The number of births in the United States declined by 1% between 2012 and 2013, to a total of 3 932 181. The general fertility rate also declined 1% to 62.5 births per 1000 women, the lowest rate ever reported. The total fertility rate was down by 1% in 2013 (to 1857.5 births per 1000 women). The teenage birth rate fell to another historic low in 2013, 26.5 births per 1000 women. Birth rates al...

Overview We are covering various techniques for analyzing approximation algorithms. There are four basic techniques: In the previous two classes we covered the reduction and sacrifice precision methods. In this class, we will consider an application of the sacrifice precision method and discuss the combine bounds method. Recall that the sacrifice precision method is used in the context where th...

In this lecture we talk about various useful applications of dimensionality reduction, specifically using JohnsonLindenstrauss lemma. JL lemma states that a small set of points in a high-dimensional space can be embedded into a space of much lower dimension in such a way that distances between the points are nearly preserved. In the previous lecture, we looked at one such linear embedding whose...

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