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Isaac Newton Institute for Mathematical Sciences (INI)

The aim of this summer school is to foster the development of a community of quantitative scientists who, while working on different application areas, share their knowledge and help address fundamental questions in the mathematics of movement. The goal is to identify common challenges and cross-fertilise concepts and techniques for modelling and analysing movement data in animal ecology and cell biology. With basic, as well as advanced, topics on the mathematics of movement the summer school welcomes early career researchers who that are new novice to the area but also those who that are already familiar with it. The first three days will be dedicated, respectively, to (i) Data Acquisition and Technology, (ii) Data Analysis, and (iii) Modelling, while the 4th and 5th days will be spent working in separate groups on specific dataset and modelling challenges. There will be sessions for early career presentations and poster sessions, as well as opportunities to hear about successful interdisciplinary collaborations and various activities to enable networking with the programme organisers and the many academic participants of the programme. There will also be a competition for the best poster.

Simulation,    Kurse und Veranstaltungen für Studenten der Mathematik

Isaac Newton Institute for Mathematical Sciences (INI)

Modelling collective group movement in animal ecology and cell biology has, over the years, followed two relatively parallel modelling paths. Most prevalent for the former are what one might define as discrete level models, whereby computational constructs are used to keep track of the spatio-temporal dynamics of each individual in a group. Problems in the latter, cell biology, have been tackled mostly by continuous models whereby the details of the individuals are neglected, in favour of a description of the entire population through, e.g. a density function. However, more recently hybrid agent-based/population models have gained increasing usage.

As the overall aim of the workshop is to create an overarching modelling framework with which to interpret common empirical features, the exchange of ideas and techniques from the different communities is an invaluable opportunity to move forward and at the same to delineate the boundaries of applicability of the different approaches in collective movement research.

Simulation,    Angewandte Mathematik (allgem.)

Isaac Newton Institute for Mathematical Sciences (INI)

The study of interactions among living entities covers broad scientific domains, ranging from molecules and cells through individual organisms and groups to species, populations and communities. Common to all domains is the need to quantify the presumed interactions at the relevant spatial and temporal scales. While no formal theory exists in the literature, there exist different approaches that aim to construct a mechanistic representation of how individuals interact with each other as well as how to measure such interactions, but in most cases such approaches are specific to the problem at hand. The common factor among the existing approaches is their intention to represent the sequential nature of how organisms interact, first acquiring information from their surroundings, then processing that information and subsequently selecting a movement response.

By cross-fertilising different ideas and techniques in animal ecology and cell biology we aim to gain a more realistic perspective on measurement and representation of organism interactions, revisiting existing concepts, and permitting new discoveries and insights.

Simulation,    Angewandte Mathematik (allgem.)

Isaac Newton Institute for Mathematical Sciences (INI)

Simulation,    Angewandte Mathematik (allgem.)

Isaac Newton Institute for Mathematical Sciences (INI)

The purpose of this workshop is to bring together scientists interested in different areas of complex movement in a biological context, from field research, to data analysis, to theoretical modelling. In particular, the focus will be on complex movement beyond the Markov property, such as memory-dependent animal foraging processes, spatial avoidance due to past deposition of animal scent or resource depletion, and directed motion in neutrophils. Despite its ubiquity, the mathematical difficulty in dealing with history dependence has hampered the study of non-Markov movement processes. Past empirical limitations are also responsible for the lack of a general theory to describe history dependent movement processes, as detection of features that would distinguish between Markov and non-Markov model predictions were not attainable. Currently, movement data may reach unprecedented resolution, and there is a renewed interest in developing non-Markov movement models, exemplified by recent theoretical studies to devise general prescriptions to simulate non-Markov stochastic processes.

Simulation,    Angewandte Mathematik (allgem.)