Related papers: Distributed Agreement in Tile Self-Assembly

The ability to control forces between sub-micron-scale building blocks offers considerable potential for designing new materials through self-assembly. A typical paradigm is to first identify a particular (crystal) structure that has some…

Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled,…

In this paper we explore the power of geometry to overcome the limitations of non-cooperative self-assembly. We define a generalization of the abstract Tile Assembly Model (aTAM), such that a tile system consists of a collection of…

Self-assembly in the laboratory can now yield `information-rich' nanostructures in which each component is of a distinct type and has a defined spatial position. Ensuring the thermodynamic stability of such structures requires…

We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a…

With the increasing importance of distributed systems as a computing paradigm, a systematic approach to their design is needed. Although the area of formal verification has made enormous advances towards this goal, the resulting…

We provide a complete characterization of both uniform and non-uniform deterministic consensus solvability in distributed systems with benign process and communication faults using point-set topology. More specifically, we non-trivially…

The Tile Automata (TA) model describes self-assembly systems in which monomers can build structures and transition with an adjacent monomer to change their states. This paper shows that seeded TA is a non-committal intrinsically universal…

We present convergence results in expectation for stochastic subspace correction schemes and their accelerated versions to solve symmetric positive-definite variational problems, and discuss their potential for achieving fault tolerance in…

This paper continues to develop a fault tolerant extension of the sparse grid combination technique recently proposed in [B. Harding and M. Hegland, ANZIAM J., 54 (CTAC2012), pp. C394-C411]. The approach is novel for two reasons, first it…

In the past few years, the problem of distributed consensus has received a lot of attention, particularly in the framework of ad hoc sensor networks. Most methods proposed in the literature address the consensus averaging problem by…

The field of complex self-assembly is moving toward the design of multi-particle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such `addressable complexity,' we need to…

Autonomous assembly is a crucial capability for robots in many applications. For this task, several problems such as obstacle avoidance, motion planning, and actuator control have been extensively studied in robotics. However, when it comes…

Distributed optimization algorithms have been studied extensively in the literature; however, underlying most algorithms is a linear consensus scheme, i.e. averaging variables from neighbors via doubly stochastic matrices. We consider…

In this paper, we study a fault-tolerant control for systems consisting of multiple homogeneous components such as parallel processing machines. This type of system is often more robust to uncertainty compared to those with a single…

Linear consensus iterations guarantee asymptotic convergence, thereby, limiting their applicability in applications where consensus value needs to be used in real time to perform a system level task. It also leads to wastage of power and…

Controlling the topology of structures self-assembled from a set of heterogeneous building blocks is highly desirable for many applications, but is poorly understood theoretically. Here we show that the thermodynamic theory of self-assembly…

Both biological and artificial self-assembly processes can take place by a range of different schemes, from the successive addition of identical building blocks, to hierarchical sequences of intermediates, all the way to the fully…

The molecular self-assembly of various structures such as micelles and vesicles has been the subject of comprehensive studies. Recently, a new approach to design these structures, the frame-guided assembly, has been developed to progress…

Distributed computing offers a high degree of flexibility to accommodate modern learning constraints and the ever increasing size of datasets involved in massive data issues. Drawing inspiration from the theory of distributed computation…