸本)9781728155852

A system of rules can approximate a trained neural classifier after sampling from that classifier. The rules define a generalized probability mixture that then describes the classifier. The size or granularity of the rule if-parts defines a foam-like structure with a few large rule if-part set bubbles in patternclass centers and many smaller if-part sets near class borders. The rule foam's mixture gives a Bayesian posterior over the rules. The posterior describes the relative importance of each rule for each observed input and output. The foam's mixture also gives the conditional variance that measures the uncertainty in its output. So the rule base is statistically interpretable as well as modular and adaptive. A rule foam with 1000 Gaussian rules approximated a 96.85% accurate MNIST neural classifier and had itself 95.66% classification accuracy. Foams can also approximate other foams. Some approximator foams out-performed the target foam that generated their training data. The rule foam's granularity mitigates the rule explosion inherent in the rule-based approximator's graph-covering structure.

关键词： Additives Neural networks Bayes methods Dispersion Uncertainty Fuzzy systems Vector quantization

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Noise can speed Markov chain Monte Carlo estimation and quantum annealing

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Physical Review E 2019年第5期100卷 053309-053309页

作者： Brandon Franzke Bart Kosko Center for Quantum Information Science and Technology Signal and Image Processing Institute Department of Electrical and Computer Engineering University of Southern California Los Angeles California 90089 USA

Carefully injected noise can speed the average convergence of Markov chain Monte Carlo (MCMC) estimates and simulated annealing optimization. This includes quantum annealing and the MCMC special case of the Metropolis-Hastings algorithm. MCMC seeks the solution to a computational problem as the equilibrium probability density of a reversible Markov chain. The algorithm must cycle through a long burn-in phase until it reaches equilibrium because the Markov samples are statistically correlated. The special injected noise reduces this burn-in period in MCMC. A related theorem shows that it reduces the cooling time in simulated annealing. Simulations showed that optimal noise gave a 76% speed-up in finding the global minimum in the Schwefel optimization benchmark. The noise-boosted simulations found the global minimum in 99.8% of trials compared with only 95.4% of trials in noiseless simulated annealing. Simulations also showed that the noise boost is robust to accelerated cooling schedules and that noise decreased convergence times by more than 32% under aggressive geometric cooling. Molecular dynamics simulations showed that optimal noise gave a 42% speed-up in finding the minimum potential energy configuration of an eight-argon-atom gas system with a Lennard-Jones 12-6 potential. The annealing speed-up also extends to quantum Monte Carlo implementations of quantum annealing. Noise improved ground-state energy estimates in a 1024-spin simulated quantum annealing simulation by 25.6%. The quantum noise flips spins along a Trotter ring. The noisy MCMC algorithm brings each Markov step closer on average to equilibrium if an inequality holds between two expectations. Gaussian or Cauchy jump probabilities reduce the noise-benefit inequality to a simple quadratic inequality. Simulations show that noise-boosted simulated annealing is more likely than noiseless annealing to sample high probability regions of the search space and to accept solutions that increase the search bre

关键词： Fluctuations & noise Noise

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Tigc-Net: Transformer-Improved Graph Convolution Network for Spatio-Temporal Prediction

SSRN

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SSRN 2022年

作者： Chen, Kai Yang, Chunfeng Zhou, Zhengyuan Liu, Yao Ji, Tianjiao Sun, Weiya Chen, Yang School of Cyber Science and Engineering Southeast University Nanjing210096 China Key Laboratory of Computer Network and Information Integration Southeast University Ministry of Education Nanjing210096 China The College of Software Engineering Southeast University Nanjing210096 China Laboratory of Image Science and Technology The School of Computer Science and Engineering Southeast University Nanjing210096 China Jiangsu Key Laboratory of Molecular and Functional Imaging Department of Radiology Zhongda Hospital Southeast University Nanjing210009 China Jiangsu Provincial Joint International Research Laboratory of Medical Information Processing School of Computer Science and Engineering Southeast University Nanjing210096 China NHC Key Laboratory of Medical Virology and Viral Diseases National Institute for Viral Disease Control and Prevention Chinese Center for Disease Control and Prevention Beijing China Beijing Institute of Tracking and Communication Technology Beijing100094 China

Modeling spatio-temporal sequences is an important topic yet challenging for existing neural networks. Most of the current spatio-temporal sequence prediction methods usually capture features separately in temporal and spatial dimensions or employ multiple mutually independent local spatio-temporal graphs to represent a spatio-temporal sequence. The first kind of method mentioned above is difficult to mine the complex spatio-temporal correlations, while the other is limited for the accuracy of long-term predictions. To handle these issues, this paper proposes a Transformer-Improved Graph Convolution Network for spatio-temporal prediction. Specifically, the temporal location encoding method is exploited to derive the spatio-temporal characteristics of the sequence utilizing a spatio-temporal feature fusion network. In addition, a spatio-temporal attention network is developed to enhance the spatio-temporal correlation of the sequence, and the dynamic spatial features of sequence are further extracted through the adaptive graph convolution network. A private dataset and a public dataset are employed to demonstrate the performance of the proposed TIGC-Net. The qualitative and quantitative results show that the proposed TIGC-Net can extract dynamic spatiotemporal properties more effectively, enhance the spatio-temporal correlation of sequences and improve the prediction accuracy compared with four stateof-the-art. © 2022, The Authors. All rights reserved.

关键词： Convolution

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Bayes Theorem Extends to Overlapping Hypotheses

Bayes Theorem Extends to Overlapping Hypotheses

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International Conference on Computational Science and Computational Intelligence (CSCI)

作者： Bart Kosko Department of Electrical and Computer Engineering Signal and Image Processing Institute University of Southern California Los Angeles California

ISBN: (数字)9781728155845

ISBN: (纸本)9781728155852

Bayes theorem extends to arbitrary overlapping hypotheses if a local probability describes the inherent uncertainty of each element in the overlap. This local probability avoids over-counting the overlap regions. It arises by normalizing the indicator function of each set hypothesis in the partition by the sum or integral of all the partition indicator functions. The default probability is that an element belongs equally likely to each overlapping hypothesis that contains it. This reduces to a trivial binary distribution in the extreme case of an exact partition with no overlap. The resulting fuzzy or uncertainty-weighted set events give a generalized theorem on total probability. This result gives in turn a Bayes theorem for any partition or collection of overlapping hypotheses. Applications include the overlapping pattern data that trains deep classification networks.

关键词： Uncertainty Fuzzy sets Weight measurement Machine learning Probability distribution Measurement uncertainty Scientific computing

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Low-rank reduced biquaternion tensor ring decomposition and tensor completion

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Applied mathematics and Computation 2025年 504卷

作者： Luo, Hui Liu, Xin Liu, Wei Zhang, Yang School of Computer Science and Engineering Faculty of Innovation Engineering Macau University of Science and Technology China Macau Institute of Systems Engineering Faculty of Innovation Engineering Macau University of Science and Technology China School of Artificial Intelligence at Sun Yat-sen University the Guangdong Key Laboratory of Big Data Analysis and Processing Guangzhou China Department of Mathematics University of Manitoba MB Canada

We define the reduced biquaternion tensor ring (RBTR) decomposition and provide a detailed exposition of the corresponding algorithm RBTR-SVD. Leveraging RBTR decomposition, we propose a novel low-rank tensor completion algorithm RBTR-TV integrating RBTR ranks with total variation (TV) regularization to optimize the process. Numerical experiments on color image and video completion tasks indicate the advantages of our method. © 2025 Elsevier Inc.

关键词： Numerical methods

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Navigating the challenges in creating complex data systems: a development philosophy

arXiv

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arXiv 2022年

作者： Dittmer, Sören Roberts, Michael Gilbey, Julian Biguri, Ander Preller, Jacobus Rudd, James H.F. Aston, John A.D. Schönlieb, Carola-Bibiane Selby, Ian Breger, Anna Thorpe, Matthew Weir-McCall, Jonathan R. Gkrania-Klotsas, Effrossyni Korhonen, Anna Jefferson, Emily Langs, Georg Yang, Guang Prosch, Helmut Stanczuk, Jan Tang, Jing Babar, Judith Sánchez, Lorena Escudero Teare, Philip Patel, Mishal Wassin, Marcel Holzer, Markus Walton, Nicholas Lió, Pietro Shadbahr, Tolou Sala, Evis Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge United Kingdom Addenbrooke’s Hospital Cambridge University Hospitals NHS Trust Cambridge United Kingdom Department of Medicine University of Cambridge Cambridge United Kingdom Department of Pure Mathematics and Mathematical Statistics University of Cambridge Cambridge United Kingdom ZeTeM University of Bremen Bremen Germany Department of Radiology University of Cambridge Cambridge United Kingdom Faculty of Mathematics University of Vienna Austria Department of Mathematics University of Manchester Manchester United Kingdom Royal Papworth Hospital Cambridge Royal Papworth Hospital NHS Foundation Trust Cambridge United Kingdom Language Technology Laboratory University of Cambridge Cambridge United Kingdom Population Health and Genomics School of Medicine University of Dundee Dundee United Kingdom Department of Biomedical Imaging and Image-guided Therapy Computational Imaging Research Lab Medical University of Vienna Vienna Austria National Heart and Lung Institute Imperial College London London United Kingdom Research Program in Systems Oncology Faculty of Medicine University of Helsinki Helsinki Finland Data Science & Artificial Intelligence AstraZeneca Cambridge United Kingdom Clinical Pharmacology & Safety Sciences AstraZeneca Cambridge United Kingdom Contextflow GmbH Vienna Austria Institute of Astronomy University of Cambridge Cambridge United Kingdom Department of Computer Science and Technology University of Cambridge Cambridge United Kingdom

In this perspective, we argue that despite the democratization of powerful tools for data science and machine learning over the last decade, developing the code for a trustworthy and effective data science system (DSS) is getting harder. Perverse incentives and a lack of widespread software engineering (SE) skills are among many root causes we identify that naturally give rise to the current systemic crisis in reproducibility of DSSs. We analyze why SE and building large complex systems is, in general, hard. Based on these insights, we identify how SE addresses those difficulties and how we can apply and generalize SE methods to construct DSSs that are fit for purpose. We advocate two key development philosophies, namely that one should incrementally grow – not biphasically plan and build – DSSs, and one should always employ two types of feedback loops during development: one which tests the code’s correctness and another that evaluates the code’s efficacy. Copyright © 2022, The Authors. All rights reserved.

关键词： Software engineering

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A Functional Equation Stemming from a Characterization of Power-based Implications

A Functional Equation Stemming from a Characterization of Po...

引用

IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

作者： Michał Baczyński Włodzimierz Fechner Sebastia Massanet Institute of Mathematics University of Silesia in Katowice Katowice Poland Institute of Mathematics Łódź University of Technology Łódź Poland Soft Computing Image Processing and Aggregation (SCOPIA) research group Department of Mathematics and Computer Science University of the Balearic Islands Palma Spain

The so-called family of T-power based implications has been introduced recently by using Zadeh's quantifiers modelled by powers of t-norms in its definition. Most of these operators satisfy the invariance with respect to powers of a continuous t-norm, an important property in approximate reasoning. When this family of fuzzy implication functions was characterized, the property I(x, y) · I(y, z) = I(x, z) in a concrete sub-domain played a key role. This property, which ensures that T-power based implications are unidimensional T'-preorders with T' the product t-norm, seems to be related to the invariance property. Therefore, the natural question of characterizing some classes of fuzzy implications with this property arises naturally. We provide such a characterization in a fairly general setting, generalizing earlier known results.

关键词： Generators mathematics Cognition Additives image processing computer science Indexes

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The effect of data augmentation on classification of atrial fibrillation in short single-lead ecg signals using deep neural networks

arXiv

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arXiv 2020年

作者： Hatamian, Faezeh Nejati Ravikumar, Nishant Vesal, Sulaiman Kemeth, Felix P. Struck, Matthias Maier, Andreas Department of Image Processing and Medical Technology Fraunhofer Institute for Integrated Circuits IIS Erlangen Germany Pattern Recognition Lab Department of Computer Science Friedrich-Alexander University Erlangen-Nrnberg Erlangen Germany School of Computing LICAMM Leeds Institute of Cardiovascular and Metabolic Medicine School of Medicine University of Leeds United Kingdom

Cardiovascular diseases are the most common cause of mortality worldwide. Detection of atrial fibrillation (AF) in the asymptomatic stage can help prevent strokes. It also improves clinical decision making through the delivery of suitable treatment such as, anticoagulant therapy, in a timely manner. The clinical significance of such early detection of AF in electrocardiogram (ECG) signals has inspired numerous studies in recent years, of which many aim to solve this task by leveraging machine learning algorithms. ECG datasets containing AF samples, however, usually suffer from severe class imbalance, which if unaccounted for, affects the performance of classification algorithms. Data augmentation is a popular solution to tackle this problem. In this study, we investigate the impact of various data augmentation algorithms, e.g., oversampling, Gaussian Mixture Models (GMMs) and Generative Adversarial Networks (GANs), on solving the class imbalance problem. These algorithms are quantitatively and qualitatively evaluated, compared and discussed in detail. The results show that deep learning-based AF signal classification methods benefit more from data augmentation using GANs and GMMs, than oversampling. Furthermore, the GAN results in circa 3% better AF classification accuracy in average while performing comparably to the GMM in terms of f1-score. Copyright © 2020, The Authors. All rights reserved.

关键词： Diseases

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