• Title/Summary/Keyword: Turing

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Turing's Cognitive Science: A Metamathematical Essay for His Centennial (튜링의 인지과학: 튜링 탄생 백주년을 기념하는 메타수학 에세이)

  • Hyun, Woo-Sik
    • Korean Journal of Cognitive Science
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    • v.23 no.3
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    • pp.367-388
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    • 2012
  • The centennial of Alan Mathison Turing(23 June 1912 - 7 June 1954) is an appropriate occasion on which to assess his profound influence on the development of cognitive science. His contributions to and attitudes toward that field are discussed from the metamathematical perspective. This essay addresses (i)Turing's mathematical analysis of cognition, (ii)universal Turing machines, (iii)the limitations of universal Turing machines, (iv)oracle Turing machine beyond universal Turing machine, and (v)Turing test for cognitive science. Turing was a ground-breaker, eager to move on to new fields. He actually opened wider the scientific windows to the mind. The results show that first, by means of mathematical logic Turing discovered a new bridge between the mind and the physical world. Second, Turing gave a new formal analysis of operations of the mind. Third, Turing investigated oracle Turing machines and connectionist network machines as new models of minds beyond the limitations of his own universal machines. This paper explores why the cognitive scientist would be ever expecting a new Turing Test on the shoulder of Alan Turing.

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Turing, Turing Instability, Computational Biology and Combustion (Turing, Turing 불안정성 그리고 수리생물학과 연소)

  • Kim, J.S.
    • Journal of the Korean Society of Combustion
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    • v.8 no.1
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    • pp.46-56
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    • 2003
  • The present paper is concerned with the development of the computational biology in the past half century and its relationship with combustion. The modem computational biology is considered to be initiated by the work of Alan Turing on the morphogenesis in 1952. This paper first touches the life and scientific achievement of Alan Turing and his theory on the morphogenesis based on the reactive-diffusive instability, called the Turing instability. The theory of Turing instability was later extended to the nonlinear realm of the reactive-diffusive systems, which is discussed in the framework of the excitable media by using the Oregonator model. Then, combustion analogies of the Turing instability and excitable media are discussed for the cellular instability, pattern forming combustion phenomena and flame edge. Finally, the recent efforts on numerical simulations of biological systems, employing the detailed bio-chemical knietic mechanism is discussed along with the possibility of applying the numerical combustion techniques to the computational cell biology.

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계산가능성 이론 형성에서의 Church's Thesis와 Turing's Thesis

  • 현우식
    • Journal for History of Mathematics
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    • v.11 no.1
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    • pp.19-26
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    • 1998
  • We investigate "Church's Thesis" and "Turing's Thesis", which are commonly considered as equivalent foundations of computability theory or recursion theory in mathematical logic and computer science. A careful historical and logical analysis of Godel's recursiveness, Church's ${\lambda}$-definability and Turing computability should distinguish between Church's Thesis and Turing's Thesis.and Turing's Thesis.

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G$\ddot{o}$del's Critique of Turings Mechanism (튜링의 기계주의에 대한 괴델의 비평)

  • Hyun Woosik
    • Journal for History of Mathematics
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    • v.17 no.4
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    • pp.27-36
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    • 2004
  • This paper addresses G$\ddot{o}$del's critique of Turing's mechanism that a configuration of the Turing machine corresponds to each state of human mind. The first part gives a quick overview of Turing's analysis of cognition as computation and its variants. In the following part, we describe the concept of Turing machines, and the third part explains the computational limitations of Turing machines as a cognitive system. The fourth part demonstrates that Godel did not agree with Turing's argument, sometimes referred to as mechanism. Finally, we discuss an oracle Turing machine and its implications.

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Bifurcation Analysis of a Spatiotemporal Parasite-host System

  • Baek, Hunki
    • Kyungpook Mathematical Journal
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    • v.60 no.2
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    • pp.335-347
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    • 2020
  • In this paper, we take into account a parasite-host system with reaction-diffusion. Firstly, we derive conditions for Hopf, Turing, and wave bifurcations of the system in the spatial domain by means of linear stability and bifurcation analysis. Secondly, we display numerical simulations in order to investigate Turing pattern formation. In fact, the numerical simulation discloses that typical Turing patterns, such as spotted, spot-stripelike mixtures and stripelike patterns, can be formed. In this study, we show that typical Turing patterns, which are well known in predator-prey systems ([7, 18, 25]), can be observed in a parasite-host system as well.

Philosophical Implication of Turing's Work -Concentrated on Halting Theorem- (튜링의 업적이 지닌 철학적 함의 -'멈춤정리'를 중심으로-)

  • Park, Chang-Kyun
    • Journal for History of Mathematics
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    • v.25 no.3
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    • pp.15-27
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    • 2012
  • This paper aims to examine Alan Turing's life at the centenary of his birth and to discuss a philosophical implication of his work by concentrating on halting theorem particularly. Turing negatively solved Hilbert's decision problem by proving impossibility of solving halting problem. In this paper I claim that the impossibility implies limits of reason, and accordingly that the marginality in cognition and/or in action should be recognized.

PATTERN FORMATION FOR A RATIO-DEPENDENT PREDATOR-PREY MODEL WITH CROSS DIFFUSION

  • Sambath, M.;Balachandran, K.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.16 no.4
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    • pp.249-256
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    • 2012
  • In this work, we analyze the spatial patterns of a predator-prey system with cross diffusion. First we get the critical lines of Hopf and Turing bifurcations in a spatial domain by using mathematical theory. More specifically, the exact Turing region is given in a two parameter space. Our results reveal that cross diffusion can induce stationary patterns which may be useful in understanding the dynamics of the real ecosystems better.

SPATIAL INHOMOGENITY DUE TO TURING BIFURCATION IN A SYSTEM OF GIERER-MEINHARDT TYPE

  • Sandor, Kovacs
    • Journal of applied mathematics & informatics
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    • v.11 no.1_2
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    • pp.125-141
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    • 2003
  • This paper treats the conditions for the existence and stability properties of stationary solutions of reaction-diffusion equations of Gierer-Meinhardt type, subject to Neumann boundary data. The domains in which diffusion takes place are of three types: a regular hexagon, a rectangle and an isosceles rectangular triangle. Considering one of the relevant features of the domains as a bifurcation parameter it will be shown that at a certain critical value a diffusion driven instability occurs and Turing bifurcation takes place: a pattern emerges.

Pattern Formations with Turing and Hopf Oscillating Pattern in a Discrete Reaction-Diffusion System

  • Lee, Il Hui;Jo, Ung In
    • Bulletin of the Korean Chemical Society
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    • v.21 no.12
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    • pp.1213-1216
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    • 2000
  • Localized structures with fronts connecting a Turing patterns and Hopf oscillations are found in discrete reaction-diffusion system. The Chorite-Iodide-Malonic Acid (CIMA) reaction model is used for a reaction scheme. Localized structures in discrete reaction-diffusion system have more diverse and interesting features than ones in continuous system. Various localized structures can be obtained when a single perturbation is applied with variation of coupling strength of two intermediates. Roles of perturbations are not so simple that perturbations are sources of both Turing patterns and Hopf oscillating domains, and spatial distribution of them is determined by strength of a perturbation applied initially.

INSTABILITY IN A PREDATOR-PREY MODEL WITH DIFFUSION

  • Aly, Shaban
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.13 no.1
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    • pp.21-29
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    • 2009
  • This paper treats the conditions for the existence and stability properties of stationary solutions of a predator-prey interaction with self and cross-diffusion. We show that at a certain critical value a diffusion driven instability occurs, i.e. the stationary solution stays stable with respect to the kinetic system (the system without diffusion) but becomes unstable with respect to the system with diffusion and that Turing instability takes place. We note that the cross-diffusion increase or decrease a Turing space (the space which the emergence of spatial patterns is holding) compared to the Turing space with self-diffusion, i.e. the cross-diffusion response is an important factor that should not be ignored when pattern emerges.

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