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Recent years witnessed the development of powerful generative models based on flows, diffusion, or autoregressive neural networks, achieving remarkable success in generating data from examples with applications in a broad range of areas. A theoretical analysis of the performance and understanding of the limitations of these methods remain, however, challenging. In this paper, we undertake a step in this direction by analyzing the efficiency of sampling by these methods on a class of problems with a known probability distribution and comparing it with the sampling performance of more traditional methods such as the Monte Carlo Markov chain and Langevin dynamics. We focus on a class of probability distribution widely studied in the statistical physics of disordered systems that relate to spin glasses, statistical inference, and constraint satisfaction problems. We leverage the fact that sampling via flow-based, diffusionbased, or autoregressive networks methods can be equivalently mapped to the analysis of a Bayes optimal denoising of a modified probability measure. Our findings demonstrate that these methods encounter difficulties in sampling stemming from the presence of a first-order phase transition along the algorithm's denoising path. Our conclusions go both ways: We identify regions of parameters where these methods are unable to sample efficiently, while that is possible using standard Monte Carlo or Langevin approaches. We also identify regions where the opposite happens: standard approaches are inefficient while the discussed generative methods work well. [ABSTRACT FROM AUTHOR]

During the last decades, macroecology has identified broad-scale patterns of abundances and diversity of microbial communities and put forward some potential explanations for them. However, these advances are not paralleled by a full understanding of the dynamical processes behind them. In particular, abundance fluctuations of different species are found to be correlated, both across time and across communities in metagenomic samples. Reproducing such correlations through appropriate population models remains an open challenge. The present paper tackles this problem and points to sparse species interactions as a necessary mechanism to account for them. Specifically, we discuss several possibilities to include interactions in population models and recognize Lotka-Volterra constants as a successful ansatz. For this, we design a Bayesian inference algorithm to extract sets of interaction constants able to reproduce empirical probability distributions of pairwise correlations for diverse biomes. Importantly, the inferred models still reproduce well-known single-species macroecological patterns concerning abundance fluctuations across both species and communities. Endorsed by the agreement with the empirically observed phenomenology, our analyses provide insights into the properties of the networks of microbial interactions, revealing that sparsity is a crucial feature. [ABSTRACT FROM AUTHOR]

Many studies anticipate that carbon capture and sequestration (CCS) will be essential to decarbonizing the U.S. economy. However, prior work has not estimated the time required to develop, approve, and implement a geologic sequestration site in the United States. We generate such an estimate by identifying six clearance points that must be passed before a sequestration site can become operational. For each clearance point (CP), we elicit expert judgments of the time required in the form of probability distributions and then use stochastic simulation to combine and sum the results. We find that, on average, there is a 90% chance that the time required lies between 5.5 and 9.6 y, with an upper bound of 12 y. Even using the most optimistic expert judgements, the lower bound on time is 2.7 y, and the upper bound is 8.3 y. Using the most pessimistic judgements, the lower bound is 3.5 y and the upper bound is 19.2 y. These estimates suggest that strategies must be found to safely accelerate the process. We conclude the paper by discussing seven potential strategies. [ABSTRACT FROM AUTHOR]