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  1. This paper develops a framework for privatizing the spectrum of the Laplacian of an undirected graph using differential privacy. We consider two privacy formulations. The first obfuscates the presence of edges in the graph and the second obfuscates the presence of nodes. We compare these two privacy formulations and show that the privacy formulation that considers edges is better suited to most engineering applications. We use the bounded Laplace mechanism to provide (epsilon, delta)-differential privacy to the eigenvalues of a graph Laplacian, and we pay special attention to the algebraic connectivity, which is the Laplacian's the second smallest eigenvalue. Analytical bounds are presented on the accuracy of the mechanisms and on certain graph properties computed with private spectra. A suite of numerical examples confirms the accuracy of private spectra in practice. 
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    Free, publicly-accessible full text available March 1, 2025
  2. In cooperative multi-agent reinforcement learning (Co-MARL), a team of agents must jointly optimize the team's longterm rewards to learn a designated task. Optimizing rewards as a team often requires inter-agent communication and data sharing, leading to potential privacy implications. We assume privacy considerations prohibit the agents from sharing their environment interaction data. Accordingly, we propose Privacy-Engineered Value Decomposition Networks (PE-VDN), a Co-MARL algorithm that models multi-agent coordination while provably safeguarding the confidentiality of the agents' environment interaction data. We integrate three privacy-engineering techniques to redesign the data flows of the VDN algorithm-an existing Co-MARL algorithm that consolidates the agents' environment interaction data to train a central controller that models multi-agent coordination-and develop PE-VDN. In the first technique, we design a distributed computation scheme that eliminates Vanilla VDN's dependency on sharing environment interaction data. Then, we utilize a privacy-preserving multi-party computation protocol to guar-antee that the data flows of the distributed computation scheme do not pose new privacy risks. Finally, we enforce differential privacy to preempt inference threats against the agents' training data-past environment interactions-when they take actions based on their neural network predictions. We implement PE-VDN in StarCraft Multi-Agent Competition (SMAC) and show that it achieves 80% of Vanilla VDN's win rate while maintaining differential privacy levels that provide meaningful privacy guarantees. The results demonstrate that PE-VDN can safeguard the confidentiality of agents' environment interaction data without sacrificing multi-agent coordination. 
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    Free, publicly-accessible full text available December 13, 2024
  3. Stochastic matrices are commonly used to analyze Markov chains, but revealing them can leak sensitive information. Therefore, in this paper we introduce a technique to privatize stochastic matrices in a way that (i) conceals the probabilities they contain, and (ii) still allows for accurate analyses of Markov chains. Specifically, we use differential privacy, which is a statistical framework for protecting sensitive data. To implement it, we introduce the Matrix Dirichlet Mechanism, which is a probabilistic mapping that perturbs a stochastic matrix to provide privacy. We prove that this mechanism provides differential privacy, and we quantify the error induced in private stochastic matrices as a function of the strength of privacy being provided. We then bound the distance between the stationary distribution of the underlying, sensitive stochastic matrix and the stationary distribution of its privatized form. Numerical results show that, under typical conditions, privacy introduces error as low as 5.05% in the stationary distribution of a stochastic matrix. 
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  4. Free, publicly-accessible full text available January 1, 2025
  5. Abstract

    Phenotypic sexual dimorphism often involves the hormonal regulation of sex-biased expression for underlying genes. However, it is generally unknown whether the evolution of hormonally mediated sexual dimorphism occurs through upstream changes in tissue sensitivity to hormone signals, downstream changes in responsiveness of target genes, or both. Here, we use comparative transcriptomics to explore these possibilities in 2 species of Sceloporus lizards exhibiting different patterns of sexual dichromatism. Sexually dimorphic S. undulatus develops blue and black ventral coloration in response to testosterone, while sexually monomorphic S. virgatus does not, despite exhibiting similar sex differences in circulating testosterone levels. We administered testosterone implants to juveniles of each species and used RNAseq to quantify gene expression in ventral skin. Transcriptome-wide responses to testosterone were stronger in S. undulatus than in S. virgatus, suggesting species differences in tissue sensitivity to this hormone signal. Species differences in the expression of genes for androgen metabolism and sex hormone-binding globulin were consistent with this idea, but expression of the androgen receptor gene was higher in S. virgatus, complicating this interpretation. Downstream of androgen signaling, we found clear species differences in hormonal responsiveness of genes related to melanin synthesis, which were upregulated by testosterone in S. undulatus, but not in S. virgatus. Collectively, our results indicate that hormonal regulation of melanin synthesis pathways contributes to the development of sexual dimorphism in S. undulatus, and that changes in the hormonal responsiveness of these genes in S. virgatus contribute to the evolutionary loss of ventral coloration.

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