Minimal Permutations and 2-Regular Skew Tableaux

Bouvel and Pergola introduced the notion of minimal permutations in the study of the whole genome duplication-random loss model for genome rearrangements. Let $\mathcal{F}_d(n)$ denote the set of minimal permutations of length $n$ with $d$ descents, and let $f_d(n)= |\mathcal{F}_d(n)|$. They derived that $f_{n-2}(n)=2^{n}-(n-1)n-2$ and $f_n(2n)=C_n$, where $C_n$ is the $n$-th Catalan number. Mansour and Yan proved that $f_{n+1}(2n+1)=2^{n-2}nC_{n+1}$. In this paper, we consider the problem of counting minimal permutations in $\mathcal{F}_d(n)$ with a prescribed set of ascents. We show that such structures are in one-to-one correspondence with a class of skew Young tableaux, which we call $2$-regular skew tableaux. Using the determinantal formula for the number of skew Young tableaux of a given shape, we find an explicit formula for $f_{n-3}(n)$. Furthermore, by using the Knuth equivalence, we give a combinatorial interpretation of a formula for a refinement of the number $f_{n+1}(2n+1)$.Comment: 19 page

SLIQ: Simple Linear Inequalities for Efficient Contig Scaffolding

Scaffolding is an important subproblem in "de novo" genome assembly in which mate pair data are used to construct a linear sequence of contigs separated by gaps. Here we present SLIQ, a set of simple linear inequalities derived from the geometry of contigs on the line that can be used to predict the relative positions and orientations of contigs from individual mate pair reads and thus produce a contig digraph. The SLIQ inequalities can also filter out unreliable mate pairs and can be used as a preprocessing step for any scaffolding algorithm. We tested the SLIQ inequalities on five real data sets ranging in complexity from simple bacterial genomes to complex mammalian genomes and compared the results to the majority voting procedure used by many other scaffolding algorithms. SLIQ predicted the relative positions and orientations of the contigs with high accuracy in all cases and gave more accurate position predictions than majority voting for complex genomes, in particular the human genome. Finally, we present a simple scaffolding algorithm that produces linear scaffolds given a contig digraph. We show that our algorithm is very efficient compared to other scaffolding algorithms while maintaining high accuracy in predicting both contig positions and orientations for real data sets.Comment: 16 pages, 6 figures, 7 table

Love motels : oriental phenomenon or emergent sector?

This study explores the 'Love Motel' concept by examining the changing attitude of consumers in Taiwan. This will increase knowledge of the sector and define love motels. The literature review charts the development of Taiwanese love motels from a duel origin; American Motels and Japanese 'Love Hotels.' This is followed by an empirical qualitative study consisting of a two-stage collection strategy: focus groups of hospitality and tourism professionals to gather a wide range of opinions on the subject area followed by semi-structured interviews with consumers. The findings split into three interrelated areas: growth of Taiwanese love motels due to more liberal attitudes towards sexual practice; a change in the public perception of motels due to increased standards and an increased satisfaction with the personal consumption experience; these hotels are designed for couples. The empirical element of this study is an exploration of consumer experience in Taiwanese love hotels. Due to the sensitive nature of some of the data that was gathered a qualitative approach has been adopted. The sexual associations with this product appear almost coincidental. If the love motel product is considered in its purest form it is simply a hotel product that provides complete anonymity for its guests. Therefore, despite its application in South East Asia, this hospitality concept has potential to be applied in a variety of guises. The phenomenon of 'Love Hotels' is absent from hospitality management literature; this paper begins to fill that gap by beginning a discussion on this possibly controversial sector