On Homogeneous Distributed Parameter Systems

International audienceA geometric homogeneity is introduced for evolution equations in a Banach space. Scalability property of solutions of homogeneous evolution equations is proven. Some qualitative characteristics of stability of trivial solution are also provided. In particular, finite-time stability of homogeneous evolution equations is studied. Theoretical results are illustrated on important classes of partial differential equations

On Characterizing the Data Movement Complexity of Computational DAGs for Parallel Execution

Technology trends are making the cost of data movement increasingly dominant, both in terms of energy and time, over the cost of performing arithmetic operations in computer systems. The fundamental ratio of aggregate data movement bandwidth to the total computational power (also referred to the machine balance parameter) in parallel computer systems is decreasing. It is there- fore of considerable importance to characterize the inherent data movement requirements of parallel algorithms, so that the minimal architectural balance parameters required to support it on future systems can be well understood. In this paper, we develop an extension of the well-known red-blue pebble game to develop lower bounds on the data movement complexity for the parallel execution of computational directed acyclic graphs (CDAGs) on parallel systems. We model multi-node multi-core parallel systems, with the total physical memory distributed across the nodes (that are connected through some interconnection network) and in a multi-level shared cache hierarchy for processors within a node. We also develop new techniques for lower bound characterization of non-homogeneous CDAGs. We demonstrate the use of the methodology by analyzing the CDAGs of several numerical algorithms, to develop lower bounds on data movement for their parallel execution

Generalized Synchronization in Ginzburg-Landau Equations with Local Coupling

The establishment of generalized chaotic synchronization in Ginzburg-Landau equations unidirectionally coupled at discrete points of space (local coupling) has been studied. It is shown that generalized syn-chronization regimes are also established with this type of coupling, but the necessary intensity of coupling issignificantly higher than that in the case of a spatially homogeneous couplingComment: 4 pages, 2 figure

A macroscopic analytical model of collaboration in distributed robotic systems

In this article, we present a macroscopic analytical model of collaboration in a group of reactive robots. The model consists of a series of coupled differential equations that describe the dynamics of group behavior. After presenting the general model, we analyze in detail a case study of collaboration, the stick-pulling experiment, studied experimentally and in simulation by Ijspeert et al. [Autonomous Robots, 11, 149-171]. The robots' task is to pull sticks out of their holes, and it can be successfully achieved only through the collaboration of two robots. There is no explicit communication or coordination between the robots. Unlike microscopic simulations (sensor-based or using a probabilistic numerical model), in which computational time scales with the robot group size, the macroscopic model is computationally efficient, because its solutions are independent of robot group size. Analysis reproduces several qualitative conclusions of Ijspeert et al.: namely, the different dynamical regimes for different values of the ratio of robots to sticks, the existence of optimal control parameters that maximize system performance as a function of group size, and the transition from superlinear to sublinear performance as the number of robots is increased

A Stochastic Process Approach of the Drake Equation Parameters

The number N of detectable (i.e. communicating) extraterrestrial civilizations in the Milky Way galaxy is usually done by using the Drake equation. This equation was established in 1961 by Frank Drake and was the first step to quantifying the SETI field. Practically, this equation is rather a simple algebraic expression and its simplistic nature leaves it open to frequent re-expression An additional problem of the Drake equation is the time-independence of its terms, which for example excludes the effects of the physico-chemical history of the galaxy. Recently, it has been demonstrated that the main shortcoming of the Drake equation is its lack of temporal structure, i.e., it fails to take into account various evolutionary processes. In particular, the Drake equation doesn't provides any error estimation about the measured quantity. Here, we propose a first treatment of these evolutionary aspects by constructing a simple stochastic process which will be able to provide both a temporal structure to the Drake equation (i.e. introduce time in the Drake formula in order to obtain something like N(t)) and a first standard error measure.Comment: 22 pages, 0 figures, 1 table, accepted for publication in the International Journal of Astrobiolog