Demystification of entangled Mass Action Law.

Recently, Gorban (2021) analysed some kinetic paradoxes of the transition state theory and proposed its revision that gave the "entangled mass action law", in which new reactions were generated as an addition to the reaction mechanism under consideration. These paradoxes arose due to the assumption of quasi-equilibrium between reactants and transition states. In this paper, we provided a brief introduction to this theory, demonstrating how the entangled mass action law equations can be derived in the framework of the standard quasi steady state approximation in combination with the quasi-equilibrium generalized mass action law for an auxiliary reaction network including reactants and intermediates.

Rosenblatt's First Theorem and Frugality of Deep Learning.

The Rosenblatt's first theorem about the omnipotence of shallow networks states that elementary perceptrons can solve any classification problem if there are no discrepancies in the training set. Minsky and Papert considered elementary perceptrons with restrictions on the neural inputs: a bounded number of connections or a relatively small diameter of the receptive field for each neuron at the hidden layer. They proved that under these constraints, an elementary perceptron cannot solve some problems, such as the connectivity of input images or the parity of pixels in them.

[Homeostatic non-shivering thermogenesis in man: facts and speculations].

In this review it is considered up-to date researches of different forms of non-shivering thermogenesis that related to thermoregulatory and substrate homeostasis. Term "homeostatic non-shivering thermogenesis (HNST)" is proposed for explanation of facultative heat production stimulated by cold exposure, food intake and accumulation of lactate during intensive muscle load. There are common and different features of physiological activity displayed in three HNST types.

[Human temperature portrait and its relations with aerobic working capacity and the level of blood lactate].

In study with participation of 53 healthy men volunteers and infra-red thermograph application we obtained data confirming thermal portrait (i.e. skin temperature distribution in muscle rest conditions with minimal thermoregulatory activation) interrelations with maximal aerobic capacity (r = +0.