Social media treats all users the same: trusted friend or total stranger, with little or nothing in between. In reality, relationships fall everywhere along this spectrum, a topic social science has investigated for decades under the theme of tie strength. Our work bridges this gap between theory and practice. In this paper, we present a predictive model that maps social media data to tie strength. The model builds on a dataset of over 2,000 social media ties and performs quite well, distinguishing between strong and weak ties with over 85% accuracy. We complement these quantitative findings with interviews that unpack the relationships we could not predict. The paper concludes by illustrating how modeling tie strength can improve social media design elements, including privacy controls, message routing, friend introductions and information prioritization.

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The inherent nature of social media content poses serious challenges to practical applications of sentiment analysis. We present VADER, a simple rule-based model for general sentiment analysis, and compare its effectiveness to eleven typical state-of-practice benchmarks including LIWC, ANEW, the General Inquirer, SentiWordNet, and machine learning oriented techniques relying on Naive Bayes, Maximum Entropy, and Support Vector Machine (SVM) algorithms. Using a combination of qualitative and quantitative methods, we first construct and empirically validate a gold-standard list of lexical features (along with their associated sentiment intensity measures) which are specifically attuned to sentiment in microblog-like contexts. We then combine these lexical features with consideration for five general rules that embody grammatical and syntactical conventions for expressing and emphasizing sentiment intensity. Interestingly, using our parsimonious rule-based model to assess the sentiment of tweets, we find that VADER outperforms individual human raters (F1 Classification Accuracy = 0.96 and 0.84, respectively), and generalizes more favorably across contexts than any of our benchmarks.

This paper considers the characterization and computation of invariant sets for discrete‐time, time‐invariant, linear systems with disturbance inputs whose values are confined to a specified compact set but are otherwise unknown. The emphasis is on determining maximal disturbance‐invariant sets X that belong to a specified subset Γ of the state space. Such d‐invariant sets have important applications in control problems where there are pointwise‐in‐time state constraints of the form χ(t) ∈ Γ . One purpose of the paper is to unite and extend in a rigorous way disparate results from the prior literature. In addition there are entirely new results. Specific contributions include: exploitation of the Pontryagin set difference to clarify conceptual matters and simplify mathematical developments, special properties of maximal invariant sets and conditions for their finite determination, algorithms for generating concrete representations of maximal invariant sets, practical computational questions, extension of the main results to general Lyapunov stable systems, applications of the computational techniques to the bounding of state and output response. Results on Lyapunov stable systems are applied to the implementation of a logic‐based, nonlinear multimode regulator. For plants with disturbance inputs and state‐control constraints it enlarges the constraint‐admissible domain of attraction. Numerical examples illustrate the various theoretical and computational results.

An efficient and reliable algorithm for computing the Euclidean distance between a pair of convex sets in R m is described. Extensive numerical experience with a broad family of polytopes in R 3 shows that the computational cost is approximately linear in the total number of vertices specifying the two polytopes. The algorithm has special features which makes its application in a variety of robotics problems attractive. These are discussed and an example of collision detection is given.