# gst: nonlocal Kramers-Moyal formulas and data-driven discovery of stochastic dynamical systems with multiplicative Lévy noise.

<< ️Traditional data-driven methods, effective for deterministic systems or stochastic differential equations (SDEs) with Gaussian noise, fail to handle the discontinuous sample paths and heavy-tailed fluctuations characteristic of Lévy processes, particularly when the noise is state-dependent. >>

<< ️To bridge this gap, (AA) establish nonlocal Kramers-Moyal formulas, rigorously generalizing the classical Kramers-Moyal relations to SDEs with multiplicative Lévy noise. These formulas provide a direct link between short-time transition probability densities (or sample path statistics) and the underlying SDE coefficients: the drift vector, diffusion matrix, Lévy jump measure kernel, and Lévy noise intensity functions. >>

<< This (AA) work provides a principled and practical toolbox for discovering interpretable SDE models governing complex systems influenced by discontinuous, heavy-tailed, state-dependent fluctuations, with broad applicability in climate science, neuroscience, epidemiology, finance, and biological physics. >>

Yang Li, Jinqiao Duan. Nonlocal Kramers-Moyal formulas and data-driven discovery of stochastic dynamical systems with multiplicative Lévy noise. arXiv: 2601.19223v1 [math.DS]. Jan 27, 2026.

https://arxiv.org/abs/2601.19223

Also: noise, random, transition, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, noise, randomness, transitions, fluctuations.

# gst: time-delayed dynamics in regular Kuramoto networks with inertia: multistability, traveling waves, chimera states, and transitions to seizure-like activity.

<< ️This (AA) study examines the complex interplay between inertia and time delay in regular rotor networks within the framework of the second-order Kuramoto model. By combining analytical and numerical methods, (AA) demonstrate that intrinsic time delays -- arising from finite information transmission speeds - induce multistability among fully synchronized phase-locked states. >>

<< ️Unlike systems without inertia, the presence of inertia destabilizes these phase-locked states, reduces their basin of attraction, and gives rise to nonlinear phase-locked dynamics over specific inertia ranges. >>

<< ️In addition, (They) show that time delays promote the emergence of turbulent chimera states, while inertia enhances their spatial extent. Notably, the combined influence of inertia and time delay produces dynamic patterns reminiscent of partial epileptic seizures. >>

Esmaeil Mahdavi, Mina Zarei, Philipp Hövel, Farhad Shahbazi. Time-Delayed Dynamics in Regular Kuramoto Networks with Inertia: Multistability, Traveling Waves, Chimera States, and Transitions to Seizure-Like Activity.  arXiv: 2512.16640v1 [nlin.AO]. Dec 18, 2025.

https://arxiv.org/abs/2512.16640

Also: network, transition, waves, chimera, turbulence, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, transitions, waves, chimera, turbulence, inertia, time delay, multistability, epileptic seizures.

# gst: from chimera states to spike avalanches and quasicriticality; the role of superdiffusive coupling.

<< ️The partial synchronization states of collective activity, as well as the spike avalanches realization in systems of interacting neurons, are extremely important distinguishing features of the neocortical circuits that have multiple empirical validations. However, at this stage, there is a limited number of studies highlighting their potential interrelationship at the level of nonlinear mathematical models. >>

<< ️In this study, (AA) investigate the development of chimera states and the emergence of spike avalanches in superdiffusive neural networks, as well as analyze the system's approach to quasicriticality. >>

<< ️The analysis of the available ideas suggests that partial synchronization states, spike avalanches, and quasicritical neuronal dynamics are all directly implicated in core cognitive functions such as information processing, attention, and memory. Given this fundamental role, the results presented in this (AA) work could have significant implications for both theoretical neuroscience and applied machine learning, particularly in the development of reservoir computing systems. >>

I. Fateev, A. Polezhaev. From chimera states to spike avalanches and quasicriticality: The role of superdiffusive coupling. Phys. Rev. E 113, 014215. Jan 20, 2026.

https://journals.aps.org/pre/abstract/10.1103/rmx5-8fys

Also: network, brain, neuro, behav, chimera, random, walk, walking, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, neuronal network models, chimera, random, walk, walking, avalanches, neuronal avalanches, collective behaviors, criticality.

# gst: quantum avalanche stability of many-body localization with power-law interactions.

<< ️(AA) investigate the stability of the many-body localized (MBL) phase against quantum avalanche instabilities in a one-dimensional Heisenberg spin chain with long-range power-law interactions (V ∝ r−α). >>

<< ️(They) finite-size scaling analysis of entanglement entropy identifies a critical interaction exponent αc ≈ 2, which separates a fragile regime, characterized by an exponentially diverging critical disorder, from a robust short-range regime. >>

<< ️(AA) results confirm that the MBL phase remains asymptotically stable in the thermodynamic limit when disorder exceeds an interaction-dependent threshold. >>

Longhui Shen, Bin Guo, Zhaoyu Sun. Quantum Avalanche Stability of Many-Body Localization with Power-Law Interactions. arXiv: 2601.13485v1 [cond-mat.dis-nn]. Jan 20, 2026.

https://arxiv.org/abs/2601.13485

Also: disorder, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, disorder, avalanche, avalanche stability, entanglement entropy, criticality. 

# gst: generation of disordered networks with targeted structural properties.

<< ️Disordered spatial networks are model systems that describe structures and interactions across multiple length scales. Scattering and interference of waves in these networks can give rise to structural phase transitions, localization, diffusion, and band gaps. >>

<< ️(AA) tune the degree and type of disorder introduced into initially crystalline networks by varying the bond-bending force constant in the strain energy and the temperature profile. >>

<< ️As a case study, (AA) statistically reproduce four disordered biophotonic networks exhibiting structural color. This work presents a versatile method for generating disordered networks with tailored structural properties. It will enable new insights into structure-property relations, such as photonic band gaps in disordered networks. >>

Florin Hemmann, Vincent Glauser, Ullrich Steiner, Matthias Saba. Computer Generation of Disordered Networks with Targeted Structural Properties. arXiv: 2601.10333v1 [cond-mat.dis-nn]. Jan 15, 2026.

https://arxiv.org/abs/2601.10333

Also: network, waves, disorder, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, disorder, disordered networks, waves, phase transitions.

# gst: dynamical entanglement percolation with spatially correlated disorder.

<< ️The distribution of entanglement between the nodes of a quantum network plays a fundamental role in quantum information applications. In this work, (AA) investigate the dynamics of a network of qubits where each edge corresponds to an independent two-qubit interaction. By applying tools from percolation theory, (They) study how entanglement dynamically spreads across the network. (They) show that the interplay between unitary evolution and spatially correlated disorder leads to a non-standard percolation phenomenology, significantly richer than uniform bond percolation and featuring hysteresis. >>

Lorenzo Cirigliano, Valentina Brosco, Claudio Castellano, et al. Dynamical entanglement percolation with spatially correlated disorder. arXiv: 2601.05925v1 [quant-ph]. Jan 9, 2026.

https://arxiv.org/abs/2601.05925

Also: network, disorder, in https://www.inkgmr.net/kwrds.html     qubit, in https://flashontrack.blogspot.com/search?q=qubit

Keywords: gst, networks, classical complex networks, quantum networks, qubit, disorder, percolation, entanglement, hysteresis.

# gst: wrinkling dynamics accelerate due to sudden changes in boundary conditions.

<< ️(AA) investigate the wrinkling dynamics of a long, flat filament immersed in a viscous fluid subjected to compression at a constant rate. Typical wrinkling dynamics proceed through three stages: initiation, development, and relaxation. The first stage, during which high mode perturbations increase exponentially while the shape and filament tension remain almost unchanged, is notably longer in the linear and nonlinear simulations than in the experiments by Chopin et al. [Phys. Rev. Lett. 119, 088001 (2017)]. >>

<< ️(AA) propose that sudden environmental changes introduce extra high-frequency perturbations beyond thermal fluctuations, which significantly accelerates the first stage. This effect is universal and inevitable for similar processes given the experimental conditions. >>

<< ️Finally, (They) analyze the relationship between the initial perturbations and the duration of the first stage. >>

Kai Liu, Wang Xiao, John Lowengrub, et al. Wrinkling dynamics accelerate due to sudden changes in boundary conditions. Phys. Rev. E 113, 015102. Jan 13, 2026.

https://journals.aps.org/pre/abstract/10.1103/18yj-mqqz

Also: transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transitions, wrinkling