Non-numerical Problems Research Articles

(Keynote) Proton-Tunable Analog Transistor Using a Coordination Polymer

Artificial neural networks (ANN), an alternative to digital logic, can supersede Moore’s law limitations, solve complex non-numeric problems, and are compatible with low-power analog hardware that can reduce energy consumption. Analog devices emulating nerve synapses offer an alternative to digital logic for ANN. Ion-based switches, such as memristors, could potentially address these challenges. However, correlated ion and charge transport in their conducting channels and numerous issues with the switching materials are a barrier to development and optimization of these potentially revolutionary concepts. Recently, Talin and coworkers developed a novel three-terminal redox transistor (RT)[1] based on conducting organic polymers (PEDOT:PSS) that can overcome the inherent limitations of two-terminal memristors for ANN and low-power computing (Fig. 1). Dozens to hundreds of conducting states are feasible, with fast switching and much lower switching voltages than CMOS transistors. They also demonstrated that these polymer redox transistors endure >109 ‘read-write’ operations and project that switching times <100 ns are feasible.[2] Gaining fundamental insight into the performance-controlling phenomena in ion-based switches such as the RT is difficult because ionic and electronic charge transport are correlated in these devices. In the RT, the complex morphology of the polymer electrodes, which have both ordered and disordered regions resembling “cooked spaghetti”[3] affects the density of states (DOS), leading to carrier concentration-dependent mobilities.[4] Consequently, disentangling the correlated effects of morphology, composition, and device architecture requires new synthetic approaches, much greater control over disorder, and operando experimental probes that can generate spatially resolved potentials and composition and microstructural maps.We are developing self-assembled nanoporous materials (SNM) as a new class of mixed conductors to enable independent control of ion and electronic charge transport. SNM offer unprecedented control over porosity to confine and rapidly transport ions, as well as long-range order and synthetic versatility to tailor electronic conductivity. In this presentation we will discuss the requirements for such materials, in particular, highlighting the potential of nanoporous framework materials to provide tailorable pore dimensions with chemical functionalities and redox behavior suitable for ion-based switching. As a starting point for determining structure-function relationships, we are considering redox-active MOFs, which can provide tunable electrical conductivity and fast ion transport combined with a structure having long-range order. An experimental device incorporating these materials will be described to illustrate the potential for using MOFs in RT devices. Fabrication methods and device assembly will also be discussed. Data from operando measurements of local composition and state-of-charge will be presented together with maps relating local morphology with conductivity to create a detailed picture of material and device performance. Finally, results from analytical modeling will be compared with these experimental to determine the validity of current models to describe the coupled ion and charge transport. Y. van de Burgt; E. Lubberman; E. J. Fuller; S. T. Keene; G. C. Faria; S. Agarwal; M. J. Marinella; A. A. Talin; A. Salleo "A non-volatile organic electrochemical device as a low-voltage artificial synapse for neuromorphic computing," Nat. Mater. 2017, 16, 414, 10.1038/nmat4856.E. J. Fuller; S. T. Keene; A. Melianas; Z. Wang; S. Agarwal; Y. Li; Y. Tuchman; C. D. James; M. J. Marinella; J. J. Yang; A. Salleo; A. A. Talin "Parallel programming of an ionic floating-gate memory array for scalable neuromorphic computing," Science 2019, 364, 570, 10.1126/science.aaw5581.R. Noriega; J. Rivnay; K. Vandewal; F. P. V. Koch; N. Stingelin; P. Smith; M. F. Toney; A. Salleo "A general relationship between disorder, aggregation and charge transport in conjugated polymers," Nat. Mater. 2013, 12, 1038, 10.1038/nmat3722.J. T. Friedlein; J. Rivnay; D. H. Dunlap; I. McCulloch; S. E. Shaheen; R. R. McLeod; G. G. Malliaras "Influence of disorder on transfer characteristics of organic electrochemical transistors," Appl. Phys. Lett. 2017, 111, 10.1063/1.4993776. Figure 1

On the Euclidean Minimum Spanning Tree Problem

Given a weighted graph G(V;E), a minimum spanning tree for G can be obtained in linear time using a randomized algorithm or nearly linear time using a deterministic algorithm. Given n points in the plane, we can construct a graph with these points as nodes and an edge between every pair of nodes. The weight on any edge is the Euclidean distance between the two points. Finding a minimum spanning tree for this graph is known as the Euclidean minimum spanning tree problem (EMSTP). The minimum spanning tree algorithms alluded to before will run in time O(n2) (or nearly O(n2)) on this graph. In this note we point out that it is possible to devise simple algorithms for EMSTP in k- dimensions (for any constant k) whose expected run time is O(n), under the assumption that the points are uniformly distributed in the space of interest.CR Categories: F2.2 Nonnumerical Algorithms and Problems; G.3 Probabilistic Algorithms

Parallel Processing Applications in Expert Systems in Power Systems

Parallel processing applications in expert systems in power sytems Parallel processing is widely used to reduce computation times. In its application to non-numerical problems, such as expert systems, inference method and problem size must be considered. A fault diagnosis expert system is considered as an example, with either a model-based or a rule-based inference, applied to power systems of various sizes.

Main transformation tools in ANALITIK-93 programming system

This article reviews the main functions incorporated in the latest version of the source language for the ANALITIK programming system. These functions are intended as transformation tools for nonnumerical models and problems, which are usually represented by systems of symbolic expressions of arbitrary length with a hierarchical structure. Such problems are often connected with nonlinear dependences and oscillating functions, which require multiple integration and differentiation, opening of parentheses, reduction of simmilar terms, various simplifications, etc. Such transformations are available in the languages of the ANALITIK family, REDUCE, Formac, Lisp, MACSYMA, Mathematica, and others. Languages of the ANALITIK family, and especially ANALITIK-93, are distinguished by greater generality and a higher level of intelligence, which is determined by an advanced automatic recognition system of functional properties of the objects being transformed and by a developed interactive system.

An equational language for data-parallelism

Data-parallelism provides a clean conceptual framework for parallel programming. We are developing two programming languages: a high level equational language, called EL * , and a low-level implementation language. Both languages exploit data-parallelism instead of control-parallelism. EL * is a declarative data-parallel language. EL * programs are high-level equational specifications that use extensive pattern-matching and recursion. The language's syntax and semantics are intended to be clear and simple. Recursive forms are restricted to enable translation to efficient data-parallel operations. EL * programs are compiled into FP * , a variant of Backus's FP, where parallel operations are more explicit and low-level. The target language has a rich set of functions for performing communication, and computation. It also has a powerful set of combining forms that generate large highly-parallel functions from smaller program units. Prototype compilers have been implemented for both languages, and they demonstrate good performance. Several linear algebra and non-numeric problems have been programmed with relative ease using EL * . We are currently developing compilation techniques for a wider range of scientific problems that have more complex parallel solutions, and are continuing to expand the language's scope.

An empirical study of automatic restructuring of nonnumerical programs for parallel processors

The feasibility of automatic restructuring of nonnumerical programs for parallel processing is studied through experiments using Parafrase, an automatic restructurer at the University of Illinois, Urbana-Champaign. Parallel processing speedup results due to automatic restructuring for several basic nonnumerical problems are presented. The loops encountered are classified at a low level. On the basis of the speedup results and the analyses of the loop types, the difficulty and the effectiveness of automatic restructuring are discussed. The experiments suggest that automatic restructuring can be a useful tool for exploiting parallelism in the sequential form of nonnumerical programs.

Non-numerical methods on parallel computers

Analysis of computation on parallel computers reveals an interleaving of local (often numeric) processing and data re-organisation. The local processing is readily handled since it is contained within individual processors and easily expressed in terms of element-by-element operations on whole arrays. The intervening data re-organisation accounts for most of the complexity and interest in parallel processing; it is important that operations and techniques are developed for these non-numeric tasks which permit the natural and concise description of algorithms and are readily implemented on parallel hardware. Basic techniques for data organisation and movement are described and illustrated in some numeric and non-numeric problems. Various aspects of matching problems on to arrays of parallel hardware, such as the ICL DAP, are considered. An approach is outlined whereby more sophisticated solutions tocertain problems, such as the fast Fourier transform and sorting, are obtained by working with a specification of the mapping of data on to the store rather than with the physical data organisation.

On non-numeric architecture

In this informal paper, we present what we believe is one of the major problems in computer science of the 70's and several approaches to the solution of this problem that are being studied by our group and by others. (A formal paper that includes a detailed bibliography on this topic is in preparation. Therefore, we are writing this paper in an informal style without references). A very large part of the computational load throughout the world is essentially business computation. Perhaps it is the majority of computation. Business computation is heavily oriented to data base management and information retrieval. We will refer to this type of computation as non-numeric processing. The main primitive operation here is the search. However, we are using standard von Neumann computers whose main primitive operation is addition. What is good for numeric problems like inverting large matrices is not necessarily good for non-numeric problems like searching large data bases. The hardware limitations of conventional von Neumann computers tend to straightjacket our approach to non-numeric processing.

Practical formula manipulation for theoretical chemistry

It is not always easy to give a paper on the applications of certain computing techniques to a highly specialized branch of science. On the other hand, theoretical chemistry is already one of the biggest "customers" of numerical computing in science and offers a wide potential of nonnumerical problems to be solved as well. Being an independent software house eager to gain practical experience in this rather new field of computing, we were very glad that wie could start on some real-world scientific problems rather than implementing yet another formula manipulation system of doubtful practical use. The purpose of this paper is to present a rough overview of theoretical chemistry and the kind of formula manipulation the practical worker encounters in this field of science.

Programming languages, logic and cooperative games

An application of computers is presented which is not restricted to a single problem area but is perhaps not general purpose enough to be considered a programming language, even a problem-oriented one. The application is a program to eliminate quantifiers and bound variables from logical statements in the theory of addition on the real numbers. These statements differ from work in linear inequalities by formal use of quantifiers. The first, introductory, part of the paper argues that from one point of view, this application does provide a higher level programming language. The second part is a description of the method, due basically to Langford, that has been programmed. The last section describes a subapplication to the problem area of bargaining sets of cooperative games where other interesting non-numerical problems arise.

An introduction to the application of Boolean algebra to psychiatry.

Recent developments in mathematics make it no longer necessary to rely on the unaided thought processes in the solution of the complex problems of psychiatry. The physicist has long since given up trying to solve problems in his head but instead turns to various mathematical tools. Scientific psychiatry has reached the point where mathematical instruments are necessary. The calculus proposed by George Boole, sometimes known as Boolean algebra, which is the forerunner of mathematical logic, provides a method for the solutions of non-numerical problems so characteristic of psychiatry.

Mathematical Foundations and Computational Methods for a Digital Logic Machine

The manipulations of the propositional calculus (and the analogous Boolean algebra) have recently become of fundamental importance in fields other than set theoretical proofs of pure mathematics. For example, in the analysis and evaluation of intelligence and military reports, preparation and analysis of tactical methods and principles, complex logical nonnumerical problems often arise more frequently than do problems of a numerical nature. Consequently there is the need for a systematic method of analyzing and solving propositional functions and equations. The purpose of this paper is to present the systematic rules of an “arithmetic” for handling propositional functions and equations, formulated in a manner amenable to easy computation and mechanization. Among the important results given are: (a) a simple method of expressing a propositional calculus in terms of the shortest digitalized words possible, (b) a systematic method for generating the simplest and absolute simplest forms for Boolean functions, (c) a method for systematically generating all true and false implications of given propositions, (d) a method for systematically generating all possible changes of variables (i.e., substitution of new variables) that can be made on a propositional calculus while preserving the logical meaning, and (e) the systematic generation of all solutions to any number of simultaneous propositional equations in any number of unknowns. The solution of this latter problem implies the ability to perform manipulations with propositional variables in a manner analogous to manipulations of ordinary algebraic equations. A number of illustrative applications to military situations are given, including an analysis of certain propositions and conclusions of Clausewitz. Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.