Order-Stability in Complex Biological,Social, and AI-Systems from Quantum Information Theory

This paper is our attempt, on the basis of physical theory, to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem’s functioning is the ability to preserve its order structure or, in mathematical terms, to prevent increasing of entropy. However, Schrödinger’s analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schrödinger also appealed to the ambiguous notion of negative entropy. We apply quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of classical entropy. We consider a complex biosystem S composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, S=(Si). We study the following problem: whether the compound system S can maintain “global order” in the situation of an increase of local disorder and if S can preserve the low entropy while other Si increase their entropies (may be essentially). We show that the entropy of a system as a whole can be constant, while the entropies of its parts rising. For classical systems, this is impossible, because the entropy of S cannot be less than the entropy of its subsystem Si. And if a subsystems’s entropy increases, then a system’s entropy should also increase, by at least the same amount. However, within the quantum information theory, the answer is positive. The significant role is played by the entanglement of a subsystems’ states. In the absence of entanglement, the increasing of local disorder implies an increasing disorder in the compound system S (as in the classical regime). In this note, we proceed within a quantum-like approach to mathematical modeling of information processing by biosystems—respecting the quantum laws need not be based on genuine quantum physical processes in biosystems. Recently, such modeling found numerous applications in molecular biology, genetics, evolution theory, cognition, psychology and decision making. The quantum-like model of order stability can be applied not only in biology, but also in social science and artificial intelligence.     

Generation of finite subgroups of the mapping class group of genus 2 surface by Dehn twists

In this note we give presentations, up to conjugacy, of all finite subgroups of the mapping class group of a closed surface of genus 2, using the Humphries generators. An application to homology representations is given.     

Injective and automorphism-invariant non-singular modules

Every automorphism-invariant non-singular right A-module is injective if and only if the factor ring of the ring A with respect to its right Goldie radical is a right strongly semiprime ring.     

含硫氨基酸与本征及缺陷石墨烯表面的相互作用

半胱氨酸及蛋氨酸是人体的两种含硫氨基酸,在生物活性中发挥着巨大的作用.本研究采用密度泛函理论方法对以上两种氨基酸在本征及缺陷石墨烯表面的吸附机理进行了详细研究.主要考虑了两种吸附体系:半胱氨酸及蛋氨酸平躺在两种石墨烯表面;两种氨基酸垂直地放置于两种石墨烯表面,且含硫的基团靠近表面.研究结果表明,半胱氨酸及蛋氨酸初始构型对它们之间的相互作用有一定的影响.两种氨基酸平躺时有较大的吸附能.此外,吸附能的结果显示两种氨基酸可以更好的与缺陷石墨烯表面紧密结合.同时,蛋氨酸与本征及缺陷石墨烯相互作用均大于半胱氨酸与本征及缺陷石墨烯相互作用.模拟结果有望为含硫氨基酸的石墨烯传感器提供有用的指导.