Abstract. Let E/F be a quadratic extension of p-adic fields. If π is an admissible representation of GLn(E) that is parabolically induced from discrete series representations, then we prove that the space of Pn(F )-invariant linear functionals on π has dimension one, where Pn(F ) is the mirabolic subgroup. As a corollary, it is deduced that if π is distinguished by GLn(F ), then the twisted tensor L-function associated to π has a pole at s = 0. It follows that if π is a discrete series representation, then at most one of the representations π and π ⊗ χ is distinguished, where χ is an extension of the local class field theory character associated to E/F . This is in agreement with a conjecture of Flicker and Rallis that relates the set of distinguished representations with the image of base change from a suitable unitary group.

According to the Center for Disease Control and Prevention, in the United States hundreds of thousands initiate smoking each year, and millions live with smoking-related diseases. Many tobacco users discuss their habits and preferences on social media. This work conceptualizes a framework for targeted health interventions to inform tobacco users about the consequences of tobacco use. We designed a Twitter bot named Notobot (short for No-Tobacco Bot) that leverages machine learning to identify users posting pro-tobacco tweets and select individualized interventions to address their interest in tobacco use. We searched the Twitter feed for tobacco-related keywords and phrases, and trained a convolutional neural network using over 4,000 tweets dichotomously manually labeled as either protobacco or not pro-tobacco. This model achieves a 90% recall rate on the training set and 74% on test data. Users posting protobacco tweets are matched with former smokers with similar interests who posted anti-tobacco tweets. Algorithmic matching, based on the power of peer influence, allows for the systematic delivery of personalized interventions based on real anti-tobacco tweets from former smokers. Experimental evaluation suggests that our system would perform well if deployed. This research offers opportunities for public health researchers to increase health awareness at scale. Future work entails deploying the fully operational Notobot system in a controlled experiment within a public health campaign.

With the tremendous increase in the number of smart phones, app stores have been overwhelmed with applications requiring geo-location access to provide their users better services through personalization. Revealing a user's location to these third-party apps, no matter at what frequency, is a severe privacy breach which can have unpleasant social consequences. In order to prevent inference attacks derived from geo-location data, a number of location obfuscation techniques have been proposed in the literature. However, none of them provides any objective measure of privacy guarantee. Some work has been done to define differential privacy for geo-location data in the form of geoindistinguishability with l privacy guarantee. These techniques do not utilize any prior background information about the Points of Interest (PoI s) of a user and apply Laplacian noise to perturb all the location coordinates. Intuitively, the utility of such a mechanism can be improved if the noise distribution is derived after considering some prior information about PoI s.In this paper, we apply the standard definition of differential privacy on geo-location data. We use first principles to model various privacy and utility constraints, prior background information available about the PoI s (distribu--tion of PoI locations in a 1D plane) and the granularity of the input required by different types of apps, to produce a more accurate and a utility maximizing differentially private algorithm for geo-location data at the OS level. We investigate this for a category of apps and for some specific scenarios. This will also help us to verify that whether Laplacian noise is still the optimal perturbation when we have such prior information.

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We look at a special case of a familiar problem: Given a locally compact group G, a subgroup H and a complex representation π + of G how does π + decompose on restriction to H .