In the last lecture a primal-dual analysis was used to show a 2-approximation for theVertex Cover problem. Here we extend these ideas to show a 2-approximation for the Steiner Forest problem using a primal-dual analysis. In the Steiner Forest problem there is a graph G = (V,E) where each edge e ∈ E has a cost ce ∈ R. We are given k pairs of terminals s1, t1, s2, t2, . . . sk, tk ∈ V . The goal ...

In the previous class, we had looked at the RMW algorithm. In this setting, the actions/decisions are referred to as experts. Assume that we have N experts. On any given day t, we choose an expert to use from among the N experts (like choosing a function h ∈ H). The adversary/world returns a loss vector lt = (lt 1, · · · lt N ). If the expert it is chosen on day t, then the performance after T ...

The aim of this study was to investigate changes in serum cytokine levels in children with handfoot-and-mouth disease (HFMD) and their clinical significance. Clinical data from 241 children with HFMD, hospitalized between May 2012 and January 2013, were analyzed retrospectively. Patients were divided into a normal case group (n=107) and a severe case group (n=134), and the clinical features of ...

Credit Market Constraints and Labor Market Decisions In this paper, we examine whether imperfections in credit markets spill over to other markets, particularly the labor market. We take the case of Italy, a country that experienced changes in the mortgage market brought about by the 1992 European unification and other institutional shifts. These events make Italy a good laboratory to study the...

In the last lecture, we were looking at clustering sparse graphs in the stochastic block model with parameters p > q, where p = a n , and q = b n , we saw that we could not do perfect clustering as w.h.p, there will be a constant fraction of isolated vertices. However, we shall see that we can still do weak recovery, i.e., by allowing a small fraction of vertices to be misplaced, we will recove...

We demonstrate our prototype of the DBO database system. DBO is designed to facilitate scalable analytic processing over large data archives. DBO’s analytic processing performance is competitive with other database systems; however, unlike any other existing research or industrial system, DBO maintains a statistically meaningful guess to the final answer to a query from start to finish during q...

Consider a flock of birds that fly interacting between them. The interactions are modelled through a hierarchical system in which each bird, at each time step, adjusts its own velocity according to his past velocity and a weighted mean of the relative velocities of its superiors in the hierarchy. We consider the additional fact, that each of the birds can fail to see any of its superiors with c...

We have already seen in previous lectures that a concept class C is PAC-learnable by the hypothesis class H if there exists an algorithm A such that for all c ∈ C, for all distributions D over X, for all > 0, for all δ > 0, A takes m = finite number of examples given in the form S = 〈 (x1, c(x1)), ..., (xm, c(xm)) 〉 , where each xi chosen from the space X at random according to the target distr...

If this is was what we had from the start then the task of clustering would be trivial. However, usually, the graphs that must be clustered are not this perfect and contain edges between S1 and S2. These edges can be considered noise in the representation of G. Therefore, a clustering algorithm would be attempting to cluster a noisy representation, G ′ , of the perfect graph G. More explicitly,...