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  1. Massoulie, Laurent (Ed.)
    Spreading processes on graphs arise in a host of application domains, from the study of online social networks to viral marketing to epidemiology. Various discrete-time probabilistic models for spreading processes have been proposed. These are used for downstream statistical estimation and prediction problems, often involving messages or other information that is transmitted along with infections caused by the process. These models generally model cascade behavior at a small time scale but are insufficiently flexible to model cascades that exhibit intermittent behavior governed by multiple scales. We argue that the presence of such time scales that are unaccounted for by a cascade model can result in degradation of performance of models on downstream statistical and time-sensitive optimization tasks. To address these issues, we formulate a model that incorporates multiple temporal scales of cascade behavior. This model is parameterized by a \emph{clock}, which encodes the times at which sessions of cascade activity start. These sessions are themselves governed by a small-scale cascade model, such as the discretized independent cascade (IC) model. Estimation of the multiscale cascade model parameters leads to the problem of \emph{clock estimation} in terms of a natural distortion measure that we formulate. Our framework is inspired by the optimization problem posed by DiTursi et al, 2017, which can be seen as providing one possible estimator (a maximum-proxy-likelihood estimator) for the parameters of our generative model. We give a clock estimation algorithm, which we call FastClock, that runs in linear time in the size of its input and is provably statistically accurate for a broad range of model parameters when cascades are generated from any spreading process model with well-concentrated session infection set sizes and when the underlying graph is at least in the semi-sparse regime. We exemplify our algorithm for the case where the small-scale model is the discretized independent cascade process and extend substantially to processes whose infection set sizes satisfy a general martingale difference property. We further evaluate the performance of FastClock empirically in comparison to the state of the art estimator from DiTursi et al, 2017. We find that in a broad parameter range on synthetic networks and on a real network, our algorithm substantially outperforms that algorithm in terms of both running time and accuracy. In all cases, our algorithm's running time is asymptotically lower than that of the baseline. 
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  2. DNA-stabilized silver nanoclusters (AgN-DNAs) are a class of nanomaterials comprised of 10-30 silver atoms held together by short synthetic DNA template strands. AgN-DNAs are promising biosensors and fluorophores due to their small sizes, natural compatibility with DNA, and bright fluorescence---the property of absorbing light and re-emitting light of a different color. The sequence of the DNA template acts as a "genome" for AgN-DNAs, tuning the size of the encapsulated silver nanocluster, and thus its fluorescence color. However, current understanding of the AgN-DNA genome is still limited. Only a minority of DNA sequences produce highly fluorescent AgN-DNAs, and the bulky DNA strands and complex DNA-silver interactions make it challenging to use first principles chemical calculations to understand and design AgN-DNAs. Thus, a major challenge for researchers studying these nanomaterials is to develop methods to employ observational data about studied AgN-DNAs to design new nanoclusters for targeted applications. In this work, we present an approach to design AgN-DNAs by employing variational autoencoders (VAEs) as generative models. Specifically, we employ an LSTM-based β-VAE architecture and regularize its latent space to correlate with AgN-DNA properties such as color and brightness. The regularization is adaptive to skewed sample distributions of available observational data along our design axes of properties. We employ our model for design of AgN-DNAs in the near-infrared (NIR) band, where relatively few AgN-DNAs have been observed to date. Wet lab experiments validate that when employed for designing new AgN-DNAs, our model significantly shifts the distribution of AgN-DNA colors towards the NIR while simultaneously achieving bright fluorescence. This work shows that VAE-based generative models are well-suited for the design of AgN-DNAs with multiple targeted properties, with significant potential to advance the promising applications of these nanomaterials for bioimaging, biosensing, and other critical technologies. 
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