On Douglas general (α,β)(\alpha,\beta)-metrics

Douglas metrics are metrics with vanishing Douglas curvature which is an important projective invariant in Finsler geometry. To find more Douglas metrics, in this paper we consider a class of Finsler metrics called general $(\alpha,\beta)$-metrics, which are defined by a Riemannian metric $\alpha=\sqrt{a_{ij}(x)y^iy^j}$ and a $1$-form $\beta=b_i(x)y^i$. We obtain the differential equations that characterizes these metrics with vanishing Douglas curvature. By solving the equivalent PDEs, the metrics in this class are totally determined. Then many new Douglas metrics are constructed

Preprint Virtual Reality Assistant Technology for Learning Primary Geography

This is the preprint version of our paper on ICWL2015. A virtual reality based enhanced technology for learning primary geography is proposed, which synthesizes several latest information technologies including virtual reality(VR), 3D geographical information system(GIS), 3D visualization and multimodal human-computer-interaction (HCI). The main functions of the proposed system are introduced, i.e. Buffer analysis, Overlay analysis, Space convex hull calculation, Space convex decomposition, 3D topology analysis and 3D space intersection detection. The multimodal technologies are employed in the system to enhance the immersive perception of the users.Comment: This is the preprint version of our paper on ICWL201

A commend on "Three Classes of Newtonian Three-Body Planar Periodic Orbits" by \v{S}uvakov and Dmitra\v{s}inovi\'{c} (PRL, 2013)

Currently, the fifteen new periodic solutions of Newtonian three-body problem with equal mass were reported by \v{S}uvakov and Dmitra\v{s}inovi\'{c} (PRL, 2013) [1]. However, using a reliable numerical approach (namely the Clean Numerical Simulation, CNS) that is based on the arbitrary-order Taylor series method and data in arbitrary-digit precision, it is found that at least seven of them greatly depart from the periodic orbits after a long enough interval of time. Therefore, the reported initial conditions of at least seven of the fifteen orbits reported by \v{S}uvakov and Dmitra\v{s}inovi\'{c} [1] are not accurate enough to predict periodic orbits. Besides, it is found that these seven orbits are unstable.Comment: 5 pages, 5 figure

On the inherent self-excited macroscopic randomness of chaotic three-body system

What is the origin of macroscopic randomness (uncertainty)? This is one of the most fundamental open questions for human being. In this paper, 10000 samples of reliable (convergent), multiple-scale (from 1.0E-60 to 100) numerical simulations of a chaotic three-body system indicate that, without any external disturbance, the microscopic inherent uncertainty (in the level of 1.0E-60) due to physical fluctuation of initial positions of the three-body system enlarges exponentially into macroscopic randomness (at the level O(1)) until t=T*, the so-called physical limit time of prediction, but propagates algebraically thereafter when accurate prediction of orbit is impossible. Note that these 10000 samples use micro-level, inherent physical fluctuations of initial position, which have nothing to do with human being. Especially, the differences of these 10000 fluctuations are mathematically so small (in the level of 1.0E-60) that they are physically the SAME since a distance shorter than a Planck length does not make physical senses according to the spring theory. It indicates that the macroscopic randomness of the chaotic three-body system is self-excited, say, without any external force or disturbances, from the inherent micro-level uncertainty. This provides us the new concept "self-excited macroscopic randomness (uncertainty)". In addition, it is found that, without any external disturbance, the chaotic three-body system might randomly disrupt with the symmetry-breaking at t=1000 in about 25% probability, which provides us the new concepts "self-excited random disruption", "self-excited random escape" and "self-excited symmetry breaking" of the chaotic three-body system. It suggests that a chaotic three-body system might randomly evolve by itself, without any external forces or disturbance.Comment: 15 pages, 5 figures, accepted by Int. J. Bifurcation and Chaos, will be published via Open Acces

The Twin Conjugacy Search Problem and Applications

We propose a new computational problem over the noncommutative group, called the twin conjugacy search problem. This problem is related to the conjugacy search problem and can be used for almost all of the same cryptographic constructions that are based on the conjugacy search problem. However, our new problem is at least hard as the conjugacy search problem. Moreover, the twin conjugacy search problem have many applications. One of the most important applications, we propose a trapdoor test which can replace the function of the decision oracle. We also show other applications of the problem, including: a non-interactive key exchange protocol and a key exchange protocol, a new encryption scheme which is secure against chosen ciphertext attack, with a very simple and tight security proof and short ciphertexts, under a weak assumption, in the random oracle model

Spin excitations in K0.84_{0.84}Fe1.99_{1.99}Se2_2 superconductor as studied by M\"ossbauer spectroscopy

M\"ossbauer spectroscopy was used to probe the site specific information of the $K_{0.84}Fe_{1.99}Se_2$ superconductor. Possibility of coexistence of superconductivity and magnetism is discussed. A spin excitation gap, $\Delta E \approx$5\,meV, is observed by analyzing the temperature dependence of the hyperfine magnetic field (HMF) at the iron site within the spin wave theory. Using a simple model suggested in the literature, the temperature dependence of the HMF is well reproduced, suggesting that, below room temperature, the iron-selenide superconductors can be regarded as ferromagnetically coupled spin blocks that interact with each other antiferromagnetically to form the observed checkerboard-like magnetic structure

Continuous-Time Inverse Quadratic Optimal Control Problem

In this paper, the problem of finite horizon inverse optimal control (IOC) is investigated, where the quadratic cost function of a dynamic process is required to be recovered based on the observation of optimal control sequences. We propose the first complete result of the necessary and sufficient condition for the existence of corresponding LQ cost functions. Under feasible cases, the analytic expression of the whole solution space is derived and the equivalence of weighting matrices in LQ problems is discussed. For infeasible problems, an infinite dimensional convex problem is formulated to obtain a best-fit approximate solution with minimal control residual. And the optimality condition is solved under a static quadratic programming framework to facilitate the computation. Finally, numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed methods.Comment: 16 pages, 2 figure

SingleGAN: Image-to-Image Translation by a Single-Generator Network using Multiple Generative Adversarial Learning

Image translation is a burgeoning field in computer vision where the goal is to learn the mapping between an input image and an output image. However, most recent methods require multiple generators for modeling different domain mappings, which are inefficient and ineffective on some multi-domain image translation tasks. In this paper, we propose a novel method, SingleGAN, to perform multi-domain image-to-image translations with a single generator. We introduce the domain code to explicitly control the different generative tasks and integrate multiple optimization goals to ensure the translation. Experimental results on several unpaired datasets show superior performance of our model in translation between two domains. Besides, we explore variants of SingleGAN for different tasks, including one-to-many domain translation, many-to-many domain translation and one-to-one domain translation with multimodality. The extended experiments show the universality and extensibility of our model.Comment: Accepted in ACCV 2018. Code is available at https://github.com/Xiaoming-Yu/SingleGA

Charge redistribution at the antiferromagnetic phase transition in SrFeAsF compound

The relationship between spin, electron, and crystal structure has been one of the foremost issues in understanding the superconducting mechanism since the discovery of iron-based high temperature superconductors. Here, we report M\"ossbauer and first-principles calculations studies of the parent compound SrFeAsF with the largest temperature gap ($\sim$50\,K) between the structural and antiferromagnetic (AFM) transitions. Our results reveal that the structural transition has little effect on the electronic structure of the compound SrFeAsF while the development of the AFM order induces a redistribution of the charges near the Fermi level.Comment: 6 Pages, 7 Figure

Shift-Net: Image Inpainting via Deep Feature Rearrangement

Deep convolutional networks (CNNs) have exhibited their potential in image inpainting for producing plausible results. However, in most existing methods, e.g., context encoder, the missing parts are predicted by propagating the surrounding convolutional features through a fully connected layer, which intends to produce semantically plausible but blurry result. In this paper, we introduce a special shift-connection layer to the U-Net architecture, namely Shift-Net, for filling in missing regions of any shape with sharp structures and fine-detailed textures. To this end, the encoder feature of the known region is shifted to serve as an estimation of the missing parts. A guidance loss is introduced on decoder feature to minimize the distance between the decoder feature after fully connected layer and the ground-truth encoder feature of the missing parts. With such constraint, the decoder feature in missing region can be used to guide the shift of encoder feature in known region. An end-to-end learning algorithm is further developed to train the Shift-Net. Experiments on the Paris StreetView and Places datasets demonstrate the efficiency and effectiveness of our Shift-Net in producing sharper, fine-detailed, and visually plausible results. The codes and pre-trained models are available at https://github.com/Zhaoyi-Yan/Shift-Net.Comment: 25 pages, 17 figures, 1 table, main paper + supplementary materia