On the functions generated by the general purpose analog computer

PreprintWe consider the General Purpose Analog Computer (GPAC), introduced by Claude Shannon in 1941 as a mathematical model of Differential Analysers, that is to say as a model of continuous-time analog (mechanical, and later one electronic) machines of that time. The GPAC generates as output univariate functions (i.e. functions f:R→R). In this paper we extend this model by: (i) allowing multivariate functions (i.e. functions f:Rn→Rm); (ii) introducing a notion of amount of resources (space) needed to generate a function, which allows the stratification of GPAC generable functions into proper subclasses. We also prove that a wide class of (continuous and discontinuous) functions can be uniformly approximated over their full domain. We prove a few stability properties of this model, mostly stability by arithmetic operations, composition and ODE solving, taking into account the amount of resources needed to perform each operation. We establish that generable functions are always analytic but that they can nonetheless (uniformly) approximate a wide range of nonanalytic functions. Our model and results extend some of the results from [19] to the multidimensional case, allow one to define classes of functions generated by GPACs which take into account bounded resources, and also strengthen the approximation result from [19] over a compact domain to a uniform approximation result over unbounded domains.info:eu-repo/semantics/acceptedVersio

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Some system considerations in configuring a digital flight control - navigation system

A trade study was conducted with the objective of providing a technical guideline for selection of the most appropriate computer technology for the automatic flight control system of a civil subsonic jet transport. The trade study considers aspects of using either an analog, incremental type special purpose computer or a general purpose computer to perform critical autopilot computation functions. It also considers aspects of integration of noncritical autopilot and autothrottle modes into the computer performing the critical autoland functions, as compared to the federation of the noncritical modes into either a separate computer or with a R-Nav computer. The study is accomplished by establishing the relative advantages and/or risks associated with each of the computer configurations

Turing machines can be efficiently simulated by the General Purpose Analog Computer

The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and at a computational complexity level modulo polynomial reductions. However, the situation is less clear in what concerns models of computation using real numbers, and no analog of the Church-Turing thesis exists for this case. Recently it was shown that some models of computation with real numbers were equivalent from a computability perspective. In particular it was shown that Shannon's General Purpose Analog Computer (GPAC) is equivalent to Computable Analysis. However, little is known about what happens at a computational complexity level. In this paper we shed some light on the connections between this two models, from a computational complexity level, by showing that, modulo polynomial reductions, computations of Turing machines can be simulated by GPACs, without the need of using more (space) resources than those used in the original Turing computation, as long as we are talking about bounded computations. In other words, computations done by the GPAC are as space-efficient as computations done in the context of Computable Analysis

NOPAL Reference Manual: Bottom-Part

Nopal is a descriptive non-procedural very high level language for writing specifications of programs for test of analog and digital electronic circuits by Automatic Test Systems (ATS). It can also be used for writing specifications of general purpose computation. Based on a NOPAL specification, the NOPAL processor generates a computer program in the ATLAS test language. A specification in NOPAL may consist of a number of modules,one of which is the main module. The main module consists of a collection of specifications of individual tests given non-procedurally in an arbiitrary order. A test in NOPAL corresponds to the notion of a physical test a unit under test (UUT). A test consists of stimuli (signals) to be applied measurements to be taken and logic for selecting diagnoses depending on the passing or failing of one or more tests. Information about the UUT and automatic test equipment (ATE) may also be included in the main module. The UUT and ATE information is used for conducting various consistency checks and is included in the produced documentation. A module, other than the main module, specify functions which apply stimuli, make measurements or evaluate variables. Interfaces among modules are provided by referencing in one module function specified in another module. The NOPAL processor analyzes the specification of module for consistency, completeness and non-ambiguity and generate error/warning messages and a number of reports which serve as the documentation for the specification. If the specification is error free, the NOPAL processor orders the program events to attain efficiency in computer time and in use of memory. Finally, it generates a program in the EQUATE-ATLAS Test Programing Language. ATLAS programs, generated from modules of a specification, are submitted together for compilation and executed on RCA EQUATE AN-USM-410 computer controlled ATE

Information Processing, Computation and Cognition

Computation and information processing are among the most fundamental notions in cognitive science. They are also among the most imprecisely discussed. Many cognitive scientists take it for granted that cognition involves computation, information processing, or both – although others disagree vehemently. Yet different cognitive scientists use ‘computation’ and ‘information processing’ to mean different things, sometimes without realizing that they do. In addition, computation and information processing are surrounded by several myths; first and foremost, that they are the same thing. In this paper, we address this unsatisfactory state of affairs by presenting a general and theory-neutral account of computation and information processing. We also apply our framework by analyzing the relations between computation and information processing on one hand and classicism and connectionism/computational neuroscience on the other. We defend the relevance to cognitive science of both computation, at least in a generic sense, and information processing, in three important senses of the term. Our account advances several foundational debates in cognitive science by untangling some of their conceptual knots in a theory-neutral way. By leveling the playing field, we pave the way for the future resolution of the debates’ empirical aspects

Wind energy system time-domain (WEST) analyzers

A portable analyzer which simulates in real time the complex nonlinear dynamics of horizontal axis wind energy systems was constructed. Math models for an aeroelastic rotor featuring nonlinear aerodynamic and inertial terms were implemented with high speed digital controllers and analog calculation. This model was combined with other math models of elastic supports, control systems, a power train and gimballed rotor kinematics. A stroboscopic display system graphically depicting distributed blade loads, motion, and other aerodynamic functions on a cathode ray tube is included. Limited correlation efforts showed good comparison between the results of this analyzer and other sophisticated digital simulations. The digital simulation results were successfully correlated with test data

A universal computer control system for motors

A control system for a multi-motor system such as a space telerobot, having a remote computational node and a local computational node interconnected with one another by a high speed data link is described. A Universal Computer Control System (UCCS) for the telerobot is located at each node. Each node is provided with a multibus computer system which is characterized by a plurality of processors with all processors being connected to a common bus, and including at least one command processor. The command processor communicates over the bus with a plurality of joint controller cards. A plurality of direct current torque motors, of the type used in telerobot joints and telerobot hand-held controllers, are connected to the controller cards and responds to digital control signals from the command processor. Essential motor operating parameters are sensed by analog sensing circuits and the sensed analog signals are converted to digital signals for storage at the controller cards where such signals can be read during an address read/write cycle of the command processing processor

Database of audio records

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