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We propose conformal generative modeling, a framework for generative modeling on 2D surfaces approximated by discrete triangle meshes. Our approach leverages advances in discrete conformal geometry to develop a map from a source triangle…
This paper delves into a systematically reduced plant system proposed by Ja\"ibi et al. [Phys. D, 2020] in arid area. They used the method of geometric singular perturbation to study the existence of abundant orbits. Instead, we deliberate…
Understanding the behavior and evolution of a dynamical many-body system by analyzing patterns in their experimentally captured images is a promising method relevant for a variety of living and non-living self-assembled systems. The arrays…
We deal with dynamical systems on complex lattices possessing chains of non-transversal heteroclinic connections between several periodic orbits. The systems we consider are inspired by the so-called \emph{toy model systems} (TMS) used to…
Turing's (1936) paper on computable numbers has played its role in underpinning different perspectives on the world of information. On the one hand, it encourages a digital ontology, with a perceived flatness of computational structure…
We investigate the iterative construction of discrete Laplacians on 2D square lattices, revealing emergent fractal-like patterns shaped by modular arithmetic. While classical 2222-style iterations reproduce known structures such as the…
In 1958, Ernest Rabinowicz suggested a simple criterion distinguishing the regimes of plastic smoothing and formation of wear particles in a contact of homogeneous sliding bodies. However, he did not consider any detailed mechanism of…
While many good textbooks are available on Protein Structure, Molecular Simulations, Thermodynamics and Bioinformatics methods in general, there is no good introductory level book for the field of Structural Bioinformatics. This book aims…
Hierarchical crack patterns that arise during the drying of thin films of colloidal dispersions or polymer solutions on a solid substrate are of interest both from a fundamental standpoint and in the context of the creation of transparent…
We introduce PlatonicGAN to discover the 3D structure of an object class from an unstructured collection of 2D images, i.e., where no relation between photos is known, except that they are showing instances of the same category. The key…
Cells exert traction forces on compliant substrates and can induce surface instabilities that appear as characteristic wrinkling patterns. Here, we develop a mechanical description of cell-induced wrinkling on soft substrates using a thin…
Understanding how living organisms spontaneously develop complex functional structures inspires innovative approaches in engineering design. Here, we introduce a decentralized generative model based on morphogenesis to autonomously grow…
The Min proteins from Escherichia coli can self-organize into traveling waves on supported lipid bilayers. In Proc. Natl. Acad. Sci. USA 109, 15283 (2012) we showed that these waves are guided along the boundaries of membrane patches. We…
Parametric 3D body models like SMPL only represent minimally-clothed people and are hard to extend to clothing because they have a fixed mesh topology and resolution. To address these limitations, recent work uses implicit surfaces or point…
The spontaneous formation of patterns in dynamical systems is a rich phenomenon that transcends scientific boundaries. Here, we report our observation of coupled optical-atomic pattern formation, which results in the creation of…
Proteins, by virtue of their central role in most biological processes, represent one of the key subjects of the study of molecular evolution. Inherent to the indispensability of proteins for living cells is the fact that a given protein…
A vertex model introduced by M. Bowick, P. Di Francesco, O. Golinelli, and E. Guitter (cond-mat/9502063) describing the folding of the triangular lattice onto the face centered cubic lattice has been studied in the hexagon approximation of…
Nonlinear bending phenomena of thin elastic structures arise in various modern and classical applications. Characterizing low energy states of elastic rods has been investigated by Bernoulli in 1738 and related models are used to determine…
Thin film coatings have been essential in development of several micro and nano-scale devices. To realize thin film coatings various deposition techniques are employed, each yielding surface morphologies with different characteristics of…
Complex textured surfaces occur in nature and industry, from fingerprints to lithography-based micropatterns. Wrinkling by confinement to an incompatible substrate is an attractive way of generating reconfigurable patterned topographies,…