Abstract. In this paper we describe the graph grammar approach to modeling self-assembly. The approach is used to describe how the topology of an assembling aggregate changes as it grows. The main purpose of the paper is to demonstrate the utility of the approach by giving detailed examples. We also describe the beginnings of our approach to physically embedding graph grammar assembly rules in physical settings, focusing on macro- and micro-scale programmable parts and a simulation environment. 1

Abstract — We describe a novel shape formation algorithm for ensembles of 2-dimensional lattice-arrayed modular robots, based on the manipulation of regularly shaped voids within the lattice (“holes”). The algorithm is massively parallel and fully distributed. Constructing a goal shape requires time proportional only to the complexity of the desired target geometry. Construction of the shape by the modules requires no global communication nor broadcast floods after distribution of the target shape. Results in simulation show 97.3 % shape compliance in ensembles of approximately 60,000 modules, and we believe that the algorithm will generalize to 3D and scale to handle millions of modules. This paper is submitted to Invited Session: New Trends in Modular Robotics. I.

The process by which a cell senses and responds to its environment, as in signal transduction, is often mediated by a network of protein-protein interactions, in which proteins combine to form complexes and undergo post-translational modifications, which regulate their enzymatic and binding activities. A typical signaling protein contains multiple sites of protein interaction and modification and may contain catalytic domains. As a result, interactions of signaling proteins have the potential to generate a combinatorially large number of complexes and modified states, and representing signal-transduction networks can be challenging. Representation, in the form of a diagram or model, usually involves a tradeoff between comprehensibility and precision: comprehensible representations tend to be ambiguous or incomplete, whereas precise representations, such as a long list of chemical species and reactions in a network, tend to be incomprehensible. Here, we develop conventions for representing signal-transduction networks that are both comprehensible and precise. Labeled nodes represent components of proteins and their states, and edges represent bonds between components. Binding and enzymatic reactions are described by reaction rules, in which left graphs define the properties of reactants and right graphs define the products that result from transformations of reactants. The reaction rules can be evaluated to derive a mathematical model.

Abstract. Self-assembly is a process in which small objects autonomously associate with each other to form larger complexes. It is ubiquitous in biological constructions at the cellular and molecular scale and has also been identified by nanoscientists as a fundamental method for building nano-scale structures. Recent years see convergent interest and efforts in studying self-assembly from mathematicians, computer scientists, physicists, chemists, and biologists. However most complexity theoretic studies of self-assembly utilize mathematical models with two limitations: 1) only attraction, while no repulsion, is studied; 2) only assembled structures of two dimensional square grids are studied. In this paper, we study the complexity of the assemblies resulting from the cooperative effect of repulsion and attraction in a more general setting of graphs. This allows for the study of a more general class of self-assembled structures than the previous tiling model. We define two novel assembly models, namely the accretive graph assembly model and the self-destructible graph assembly model, and identify one fundamental problem in them: the sequential construction of a given graph, referred to as Accretive Graph Assembly Problem (AGAP) and Self-Destructible Graph Assembly Problem (DGAP), respectively. Our main results are: (i) AGAP is ¤¦ ¥-complete even if the maximum degree of the graph is restricted to 4 or the graph is restricted to be planar with maximum degree 5; (ii) counting the number of sequential assembly orderings that result in a target graph (#AGAP) is §¨ ¥-complete; and (iii) DGAP is ¥�©�¥����� �-complete even if the maximum degree of the graph is restricted to 6 (this is the first ¥�©�¥����¨ �-complete result in self-assembly). We also extend the accretive graph assembly model to a stochastic model, and prove that determining the probability of a given assembly in this model is §� ¥-complete. 1

We present a method for generating a biochemical reaction network from a description of the interactions of components of biomolecules. The interactions are specified in the form of reaction rules, each of which defines a class of reaction associated with a type of interaction. Reactants within a class have shared properties, which are specified in the rule defining the class. A rule also provides a rate law, which governs each reaction in a class, and a template for transforming reactants into products. A set of reaction rules can be applied to a seed set of chemical species and, subsequently, any new species that are found as products of reactions to generate a list of reactions and a list of the chemical species that participate in these reactions, i.e., a reaction network, which can be translated into a mathematical model. © 2005 Wiley Periodicals, Inc. Complexity 10: 22–41, 2005 Key Words: local rules; automatic model generation; networks; signal transduction; combinatorial complexity; systems biology The cell is a complex adaptive system whose emergent behavior we understand only poorly. One reason for our lack of understanding is the complexity of cellular decision making, which is often mediated by a system of interacting proteins. Systems of interacting proteins are particularly prominent in signal transduction [1], 1 the focus Correspondence to: William S. Hlavacek,

Self-assembly is a ubiquitous process in nature in which a disordered set of components autonomously assemble into a complex and more ordered structure. Components interact with each other without the presence of central control or external intervention. Self-assembly is a rapidly growing research topic and has been studied in various domains including nano-science and technology, robotics, micro-electro-mechanical systems, etc. Software self-assembly, on the other hand, has been lacking in research efforts. In this research, I introduced Automated Self-Assembly Programming Paradigm (ASAP 2), a software self-assembly system whereby a set of human made components are collected in a software repository and later integrated through self-assembly into a specific software architecture. The goal of this research is to push the understanding of software selfassembly and investigate if it can complement current automatic programming approaches such as Genetic Programming. The research begins by studying the behaviour of unguided software self-assembly, a process loosely inspired by ideal gases. The effect of the externally defined environmental

Abstract. This paper proposes a novel method for localizing a stationary infrared source of unknown orientation relative to a static docking sensor. This method uses elliptical approximations of likely positions of the infrared source and computes the intersections to find the most probable locations. It takes only a few samples to localize, is easily computed with inexpensive microcontrollers, and is robust to sensor noise. We then compare our approach with two other methods. The first uses a Bayesian filter across a map of discrete locations in the robot’s operational workspace to determine the suspected source position. The second also uses a probability distribution map but uses the method described by Elfes in his paper on probabilistic sonar-based mapping and navigation [1]. We show that our approach localizes quickly with a single sensor and is no more computationally demanding than other methods.

Self-assembly of active, robotic agents, rather than of passive agents such as molecules, is an emerging research field that is attracting increasing attention. Active self-assembly techniques are especially attractive at very small spatial scales, where alternative construction methods are unavailable or have severe limitations. Building nanostructures by using swarms of very simple nanorobots is a promising approach for manufacturing nanoscale devices and systems. The method described in this paper allows a group of simple, physically identical, identically programmed and memoryless agents to construct and repair polygonal approximations to arbitrary structures in the plane. The distributed algorithms presented here are tolerant of robot failures and of externally-induced disturbances. The structures are self-healing, and self-replicating to a limited extent. Their components can be re-used once the structures are no longer needed. A specification of vertices at relative positions, and the edges between them, is translated by a compiler into reactive rules for assembly agents. These rules lead to the construction and repair of the specified shape. Simulation results are presented, which validate the proposed algorithms.

Abstract. We propose a self-assembly model in which the glue strength between two juxtaposed tiles is a function of the time they have been in neighboring positions. We then present an implementation of our model using strand displacement reactions on DNA tiles. Under our model, we can demonstrate and study catalysis and self-replication in the tile assembly. We then study the tile complexity for assembling shapes in our model and show that a thin rectangle of ¤¦¥¨ § size can be assembled ©¦�� � ����� using types of tiles.

Abstract — We describe a model for planar distributed assembly, in which agents move randomly and independently on a twodimensional grid, joining square blocks together to form a desired target structure. The agents have limited capabilities, including local sensing and rule-based reactive control only, and operate without centralized coordination. We define the spatiotemporal constraints necessary for the ordered assembly of a structure and give a procedure for encoding these constraints in a rule set, such that production of the desired structure is guaranteed. Our main contribution is a stochastic optimization algorithm which is able to significantly reduce the number of environmental features that an agent must recognize to build a structure. Experiments show that our optimization algorithm outperforms existing techniques. I.