Effective Circle Count for Apollonian packings and Closed horospheres

The main result of this paper is an effective count for Apollonian circle packings that are either bounded or contain two parallel lines. We obtain this by proving an effective equidistribution of closed horospheres in the unit tangent bundle of a geometrically finite hyperbolic 3-manifold of infinite volume, whose fundamental group has critical exponent bigger than 1. We also discuss applications to Affine sieves. Analogous results for surfaces are treated as well.Comment: 43 pages, 2 figures, To appear in GAF

Shaken not stirred — On internal flow patterns in oscillating sessile drops

We use numerical (volume of fluid) simulations to study the flow in an oscillating sessile drop immersed in an ambient immiscible fluid. The drop is excited by a sinusoidal variation of the contact angle at variable frequency. We identify the eigenfrequencies and eigenmodes of the drops and analyze the internal flow fields by following the trajectories of tracer particles. The flow fields display an oscillatory component as well as a time-averaged mean component. The latter is oriented upward along the surface of the drop from the contact line towards the apex and downward along the symmetry axis. It vanishes at high and low frequencies and displays a broad maximum around f =200–300Hz. We show that the frequency dependence of the mean flow can be described in terms of Stokes drift driven by capillary waves that originate from the contact line, in agreement with recent experiments

DeepStory: Video Story QA by Deep Embedded Memory Networks

Question-answering (QA) on video contents is a significant challenge for achieving human-level intelligence as it involves both vision and language in real-world settings. Here we demonstrate the possibility of an AI agent performing video story QA by learning from a large amount of cartoon videos. We develop a video-story learning model, i.e. Deep Embedded Memory Networks (DEMN), to reconstruct stories from a joint scene-dialogue video stream using a latent embedding space of observed data. The video stories are stored in a long-term memory component. For a given question, an LSTM-based attention model uses the long-term memory to recall the best question-story-answer triplet by focusing on specific words containing key information. We trained the DEMN on a novel QA dataset of children's cartoon video series, Pororo. The dataset contains 16,066 scene-dialogue pairs of 20.5-hour videos, 27,328 fine-grained sentences for scene description, and 8,913 story-related QA pairs. Our experimental results show that the DEMN outperforms other QA models. This is mainly due to 1) the reconstruction of video stories in a scene-dialogue combined form that utilize the latent embedding and 2) attention. DEMN also achieved state-of-the-art results on the MovieQA benchmark.Comment: 7 pages, accepted for IJCAI 201

Kinetics and thermodynamics of ceramic/metal interface reactions related to high T(sub c) superconducting applications

Superconducting ceramic materials, no matter what their form, size or shape, must eventually make contact with non-superconducting materials in order to accomplish current transfer to other parts of a real operating system, or for testing and measurement of properties. Thus, whether the configuration is a clad wire, a bulk superconducting disc, tape, or a thick or thin superconducting film on a substrate, the physical and mechanical behavior of interface (interconnections, joints, etc.) between superconductors and normal conductor materials of all kinds is of extreme importance to the technological development of these systems. Fabrication heat treatments associated with the particular joining process allow possible reactions between the superconducting ceramic and the contact to occur, and consequently influence properties at the interface region. The nature of these reactions is therefore of great broad interest, as these may be a primary determinant for the real capability of these materials. Research related both to fabrication of composite sheathed wire products, and the joining contacts for physical property measurements, as well as, a review of other related literature in the field are described. Comparison are made between 1-2-3, Bi-, and Tl-based ceramic superconductors joined to a variety of metals including Cu, Ni, Fe, Cr, Ag, Ag-Pd, Au, In, and Ga. The morphology of reaction products and the nature of interface degradation as a function of time will be highlighted