Ting-Li ChenInstitute of Statistical Science, Academia SinicaDai-Ni HsiehInstitute of Statistical Science, Academia SinicaHung HungInstitute of Epidemiology and Preventive Medicine I-Ping TuInstitute of Statistical Science, Academia SinicaPei-Shien WuDept. of Biostatistics, Duke UniversityYi-Ming WuInstitute of Chemistry, Academia SinicaWei-Hau ChangInstitute of Chemistry, Academia SinicaSu-Yun HuangInstitute of Statistical Science, Academia Sinica
Statistics Theory and MethodsData Analysis, Bio-Statistics, Bio-Mathematicsmathscidoc:2004.33002
The Annals of Applied Statistics , 8, (1), 259-285, 2014
Cryo-electron microscopy (cryo-EM) has recently emerged as a powerful
tool for obtaining three-dimensional (3D) structures of biological macromolecules
in native states. A minimum cryo-EM image data set for deriving a
meaningful reconstruction is comprised of thousands of randomly orientated
projections of identical particles photographed with a small number of electrons.
The computation of 3D structure from 2D projections requires clustering,
which aims to enhance the signal to noise ratio in each view by grouping
similarly oriented images. Nevertheless, the prevailing clustering techniques
are often compromised by three characteristics of cryo-EM data: high noise
content, high dimensionality and large number of clusters. Moreover, since
clustering requires registering images of similar orientation into the same
pixel coordinates by 2D alignment, it is desired that the clustering algorithm
can label misaligned images as outliers. Herein, we introduce a clustering algorithm
γ-SUP to model the data with a q-Gaussian mixture and adopt the
minimum γ-divergence for estimation, and then use a self-updating procedure
to obtain the numerical solution. We apply γ-SUP to the cryo-EM images
of two benchmark macromolecules, RNA polymerase II and ribosome.
In the former case, simulated images were chosen to decouple clustering from
alignment to demonstrate γ-SUP is more robust to misalignment outliers than
the existing clustering methods used in the cryo-EM community. In the latter
case, the clustering of real cryo-EM data by our γ-SUP method eliminates
noise in many views to reveal true structure features of ribosome at the projection
We treat all the bivariate lack-of-memory (BLM) distributions in a unified approach and develop some new general properties of the BLM distributions, including joint moment generating function, product moments, and dependence structure. Necessary and sufficient conditions for the survival functions of BLM distributions to be totally positive of order two are given. Some previous results about specific BLM distributions are improved. In particular, we show that both the Marshall–Olkin survival copula and survival function are totally positive of all orders, regardless of parameters. Besides, we point out that Slepian’s inequality also holds true for BLM distributions.
This paper is about the propagation of the singularities in the solutions to the Cauchy problem of the spatially inhomogeneous Boltzmann equation with angular cutoff assumption. It is motivated by the work of BoudinDesvillettes on the propagation of singularities in solutions near vacuum. It shows that for the solution near a global Maxwellian, singularities in the initial data propagate like the free transportation. Precisely, the solution is the sum of two parts in which one keeps the singularities of the initial data and the other one is regular with locally bounded derivatives of fractional order in some Sobolev space. In addition, the dependence of the regularity on the cross-section is also given.
In this paper, we provide the O() corrections to the hydrodynamic model derived by Degond and Motsch from a kinetic version of the model by Vicsek and co-authors describing flocking biological agents. The parameter stands for the ratio of the microscopic to the macroscopic scales. The O() corrected model involves diffusion terms in both the mass and velocity equations as well as terms which are quadratic functions of the first-order derivatives of the density and velocity. The derivation method is based on the standard ChapmanEnskog theory, but is significantly more complex than usual due to both the non-isotropy of the fluid and the lack of momentum conservation.
The approach combines second and fourth order statistics to perform BSS of instantaneous mixtures. It applies for any number of receivers if they are as many as sources. It is a batch algorithm that uses non-Gaussianity and stationarity of source signals. It is linear algebra based direct method, reliable and robust, though large dimensions of sources may slow down the computation significantly. It is however limited to instantaneous mixtures.