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- Löfgren, Lars
(författare)
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An axiomatic explanation of complete self-reproduction
- 1968
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Ingår i: Bulletin of Mathematical Biophysics. - 0007-4985. ; 30:3, s. 415-425
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Tidskriftsartikel (refereegranskat)abstract
- A similarity between the concepts of reproduction and explanation is observed which implies a similarity between the less well understood concepts of complete self-reproduction and complete self-explanation. These latter concepts are shown to be independent from ordinary logical-mathematical-biological reasoning, and a special form of complete self-reproduction is shown to be axiomatizable. Involved is the question whether there exists a function that belongs to its own domain or range. Previously, Wittgenstein has argued, on intuitive grounds, that no function can be its own argument. Similarly, Rosen has argued that a paradox is implied by the notion of a function which is a member of its own range. Our result shows that such functions indeed are independent from ordinary logical-mathematical reasoning, but that they need not imply any inconsistencies. Instead such functions can be axiomatized, and in this sense they really do exist. Finally, the introduced notion of complete self-reproduction is compared with “self-reproduction” of ordinary biological language. It is pointed out that complete self-reproduction is primarily of interest in connection with formal theories of evolution.
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| 4. |
- Åström, Karl Johan
(författare)
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Computer Control of a Paper Machine : An Application of Linear Stochastic Control Theory
- 1967
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Ingår i: IBM Journal of Research and Development. - : IBM. - 2151-8556 .- 0018-8646. ; 11:4, s. 389-405
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Tidskriftsartikel (refereegranskat)abstract
- This paper describes an attempt to apply linear optimal control theory to computer control of an industrial process. The applicability of the theory is discussed. Particular attention is given to the problem of obtaining a mathematical model of process dynamics and disturbances. Results of actual measurements as well as results from on-line control experience are presented.
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| 5. |
- Åström, Karl Johan
(författare)
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On a first-order stochastic differential equation
- 1965
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Ingår i: International Journal of Control. - : Informa UK Limited. - 0020-7179 .- 1366-5820. ; 1:4, s. 301-326
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Tidskriftsartikel (refereegranskat)abstract
- A first-order system with random parameters and random forcing is studied. The analysis is concentrated on the probability distributions. It is shown that considerable qualitative information can be obtained from Feller's classification of the singular points of the forward and backward Kolmogorov equations. It is found that there is a drastic difference between the cases of uncorrelated and strongly correlated disturbances. The existence of stationary distributions is shown and their structure is analysed; it is found that the steady-state distributions are of the Pearson type. Some examples exhibit in detail the differences between uncorrelated and strongly correlated disturbances, giving the rather surprising effect that by making the fluctuations of the parameters sufficiently large, the probability of finding the state of the system in tin interval around the origin can be made arbitrarily close to one ‘peaking’. The results of some numerical computations are presented. A case where the energy of the fluctuation in parameters is limited within a certain frequency band shows that this situation is different from the case of ‘ white noise ’. For example, ‘ peaking ’ of the distributions does not occur. It is found that, for the purpose of analysing probability distributions the system obtained can be approximated by a different system with white noise coefficients, These results are also illustrated by numerical computations.
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| 6. |
- Åström, Karl Johan
(författare)
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On the Choice of Sampling Rates in Parametric Identification of Time Series
- 1969
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Ingår i: Information Sciences. - 0020-0255. ; 1:3, s. 273-278
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Tidskriftsartikel (refereegranskat)abstract
- Aliasing gives a lower bound for the sampling rate in ordinary spectral analysis of a time series. In parametric it appears at first sight that no such limitations are present. In this note we will obtain insight into this paradox by analyzing a simple Gauss-Markov process. We assume that a time series analysis is performed based on N samples of the series at equal spacing h. The result shows that there is an optimal choice of h and that the variance increases rapidly when h increases from the optimal value. The analysis of a time series of fixed length T with different number of samplings is also discussed.
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| 9. |
- Åström, Karl Johan, et al.
(författare)
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Vertical indication with a physical pendulum based on electromechanical synthesis of a high moment of inertia.
- 1965
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Ingår i: Elteknik. - 0013-6425. ; 8:4, s. 53-59
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Artikeln beskriver ett nytt sätt att syntetisera tröghetsnavigeringssystem. Systemet är baserat på en princip för vertikalindikering, som uppfanns av författarna 1959. Ett komplett navigeringssystem enligt den nya principen har utvecklats och byggts av Philips Teleindustri i Stockholm. Detta system har genomgått en omfattande testning i flygplan. De första testflygningarna utfördes med ett litet tvåmotorigt propellerplan. Ett stort antal testflygningar har nyligen genomförts med ett jetplan med flygtider upp till tio timmar. Syftet med testflygningarna har varit, att prova de nya systemprinciperna i praktiken samt att undersöka om navigeringsnoggrannheten är i överensstämmelse med vad som erhållits ur system analysen. Testflygningarna har genomförts planenligt och de nya systemprincipernas hållbarhet har alltså praktiskt demonstrerats för flygplan med hög hastighet. Denna artikel är baserad på den första rapport, som skrivits om systemet. Denna rapport utgavs av TTN-gruppen (Teoretiska Tröghetsnavigeringsgruppen under professor B J Andersson vid KTH) i augusti 1959, och finns även tillgänglig som en FOA-rapport. Artikeln behandlar en förenklad enaxlig version av systemet.
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