Building a sequence map of the pig pan-genome from multiple de novo assemblies and Hi-C data

Pigs were domesticated independently in the Near East and China,indicating that a single reference genome from one individual is unable to represent the full spectrum of divergent sequences in pigs worldwide.Therefore,12 de novo pig assemblies from Eurasia were compared in this study to identify the missing sequences from the reference genome.As a result,72.5 Mb of nonredundant sequences(~3% of the genome)were found to be absent from the reference genome(Sscrofa11.1)and were defined as pan-sequences.Of the pan-sequences,9.0 Mb were dominant in Chinese pigs,in contrast with their low frequency in European pigs.One sequence dominant in Chinese pigs contained the complete genic region of the tazarotene-induced gene 3(TIG3)gene which is involved in fatty acid metabolism.Using flanking sequences and Hi-C based methods,27.7% of the sequences could be anchored to the reference genome.The supplementation of these sequences could contribute to the accurate interpretation of the 3D chromatin structure.A web-based pan-genome database was further provided to serve as a primary resource for exploration of genetic diversity and promote pig breeding and biomedical research.

Solutions of the Generalized Lennard-Jones System

In this paper, we study solution structures of the following generalized Lennard-Jones system in R^n,x（-α/｜x｜α＋2＋β/｜x｜β＋2）xwith 0 〈 α 〈β. Considering periodic solutions with zero angular momentum, we prove that the corre- sponding problem degenerates to I-dimensional and possesses infinitely many periodic solutions which must be oscillating line solutions or constant solutions. Considering solutions with non-zero angular momentum, we compute Morse indices of the circular solutions first, and then apply the mountain pass theorem to show the existence of non-circular solutions with non-zero topological degrees. We further prove that besides circular solutions the system possesses in fact countably many periodic solutions with arbitrarily large topological degree, infinitely many quasi-periodic solutions, and infinitely many asymptotic solutions.

Index Iteration Theory for Brake Orbit Type Solutions and Applications

In this paper,we give a survey on the index iteration theory of an index theory for brake orbit type solutions and its applications in the study of brake orbit problems including the Seifert conjecture and the minimal period solution problems in brake orbit cases.

Symmetric Closed Characteristics on Symmetric Compact Convex Hypersurfaces in R^8

Let ∑be a C^3 compact symmetric convex hypersurface in R^8.We prove that when ∑ carries exactly four geometrically distinct closed characteristics,then all of them must be symmetric.Due to the example of weakly non-resonant ellipsoids,our result is sharp.

Geometric characterizations for variational minimizing solutions of charged 3-body problems

We study the charged 3-body problem with the potential function being （-a）-homogeneous on the mutual distances of any two particles via the variational method and try to find the geometric characterizations of the minimizers. We prove that if the charged 3-body problem admits a triangular central configuration, then the variational minimizing solutions of the problem in the τ/2-antiperiodic function space are exactly defined by the circular motions of this triangular central configuration.

An optimal increasing estimate of the iterated Maslov-type indices

An optimal increasing estimate of the Maslov_type index theory for iterations is proved.