Generalized Dantzig Selector: Application to the k-support norm

We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS, and non-asymptotic high-probability bounds are established on the estimation error, which rely on Gaussian width of unit norm ball and suitable set encompassing estimation error. Further, we consider a non-trivial example of the GDS using $k$-support norm. We derive an efficient method to compute the proximal operator for $k$-support norm since existing methods are inapplicable in this setting. For statistical analysis, we provide upper bounds for the Gaussian widths needed in the GDS analysis, yielding the first statistical recovery guarantee for estimation with the $k$-support norm. The experimental results confirm our theoretical analysis.Comment: Updates to boun

Natural SUSY at LHC with Right-Sneutrino LSP

We study an extension of the minimal supersymmetric standard model (MSSM) with additional right-handed singlet neutrino superfields. While such an extension incorporates a mechanism for the neutrino mass, it also opens up the possibility of having the right-sneutrinos ($\widetilde{\nu}$) as the lightest supersymmetric particle (LSP). In this work, we focus on the the viability of rather small ($\lesssim 500$ GeV) higgsino mass parameter ($\mu$), an important ingredient for "naturalness", in the presence of such a LSP. For simplicity, we assume that the bino and wino mass parameters are much heavier, thus we only consider (almost) pure and compressed higgsino-like states, with small $\mathcal{O}(10^{-2})$ gaugino admixture. Considering only prompt decays of the higgino-like states, especially the lightest chargino, we discuss the importance of leptonic channels consisting of up to two leptons with large missing transverse energy to probe this scenario at the Large Hadron Collider (LHC). Further, we emphasize on how the gaugino mass parameters, although very heavy, affects the decay of the low-lying higgsino-like states, thus significantly affecting the proposed signatures at LHC.Comment: matches published versio

Unifying averaged dynamics of the Fokker-Planck equation for Paul traps

Collective dynamics of a collisional plasma in a Paul trap is governed by the Fokker-Planck equation, which is usually assumed to lead to a unique asymptotic time-periodic solution irrespective of the initial plasma distribution. This uniqueness is, however, hard to prove in general due to analytical difficulties. For the case of small damping and diffusion coefficients, we apply averaging theory to a special solution to this problem, and show that the averaged dynamics can be represented by a remarkably simple 2D phase portrait, which is independent of the applied rf field amplitude. In particular, in the 2D phase portrait, we have two regions of initial conditions. From one region, all solutions are unbounded. From the other region, all solutions go to a stable fixed point, which represents a unique time-periodic solution of the plasma distribution function, and the boundary between these two is a parabola.Comment: 10 page

Right Sneutrino Dark Matter and a Monochromatic Photon Line

The inclusion of right-chiral sneutrino superfields is a rather straightforward addition to a supersymmetric scenario. A neutral scalar with a substantial right sneutrino component is often a favoured dark matter candidate in such cases. In this context, we focus on the tentative signal in the form of a monochromatic photon, which may arise from dark matter annihilation and has drawn some attention in recent times. We study the prospect of such a right sneutrino dark matter candidate in the contexts of both MSSM and NMSSM extended with right sneutrino superfields, with special reference to the Fermi-LAT data