Primitive Fitting Using Deep Boundary Aware Geometric Segmentation

To identify and fit geometric primitives (e.g., planes, spheres, cylinders, cones) in a noisy point cloud is a challenging yet beneficial task for fields such as robotics and reverse engineering. As a multi-model multi-instance fitting problem, it has been tackled with different approaches including RANSAC, which however often fit inferior models in practice with noisy inputs of cluttered scenes. Inspired by the corresponding human recognition process, and benefiting from the recent advancements in image semantic segmentation using deep neural networks, we propose BAGSFit as a new framework addressing this problem. Firstly, through a fully convolutional neural network, the input point cloud is point-wisely segmented into multiple classes divided by jointly detected instance boundaries without any geometric fitting. Thus, segments can serve as primitive hypotheses with a probability estimation of associating primitive classes. Finally, all hypotheses are sent through a geometric verification to correct any misclassification by fitting primitives respectively. We performed training using simulated range images and tested it with both simulated and real-world point clouds. Quantitative and qualitative experiments demonstrated the superiority of BAGSFit

An Integrated Quadratic Reconstruction for Finite Volume Schemes to Scalar Conservation Laws in Multiple Dimensions

We proposed a piecewise quadratic reconstruction method in multiple dimensions, which is in an integrated style, for finite volume schemes to scalar conservation laws. This integrated quadratic reconstruction is parameter-free and applicable on flexible grids. We show that the finite volume schemes with the new reconstruction satisfy a local maximum principle with properly setup on time steplength. Numerical examples are presented to show that the proposed scheme attains a third-order accuracy for smooth solutions in both 2D and 3D cases. It is indicated by numerical results that the local maximum principle is helpful to prevent overshoots in numerical solutions

A Note on Gradually Varied Functions and Harmonic Functions

Any constructive continuous function must have a gradually varied approximation in compact space. However, the refinement of domain for $\sigma-$-net might be very small. Keeping the original discretization (square or triangulation), can we get some interesting properties related to gradual variation? In this note, we try to prove that many harmonic functions are gradually varied or near gradually varied; this means that the value of the center point differs from that of its neighbor at most by 2. It is obvious that most of the gradually varied functions are not harmonic.This note discusses some of the basic harmonic functions in relation to gradually varied functions.Comment: 7 pages and 2 figure

f-Orthomorphisms and f-Linear Operators on the Order Dual of an f-Algebra

In this paper we consider the $f$-orthomorphisms and $f$-linear operators on the order dual of an $f$-algebra. In particular, when the $f$-algebra has the factorization property (not necessarily unital), we prove that the orthomorphisms, $f$-orthomorphisms and $f$-linear operators on the order dual are precisely the same class of operators.Comment: 8 page

State-independent Uncertainty Relations and Entanglement Detection

The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of zero lower bounds. Here we develop a method to get uncertainty relations with state-independent lower bounds. The method works by exploring the eigenvalues of a Hermitian matrix composed by Bloch vectors of incompatible observables and is applicable for both pure and mixed states and for arbitrary number of N- dimensional observables. The uncertainty relation for incompatible observables can be explained by geometric relations related to the parallel postulate and the inequalities in Horn's conjecture on Hermitian matrix sum. Practical entanglement criteria are also presented based on the derived uncertainty relations.Comment: 15 pages, no figure

A reaction-diffusion-advection competition model with two free boundaries in heterogeneous time-periodic environment

In this paper, we study the dynamics of a two-species competition model with two different free boundaries in heterogeneous time-periodic environment, where the two species adopt a combination of random movement and advection upward or downward along the resource gradient. We show that the dynamics of this model can be classified into four cases, which forms a spreading-vanishing quartering. The notion of the minimal habitat size for spreading is introduced to determine if species can always spread. Rough estimates of the asymptotic spreading speed of free boundaries and the long time behavior of solutions are also established when spreading occurs. Furthermore, some sufficient conditions for spreading and vanishing are provided.Comment: 26 page

An Alternating Direction Method Approach to Cloud Traffic Management

In this paper, we introduce a unified framework for studying various cloud traffic management problems, ranging from geographical load balancing to backbone traffic engineering. We first abstract these real-world problems as a multi-facility resource allocation problem, and then present two distributed optimization algorithms by exploiting the special structure of the problem. Our algorithms are inspired by Alternating Direction Method of Multipliers (ADMM), enjoying a number of unique features. Compared to dual decomposition, they converge with non-strictly convex objective functions; compared to other ADMM-type algorithms, they not only achieve faster convergence under weaker assumptions, but also have lower computational complexity and lower message-passing overhead. The simulation results not only confirm these desirable features of our algorithms, but also highlight several additional advantages, such as scalability and fault-tolerance

A diffusive logistic problem with a free boundary in time-periodic environment: favorable habitat or unfavorable habitat

We study the diffusive logistic equation with a free boundary in timeperiodic environment. To understand the effect of the dispersal rate $d$, the original habitat radius $h_0$, the spreading capability $\mu$, and the initial density $u_0$ on the dynamics of the problem, we divide the time-periodic habitat into two cases: favorable habitat and unfavorable habitat. By choosing $d$, $h_0$, $\mu$ and $u_0$ as variable parameters, we obtain a spreading-vanishing dichotomy and sharp criteria for the spreading and vanishing in time-periodic environment. We introduce the principal eigenvalue $\lambda_1(d, \alpha, \gamma, h(t), T)$ to determine the spreading and vanishing of the invasive species. We prove that if $\lambda_1(d, \alpha, \gamma, h_0, T)\leq 0$, the spreading must happen; while if $\lambda_1(d, \alpha, \gamma, h_0, T)> 0$, the spreading is also possible. Our results show that the species in the favorable habitat can establish itself if the dispersal rate is slow or the occupying habitat is large. In an unfavorable habitat, the species vanishes if the initial density of the species is small, while survive successfully if the initial value is big. Moreover, when spreading occurs, the asymptotic spreading speed of the free boundary is determined.Comment: 24 pages. arXiv admin note: text overlap with arXiv:1311.7254 by other author

The diffusive competition problem with a free boundary in heterogeneous time-periodic environment

In this paper, we consider the diffusive competition problem with a free boundary and sign-changing intrinsic growth rate in heterogeneous time-periodic environment, consisting of an invasive species with density $u$ and a native species with density $v$. We assume that $v$ undergoes diffusion and growth in $R^{N}$ , and $u$ exists initially in a ball $B_{h_0}(0)$, but invades into the environment with spreading front $\{r = h(t)\}$. The effect of the dispersal rate $d_1$, the initial occupying habitat $h_0$, the initial density $u_0$ of invasive species $u$, and the parameter $\mu$ (see (1.3)) on the dynamics of this free boundary problem are studied. A spreading-vanishing dichotomy is obtained and some sufficient conditions for the invasive species spreading and vanishing are provided. Moreover, when spreading of $u$ happens, some rough estimates of the spreading speed are also given.Comment: 22 pages. arXiv admin note: text overlap with arXiv:1303.0454 by other author

Tuning Transport Properties of Topological Edge States of Bi(111) Bilayer Film by Edge Adsorption

Based on first-principles and tight-binding calculations, we report that the transport properties of topological edge states of zigzag Bi(111) nanoribbon can be significantly tuned by H edge adsorption. The Fermi velocity is increased by one order of magnitude, as the Dirac point is moved from Brillouin zone boundary to Brillouin zone center and the real-space distribution of Dirac states are made twice more delocalized. These intriguing changes are explained by an orbital filtering effect of edge H atoms, which removes certain components of $p$ orbits of edge Bi atoms that reshapes the topological edge states. In addition, the spin texture of the Dirac states is also modified, which is described by introducing an effective Hamiltonian. Our findings not only are of fundamental interest but also have practical implications in potential applications of topological insulators.Comment: 5 pages, 4 figure