Nonconvex Generalization of ADMM for Nonlinear Equality Constrained Problems

The ever-increasing demand for efficient and distributed optimization algorithms for large-scale data has led to the growing popularity of the Alternating Direction Method of Multipliers (ADMM). However, although the use of ADMM to solve linear equality constrained problems is well understood, we lacks a generic framework for solving problems with nonlinear equality constraints, which are common in practical applications (e.g., spherical constraints). To address this problem, we are proposing a new generic ADMM framework for handling nonlinear equality constraints, neADMM. After introducing the generalized problem formulation and the neADMM algorithm, the convergence properties of neADMM are discussed, along with its sublinear convergence rate $o(1/k)$, where $k$ is the number of iterations. Next, two important applications of neADMM are considered and the paper concludes by describing extensive experiments on several synthetic and real-world datasets to demonstrate the convergence and effectiveness of neADMM compared to existing state-of-the-art methods

Di-photon excess illuminates Dark Matter

We propose a simplified model of dark matter with a scalar mediator to accommodate the di-photon excess recently observed by the ATLAS and CMS collaborations. Decays of the resonance into dark matter can easily account for a relatively large width of the scalar resonance, while the magnitude of the total width combined with the constraint on dark matter relic density lead to sharp predictions on the parameters of the Dark Sector. Under the assumption of a rather large width, the model predicts a signal consistent with ~300 GeV dark matter particle in channels with large missing energy. This prediction is not yet severely bounded by LHC Run I searches and will be accessible at the LHC Run II in the jet plus missing energy channel with more luminosity. Our analysis also considers astrophysical constraints, pointing out that future direct detection experiments will be sensitive to this scenario.Comment: 23 pages, 8 figures. Added 2 figures and more discussion

New physics searches at near detectors of neutrino oscillation experiments

We systematically investigate the prospects of testing new physics with tau sensitive near detectors at neutrino oscillation facilities. For neutrino beams from pion decay, from the decay of radiative ions, as well as from the decays of muons in a storage ring at a neutrino factory, we discuss which effective operators can lead to new physics effects. Furthermore, we discuss the present bounds on such operators set by other experimental data currently available. For operators with two leptons and two quarks we present the first complete analysis including all relevant operators simultaneously and performing a Markov Chain Monte Carlo fit to the data. We find that these effects can induce tau neutrino appearance probabilities as large as O(10^{-4}), which are within reach of forthcoming experiments. We highlight to which kind of new physics a tau sensitive near detector would be most sensitive.Comment: 20 pages, 2 figures, REVTeX

Precision Tests of Parity Violation Over Cosmological Distances

Recent measurements of the Cosmic Microwave Background $B$-mode polarization power spectrum by the BICEP2 and POLARBEAR experiments have demonstrated new precision tools for probing fundamental physics. Regardless of origin, the fact that we can detect sub-$\mu$K CMB polarization represents a tremendous technological breakthrough. Yet more information may be latent in the CMB's polarization pattern. Because of its tensorial nature, CMB polarization may also reveal parity-violating physics via a detection of cosmic polarization rotation. Although current CMB polarimeters are sensitive enough to measure one degree-level polarization rotation with $>5\sigma$ statistical significance, they lack the ability to differentiate this effect from a systematic instrumental polarization rotation. Here, we motivate the search for cosmic polarization rotation from current CMB data as well as independent radio galaxy and quasar polarization measurements. We argue that an improvement in calibration accuracy would allow the precise measurement of parity- and Lorentz-violating effects. We describe the CalSat space-based polarization calibrator that will provide stringent control of systematic polarization angle calibration uncertainties to $0.05^\circ$ -- an order of magnitude improvement over current CMB polarization calibrators. CalSat-based calibration could be used with current CMB polarimeters searching for $B$-mode polarization, effectively turning them into probes of cosmic parity violation, i.e. without the need to build dedicated instruments.Comment: 11 pages, 3 figure