Tim Pollmann and Jochen Staudacher

Complexities 2026, 2(1), 7

Shapley values are the most widely used point-valued solution concept for cooperative games and have recently garnered attention for their applicability in explainable machine learning. Due to the complexity of Shapley value computation, users mostly resort to Monte Carlo approximations for large problems. We take a detailed look at an approximation method grounded in multilinear extensions proposed in 2021 under the name “Owen sampling”. We point out why Owen sampling is biased and propose unbiased alternatives based on combining multilinear extensions with stratified sampling and importance sampling. Finally, we discuss empirical results of the presented algorithms for various cooperative games, including real-world explainability scenarios.

Read the full article at: www.mdpi.com

Kishore Vasan, Márton Karsai & Albert-László Barabási
Scientific Reports

The metaverse is a virtual space enabling interactions beyond geographical boundaries, promising to transform how people engage with each other both in the digital and the physical worlds. The lack of geographical boundaries and travel costs in the metaverse prompts us to ask if the fundamental laws that govern human mobility in the physical world apply. We collected data on avatar movements from Decentraland, along with their network mobility extracted from NFT purchases on Ethereum and Polygon. We find that despite the absence of mobility costs, an individual’s inclination to visit new locations diminishes over time, limiting movement to a small fraction of the metaverse. We also find a lack of correlation between land prices and visitation, a deviation from the patterns characterizing the physical world. Finally, we identify the scaling laws that characterize meta mobility and show that we need to add preferential selection to the existing models to explain quantitative patterns of metaverse mobility. Our ability to predict the characteristics of the emerging meta mobility network implies that the laws governing human mobility are rooted in fundamental patterns of human dynamics, rather than the nature of space and cost of movement.

Read the full article at: www.nature.com

Adams, Fred C.
Both the fundamental constants that describe the laws of physics and the cosmological parameters that determine the properties of our universe must fall within a range of values in order for the cosmos to develop astrophysical structures and ultimately support life. This paper reviews the current constraints on these quantities. The discussion starts with an assessment of the parameters that are allowed to vary. The standard model of particle physics contains both coupling constants (α ,αs ,αw) and particle masses (mu ,md ,me) , and the allowed ranges of these parameters are discussed first. We then consider cosmological parameters, including the total energy density of the universe (Ω) , the contribution from vacuum energy (ρΛ) , the baryon-to-photon ratio (η) , the dark matter contribution (δ) , and the amplitude of primordial density fluctuations (Q) . These quantities are constrained by the requirements that the universe lives for a sufficiently long time, emerges from the epoch of Big Bang Nucleosynthesis with an acceptable chemical composition, and can successfully produce large scale structures such as galaxies. On smaller scales, stars and planets must be able to form and function. The stars must be sufficiently long-lived, have high enough surface temperatures, and have smaller masses than their host galaxies. The planets must be massive enough to hold onto an atmosphere, yet small enough to remain non-degenerate, and contain enough particles to support a biosphere of sufficient complexity. These requirements place constraints on the gravitational structure constant (αG) , the fine structure constant (α) , and composite parameters (C⋆) that specify nuclear reaction rates. We then consider specific instances of possible fine-tuning in stellar nucleosynthesis, including the triple alpha reaction that produces carbon, the case of unstable deuterium, and the possibility of stable diprotons. For all of the issues outlined above, viable universes exist over a range of parameter space, which is delineated herein. Finally, for universes with significantly different parameters, new types of astrophysical processes can generate energy and thereby support habitability.

Read the full article at: ui.adsabs.harvard.edu