Related papers: Differentiable Voronoi Diagrams for Simulation of …
Fast and realistic coupling of blood flow and vessel wall is of great importance to virtual surgery. In this paper, we propose a novel data-driven coupling method that formulates physics-based blood flow simulation as a regression problem,…
For pedestrians moving without spatial constraints, extensive research has been devoted to develop methods of density estimation. In this paper we present a new approach based on Voronoi cells, offering a means to estimate density for…
Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…
We use Topological Data Analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify lifetime of…
We derive and simulate a mathematical model for mechanotransduction related to the Rho GTPase signalling pathway. The model addresses the bidirectional coupling between signalling processes and cell mechanics. A numerical method based on…
Intracellular networks process cellular-level information and control cell fate. They can be computationally modeled using Boolean networks, which are implicit-time causal models of discrete binary events. These networks can be embedded in…
We present an optimized conductance-based retina microcircuit simulator which transforms light stimuli into a series of graded and spiking action potentials through photo transduction. We use discrete retinal neuron blocks based on a…
As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…
Many living and physical systems such as cell aggregates, tissues or bacterial colonies behave as unconventional systems of particles that are strongly constrained by volume exclusion and shape interactions. Understanding how these…
There are a wide range of features that tactile contact provides, each with different aspects of information that can be used for object grasping, manipulation, and perception. In this paper inference of some key tactile features, tip…
The positioning of new cellular walls during cell division plays a key role in shaping plant tissue organization. The influence of cell geometry on the positioning of division planes has been previously captured into various geometrical…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
Recent advances in (scanning) transmission electron microscopy have enabled routine generation of large volumes of high-veracity structural data on 2D and 3D materials, naturally offering the challenge of using these as starting inputs for…
Mesh-based simulations are central to modeling complex physical systems in many disciplines across science and engineering. Mesh representations support powerful numerical integration methods and their resolution can be adapted to strike…
We propose a conceptually novel method of reconstructing the topology of dynamical networks. By examining the correlation between the variable of one node and the derivative of another node, we derive a simple matrix equation yielding the…
Accurately and efficiently simulating complex fluid dynamics is a challenging task that has traditionally relied on computationally intensive methods. Neural network-based approaches, such as convolutional and graph neural networks, have…
We introduce a dynamical system based on the vertices of Voronoi tessellations. This dynamical system acts on finite or discrete point sets in the plane, taking a point set to the vertex set of its Voronoi tessellation. We explore the…
Real complex networks are often characterized by spatial constraints such as the relative position and adjacency of nodes. The present work describes how Voronoi tessellations of the space where the network is embedded provide not only a…
Deformable objects present a formidable challenge for robotic manipulation due to the lack of canonical low-dimensional representations and the difficulty of capturing, predicting, and controlling such objects. We construct compact…
The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define…