This full research paper looks at data science, which is an increasingly important topic of interest across all academic disciplines and industry sectors. As such, the need for curricula and learning designs for teaching data science has never been greater. One increasingly useful institutional initiative for building critical skills is living learning communities. This study reports on a data science learning community, called The Data Mine. As part of this learning community, students worked on similar tasks, took classes together, and participated in industry related assignments. This exploratory study aims to understand how students navigated learning challenges, what self-regulation strategies were adopted, and what students ultimately learned through participating in the Data Mine Learning Community. Students were grouped into achievement categories using a developed rubric on course assignments and their responses to open ended questions were evaluated for patterns among those in their achievement group. The results indicate that the highest performing students avoided coding errors and were highly focused on learning gains.

We discuss the structure of periods in subtraction games. In particular, we discuss ways that a computational approach yields insights to the periods that emerge in the asymptotic structure of these combinatorial games.

We consider auctions in which the winning bid is the smallest bid that is unique. Only the upper-price limit is given. Neither the number of participants nor the distribution of the offers are known, so that the problem of placing a bid to win with maximum probability looks, a priori, ill-posed. Indeed, the essence of the problem is to inject a (final) minimum into a random subset (of unique offers) of a larger random set. We will see, however, that here no more than two external (and almost compelling) arguments make the problem meaningful. By appropriately modeling the relationship between the number of participants and the distribution of the bids, we can then maximize our chances of winning the auction and propose a computable algorithm for placing our bid.

We propose a joint source-channel coding algorithm capable of correcting some errors in the popular Lempel-Ziv'77 (LZ'77) scheme without introducing any measurable degradation in the compression performance. This can be achieved because the LZ'77 encoder does not completely eliminate the redundancy present in the input sequence. One source of redundancy can be observed when an LZ'77 phrase has multiple matches. In this case, LZ'77 can issue a pointer to any of those matches, and a particular choice carries some additional bits of information. We call a scheme with embedded redundant information the LZS'77 algorithm. We analyze the number of longest matches in such a scheme and prove that it follows the logarithmic series distribution with mean 1/h (plus some fluctuations), where h is the source entropy. Thus, the distribution associated with the number of redundant bits is well concentrated around its mean, a highly desirable property for error correction. These analytic results are proved by a combination of combinatorial, probabilistic, and analytic methods (e.g., Mellin transform, depoissonization, combinatorics on words). In fact, we analyze LZS'77 by studying the multiplicity matching parameter in a suffix tree, which in turn is analyzed via comparison to its independent version, called trie. Finally, we present an algorithm in which a channel coder (e.g., Reed-Solomon (RS) coder) succinctly uses the inherent additional redundancy left by the LZS'77 encoder to detect and correct a limited number of errors. We call such a scheme the LZRS'77 algorithm. LZRS'77 is perfectly backward-compatible with LZ'77, that is, a file compressed with our error-resistant LZRS'77 can still be decompressed by a generic LZ'77 decoder

The devastating effect of errors in adaptive data compression is a long-standing open problem. In this paper LZ'77 is changed theoretically and experimentally observed, such that in a significant proportion of LZ'77 phrases, there is more than one copy of the longest prefix in the compressed file. Once the redundant bits of LZ'77 have been identified, it is exploited for channel coding. For error correction and detection RS (255,255-2e) Reed-Solomon codes are used.