Given a finite setX, a collection T of rooted phylogenetic trees onX and an integer k, the Hybridization Number problem asks if there exists a phylogenetic network on X that displays all trees from T and has reticulation number at most k. We show two kernelization algorithms for Hybridization Number, with kernel sizes 4k(5k) and 20k(∆ − 1) respectively, with t the number of input trees and ∆ th...

Let T X be the full transformation semigroup on the setX and let T X,Y {α ∈ T X : Xα ⊆ Y}. Then T X,Y is a sub-semigroup of T X determined by a nonempty subset Y of X. In this paper, we give a necessary and sufficient condition for T X,Y to be regular. In the case that T X,Y is not regular, the largest regular sub-semigroup is obtained and this sub-semigroup is shown to determine the Green’s re...

Transcription termination is a critical step for gene regulation and genome integrity among all kingdoms of life. In <i>Saccharomyces cerevisiae</i>, one the major pathways accomplished by Sen1 helicase, homolog to human Senataxin (SETX), defection which raises diseases central nervus system human. Although it has been proposed that translocates along nucleic acids consuming adenosi...

Senataxin is a large 303 kDa protein linked to neuron survival, as recessive mutations cause Ataxia with Oculomotor Apraxia type 2 (AOA2), and dominant mutations cause amyotrophic lateral sclerosis type 4 (ALS4). Senataxin contains an amino-terminal protein-interaction domain and a carboxy-terminal DNA/RNA helicase domain. In this study, we focused upon the common ALS4 mutation, L389S, by perfo...

This note is a sequel to [7] where we investigated the endomorphisms of a certain class of Banach algebras of infinitely differentiable functions on the unit interval. Start with a perfect, compact plane setX. We say that a complex-valued function f defined on X is complex-differentiable at a point a ∈ X if the limit f (a) = lim z→a, z∈X f(z)− f(a) z − a exists. We call f ′(a) the complex deriv...

AIM Folate is vital for cell growth and development through its important role in one-carbon metabolism - an essential process in the synthesis of amino acids and nucleic acids. Folate pathway genes have been considered as therapeutic targets of drugs for the treatment of cancer and other diseases. Racial and ethnic disparities of folate metabolism and outcome of antifolate therapies have been ...

To date, at least 18 causative genes have been identified in amyotrophic lateral sclerosis (ALS). Because of the clinical and genetic heterogeneity, molecular diagnosis for ALS faces great challenges. HaloPlex target enrichment system is a new targeted sequencing approach, which can detect already known mutations or candidate genes. We performed this approach to screen 18 causative genes of ALS...