Iterative Algorithm for Common Fixed Points of Infinite Family of Nonexpansive Mappings in Banach Spaces

Let C be a nonempty closed convex subset of a real uniformly smooth Banach space X, {Tk}k=1∞:C→C an infinite family of nonexpansive mappings with the nonempty set of common fixed points ⋂k=1∞Fix⁡(Tk), and f:C→C a contraction. We introduce an explicit iterative algorithm xn+1=αnf(xn)+(1-αn)Lnxn, where Ln=∑k=1n(ωk/sn)Tk,Sn=∑k=1nωk,   and wk>0 with ∑k=1∞ωk=1. Under certain appropriate conditions on {αn}, we prove that {xn} converges strongly to a common fixed point x* of {Tk}k=1∞, which solves the following variational inequality: 〈x*-f(x*),J(x*-p)〉≤0,    p∈⋂k=1∞Fix(Tk), where J is the (normalized) duality mapping of X. This algorithm is brief and needs less computational work, since it does not involve W-mapping

Strong Convergence Theorems for the Split Common Fixed Point Problem for Countable Family of Nonexpansive Operators

We introduce a new iterative algorithm for solving the split common fixed point problem for countable family of nonexpansive operators. Under suitable assumptions, we prove that the iterative algorithm strongly converges to a solution of the problem

Modified Projection Algorithms for Solving the Split Equality Problems

The split equality problem (SEP) has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Byrne and Moudafi (2013) proposed a CQ algorithm for solving it. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively and performs an additional projection step onto two half-spaces in each iteration. We further propose a relaxation scheme for the self-adaptive projection algorithm by using projections onto half-spaces instead of those onto the original convex sets, which is much more practical. Weak convergence results for both algorithms are analyzed

Gene and Genome Parameters of Mammalian Liver Circadian Genes (LCGs)

The mammalian circadian system controls various physiology processes and behavior responses by regulating thousands of circadian genes with rhythmic expressions. In this study, we redefined circadian-regulated genes based on published results in the mouse liver and compared them with other gene groups defined relative to circadian regulations, especially the non-circadian-regulated genes expressed in liver at multiple molecular levels from gene position to protein expression based on integrative analyses of different datasets from the literature. Based on the intra-tissue analysis, the liver circadian genes or LCGs show unique features when compared to other gene groups. First, LCGs in general have less neighboring genes and larger in both genomic and 3′-UTR lengths but shorter in CDS (coding sequence) lengths. Second, LCGs have higher mRNA and protein abundance, higher temporal expression variations, and shorter mRNA half-life. Third, more than 60% of LCGs form major co-expression clusters centered in four temporal windows: dawn, day, dusk, and night. In addition, larger and smaller LCGs are found mainly expressed in the day and night temporal windows, respectively, and we believe that LCGs are well-partitioned into the gene expression regulatory network that takes advantage of gene size, expression constraint, and chromosomal architecture. Based on inter-tissue analysis, more than half of LCGs are ubiquitously expressed in multiple tissues but only show rhythmical expression in one or limited number of tissues. LCGs show at least three-fold lower expression variations across the temporal windows than those among different tissues, and this observation suggests that temporal expression variations regulated by the circadian system is relatively subtle as compared with the tissue expression variations formed during development. Taken together, we suggest that the circadian system selects gene parameters in a cost effective way to improve tissue-specific functions by adapting temporal variations from the environment over evolutionary time scales

Conservative flux recovery from the Q1 conforming finite element method on quadrilateral grids

Compared with standard Galerkin finite element methods, mixed methods for second-order elliptic problems give readily available flux approximation, but in general at the expense of having to deal with a more complicated discrete system. This is especially true when conforming elements are involved. Hence it is advantageous to consider a direct method when finding fluxes is just a small part of the overall modeling processes. The purpose of this article is to introduce a direct method combining the standard Galerkin Q1 conforming method with a cheap local flux recovery formula. The approximate flux resides in the lowest order Raviart-Thomas space and retains local conservation property at the cluster level. A cluster is made up of at most four quadrilaterals

Banach

Convergence theorems of a general approximation method for common fixed points of a finite family of asymptotically-quasi nonexpansive mappings i

A complete mitochondrial genome sequence of the wild two-humped camel (Camelus bactrianus ferus): an evolutionary history of camelidae

<p>Abstract</p> <p>Background</p> <p>The family Camelidae that evolved in North America during the Eocene survived with two distinct tribes, Camelini and Lamini. To investigate the evolutionary relationship between them and to further understand the evolutionary history of this family, we determined the complete mitochondrial genome sequence of the wild two-humped camel (<it>Camelus bactrianus ferus</it>), the only wild survivor of the Old World camel.</p> <p>Results</p> <p>The mitochondrial genome sequence (16,680 bp) from <it>C. bactrianus ferus </it>contains 13 protein-coding, two rRNA, and 22 tRNA genes as well as a typical control region; this basic structure is shared by all metazoan mitochondrial genomes. Its protein-coding region exhibits codon usage common to all mammals and possesses the three cryptic stop codons shared by all vertebrates. <it>C. bactrianus ferus </it>together with the rest of mammalian species do not share a triplet nucleotide insertion (GCC) that encodes a proline residue found only in the <it>nd1 </it>gene of the New World camelid <it>Lama pacos</it>. This lineage-specific insertion in the <it>L. pacos </it>mtDNA occurred after the split between the Old and New World camelids suggests that it may have functional implication since a proline insertion in a protein backbone usually alters protein conformation significantly, and <it>nd1 </it>gene has not been seen as polymorphic as the rest of ND family genes among camelids. Our phylogenetic study based on complete mitochondrial genomes excluding the control region suggested that the divergence of the two tribes may occur in the early Miocene; it is much earlier than what was deduced from the fossil record (11 million years). An evolutionary history reconstructed for the family Camelidae based on <it>cytb </it>sequences suggested that the split of bactrian camel and dromedary may have occurred in North America before the tribe Camelini migrated from North America to Asia.</p> <p>Conclusion</p> <p>Molecular clock analysis of complete mitochondrial genomes from <it>C. bactrianus ferus </it>and <it>L. pacos </it>suggested that the two tribes diverged from their common ancestor about 25 million years ago, much earlier than what was predicted based on fossil records.</p

A Novel Role for Minimal Introns: Routing mRNAs to the Cytosol

BACKGROUND: Introns and their splicing are tightly coupled with the subsequent mRNA maturation steps, especially nucleocytoplasmic export. A remarkable fraction of vertebrate introns have a minimal size of about 100 bp, while majority of introns expand to several kilobases even megabases in length. PRINCIPAL FINDINGS: We carried out analyses on the evolution and function of minimal introns (50-150 bp) in human and mouse genomes. We found that minimal introns are conserved in terms of both length and sequence. They are preferentially located toward 3' end of mRNA and non-randomly distributed among chromosomes. Both the evolutionary conservation and non-random distribution are indicative of biological relevance. We showed that genes with minimal introns have higher abundance, larger size, and tend to be universally expressed as compared to genes with only large introns and intron-less genes. Genes with minimal introns replicate earlier and preferentially reside in the vicinities of open chromatin, suggesting their unique nuclear position and potential relevance to the regulation of gene expression and transcript export. CONCLUSIONS: Based on these observations, we proposed a nuclear-export routing model, where minimal introns play a regulatory role in selectively exporting the highly abundant and large housekeeping genes that reside at the surface of chromatin territories, and thus preventing entanglement with other genes located at the interior locations