Anapole Dark Matter

We consider dark matter (DM) that interacts with ordinary matter exclusively through an electromagnetic anapole, which is the only allowed electromagnetic form factor for Majorana fermions. We show that unlike DM particles with an electric or magnetic dipole moment, anapole dark matter particles annihilate exclusively into fermions via purely p-wave interactions, while tree-level annihilations into photons are forbidden. We calculate the anapole moment needed to produce a thermal relic abundance in agreement with cosmological observations, and show that it is consistent with current XENON100 detection limits on the DM-nucleus cross-section for all masses, while lying just below the detection threshold for a mass ~ 30-40 GeV.Comment: 7 pages, 5 figures, v3: version to appear in PL

Secular Evolution of Hierarchical Planetary Systems

(Abridged) We investigate the dynamical evolution of coplanar hierarchical two-planet systems where the ratio of the orbital semimajor axes alpha=a_1/a_2 is small. The orbital parameters obtained from a multiple Kepler fit to the radial velocity variations of a star are best interpreted as Jacobi coordinates and Jacobi coordinates should be used in any analyses of hierarchical planetary systems. An approximate theory that can be applied to coplanar hierarchical two-planet systems with a wide range of masses m_j and orbital eccentricities e_j is the octupole-level secular perturbation theory (OSPT). The OSPT shows that if the ratio of the maximum orbital angular momenta, lambda \approx (m_1/m_2) alpha^{1/2}, for given a_j is approximately equal to a critical value lambda_{crit}, then libration of the difference in the longitudes of periapse, w_1-w_2, about either 0 or 180 deg. is almost certain, with possibly large amplitude variations of both e_j. We establish that the OSPT is highly accurate for systems with alpha<0.1 and reasonably accurate even for systems with alpha as large as 1/3, provided that alpha is not too close to a significant mean-motion commensurability or above the stability boundary. The HD 168443 system is not in a secular resonance and its w_1-w_2 circulates. The HD 12661 system is the first extrasolar planetary system found to have w_1-w_2 librating about 180 deg. The libration of w_1-w_2 and the large-amplitude variations of both e_j in the HD 12661 system are consistent with the analytic results on systems with lambda \approx lambda_{crit}. The HD 12661 system with the best- fit orbital parameters and sin i = 1 is affected by the close proximity to the 11:2 commensurability, but small changes in the outer orbital period can result in configurations that are not affected by mean-motion commensurabilities.Comment: 32 pages, including 8 figures; uses AASTeX v5.0; accepted for publication in Ap

A Primordial Origin of the Laplace Relation Among the Galilean Satellites

Understanding the origin of the orbital resonances of the Galilean satellites of Jupiter will constrain the longevity of the extensive volcanism on Io, may explain a liquid ocean on Europa, and may guide studies of the dissipative properties of stars and Jupiter-like planets. The differential migration of the newly formed Galilean satellites due to interactions with a circumjovian disk can lead to the primordial formation of the Laplace relation n_1 - 3 n_2 + 2 n_3 = 0, where the n_i are the mean orbital angular velocities of Io, Europa, and Ganymede, respectively. This contrasts with the formation of the resonances by differential expansion of the orbits from tidal torques from Jupiter.Comment: 13 pages, including 4 figures; uses scicite.st

Mode Variational LSTM Robust to Unseen Modes of Variation: Application to Facial Expression Recognition

Spatio-temporal feature encoding is essential for encoding the dynamics in video sequences. Recurrent neural networks, particularly long short-term memory (LSTM) units, have been popular as an efficient tool for encoding spatio-temporal features in sequences. In this work, we investigate the effect of mode variations on the encoded spatio-temporal features using LSTMs. We show that the LSTM retains information related to the mode variation in the sequence, which is irrelevant to the task at hand (e.g. classification facial expressions). Actually, the LSTM forget mechanism is not robust enough to mode variations and preserves information that could negatively affect the encoded spatio-temporal features. We propose the mode variational LSTM to encode spatio-temporal features robust to unseen modes of variation. The mode variational LSTM modifies the original LSTM structure by adding an additional cell state that focuses on encoding the mode variation in the input sequence. To efficiently regulate what features should be stored in the additional cell state, additional gating functionality is also introduced. The effectiveness of the proposed mode variational LSTM is verified using the facial expression recognition task. Comparative experiments on publicly available datasets verified that the proposed mode variational LSTM outperforms existing methods. Moreover, a new dynamic facial expression dataset with different modes of variation, including various modes like pose and illumination variations, was collected to comprehensively evaluate the proposed mode variational LSTM. Experimental results verified that the proposed mode variational LSTM encodes spatio-temporal features robust to unseen modes of variation.Comment: Accepted in AAAI-1