Related papers: Data-driven quasiconformal morphodynamic flows
We consider the method of mappings for performing shape optimization for unsteady fluid-structure interaction (FSI) problems. In this work, we focus on the numerical implementation. We model the optimization problem such that it takes…
We present a notion of super Ricci flow for time-dependent finite weighted graphs. A challenging feature is that these flows typically encounter singularities where the underlying graph structure changes. Our notion is robust enough to…
We study one-parameter curves on the universal Teichm\"uller space $T$ and on the homogeneous space $M=\Diff S^1/\Rot S^1$ embedded into $T$. As a result, we deduce evolution equations for conformal maps that admit quasiconformal extensions…
Given a completely arbitrary surface, whether or not it has bounded curvature, or even whether or not it is complete, there exists an instantaneously complete Ricci flow evolution of that surface that exists for a specific amount of time…
Optimal-order uniform-in-time $H^1$-norm error estimates are given for semi- and full discretizations of mean curvature flow of surfaces in arbitrarily high codimension. The proposed and studied numerical method is based on a parabolic…
We consider the normalized Ricci flow evolving from an initial metric which is conformally compactifiable and asymptotically hyperbolic. We show that there is a unique evolving metric which remains in this class, and that the flow exists up…
Many natural shapes have most of their characterizing features concentrated over a few regions in space. For example, humans and animals have distinctive head shapes, while inorganic objects like chairs and airplanes are made of…
Efficient and fast reconstruction of anatomical structures plays a crucial role in clinical practice. Minimizing retrieval and processing times not only potentially enhances swift response and decision-making in critical scenarios but also…
Nature offers remarkable examples of complex photonic architectures such as those responsible for the iridescent colors of butterfly wings that emerge spontaneously during growth, well before any centralized control takes place. Arising…
We investigate the evolution of axis ratios, roundness (isoperimetric ratio) and the number of static balance points under distance-driven flows. The latter have already been proposed by Aristotle as models of particle shape evolution and…
In this article we use Ricci flow to show that complete PIC1 manifolds with maximal volume growth are diffeomorphic to $\mathbb{R}^n$. One of the key ingredients is local estimates of curvature lower bounds on an initial time interval of…
Modern continuous-time generative models typically induce \emph{V-shaped} flows: each sample travels independently along a nearly straight trajectory from the prior to the data. Although effective, this independent movement overlooks the…
An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. We consider a nudging-based approach for data assimilation that constructs an approximate solution based on a…
The analysis of a timeseries can provide many new perspectives if it is accompanied by the assumption that the timeseries is generated from an underlying dynamical system. For example, statistical properties of the data can be related to…
In this paper, the dynamics of spontaneous shape fluctuations of a single, giant quasi-spherical vesicle formed of a single lipid species is revisited theoretically. A coherent physical theory for the dynamics is developed based on a number…
Deformable shape modeling approaches that describe objects in terms of their medial axis geometry (e.g., m-reps [Pizer et al., 2003]) yield rich geometrical features that can be useful for analyzing the shape of sheet-like biological…
Given that observational and numerical climate data are being produced at ever more prodigious rates, increasingly sophisticated and automated analysis techniques have become essential. Deep learning is quickly becoming a standard approach…
Normalizing Flows are a powerful technique for learning and modeling probability distributions given samples from those distributions. The current state of the art results are built upon residual flows as these can model a larger hypothesis…
We find a local solution to the Ricci flow equation under a negative lower bound for many known curvature conditions. The flow exists for a uniform amount of time, during which the curvature stays bounded below by a controllable negative…
We consider the Kaehler-Ricci flow on complete finite-volume metrics that live on the complement of a divisor in a compact Kaehler manifold X. Assuming certain spatial asymptotics on the initial metric, we compute the singularity time in…