14,480 research outputs found

    Stochastic self-assembly

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    We present methods for distributed self-assembly that utilize simple rule-of-thumb control and communication schemes providing probabilistic performance guarantees. These methods represents a staunch departure from existing approaches that require more sophisticated control and communication, but provide deterministic guarantees. In particular, we show that even under severe communication restrictions, any assembly described by an acyclic weighted graph can be assembled with a rule set that is linear in the number of nodes contained in the desired assembly graph. We introduce the concept of stochastic stability to the self-assembly problem and show that stochastic stability of desirable configurations can be exploited to provide probabilistic performance guarantees for the process. Relaxation of the communication restrictions allows simple approaches giving deterministic guarantees. We establish a clear relationship between availability of communication and convergence properties. We consider Self-assembly tasks for the cases of many and few agents as well as large and small assembly goals. We analyze sensitivity of the presented process to communication errors as well as ill-intentioned agents. We discuss convergence rates of the presented process and directions for improving them.M.S.Committee Chair: Jeff Shamma; Committee Member: Magnus Egerstedt; Committee Member: Martha Grove

    A Game-theoretic Formulation of the Homogeneous Self-Reconfiguration Problem

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    In this paper we formulate the homogeneous two- and three-dimensional self-reconfiguration problem over discrete grids as a constrained potential game. We develop a game-theoretic learning algorithm based on the Metropolis-Hastings algorithm that solves the self-reconfiguration problem in a globally optimal fashion. Both a centralized and a fully distributed algorithm are presented and we show that the only stochastically stable state is the potential function maximizer, i.e. the desired target configuration. These algorithms compute transition probabilities in such a way that even though each agent acts in a self-interested way, the overall collective goal of self-reconfiguration is achieved. Simulation results confirm the feasibility of our approach and show convergence to desired target configurations.Comment: 8 pages, 5 figures, 2 algorithm

    Time-delayed autosynchronous swarm control

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    In this paper a general Morse potential model of self-propelling particles is considered in the presence of a time-delayed term and a spring potential. It is shown that the emergent swarm behavior is dependent on the delay term and weights of the time-delayed function which can be set to induce a stationary swarm, a rotating swarm with uniform translation and a rotating swarm with a stationary center-of-mass. An analysis of the mean field equations shows that without a spring potential the motion of the center-of-mass is determined explicitly by a multi-valued function. For a non-zero spring potential the swarm converges to a vortex formation about a stationary center-of-mass, except at discrete bifurcation points where the center-of-mass will periodically trace an ellipse. The analytical results defining the behavior of the center-of-mass are shown to correspond with the numerical swarm simulations

    Consensus problems in networks of agents with switching topology and time-delays

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    In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results

    Analysis of Large Unreliable Stochastic Networks

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    In this paper a stochastic model of a large distributed system where users' files are duplicated on unreliable data servers is investigated. Due to a server breakdown, a copy of a file can be lost, it can be retrieved if another copy of the same file is stored on other servers. In the case where no other copy of a given file is present in the network, it is definitively lost. In order to have multiple copies of a given file, it is assumed that each server can devote a fraction of its processing capacity to duplicate files on other servers to enhance the durability of the system. A simplified stochastic model of this network is analyzed. It is assumed that a copy of a given file is lost at some fixed rate and that the initial state is optimal: each file has the maximum number dd of copies located on the servers of the network. Due to random losses, the state of the network is transient and all files will be eventually lost. As a consequence, a transient dd-dimensional Markov process (X(t))(X(t)) with a unique absorbing state describes the evolution this network. By taking a scaling parameter NN related to the number of nodes of the network. a scaling analysis of this process is developed. The asymptotic behavior of (X(t))(X(t)) is analyzed on time scales of the type tNptt\mapsto N^p t for 0pd10\leq p\leq d{-}1. The paper derives asymptotic results on the decay of the network: Under a stability assumption, the main results state that the critical time scale for the decay of the system is given by tNd1tt\mapsto N^{d-1}t. When the stability condition is not satisfied, it is shown that the state of the network converges to an interesting local equilibrium which is investigated. As a consequence it sheds some light on the role of the key parameters λ\lambda, the duplication rate and dd, the maximal number of copies, in the design of these systems

    Water and molecular chaperones act as weak links of protein folding networks: energy landscape and punctuated equilibrium changes point towards a game theory of proteins

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    Water molecules and molecular chaperones efficiently help the protein folding process. Here we describe their action in the context of the energy and topological networks of proteins. In energy terms water and chaperones were suggested to decrease the activation energy between various local energy minima smoothing the energy landscape, rescuing misfolded proteins from conformational traps and stabilizing their native structure. In kinetic terms water and chaperones may make the punctuated equilibrium of conformational changes less punctuated and help protein relaxation. Finally, water and chaperones may help the convergence of multiple energy landscapes during protein-macromolecule interactions. We also discuss the possibility of the introduction of protein games to narrow the multitude of the energy landscapes when a protein binds to another macromolecule. Both water and chaperones provide a diffuse set of rapidly fluctuating weak links (low affinity and low probability interactions), which allow the generalization of all these statements to a multitude of networks.Comment: 9 pages, 1 figur

    Fast, Scalable, and Interactive Software for Landau-de Gennes Numerical Modeling of Nematic Topological Defects

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    Numerical modeling of nematic liquid crystals using the tensorial Landau-de Gennes (LdG) theory provides detailed insights into the structure and energetics of the enormous variety of possible topological defect configurations that may arise when the liquid crystal is in contact with colloidal inclusions or structured boundaries. However, these methods can be computationally expensive, making it challenging to predict (meta)stable configurations involving several colloidal particles, and they are often restricted to system sizes well below the experimental scale. Here we present an open-source software package that exploits the embarrassingly parallel structure of the lattice discretization of the LdG approach. Our implementation, combining CUDA/C++ and OpenMPI, allows users to accelerate simulations using both CPU and GPU resources in either single- or multiple-core configurations. We make use of an efficient minimization algorithm, the Fast Inertial Relaxation Engine (FIRE) method, that is well-suited to large-scale parallelization, requiring little additional memory or computational cost while offering performance competitive with other commonly used methods. In multi-core operation we are able to scale simulations up to supra-micron length scales of experimental relevance, and in single-core operation the simulation package includes a user-friendly GUI environment for rapid prototyping of interfacial features and the multifarious defect states they can promote. To demonstrate this software package, we examine in detail the competition between curvilinear disclinations and point-like hedgehog defects as size scale, material properties, and geometric features are varied. We also study the effects of an interface patterned with an array of topological point-defects.Comment: 16 pages, 6 figures, 1 youtube link. The full catastroph
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