Abstract:
Generation of epithelial cell polarity requires mechanisms to sort plasma membrane proteins to the apical and basolateral domains. Sorting involves incorporation into specific vesicular carriers and subsequent fusion to the correct target membranes mediated by specific SNARE proteins. In polarized epithelial cells, the SNARE protein syntaxin 4 localizes exclusively to the basolateral plasma membrane and plays an important role in basolateral trafficking pathways. However, the mechanism of basolateral targeting of syntaxin 4 itself has remained poorly understood. Here we show that newly synthesized syntaxin 4 is directly targeted to the basolateral plasma membrane in polarized Madin-Darby canine kidney (MDCK) cells. Basolateral targeting depends on a signal that is centered around residues 24–29 in the N-terminal domain of syntaxin 4. Furthermore, basolateral targeting of syntaxin 4 is dependent on the epithelial cell-specific clathrin adaptor AP1B. Disruption of the basolateral targeting signal of syntaxin 4 leads to non-polarized delivery to both the apical and basolateral surface, as well as partial intercellular retention in the trans-Golgi network. Importantly, disruption of the basolateral targeting signal of syntaxin 4 leads to the inability of MDCK cells to establish a polarized morphology which suggests that restriction of syntaxin 4 to the basolateral domain is required for epithelial cell polarity.

Abstract:
In a totally ordered set the notion of sorting a finite sequence is defined through a suitable permutation of the sequence's indices. In this paper we prove a simple formula that explicitly describes how the elements of a sequence are related to those of its sorted counterpart. As this formula relies only on the minimum and maximum functions we use it to define the notion of sorting for lattices. A major difference of sorting in lattices is that it does not guarantee that sequence elements are only rearranged. However, we can show that other fundamental properties that are associated with sorting are preserved.

Abstract:
A kind of heap sorting method based on array sorting was proposed. Some advantages and disadvantages of it were discussed. It was compared with the traditional method of direct application. In the method, the ordered keywords in the array are put into the heap one by one after building an empty heap. This method needs relatively less space and is fit for ordered sequence.

Abstract:
We consider a bivariate polynomial that generalizes both the length and reflection length generating functions in a finite Coxeter group. In seeking a combinatorial description of the coefficients, we are led to the study of a new Mahonian statistic, which we call the sorting index. The sorting index of a permutation and its type B and type D analogues have natural combinatorial descriptions which we describe in detail.

Abstract:
Mutations in BEST1 gene, encoding the bestrophin-1 (Best1) protein are associated with macular dystrophies. Best1 is predominantly expressed in the retinal pigment epithelium (RPE), and is inserted in its basolateral membrane. We investigated the cellular localization in polarized MDCKII cells of disease-associated Best1 mutant proteins to study specific sorting motifs of Best1. Real-time PCR and western blots for endogenous expression of BEST1 in MDCK cells were performed. Best1 mutant constructs were generated using site-directed mutagenesis and transfected in MDCK cells. For protein sorting, confocal microscopy studies, biotinylation assays and statistical methods for quantification of mislocalization were used. Analysis of endogenous expression of BEST1 in MDCK cells revealed the presence of BEST1 transcript but no protein. Confocal microscopy and quantitative analyses indicate that transfected normal human Best1 displays a basolateral localization in MDCK cells, while cell sorting of several Best1 mutants (Y85H, Q96R, L100R, Y227N, Y227E) was altered. In contrast to constitutively active Y227E, constitutively inactive Y227F Best1 mutant localized basolaterally similar to the normal Best1 protein. Our data suggest that at least three basolateral sorting motifs might be implicated in proper Best1 basolateral localization. In addition, non-phosphorylated tyrosine 227 could play a role for basolateral delivery.

Abstract:
The objective of this paper is to review the folklore knowledge seen in research work devoted on synthesis, optimization, and effectiveness of various sorting algorithms. We will examine sorting algorithms in the folklore lines and try to discover the tradeoffs between folklore and theorems. Finally, the folklore knowledge on complexity values of the sorting algorithms will be considered, verified and subsequently converged in to theorems.

Abstract:
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors and applied problems with data streams, sorting changed its face. This changes and generalizations are the subject of investigation in the research below.

Abstract:
In 1966, Claude Berge proposed the following sorting problem. Given a string of $n$ alternating white and black pegs on a one-dimensional board consisting of an unlimited number of empty holes, rearrange the pegs into a string consisting of $\lceil\frac{n}{2}\rceil$ white pegs followed immediately by $\lfloor\frac{n}{2}\rfloor$ black pegs (or vice versa) using only moves which take 2 adjacent pegs to 2 vacant adjacent holes. Avis and Deza proved that the alternating string can be sorted in $\lceil\frac{n}{2}\rceil$ such {\em Berge 2-moves} for $n\geq 5$. Extending Berge's original problem, we consider the same sorting problem using {\em Berge $k$-moves}, i.e., moves which take $k$ adjacent pegs to $k$ vacant adjacent holes. We prove that the alternating string can be sorted in $\lceil\frac{n}{2}\rceil$ Berge 3-moves for $n\not\equiv 0\pmod{4}$ and in $\lceil\frac{n}{2}\rceil+1$ Berge 3-moves for $n\equiv 0\pmod{4}$, for $n\geq 5$. In general, we conjecture that, for any $k$ and large enough $n$, the alternating string can be sorted in $\lceil\frac{n}{2}\rceil$ Berge $k$-moves. This estimate is tight as $\lceil\frac{n}{2}\rceil$ is a lower bound for the minimum number of required Berge $k$-moves for $k\geq 2$ and $n\geq 5$.

Abstract:
This paper shows an application of the theory of sorting networks to facilitate the synthesis of optimized general purpose sorting libraries. Standard sorting libraries are often based on combinations of the classic Quicksort algorithm with insertion sort applied as the base case for small fixed numbers of inputs. Unrolling the code for the base case by ignoring loop conditions eliminates branching and results in code which is equivalent to a sorting network. This enables the application of further program transformations based on sorting network optimizations, and eventually the synthesis of code from sorting networks. We show that if considering the number of comparisons and swaps then theory predicts no real advantage of this approach. However, significant speed-ups are obtained when taking advantage of instruction level parallelism and non-branching conditional assignment instructions, both of which are common in modern CPU architectures. We provide empirical evidence that using code synthesized from efficient sorting networks as the base case for Quicksort libraries results in significant real-world speed-ups.

Abstract:
An important issue in computer science is ordering a list of items. Sorting is the process of putting data in order; either numerically or alphabetically. Sorting problem has attracted a great deal of research because efficient sorting is important to optimize the use of other algorithms such as binary search. This paper presents a model that will split large array in sub parts and then all the sub parts are processed in parallel using existing sorting algorithms and finally outcome would be merged. To process sub parts in parallel multithreading has been introduced.