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Differential privacy is the dominant standard for formal and quantifiable privacy and has been used in major deployments that impact millions of people. Many differentially private algorithms for query release and synthetic data contain steps that reconstruct answers to queries from answers to other queries that have been measured privately. Reconstruction is an important subproblem for such mecha- nisms to economize the privacy budget, minimize error on reconstructed answers, and allow for scalability to high-dimensional datasets. In this paper, we introduce a principled and efficient postprocessing method ReM (Residuals-to-Marginals) for reconstructing answers to marginal queries. Our method builds on recent work on efficient mechanisms for marginal query release, based on making measurements using a residual query basis that admits efficient pseudoinversion, which is an important primitive used in reconstruction. An extension GReM-LNN (Gaussian Residuals-to-Marginals with Local Non-negativity) reconstructs marginals under Gaussian noise satisfying consistency and non-negativity, which often reduces error on reconstructed answers. We demonstrate the utility of ReM and GReM-LNN by applying them to improve existing private query answering mechanisms. 

Advanced Air Mobility (AAM) presents an emerging alternative to traditional car driving for commuting in metropolitan areas. However, its feasibility has not been thoroughly studied nor well understood at the operational level. Given that AAM has not been in place, this study explores the economic, energy, and environmental feasibility of AAM for commuting at an early stage of AAM deployment. We propose a time expanded network model to characterize the dynamics of eVTOL operations between a vertiport pair in different states: in-service flying, relocation flying, charging, and parking, while respecting various operational and commuter time window constraints. By jointly considering eVTOL flying with vertiport access and egress and using real-world data, we demonstrate an application of the model in the Chicago metropolitan area in the US. Different vertiport pairs and eVTOL aircraft models are investigated. We find substantial travel time saving if commuting by AAM. While vehicle operating cost will be higher using eVTOLs than using auto, the generalized travel cost will be less for commuters. On the other hand, with current eVTOL power requirement, the energy consumption and CO2 emissions of AAM will be greater than those of auto driving, with an important contributor being the significance presence of empty flights relocation. These findings, along with sensitivity analysis, shed light on future eVTOL development to enhance the competitiveness of AAM as a viable option for commuting. 

Abstract <bold>Background</bold>Microorganisms are found in almost every environment, including soil, water, air and inside other organisms, such as animals and plants. While some microorganisms cause diseases, most of them help in biological processes such as decomposition, fermentation and nutrient cycling. Much research has been conducted on the study of microbial communities in various environments and how their interactions and relationships can provide insight into various diseases. Co-occurrence network inference algorithms help us understand the complex associations of micro-organisms, especially bacteria. Existing network inference algorithms employ techniques such as correlation, regularized linear regression, and conditional dependence, which have different hyper-parameters that determine the sparsity of the network. These complex microbial communities form intricate ecological networks that are fundamental to ecosystem functioning and host health. Understanding these networks is crucial for developing targeted interventions in both environmental and clinical settings. The emergence of high-throughput sequencing technologies has generated unprecedented amounts of microbiome data, necessitating robust computational methods for network inference and validation. <bold>Results</bold>Previous methods for evaluating the quality of the inferred network include using external data, and network consistency across sub-samples, both of which have several drawbacks that limit their applicability in real microbiome composition data sets. We propose a novel cross-validation method to evaluate co-occurrence network inference algorithms, and new methods for applying existing algorithms to predict on test data. Our method demonstrates superior performance in handling compositional data and addressing the challenges of high dimensionality and sparsity inherent in real microbiome datasets. The proposed framework also provides robust estimates of network stability. <bold>Conclusions</bold>Our empirical study shows that the proposed cross-validation method is useful for hyper-parameter selection (training) and comparing the quality of inferred networks between different algorithms (testing). This advancement represents a significant step forward in microbiome network analysis, providing researchers with a reliable tool for understanding complex microbial interactions. The method’s applicability extends beyond microbiome studies to other fields where network inference from high-dimensional compositional data is crucial, such as gene regulatory networks and ecological food webs. Our framework establishes a new standard for validation in network inference, potentially accelerating discoveries in microbial ecology and human health. 

Variability of oxygen isotopes in environmental water is recorded in tooth enamel, providing a record of seasonal change, dietary variability, and mobility. Physiology dampens this variability, however, as oxygen passes from environmental sources into blood and forming teeth. We showcase two methods of high resolution, 2-dimensional enamel sampling, and conduct modeling, to report why and how environmental oxygen isotope variability is reduced in animal bodies and teeth. First, using two modern experimental sheep, we introduce a sampling method, die-saw dicing, that provides high-resolution physical samples (n = 109 and 111 sample locations per tooth) for use in conventional stable isotope and molecular measurement protocols. Second, we use an ion microprobe to sample innermost enamel in an experimental sheep (n = 156 measurements), and in a Pleistocene orangutan (n = 176 measurements). Synchrotron and conventional μCT scans reveal innermost enamel thicknesses averaging 18 and 21 μm in width. Experimental data in sheep show that compared to drinking water, oxygen isotope variability in blood is reduced to 70–90 %; inner and innermost enamel retain between 36 and 48 % of likely drinking water stable isotope range, but this recovery declines to 28–34 % in outer enamel. 2D isotope sampling suggests that declines in isotopic variability, and shifted isotopic oscillations throughout enamel, result from the angle of secretory hydroxyapatite deposition and its overprinting by maturation. This overprinting occurs at all locations including innermost enamel, and is greatest in outer enamel. These findings confirm that all regions of enamel undergo maturation to varying degrees and confirm that inner and innermost enamel preserve more environmental variability than other regions. We further show how the resolution of isotope sampling — not only the spatial resolution within teeth, but also the temporal resolution of water in the environment — impacts our estimate of how much variation teeth recover from the environment. We suggest inverse methods, or multiplication by standard factors determined by ecology, taxon, and sampling strategy, to reconstruct the full scale of seasonal environmental variability. We advocate for combined inverse modeling and high-resolution sampling informed by the spatiotemporal pattern of enamel formation, and at the inner or innermost enamel when possible, to recover seasonal records from teeth. 

A series of 1,3,5,7-tetraphenyl-aza-BODIPY dyes functionalized with electron-donating or withdrawing groups at the para-positions of the phenyl rings on either the 1,7- or 3,5-positions were synthesized and characterized. The electron-donating group selected was –NH2, while the electron-withdrawing groups spanned a range of strengths, from strong (-NO2) to moderate (-NH3+) and mild (-Ndouble bondCdouble bondS). The structural modifications were strategically implemented to investigate their impact on the dyes photophysical properties. Spectroscopic studies revealed that these dyes exhibit intense absorption and emission in the near-infrared (NIR) region (678–855 nm). The photophysical properties, including molar absorptivity, fluorescence quantum yield, and Stokes shift were found to depend significantly on both the electronic nature (donating/withdrawing) and positioning (1,7- vs. 3,5-) of the substituents. Complementary computational studies provided insights into the electronic structures and excited-state dynamics, corroborating experimental observations. Time-dependent density functional theory (TD-DFT) calculations revealed that the electron density distribution and the frontier orbitals’ energies and shapes were significantly influenced by the electronic effects of the substituent groups. This study underscores the tunability of aza-BODIPY dyes through rational molecular design, enabling precise control over their optical properties for tailored NIR applications.