arXiv subjects

Joshua A. Bull

Publications and source records attributed to Joshua A. Bull.

4 recordsLinked to original sources

arXiv2026

Topology of Multi-species Localization

Spatial relationships in multi-species data can indicate and affect system outcomes and behaviors, ranging from disease progression in cancer to coral reef resilience in ecology; therefore, quantifying these relationships is an important problem across scientific disciplines. Persistent homology (PH), a key mathematical and computational tool in topological data analysis (TDA), provides a multiscale description of the shape of data. While it effectively describes spatial organization of species, such as cellular patterns in pathology, it cannot detect the shape relations between different types of species. Traditionally, PH analyzes single-species data, which limits the spatial analysis of interactions between different species. Leveraging recent developments in TDA and computational geometry, we introduce a scalable approach to quantify higher-order interactions in multi-species data. The framework can distinguish the presence of shape features or patterns in the data that are (i) common to multiple species of points, (ii) present in some species but disappear in the presence of other species, (iii) only visible when multiple species are considered together, and (iv) formed by some species and remain visible in the presence of others. We demonstrate our approach on two example applications. We identify (1) different behavioral regimes in a synthetic tumor micro-environment model, and (2) interspecies spatial interactions that are most significantly altered in colorectal cancer tissue samples during disease progression.

math.AT↗

arXiv2023

Relational persistent homology for multispecies data with application to the tumor microenvironment

Topological data analysis (TDA) is an active field of mathematics for quantifying shape in complex data. Standard methods in TDA such as persistent homology (PH) are typically focused on the analysis of data consisting of a single entity (e.g., cells or molecular species). However, state-of-the-art data collection techniques now generate exquisitely detailed multispecies data, prompting a need for methods that can examine and quantify the relations among them. Such heterogeneous data types arise in many contexts, ranging from biomedical imaging, geospatial analysis, to species ecology. Here, we propose two methods for encoding spatial relations among different data types that are based on Dowker complexes and Witness complexes. We apply the methods to synthetic multispecies data of a tumor microenvironment and analyze topological features that capture relations between different cell types, e.g., blood vessels, macrophages, tumor cells, and necrotic cells. We demonstrate that relational topological features can extract biological insight, including the dominant immune cell phenotype (an important predictor of patient prognosis) and the parameter regimes of a data-generating model. The methods provide a quantitative perspective on the relational analysis of multispecies spatial data, overcome the limits of traditional PH, and are readily computable.

math.AT↗

arXiv2023

Topological classification of tumour-immune interactions and dynamics

The complex and dynamic crosstalk between tumour and immune cells results in tumours that can exhibit distinct qualitative behaviours - elimination, equilibrium, and escape - and intricate spatial patterns, yet share similar cell configurations in the early stages. We offer a topological approach to analyse time series of spatial data of cell locations (including tumour cells and macrophages) in order to predict malignant behaviour. We propose four topological vectorisations specialised to such cell data: persistence images of Vietoris-Rips and radial filtrations at static time points, and persistence images for zigzag filtrations and persistence vineyards varying in time. To demonstrate the approach, synthetic data are generated from an agent-based model with varying parameters. We compare the performance of topological summaries in predicting - with logistic regression at various time steps - whether tumour niches surrounding blood vessels are present at the end of the simulation, as a proxy for metastasis (i.e., tumour escape). We find that both static and time-dependent methods accurately identify perivascular niche formation, significantly earlier than simpler markers such as the number of tumour cells and the macrophage phenotype ratio. We find additionally that dimension 0 persistence applied to macrophage data, representing multi-scale clusters of the spatial arrangement of macrophages, performs best at this classification task at early time steps, prior to full tumour development, and performs even better when time-dependent data are included; in contrast, topological measures capturing the shape of the tumour, such as tortuosity and punctures in the cell arrangement, perform best at intermediate and later stages. The logistic regression coefficients reveal detailed shape differences between the classes.

q-bio.CB↗

arXiv2018

Optonanofluidics: Modelling fluid flow through surfactant-modified liquid tethers by laser beams

When a surfactant-stabilised oil droplet with an ultralow interfacial tension is trapped in the focus of two laser beams and pulled apart (by moving the laser beams) a configuration of two droplets connected by a thin tether of oil results. The tether radius depends on the ratio of the bending modulus to the renormalized interfacial tension, which takes into account the spontaneous curvature of the interface. The force exerted by the tether on the droplets is shown to be asymmetric with respect to the phase inversion temperature of the emulsion, in agreement with experiment. Fluid can be pumped from one droplet to the other via the tether by increasing the optical pressure on one droplet. The flow is a combination of Poiseuille flow within the thread of oil and the external flow around a rigid cylinder, with the surface velocity determined by tangential stress balance. For typical viscosities of oils and the continuous aqueous medium, flow is predominantly in the external medium. The normal stress balance leads to a variation in the radius of the thread with distance. The radius is shown to decrease approximately linearly with a slope proportional to the volumetric flow rate through the tether. For a tether of a given length, there is therefore an upper limit to the flow rate that can be generated by pumping with optical traps.

cond-mat.soft↗