In this chapter we give main definitions and useful facts of the theory of Gibbs measures of
lattice spin systems. In the first section we give general definitions. This chapter also …

We analyze the renormalization group fixed point of the two-dimensional Ising model at
criticality. In contrast with expectations from tensor network renormalization (TNR), we show …

Networks are crucial in structuring biological systems in terms of interactions, to investigate
the related properties and dynamics. Network analysis plays a relevant role in knowledge …

Cancers are complex adaptive diseases regulated by the nonlinear feedback systems
between genetic instabilities, environmental signals, cellular protein flows, and gene …

In this work we consider a superradiant phase transition problem for the Dicke-Ising model,
which generalizes the Dicke and Ising models for annealed complex networks presuming …

Chemical reaction networks are powerful tools for modeling cell signaling and its disruptions
in diseases like cancer. Realistic chemical reaction networks involve hundreds of proteins …

Genes communicate with each other through different regulatory effects, which lead to the
emergence of complex network structures in cells, and such structures are expected to be …

Critical transitions can be conceptualized as abrupt shifts in the state of a system typically
induced by changes in the system's critical parameter. They have been observed in a variety …

At the cellular level, cancer is triggered by mutations of the proteins involved in signalling
networks made of hundreds of reacting species. The corresponding mathematical model …

Machine learning has become a central technique for modeling in science and engineering,
either complementing or as surrogates to physics-based models. Significant efforts have …