Use of the quantum entropy of non-probabilistic matrices in automatic control

The quantum mechanical entropy of density matrices defined by Von Neumann in quantum physics has been generalized in the form of quantum entropy of non-probabilistic matrices, and it is shown that the latter can be of some use in automatic control. This quantum entropy can be thought of as a measure of structure complexity and its application is quite relevant and meaningful in the following topics: stability of linear and non-linear systems, robustness and order reduction. Quantum entropy appears to be a new weighted combination of eigenvalues which would allow us to re-examine some problems with new points of view relating to information theory without probability.     

Tracking control of non-linear stochastic systems by using path cross-entropy and Fokker-Planck equation

The stochastic control problem is defined in terms of state probability. Clearly, the system is designed in such a manner that its state probability tracks the desired state probability of the reference system. The tracking criterion to be minimized is the path cross-entropy (or relative entropy or Kullback entropy) of the two probability density functions, and the problem then turns out to be a distributed parameter one in which the state dynamical equation is the Fokker-Planck equation. The explicit solution of the conjugate equation is obtained by using expansions in Hermite's polynomials. In the special case of neighbouring-optimal control, a slight extension of the LQG approach is proposed, by using a cost function which is a weighted combination of the path cross-entropy and a control quadratic term. Future improvements are discussed.     

Structural entropy,information potential,information balance and evolution in self-organizing systems†

This paper is the continuation of a preceding one which appeared in this journal, and presented an approach to self-organizing systems based upon information theory. To begin with, some illustrating examples try to show why one can think that the concept of information should play a crucial role in a theory of general systems. Then the concept of ‘ structural entropy ’, and the ‘ evolution principle ’ that we have previously introduced, are improved here in a definitive form. The concept of ‘ information potential ’ is defined and we show that the capacity of an information source is given by the logarithm of its inverse entropy rather than by its negative entropy. Composition laws for the structural entropy are stated and it is shown that these concepts provide an approach to information balance. Some simple examples are outlined to connect this approach with well known existing results.     

USING A FUNCTIONAL LANGUAGE FOR PARSING AND SEMANTIC PROCESSING

This paper describes an original approach to semantics representation based on the use of a non-strict functional programming language with polymorphic typing. This approach provides a unified formalism needing no preprocessing or postprocessing to the functional language itself: parsing and semantics are declared naturally using function definition and evaluation is done by lambda application along the lines of Montague. We show that by changing only the model we can, after parsing, compute either the truth value of a sentence or its parse tree.     

Hydrolysis and Ultrafiltration Treatment to Improve the Nutritive Value of Rapeseed Proteins

In order to improve their nutritive value, rapeseed proteins were hydrolyzed with pepsin (60 min) and trypsin (120 min). The hydrolysate was centrifuged at 10,000 ×g for 10 mln and the soluble fraction was ultrafiltered with a Romicon cartridge having a molecular weight cut-off of 10,000 daltons. Nutritional experiments with rats demonstrated that the net protein ratios obtained with rapeseed hydrolysate and ultrafdtrate (4.68 and 4.55 respectively) were higher (P < 0.05) than that of casein (4.40). The protein digestibility of the ultrafiltrate (90.3) was not different from that of casein (91.1) but higher than that of raw rapeseed flour (81.9). These hydrolysis and ultrafiltration treatments improved the nutritive value of rapeseed proteins by permitting the isolation of by-products of a molecular weight lower than 5000 daltons.     

Internal Friction of Simple Alkali Silicate Glasses Containing Alkaline-Earth Oxides: II, Interpretation and Discussion

The results of internal friction measurements on simple three-component glasses that were reported in Part I of this paper are discussed. From a consideration of the basic equations governing internal friction and examination of the results of other investigators, a basis of interpretation is developed. It is shown that changes in peak-temperature position can be explained by changes in the activation energy of the process causing the peak. A change in peak height not accompanied by a change in the shape of the peak is shown to be due to a change in the concentration of the relaxation mechanisms. Using this information the changes in the peaks due to composition variations are explained on a structural basis. A mechanism is also suggested to explain the new high-temperature peak. A critical examination of the measurements on alkali-free and phosphate glasses leads to the conclusion that it may be necessary to re-evaluate some of the concepts concerning the low-temperature peak in alkali silicate glasses.