Related papers: Two-dimensional tile displacement can simulate cel…
2D display is a fast and economical way of visualizing polymorphism and comparing genomes, which is based on the separation of DNA fragments in two steps, according first to their size and then to their sequence composition. In this paper,…
In cellular reprogramming, almost all epigenetic memories of differentiated cells are erased by the overexpression of few genes, regaining pluripotency, potentiality for differentiation. Considering the interplay between oscillatory gene…
Tile Automata is a recently defined model of self-assembly that borrows many concepts from cellular automata to create active self-assembling systems where changes may be occurring within an assembly without requiring attachment. This model…
Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function.…
In this paper, we investigate the abilities of systems of self-assembling tiles which can each pass a constant number of signals to their immediate neighbors to create replicas of input shapes. Namely, we work within the Signal-passing Tile…
We show the first asymptotically efficient constructions in the so-called "noncooperative planar tile assembly" model. Algorithmic self-assembly is the study of the local, distributed, asynchronous algorithms ran by molecules to…
Mesoscale molecular assemblies on the cell surface, such as cilia and filopodia, integrate information, control transport and amplify signals. Synthetic devices mimicking these structures could sensitively monitor these cellular functions…
Two-dimensional random tilings of rhombi can be seen as projections of two-dimensional membranes embedded in hypercubic lattices of higher dimensional spaces. Here, we consider tilings projected from a $D$-dimensional space. We study the…
The transport of macromolecules, such as DNA, through the cytoskeleton is critical to wide-ranging cellular processes from cytoplasmic streaming to transcription. The rigidity and steric hindrances imparted by the network of filaments…
DNA nanotechnology uses predictable interactions of nucleic acids to precisely engineer complex nanostructures. Characterizing these self-assembled structures at the single-structure level is crucial for validating their design and…
This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully…
Simulators driven by deep learning are gaining popularity as a tool for efficiently emulating accurate but expensive numerical simulators. Successful applications of such neural simulators can be found in the domains of physics, chemistry,…
We define rules for cellular automata played on quasiperiodic tilings of the plane arising from the multigrid method in such a way that these cellular automata are isomorphic to Conway's Game of Life. Although these tilings are nonperiodic,…
In this paper we demonstrate the power of a model of tile self-assembly based on active glues which can dynamically change state. We formulate the Signal-passing Tile Assembly Model (STAM), based on the model of Padilla, Liu, and Seeman to…
We investigate the dynamics of tiling dynamical systems and their deformations. If two tiling systems have identical combinatorics, then the tiling spaces are homeomorphic, but their dynamical properties may differ. There is a natural map…
We present a simple route to circumvent kinetic traps which affect many types of DNA nanostructures in their self-assembly process. Using this method, a new 2D DNA lattice made up of short, single-stranded tile (SST) motifs was created.…
Animals (especially humans) have an amazing ability to learn new tasks quickly, and switch between them flexibly. How brains support this ability is largely unknown, both neuroscientifically and algorithmically. One reasonable supposition…
Here I describe a view of the evolution of cellular automata that allows to operate on larger structures. Instead of calculating the next state of all cells in one step, the method here developed uses a time slice that can proceed at…
We propose reactive Turing machines (RTMs), extending classical Turing machines with a process-theoretical notion of interaction, and use it to define a notion of executable transition system. We show that every computable transition system…
We extend previously known two-dimensional multiplication tiling systems that simulate multiplication by two natural numbers $p$ and $q$ in base $pq$ to higher dimensional multiplication tessellation systems. We develop the theory of these…