arXiv subjects

Li Chen

Publications and source records attributed to Li Chen.

747 records · Page 42Linked to original sources

arXiv2008

Linear Time Recognition Algorithms for Topological Invariants in 3D

In this paper, we design linear time algorithms to recognize and determine topological invariants such as the genus and homology groups in 3D. These properties can be used to identify patterns in 3D image recognition. This has tremendous amount of applications in 3D medical image analysis. Our method is based on cubical images with direct adjacency, also called (6,26)-connectivity images in discrete geometry. According to the fact that there are only six types of local surface points in 3D and a discrete version of the well-known Gauss-Bonnett Theorem in differential geometry, we first determine the genus of a closed 2D-connected component (a closed digital surface). Then, we use Alexander duality to obtain the homology groups of a 3D object in 3D space.

cs.CV↗

arXiv2008

lambda-Connectedness Determination for Image Segmentation

Image segmentation is to separate an image into distinct homogeneous regions belonging to different objects. It is an essential step in image analysis and computer vision. This paper compares some segmentation technologies and attempts to find an automated way to better determine the parameters for image segmentation, especially the connectivity value of $λ$ in $λ$-connected segmentation. Based on the theories on the maximum entropy method and Otsu's minimum variance method, we propose:(1)maximum entropy connectedness determination: a method that uses maximum entropy to determine the best $λ$ value in $λ$-connected segmentation, and (2) minimum variance connectedness determination: a method that uses the principle of minimum variance to determine $λ$ value. Applying these optimization techniques in real images, the experimental results have shown great promise in the development of the new methods. In the end, we extend the above method to more general case in order to compare it with the famous Mumford-Shah method that uses variational principle and geometric measure.

cs.CV↗

arXiv2008

Hsiao-Code Check Matrices and Recursively Balanced Matrices

The key step of generating the well-known Hsiao code is to construct a {0,1}-check-matrix in which each column contains the same odd-number of 1's and each row contains the same number of 1's or differs at most by one for the number of 1's. We also require that no two columns are identical in the matrix. The author solved this problem in 1986 by introducing a type of recursively balanced matrices. However, since the paper was published in Chinese, the solution for such an important problem was not known by international researchers in coding theory. In this note, we focus on how to practically generate the check matrix of Hsiao codes. We have modified the original algorithm to be more efficient and effective. We have also corrected an error in algorithm analysis presented in the earlier paper. The result shows that the algorithm attained optimum in average cases if a divide-and-conquer technique must be involved in the algorithm.

cs.DM↗

arXiv2007

High spatial resolution X-ray spectroscopy of SNR Cassiopeia A with {\sl Chandra}

We present high spatial resolution X-ray spectroscopy of supernova remnant Cassiopeia A with the {\sl Chandra} observations. The X-ray emitting region of this remnant was divided into 38 $\times$ 34 pixels with a scale of 10$\arcsec$ $\times$ 10$\arcsec$ each. Spectra of 960 pixels were created and fitted with an absorbed two component non-equilibrium ionization model. With the spectral analysis results we obtained maps of absorbing column density, temperatures, ionization ages, and the abundances for Ne, Mg, Si, S, Ca and Fe. The Si, S and possibly Ca abundance maps show obviously jet structures, while Fe doesn't follow the jet but seems to be distributed perpendicular to it. In the range of about two orders of magnitude, the abundances of Si, S and Ca show tight correlations between each other, suggesting them to be ejecta from explosive O-burning and incomplete Si-burning. Meanwhile, Ne abundance is well correlated with that of Mg, indicating them to be the ashes of explosive C/Ne burning. The Fe abundance is positively correlated with that of Si when Si abundance is lower than 3 solar abundances, but a negative correlation appears when the Si abundance is higher. We suggest that such a two phase correlation is the results of different ways in which Fe is synthesized.

astro-ph↗

arXiv2005

Simple Graphs and Commutative Zero-Divisor Semigroups

In this paper, we study commutative zero-divisor semigroups determined by graphs. We prove a uniqueness theorem for a class of graphs. We show two classes of graphs that have no corresponding semigroups. In particular, any complete graph $K_n$ together with more than three end vertices and any complete bipartite graph together with more than one end vertices have no corresponding semigroups. We also determine all possible zero-divisor semigroups whose zero-divisor graph is the com- plete graph $K_3$ together with two end vertices.

math.RA↗

arXiv2005

Projecting the Forward Rate Flow onto a Finite Dimensional Manifold

Given a Heath-Jarrow-Morton (HJM) interest rate model $\mathcal{M}$ and a parametrized family of finite dimensional forward rate curves $\mathcal{G}$, this paper provides a technique for projecting the infinite dimensional forward rate curve $r_{t}$ given by $\mathcal{M}$ onto the finite dimensional manifold $\mathcal{G}$.The Stratonovich dynamics of the projected finite dimensional forward curve are derived and it is shown that, under the regularity conditions, the given Stratonovich differential equation has a unique strong solution. Moreover, this projection leads to an efficient algorithm for implicit parametric estimation of the infinite dimensional HJM model. The feasibility of this method is demonstrated by applying the generalized method of moments.

cs.CE↗

arXiv2005

Consistency Problems for Jump-Diffusion Models

In this paper consistency problems for multi-factor jump-diffusion models, where the jump parts follow multivariate point processes are examined. First the gap between jump-diffusion models and generalized Heath-Jarrow-Morton (HJM) models is bridged. By applying the drift condition for a generalized arbitrage-free HJM model, the consistency condition for jump-diffusion models is derived. Then we consider a case in which the forward rate curve has a separable structure, and obtain a specific version of the general consistency condition. In particular, a necessary and sufficient condition for a jump-diffusion model to be affine is provided. Finally the Nelson-Siegel type of forward curve structures is discussed. It is demonstrated that under regularity condition, there exists no jump-diffusion model consistent with the Nelson-Siegel curves.

cs.IT↗

arXiv2005

Polarization in Gamma-Ray Bursts Produced by Pinch Discharge

Large-voltage and high-temperature plasma columns produced by pinch discharge can generate gamma-ray flashes with energy spectra and spectral evolution consistent with that observed in gamma-ray bursts (GRBs). The inverse Compton scattering (ICS) during the discharge process can produce high linear polarization. The calculation indicates that the observed polarization depends on the angle between the observer's line-of-sight to the GRB and the direction of the pinch discharge, but only weakly depends on observed gamma-ray energy.

astro-ph↗

arXiv2002

The largest virialized dark halo in the universe

Using semi-analytic approach, we present an estimate of the properties of the largest virialized dark halos in the present universe for three different scenarios of structure formation: SCDM, LCDM and OCDM models. The resulting virial mass and temperature increase from the lowest values of $1.6 \times 10^{15}h^{-1}M_{\odot}$ and 9.8 keV in OCDM, the mid-range values of $9.0 \times 10^{15}h^{-1}M_{\odot}$ and 31 keV in LCDM, to the highest values of $20.9 \times 10^{15}h^{-1}M_{\odot}$, 65 keV in SCDM. As compared with the largest virialized object seen in the universe, the richest clusters of galaxies, we can safely rule out the OCDM model. In addition, the SCDM model is very unlikely because of the unreasonably high virial mass and temperature. Our computation favors the prevailing LCDM model in which superclusters may be marginally regarded as dynamically-virialized systems.

astro-ph↗