Federalism, Liberty, and Equality in United States v. Windsor

This essay argues that federalism played a profoundly important role in the Supreme Court\u27s decision in United States v. Windsor, which struck down the federal Defense of Marriage Act. Arguments to the contrary have failed to appreciate how Justice Kennedy\u27s opinion employed federalism not as a freestanding argument but as an essential component of his rights analysis. Far from being a muddle, as many have claimed, Justice Kennedy\u27s analysis offered one of the most sophisticated examples to date of the interconnections between federalism, liberty, and equality

Searches for Clean Anomalous Gauge Couplings effects at present and future e+e−e^+e^- colliders

We consider the virtual effects of a general type of Anomalous (triple) Gauge Couplings on various experimental observables in the process of electron-positron annihilation into a final fermion-antifermion state. We show that the use of a recently proposed "$Z$-peak subtracted" theoretical description of the process allows to reduce substantially the number of relevant parameters of the model, so that a calculation of observability limits can be performed in a rather simple way. As an illustration of our approach, we discuss the cases of future measurements at LEP2 and at a new 500 GeV linear collider.Comment: 23 pages incl. 5 figures (e-mail [email protected]

Future neutrino oscillation facilities

The recent discovery that neutrinos have masses opens a wide new field of experimentation. Accelerator-made neutrinos are essential in this program. Ideas for future facilities include high intensity muon neutrino beams from pion decay (`SuperBeam'), electron neutrino beams from nuclei decays (`Beta Beam'), or muon and electron neutrino beams from muon decay (`Neutrino Factory'), each associated with one or several options for detector systems. Each option offers synergetic possibilities, e.g. some of the detectors can be used for proton decay searches, while the Neutrino Factory is a first step towards muon colliders. A summary of the perceived virtues and shortcomings of the various options, and a number of open questions are presented.Comment: Originally written for the CERN Strategy Grou

Cram\'er-Rao bounds for synchronization of rotations

Synchronization of rotations is the problem of estimating a set of rotations R_i in SO(n), i = 1, ..., N, based on noisy measurements of relative rotations R_i R_j^T. This fundamental problem has found many recent applications, most importantly in structural biology. We provide a framework to study synchronization as estimation on Riemannian manifolds for arbitrary n under a large family of noise models. The noise models we address encompass zero-mean isotropic noise, and we develop tools for Gaussian-like as well as heavy-tail types of noise in particular. As a main contribution, we derive the Cram\'er-Rao bounds of synchronization, that is, lower-bounds on the variance of unbiased estimators. We find that these bounds are structured by the pseudoinverse of the measurement graph Laplacian, where edge weights are proportional to measurement quality. We leverage this to provide interpretation in terms of random walks and visualization tools for these bounds in both the anchored and anchor-free scenarios. Similar bounds previously established were limited to rotations in the plane and Gaussian-like noise

Physics opportunities with future proton accelerators at CERN

We analyze the physics opportunities that would be made possible by upgrades of CERN's proton accelerator complex. These include the new physics possible with luminosity or energy upgrades of the LHC, options for a possible future neutrino complex at CERN, and opportunities in other physics including rare kaon decays, other fixed-target experiments, nuclear physics and antiproton physics, among other possibilities. We stress the importance of inputs from initial LHC running and planned neutrino experiments, and summarize the principal detector R&D issues.Comment: 39 page, word document, full resolution version available from http://cern.ch/pofpa/POFPA-arXive.pd

Reachability problems for PAMs

Piecewise affine maps (PAMs) are frequently used as a reference model to show the openness of the reachability questions in other systems. The reachability problem for one-dimentional PAM is still open even if we define it with only two intervals. As the main contribution of this paper we introduce new techniques for solving reachability problems based on p-adic norms and weights as well as showing decidability for two classes of maps. Then we show the connections between topological properties for PAM's orbits, reachability problems and representation of numbers in a rational base system. Finally we show a particular instance where the uniform distribution of the original orbit may not remain uniform or even dense after making regular shifts and taking a fractional part in that sequence.Comment: 16 page