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1. Compress-and-Forward via Multilevel Coding

   Wan, H.; Host-Madsen, A.; Nosratinia, A. (July 2019, IEEE International Symposium on Information Theory)

   We investigate the performance of discrete (coded) modulations in the full-duplex compress-forward relay channel using multilevel coding. We numerically analyze the rates assigned to component binary codes of all levels. LDPC codes are used as the component binary codes to provide error protection. The compression at the relay is done via a nested scalar quantizer whose output is mapped to a codeword through LDPC codes. A compound Tanner graphical model and information-exchange algorithm are described for joint decoding of both messages sent from the source and relay. Simulation results show that the performance of the proposed system based on multilevel coding is better than that based on BICM, and is separated from the SNR threshold of the known CF achievable rate by two factors consisting approximately of the sum of the shaping gain (due to scalar quantization) and the separation of the LDPC code implementation from AWGN capacity. 

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2. Multilevel Network Alignment

   https://doi.org/10.1145/3308558.3313484  

   Zhang, Si; Tong, Hanghang; Maciejewski, Ross; Eliassi-Rad, Tina (January 2019, WWW '19 The World Wide Web Conference)

   Network alignment, which aims to find the node correspondence across multiple networks, is a fundamental task in many areas, ranging from social network analysis to adversarial activity detection. The state-of-the-art in the data mining community often view the node correspondence as a probabilistic cross-network node similarity, and thus inevitably introduce an O(n2) lower bound on the computational complexity. Moreover, they might ignore the rich patterns (e.g., clusters) accompanying the real networks. In this paper, we propose a multilevel network alignment algorithm (Moana) which consists of three key steps. It first efficiently coarsens the input networks into their structured representations, and then aligns the coarsest representations of the input networks, followed by the interpolations to obtain the alignment at multiple levels including the node level at the finest granularity. The proposed coarsen-align-interpolate method bears two key advantages. First, it overcomes the O(n2) lower bound, achieving a linear complexity. Second, it helps reveal the alignment between rich patterns of the input networks at multiple levels (e.g., node, clusters, super-clusters, etc.). Extensive experimental evaluations demonstrate the efficacy of the proposed algorithm on both the node-level alignment and the alignment among rich patterns (e.g., clusters) at different granularities. 

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3. Multilevel Decision‐Making and Protected Area Prioritization

   https://doi.org/10.1111/nrm.70004  

   Armsworth, Paul R; Dilkina, Bistra; Jackson, Heather B; Kroetz, Kailin; Sims, Charles (August 2025, Natural Resource Modeling)

   ABSTRACT Conservation initiatives depend on interactions among organizations and communities that have different goals. Multilevel hierarchies provide a common decision‐making structure with different actors responsible for conservation decisions over nested spatial scales. We examine consequences of hierarchical decision‐making for spatial prioritization of new protected areas. We combine insights from general theory, an algebraic example, and a numerical application, the latter motivated by federal‐to‐state grant‐giving in the western United States. Working through a decision‐making hierarchy means fewer species can be protected for a given budget than suggested by analyses that ignore the role of conservation institutions in decision‐making. This efficiency cost results from higher level decision‐makers—the federal government in our numerical application—giving up control to lower level actors—state governments in this case. Ensuring close agreement over spatial priorities between actors can limit potential losses in how much biodiversity can be protected. By reallocating funds among lower level actors, the higher level actor can mitigate remaining losses. Spatial optimization approaches that ignore the integral role of institutions in conservation, like decision‐making hierarchies, overestimate what protected area programs can achieve and risk misallocating limited conservation funds. Accounting for multilevel decision‐making reveals where building consensus among actors will be particularly important and suggests alternative strategies that conservation funders can pursue. 

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4. Cyclic and multilevel causation in evolutionary processes

   https://doi.org/10.1007/s10539-020-09753-3  

   Warrell, Jonathan; Gerstein, Mark (October 2020, Biology & Philosophy)

   null (Ed.)

   Abstract Many models of evolution are implicitly causal processes. Features such as causal feedback between evolutionary variables and evolutionary processes acting at multiple levels, though, mean that conventional causal models miss important phenomena. We develop here a general theoretical framework for analyzing evolutionary processes drawing on recent approaches to causal modeling developed in the machine-learning literature, which have extended Pearls do-calculus to incorporate cyclic causal interactions and multilevel causation. We also develop information-theoretic notions necessary to analyze causal information dynamics in our framework, introducing a causal generalization of the Partial Information Decomposition framework. We show how our causal framework helps to clarify conceptual issues in the contexts of complex trait analysis and cancer genetics, including assigning variation in an observed trait to genetic, epigenetic and environmental sources in the presence of epigenetic and environmental feedback processes, and variation in fitness to mutation processes in cancer using a multilevel causal model respectively, as well as relating causally-induced to observed variation in these variables via information theoretic bounds. In the process, we introduce a general class of multilevel causal evolutionary processes which connect evolutionary processes at multiple levels via coarse-graining relationships. Further, we show how a range of fitness models can be formulated in our framework, as well as a causal analog of Prices equation (generalizing the probabilistic Rice equation), clarifying the relationships between realized/probabilistic fitness and direct/indirect selection. Finally, we consider the potential relevance of our framework to foundational issues in biology and evolution, including supervenience, multilevel selection and individuality. Particularly, we argue that our class of multilevel causal evolutionary processes, in conjunction with a minimum description length principle, provides a conceptual framework in which identification of multiple levels of selection may be reduced to a model selection problem. 

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5. Improving Multilevel Regression and Poststratification with Structured Priors

   https://doi.org/10.1214/20-BA1223  

   Gao, Yuxiang; Kennedy, Lauren; Simpson, Daniel; Gelman, Andrew (September 2021, Bayesian Analysis)