Heterogeneous and complex networks represent intertwined interactions between real-world elements or agents. Determining the multiscale mesoscopic organization of clusters structures is still a fundamental open problem network theory. By taking advantage recent Laplacian renormalization group (LRG), we scrutinize information diffusion pathways throughout to shed further light on this issue. Based internode communicability, our definition provides clear-cut framework for resolving mesh in...

Scale invariance profoundly influences the dynamics and structure of complex systems, spanning from critical phenomena to network architecture. Here, we propose a precise definition scale-invariant networks by leveraging concept constant entropy-loss rate across scales in renormalization-group coarse-graining setting. This framework enables us differentiate between scale-free networks, revealing distinct characteristics within each class. Furthermore, offer comprehensive inventory genuinely...

The emergence of collective oscillations and synchronization is a widespread phenomenon in complex systems. While widely studied the setting dynamical systems, this not well understood context out-of-equilibrium phase transitions many-body Here we consider three classical lattice models, namely Ising, Blume-Capel, Potts provided with feedback among order control parameters. With help linear response theory derive low-dimensional nonlinear systems for mean-field cases. These quantitatively...

In view of the future plans to measure Lamb shift in muonic Lithium atoms we address microscopic theory \mu\, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>μ</mml:mi><mml:mspace width="0.167em" /></mml:mrow></mml:math> - ^6 display="inline"><mml:msup><mml:mi /><mml:mn>6</mml:mn></mml:msup></mml:math> Li ^{2+} /><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math> and ^7 /><mml:mn>7</mml:mn></mml:msup></mml:math>...

Scale invariance profoundly influences the dynamics and structure of complex systems, spanning from critical phenomena to network architecture. Here, we propose a precise definition scale-invariant networks by leveraging concept constant entropy loss rate across scales in renormalization-group coarse-graining setting. This framework enables us differentiate between scale-free networks, revealing distinct characteristics within each class. Furthermore, offer comprehensive inventory genuinely...

Heterogeneous and complex networks represent the intertwined interactions between real-world elements or agents. A fundamental problem of network theory involves finding inherent partitions, clusters, communities. By taking advantage recent Laplacian Renormalization Group approach, we scrutinize information diffusion pathways throughout to shed further light on this issue. Based inter-node communicability, our definition provides a unifying framework for multiple partitioning measures:...

The emergence of collective oscillations and synchronization is a widespread phenomenon in complex systems. While widely studied dynamical systems theory, this not well understood the context out-of-equilibrium phase transitions. Here we consider classical lattice models, namely Ising, Blume-Capel Potts with feedback among order control parameters. With linear response theory derive low-dimensional for mean field cases that quantitatively reproduce many-body stochastic simulations. In...

In view of the future plans to measure Lamb shift in muonic Lithium atoms we address microscopic theory $\mu$-$^6$Li$^{2+}$ and $\mu$-$^7$Li$^{2+}$ systems. The goal CREMA collaboration is extract charge radius with high precision compare it electron scattering data or atomic spectroscopy see if interesting puzzles, such as proton deuteron arise. For this experiment be successful, theoretical information on nuclear structure corrections needed. there exist only estimates based experimental...