The Johnson-Lindenstrauss lemma shows that any n points in Euclidean space (i.e., R n with distances measured under the 2 norm) may be mapped down to O((log n)/ε 2 ) dimensions such that no pairwise distance is distorted by more than a (1 + ε) factor. Determining whether such dimension reduction is possible in 1 has been an intriguing open question. We show strong lower bounds for general dimension reduction in 1 . We give an explicit family of n points in 1 such that any embedding with constant distortion D requires n (1/D 2 ) dimensions. This proves that there is no analog of the Johnson-Lindenstrauss lemma for 1 ; in fact, embedding with any constant distortion requires n (1) dimensions. Further, embedding the points into 1 with (1 + ε) distortion requires ndimensions. Our proof establishes this lower bound for shortest path metrics of series-parallel graphs. We make extensive use of linear programming and duality in devising our bounds. We expect that the tools and techniques we develop will be useful for future investigations of embeddings into 1 .
The lack of diversity in the tech industry is a widely remarked phenomenon. The majority of workers in tech roles are either white or Asian men, with all other groups being under-represented. Some authors point to cultural factors influencing selfefficacy, leading to a lack of diversity at the start of the "pipeline" of IT talent. Others point to toxic workplace culture that can lead skilled tech workers to drop out of the industry. While these effects are very real and important, this paper focuses on a third concept contributing to lack of diversity, communal goal congruity. We present a growing body of evidence suggesting that working with others, and in the service of others, are important career goals that many believe tech careers lack. We describe prior work that shows that these beliefs also have a significant impact on the pipeline of tech talent. We then report on the first pieces of data out of the first long-term intervention designed with this communal goal congruity perspective in mind. We have created a cohortbased service-learning program in computer science, computer engineering, electrical engineering, and software engineering. The result is a program with 26.3% women and 31.6% African American and/or Hispanic students, including 15.8% African American and/or Hispanic women, at an institution that has never previously seen this level of diversity in its computing majors.
We consider questions about vertex cuts in graphs, random walks in metric spaces, and dimension reduction in L1 and L2; these topics are intimately connected because they can each be reduced to the existence of various families of realvalued Lipschitz maps on certain metric spaces. We view these issues through the lens of shortest-path metrics on series-parallel graphs, and we discuss the implications for a variety of well-known open problems. Our main results follow.-Every n-point series-parallel metric embeds into dom 1 with O( √ log n) distortion, matching a lower bound of Newman and Rabinovich. Our embeddings yield an O( √ log n) approximation algorithm for vertex sparsest cut in such graphs, as well as an O( √ log k) approximate max-flow/min-vertexcut theorem for series-parallel instances with k terminals, improving over the O(log n) and O(log k) bounds for general graphs.-Every n-point series-parallel metric embeds with distortion D into d 1 with d = n 1/Ω(D 2 ) , matching the dimension reduction lower bound of Brinkman and Charikar.-There exists a constant C > 0 such that if (X, d) is a series-parallel metric then for every stationary, reversible Markov chain {Zt} ∞ t=0 on X, we have for all t ≥ 0,More generally, we show that series-parallel metrics have Markov type 2. This generalizes a result of Naor, Peres, Schramm, and Sheffield for trees. * brinkmwj@muohio.edu †
Plagiarism detection services are a powerful tool to help encourage academic integrity. Adoption of these services has proven to be controversial due to ethical concerns about students' rights. Central to these concerns is the fact that most such systems make permanent archives of student work to be re-used in plagiarism detection. This computerization and automation of plagiarism detection is changing the relationships of trust and responsibility between students, educators, educational institutions, and private corporations. Educators must respect student privacy rights when implementing such systems. Student work is personal information, not the property of the educator or institution. The student has the right to be fully informed about how plagiarism detection works, and the fact that their work will be permanently archived as a result. Furthermore, plagiarism detection should not be used if the permanent archiving of a student's work may expose him or her to future harm.
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