Prepositions are highly polysemous, and their variegated senses encode significant semantic information.In this paper we match each preposition's left-and right context, and their interplay to the geometry of the word vectors to the left and right of the preposition.Extracting these features from a large corpus and using them with machine learning models makes for an efficient preposition sense disambiguation (PSD) algorithm, which is comparable to and better than state-of-the-art on two benchmark datasets.Our reliance on no linguistic tool allows us to scale the PSD algorithm to a large corpus and learn sensespecific preposition representations.The crucial abstraction of preposition senses as word representations permits their use in downstream applications-phrasal verb paraphrasing and preposition selection-with new state-ofthe-art results.

Computing outliers and related statistical aggregation functions from large-scale big data sources is a critical operation in many cloud computing scenarios, e.g. service quality assurance, fraud detection, or novelty discovery. Such problems commonly have to be solved in a distributed environment where each node only has a local slice of the entirety of the data. To process a query on the global data, each node must transmit its local slice of data or an aggregated subset thereof to a global aggregator node, which can then compute the desired statistical aggregation function. In this context, reducing the total communication cost is often critical to the overall efficiency.

It is well known that avalanche effect errors in received noisy ciphertexts will cause severe error propagation in block-ciphered encryption systems, thus resulting in a large reduction in the achievable throughput. However, little is known about the statistical properties of the underlying error sequences in decrypted plaintexts in block-ciphered systems when channel errors are present. A rigorous study of the statistical properties of the errors in block-ciphered crypto-systems operating in cipher block chaining (CBC) mode is provided. The equivalent channel transition probability is obtained and then used to derive error statistics including both error weight probabilities and gap distributions. The validity of the theoretical analyses is confirmed by the excellent match with results obtained by simulated data encryption standard (DES)-based and advanced encryption standard (AES)-based crypto-systems operating in CBC mode. The error statistics will be valuable in the design and performance evaluation of communication protocols, as well as in error-control schemes for block-ciphered crypto-systems in the presence of erroneous ciphertexts, where errors are intentionally left to enhance security against passive eavesdroppers.