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A singular perturbation analysis for the Brusselator
No full textIn this work we study the Brusselator – a prototypical model for chemical oscillations– under the assump-
tion that the bifurcation parameter is of order O(1/ϵ) for positive ϵ ≪ 1. The dynamics of this mathematical
model exhibits a time scale separation visible via fast and slow regimes along its unique attracting limit cy-
cle. This limit cycle accumulates at infinity as ϵ → 0, so that appropriate coordinates (w, z) are used to
analyse the dynamics near the line at infinity, corresponding to the set {z = 0}. This object becomes a non-
hyperbolic invariant manifold for which we use a desingularising rescaling, in order to study the closeby
dynamics. Further use of geometric singular perturbation techniques allows us to give a decomposition of
the Brusselator limit cycle in terms of four different fully quantified time scales for small ϵ
Toward Dynamic Phase-Field Fracture at Finite Strains
No full textWe investigate the evolution of dynamic phase-field fracture in the finite-strain setting, extending our previous work in the small-strain viscoelastodynamic regime. The elastodynamic equations are coupled with a dissipative damage evolution for the phase-field variable . The material response is described with a polyconvex stored energy density
, where denotes the gradient of the deformation, its cofactor, and
its determinant. This ensures compatibility with the principles of nonlinear elasticity.
A fully discrete time-staggered approximation scheme is proposed, along with associated stability of discrete solutions. We present compactness results and analyze the convergence of the discrete approximations. While convergence of the phase-field variable and the compatibility of the kinematic variables can be demonstrated, the identification of the limit stress in the momentum balance remains open. To address this, two strategies are outlined: an extension of the classical (weak) framework using generalized Young or defect measures, and an alternative formulation via energetic-variational solutions that avoids the explicit measure construction. Partial results on existence and the structure of the limit system are discussed
Physician-level classification performance across multiple imaging domains with a diagnostic medical foundation model and a large dataset of annotated medical images
No full textA diagnostic medical foundation model (MedFM) is an artificial intelligence (AI) system engineered to accurately determine diagnoses across various medical imaging modalities and specialties. To train MedFM, we created the PubMed Central Medical Images Dataset (PMCMID), the largest annotated medical image dataset to date, comprising 16,126,659 images from 3,021,780 medical publications. Using AI- and ontology-based methods, we identified 4,482,237 medical images (e.g., clinical photos, X-rays, ultrasounds) and generated comprehensive annotations. To optimize MedFM’s performance and assess biases, 13,266 images were manually annotated to establish a multimodal benchmark. MedFM achieved physician-level performance in diagnosis tasks spanning radiology, dermatology, and infectious diseases without requiring specific training. Additionally, we developed the Image2Paper app, allowing clinicians to upload medical images and retrieve relevant literature. The correct diagnoses appeared within the top ten results in 88.4% and at least one relevant differential diagnosis in 93.0%. MedFM and PMCMID were made publicly available.Funding Research reported here was partially supported by the National Cancer Institute (NCI) (R01 CA260271), the Saudi Company for Artificial Intelligence (SCAI) Authority, and the German Federal Ministry for Economic Affairs and Climate Action (BMWK) under the project DAKI-FWS (01MK21009E). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.Competing Interest StatementThe authors have declared no competing interest.Funding StatementResearch reported here was partially supported by the National Cancer Institute (NCI) (R01 CA260271), the Saudi Company for Artificial Intelligence (SCAI) Authority, and the German Federal Ministry for Economic Affairs and Climate Action (BMWK) under the project DAKI-FWS (01MK21009E). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.Author DeclarationsI confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained.YesThe details of the IRB/oversight body that provided approval or exemption for the research described are given below:Open Access PublicationsI confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals.YesI understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).YesI have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable.YesAll data produced in the present study are available upon reasonable request to the authors
Integrating Agent-Based and Compartmental Models for Infectious Disease Modeling: A Novel Hybrid Approach
No full textThis study investigates the spatial integration of agent-based models (ABMs) and compartmental models for infectious disease modeling, presenting a novel hybrid approach and examining its implications. ABMs offer detailed insights by simulating interactions and decisions among individuals but are computationally expensive for large populations. Compartmental models capture population-level dynamics more efficiently but lack granular detail. We developed a hybrid model that aims to balance the granularity of ABMs with the computational efficiency of compartmental models, offering a more nuanced understanding of disease spread in diverse scenarios, including large populations. This model spatially couples discrete and continuous populations by integrating an ordinary differential equation model with a spatially explicit ABM. Our key objectives were to systematically assess the consistency of disease dynamics and the computational efficiency across various configurations. For this, we evaluated two experimental scenarios and varied the influence of each sub-model via spatial distribution. In the first, the ABM component modeled a homogeneous population; in the second, it simulated a heterogeneous population with landscape-driven movement. Results show that the hybrid model can significantly reduce computational costs but is sensitive to between-model differences, highlighting the importance of model equivalence in hybrid approaches. The code is available at: git.zib.de/ibostanc/hybrid_abm_ode
A general thermodynamical model for finitely-strained continuum with inelasticity and diffusion, its GENERIC derivation in Eulerian formulation, and some application
No full textA thermodynamically consistent visco-elastodynamical model at finite strains is derived that also allows for inelasticity (like plasticity or creep), thermal coupling, and poroelasticity with diffusion. The theory is developed in the Eulerian framework and is shown to be consistent with the thermodynamic framework given by General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC). For the latter we use that the transport terms are given in terms of Lie derivatives. Application is illustrated by two examples, namely volumetric phase transitions with dehydration in rocks and martensitic phase transitions in shape-memory alloys. A strategy toward a rigorous mathematical analysis is only very briefly outlined
Self-supervised pre-training with joint-embedding predictive architecture boosts ECG classification performance
No full textAccurate diagnosis of heart arrhythmias requires the interpretation of electrocardiograms (ECG), which capture the electrical activity of the heart. Automating this process through machine learning is challenging due to the need for large annotated datasets, which are difficult and costly to collect. To address this issue, transfer learning is often employed, where models are pre-trained on large datasets and fine-tuned for specific ECG classification tasks with limited labeled data. Self-supervised learning has become a widely adopted pre-training method, enabling models to learn meaningful representations from unlabeled datasets. In this work, we explore the joint-embedding predictive architecture (JEPA) for self-supervised learning from ECG data. Unlike invariance-based methods, JEPA does not rely on hand-crafted data augmentations, and unlike generative methods, it predicts latent features rather than reconstructing input data. We create a large unsupervised pre-training dataset by combining ten public ECG databases, amounting to over one million records. We pre-train Vision Transformers using JEPA on this dataset and fine-tune them on various PTB-XL benchmarks. Our results show that JEPA outperforms existing invariance-based and generative approaches, achieving an AUC of 0.945 on the PTB-XL all statements task. JEPA consistently learns the highest quality representations, as demonstrated in linear evaluations, and proves advantageous for pre-training even in the absence of additional data
Explicit solutions of Genz test integrals
No full textAbstract
A collection of test integrals introduced by Genz (1984) has remained popular to this day for assessing the robustness of high-dimensional numerical integration algorithms. However, the explicit solutions to these integrals do not appear to be readily available in the existing literature: typically the true values of the test integrals are simply approximated using “overkill” numerical solutions. In this paper, analytic solutions are presented for the Genz test integral
Rough homogenization for Langevin dynamics on fluctuating Helfrich surfaces
No full textIn this article, we study different scaling rough path limit regimes in space and time for the Langevin dynamics on a quasi-planar fluctuating Helfrich surface. The convergence results of the processes were already proven in [Citation1]. We extend this work by proving the convergence of the Itô and Stratonovich rough path lift. For the rough path limit, there appears, typically, an area correction term to the Itô iterated integrals and, in certain regimes, to the Stratonovich iterated integrals. This yields additional information on the homogenization limit and enables us to conclude on homogenization results for diffusions driven by the Brownian motion on the membrane using the continuity of the Itô-Lyons map in rough paths topology
Environments and lifting mechanisms of cold-frontal convective cells during the warm season in Germany
No full textConvection often initiates in proximity to cold fronts during the warm season, but how various processes favour convective initiation at different regions relative to the front is still not well-understood. By combining automatic front detection methods and a convective-cell tracking and detection dataset, the environments and availability of different lifting mechanisms are analysed. Our results indicate that pre-surface-frontal cells form in the environments with the highest surface dew points and convective available potential energy (CAPE). Behind the surface front, cells form in environments with lower CAPE and surface dew points, though they are still significantly higher than regions without cells. Mid-level relative humidity discriminates particularly well between post-frontal cell locations and regions without cells. Pre-surface-frontal cells form in environments with the strongest synoptic-scale lifting at 700 hPa and also with the strongest convective inhibition. We also observe the importance of post-frontal synoptic-scale lifting, particularly at 500 hPa. Observational sunshine duration data indicate less sunshine before cell initiation compared to regions without cells in most front-relative regions, which highlights that solar heating may not be responsible for the majority of cold-frontal cell initiation. The results in this study are an important step towards a deeper understanding of the drivers of cold-frontal convection at different regions relative to the front
