ELFT HÍRADÓ

[StatFizSzeminar <statfiz AT glu.elte.hu>]

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                   ELTE Institute of Physics
                SEMINARS IN STATISTICAL PHYSICS


                      Extraordinary time!


                        10th June 2016
                        Friday, 11 a.m.
                          Room 2.54

                       Zoltán Toroczkai

       Physics Department, University of Notre Dame, USA

                  "The physics of inference"


Jaynes's maximum entropy method provides a family of principled models that
allow the prediction of a system's properties as constrained by empirical data
(observables). However, their use is often hindered by the degeneracy problem
characterized by spontaneous symmetry breaking, where predictions fail. Here 
we
show that degeneracy appears when the corresponding density of states function
is not log-concave, which is typically the consequence of nonlinear
relationships between the constraining observables. We illustrate this
phenomenon on examples from a wide range of areas, including complex networks,
combinatorics and classical spin systems (e.g., Blume-Emery-Griffiths
lattice-spin models). Exploiting these nonlinear relationships here we 
propose a
solution to the degeneracy problem for a large class of systems via
transformations that render the density of states function log-concave. The
effectiveness of the method is demonstrated using real-world network data.
Finally, we discuss the implications of these findings on the relationship
between the geometrical properties of the density of states function and phase
transitions in spin systems.


     1117 Budapest, Pázmány P. sétány 1/A (Northern Block)
              home page: http://glu.elte.hu/~statfiz


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