Related papers: On the Shape Containment Problem within the Amoebo…
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…
Leader Election is an important primitive for programmable matter, since it is often an intermediate step for the solution of more complex problems. Although the leader election problem itself is well studied even in the specific context of…
A fundamental problem in Distributed Computing is the Pattern Formation problem, where some independent mobile entities, called robots, have to rearrange themselves in such a way as to form a given figure from every possible…
We describe a group theoretic analysis of Shor's algorithm and other related hidden subgroup problems in mathematics and relate these to symmetries of molecular and condensed phase assemblies. By recasting Shor's algorithm through the lens…
A configuration of $n$ unit-cube-shaped \textit{modules} (or \textit{robots}) is a lattice-aligned placement of the $n$ modules so that their union is face-connected. The reconfiguration problem aims at finding a sequence of moves that…
We address a long-standing problem in colloid and nanoparticle science: particle shape selection in solution synthesis. Our main finding is that a proper balance of two processes, preferential attachment of transported monomers at the…
Spins confined in quantum dots are a leading candidate for solid-state quantum bits that can be coherently controlled by optical pulses. There are, however, many challenges to developing a scalable multibit information processing device…
We study an elementary problem of the topological robotics: collective motion of a set of $n$ distinct particles which one has to move from an initial configuration to a final configuration, with the requirement that no collisions occur in…
Creating materials with structure that is independently controllable at a range of scales requires breaking naturally occurring hierarchies. Breaking these hierarchies can be achieved via the decoupling of building block attributes from…
Active matter physics and swarm robotics have provided powerful tools for the study and control of ensembles driven by internal sources. At the macroscale, controlling swarms typically utilizes significant memory, processing power, and…
This paper demonstrates the impact of a phase field method on shape registration to align shapes of possibly different topology. It yields new insights into the building of discrepancy measures between shapes regardless of topology, which…
Particle systems are physical systems of simple computational particles that can bond to neighboring particles and use these bonds to move from one spot to another (non-occupied) spot. These particle systems are supposed to be able to…
Photographing optoelectronic displays often introduces unwanted moir\'e patterns due to analog signal interference between the pixel grids of the display and the camera sensor arrays. This work identifies two problems that are largely…
Shape transformation is crucial for the survival, adaptation, predation, defense, and reproduction of organisms in complex environments. It also serves as a key mechanism for the development of various applications, including soft robotics,…
Assembly of large scale structural systems in space is understood as critical to serving applications that cannot be deployed from a single launch. Recent literature proposes the use of discrete modular structures for in-space assembly and…
Random packings of objects of a particular shape are ubiquitous in science and engineering. However, such jammed matter states have eluded any systematic theoretical treatment due to the strong positional and orientational correlations…
We consider collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with a random perturbation (i.e. rotational fluctuation). They…
The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…
Shape-constrained optimization arises in a wide range of problems including distributionally robust optimization (DRO) that has surging popularity in recent years. In the DRO literature, these problems are usually solved via reduction into…
Biological and robotic systems often operate in confined environments where material must be gathered without centralized control. Inspired by the effective collection strategies of aquatic worms (Lumbriculus variegatus and Tubifex…