In large federated and shared-nothing databases, resources can exhibit widely fluctuating characteristics. Assumptions made at the time a query is submitted will rarely hold throughout the duration of query processing. As a result, traditional static query optimization and execution techniques are ineffective in these environments. In this paper we introduce a query processing mechanism called an eddy, which continuously reorders operators in a query plan as it runs. We characterize the moments of symmetry during which pipelined joins can be easily reordered, and the synchronization barriers that require inputs from different sources to be coordinated. By combining eddies with appropriate join algorithms, we merge the optimization and execution phases of query processing, allowing each tuple to have a flexible ordering of the query operators. This flexibility is controlled by a combination of fluid dynamics and a simple learning algorithm. Our initial implementation demonstrates prom...

This paper deals with finite size networks which consist of interconnections of synchronously evolving processors. Each processor updates its state by applying a "sigmoidal" function to a linear combination of the previous states of all units. We prove that one may simulate all Turing Machines by such nets. In particular, one can simulate any multi-stack Turing Machine in real time, and there is a net made up of 886 processors which computes a universal partial-recursive function. Products (high order nets) are not required, contrary to what had been stated in the literature. Non-deterministic Turing Machines can be simulated by non-deterministic rational nets, also in real time. The simulation result has many consequences regarding the decidability, or more generally the complexity, of questions about recursive nets.

As query engines are scaled and federated, they must cope with highly unpredictable and changeable environments. In the Telegraph project, we are attempting to architect and implement a continuously adaptive query engine suitable for global-area systems, massive parallelism, and sensor networks. To set the stage for our research, we present a survey of prior work on adaptive query processing, focusing on three characterizations of adaptivity: the frequency of adaptivity, the effects of adaptivity, and the extent of adaptivity. Given this survey, we sketch directions for research in the Telegraph project.

Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary first step in trying to understand interconnections, especially including feedback loops, built up out of monotone components. Basic definitions and theorems are provided, as well as an application to the study of a model of one of the cell's most important subsystems.

In this work we suggest a novel methodology for synthesizing switching controllers for continuous and hybrid systems whose dynamics are defined by linear differential equations. We formulate the synthesis problem as finding the conditions upon which a controller should switch the behavior of the system from one "mode" to another in order to avoid a set of bad states, and propose an abstract algorithm which solves the problem by an iterative computation of reachable states. We have implemented a concrete version of the algorithm, which uses a new approximation scheme for reachability analysis of linear systems.

We present two constructions of controllers that globally stabilize linear systems subject to control saturation. We allow essentially arbitrary saturation functions. The only conditions imposed on the system are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold. One of the constructions is in terms of a ”neural-network type ” one-hidden layer architecture, while the other one is in terms of cascades of linear maps and saturations.

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This paper deals with concepts of output stability. Inspired in part by regulator theory, several variants are considered, which differ from each other in the requirements imposed upon transient behavior. The main results provide a comparison among the various notions, all of which specialize to input to state stability (iss) when the output equals the complete state.

. This paper summarizes the definitions and several of the main results of an approach to hybrid systems, which combines finite automata and linear systems, developed by the author in the early 1980s. Some related more recent results are briefly mentioned as well. 1 Introduction - The Need for Hybrid Systems Linear control theory is well-developed and highly sophisticated, and is widely applied in areas ranging from aerospace to automotive control. Linear systems provide highly accurate models of many physical systems; furthermore, the use of linear systems as "robust" controllers often allows the tolerance of even severe model nonlinearities and uncertainties. However, it remains a fact that many continuous physical processes cannot be satisfactorily modeled linearly, nor can be adequately regulated by means of linear controllers alone. It has long been recognized that the control of more complex systems than those handled by the linear theory will require switching mechanisms (disco...

. This paper shows the existence of a finite neural network, made up of sigmoidal neurons, which simulates a universal Turing machine. It is composed of less than 10 5 synchronously evolving processors, interconnected linearly. High-order connections are not required. 1. Introduction This paper addresses the question: What ultimate limitations, if any, are imposed by the use of neural nets as computing devices? In particular, and ignoring issues of training and practicality of implementation, one would like to know if every problem that can be solved by a digital computer is also solvable --in principle-- using a net. This question has been asked before in the literature. Indeed, Jordan Pollack ([7]) showed that a certain recurrent net model --which he called a "neuring machine," for "neural Turing"-- is universal. In his model, all neurons synchronously update their states according to a quadratic combination of past activation values. In general, one calls high-order nets those in...