Related papers: Universal Computation with Arbitrary Polyomino Til…
In self-assembly, a $k$-counter is a tile set that grows a horizontal ruler from left to right, containing $k$ columns each of which encodes a distinct binary string. Counters have been fundamental objects of study in a wide range of…
We consider a problem concerning tilings of rectangular regions by a finite library of polyominoes. We specifically look at rectangular regions of dimension $n\times m$ and ask whether or not a tiling of this region can be rearranged so…
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…
We study the computational strength of quantum particles (each of finite dimensionality) arranged on a line. First, we prove that it is possible to perform universal adiabatic quantum computation using a one-dimensional quantum system (with…
Polar codes are the first error-correcting codes to provably achieve the channel capacity but with infinite codelengths. For finite codelengths the existing decoder architectures are limited in working frequency by the partial sums…
Computing devices are composed of spatial arrangements of simple funda- mental logic gates. These gates may be combined to form more complex adding circuits and, ultimately, complete computer systems. Implementing classical adding circuits…
Topological quantum computation encodes quantum information in the internal fusion space of non-Abelian anyonic quasiparticles, whose braiding implements logical gates. This goes beyond Abelian topological order (TO) such as the toric code,…
Computing-in-Memory (CiM) is a promising paradigm to address the memory bottleneck constraining traditional systems. Most power-efficient CiM variants can directly perform Boolean operations in non-volatile memory arrays. Higher…
We introduce the concept of Almost-Companion Matrix (ACM) by relaxing the non-derogatory property of the standard Companion Matrix (CM). That is, we define an ACM as a matrix whose characteristic polynomial coincides with a given monic and…
We show that in the hierarchical tile assembly model, if there is a producible assembly that overlaps a nontrivial translation of itself consistently (i.e., the pattern of tile types in the overlap region is identical in both translations),…
Athermal (i.e. zero-temperature) under-constrained systems are typically floppy, but they can be rigidified by the application of external strain. Following our recently developed analytical theory for the athermal limit, here and in the…
Processing-in-DRAM (DRAM-PIM) has emerged as a promising technology for accelerating memory-intensive operations in modern applications, such as Large Language Models (LLMs). Despite its potential, current software stacks for DRAM-PIM face…
We examine the cooling of networks of oscillators through repeated unitary evolution followed by conditional measurement on a finite-dimensional auxiliary system, coupled via Jaynes-Cummings type interaction. We prove that near-perfect…
We study the fundamental problem of polytope membership aiming at large convex polytopes, i.e. in high dimension and with many facets, given as an intersection of halfspaces. Standard data-structures as well as brute force methods cannot…
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…
We investigate general properties of non-deterministic self-assembly with asymmetric interactions, using a computational model and DNA tile assembly experiments. By contrasting symmetric and asymmetric interactions we show that the latter…
Architected materials derive their properties from the geometric arrangement of their internal structural elements. Their designs rely on continuous networks of members to control the global mechanical behavior of the bulk. Here, we…
This paper, about a fluid-like system of spatially confined particles, reveals the analytic structure for both, the canonical and grand canonical partition functions. The studied system is inhomogeneously distributed in a region whose…
Self-assembly is a fundamental process by which supramolecular species form spontaneously from their components. This process is ubiquitous throughout the life chemistry and is central to biological information processing. Algorithms for…
The microstructure of metals and foams can be effectively modelled with anisotropic power diagrams (APDs), which provide control over the shape of individual grains. One major obstacle to the wider adoption of APDs is the computational cost…