arXiv subjects

Guram Mikaberidze

Publications and source records attributed to Guram Mikaberidze.

7 recordsLinked to original sources

arXiv2026

Emergent Topology of Optimal Networks for Synchrony

Designing high-performing networks requires optimizing for functionality while respecting physical, spatial, or budget constraints. Yet, mathematical and computational tools to design such systems remain limited, particularly for collective dynamics arising from heterogeneous dynamical units. Here, we develop a gradient-based optimization framework to identify synchrony-optimal weighted networks under a constrained coupling budget. The resulting networks exhibit counterintuitive properties: they are sparse, bipartite, elongated, and extremely monophilic (i.e., the neighbors of any node are similar to one another while differing from the node itself). These structural patterns persist across dynamical models ranging from the power-grid swing equations to chaotic Rössler systems, suggesting broad applicability to coupled oscillator technologies. To gain insight, we develop a ``constructive'' theory for coupled Kuramoto oscillators: a nonlinear differential equation identifies which pairs of nodes are coupled, while a variational principle prescribes the budget allocated to each node. Dynamics unfolding over optimal networks provably lack a synchronization threshold; instead, as the budget exceeds a calculable critical value, the system globally phase-locks, exhibiting critical scaling at the transition. Together, our findings offer design principles for synchrony-dependent technologies with potential applications ranging from microgrids to laser arrays and quantum oscillators.

nlin.AO↗

arXiv2026

Optimality as a Generative Principle for Network Structure

Most real-world networks have evolved or been engineered to optimize some function, yet a unified framework for studying optimal networks across domains is lacking. We introduce GradNet, an AI-enabled framework that treats network topology as a continuously differentiable object, enabling the design and study of networks that optimize structural and dynamical objectives amenable to automatic differentiation under realistic constraints. We derive general optimality conditions, including an equimarginal principle for linear budgets, that make optimized networks analytically tractable. Canonical network features emerge spontaneously from constrained optimization: maximizing Kuramoto synchronization under coupling budgets yields sparse, bipartite, frequency-disassortative networks; minimizing social tension in opinion dynamics reproduces the factional split in Zachary's karate club; and maximizing communication capacity in spatial quantum networks under distance-dependent costs recovers minimum spanning trees. GradNet thus serves both as a network design tool scalable beyond $10^5$ nodes and as a scientific probe of structure-function relationships.

physics.soc-ph↗

arXiv2026

MoveBench: A Benchmark for Global-Scale Wildlife Movement Forecasting

Understanding and predicting wildlife movement is critical for ecology and conservation. While trajectory forecasting has advanced for human and vehicle movement, wildlife trajectories present distinct challenges: they are unconstrained in space, highly stochastic, and influenced by environmental conditions. We introduce MoveBench, the first large-scale benchmark for probabilistic wildlife movement forecasting, containing 2.6M GPS locations from 800+ individuals across 110 species in 127 countries, paired with 1.6B environmental raster tiles capturing 160 covariates known or hypothesized to influence movement. We propose a probabilistic evaluation protocol for movement trajectory forecasts, addressing limitations of point-prediction metrics for inherently stochastic phenomena. Through comprehensive empirical evaluation of four method families across multiple temporal and spatial scales, we reveal that: (1) existing predictive methods generalize better to future timepoints than to unseen individuals, (2) deep learning approaches do not consistently outperform simpler baselines, and (3) environmental covariate selection significantly impacts performance. MoveBench enables standardized evaluation of movement forecasting methods and provides a foundation for methodological advances on this ecologically important task.

cs.LG↗

arXiv2023

Consensus Formation Among Mobile Agents in Networks of Heterogeneous Interaction Venues

Exploring the collective behavior of interacting entities is of great interest and importance. Rather than focusing on static and uniform connections, we examine the co-evolution of diverse mobile agents experiencing varying interactions across both space and time. Analogous to the social dynamics of intrinsically diverse individuals who navigate between and interact within various physical or digital locations, agents in our model traverse a complex network of heterogeneous environments and engage with everyone they encounter. The precise nature of agents internal dynamics and the various interactions that nodes induce are left unspecified and can be tailored to suit the requirements of individual applications. We derive effective dynamical equations for agent states which are instrumental in investigating thresholds of consensus, devising effective attack strategies to hinder coherence, and designing optimal network structures with inherent node variations in mind. We demonstrate that agent cohesion can be promoted by increasing agent density, introducing network heterogeneity, and intelligently designing the network structure, aligning node degrees with the corresponding interaction strengths they facilitate. Our findings are applied to two distinct scenarios: the synchronization of brain activities between interacting individuals, as observed in recent collective MRI scans, and the emergence of consensus in a cusp catastrophe model of opinion dynamics.

physics.soc-ph↗

arXiv2023

Dragon kings in self-organized criticality systems

The spontaneous emergence of scale invariance, called self-organized criticality (SOC), is often attributed to a second-order absorbing-state phase transition (ASPT). Many real-world systems display SOC, yet extreme events are often overrepresented, causing significant disruption, and are called dragon kings (DK). We show analytically that the tradeoff between driving impulse and dissipation rate can create DKs in a second-order ASPT. This establishes that DKs exist in SOC systems, reveals a taxonomy of DKs, and shows that larger dissipation and smoother driving lower risk of extreme events.

nlin.AO↗

arXiv2022

Sandpile cascades on oscillator networks: the BTW model meets Kuramoto

Cascading failures abound in complex systems and the BTW sandpile model provides a theoretical underpinning for their analysis. Yet, it does not account for the possibility of nodes having oscillatory dynamics such as in power grids and brain networks. Here we consider a network of Kuramoto oscillators upon which the BTW model is unfolding, enabling us to study how the feedback between the oscillatory and cascading dynamics can lead to new emergent behaviors. We assume that the more out-of-sync a node is with its neighbors the more vulnerable it is and lower its load-carrying capacity accordingly. And when a node topples and sheds load, its oscillatory phase is reset at random. This leads to novel cyclic behavior at an emergent, long timescale. The system spends the bulk of its time in a synchronized state where load builds up with minimal cascades. Yet, eventually the system reaches a tipping point where a large cascade triggers a "cascade of larger cascades," which can be classified as a Dragon King event. The system then undergoes a short transient back to the synchronous, build-up phase. The coupling between capacity and synchronization gives rise to endogenous cascade seeds in addition to the standard exogenous ones, and we show their respective roles. We establish the phenomena from numerical studies and develop the accompanying mean-field theory to locate the tipping point, calculate the load in the system, determine the frequency of the long-time oscillations and find the distribution of cascade sizes during the build-up phase.

nlin.AO↗

arXiv2019

Convergent Momentum-Space OPE and Bootstrap Equations in Conformal Field Theory

General principles of quantum field theory imply that there exists an operator product expansion (OPE) for Wightman functions in Minkowski momentum space that converges for arbitrary kinematics. This convergence is guaranteed to hold in the sense of a distribution, meaning that it holds for correlation functions smeared by smooth test functions. The conformal blocks for this OPE are conceptually extremely simple: they are products of 3-point functions. We construct the conformal blocks in 2-dimensional conformal field theory and show that the OPE in fact converges pointwise to an ordinary function in a specific kinematic region. Using microcausality, we also formulate a bootstrap equation directly in terms of momentum space Wightman functions.

hep-th↗