Field theoretic formulation and empirical tracking of spatial processes

Spatial processes are attacked on two fronts. On the one hand, tools from theoretical and statistical physics can be used to understand behaviour in complex, spatially-extended multi-body systems. On the other hand, computer vision and statistical analysis can be used to study 4D microscopy data to observe and understand real spatial processes in vivo. On the rst of these fronts, analytical models are developed for abstract processes, which can be simulated on graphs and lattices before considering real-world applications in elds such as biology, epidemiology or ecology. In the eld theoretic formulation of spatial processes, techniques originating in quantum eld theory such as canonical quantisation and the renormalization group are applied to reaction-di usion processes by analogy. These techniques are combined in the study of critical phenomena or critical dynamics. At this level, one is often interested in the scaling behaviour; how the correlation functions scale for di erent dimensions in geometric space. This can lead to a better understanding of how macroscopic patterns relate to microscopic interactions. In this vein, the trace of a branching random walk on various graphs is studied. In the thesis, a distinctly abstract approach is emphasised in order to support an algorithmic approach to parts of the formalism. A model of self-organised criticality, the Abelian sandpile model, is also considered. By exploiting a bijection between recurrent con gurations and spanning trees, an e cient Monte Carlo algorithm is developed to simulate sandpile processes on large lattices. On the second front, two case studies are considered; migratory patterns of leukaemia cells and mitotic events in Arabidopsis roots. In the rst case, tools from statistical physics are used to study the spatial dynamics of di erent leukaemia cell lineages before and after a treatment. One key result is that we can discriminate between migratory patterns in response to treatment, classifying cell motility in terms of sup/super/di usive regimes. For the second case study, a novel algorithm is developed to processes a 4D light-sheet microscopy dataset. The combination of transient uorescent markers and a poorly localised specimen in the eld of view leads to a challenging tracking problem. A fuzzy registration-tracking algorithm is developed to track mitotic events so as to understand their spatiotemporal dynamics under normal conditions and after tissue damage.Open Acces

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Dipterocarps protected by Jering local wisdom in Jering Menduyung Nature Recreational Park, Bangka Island, Indonesia

Apart of the oil palm plantation expansion, the Jering Menduyung Nature Recreational Park has relatively diverse plants. The 3,538 ha park is located at the north west of Bangka Island, Indonesia. The minimum species-area curve was 0.82 ha which is just below Dalil conservation forest that is 1.2 ha, but it is much higher than measurements of several secondary forests in the Island that are 0.2 ha. The plot is inhabited by more than 50 plant species. Of 22 tree species, there are 40 individual poles with the average diameter of 15.3 cm, and 64 individual trees with the average diameter of 48.9 cm. The density of Dipterocarpus grandiflorus (Blanco) Blanco or kruing, is 20.7 individual/ha with the diameter ranges of 12.1 – 212.7 cm or with the average diameter of 69.0 cm. The relatively intact park is supported by the local wisdom of Jering tribe, one of indigenous tribes in the island. People has regulated in cutting trees especially in the cape. The conservation agency designates the park as one of the kruing propagules sources in the province. The growing oil palm plantation and the less adoption of local wisdom among the youth is a challenge to forest conservation in the province where tin mining activities have been the economic driver for decades. More socialization from the conservation agency and the involvement of university students in raising environmental awareness is important to be done