For systems with long-range interactions, the two-body potential decays at large distances
as V (r)∼ 1/rα, with α≤ d, where d is the space dimension. Examples are: gravitational …

Locating multiple roots of nonlinear equation systems (NESs) remains a challenging and
meaningful task in the numerical optimization community. Although a large number of NES …

Graph theory is now becoming a standard tool in system-level neuroscience. However,
endowing observed brain anatomy and dynamics with a complex network structure does not …

Nonlinear Equations (NEs), which may usually have multiple roots, are ubiquitous in diverse
fields. One of the main purposes of solving NEs is to locate as many roots as possible …

We review the effects of excited-state quantum phase transitions (ESQPTs) in interacting
many-body systems with finite numbers of collective degrees of freedom. We classify typical …

Self-sustained dynamical phases of living matter can exhibit remarkable similarities over a
wide range of scales, from mesoscopic vortex structures in microbial suspensions and …

Functional brain networks are often constructed by quantifying correlations between time
series of activity of brain regions. Their topological structure includes nodes, edges …

Nonlinear equations system (NES) arises commonly in science and engineering. Repulsion
techniques are considered to be the effective methods to locate different roots of NES. In …

We use persistent homology and persistence images as an observable of three variants of
the two-dimensional XY model to identify and study their phase transitions. We examine …

Quantum systems with a finite number of freedom degrees f develop robust singularities in
the energy spectrum of excited states as the system's size increases to infinity. We analyze …