Related papers: New Geometric Algorithms for Fully Connected Stage…
A classical problem in computational geometry and graph algorithms is: given a dynamic set S of geometric shapes in the plane, efficiently maintain the connectivity of the intersection graph of S. Previous papers studied the setting where,…
This work presents a multi-stage coupled ring oscillator based Potts machine, designed with phase-shifted Sub Harmonic-Injection-Locking (SHIL) to represent multi valued Potts spins at different solution stages with os cillator phases. The…
We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have 3-, 4-, or 6-fold rotational symmetry. The symmetry groups of…
Self-assembly is the autonomous organization of components into patterns or structures: an essential ingredient of biology and a desired route to complex organization. At equilibrium, the structure is encoded through specific interactions,…
The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…
The assembly of colloids in nematic liquid crystals via topological defects has been extensively studied for spherical particles, and investigations of other colloid shapes have revealed a wide array of new assembly behaviors. We show,…
Winfree (1998) showed that discrete Sierpinski triangles can self-assemble in the Tile Assembly Model. A striking molecular realization of this self-assembly, using DNA tiles a few nanometers long and verifying the results by atomic-force…
Shape formation is one of the most thoroughly studied problems in programmable matter and swarm robotics. However, in many models, the class of shapes that can be formed is highly restricted due to the particles' limited memory. In the…
Aggregating base elements into rigid objects such as furniture or sculptures is a great way for designers to convey a specific look and feel. Unfortunately, there is no existing solution to help model structurally sound aggregates. The…
Embeddings of graphs into distributions of trees that preserve distances in expectation are a cornerstone of many optimization algorithms. Unfortunately, online or dynamic algorithms which use these embeddings seem inherently randomized and…
In this paper, we develop a high-order adaptive virtual element method (VEM) to simulate the self-consistent field theory (SCFT) model in arbitrary domains. The VEM is very flexible in handling general polygon elements and can treat hanging…
We introduce framed formal curves, which are formal algebraic curves with boundary components parametrized by the punctured formal disk. We study the moduli space of nodal framed formal curves, which we endow with a logarithmic structure.…
In this work, we present a new method for generating a threshold structure. This kind of structure can be advantageously used in various halftoning algorithms such as clustered-dot or dispersed-dot dithering, error diffusion with threshold…
We have statistically characterized the self-assembly of multi-layer polystyrene colloidal crystals, using the technique of vertical deposition, with parameters chosen to produce thick layers of self-assembled crystals in one deposition…
We report many different nano-structures which are formed when model nano-particles of different sizes (diameter {\sigma} n ) are allowed to aggregate in a background matrix of semi-flexible self assembled polymeric worm like micellar…
Recent advances enable the creation of nanoscale building blocks with complex geometries and interaction specificities for self-assembly. This nearly boundless design space necessitates design principles for defining the mutual interactions…
We give a general procedure for gluing together possibly noncompact manifolds of constant scalar curvature which satisfy an extra nondegeneracy hypothesis. Our aim is to provide a simple paradigm for making `analytic' connected sums. In…
Self-assembly is a ubiquitous process in synthetic and biological systems, broadly defined as the spontaneous organization of multiple subunits (e.g. macromolecules, particles) into ordered multi-unit structures. The vast majority of…
Despite tremendous progress in the research on self-assembled nanotechnological building blocks such as macromolecules, nanowires, and two-dimensional materials, synthetic self-assembly methods bridging nanoscopic to macroscopic dimensions…
The homology group of a tiling introduced by M. Reid is studied for certain topological tilings. As in the planar case, for finite square grids on topological surfaces, the method of homology groups, namely the non-triviality of some…