Christen, Patrik
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Philosophy-guided mathematical formalism for complex systems modelling
We recently presented the so-called allagmatic method, which includes a system metamodel providing a framework for describing, modelling, simulating, and interpreting complex systems. Its development and programming was guided by philosophy, especially by Gilbert Simondon’s philosophy of individuation, Alfred North Whitehead’s philosophy of organism, and concepts from cybernetics. Here, a mathematical formalism is presented to better describe and define the system metamodel of the allagmatic method, thereby further generalising it and extending its reach to a more formal treatment and allowing more theoretical studies. By using the formalism, an example for such a further study is provided with mathematical definitions and proofs for model creation and equivalence of cellular automata and artificial neural networks.
I show you how I solved It! - Empowering novice university students to learn programming and mathematics through self-produced videos to potentially teach to their peers
Automated segmentation of fractured distal radii by 3D geodesic active contouring of in vivo HR-pQCT images
Radius fractures are among the most common fracture types; however, there is limited consensus on the standard of care. A better understanding of the fracture healing process could help to shape future treatment protocols and thus improve functional outcomes of patients. High-resolution peripheral quantitative computed tomography (HR-pQCT) allows monitoring and evaluation of the radius on the micro-structural level, which is crucial to our understanding of fracture healing. However, current radius fracture studies using HR-pQCT are limited by the lack of automated contouring routines, hence only including small number of patients due to the prohibitively time-consuming task of manually contouring HR-pQCT images. In the present study, a new method to automatically contour images of distal radius fractures based on 3D morphological geodesic active contours (3D-GAC) is presented. Contours of 60 HR-pQCT images of fractured and conservatively treated radii spanning the healing process up to one year post-fracture are compared to the current gold standard, hand-drawn 2D contours, to assess the accuracy of the algorithm. Furthermore, robustness was established by applying the algorithm to HR-pQCT images of intact radii of 73 patients and comparing the resulting morphometric indices to the gold standard patient evaluation including a threshold- and dilation-based contouring approach. Reproducibility was evaluated using repeat scans of intact radii of 19 patients. The new 3D-GAC approach offers contours within inter-operator variability for images of fractured distal radii (mean Dice score of 0.992 ± 0.004 versus median operator Dice score of 0.993 ± 0.006). The generated contours for images of intact radii yielded morphometric indices within the in vivo reproducibility limits compared to the current gold standard. Additionally, the 3D-GAC approach shows an improved robustness against failure (n = 4) when dealing with cortical interruptions, fracture fragments, etc. compared with the automatic, default manufacturer pipeline (n = 40). Using the 3D-GAC approach assures consistent results, while reducing the need for time-consuming hand-contouring.
Philosophy-guided modelling and implementation of adaptation and control in complex systems
Curb your self-modifying code
Self-modifying code has many intriguing applications in a broad range of fields including software security, artificial general intelligence, and open-ended evolution. Having control over self-modifying code, however, is still an open challenge since it is a balancing act between providing as much freedom as possible so as not to limit possible solutions, while at the same time imposing restriction to avoid security issues and invalid code or solutions. In the present study, I provide a prototype implementation of how one might curb self-modifying code by introducing control mechanisms for code modifications within specific regions and for specific transitions between code and data. I show that this is possible to achieve with the so-called allagmatic method - a framework to formalise, model, implement, and interpret complex systems inspired by Gilbert Simondon’s philosophy of individuation and Alfred North Whitehead’s philosophy of organism. Thereby, the allagmatic method serves as guidance for self-modification based on concepts defined in a metaphysical framework. I conclude that the allagmatic method seems to be a suitable framework for control mechanisms in self-modifying code and that there are intriguing analogies between the presented control mechanisms and gene regulation.