Kevin Schewior

CD8+ T-Cell Response Promotes Evolution of Hepatitis C Virus Nonstructural Proteins

BACKGROUND & AIMS Hepatitis C virus (HCV) acquires mutations that allow it to escape the CD8+ T-cell response, although the extent to which this process contributes to viral evolution at the population level is not clear. We studied viral adaptation using data from a large outbreak of HCV genotype 1b infection that occurred among women immunized with contaminated immunoglobulin from 1977 to 1978. METHODS The HCV nonstructural protein coding regions NS3-NS5B were sequenced from 78 patients, and mutations were mapped according to their location inside or outside previously described CD8+ T-cell epitopes. A statistical approach was developed to identify sites/regions under reproducible selection pressure associated with HLA class I. RESULTS The frequency of nonsynonymous mutations was significantly higher inside previously described CD8+ T-cell epitopes than outside-particularly in NS3/4A and NS5B. We identified new regions that are under selection pressure, indicating that not all CD8+ T-cell epitopes have been identified; 6 new epitopes that interact with CD8+ T cells were identified and confirmed in vitro. In some CD8+ T-cell epitopes mutations were reproducibly identified in patients that shared the relevant HLA allele, indicating immune pressure at the population level. There was statistical support for selection of mutations in 18 individual epitopes. Interestingly, 14 of these were restricted by HLA-B allele. CONCLUSIONS HLA class I-associated selection pressure on the nonstructural proteins and here predominantly on NS3/4A and NS5B promotes evolution of HCV. HLA-B alleles have a dominant effect in this selection process. Adaptation of HCV to the CD8+ T-cell response at the population level creates challenges for vaccine design.

Chasing Convex Bodies and Functions

We consider three related online problems: Online Convex Optimization, Convex Body Chasing, and Lazy Convex Body Chasing. In Online Convex Optimization the input is an online sequence of convex functions over some Euclidean space. In response to a function, the online algorithm can move to any destination point in the Euclidean space. The cost is the total distance moved plus the sum of the function costs at the destination points. Lazy Convex Body Chasing is a special case of Online Convex Optimization where the function is zero in some convex region, and grows linearly with the distance from this region. And Convex Body Chasing is a special case of Lazy Convex Body Chasing where the destination point has to be in the convex region. We show that these problems are equivalent in the sense that if any of these problems have an O(1)-competitive algorithm then all of the problems have an O(1)-competitive algorithm. By leveraging these results we then obtain the first O(1)-competitive algorithm for Online Convex Optimization in two dimensions, and give the first O(1)-competitive algorithm for chasing linear subspaces. We also give a simple algorithm and O(1)-competitiveness analysis for chasing lines.

A 2-Competitive Algorithm For Online Convex Optimization With Switching Costs

We consider a natural online optimization problem set on the real line. The state of the online algorithm at each integer time is a location on the real line. At each integer time, a convex function arrives online. In response, the online algorithm picks a new location. The cost paid by the online algorithm for this response is the distance moved plus the value of the function at the final destination. The objective is then to minimize the aggregate cost over all time. The motivating application is rightsizing power-proportional data centers. We give a 2-competitive algorithm for this problem. We also give a 3-competitive memoryless algorithm, and show that this is the best competitive ratio achievable by a deterministic memoryless algorithm. Finally we show that this online problem is strictly harder than the standard ski rental problem.

Routing Games With Progressive Filling

Max-min fairness (MMF) is a widely known approach to a fair allocation of bandwidth to each of the users in a network. This allocation can be computed by uniformly raising the bandwidths of all users without violating capacity constraints. We consider an extension of these allocations by raising the bandwidth with arbitrary and not necessarily uniform time-depending velocities (allocation rates). These allocations are used in a game-theoretic context for routing choices, which we formalize in progressive filling games (PFGs). We present a variety of results for equilibria in PFGs. We show that these games possess pure Nash and strong equilibria. While computation in general is NP-hard, there are polynomial-time algorithms for prominent classes of Max-Min-Fair Games (MMFG), including the case when all users have the same source-destination pair. We characterize prices of anarchy and stability for pure Nash and strong equilibria in PFGs and MMFGs when players have different or the same source-destination pairs. In addition, we show that when a designer can adjust allocation rates, it is possible to design games with optimal strong equilibria. Some initial results on polynomial-time algorithms in this direction are also derived.

Tight bounds for online TSP on the line

We consider the online traveling salesperson problem (TSP), where requests appear online over time on the real line and need to be visited by a server initially located at the origin. We distinguish between closed and open online TSP, depending on whether the server eventually needs to return to the origin or not. While online TSP on the line is a very natural online problem that was introduced more than two decades ago, no tight competitive analysis was known to date. We settle this problem by providing tight bounds on the competitive ratios for both the closed and the open variant of the problem. In particular, for closed online TSP, we provide a 1.64-competitive algorithm, thus matching a known lower bound. For open online TSP, we give a new upper bound as well as a matching lower bound that establish the remarkable competitive ratio of 2.04. Additionally, we consider the online D ial -A-R ide problem on the line, where each request needs to be transported to a specified destination. We provide an improved non-preemptive lower bound of 1.75 for this setting, as well as an improved preemptive algorithm with competitive ratio 2.41. Finally, we generalize known and give new complexity results for the underlying offline problems. In particular, we give an algorithm with running time O(n2) for closed offline TSP on the line with release dates and show that both variants of offline D ial -A-R ide on the line are NP-hard for any capacity c ≥ 2 of the server.

Routing Games with Progressive Filling

Max-min fairness (MMF) is a widely known approach to a fair allocation of bandwidth to each of the users in a network. This allocation can be computed by uniformly raising the bandwidths of all users without violating capacity constraints. We consider an extension of these allocations by raising the bandwidth with arbitrary and not necessarily uniform time-depending velocities (allocation rates). These allocations are used in a game-theoretic context for routing choices, which we formalize in progressive filling games (PFGs).We present a variety of results for equilibria in PFGs. We show that these games possess pure Nash and strong equilibria. While computation in general is NP-hard, there are polynomial-time algorithms for prominent classes of Max-Min-Fair Games (MMFG), including the case when all users have the same source-destination pair. We characterize prices of anarchy and stability for pure Nash and strong equilibria in PFGs and MMFGs when players have different or the same source-destination pairs. In addition, we show that when a designer can adjust allocation rates, it is possible to design games with optimal strong equilibria. Some initial results on polynomial-time algorithms in this direction are also derived.