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THE MODELLING ERROR IN MULTI-DIMENSIONAL TIME-DEPENDENT SOLUTE TRANSPORT MODELS

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arXiv 2023年

作者： Masri, Rami Zeinhofer, Marius Kuchta, Miroslav Rognes, Marie E. Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Norway

Starting from full-dimensional models of solute transport, we derive and analyze multi-dimensional models of time-dependent convection, diffusion, and exchange in and around pulsating vascular and perivascular networks. These models are widely applicable for modelling transport in vascularized tissue, brain perivascular spaces, vascular plants and similar environments. We show the existence and uniqueness of solutions to both the full- and the multi-dimensional equations under suitable assumptions on the domain velocity. Moreover, we quantify the associated modelling errors by establishing a-priori estimates in evolving Bochner spaces. In particular, we show that the modelling error decreases with the characteristic vessel diameter and thus vanishes for infinitely slender vessels. numerical tests in idealized geometries corroborate and extend upon our theoretical *** Codes 35K45, 65G99, 65J08, 65M15, 92-10 © 2023, CC BY-NC-SA.

关键词： Solute transport

Cross-Modality Gait Recognition: Bridging LiDAR and Camera Modalities for Human Identification 18

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Cross-Modality Gait Recognition: Bridging LiDAR and Camera M...

18th IEEE International Joint Conference on Biometrics, IJCB 2024

作者： Wang, Rui Shen, Chuanfu Marin-Jimenez, Manuel J. Huang, George Q. Yu, Shiqi Southern University of Science and Technology Department of Computer Science and Engineering China The University of Hong Kong Department of Industrial and Manufacturing Systems Engineering Hong Kong University of Cordoba Department of Computing and Numerical Analysis Spain The Hong Kong Polytechnic University Department of Industrial and Systems Engineering Hong Kong

ISBN: (纸本)9798350364132

Current gait recognition research mainly focuses on identifying pedestrians captured by the same type of sensor, neglecting the fact that individuals may be captured by different sensors in order to adapt to various environments. A more practical approach should involve cross-modality matching across different sensors. Hence, this paper focuses on investigating the problem of cross-modality gait recognition, with the objective of accurately identifying pedestrians across diverse vision sensors. We present CrossGait inspired by the feature alignment strategy, capable of cross retrieving diverse data modalities. Specifically, we investigate the cross-modality recognition task by initially extracting features within each modality and subsequently aligning these features across modalities. To further enhance the cross-modality performance, we propose a Prototypical Modality-shared Attention Module that learns modality-shared features from two modality-specific features. Additionally, we design a Cross-modality Feature Adapter that transforms the learned modality-specific features into a unified feature space. Extensive experiments conducted on the SUSTech1K dataset demonstrate the effectiveness of CrossGait: (1) it exhibits promising cross-modality ability in retrieving pedestrians across various modalities from different sensors in diverse scenes, and (2) CrossGait not only learns modality-shared features for cross-modality gait recognition but also maintains modality-specific features for single-modality recognition. © 2024 IEEE.

关键词： Unattended sensors

Use of recommendation models to provide support to dyslexic students

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arXiv 2024年

作者： Morciano, Gianluca Llergo, José Manuel Alcalde Zingoni, Andrea Bolívar, Enrique Yeguas Taborri, Juri Calabrò, Giuseppe University of Tuscia Viterbo01100 Italy Department of Computing and Numerical Analysis Córdoba University Córdoba14071 Spain

Dyslexia is the most widespread specific learning disorder and significantly impair different cognitive domains. This, in turn, negatively affects dyslexic students during their learning path. Therefore, specific support must be given to these students. In addition, such a support must be highly personalized, since the problems generated by the disorder can be very different from one to another. In this work, we explored the possibility of using AI to suggest the most suitable supporting tools for dyslexic students, so as to provide a targeted help that can be of real utility. To do this, we relied on recommendation algorithms, which are a branch of machine learning, that aim to detect personal preferences and provide the most suitable suggestions. We hence implemented and trained three collaborative-filtering recommendation models, namely an item-based, a user-based and a weighted-hybrid model, and studied their performance on a large database of 1237 students’ information, collected with a self-evaluating questionnaire regarding all the most used supporting strategies and digital tools. Each recommendation model was tested with three different similarity metrics, namely Pearson correlation, Euclidean distance and Cosine similarity. The obtained results showed that a recommendation system is highly effective in suggesting the optimal help tools/strategies for everyone, with an error less then 12%. As a further evidence of the effectiveness of the implemented system, its precision was 0.85 and its recall was 0.83. The best performing filter was the hybrid one, when Pearson’s correlation is used to measure the distance among users and/or items. In addition, in a final testing performed on 50 students, dyslexic students who used the recommendation algorithm increased their academic scores of almost 1 point in a 1 to 10 scale, showing higher learning performance compared to students who did not use it. This demonstrates that the proposed approach is successful and can

关键词： Students

Regularity for Diffusion Equations with Non-smooth Data

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Results in Mathematics 2023年第4期78卷 1-22页

作者： Dondl, Patrick Zeinhofer, Marius Department of Applied Mathematics University of Freiburg Freiburg im Breisgau Germany Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Oslo Norway

We prove an $$L^p(I,C^\alpha (\Omega ))$$ regularity result for a diffusion equation with mixed boundary conditions, $$L^\infty $$ coefficients and an $$L^{ q }$$ initial condition. We provide explicit control of the $$L^p(I,C^\alpha (\Omega ))$$ norm with respect to the data. To prove our result, we first establish $$C^\alpha (\Omega )$$ control of the stationary equation, extending a result by Haller-Dintelmann et al. (Appl Math Optim 60(3):397–428, 2009).

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Barycentre Averaging for the Move-Split-Merge Time Series Distance Measure 15

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Barycentre Averaging for the Move-Split-Merge Time Series Di...

15th International Conference on Knowledge Discovery and Information Retrieval, KDIR 2023 as part of the 15th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management, IC3K 2023

作者： Holder, Christopher Guijo-Rubio, David Bagnall, Anthony School of Computing Sciences University of East Anglia Norwich United Kingdom Department of Computer Science and Numerical Analysis University of Córdoba Córdoba Spain School of Electronics and Computer Science University of Southampton Southampton United Kingdom

ISBN: (纸本)9789897586712

Distance functions play a core role in many time series machine learning algorithms for tasks such as clustering, classification and regression. Time series often require bespoke distance functions because small offsets in time can lead to large distances between series that are conceptually similar. Elastic distances compensate for misalignment by creating a path through a cost matrix by warping and/or editing time series. Time series are most commonly clustered with partitional algorithms such as k-means and k-medoids using elastic distance measures such as Dynamic Time Warping (DTW). The distance is used to assign cases to the closest cluster representative. k-means requires the averaging of time series to find these representative centroids. If DTW is used to assign membership, but the arithmetic mean is used to find centroids, k-means performance degrades significantly. An averaging technique specific to DTW, called DTW Barycentre Averaging (DBA), overcomes the averaging problem however, can only be used with DTW. As such alternative distance functions such as Move-Split-Merge (MSM) are forced to use the arithmetic mean to compute new centroids and suffer similar degraded performance as k-means-DTW without DBA. To address this we propose a averaging method for MSM distance, MSM Barycentre Averaging (MBA) and show that when used to find centroids it significantly improves MSM based k-means and is better than commonly used alternatives. Copyright © 2023 by SCITEPRESS - Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

关键词： Time series

Subgroup Discovery in MOOCs: A Big Data Application for Describing Different Types of Learners

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arXiv 2024年

作者： Luna, J.M. Fardoun, H.M. Padillo, F. Romero, C. Ventura, S. Department of Computer Science and Numerical Analysis University of Cordoba Cordoba Spain Faculty of Computing and Information Technology King Abdulaziz University Saudi Arabia

The aim of this paper is to categorize and describe different types of learners in massive open online courses (MOOCs) by means of a subgroup discovery approach based on MapReduce. The final objective is to discover IF-THEN rules that appear in different MOOCs. The proposed subgroup discovery approach, which is an extension of the well-known FP-Growth algorithm, considers emerging parallel methodologies like MapReduce to be able to cope with extremely large datasets. As an additional feature, the proposal includes a threshold value to denote the number of courses that each discovered rule should satisfy. A post-processing step is also included so redundant subgroups can be removed. The experimental stage is carried out by considering de-identified data from the first year of 16 MITx and HarvardX courses on the edX platform. Experimental results demonstrate that the proposed MapReduce approach outperforms traditional sequential subgroup discovery approaches, achieving a runtime that is almost constant for different courses. Additionally, thanks to the final post-processing step, only interesting and not-redundant rules are discovered, hence reducing the number of subgroups in one or two orders of magnitude. Finally, the discovered subgroups are easily used by courses’ instructors not only for descriptive purposes but also for additional tasks such as recommendation or personalization. Copyright © 2024, The Authors. All rights reserved.

关键词： MapReduce

A UNIFIED FRAMEWORK FOR THE ERROR analysis OF PHYSICS-INFORMED NEURAL NETWORKS

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arXiv 2023年

作者： Zeinhofer, Marius Masri, Rami Mardal, Kent-André Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Oslo0164 Norway Department of Mathematics University of Oslo Norway

We prove a priori and a posteriori error estimates for physics-informed neural networks (PINNs) for linear PDEs. We analyze elliptic equations in primal and mixed form, elasticity, parabolic, hyperbolic and Stokes equations;and a PDE constrained optimization problem. For the analysis, we propose an abstract framework in the common language of bilinear forms, and we show that coercivity and continuity lead to error estimates. The obtained estimates are sharp and reveal that the L2 penalty approach for initial and boundary conditions in the PINN formulation weakens the norm of the error decay. Finally, utilizing recent advances in PINN optimization, we present numerical examples that illustrate the ability of the method to achieve accurate *** Codes 65M12, 65M15 Copyright © 2023, The Authors. All rights reserved.

关键词： Error analysis

An energy stable and conservative multiplicative dynamical low-rank discretization for the Su-Olson problem

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arXiv 2025年

作者： Baumann, Lena Einkemmer, Lukas Klingenberg, Christian Kusch, Jonas University of Wuerzburg Department of Mathematics Wuerzburg Germany University of Innsbruck Numerical Analysis and Scientific Computing Innsbruck Austria Norwegian University of Life Sciences Department of Data Science Ås Norway

computing numerical solutions of the thermal radiative transfer equations on a finely resolved grid can be costly due to high computational and memory requirements. A numerical reduced order method that has recently been applied to a wide variety of kinetic partial differential equations is the concept of dynamical low-rank approximation (DLRA). In this paper, we consider the thermal radiative transfer equations with Su-Olson closure, leading to a linearized kinetic model. For the conducted theoretical and practical considerations we use a multiplicative splitting of the distribution function that poses additional challenges in finding an energy stable discretization and deriving a hyperbolic Courant-Friedrichs-Lewy (CFL) condition. We propose such an energy stable DLRA scheme that makes use of the augmented basis update & Galerkin integrator. This integrator allows for additional basis augmentations, enabling us to give a mathematically rigorous proof of energy stability and local mass conservation. numerical examples confirm the derived properties and show the computational advantages of the DLRA scheme compared to a numerical solution of the full system of *** Codes 35L65, 35Q49, 65M12, 65M22 © 2025, CC BY-NC-ND.

关键词： Radiative transfer

Hexagons all the way down: grid cells as a conformal isometric map of space

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PLoS Computational Biology 2025年第2期21卷 e1012804页

作者： Schøyen, Vemund Sigmundson Beshkov, Kosio Pettersen, Markus Borud Hermansen, Erik Holzhausen, Konstantin Malthe-Sørenssen, Anders Fyhn, Marianne Lepperød, Mikkel Elle Department of Biosciences University of Oslo Oslo Norway Department of Physics University of Oslo Oslo Norway Department of Mathematical Sciences Norwegian University of Science and Technology Trondheim Norway Department of Numerical Analysis and Scientific Computing Simula Research Laboratory AS Oslo Norway

Grid cells in the entorhinal cortex are known for their hexagonal spatial activity patterns and are thought to provide a neural metric for space, and support path integration. In this study, we further investigate grid cells as a metric of space by optimising them for a conformal isometric (CI) map of space using a model based on a superposition of plane waves. By optimising the phases within a single grid cell module, we find that the module can form a CI of two-dimensional flat space with phases arranging into a regular hexagonal pattern, supporting an accurate spatial metric. Additionally, we find that experimentally recorded grid cells exhibit CI properties, with one example module showing a phase arrangement similar to the hexagonal pattern observed in our model. These findings provide computational and preliminary experimental support for grid cells as a CI-based spatial representation. We also examine other properties that emerge in CI-optimised modules, including consistent energy expenditure across space and the minimal cell count required to support unique representation of space and maximally topologically persistent toroidal population activity. Altogether, our results suggest that grid cells are well-suited to form a CI map, with several beneficial properties arising from this organisation. © 2025 Schøyen et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

关键词： Cytology