Tuesday 25 February 2025, 13:00-14:00
Arts, Lecture Room 3
The cells of the intestinal epithelium are produced within invaginations called crypts, whose constituent cells carefully balance proliferation and differentiation to maintain a functional intestinal epithelium. To investigate these dynamics, we built a multi-scale agent-based model (ABM) of cells interacting in the intestinal crypt that reproduces the observed dynamic self-organisation necessary for a healthy intestinal epithelium. In our model, this adaptive homeostasis emerges from the interaction of multiple signalling pathways (including simulated Wnt, Notch, BMP and RNF43/ZNRF3 pathways) that control the spatial distribution and relative abundance of the different cell types found in the crypt. Additionally, each cell simulates its cell cycle protein network that can be perturbed to simulate the effect of drugs, which then propagates from a single-cell disruption to tissue-scale injury. This talks focuses on the design and implementation of the ABM and its constituent pieces.
Tuesday 4 March 2025, 11:00-12:00
Physics West, Lecture Theatre 117
The functionality of multicellular systems is closely linked to their morphology. Mechanical and chemical interactions between cells or tissues are determined by their spatial arrangement. To investigate this connection, we use data-driven, spatially explicit, mechanistic modelling in combination with machine learning. We have successfully applied this approach to multiple systems.
In mouse embryos, we consider detailed quantitative information on the spatial distribution of the cell fates 1–3. By doing so, we identified that only incorporating intercellular communication beyond the nearest neighbours generates the correct cell fate ratio and spatial distribution.
In our studies on gas exchange in the human lung, we propose a new paradigm: The classical approach is to start with a given alveolus morphology and perform blood flow simulations to infer physiological measurements. We suggest to turn the tables by demonstrating how to infer morphology from physiology4: For given blood flow characteristics, our approach enables us to draw conclusions about the connectivity of the alveolar capillary network to arterioles and venules. Our paradigm is not limited to the alveolus but serves as a blueprint for studies on other organs.
This research advances our understanding of multicellular organization, providing a robust framework for investigating spatiotemporal dynamics in developmental biology and physiology.
1. Fischer, S. C., Schardt, S., Lilao-Garzón, J. & Muñoz-Descalzo, S. The salt-and-pepper pattern in mouse blastocysts is compatible with signaling beyond the nearest neighbors. iScience 26, 108106 (2023).
2. Dirk, R., Fischer, J. L., Schardt, S., Ankenbrand, M. J. & Fischer, S. C. Recognition and reconstruction of cell differentiation patterns with deep learning. PLoS Computational Biology 19, e1011582 (2023).
3. Schardt, S. & Fischer, S. C. Adjusting the range of cell–cell communication enables fine-tuning of cell fate patterns from checkerboard to engulfing. J. Math. Biol. 87, 54 (2023).
4. Schmid, K. et al. Inference of alveolar capillary network connectivity from blood flow dynamics. Am J Physiol Lung Cell Mol Physiol 327, L852–L866 (2024).
Tuesday 4 March 2025, 13:00-14:00
Arts, Lecture Room 201
The fluctuation-dissipation theorem is a cornerstone result in statistical mechanics that can be used to translate the statistics of the free natural variability of a system into information on its forced response to perturbations. By combining this viewpoint on response theory with the key ingredients of Koopmanism, it is possible to deconstruct virtually any response operator into a sum of terms, each associated with a specific mode of natural variability of the system. This dramatically improves the interpretability of the resulting response formulas. We showcase some simple yet mathematically meaningful examples how to use the Extended Dynamical Mode Decomposition (EDMD) algorithm on an individual trajectory of the system to compute with high accuracy correlation functions as well as Green functions associated with acting forcings. This demonstrates the great potential of using Koopman analysis for the key problem of evaluating and testing the sensitivity of a complex system. The formalism developed here also allows for a clearer understanding of critical transitions, as it is possible to identify the critical mode associated with the critical behaviour. Additionally, the combination of Koopmanism and response theory provides a powerful framework for clarifying and extending some key aspects of the so-called Hasselmann programme, which is the basis of our understanding of the link between climate variability and climate change.
Tuesday 25 March 2025, 13:00-14:00
Watson Building, Lecture Theatre A
The cells of the intestinal epithelium are produced within invaginations called crypts, whose constituent cells carefully balance proliferation and differentiation to maintain a functional intestinal epithelium. To investigate these dynamics, we built a multi-scale agent-based model (ABM) of cells interacting in the intestinal crypt that reproduces the observed dynamic self-organisation necessary for a healthy intestinal epithelium. In our model, this adaptive homeostasis emerges from the interaction of multiple signalling pathways (including simulated Wnt, Notch, BMP and RNF43/ZNRF3 pathways) that control the spatial distribution and relative abundance of the different cell types found in the crypt. Additionally, each cell simulates its cell cycle protein network that can be perturbed to simulate the effect of drugs, which then propagates from a single-cell disruption to tissue-scale injury. This talks focuses on the design and implementation of the ABM and its constituent pieces.
Monday 28 October 2024, 13:00-14:00
Watson B16
The brain interdependencies can be studied from either a structural or functional perspective. The former focuses typically on structural connectivity (SC), while the second considers statistical interactions (usually functional connectivity, FC). While SC is inherently pairwise because it describes white-matter fibers projecting from one region to another, FC is not limited to pairwise interdependencies. Despite this, FC analyses predominantly concentrate on pairwise statistics, usually neglecting the possibility of higher-order interactions. Moreover, the precise relationship between high-order and SC is largely unknown, partly due to the absence of mechanistic models that can efficiently map brain connectomics to functional connectivity.
To investigate these interlinked issues, we have built whole-brain computational models using anatomical and functional MRI data in two applications: healthy aging and transcranial ultrasound stimulation (TUS). We show that non-linear variations in the structural connectome can largely explain the differences in high-order functional interactions between age groups. Moreover, we showed the extent of perturbations in dynamical models to describe the high-order effects of TUS in two different brain targets.
Monday 4 November 2024, 13:00-14:00
Arts 201
Stochastic differential equations (SDE) driven by white noise are important models for stochastic dynamical systems in natural science and engineering. The statistical inference of the parameters of such models based on noisy observations has also attracted considerable interest in the machine learning community. Using Girsanov's change of measure approach one can apply powerful variational techniques to solve the inference problem. A limitation of standard SDE models is the fact that they show typically a fast decay of correlation functions. If one is interested in stochastic processes with a long-time memory, a well-known possibility is to replace the Brownian motion in the SDE by the so called fractional Brownian motion (fBM) which is no longer a Markov process. Unfortunately, variational inference for this case is much less straightforward. Our approach to this problem utilises a somewhat overlooked idea by Carmona and Coutin (1998) who showed that fBM can be exactly represented as an infinite-dimensional linear combination of Ornstein-Uhlenbeck processes with different time constants. Using an appropriate discretisation, we arrive at a finite dimensional approximation which is an 'ordinary' SDE model in an augmented space. For this new model we can apply (more or less) off-the shelve variational inference approaches.
Monday 4 November 2024, 14:00-15:00
Arts 201
In this talk, I will give an overview of the field of graph-based learning, a field that has matured over the last 15 years and is rich in both practical applications and theoretical underpinnings. The key idea of graph-based learning is to understand interrelated data as a graph, to solve variational problems and PDEs on that graph to analyse that data, and to study the limits of such models as the number of nodes goes to infinity. I will begin by motivating the approach and then will discuss the mathematical framework, three classic methods in the field, the nuances of implementing these methods, and finally the theoretical underpinnings of this field.
Monday 18 November 2024, 13:00-14:00
Watson B16
In this talk, I will develop a comprehensive geometrically-exact theory for an end-loaded elastic rod constrained to deform on a cylindrical surface. By viewing the rod-cylinder system as a special case of an elastic braid, it will be shown that all forces and moments imparted by the deforming rod to the cylinder as well as all contact reactions can be obtained. This framework allows us to give a complete treatment of static friction consistent with force and moment balance. In addition to the commonly considered model of hard frictionless contact, I analyse two friction models in which the rod, possibly with intrinsic curvature, experiences either lateral or tangential friction. Applications of the theory include studying buckling of the constrained rod under compressive and torsional loads, finding critical loads to depend on Coulomb-like friction parameters, as well as the tendency of the rod to lift off the cylinder under further loading. The cylinder can also have arbitrary orientation relative to the direction of gravity. The cases of a horizontal and vertical cylinder, with gravity having only a lateral or axial component, are amenable to exact analysis, while numerical results map out the transition in buckling mechanism between the two extremes. Weight has a stabilising effect for near-horizontal cylinders, while for near-vertical cylinders it introduces the possibility of buckling purely due to self-weight. The results are relevant for many engineering and medical applications in which a slender structure winds inside or outside a cylindrical boundary.
Monday 25 November 2024, 13:00-14:00
Watson B16
The evaporation of liquid droplets has received significant research interest due to its fundamental significance in a variety of industrial and engineering applications such as inkjet printing, microscale and colloidal patterning, DNA microarray technologies and the manufacture of Q/OLEDs. One of the key reasons for this is the familiar ‘coffee-ring’ effect that refers to the ringlike stain left behind after a solute-laden droplet evaporates on a surface and its potential use in depositing specific patterns. While deceptively simple, there is a wealth of complexity in the problem, primarily embedded in the – potentially coupled – aspects of evaporation, the associated liquid flow and particle transport. These difficulties have limited the vast majority of existing models to only treating the simplest possible cases of asymptotically flat, circular droplets evaporating in isolation. This has dramatically limited their applicability in real-world contexts, in which these simplifications are generally broken. In this talk, we will discuss recent advances that attempt to broaden the existing theory with an eye on the ultimate goal of dynamically controlling the process to suit a specific application.
Monday 2 December 2024, 13:00-14:00
Watson Building B16
The Hypothalamic-Pituitary-Adrenal (HPA) axis is a major neuroendocrine system, and its dysregulation is implicated in various diseases. This system also presents interesting mathematical challenges for modelling. We consider a non-linear delay differential equation model and calculate pseudospectra of three different linearisations: a time-dependent Jacobian, linearisation around the limit cycle, and dynamic mode decomposition (DMD) analysis of Koopman operators (global linearisation). The time-dependent Jacobian provided insight into experimental phenomena, explaining why rats respond differently to perturbations during corticosterone secretion's upward versus downward slopes. We developed new mathematical techniques for the other two linearisations to calculate pseudospectra on Banach spaces and apply DMD to delay differential equations, respectively. These methods helped establish local and global limit cycle stability and study transients. Additionally, we discuss using pseudospectra to substantiate the model in experimental contexts and establish bio-variability via data-driven methods. This work is the first to utilise pseudospectra to explore the HPA axis.
Monday 2 December 2024, 14:00-15:00
Watson Building B16
Time series analysis has proven to be a powerful method to characterise several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Several methods have been proposed for the analysis of multivariate time series, yet most of them neglect the effect of non-pairwise interactions on the emerging dynamics. In this talk I will introduce a framework to characterise the temporal evolution of higher-order dependencies within multivariate time series. Using network analysis and topology, I will show that our framework robustly differentiates various spatiotemporal regimes of coupled chaotic maps. This includes chaotic dynamical phases and various types of synchronisation. Furthermore, using the higher-order co-fluctuation patterns in simulated dynamical processes as a guide, I will highlight and quantify signatures of higher-order patterns in data from brain functional activity, financial markets and epidemics. Overall, this approach sheds light on the higher-order organisation of multivariate time series, allowing a better characterization of dynamical group dependencies inherent to real-world data.