34899932
Paths and Cycles in Breakpoint Graph of Random Multichromosomal Genomes
We study the probability distribution of the distance d = n + chi - kappa - psi between two genomes with n markers distributed on chi chromosomes and with breakpoint graphs containing kappa cycles and psi "good" paths, under the hypothesis of random gene order. We interpret the random order assumption in terms of a stochastic method for constructing the bicolored breakpoint graph. We show that the limiting expectation of E[d] = n - 1/2chi - 1/2 log n+chi/2chi. We also calculate the variance, the effect of different numbers of chromosomes in the two genomes, and the number of plasmids, or circular chromosomes, generated by the random breakpoint graph construction. A more realistic model allows intra- and interchromosomal operations to have different probabilities, and simulations show that for a fixed number of rearrangements, kappa and d depend on the relative proportions of the two kinds of operation.
16954571
Poisson adjacency distributions in genome comparison: multichromosomal, circular, signed and unsigned cases
The number of common adjacencies of genetic markers, as a measure of the similarity of two genomes, has been widely used as indicator of evolutionary relatedness and as the basis for inferring phylogenetic relationships. Its probability distribution enables statistical tests in detecting whether significant evolutionary signal remains in the marker order. In this article, we derive the probability distributions of the number of adjacencies for a number of types of genome--signed or unsigned, circular or linear, single-chromosome or multichromosomal. Generating functions are found for singlechromosome cases, from which exact counts can be calculated. Probability approaches are adopted for multichromosomal cases, where we.nd the exact values for expectations and variances. In both cases, the limiting distributions are derived in term of numbers of adjacencies. For all unsigned cases, the limiting distribution is Poisson with parameter 2; for all signed cases, the limiting distribution is Poisson with parameter (1/2).
35283967
Detection function method and its application to a class of quintic Hamiltonian systems with quintic perturbations
By using the bifurcation theory of planar dynamical systems and the method of detection functions to investigate the bifurcation of limit cycles of a perturbed quintic Hamiltonian system. It is shown that under two different sets of controlled parameters, the given system has at least 23 limit cycles having two different configurations of the compound eyes, respectively.
38063423
A series of explicit and exact travelling wave solutions of the B(m, n) equations
Abstract In this paper, explicit and exact travelling wave solutions of B ( m ,  n ) equations are investigated by using a generalized algebraic method. A series of explicit exact solutions, such as solitary wave, triangular periodic, rational, Jacobi and Weierstrass elliptic function periodic solutions are obtained. Many new results are presented.
485740
Training Hierarchical Feed-Forward Visual Recognition Models Using Transfer Learning from Pseudo-Tasks
Building visual recognition models that adapt across different domains is a challenging task for computer vision. While feature-learning machines in the form of hierarchial feed-forward models (e.g., convolutional neural networks) showed promise in this direction, they are still difficult to train especially when few training examples are available. In this paper, we present a framework for training hierarchical feed-forward models for visual recognition, using transfer learning from pseudo tasks. These pseudo tasks are automatically constructed from data without supervision and comprise a set of simple pattern-matching operations. We show that these pseudo tasks induce an informative inverse-Wishart prior on the functional behavior of the network, offering an effective way to incorporate useful prior knowledge into the network training. In addition to being extremely simple to implement, and adaptable across different domains with little or no extra tuning, our approach achieves promising results on challenging visual recognition tasks, including object recognition, gender recognition, and ethnicity recognition.
11714898
On the number of limit cycles of a cubic polynomials Hamiltonian system under quintic perturbation
Abstract This paper is concerned with the number and distribution of limit cycles of a cubic Hamiltonian system under quintic perturbation. By using the bifurcation theory and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C 9 1 ⊃ [ C 1 1 + 2 ( C 3 2 ⊃ 2 C 1 2 ) ] . These results in the paper are useful for the study of the weakened Hilbert’s 16th problem.
23372402
Information Concept Lattice and Its Reductions
In this paper, the combination of formal concept analysis and rough set theory is considered. The notion of information concept lattice is presented and some properties are given. We present the reduction theory of information concept lattice and obtain the reduction method. Information concept lattice is compared with rough set theory and concept lattice.