Abnormal oscillation modes in a waning light bridge

A sunspot acts as a waveguide in response to the dynamics of the solar interior; the trapped waves and oscillations could reveal its thermal and magnetic structures. We study the oscillations in a sunspot intruded by a light bridge, the details of the oscillations could reveal the fine structure of the magnetic topology. We use the Solar Dynamics Observatory/Atmospheric Imaging Assembly data to analyse the oscillations in the emission intensity of light bridge plasma at different temperatures and investigate their spatial distributions. The extreme ultraviolet emission intensity exhibits two persistent oscillations at five-minute and sub-minute ranges. The spatial distribution of the five-minute oscillation follows the spine of the bridge; whereas the sub-minute oscillations overlap with two flanks of the bridge. Moreover, the sub-minute oscillations are highly correlated in spatial domain, however, the oscillations at the eastern and western flanks are asymmetric with regard to the lag time. In the meanwhile, jet-like activities are only found at the eastern flank. Asymmetries in forms of oscillatory pattern and jet-like activities \textbf{are} found between two flanks of a granular light bridge. Based on our study and recent findings, we propose a new model of twisted magnetic field for a light bridge and its dynamic interactions with the magnetic field of a sunspot.Comment: 5 figures, Accepted version in A&

Origins of Inert Higgs Doublets

We consider beyond the standard model embedding of inert Higgs doublet fields. We argue that inert Higgs doublets can arise naturally in grand unified theories where the necessary associated $Z_2$ symmetry can occur automatically. Several examples are discussed.Comment: 14 pages, 1 table, no figure. References adde

Balanced Symmetric Functions over GF(p)GF(p)

Under mild conditions on $n,p$, we give a lower bound on the number of $n$-variable balanced symmetric polynomials over finite fields $GF(p)$, where $p$ is a prime number. The existence of nonlinear balanced symmetric polynomials is an immediate corollary of this bound. Furthermore, we conjecture that $X(2^t,2^{t+1}l-1)$ are the only nonlinear balanced elementary symmetric polynomials over GF(2), where $X(d,n)=\sum_{i_1<i_2<...<i_d}x_{i_1} x_{i_2}... x_{i_d}$, and we prove various results in support of this conjecture.Comment: 21 page

N-fold way simulated tempering for pairwise interaction point processes

Pairwise interaction point processes with strong interaction are usually difficult to sample. We discuss how Besag lattice processes can be used in a simulated tempering MCMC scheme to help with the simulation of such processes. We show how the N-fold way algorithm can be used to sample the lattice processes efficiently and introduce the N-fold way algorithm into our simulated tempering scheme. To calibrate the simulated tempering scheme we use the Wang-Landau algorithm