Idempotent Analysis

1992 ◽  
Keyword(s):  
Idempotent Analysis

Axiomatics of thermodynamics and idempotent analysis

Idempotency ◽  
1998 ◽  
pp. 416-419 ◽  
Author(s):  
Victor P. Maslov
Keyword(s):  
Idempotent Analysis

Idempotent Analysis and Its Applications

1997 ◽  
Author(s):  
Vassili N. Kolokoltsov ◽  
Victor P. Maslov
Keyword(s):  
Idempotent Analysis

scholarly journals The Rényi Entropies Operate in Positive Semifields

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 780 ◽  
Author(s):  
Francisco J. Valverde-Albacete ◽  
Carmen Peláez-Moreno
Keyword(s):  
Computational Intelligence ◽  
Viterbi Algorithm ◽  
Morphological Processing ◽  
Information Function ◽  
Tropical Algebra ◽  
Idempotent Analysis ◽  
Standard Product ◽  
Rényi Entropies ◽  
Domain Transformation ◽  
Renyi Entropies

We set out to demonstrate that the Rényi entropies are better thought of as operating in a type of non-linear semiring called a positive semifield. We show how the Rényi’s postulates lead to Pap’s g-calculus where the functions carrying out the domain transformation are Rényi’s information function and its inverse. In its turn, Pap’s g-calculus under Rényi’s information function transforms the set of positive reals into a family of semirings where “standard” product has been transformed into sum and “standard” sum into a power-emphasized sum. Consequently, the transformed product has an inverse whence the structure is actually that of a positive semifield. Instances of this construction lead to idempotent analysis and tropical algebra as well as to less exotic structures. We conjecture that this is one of the reasons why tropical algebra procedures, like the Viterbi algorithm of dynamic programming, morphological processing, or neural networks are so successful in computational intelligence applications. But also, why there seem to exist so many computational intelligence procedures to deal with “information” at large.

Idempotent Analysis

1997 ◽  
pp. 1-44 ◽  
Author(s):  
Vassili N. Kolokoltsov ◽  
Victor P. Maslov
Keyword(s):  
Idempotent Analysis

On linear, additive, and homogeneous operators in idempotent analysis

1992 ◽  
pp. 87-102 ◽  
Author(s):  
V. Kolokoltsov
Keyword(s):  
Idempotent Analysis ◽  
Homogeneous Operators

Some Relations Between Linear Mappings and Conjugations in Idempotent Analysis

2001 ◽  
Vol 34 (13) ◽  
pp. 31-42
Author(s):  
Ivan Singer
Keyword(s):  
Idempotent Analysis

Thermodynamics, idempotent analysis, and tropical geometry as a return to primitivism

2016 ◽  
Vol 23 (2) ◽  
pp. 278-280
Author(s):  
V. P. Maslov
Keyword(s):  
Tropical Geometry ◽  
Idempotent Analysis

scholarly journals Idempotent analysis and its applications

1997 ◽  
Vol 34 (10) ◽  
pp. 142
Keyword(s):  
Idempotent Analysis

The Lagrange problem from the point of view of idempotent analysis

Idempotency ◽  
1998 ◽  
pp. 303-321 ◽  
Author(s):  
Serguei Samborskii
Keyword(s):  
Point Of View ◽  
Lagrange Problem ◽  
Idempotent Analysis
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