A Universal Construction of Calogero-Moser System with Two Types Spins Interaction

2019 ◽  
Vol 71 (5) ◽  
pp. 533
Author(s):  
Jia-Liang Dai
2019 ◽  
Vol 198 (5) ◽  
pp. 1513-1540
Author(s):  
A. Ibort ◽  
G. Marmo ◽  
M. A. Rodríguez ◽  
P. Tempesta

2017 ◽  
Vol 40 ◽  
Author(s):  
Steven Phillips ◽  
Yuji Takeda

AbstractWe provide a mathematical category theory account of the size and location of the authors' Functional View Field (FVF). Category theory explains systematic cognitive ability via universal construction, that is, a necessary and sufficient condition for composition of cognitive processes. Similarly, FVF size and location is derived from a (universal) construction called a fibre (pullback) bundle.


2018 ◽  
Vol 17 (3) ◽  
pp. 258-280 ◽  
Author(s):  
A A Ellery

AbstractRecent work in developing self-replicating machines has approached the problem as an engineering problem, using engineering materials and methods to implement an engineering analogue of a hitherto uniquely biological function. The question is – can anything be learned that might be relevant to an astrobiological context in which the problem is to determine the general form of biology independent of the Earth. Compared with other non-terrestrial biology disciplines, engineered life is more demanding. Engineering a self-replicating machine tackles real environments unlike artificial life which avoids the problem of physical instantiation altogether by examining software models. Engineering a self-replicating machine is also more demanding than synthetic biology as no library of functional components exists. Everything must be constructed de novo. Biological systems already have the capacity to self-replicate but no engineered machine has yet been constructed with the same ability – this is our primary goal. On the basis of the von Neumann analysis of self-replication, self-replication is a by-product of universal construction capability – a universal constructor is a machine that can construct anything (in a functional sense) given the appropriate instructions (DNA/RNA), energy (ATP) and materials (food). In the biological cell, the universal construction mechanism is the ribosome. The ribosome is a biological assembly line for constructing proteins while DNA constitutes a design specification. For a photoautotroph, the energy source is ambient and the food is inorganic. We submit that engineering a self-replicating machine opens up new areas of astrobiology to be explored in the limits of life.


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