Total variation distance (TV distance) is an important measure for the difference between two distributions.

A secret-sharing scheme enables a dealer to share a secret s among n parties such that only authorized subsets of parties, specified by a monotone access structure f:{0,1}n→{0,1}, can reconstruct s from their shares. Other subsets of parties learn nothing about s.

Garbling schemes, also known as decomposable randomized encodings (DRE), have found many applications in cryptography. However, despite a large body of work on constructing such schemes, very little is known about their limitations. We initiate a systematic study of the DRE complexity of Boolean functions, obtaining the following main results: - Near-quadratic lower bounds. We use a classical lower bound technique of Nečiporuk [Dokl. Akad. Nauk SSSR '66] to show an Ω(n²/log n) lower bound on the size of any DRE for many explicit Boolean functions. For some natural functions, we obtain a corresponding upper bound, thus settling their DRE complexity up to polylogarithmic factors. Prior to our work, no superlinear lower bounds were known, even for non-explicit functions. - Garbling-friendly PRFs. We show that any exponentially secure PRF has Ω(n²/log n) DRE size, and present a plausible candidate for a "garbling-optimal" PRF that nearly meets this bound. This candidate establishes a barrier for super-quadratic DRE lower bounds via natural proof techniques. In contrast, we show a candidate for a weak PRF with near-exponential security and linear DRE size. Our results establish several qualitative separations, including near-quadratic separations between computational and information-theoretic DRE size of Boolean functions, and between DRE size of weak vs. strong PRFs.

We study secret sharing schemes for general (non-threshold) access structures. A general secret sharing scheme for n parties is associated to a monotone function F:{0,1}n→{0,1}. In such a scheme, a dealer distributes shares of a secret s among n parties. Any subset of parties T ⊆ [n] should be able to put together their shares and reconstruct the secret s if F(T)=1, and should have no information about s if F(T)=0. One of the major long-standing questions in information-theoretic cryptography is to minimize the (total) size of the shares in a secret-sharing scheme for arbitrary monotone functions F.

OBJECTIVE: To create an end-to-end system to identify temporal relation in discharge summaries for the 2012 i2b2 challenge. The challenge includes event extraction, timex extraction, and temporal relation identification. DESIGN: An end-to-end temporal relation system was developed. It includes three subsystems: an event extraction system (conditional random fields (CRF) name entity extraction and their corresponding attribute classifiers), a temporal extraction system (CRF name entity extraction, their corresponding attribute classifiers, and context-free grammar based normalization system), and a temporal relation system (10 multi-support vector machine (SVM) classifiers and a Markov logic networks inference system) using labeled sequential pattern mining, syntactic structures based on parse trees, and results from a coordination classifier. Micro-averaged precision (P), recall (R), averaged P&R (P&R), and F measure (F) were used to evaluate results. RESULTS: For event extraction, the system achieved 0.9415 (P), 0.8930 (R), 0.9166 (P&R), and 0.9166 (F). The accuracies of their type, polarity, and modality were 0.8574, 0.8585, and 0.8560, respectively. For timex extraction, the system achieved 0.8818, 0.9489, 0.9141, and 0.9141, respectively. The accuracies of their type, value, and modifier were 0.8929, 0.7170, and 0.8907, respectively. For temporal relation, the system achieved 0.6589, 0.7129, 0.6767, and 0.6849, respectively. For end-to-end temporal relation, it achieved 0.5904, 0.5944, 0.5921, and 0.5924, respectively. With the F measure used for evaluation, we were ranked first out of 14 competing teams (event extraction), first out of 14 teams (timex extraction), third out of 12 teams (temporal relation), and second out of seven teams (end-to-end temporal relation). CONCLUSIONS: The system achieved encouraging results, demonstrating the feasibility of the tasks defined by the i2b2 organizers. The experiment result demonstrates that both global and local information is useful in the 2012 challenge.