We study a pessimistic stochastic bilevel program in the context of sequential two-player games, where the leader makes a binary here-and-now decision, and the follower responds with a continuous wait-and-see decision after observing the leader’s action and revelation of uncertainty. We assume that only the information regarding the mean, covariance, and support is known. We formulate the problem as a distributionally robust (DR) two-stage problem. The pessimistic DR bilevel program is shown to be equivalent to a generic two-stage distributionally robust stochastic (nonlinear) program with both a random objective and random constraints under proper conditions of ambiguity sets. Under continuous distributions, using linear decision rule approaches, we construct upper bounds on the pessimistic DR bilevel program based on (1) a 0-1 semidefinite programming (SDP) approximation and (2) an exact 0-1 copositive programming reformulation. When the ambiguity set is restricted to discrete distributions, an exact 0-1 SDP reformulation is developed, and explicit construction of the worst-case distribution is derived. To further improve the computation of the proposed 0-1 SDPs, a cutting-plane framework is developed. Moreover, based on a mixed-integer linear programming approximation, another cutting-plane algorithm is proposed. Extensive numerical studies are conducted to demonstrate the effectiveness of the proposed approaches on a facility location problem. History: Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0168 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0168 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Recent observations have revealed that closely related strains of the same microbial species can stably coexist in natural and laboratory settings subject to boom and bust dynamics and serial dilutions, respectively. However, the possible mechanisms enabling the coexistence of only a handful of strains, but not more, have thus far remained unknown. Here, using a consumer-resource model of microbial ecosystems, we propose that by differentiating along Monod parameters characterizing microbial growth rates in high and low nutrient conditions, strains can coexist in patterns similar to those observed. In our model, boom and bust environments create satellite niches due to resource concentrations varying in time. These satellite niches can be occupied by closely related strains, thereby enabling their coexistence. We demonstrate that this result is valid even in complex environments consisting of multiple resources and species. In these complex communities, each species partitions resources differently and creates separate sets of satellite niches for their own strains. While there is no theoretical limit to the number of coexisting strains, in our simulations, we always find between 1 and 3 strains coexisting, consistent with known experiments and observations.

We investigate the problem of correlated subgraphs mining (CSM) where the goal is to identify pairs of subgraph patterns that frequently co-occur in proximity within a single graph. Correlated subgraph patterns are different from frequent subgraphs due to the flexibility in connections between constituent subgraph instances and thus, existing frequent subgraphs mining algorithms cannot be directly applied for CSM. Moreover, computing the degree of correlation between two patterns requires enumerating and finding distances between every pair of subgraph instances of both patterns - a task that is both memory-intensive as well as computationally demanding. To this end, we propose two holistic best-first exploration algorithms: CSM-E (an exact method) and CSM-A (a more efficient approximate method with near-optimal quality). To further improve efficiency, we propose a top- k pruning strategy, while to reduce memory footprint, we develop a compressed data structure called R eplica, which stores all instances of a subgraph pattern on demand. Our empirical results demonstrate that the proposed algorithms not only mine interesting correlations, but also achieve good scalability over large networks.

The human gut microbiome is a complex ecosystem, in which hundreds of microbial species and metabolites coexist, in part due to an extensive network of cross-feeding interactions. However, both the large-scale trophic organization of this ecosystem, and its effects on the underlying metabolic flow, remain unexplored. Here, using a simplified model, we provide quantitative support for a multi-level trophic organization of the human gut microbiome, where microbes consume and secrete metabolites in multiple iterative steps. Using a manually-curated set of metabolic interactions between microbes, our model suggests about four trophic levels, each characterized by a high level-to-level metabolic transfer of byproducts. It also quantitatively predicts the typical metabolic environment of the gut (fecal metabolome) in approximate agreement with the real data. To understand the consequences of this trophic organization, we quantify the metabolic flow and biomass distribution, and explore patterns of microbial and metabolic diversity in different levels. The hierarchical trophic organization suggested by our model can help mechanistically establish causal links between the abundances of microbes and metabolites in the human gut.