IMPORTANCEEvery day in the United States, more than 200 people are murdered or assaulted with a firearm. Little research has considered the role of interpersonal ties in the pathways through which gun violence spreads.OBJECTIVE To evaluate the extent to which the people who will become subjects of gun violence can be predicted by modeling gun violence as an epidemic that is transmitted between individuals through social interactions.DESIGN, SETTING, AND PARTICIPANTS This study was an epidemiological analysis of a social network of individuals who were arrested during an 8-year period in Chicago, Illinois, with connections between people who were arrested together for the same offense. Modeling of the spread of gunshot violence over the network was assessed using a probabilistic contagion model that assumed individuals were subject to risks associated with being arrested together, in addition to demographic factors, such as age, sex, and neighborhood residence. Participants represented a network of 138 163 individuals who were arrested between January 1, 2006, and March 31, 2014 (29.9% of all individuals arrested in Chicago during this period), 9773 of whom were subjects of gun violence. Individuals were on average 27 years old at the midpoint of the study, predominantly male (82.0%) and black (75.6%), and often members of a gang (26.2%). MAIN OUTCOMES AND MEASURESExplanation and prediction of becoming a subject of gun violence (fatal or nonfatal) using epidemic models based on person-to-person transmission through a social network.RESULTS Social contagion accounted for 63.1% of the 11 123 gunshot violence episodes; subjects of gun violence were shot on average 125 days after their infector (the person most responsible for exposing the subject to gunshot violence). Some subjects of gun violence were shot more than once. Models based on both social contagion and demographics performed best; when determining the 1.0% of people (n = 1382) considered at highest risk to be shot each day, the combined model identified 728 subjects of gun violence (6.5%) compared with 475 subjects of gun violence (4.3%) for the demographics model (53.3% increase) and 589 subjects of gun violence (5.3%) for the social contagion model (23.6% increase).CONCLUSIONS AND RELEVANCE Gunshot violence follows an epidemic-like process of social contagion that is transmitted through networks of people by social interactions. Violence prevention efforts that account for social contagion, in addition to demographics, have the potential to prevent more shootings than efforts that focus on only demographics.

In the classical experimental design setting, an experimenter E has access to a population of $n$ potential experiment subjects $i\in \{1,...,n\}$, each associated with a vector of features $x_i\in R^d$. Conducting an experiment with subject $i$ reveals an unknown value $y_i\in R$ to E. E typically assumes some hypothetical relationship between $x_i$'s and $y_i$'s, e.g., $y_i \approx \beta x_i$, and estimates $\beta$ from experiments, e.g., through linear regression. As a proxy for various practical constraints, E may select only a subset of subjects on which to conduct the experiment. We initiate the study of budgeted mechanisms for experimental design. In this setting, E has a budget $B$. Each subject $i$ declares an associated cost $c_i >0$ to be part of the experiment, and must be paid at least her cost. In particular, the Experimental Design Problem (EDP) is to find a set $S$ of subjects for the experiment that maximizes $V(S) = \log\det(I_d+\sum_{i\in S}x_i\T{x_i})$ under the constraint $\sum_{i\in S}c_i\leq B$; our objective function corresponds to the information gain in parameter $\beta$ that is learned through linear regression methods, and is related to the so-called $D$-optimality criterion. Further, the subjects are strategic and may lie about their costs. We present a deterministic, polynomial time, budget feasible mechanism scheme, that is approximately truthful and yields a constant factor approximation to EDP. In particular, for any small $\delta > 0$ and $\epsilon > 0$, we can construct a (12.98, $\epsilon$)-approximate mechanism that is $\delta$-truthful and runs in polynomial time in both $n$ and $\log\log\frac{B}{\epsilon\delta}$. We also establish that no truthful, budget-feasible algorithms is possible within a factor 2 approximation, and show how to generalize our approach to a wide class of learning problems, beyond linear regression

In recent years, social networking platforms have developed into extraordinary channels for spreading and consuming information. Along with the rise of such infrastructure, there is continuous progress on techniques for spreading information effectively through influential users. In many applications, one is restricted to select influencers from a set of users who engaged with the topic being promoted, and due to the structure of social networks, these users often rank low in terms of their influence potential. An alternative approach one can consider is an adaptive method which selects users in a manner which targets their influential neighbors. The advantage of such an approach is that it leverages the friendship paradox in social networks: while users are often not influential, they often know someone who is.Despite the various complexities in such optimization problems, we show that scalable adaptive seeding is achievable. In particular, we develop algorithms for linear influence models with provable approximation guarantees that can be gracefully parallelized. To show the effectiveness of our methods we collected data from various verticals social network users follow. For each vertical, we collected data on the users who responded to a certain post as well as their neighbors, and applied our methods on this data. Our experiments show that adaptive seeding is scalable, and importantly, that it obtains dramatic improvements over standard approaches of information dissemination.

This paper shows several connections between data structure problems and cryptography against preprocessing attacks. Our results span data structure upper bounds, cryptographic applications, and data structure lower bounds, as summarized next.First, we apply Fiat-Naor inversion, a technique with cryptographic origins, to obtain a data structure upper bound. In particular, our technique yields a suite of algorithms with space 𝑆 and (online) time 𝑇 for a preprocessing version of the 𝑁 -input 3SUM problem where 𝑆 3 •𝑇 = 𝑂 (𝑁 6 ). This disproves a strong conjecture (Goldstein et al., WADS 2017) that there is no data structure that solves this problem for 𝑆 = 𝑁 2−𝛿 and 𝑇 = 𝑁 1−𝛿 for any constant 𝛿 > 0.Secondly, we show equivalence between lower bounds for a broad class of (static) data structure problems and one-way functions in the random oracle model that resist a very strong form of preprocessing attack. Concretely, given a random function 𝐹 : [𝑁 ] → [𝑁 ] (accessed as an oracle) we show how to compile it into a function 𝐺 𝐹 : [𝑁 2 ] → [𝑁 2 ] which resists 𝑆-bit preprocessing attacks that run in query time 𝑇 where 𝑆𝑇 = 𝑂 (𝑁 2−𝜀 ) (assuming a corresponding data structure lower bound on 3SUM). In contrast, a classical result of Hellman tells us that 𝐹 itself can be more easily inverted, say with 𝑁 2/3 -bit preprocessing in 𝑁 2/3 time. We also show that much stronger lower bounds follow from the hardness of kSUM. Our results can be equivalently interpreted as security against adversaries that are very non-uniform, or have large auxiliary input, or as security in the face of a powerfully backdoored random oracle.Thirdly, we give non-adaptive lower bounds for 3SUM which match the best known lower bounds for static data structure problems. Moreover, we show that our lower bound generalizes to a range of geometric problems, such as three points on a line, polygon containment, and others.

In the Graph Inference problem, one seeks to recover the edges of an unknown graph from the observations of cascades propagating over this graph. We approach this problem from the sparse recovery perspective. We introduce a general model of cascades, including the voter model and the independent cascade model, for which we provide the first algorithm which recovers the graph's edges with high probability and O(s log m) measurements where s is the maximum degree of the graph and m is the number of nodes. Furthermore, we show that our algorithm also recovers the edge weights (the parameters of the diffusion process) and is robust in the context of approximate sparsity. Finally we validate our approach empirically on synthetic graphs.