Ge Nanowires Anode sheathed with Amorphous Carbon for Rechargeable Lithium batteries

Interdisciplinary School of Green EnergyThe composite electrode composed of single crystalline Ge NWs sheathed with amorphous carbon showed excellent electrochemical properties of large reversible capacity, high coulombic efficiency, excellent rate capability and stable cycle performance. c-Ge NWs synthesized by using thermal decomposition of C2H2 gas at 700 °C under Ar atmosphere after SLS (solution-liquid-solid) growth were found to have good performance during cycling with Li. The rate capability for charging was shown reversible capacity of 963 mAh/g with a coulombic efficiency of 90% and 700 mAh/g at the rate of 6C (= 4800mA/g). Capacity retention after 100 cycles was 72% at the rate of 0.5C. The improved electrochemical performance of c-Ge-NWs fabricated in our experiment was attributed to the formation of amorphous Ge NWs during cycling and a homogenous carbon coating on Ge NWs. Thus, these results suggest that the use of nanowires structure can be promising for alloy anode materials in lithium ion batteries

Dirichlet series of Rankin-Cohen Brackets

Given modular forms $f$ and $g$ of weights $k$ and $\ell$, respectively, their Rankin-Cohen bracket $[f,g]^{(k, \ell)}_n$ corresponding to a nonnegative integer $n$ is a modular form of weight $k +\ell +2n$, and it is given as a linear combination of the products of the form $f^{(r)} g^{(n-r)}$ for $0 \leq r \leq n$. We use a correspondence between quasimodular forms and sequences of modular forms to express the Dirichlet series of a product of derivatives of modular forms as a linear combination of the Dirichlet series of Rankin-Cohen brackets

A perturbative approach to a class of Fokker-Planck equations

In this paper we present a direct perturbative method to solving certain Fokker-Planck equations, which have constant diffusion coefficients and some small parameters in the drift coefficients. The method makes use of the connection between the Fokker-Planck and Schr\"odinger equations. Two examples are used to illustrate the method. In the first example the drift coefficient depends only on time but not on space. In the second example we consider the Uhlenbeck-Ornstein process with a small drift coefficient. These examples show that the such perturbative approach can be a useful tool to obtain approximate solutions of Fokker-Planck equations with constant diffusion coefficients.Comment: 5 pages, no figure

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

Tilings of the Sphere by Edge Congruent Pentagons

We study edge-to-edge tilings of the sphere by edge congruent pentagons, under the assumption that there are tiles with all vertices having degree 3. We develop the technique of neighborhood tilings and apply the technique to completely classify edge congruent earth map tilings.Comment: 36 pages, 34 figure