Abstract:
In this paper, a novel algorithm for mammographic images enhancement and denoising based on Multiscale Geometric Analysis (MGA) is proposed. Firstly mammograms are decomposed into different scales and directional subbands using Nonsubsampled Contourlet Transform (NSCT). After modeling the coefficients of each directional subbands using Generalized Gaussian Mixture Model (GGMM) according to the statistical property, they are categorized into strong edges, weak edges and noise by Bayesian classifier. To enhance the suspicious lesion and suppress the noise, a nonlinear mapping function is designed to adjust the coefficients adaptively so as to obtain a good enhancement result with significant features. Finally, the resulted mammographic images are obtained by reconstructing with the modified coefficients using NSCT. Experimental results illustrate that the proposed approach is practicable and robustness, which outperforms the spatial filters and other methods based on wavelets in terms of mass and microcalcification denoising and enhancement.

Abstract:
A unified, fast, and effective approach is developed for numerical calculation of the well-known plasma dispersion function with extensions from Maxwellian distribution to almost arbitrary distribution functions, such as the $\delta$, flat top, triangular, $\kappa$ or Lorentzian, slowing down, and incomplete Maxwellian distributions. The singularity and analytic continuation problems are also solved generally. Given that the usual conclusion $\gamma\propto\partial f_0/\partial v$ is only a rough approximation when discussing the distribution function effects on Landau damping, this approach provides a useful tool for rigorous calculations of the linear wave and instability properties of plasma for general distribution functions. The results are also verified via a linear initial value simulation approach. Intuitive visualizations of the generalized plasma dispersion function are also provided.

Abstract:
A general dispersion-relation solver that numerically evaluates the full propagation properties of all the waves in fluid plasmas is presented. The effects of anisotropic pressure, external magnetic fields and beams, relativistic dynamics, as well as local plasma inhomogeneity are included. [Computer Physics Communications, (2013); doi: 10.1016/j.cpc.2013.10.012; code: http://cpc.cs.qub.ac.uk/summaries/AERF\_v1\_0.html]

Abstract:
There are two usual computational methods for linear (waves and instabilities) problem: eigenvalue (dispersion relation) solver and initial value solver. In fact, we can introduce an idea of the combination of them, i.e., we keep time derivative dt term (and other term if have, e.g., kinetic dv term), but transform the linear spatial derivatives dx term to ik, which then can reduce the computational dimensions. For example, most (fluid and kinetic) normal mode problems can be reduced from treating cumbersome PDEs to treating simple ODEs. Examples for MHD waves, cold plasma waves and kinetic Landau damping are given, which show to be extremely simple or even may be the simplest method for simulating them. [I don't know whether this idea is new, but it seems very interesting and useful. So, I choose making it public.]

Abstract:
There is no wide accepted theory for ELM (Edge Localized Mode) yet. Some fusion people feel that we may never get a final theory for ELM and H-mode, since which are too complicated (also related to the unsolved turbulence problem) and with at least three time scales. The only way out is using models. (This is analogous to that we believe quantum mechanics can explain chemistry and biology, but no one can calculate DNA structure from Schrodinger equation directly.) This manuscript gives some possible mathematical approaches to it. I should declare that these are just math toys for me yet. They may inspire to good understandings of ELM and H-mode, may not. Useful or useless, I don't know. One need not take too much care of it. Just for fun and enjoying different interesting ideas.

Abstract:
We bring a totally new concept for plasma simulation, other than the conventional two ways: Fluid/Kinetic Continuum (FKC) method and Particle-in-Cell (PIC) method. This method is based on Pure Monte Carlo (PMC), but far beyond traditional treatments. PMC solves all the equations (kinetic, fluid, field) and treats all the procedures (collisions, others) in the system via MC method. As shown in two paradigms, many advantages have found. It has shown the capability to be the third importance approach for plasma simulation or even completely substitute the other two in the future. It's also suitable for many unsolved problems, then bring plasma simulation to a new era.

Abstract:
A hitherto difficult and unsolved issue in plasma physics is how to give a general numerical solver for complicated plasma dispersion relation, although we have long known the general analytical forms. We transform the task to a full-matrix eigenvalue problem, which allows to numerically calculate all the dispersion relation solutions exactly free from convergence problem and give polarizations naturally for arbitrarily complicated multi-scale fluid plasma with arbitrary number of components. Attempt to kinetic plasma via $N$-point Pad\'e approximation of plasma dispersion function also shows good results.

Abstract:
In a collisionless Vlasov-Poisson (V-P) electron plasma system, two types of modes for electric field perturbation exist: the exponentially Landau damped electron plasma waves and the initial-value sensitive ballistic modes. Here, the V-P system is modified slightly to a Vlasov-Ampere (V-A) system. A new constant residual mode is revealed. Mathematically, this mode comes from the Laplace transform of an initial electric field perturbation, and physically represents that an initial perturbation (e.g., external electric field perturbation) would not be damped away. Thus, this residual mode is more difficult to be damped than the ballistic mode. [Physics of Plasmas 20, 112108 (2013); doi: 10.1063/1.4831761]

Abstract:
Understanding the evolution of karst rocky desertification (KRD)
quantitatively is essential to obtain objective knowledge about the concept of
KRD and the form reason of KRD, and is useful to restore KRD land. Houzhaihe
area located in central plateau in Guizhou Province was studied here as a
representative assemblage landform and its KRD’ s evolution and driving factors
were studied, based mainly on high-resolution remote sensing image in 1963,
1978, 2005 and 2010. The KRD land comprises light KRD, moderate KRD and severe
KRD. The results demonstrated that the evolution process of KRD can be divided
into four modes such as unchanged, weakened, fluctuated and aggravated in the
study area. The KRD with no changes from 1963 to 2010, namely, unchanged mode,
accounted for 43.76% of the total area of the KRD in 2010; it distributed in
the area with the slope of 15° - 25° and >25° basically. Furthermore, the
severe KRD distributed mainly in the areas within 300 - 600 m distance from
settlement; when the distance away from the rural settlements was more than 900
m, the severe KRD declined, and its proportion was 28.6% and 10.6% in 1963 and
2010 respectively. In the peak-cluster depressions, located in central study
area, the slope cropland with slope of 15° - 25° was still abounding, and was
seriously rocky desertification generally. So, we propose that the existence of
a large number of slope croplands is still the major driving factor of land
rocky desertification. Therefore, for the rocky desertification control, the
authors consider that the focal point is to alter the land use of steep-slope
cropland at present.