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A common starting point for drug design is to find small chemical groups or "fragments" that form interactions with distinct subregions in a protein binding pocket. The subsequent challenge is to assemble these fragments into a molecule…
Alignable nets are grid structures that can collapse to a planar strip, which is in fact the real-world counterpart of a curve. This property simplifies on-site assembly and enables compact transport and storage. These grid structures can…
Self-folding origami, structures that are engineered flat to fold into targeted, three-dimensional shapes, have many potential engineering applications. Though significant effort in recent years has been devoted to designing fold patterns…
Principal manifolds serve as useful tool for many practical applications. These manifolds are defined as lines or surfaces passing through "the middle" of data distribution. We propose an algorithm for fast construction of grid…
The presence of cuts in a thin planar sheet can dramatically alter its mechanical and geometrical response to loading, as the cuts allow the sheet to deform strongly in the third dimension. We use numerical experiments to characterize the…
The Indoor Geometry Generator (IGG) is able to generate automatically simplified indoor geometry and its associated unstructured mesh for Computational Fluid Dynamics (CFD) simulations purposes given very simple user inputs. A large number…
Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…
The proliferation of 3D representations, from explicit meshes to implicit neural fields and more, motivates the need for simulators agnostic to representation. We present a data-, mesh-, and grid-free solution for elastic simulation for any…
Air-dispersed sensor networks deployed from aerial robotic systems (e.g., UAVs) provide a low-cost approach to wide-area environmental monitoring. However, existing methods often rely on active actuators for mid-air shape or trajectory…
Fine scale elastic structures are widespread in nature, for instances in plants or bones, whenever stiffness and low weight are required. These patterns frequently refine towards a Dirichlet boundary to ensure an effective load transfer.…
Origami, which transforms flat sheets into three-dimensional shapes through folding patterns, has inspired the emergence of deployable systems in architecture and civil realms. Most existing origami-inspired deployable systems are based on…
Novel view synthesis (NVS) is crucial in computer vision and graphics, with wide applications in AR, VR, and autonomous driving. While 3D Gaussian Splatting (3DGS) enables real-time rendering with high appearance fidelity, it suffers from…
In this paper, we explore an open research problem concerning the reconstruction of 3D scenes from images. Recent methods have adopt 3D Gaussian Splatting (3DGS) to produce 3D scenes due to its efficient training process. However, these…
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…
This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) space, rather…
Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…
Confined thin structures are ubiquitous in nature. Spatial and length constraints have led to a number of novel packing strategies at both the micro-scale, as when DNA packages inside a capsid, and the macro-scale, seen in plant root…
The exceptional mechanical properties of graphene have made it attractive for nano-mechanical devices and functional composite materials. Two key aspects of graphene's mechanical behavior are its elastic and adhesive properties. These are…
Geospatial Knowledge Graphs (GeoKGs) model geoentities (e.g., places and natural features) and spatial relationships in an interconnected manner, providing strong knowledge support for geographic applications, including data retrieval,…
This paper has several goals. The first idea is to study the geometric PDEs of connection-flatness, curvature-flatness, Ricci-flatness, scalar curvature-flatness in a modern and rigorous way. Although the idea is not new, our main Theorems…