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  1. Article: Besondere Herausforderungen bei Sucheinsatz in „Üble Schlucht“

    Burger, Martin

    Flugmedizin · Tropenmedizin · Reisemedizin - FTR

    2023  Volume 30, Issue 02, Page(s) 48–51

    Language German
    Publishing date 2023-04-01
    Publisher Georg Thieme Verlag KG
    Publishing place Stuttgart ; New York
    Document type Article
    ZDB-ID 2277004-5
    ISSN 1864-175X ; 1864-4538
    ISSN (online) 1864-175X
    ISSN 1864-4538
    DOI 10.1055/a-2041-9466
    Database Thieme publisher's database

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  2. Article ; Online: Network Structured Kinetic Models of Social Interactions.

    Burger, Martin

    Vietnam journal of mathematics

    2021  Volume 49, Issue 3, Page(s) 937–956

    Abstract: The aim of this paper is to study the derivation of appropriate meso- and macroscopic models for interactions as appearing in social processes. There are two main characteristics the models take into account, namely a network structure of interactions, ... ...

    Abstract The aim of this paper is to study the derivation of appropriate meso- and macroscopic models for interactions as appearing in social processes. There are two main characteristics the models take into account, namely a network structure of interactions, which we treat by an appropriate mesoscopic description, and a different role of interacting agents. The latter differs from interactions treated in classical statistical mechanics in the sense that the agents do not have symmetric roles, but there is rather an active and a passive agent. We will demonstrate how a certain form of kinetic equations can be obtained to describe such interactions at a mesoscopic level and moreover obtain macroscopic models from monokinetics solutions of those. The derivation naturally leads to systems of nonlocal reaction-diffusion equations (or in a suitable limit local versions thereof), which can explain spatial phase separation phenomena found to emerge from the microscopic interactions. We will highlight the approach in three examples, namely the evolution and coarsening of dialects in human language, the construction of social norms, and the spread of an epidemic.
    Language English
    Publishing date 2021-05-18
    Publishing country Singapore
    Document type Journal Article
    ZDB-ID 1481450-X
    ISSN 2305-2228 ; 2305-221X
    ISSN (online) 2305-2228
    ISSN 2305-221X
    DOI 10.1007/s10013-021-00505-8
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  3. Article: Network structured kinetic models of social interactions

    Burger, Martin

    Abstract: The aim of this paper is to study the derivation of appropriate meso- and macroscopic models for interactions as appearing in social processes. There are two main characteristics the models take into account, namely a network structure of interactions, ... ...

    Abstract The aim of this paper is to study the derivation of appropriate meso- and macroscopic models for interactions as appearing in social processes. There are two main characteristics the models take into account, namely a network structure of interactions, which we treat by an appropriate mesoscopic description, and a different role of interacting agents. The latter differs from interactions treated in classical statistical mechanics in the sense that the agents do not have symmetric roles, but there is rather an active and a passive agent. We will demonstrate how a certain form of kinetic equations can be obtained to describe such interactions at a mesoscopic level and moreover obtain macroscopic models from monokinetics solutions of those. The derivation naturally leads to systems of nonlocal reaction-diffusion equations (or in a suitable limit local versions thereof), which can explain spatial phase separation phenomena found to emerge from the microscopic interactions. We will highlight the approach in three examples, namely the evolution and coarsening of dialects in human language, the construction of social norms, and the spread of an epidemic.
    Keywords covid19
    Publisher ArXiv
    Document type Article
    Database COVID19

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  4. Book ; Online: Learned Regularization for Inverse Problems

    Burger, Martin / Kabri, Samira

    Insights from a Spectral Model

    2023  

    Abstract: The aim of this paper is to provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems. We give an extended definition of regularization methods and their convergence in terms of the underlying data ... ...

    Abstract The aim of this paper is to provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems. We give an extended definition of regularization methods and their convergence in terms of the underlying data distributions, which paves the way for future theoretical studies. Based on a simple spectral learning model previously introduced for supervised learning, we investigate some key properties of different learning paradigms for inverse problems, which can be formulated independently of specific architectures. In particular we investigate the regularization properties, bias, and critical dependence on training data distributions. Moreover, our framework allows to highlight and compare the specific behavior of the different paradigms in the infinite-dimensional limit.
    Keywords Mathematics - Numerical Analysis ; Computer Science - Machine Learning
    Publishing date 2023-12-15
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  5. Book ; Online: Lane formation and aggregation spots in a model of ants

    Bruna, Maria / Burger, Martin / de Wit, Oscar

    2024  

    Abstract: We investigate an interacting particle model to simulate a foraging colony of ants, where each ant is represented as an active Brownian particle. The interactions among ants are mediated through chemotaxis, aligning their orientations with the upward ... ...

    Abstract We investigate an interacting particle model to simulate a foraging colony of ants, where each ant is represented as an active Brownian particle. The interactions among ants are mediated through chemotaxis, aligning their orientations with the upward gradient of the pheromone field. Unlike conventional models, our study introduces a parameter that enables the reproduction of two distinctive behaviors: the well-known Keller--Segel collapse and the formation of traveling clusters, without relying on external constraints such as food sources or nests. We consider the associated mean-field limit partial differential equation (PDE) of this system and establish the analytical and numerical foundations for understanding these particle behaviors. Remarkably, the mean-field PDE not only supports Keller--Segel collapse and lane formation but also unveils a bistable region where these two behaviors compete. The patterns associated with these phenomena are elucidated by the shape of the growing eigenfunctions derived from linear stability analysis. This study not only contributes to our understanding of complex ant colony dynamics but also introduces a novel parameter-dependent perspective on pattern formation in collective systems.
    Keywords Mathematics - Analysis of PDEs ; Mathematics - Dynamical Systems ; Quantitative Biology - Populations and Evolution
    Publishing date 2024-01-26
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  6. Book ; Online ; Thesis: Bewertung der adäquaten und inadäquaten Inanspruchnahme des Rettungsdienstes im Rahmen der pädiatrischen Notfallversorgung am Universitätsklinikum des Saarlandes

    Burger, Martin [Verfasser]

    The Pediatric Emergency and Ambulance Critical Evaluation Study (PEACE-Study)

    2020  

    Author's details Martin Burger
    Keywords Medizin, Gesundheit ; Medicine, Health
    Subject code sg610
    Language German
    Publisher Saarländische Universitäts- und Landesbibliothek
    Publishing place Saarbrücken
    Document type Book ; Online ; Thesis
    Database Digital theses on the web

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  7. Book ; Online: Analysis of Kinetic Models for Label Switching and Stochastic Gradient Descent

    Burger, Martin / Rossi, Alex

    2022  

    Abstract: In this paper we provide a novel approach to the analysis of kinetic models for label switching, which are used for particle systems that can randomly switch between gradient flows in different energy landscapes. Besides problems in biology and physics, ... ...

    Abstract In this paper we provide a novel approach to the analysis of kinetic models for label switching, which are used for particle systems that can randomly switch between gradient flows in different energy landscapes. Besides problems in biology and physics, we also demonstrate that stochastic gradient descent, the most popular technique in machine learning, can be understood in this setting, when considering a time-continuous variant. Our analysis is focusing on the case of evolution in a collection of external potentials, for which we provide analytical and numerical results about the evolution as well as the stationary problem.
    Keywords Mathematics - Analysis of PDEs ; Computer Science - Machine Learning ; Mathematical Physics ; Mathematics - Optimization and Control
    Publishing date 2022-07-01
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  8. Book ; Online: Sharp interface analysis of a diffuse interface model for cell blebbing with linker dynamics

    Nöldner, Philipp / Burger, Martin / Garcke, Harald

    2023  

    Abstract: We investigate the convergence of solutions of a recently proposed diffuse interface/phase field model for cell blebbing by means of matched asymptotic expansions. It is a biological phenomenon that increasingly attracts attention by both experimental ... ...

    Abstract We investigate the convergence of solutions of a recently proposed diffuse interface/phase field model for cell blebbing by means of matched asymptotic expansions. It is a biological phenomenon that increasingly attracts attention by both experimental and theoretical communities. Key to understanding the process of cell blebbing mechanically are proteins that link the cell cortex and the cell membrane. Another important model component is the bending energy of the cell membrane and cell cortex which accounts for differential equations up to sixth order. Both aspects pose interesting mathematical challenges that will be addressed in this work like showing non-singularity formation for the pressure at boundary layers, deriving equations for asymptotic series coefficients of uncommonly high order, and dealing with a highly coupled system of equations.

    Comment: 32 pages, 1 figure
    Keywords Mathematics - Analysis of PDEs ; 34E05 ; 35K60 ; 92C37
    Subject code 612
    Publishing date 2023-02-09
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  9. Book ; Online: Resolution-Invariant Image Classification based on Fourier Neural Operators

    Kabri, Samira / Roith, Tim / Tenbrinck, Daniel / Burger, Martin

    2023  

    Abstract: In this paper we investigate the use of Fourier Neural Operators (FNOs) for image classification in comparison to standard Convolutional Neural Networks (CNNs). Neural operators are a discretization-invariant generalization of neural networks to ... ...

    Abstract In this paper we investigate the use of Fourier Neural Operators (FNOs) for image classification in comparison to standard Convolutional Neural Networks (CNNs). Neural operators are a discretization-invariant generalization of neural networks to approximate operators between infinite dimensional function spaces. FNOs - which are neural operators with a specific parametrization - have been applied successfully in the context of parametric PDEs. We derive the FNO architecture as an example for continuous and Fr\'echet-differentiable neural operators on Lebesgue spaces. We further show how CNNs can be converted into FNOs and vice versa and propose an interpolation-equivariant adaptation of the architecture.
    Keywords Computer Science - Computer Vision and Pattern Recognition ; Computer Science - Machine Learning ; Mathematics - Numerical Analysis ; 68T45 ; 65T40
    Publishing date 2023-04-02
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  10. Article ; Online: Beauveria bassiana zur Regulierung von Waldmaikäfer-Engerlingen auf Forstkulturen in der Oberrheinebene

    Burger, Martin / Höland, Johannes / Delb, Horst

    2023  

    Keywords Text ; abstract_or_summary ; ddc:630
    Language German
    Publisher Julius Kühn-Institut
    Publishing country de
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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