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In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…
When planning motions in a configuration space that has underlying symmetries (e.g. when manipulating one or multiple symmetric objects), the ideal planning algorithm should take advantage of those symmetries to produce shorter…
Inverse design can be a useful strategy for discovering interactions that drive particles to spontaneously self-assemble into a desired structure. Here, we extend an inverse design methodology--relative entropy optimization--to determine…
Addressable self-assembly is the formation of a target structure from a set of unique molecular or colloidal building-blocks, each of which occupies a defined location in the target. The requirement that each type of building-block appears…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
The design of minimum-compliance bending-resistant structures with continuous cross-section parameters is a challenging task because of its inherent non-convexity. Our contribution develops a strategy that facilitates computing all…
Optimal Morse matchings reveal essential structures of cell complexes which lead to powerful tools to study discrete geometrical objects, in particular discrete 3-manifolds. However, such matchings are known to be NP-hard to compute on…
Inverse design of high-resolution and fine-detailed 3D lightweight mechanical structures is notoriously expensive due to the need for vast computational resources and the use of very fine-scaled complex meshes. Furthermore, in designing for…
Controlling the size and shape of assembled structures is a fundamental challenge in self-assembly, and is highly relevant in material design and biology. Here, we show that specific, but promiscuous, short-range binding interactions make…
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…
With the goal of optimizing the CM capacity of a finite constellation over a Rayleigh fading channel, we construct for all dimensions which are a power of 2 families of rotation matrices which optimize a certain objective function…
The ability to control forces between sub-micron-scale building blocks offers considerable potential for designing new materials through self-assembly. A typical paradigm is to first identify a particular (crystal) structure that has some…
Polynomial optimization problems are infinite-dimensional, nonconvex, NP-hard, and are often handled in practice with the moment-sums of squares hierarchy of semidefinite programming bounds. We consider problems where the objective function…
We study the problem of the self-assembly of nanoparticles (NPs) into finite mesoscopic structures with a programmed local morphology and complex overall shape. Our proposed building blocks are NPs directionally-functionalized with DNA. The…
A challenge of molecular self-assembly is to understand how to design particles that self-assemble into a desired structure and not any of a potentially large number of undesired structures. Here we use simulation to show that a strategy of…
In eXplainable Constraint Solving (XCS), it is common to extract a Minimal Unsatisfiable Subset (MUS) from a set of unsatisfiable constraints. This helps explain to a user why a constraint specification does not admit a solution. Finding…
A fundamental assumption in classical mechanism design is that buyers are perfect optimizers. However, in practice, buyers may be limited by their computational capabilities or a lack of information, and may not be able to perfectly…
The ability to rapidly manufacture building blocks with specific binding interactions is a key aspect of programmable assembly. Recent developments in DNA nanotechnology and colloidal particle synthesis have significantly advanced our…
The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such…
Soft robot serial chain manipulators with the capability for growth, stiffness control, and discrete joints have the potential to approach the dexterity of traditional robot arms, while improving safety, lowering cost, and providing an…