Effect of initial inoculum on the temporal and spatial dynamics of wheat blast under field conditions in Bolivia.

Epidemiological studies to better understand wheat blast (WB) spatial and temporal patterns were conducted in three field environments in Bolivia between 2019 and 2020. The temporal dynamics of wheat leaf blast (WLB) and spike blast (WSB) were best described by the logistic model compared to the Gompertz and exponential models. The non-linear logistic infection rates (rL) were higher under defined inoculation in experiments two and three than under undefined inoculation in experiment one, and they were also higher for WSB than for WLB. The onset of WLB began with a spatial cluster pattern according to autocorrelation analysis and Moran's Index (I) values, with higher severity and earlier onset for defined than for undefined inoculation until the last sampling time. The WSB onset did not start with a spatial cluster pattern; instead, it was detected later until the last sampling date across experiments, with higher severity and earlier onset for defined than for undefined inoculation. Maximum severity (Kmax) was 1.0 for WSB, and less than 1.0 for WLB. Aggregation of WLB and WSB was higher for defined than for undefined inoculation. The directionality of hotspot development was similar for both WLB and WSB, mainly occurring concentrically for defined inoculation. Our results show no evidence of synchronized development but suggest a temporal and spatial progression of disease symptoms on wheat leaves and spikes. Thus, we recommend that monitoring and management of WB should be considered during early growth stages of wheat planted in areas of high risk.

Topological data analysis of spatial patterning in heterogeneous cell populations: clustering and sorting with varying cell-cell adhesion.

Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other cell types. However, automated and unsupervised classification of these multicellular spatial patterns remains challenging, particularly given their structural diversity and biological variability. Recent developments based on topological data analysis are intriguing to reveal similarities in tissue architecture, but these methods remain computationally expensive. In this article, we show that multicellular patterns organized from two interacting cell types can be efficiently represented through persistence images. Our optimized combination of dimensionality reduction via autoencoders, combined with hierarchical clustering, achieved high classification accuracy for simulations with constant cell numbers. We further demonstrate that persistence images can be normalized to improve classification for simulations with varying cell numbers due to proliferation. Finally, we systematically consider the importance of incorporating different topological features as well as information about each cell type to improve classification accuracy. We envision that topological machine learning based on persistence images will enable versatile and robust classification of complex tissue architectures that occur in development and disease.

How do classroom-turnover times depend on lecture-hall size?

Academic spaces in colleges and universities span classrooms for 10 students to lecture halls that hold over 600 people. During the break between consecutive classes, students from the first class must leave and the new class must find their desks, regardless of whether the room holds 10 or 600 people. Here we address the question of how the size of large lecture halls affects classroom-turnover times, focusing on non-emergency settings. By adapting the established social-force model, we treat students as individuals who interact and move through classrooms to reach their destinations. We find that social interactions and the separation time between consecutive classes strongly influence how long it takes entering students to reach their desks, and that these effects are more pronounced in larger lecture halls. While the median time that individual students must travel increases with decreased separation time, we find that shorter separation times lead to shorter classroom-turnover times overall. This suggests that the effects of scheduling gaps and lecture-hall size on classroom dynamics depends on the perspective-individual student or whole class-that one chooses to take.

Influenza spread on context-specific networks lifted from interaction-based diary data.

Studying the spread of infections is an important tool in limiting or preventing future outbreaks. A first step in understanding disease dynamics is constructing networks that reproduce features of real-world interactions. In this paper, we generate networks that maintain some features of the partial interaction networks that were recorded in an existing diary-based survey at the University of Warwick. To preserve realistic structure in our artificial networks, we use a context-specific approach. In particular, we propose different algorithms for producing larger home, work and social networks. Our networks are able to maintain much of the interaction structure in the original diary-based survey and provide a means of accounting for the interactions of survey participants with non-participants. Simulating a discrete susceptible-infected-recovered model on the full network produces epidemic behaviour which shares characteristics with previous influenza seasons. Our approach allows us to explore how disease transmission and dynamic responses to infection differ depending on interaction context. We find that, while social interactions may be the first to be reduced after influenza infection, limiting work and school encounters may be significantly more effective in controlling the overall severity of the epidemic.

Linking genotype, cell behavior, and phenotype: multidisciplinary perspectives with a basis in zebrafish patterns.

Zebrafish are characterized by dark and light stripes, but mutants display a rich variety of altered patterns. These patterns arise from the interactions of brightly colored pigment cells, making zebrafish a self-organization problem. The diversity of patterns present in zebrafish and other emerging fish models provides an excellent system for elucidating how genes, cell behavior, and visible animal characteristics are related. With the goal of highlighting how experimental and mathematical approaches can be used to link these scales, I overview current descriptions of zebrafish patterning, describe advances in the understanding of the mechanisms underlying cell communication, and discuss new work that moves beyond zebrafish to explore patterning in evolutionary relatives.

Topological data analysis of zebrafish patterns.

Self-organized pattern behavior is ubiquitous throughout nature, from fish schooling to collective cell dynamics during organism development. Qualitatively these patterns display impressive consistency, yet variability inevitably exists within pattern-forming systems on both microscopic and macroscopic scales. Quantifying variability and measuring pattern features can inform the underlying agent interactions and allow for predictive analyses. Nevertheless, current methods for analyzing patterns that arise from collective behavior capture only macroscopic features or rely on either manual inspection or smoothing algorithms that lose the underlying agent-based nature of the data. Here we introduce methods based on topological data analysis and interpretable machine learning for quantifying both agent-level features and global pattern attributes on a large scale. Because the zebrafish is a model organism for skin pattern formation, we focus specifically on analyzing its skin patterns as a means of illustrating our approach. Using a recent agent-based model, we simulate thousands of wild-type and mutant zebrafish patterns and apply our methodology to better understand pattern variability in zebrafish. Our methodology is able to quantify the differential impact of stochasticity in cell interactions on wild-type and mutant patterns, and we use our methods to predict stripe and spot statistics as a function of varying cellular communication. Our work provides an approach to automatically quantifying biological patterns and analyzing agent-based dynamics so that we can now answer critical questions in pattern formation at a much larger scale.

Noise-induced tipping under periodic forcing: Preferred tipping phase in a non-adiabatic forcing regime.

We consider a periodically forced 1D Langevin equation that possesses two stable periodic solutions in the absence of noise. We ask the question: is there a most likely noise-induced transition path between these periodic solutions that allows us to identify a preferred phase of the forcing when tipping occurs? The quasistatic regime, where the forcing period is long compared to the adiabatic relaxation time, has been well studied; our work instead explores the case when these time scales are comparable. We compute optimal paths using the path integral method incorporating the Onsager-Machlup functional and validate results with Monte Carlo simulations. Results for the preferred tipping phase are compared with the deterministic aspects of the problem. We identify parameter regimes where nullclines, associated with the deterministic problem in a 2D extended phase space, form passageways through which the optimal paths transit. As the nullclines are independent of the relaxation time and the noise strength, this leads to a robust deterministic predictor of the preferred tipping phase in a regime where forcing is neither too fast nor too slow.

Iridophores as a source of robustness in zebrafish stripes and variability in Danio patterns.

Zebrafish (Danio rerio) feature black and yellow stripes, while related Danios display different patterns. All these patterns form due to the interactions of pigment cells, which self-organize on the fish skin. Until recently, research focused on two cell types (melanophores and xanthophores), but newer work has uncovered the leading role of a third type, iridophores: by carefully orchestrated transitions in form, iridophores instruct the other cells, but little is known about what drives their form changes. Here we address this question from a mathematical perspective: we develop a model (based on known interactions between the original two cell types) that allows us to assess potential iridophore behavior. We identify a set of mechanisms governing iridophore form that is consistent across a range of empirical data. Our model also suggests that the complex cues iridophores receive may act as a key source of redundancy, enabling both robust patterning and variability within Danio.

Modelling stripe formation in zebrafish: an agent-based approach.

Zebrafish have distinctive black stripes and yellow interstripes that form owing to the interaction of different pigment cells. We present a two-population agent-based model for the development and regeneration of these stripes and interstripes informed by recent experimental results. Our model describes stripe pattern formation, laser ablation and mutations. We find that fish growth shortens the necessary scale for long-range interactions and that iridophores, a third type of pigment cell, help align stripes and interstripes.