Related papers: Improved lower and upper bounds on the tile comple…
Simulated annealing is an effective and general means of optimization. It is in fact inspired by metallurgy, where the temperature of a material determines its behavior in thermodynamics. Likewise, in simulated annealing, the actions that…
We introduce a new property of tile self-assembly systems that we call size-separability. A system is size-separable if every terminal assembly is a constant factor larger than any intermediate assembly. Size-separability is motivated by…
This note is about promoting singularity subtraction as a helpful tool in the discretization of singular integral operators on curved surfaces. Singular and nearly singular kernels are expanded in series whose terms are integrated on…
Tilings of the plane resemble the simplicial and other complexes from algebraic topology, but have not been studied from this perspective. We construct finite categories corresponding to polygons with labeled directed edges, and introduce…
It is shown that when $d\ge 3$, the growing random surface generated by the $(d+1)$-dimensional directed polymer model at sufficiently high temperature, after being smoothed by taking microscopic local averages, converges to a solution of…
Algorithmic self-assembly, a generalization of crystal growth processes, has been proposed as a mechanism for autonomous DNA computation and for bottom-up fabrication of complex nanostructures. A `program' for growing a desired structure…
The field of complex self-assembly is moving toward the design of multi-particle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such `addressable complexity,' we need to…
We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is computed with…
We consider the construction of point processes from tilings, with equal volume tiles, of d-dimensional Euclidean space. We show that one can generate, with simple algorithms ascribing one or more points to each tile, point processes which…
Directed polymers on 1+1 dimensional lattices coupled to a heat bath at temperature $T$ are studied numerically for three ensembles of the site disorder. In particular correlations of the disorder as well as fractal patterning are…
Self-assembly is one of the most promising strategies for making functional materials at the nanoscale, yet new design principles for making self-limiting architectures, rather than spatially unlimited periodic lattice structures, are…
This paper presents a density-based topology optimization method for designing 3D thin-walled structures with adaptive meshing. Uniform wall thickness is achieved by simultaneously constraining the minimum and maximum feature sizes using…
The problem that we consider is the following: given an $n \times n$ array $A$ of positive numbers, find a tiling using at most $p$ rectangles (which means that each array element must be covered by some rectangle and no two rectangles must…
The molecular self-assembly of various structures such as micelles and vesicles has been the subject of comprehensive studies. Recently, a new approach to design these structures, the frame-guided assembly, has been developed to progress…
It is shown that any smooth closed orientable manifold of dimension $2k + 1$, $k \geq 2$, admits a smooth polynomially convex embedding into $\mathbb C^{3k}$. This improves by $1$ the previously known lower bound of $3k+1$ on the possible…
Given a non-negative $n \times n$ matrix viewed as a set of distances between $n$ points, we consider the property testing problem of deciding if it is a metric. We also consider the same problem for two special classes of metrics, tree…
The recently introduced Thermodynamic Binding Networks (TBN) model was developed with the purpose of studying self-assembling systems by focusing on their thermodynamically favorable final states, and ignoring the kinetic pathways through…
We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are…
We present a strict separation between the class of "mismatch free" self-assembly systems and general aTAM systems. Mismatch free systems are those systems in which concurrently grown parts must always agree with each other. Tile…
We give new polynomial lower bounds for a number of dynamic measure problems in computational geometry. These lower bounds hold in the Word-RAM model, conditioned on the hardness of either 3SUM, APSP, or the Online Matrix-Vector…