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Abstract The HIV reservoir consists of infected cells in which the HIV-1 genome persists as provirus despite effective antiretroviral therapy (ART). Studies exploring HIV cure therapies often measure intact proviral DNA levels, time to rebound after ART interruption, or ex vivo stimulation assays of latently infected cells. This study utilizes barcoded HIV to analyze the reservoir in humanized mice. Using bulk PCR and deep sequencing methodologies, we retrieve 890 viral RNA barcodes and 504 proviral barcodes linked to 15,305 integration sites at the single RNA or DNA molecule in vivo. We track viral genetic diversity throughout early infection, ART, and rebound. The proviral reservoir retains genetic diversity despite cellular clonal proliferation and viral seeding by rebounding virus. Non-proliferated cell clones are likely the result of elimination of proviruses associated with transcriptional activation and viremia. Elimination of proviruses associated with viremia is less prominent among proliferated cell clones. Proliferated, but not massively expanded, cell clones contribute to proviral expansion and viremia, suggesting they fuel viral persistence. This approach enables comprehensive assessment of viral levels, lineages, integration sites, clonal proliferation and proviral epigenetic patterns in vivo. These findings highlight complex reservoir dynamics and the role of proliferated cell clones in viral persistence. 

The spectral properties of traditional (dyadic) graphs, where an edge connects exactly two vertices, are widely studied in different applications. These spectral properties are closely connected to the structural properties of dyadic graphs. We generalize such connections and characterize higher-order networks by their spectral information. We first split the higher-order graphs by their “edge orders” into several uniform hypergraphs. For each uniform hypergraph, we extract the corresponding spectral information from the transition matrices of carefully designed random walks. From each spectrum, we compute the first few spectral moments and use all such spectral moments across different “edge orders” as the higher-order graph representation. We show that these moments not only clearly indicate the return probabilities of random walks but are also closely related to various higher-order network properties such as degree distribution and clustering coefficient. Extensive experiments show the utility of this new representation in various settings. For instance, graph classification on higher-order graphs shows that this representation significantly outperforms other techniques. 

Abstract Nonlocal models have demonstrated their indispensability in numerical simulations across a spectrum of critical domains, ranging from analyzing crack and fracture behavior in structural engineering to modeling anomalous diffusion phenomena in materials science and simulating convection processes in heterogeneous environments. In this study, we present a novel framework for constructing nonlocal convection–diffusion models using Gaussian‐type kernels. Our framework uniquely formulates the diffusion term by correlating the constant diffusion coefficient with the variance of the Gaussian kernel. Simultaneously, the convection term is defined by integrating the variable velocity field into the kernel as the expectation of a multivariate Gaussian distribution, facilitating a comprehensive representation of convective transport phenomena. We rigorously establish the well‐posedness of the proposed nonlocal model and derive a maximum principle to ensure its stability and reliability in numerical simulations. Furthermore, we develop a meshfree discretization scheme tailored for numerically simulating our model, designed to uphold both the discrete maximum principle and asymptotic compatibility. Through extensive numerical experiments, we validate the efficacy and versatility of our framework, demonstrating its superior performance compared to existing approaches. 

Network data has become widespread, larger, and more complex over the years. Traditional network data is dyadic, capturing the relations among pairs of entities. With the need to model interactions among more than two entities, significant research has focused on higher-order networks and ways to represent, analyze, and learn from them. There are two main directions to studying higher-order networks. One direction has focused on capturing higher-order patterns in traditional (dyadic) graphs by changing the basic unit of study from nodes to small frequently observed subgraphs, called motifs. As most existing network data comes in the form of pairwise dyadic relationships, studying higher-order structures within such graphs may uncover new insights. The second direction aims to directly model higher-order interactions using new and more complex representations such as simplicial complexes or hypergraphs. Some of these models have long been proposed, but improvements in computational power and the advent of new computational techniques have increased their popularity. Our goal in this paper is to provide a succinct yet comprehensive summary of the advanced higher-order network analysis techniques. We provide a systematic review of the foundations and algorithms, along with use cases and applications of higher-order networks in various scientific domains. 

Flowers are critical for successful reproduction and have been a major axis of diversification among angiosperms. As the frequency and severity of droughts are increasing globally, maintaining water balance of flowers is crucial for food security and other ecosystem services that rely on flowering. Yet remarkably little is known about the hydraulic strategies of flowers. We characterized hydraulic strategies of leaves and flowers of ten species by combining anatomical observations using light and scanning electron microscopy with measurements of hydraulic physiology (minimum diffusive conductance ( g min ) and pressure-volume (PV) curves parameters). We predicted that flowers would exhibit higher g min and higher hydraulic capacitance than leaves, which would be associated with differences in intervessel pit traits because of their different hydraulic strategies. We found that, compared to leaves, flowers exhibited: 1) higher g min , which was associated with higher hydraulic capacitance ( C T ); 2) lower variation in intervessel pit traits and differences in pit membrane area and pit aperture shape; and 3) independent coordination between intervessel pit traits and other anatomical and physiological traits; 4) independent evolution of most traits in flowers and leaves, resulting in 5) large differences in the regions of multivariate trait space occupied by flowers and leaves. Furthermore, across organs intervessel pit trait variation was orthogonal to variation in other anatomical and physiological traits, suggesting that pit traits represent an independent axis of variation that have as yet been unquantified in flowers. These results suggest that flowers, employ a drought-avoidant strategy of maintaining high capacitance that compensates for their higher g min to prevent excessive declines in water potentials. This drought-avoidant strategy may have relaxed selection on intervessel pit traits and allowed them to vary independently from other anatomical and physiological traits. Furthermore, the independent evolution of floral and foliar anatomical and physiological traits highlights their modular development despite being borne from the same apical meristem.