Bootstrapping Real-world Deployment of Future Internet Architectures

The past decade has seen many proposals for future Internet architectures. Most of these proposals require substantial changes to the current networking infrastructure and end-user devices, resulting in a failure to move from theory to real-world deployment. This paper describes one possible strategy for bootstrapping the initial deployment of future Internet architectures by focusing on providing high availability as an incentive for early adopters. Through large-scale simulation and real-world implementation, we show that with only a small number of adopting ISPs, customers can obtain high availability guarantees. We discuss design, implementation, and evaluation of an availability device that allows customers to bridge into the future Internet architecture without modifications to their existing infrastructure

Generating Probability Distributions using Multivalued Stochastic Relay Circuits

The problem of random number generation dates back to von Neumann's work in 1951. Since then, many algorithms have been developed for generating unbiased bits from complex correlated sources as well as for generating arbitrary distributions from unbiased bits. An equally interesting, but less studied aspect is the structural component of random number generation as opposed to the algorithmic aspect. That is, given a network structure imposed by nature or physical devices, how can we build networks that generate arbitrary probability distributions in an optimal way? In this paper, we study the generation of arbitrary probability distributions in multivalued relay circuits, a generalization in which relays can take on any of N states and the logical 'and' and 'or' are replaced with 'min' and 'max' respectively. Previous work was done on two-state relays. We generalize these results, describing a duality property and networks that generate arbitrary rational probability distributions. We prove that these networks are robust to errors and design a universal probability generator which takes input bits and outputs arbitrary binary probability distributions

Finite reflection groups and graph norms

Given a graph $H$ on vertex set $\{1,2,\cdots, n\}$ and a function $f:[0,1]^2 \rightarrow \mathbb{R}$, define \begin{align*} \|f\|_{H}:=\left\vert\int \prod_{ij\in E(H)}f(x_i,x_j)d\mu^{|V(H)|}\right\vert^{1/|E(H)|}, \end{align*} where $\mu$ is the Lebesgue measure on $[0,1]$. We say that $H$ is norming if $\|\cdot\|_H$ is a semi-norm. A similar notion $\|\cdot\|_{r(H)}$ is defined by $\|f\|_{r(H)}:=\||f|\|_{H}$ and $H$ is said to be weakly norming if $\|\cdot\|_{r(H)}$ is a norm. Classical results show that weakly norming graphs are necessarily bipartite. In the other direction, Hatami showed that even cycles, complete bipartite graphs, and hypercubes are all weakly norming. We demonstrate that any graph whose edges percolate in an appropriate way under the action of a certain natural family of automorphisms is weakly norming. This result includes all previously known examples of weakly norming graphs, but also allows us to identify a much broader class arising from finite reflection groups. We include several applications of our results. In particular, we define and compare a number of generalisations of Gowers' octahedral norms and we prove some new instances of Sidorenko's conjecture.Comment: 29 page

Regression Discontinuity Inference with Specification Error

A regression discontinuity (RD) research design is appropriate for program evaluation problems in which treatment status (or the probability of treatment) depends on whether an observed covariate exceeds a fixed threshold. In many applications the treatment-determining covariate is discrete. This makes it impossible to compare outcomes for observations "just above" and "just below" the treatment threshold, and requires the researcher to choose a functional form for the relationship between the treatment variable and the outcomes of interest. We propose a simple econometric procedure to account for uncertainty in the choice of functional form for RD designs with discrete support. In particular, we model deviations of the true regression function from a given approximating function -- the specification errors -- as random. Conventional standard errors ignore the group structure induced by specification errors and tend to overstate the precision of the estimated program impacts. The proposed inference procedure that allows for specification error also has a natural interpretation within a Bayesian framework.

Supersymmetry for Gauged Double Field Theory and Generalised Scherk-Schwarz Reductions

Previous constructions of supersymmetry for double field theory have relied on the so called strong constraint. In this paper, the strong constraint is relaxed and the theory is shown to possess supersymmetry once the generalised Scherk-Schwarz reduction is imposed. The equivalence between the generalised Scherk-Schwarz reduced theory and the gauged double field theory is then examined in detail for the supersymmetric theory. As a byproduct we write the generalised Killing spinor equations for the supersymmetric double field theory.Comment: 29 pages, LateX, v2 typos fixed and some improved discussion, version as in Journa