Related papers: Identifying Shapes Using Self-Assembly (extended a…

We consider a simply supported plate with constant thickness, defined on an unknown multiply connected domain. We optimize its shape according to some given performance functional. Our method is of fixed domain type, easy to be implemented,…

People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…

We define the concept of self-similarity of an object by considering endomorphisms of the object as `similarity' maps. A variety of interesting examples of self-similar objects in geometry, algebra and arithmetic are introduced.…

Existing deep learning-based approaches for monocular 3D object detection in autonomous driving often model the object as a rotated 3D cuboid while the object's geometric shape has been ignored. In this work, we propose an approach for…

In this paper, we work in a 2D version of the probabilistic variant of Winfree's abstract Tile Assembly Model defined by Chandran, Gopalkrishnan and Reif (SICOMP 2012) in which attaching tiles are sampled uniformly with replacement. First,…

Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…

Since the work of Creutz, identifying the group identities for the Abelian Sandpile Model (ASM) on a given lattice is a puzzling issue: on rectangular portions of Z^2 complex quasi-self-similar structures arise. We study the ASM on the…

We consider the problem of analyzing the structure of spectroscopic cubes using unsupervised machine learning techniques. We propose representing the target's signal as a homogeneous set of volumes through an iterative algorithm that…

2D irregular shape packing is a necessary step to arrange UV patches of a 3D model within a texture atlas for memory-efficient appearance rendering in computer graphics. Being a joint, combinatorial decision-making problem involving all…

Regular hypermaps with underlying simple hypergraphs are analysed. We obtain an algorithm to classify the regular embeddings of simple hypergraphs with given order, and determine the automorphism groups of regular embedding of simple…

3D shape creation and modeling remains a challenging task especially for novice users. Many methods in the field of computer graphics have been proposed to automate the often repetitive and precise operations needed during the modeling of…

Recent advances in deep learning have significantly transformed the field of 3D shape generation, enabling the synthesis of complex, diverse, and semantically meaningful 3D objects. This survey provides a comprehensive overview of the…

We show how to design a universal shape replicator in a self-assembly system with both attractive and repulsive forces. More precisely, we show that there is a universal set of constant-size objects that, when added to any unknown hole-free…

The inverse problem of designing component interactions to target emergent structure is fundamental to numerous applications in biotechnology, materials science, and statistical physics. Equally important is the inverse problem of designing…

Reconstructing and processing the 3D objects are popular activities in the research field of computer graphics, image processing and computer vision. The 3D objects are processed based on the methods like geometric modeling, a branch of…

Self-closing assembly is prone to polymorphism due to thermally-excited bending fluctuations, which permit the formation of off-target assemblies at the point of self-closure. One way to overcome this source of polymorphism is to use…

We first prove that the set of domino tilings of a fixed finite figure is a distributive lattice, even in the case when the figure has holes. We then give a geometrical interpretation of the order given by this lattice, using (not…

Most design methods contain a forward framework, asking for primary specifications of a building to generate an output or assess its performance. However, architects urge for specific objectives though uncertain of the proper design…

We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…

Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve…