Service in Your Neighborhood: Fairness in Center Location

When selecting locations for a set of centers, standard clustering algorithms may place unfair burden on some individuals and neighborhoods. We formulate a fairness concept that takes local population densities into account. In particular, given k centers to locate and a population of size n, we define the "neighborhood radius" of an individual i as the minimum radius of a ball centered at i that contains at least n/k individuals. Our objective is to ensure that each individual has a center that is within at most a small constant factor of her neighborhood radius. We present several theoretical results: We show that optimizing this factor is NP-hard; we give an approximation algorithm that guarantees a factor of at most 2 in all metric spaces; and we prove matching lower bounds in some metric spaces. We apply a variant of this algorithm to real-world address data, showing that it is quite different from standard clustering algorithms and outperforms them on our objective function and balances the load between centers more evenly

Private Pareto Optimal Exchange

We consider the problem of implementing an individually rational, asymptotically Pareto optimal allocation in a barter-exchange economy where agents are endowed with goods and have preferences over the goods of others, but may not use money as a medium of exchange. Because one of the most important instantiations of such economies is kidney exchange -- where the "input"to the problem consists of sensitive patient medical records -- we ask to what extent such exchanges can be carried out while providing formal privacy guarantees to the participants. We show that individually rational allocations cannot achieve any non-trivial approximation to Pareto optimality if carried out under the constraint of differential privacy -- or even the relaxation of \emph{joint} differential privacy, under which it is known that asymptotically optimal allocations can be computed in two-sided markets, where there is a distinction between buyers and sellers and we are concerned only with privacy of the buyers~\citep{Matching}. We therefore consider a further relaxation that we call \emph{marginal} differential privacy -- which promises, informally, that the privacy of every agent $i$ is protected from every other agent $j \neq i$ so long as $j$ does not collude or share allocation information with other agents. We show that, under marginal differential privacy, it is possible to compute an individually rational and asymptotically Pareto optimal allocation in such exchange economies

Approximately Stable, School Optimal, and Student-Truthful Many-to-One Matchings (via Differential Privacy)

We present a mechanism for computing asymptotically stable school optimal matchings, while guaranteeing that it is an asymptotic dominant strategy for every student to report their true preferences to the mechanism. Our main tool in this endeavor is differential privacy: we give an algorithm that coordinates a stable matching using differentially private signals, which lead to our truthfulness guarantee. This is the first setting in which it is known how to achieve nontrivial truthfulness guarantees for students when computing school optimal matchings, assuming worst- case preferences (for schools and students) in large markets

Randomized Pursuit-Evasion with Local Visibility

We study the following pursuit-evasion game: One or more hunters are seeking to capture an evading rabbit on a graph. At each round, the rabbit tries to gather information about the location of the hunters but it can see them only if they are located on adjacent nodes. We show that two hunters su#ce for catching rabbits with such local visibility with high probability. We distinguish between reactive rabbits who move only when a hunter is visible and general rabbits who can employ more sophisticated strategies. We present polynomial time algorithms that decide whether a graph G is hunter-win, that is, if a single hunter can capture a rabbit of either kind on G

Smegma in diabetes mellitus

A 37-year-old male patient presented with 1-month history of pain over the bulb of penis during retraction of foreskin. Patient suffered from type 1 diabetes mellitus on poor glycemic control. On examination multiple white patches of 1 mm x 3 mm dimension were observed with pain during retraction of prepuce. Smegma deposition over the glans penis and erythematous areas were revealed while scraping the lesions. The patient, screened for urinary tract infection (UTI) and sexually transmitted disease (STD) including hepatitis B, syphilis and HIV which were negative and complete blood count was normal. Since smegma can be a precursor for genital infections, physicians must scrupulously examine diabetic patients presenting as timely diagnosis and treatment would improve patient´s quality of life. The patient, put on long acting insulin and advised personal hygiene and showed significant improvement during his follow-up visit, 1 month later

Steering of Discrete Event Systems: Control Theory Approach

Runtime verification involves monitoring the system at runtime to check for conformance of the execution trace to user defined safety properties. Typically, run-time verifiers do not assume a system model and hence cannot predict violations until they occur. This limits the practical applicability of runtime verification. Steering is the process of predicting the occurrence of violations and preventing them by controlling system execution. Steerers can achieve this using a limited knowledge of the system model even in situations where it is infeasible to store the entire model. In this paper, we explore a control-theoretic view of steering for discrete event systems. We introduce an architecture for steering and also describe different steering paradigms