We develop a cross-platform open-source Java application (BACOM2) with graphic user interface (GUI), and users also can use a XML file to set the parameters of algorithm model, file paths and the dataset of paired samples. BACOM2 implements the new e
ntire pipeline of copy number change analysis for heterogeneous cancer tissues, including extraction of raw copy number signals from CEL files of paired samples, attenuation correction, identification of balanced AB-genotype loci, copy number detection and segmentation, global baseline calculation and absolute normalization, differentiation of deletion types, estimation of the normal tissue fraction and correction of normal tissue contamination. BACOM2 focuses on the common tools for data preparation and absolute normalization for copy number analysis of heterogeneous cancer tissues. The software provides an additional choice for scientists who require a user-friendly, high-speed processing, cross-platform computing environment for large copy number data analysis.
Orbit-attitude hovering of a spacecraft at the natural relative equilibria in the body-fixed frame of a uniformly rotating asteroid is discussed in the framework of the full spacecraft dynamics, in which the spacecraft is modeled as a rigid body with
the gravitational orbit-attitude coupling. In this hovering model, both the position and attitude of the spacecraft are kept to be stationary in the asteroid body-fixed frame. A Hamiltonian structure-based feedback control law is proposed to stabilize the relative equilibria of the full dynamics to achieve the orbit-attitude hovering. The control law is consisted of two parts: potential shaping and energy dissipation. The potential shaping is to make the relative equilibrium a minimum of the modified Hamiltonian on the invariant manifold by modifying the potential artificially. With the energy-Casimir method, it is shown that the unstable relative equilibrium can always be stabilized in the Lyapunov sense by the potential shaping with sufficiently large feedback gains. Then the energy dissipation leads the motion to converge asymptotically to the minimum of the modified Hamiltonian on the invariant manifold, i.e., the relative equilibrium. The feasibility of the proposed stabilization control law is validated through numerical simulations in the case of a spacecraft orbiting around a small asteroid. The main advantage of the proposed hovering control law is that it is very simple and is easy to implement autonomously by the spacecraft with little computation. This advantage is attributed to the utilization of dynamical behaviors of the system in the control design.
The motion of a point mass in the J2 problem is generalized to that of a rigid body in a J2 gravity field. Different with the original J2 problem, the gravitational orbit-rotation coupling of the rigid body is considered in this generalized problem.
The linear stability of the classical type of relative equilibria of the rigid body, which have been obtained in our previous paper, is studied in the framework of geometric mechanics with the second-order gravitational potential. Non-canonical Hamiltonian structure of the problem, i.e., Poisson tensor, Casimir functions and equations of motion, are obtained through a Poisson reduction process by means of the symmetry of the problem. The linear system matrix at the relative equilibria is given through the multiplication of the Poisson tensor and Hessian matrix of the variational Lagrangian. Based on the characteristic equation of the linear system matrix, the conditions of linear stability of the relative equilibria are obtained. With the stability conditions obtained, the linear stability of the relative equilibria is investigated in details in a wide range of the parameters of the gravity field and the rigid body. We find that both the zonal harmonic J2 and the characteristic dimension of the rigid body have significant effects on the linear stability. Similar to the attitude stability in a central gravity field, the linear stability region is also consisted of two regions that are analogues of the Lagrange region and the DeBra-Delp region. Our results are very useful for the studies on the motion of natural satellites in our solar system.
The classical problem of attitude stability in a central gravity field is generalized to that on a stationary orbit around a uniformly-rotating asteroid. This generalized problem is studied in the framework of geometric mechanics. Based on the natura
l symplectic structure, the non-canonical Hamiltonian structure of the problem is derived. The Poisson tensor, Casimir functions and equations of motion are obtained in a differential geometric method. The equilibrium of the equations of motion, i.e. the equilibrium attitude of the spacecraft, is determined from a global point of view. Nonlinear stability conditions of the equilibrium attitude are obtained with the energy-Casimir method. The nonlinear attitude stability is then investigated versus three parameters of the asteroid, including the ratio of the mean radius to the stationary orbital radius, the harmonic coefficients C20 and C22. It is found that when the spacecraft is located on the intermediate-moment principal axis of the asteroid, the nonlinear stability domain can be totally different from the classical Lagrange region on a circular orbit in a central gravity field.
The dynamical behavior of spacecraft around asteroids is a key element in design of such missions. An asteroids irregular shape, non-spherical mass distribution and its rotational sate make the dynamics of spacecraft quite complex. This paper focuses
on the gravity gradient torque of spacecraft around non-spherical asteroids. The gravity field of the asteroid is approximated as a 2nd degree and order-gravity field with harmonic coefficients C20 and C22. By introducing the spacecrafts higher-order inertia integrals, a full fourth-order gravity gradient torque model of the spacecraft is established through the gravitational potential derivatives. Our full fourth-order model is more precise than previous fourth-order model due to the consideration of higher-order inertia integrals of the spacecraft. Some interesting conclusions about the gravity gradient torque model are reached. Then a numerical simulation is carried out to verify our model. In the numerical simulation, a special spacecraft consisted of 36 point masses connected by rigid massless rods is considered. We assume that the asteroid is in a uniform rotation around its maximum-moment principal axis, and the spacecraft is on the stationary orbit in the equatorial plane. Simulation results show that the motion of previous fourth-order model is quite different from the exact motion, while our full fourth-order model fits the exact motion very well. And our model is precise enough for practical applications.
Einstein utilized Lorentz invariance from Maxwells equations to modify mechanical laws and establish the special theory of relativity. Similarly, we may have a different theory if there exists another covariance of Maxwells equations. In this paper,
we find such a new transformation where Maxwells equations are still unchanged. Consequently, Veselagos metamaterial and other systems have negative phase velocities without double negative permittivity and permeability can be described by a unified theory. People are interested in the application of metamaterials and negative phase velocities but do not appreciate the magnitude and significance to the spacetime conception of modern physics and philosophy.
Purpose: This paper presents a full fourth-order model of the gravity gradient torque of spacecraft around asteroids by taking into consideration of the inertia integrals of the spacecraft up to the fourth order, which is an improvement of the previo
us fourth-order model of the gravity gradient torque. Design, methodology and approach: The fourth-order gravitational potential of the spacecraft is derived based on Taylor expansion. Then the expression of the gravity gradient torque in terms of gravitational potential derivatives is derived. By using the formulation of the gravitational potential, explicit formulations of the full fourth-order gravity gradient torque are obtained. Then a numerical simulation is carried out to verify our model. Findings: We find that our model is more sound and precise than the previous fourth-order model due to the consideration of higher-order inertia integrals of the spacecraft. Numerical simulation results show that the motion of the previous fourth-order model is quite different from the exact motion, while our full fourth-order model fits the exact motion very well. Our full fourth-order model is precise enough for high-precision attitude dynamics and control around asteroids. Practical implications: This high-precision model is of importance for the future asteroids missions for scientific explorations and near-Earth objects mitigation. Originality and value: In comparison with the previous model, a gravity gradient torque model around asteroids that is more sound and precise is established. This model is valuable for high-precision attitude dynamics and control around asteroids.
BACOM is a statistically principled and unsupervised method that detects copy number deletion types (homozygous versus heterozygous), estimates normal cell fraction, and recovers cancer specific copy number profiles, using allele specific copy number
signals. In a subsequent analysis of TCGA ovarian cancer dataset, the average normal cell fraction estimated by BACOM was found higher than expected. In this letter, we first discuss the advantages of the BACOM in relation to alternative approaches. Then, we show that this elevated estimate of normal cell fraction is the combined result of inaccurate signal modeling and normalization. Lastly, we describe an allele specific signal modeling and normalization scheme that can enhance BACOM applications in many biological contexts. An open source MATLAB program was developed to implement our extended method and it is publically available.
Intercellular heterogeneity serves as both a confounding factor in studying individual clones and an information source in characterizing any heterogeneous tissues, such as blood, tumor systems. Due to inevitable sequencing errors and other sample pr
eparation artifacts such as PCR errors, systematic efforts to characterize intercellular genomic heterogeneity must effectively distinguish genuine clonal sequences from fake derivatives. We developed a novel approach (SIGH) for identifying significant genuine clonal sequences directly from mixed sequencing reads that can improve genomic analyses in many biological contexts. This method offers several attractive features: (1) it automatically estimates the error rate from raw sequence reads and identifies genuine clonal sequences; (2) it is robust to the large variety of error rate due to the various experimental conditions; (3) it is supported by a well grounded statistical framework that exploits probabilistic characteristics of sequencing errors; (4) its unbiased strategy allows detecting rare clone(s) despite that clone relative abundance; and (5) it estimates constituent proportions in each sample. Extensive realistic simulation studies show that our method can reliably estimate the error rates and faithfully distinguish the genuine clones from fake derivatives, paving the way for follow up analysis that is otherwise ruined by the often dominant fake clones.
Tissue heterogeneity is a major confounding factor in studying individual populations that cannot be resolved directly by global profiling. Experimental solutions to mitigate tissue heterogeneity are expensive, time consuming, inapplicable to existin
g data, and may alter the original gene expression patterns. Here we ask whether it is possible to deconvolute two-source mixed expressions (estimating both proportions and cell-specific profiles) from two or more heterogeneous samples without requiring any prior knowledge. Supported by a well-grounded mathematical framework, we argue that both constituent proportions and cell-specific expressions can be estimated in a completely unsupervised mode when cell-specific marker genes exist, which do not have to be known a priori, for each of constituent cell types. We demonstrate the performance of unsupervised deconvolution on both simulation and real gene expression data, together with perspective discussions.
