Is string theory a theory of quantum gravity?

Some problems in finding a complete quantum theory incorporating gravity are discussed. One is that of giving a consistent unitary description of high-energy scattering. Another is that of giving a consistent quantum description of cosmology, with appropriate observables. While string theory addresses some problems of quantum gravity, its ability to resolve these remains unclear. Answers may require new mechanisms and constructs, whether within string theory, or in another framework.Comment: Invited contribution for "Forty Years of String Theory: Reflecting on the Foundations," a special issue of Found. Phys., ed. by G 't Hooft, E. Verlinde, D. Dieks, S. de Haro. 32 pages, 5 figs., harvmac. v2: final version to appear in journal (small revisions

Measurement of the Z boson differential cross section in transverse momentum and rapidity in proton-proton collisions at 8 TeV

Peer reviewe

Online Checkpointing with Improved Worst-Case Guarantees

Abstract. In the online checkpointing problem, the task is to continuously maintain a set of k checkpoints that allow to rewind an ongoing computation faster than by a full restart. The only operation allowed is to remove an old checkpoint and to store the current state instead. Our aim are checkpoint placement strategies that minimize rewinding cost, i.e., such that at all times T when requested to rewind to some time t ≤ T the number of computation steps that need to be redone to get to t from a checkpoint before t is as small as possible. In particular, we want that the closest checkpoint earlier than t is not further away from t than pk times the ideal distance T/(k + 1), where pk is a small constant. Improving over earlier work showing 1 + 1/k ≤ pk ≤ 2, we show that pk can be chosen less than 2 uniformly for all k. More precisely, we show the uniform bound pk ≤ 1.7 for all k, and present algorithms with asymptotic performance pk ≤ 1.59 + o(1) valid for all k and pk ≤ ln(4) + o(1) ≤ 1.39+o(1) valid for k being a power of two. For small values of k, we show how to use a linear programming approach to compute good checkpointing algorithms. This gives performances of less than 1.53 for k ≤ 10. One the more theoretical side, we show the first lower bound that is asymptotically more than one, namely pk ≥ 1.30 − o(1). We also show that optimal algorithms (yielding the infimum performance) exist for all k.

Connections in Networks: Hardness of Feasibility versus Optimality

We study the complexity of combinatorial problems that consist of competing infeasibility and optimization components. In particular, we investigate the complexity of the connection subgraph problem, which occurs, e.g., in resource environment economics and social networks. We present results on its worst-case hardness and approximability. We then provide a typical-case analysis by means of a detailed computational study. First, we identify an easy-hard-easy pattern, coinciding with the feasibility phase transition of the problem. Second, our experimental results reveal an interesting interplay between feasibility and optimization. They surprisingly show that proving optimality of the solution of the feasible instances can be substantially easier than proving infeasibility of the infeasible instances in a computationally hard region of the problem space. We also observe an intriguing easy-hard-easy profile for the optimization component itself

The Steiner Tree Reoptimization Problem with Sharpened Triangle Inequality

In this paper, we deal with several reoptimization variants of the Steiner tree problem in graphs obeying a sharpened β-triangle inequality. A reoptimization algorithm exploits the knowledge of an optimal solution to a problem instance for finding good solutions for a locally modified instance. We show that, in graphs satisfying a sharpened triangle inequality (and even in graphs where edge-costs are restricted to the values 1 and 1+ for an arbitrary small > 0), Steiner tree reoptimization still is NP-hard for several different types of local modifications, and even APX-hard for some of them.As for the upper bounds, for some local modifications, we design lineartime (1/2+β)-approximation algorithms, and even polynomial-time approximation schemes, whereas for metric graphs (β = 1), none of these reoptimization variants is known to permit a PTAS. As a building block for some of these algorithms, we employ a 2β-approximation algorithm for the classical Steiner tree problem on such instances, which might be of independent interest since it improves over the previously best known ratio for any β < 1/2 + ln(3)/4 0.775