Abstract

Abstract
The availability of small inexpensive sensor elements enables the employment of large wired or wireless sensor networks for feeding control systems. Unfortunately, the need to transmit a large number of sensor measurements over a network negatively affects the timing parameters of the control loop. This paper presents a solution to this problem by representing sensor measurements with an approximate representation-an interpolation of sensor measurements as a function of space coordinates. A priority-based medium access control (MAC) protocol is used to select the sensor messages with high information content. Thus, the information from a large number of sensor measurements is conveyed within a few messages. This approach greatly reduces the time for obtaining a snapshot of the environment state and therefore supports the real-time requirements of feedback control loops.

Abstract
Many time series encountered in practice are nonstationary, and instead are often generated from a process with a unit root. Because of the process of data collection or the practice of researchers, time series used in analysis and modeling are frequently obtained through temporal aggregation. As a result, the series used in testing for a unit root are often time series aggregates. In this paper, we study the effects of the use of aggregate time series on the Dickey-Fuller test for a unit root. We start by deriving a proper model for the aggregate series. Based on this model, we find the limiting distributions of the test statistics and illustrate how the tests are affected by the use of aggregate time series. The results show that those distributions shift to the right and that this effect increases with the order of aggregation, causing a strong impact both on the empirical significance level and on the power of the test. To correct this problem, we present tables of critical points appropriate for the tests based on aggregate time series and demonstrate their adequacy. Examples illustrate the conclusions of our analysis.

Abstract

Abstract
In this paper we will try to understand how oracles and advice functions, which are mathematical abstractions in the theory of computability and complexity, can be seen as physical measurements in Classical Physics. First, we consider how physical measurements are a natural external source of information to an algorithmic computation, using a simple and engaging case study, namely: Hoyle's algorithm for calculating eclipses at Stonehenge. Next, we argue that oracles and advice functions can help us understand how the structure of space and time has information content that can be processed by Turing machines. Using an advanced case study from Newtonian kinematics, we show that non-uniform complexity is an adequate framework for classifying feasible computations by Turing machines interacting with an oracle in Nature, and that by classifying the information content of such a natural oracle, using Kolmogorov complexity, we obtain a hierarchical structure based on measurements, advice classes and information.

Abstract