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The prisoner's dilemma (PD) game is a simple model for understanding cooperative patterns in complex systems consisting of selfish individuals. Here, we study a PD game problem in scale-free networks containing hierarchically organized…
The physics of $k$-core percolation pertains to those systems whose constituents require a minimum number of $k$ connections to each other in order to participate in any clustering phenomenon. Examples of such a phenomenon range from…
Large-eddy simulation (LES) is a well-established numerical technique, which resolves the most energetic turbulent fluctuations in the planetary boundary layers. Averaging these fluctuations, high-quality profiles of mean values and…
During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous…
In this paper we have explored computationally the solidification process of large nickel clusters. This process has the characteristic features of the first order phase transition occurring in a finite system. The focus of our research is…
Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…
Hierarchical decision making problems, such as bilevel programs and Stackelberg games, are attracting increasing interest in both the engineering and machine learning communities. Yet, existing solution methods lack either convergence…
Lattice rules are among the most prominently studied quasi-Monte Carlo methods to approximate multivariate integrals. A rank-1 lattice rule to approximate an $s$-dimensional integral is fully specified by its generating vector $\mathbf{z}…
Percolation plays an important role in fields and phenomena as diverse as the study of social networks, the dynamics of epidemics, the robustness of electricity grids, conduction in disordered media, and geometric properties in statistical…
We investigate bond- and site-percolation models on several two-dimensional lattices numerically, by means of transfer-matrix calculations and Monte Carlo simulations. The lattices include the square, triangular, honeycomb kagome and diced…
We present an alternative geometric representation for the eleven Archimedean lattices, in which each site and bond is uniquely labeled by an ordered pair of integers and characterized via a modular function. This structured labeling…
Computer simulations of structure formation in network forming materials (such as amorphous semiconductors, glasses, or fluids containing hydrogen bonds) are challenging. The problem is that large structural changes in the network topology…
Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes. Such deletions include, for example, the failure of internet routers or…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
Cooperation played a significant role in the self-organization and evolution of living organisms. Both network topology and the initial position of cooperators heavily affect the cooperation of social dilemma games. We developed a novel…
Large Language Models (LLMs) exhibit exceptional proficiency in handling extensive context windows in natural language. Nevertheless, the quadratic scaling of attention computation relative to sequence length creates substantial efficiency…
Many random growth models have the property that the set of discovered sites, scaled properly, converges to some deterministic set as time grows. Such results are known as shape theorems. Typically, not much is known about the shapes. For…
In this work we investigate the problem of estimating the percolation centrality of every vertex in a graph. This centrality measure quantifies the importance of each vertex in a graph going through a contagious process. It is an open…
Graph pebbling is a combinatorial game played on an undirected graph with an initial configuration of pebbles. A pebbling move consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The pebbling…
We apply a variant of the explosive percolation procedure to large real-world networks, and show with finite-size scaling that the university class, ordinary or explosive, of the resulting percolation transition depends on the structural…