Banca de DEFESA: RUTE MELO DE OLIVEIRA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : RUTE MELO DE OLIVEIRA
DATE: 13/05/2022
TIME: 09:00
LOCAL: Google Meet
TITLE:

Connecting geographical complex networks q-Statistical

KEY WORDS:

Complex networks, Scale-Free networks, Nonextensive statistical mechanics

PAGES: 109
BIG AREA: Ciências Exatas e da Terra
AREA: Física
SUMMARY:

Networks are abound in nature, therefore, Network science is a very interdisciplinary theory and has been
widely successfully used to study huge connected systems. The nonextensive statistical mechanics
naturally emerge from the limitations of the BoltzmannGibbs statistic, being capable to describe systems
in the regimes where the standard statistical mechanics fails. Nowadays the connections between these
two areas are well known. In this thesis we study a d-dimensional geographically located network
(characterized by the index αG ≥ 0; d = 1, 2, 3, 4) whose links are weighted through a predefined random
probability distribution, namely P(w). In this model, each site has an evolving degree ki and a local
energy εi ≡ Pki j=1 wij/2 (i = 1, 2, ..., N) that depend on the weights of the links connected to it. At the
thermodynamic limit, the energy distribution is the form p(ε) ∝ exp(−βqε)_q , where exp(z)_q is the q-
exponential defined by exp(z)_q ≡ [1 + (1−q)z] 1/(1−q) which optimizes the non-additive entropy Sq and
when q → 1 the Boltzmann-Gibbs entropy is recovered. The parameters q and βq depends only on αA/d,
thus exhibiting universality. Also, we provide here strong numerical evidence that a isomorphism appears
to emerge connecting the energy q-exponential distribution (with q = 4/3 and βqω0 = 10/3) with a specific
geographic growth random model based on preferential attachment through exponentially-distributed
weighted links.

BANKING MEMBERS:
Externo à Instituição - CONSTANTINO TSALLIS - CBPF
Interno - 2492756 - JOAO MEDEIROS DE ARAUJO
Externo à Instituição - JOSÉ SOARES DE ANDRADE JÚNIOR - UFC
Presidente - 6346140 - LUCIANO RODRIGUES DA SILVA
Interno - 1294916 - MADRAS VISWANATHAN GANDHI MOHAN
Externa à Instituição - SAMURAÍ GOMES DE AGUIAR BRITO - UFRN