• A Study and Comparison of First and Second Order Cellular Automata with Examples 

      Thaulow, Lauritz Vesteraas (Master thesis, 2010)
      This thesis will give an introduction to the concepts of cellular automata and higher order cellular automata, and go through several examples of both. Cellular automata are discrete systems of cells in an n-dimensional ...
    • A Study of higher order Cellular Automata with Examples 

      Barker, Daniel Martin Lewis (Master thesis, 2008)
      Cellular automata are discrete dynamical systems which are practical to use for simulations. Higher order cellular automata are a natural extension of cellular automata, and are expected to be a useful way of improving ...
    • Aspects of first and second order cellular automata 

      Davik, Pål (Master thesis, 2010)
      An introduction to the field of Higher-Order Cellular Automata (HOCA) is provided. Key concepts are defined and illustrated using examples. Some of the possibilities offered by this framework are explored, and used to take ...
    • Decoding of neural data using cohomological feature extraction 

      Rybakken, Erik; Baas, Nils A.; Dunn, Benjamin Adric (Journal article; Peer reviewed, 2019)
      We introduce a novel data-driven approach to discover and decode features in the neural code coming from large population neural recordings with minimal assumptions, using cohomological feature extraction. We apply our ...
    • Kobordismer, Høyere Kategorier og Topologiske Kvantefeltteorier 

      Rybakken, Erik (Master thesis, 2015)
      Først vil en her studere kobordismeteori, for så å se på topologiske kvantefeltteorier. Deretter vil en se på høyere kategorier, drøfte forskjellige definisjoner, og bruke disse til å definere utvidede kvantefeltteorier.
    • On Strict Higher Categories and their Application to Cobordism Theory 

      Nielsen, Espen Auseth (Master thesis, 2015)
      The main goal of the present thesis is an exposition of the Bökstedt-Madsen theorem ([1]), which relates the classifying space of the embedded cobordism category to certain iterated loop spaces of the Thom space of universal ...
    • On the Mapper Algorithm: A study of a new topological method for data analysis 

      Stovner, Roar Bakken (Master thesis, 2012)
      Mapper is an algorithm for describing high-dimensional datasets in terms of simple geometric objects. We give a new definition of Mapper, with which we are able to prove that Mapper is a functor and that Mapper is a homotopy ...
    • On the mathematics of higher structures 

      Baas, Nils A. (Journal article; Peer reviewed, 2019)
      In a series of papers, we have discussed higher structures in science in general, and developed a framework called hyperstructures for describing and working with higher structures. We discussed the philosophy behind higher ...
    • On the philosophy of higher structures 

      Baas, Nils A. (Journal article; Peer reviewed, 2019)
      Higher structures occur and play an important role in all sciences and their applications. In a series of papers, we have developed a framework called Hyperstructures for describing and working with higher structures. The ...
    • Pursuing a Polynomial Invariant of 2-knots 

      Hagland, Therese Mardal (Master thesis, 2014)
      We construct an invariant of 2-knots akin to the Jones polynomial of a knot. To achieve this, we adopt a new point of view on the foundations of diagrammatic 2-knot theory, and introduce a series of ideas to address questions ...
    • Stability of Persistence Modules 

      Bjerkevik, Håvard Bakke (Master thesis, 2016)
      We present a new proof of the algebraic stability theorem, perhaps the main theorem in the theory of stability of persistent homology. We also give an example showing that an analogous result does not hold for a certain ...
    • Topological Data Analysis with Applications to Neuroscience 

      Rybakken, Erik (Doctoral theses at NTNU;2020:20, Doctoral thesis, 2020)
    • Topological Detection in Spatially and Directionally Tuned Neural Network Activity 

      Hermansen, Erik (Master thesis, 2017)
      Persistent homology has become the main tool in topological data analysis, using methods from algebraic topology to describe the underlying space of data sets. In this thesis, persistent homology is used to detect topological ...
    • Topology and Data 

      Brekke, Birger (Master thesis, 2010)
      In the last years, there has been done research in using topology as a new tool for studying data sets, typically high dimensional data. These studies have brought new methods for qualitative analysis, simplification, and ...
    • Topology and Data 

      Brekke, Øyvind (Master thesis, 2010)
      Today there is an immense production of data, and the need for better methods to analyze data is ever increasing. Topology has many features and good ideas which seem favourable in analyzing certain datasets where statistics ...
    • Topology and Data 

      Hatlem, Hans Olav (Master thesis, 2015)
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    • Using persistent homology to reveal hidden covariates in systems governed by the kinetic Ising model 

      Spreemann, Gard; Dunn, Benjamin Adric; Botnan, Magnus; Baas, Nils A. (Journal article; Peer reviewed, 2018)
      We propose a method, based on persistent homology, to uncover topological properties of a priori unknown covariates in a system governed by the kinetic Ising model with time-varying external fields. As its starting point ...