On large deviations and relative entropy of Markov random fields

Author(s):  
H. Föllmer
2008 ◽  
Vol 380 ◽  
pp. 3-14
Author(s):  
Elena Beretta ◽  
Alberto Gandolfi ◽  
C.C.A. Sastri

We present some examples of mathematical discoveries whose original import was mainly theoretical but which later ended up triggering extraordinary ad- vances in engineering, sometimes all the way down to technological realizations and market products. The examples we cite include Markov chains and Markov random fields, spin glasses, large deviations and the inverse conductivity problem, and their effects in various areas such as communication and imaging technologies.


2008 ◽  
Vol 48 ◽  
pp. 1041 ◽  
Author(s):  
Daniel Peter Simpson ◽  
Ian W. Turner ◽  
A. N. Pettitt

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1389
Author(s):  
Julia García Cabello ◽  
Pedro A. Castillo ◽  
Maria-del-Carmen Aguilar-Luzon ◽  
Francisco Chiclana ◽  
Enrique Herrera-Viedma

Standard methodologies for redesigning physical networks rely on Geographic Information Systems (GIS), which strongly depend on local demographic specifications. The absence of a universal definition of demography makes its use for cross-border purposes much more difficult. This paper presents a Decision Making Model (DMM) for redesigning networks that works without geographical constraints. There are multiple advantages of this approach: on one hand, it can be used in any country of the world; on the other hand, the absence of geographical constraints widens the application scope of our approach, meaning that it can be successfully implemented either in physical (ATM networks) or non-physical networks such as in group decision making, social networks, e-commerce, e-governance and all fields in which user groups make decisions collectively. Case studies involving both types of situations are conducted in order to illustrate the methodology. The model has been designed under a data reduction strategy in order to improve application performance.


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