arXiv subjects

Shahrzad Heydarshahi

Publications and source records attributed to Shahrzad Heydarshahi.

3 recordsLinked to original sources

arXiv2023

DNA tile self-assembly for 3D-surfaces: Towards genus identification

We introduce a new DNA tile self-assembly model: the Surface Flexible Tile Assembly Model (SFTAM), where 2D tiles are placed on host 3D surfaces made of axis-parallel unit cubes glued together by their faces, called polycubes. The bonds are flexible, so that the assembly can bind on the edges of the polycube. We are interested in the study of SFTAM self-assemblies on 3D surfaces which are not always embeddable in the Euclidean plane, in order to compare their different behaviors and to compute the topological properties of the host surfaces. We focus on a family of polycubes called cuboids. Order-0 cuboids are polycubes that have six rectangular faces, and order-1 cuboids are made from two order-0 cuboids by substracting one from the other. Thus, order-1 cuboids can be of genus 0 or of genus 1 (then they contain a tunnel). We are interested in the genus of these structures, and we present a SFTAM tile assembly system that determines the genus of a given order-1 cuboid. The SFTAM tile assembly system which we design, contains a specific set $Y$ of tile types with the following properties. If the assembly is made on a host order-1 cuboid $C$ of genus 0, no tile of $Y$ appears in any producible assembly, but if $C$ has genus 1, every terminal assembly contains at least one tile of $Y$. Thus, we are able to distinguish the host surfaces according to their genus, by the tiles used in the assembly. This system is specific to order-1 cuboids but the techniques we use should be generalizable to other families of shapes.

cs.DM↗

arXiv2020

Domination and location in twin-free digraphs

A dominating set $D$ in a digraph is a set of vertices such that every vertex is either in $D$ or has an in-neighbour in $D$. A dominating set $D$ of a digraph is locating-dominating if every vertex not in $D$ has a unique set of in-neighbours within $D$. The location-domination number $γ_L(G)$ of a digraph $G$ is the smallest size of a locating-dominating set of $G$. We investigate upper bounds on $γ_L(G)$ in terms of the order of $G$. We characterize those digraphs with location-domination number equal to the order or the order minus one. Such digraphs always have many twins: vertices with the same (open or closed) in-neighbourhoods. Thus, we investigate the value of $γ_L(G)$ in the absence of twins and give a general method for constructing small locating-dominating sets by the means of special dominating sets. In this way, we show that for every twin-free digraph $G$ of order $n$, $γ_L(G)\leq\frac{4n}{5}$ holds, and there exist twin-free digraphs $G$ with $γ_L(G)=\frac{2(n-2)}{3}$. If moreover $G$ is a tournament or is acyclic, the bound is improved to $γ_L(G)\leq\lceil\frac{n}{2}\rceil$, which is tight in both cases.

math.CO↗

arXiv2019

Abstract Geometrical Computation 10: An Intrinsically Universal Family of Signal Machines

Signal machines form an abstract and idealised model of collision computing. Based on dimensionless signals moving on the real line, they model particle/signal dynamics in Cellular Automata. Each particle, or signal, moves at constant speed in continuous time and space. When signals meet, they get replaced by other signals. A signal machine defines the types of available signals, their speeds and the rules for replacement in collision. A signal machine A simulates another one B if all the space-time diagrams of B can be generated from space-time diagrams of A by removing some signals and renaming other signals according to local information. Given any finite set of speeds S, we construct a signal machine that is able to simulate any signal machine whose speeds belong to S. Each signal is simulated by a macro-signal, a ray of parallel signals. Each macro-signal has a main signal located exactly where the simulated signal would be, as well as auxiliary signals which encode its id and the collision rules of the simulated machine. The simulation of a collision, a macro-collision, consists of two phases. In the first phase, macro-signals are shrunk, then the macro-signals involved in the collision are identified and it is ensured that no other macro-signal comes too close. If some do, the process is aborted and the macro-signals are shrunk, so that the correct macro-collision will eventually be restarted and successfully initiated. Otherwise, the second phase starts: the appropriate collision rule is found and new macro-signals are generated accordingly. Considering all finite set of speeds S and their corresponding simulators provides an intrinsically universal family of signal machines.

cs.FL↗