Inapproximability of maximal strip recovery

In comparative genomic, the first step of sequence analysis is usually to decompose two or more genomes into syntenic blocks that are segments of homologous chromosomes. For the reliable recovery of syntenic blocks, noise and ambiguities in the genomic maps need to be removed first. Maximal Strip Recovery (MSR) is an optimization problem proposed by Zheng, Zhu, and Sankoff for reliably recovering syntenic blocks from genomic maps in the midst of noise and ambiguities. Given $d$ genomic maps as sequences of gene markers, the objective of \msr{d} is to find $d$ subsequences, one subsequence of each genomic map, such that the total length of syntenic blocks in these subsequences is maximized. For any constant $d \ge 2$, a polynomial-time 2d-approximation for \msr{d} was previously known. In this paper, we show that for any $d \ge 2$, \msr{d} is APX-hard, even for the most basic version of the problem in which all gene markers are distinct and appear in positive orientation in each genomic map. Moreover, we provide the first explicit lower bounds on approximating \msr{d} for all $d \ge 2$. In particular, we show that \msr{d} is NP-hard to approximate within $\Omega(d/\log d)$. From the other direction, we show that the previous 2d-approximation for \msr{d} can be optimized into a polynomial-time algorithm even if $d$ is not a constant but is part of the input. We then extend our inapproximability results to several related problems including \cmsr{d}, \gapmsr{\delta}{d}, and \gapcmsr{\delta}{d}.Comment: A preliminary version of this paper appeared in two parts in the Proceedings of the 20th International Symposium on Algorithms and Computation (ISAAC 2009) and the Proceedings of the 4th International Frontiers of Algorithmics Workshop (FAW 2010

Attachment Styles Within the Coach-Athlete Dyad: Preliminary Investigation and Assessment Development

The present preliminary study aimed to develop and examine the psychometric properties of a new sport-specific self-report instrument designed to assess athletes’ and coaches’ attachment styles. The development and initial validation comprised three main phases. In Phase 1, a pool of items was generated based on pre-existing self-report attachment instruments, modified to reflect a coach and an athlete’s style of attachment. In Phase 2, the content validity of the items was assessed by a panel of experts. A final scale was developed and administered to 405 coaches and 298 athletes (N = 703 participants). In Phase 3, confirmatory factor analysis of the obtained data was conducted to determine the final items of the Coach-Athlete Attachment Scale (CAAS). Confirmatory factor analysis revealed acceptable goodness of fit indexes for a 3-first order factor model as well as a 2-first order factor model for both the athlete and the coach data, respectively. A secure attachment style positively predicted relationship satisfaction, while an insecure attachment style was a negative predictor of relationship satisfaction. The CAAS revealed initial psychometric properties of content, factorial, and predictive validity, as well as reliability

Caveolin-1 Gene Disruption Promotes Mammary Tumorigenesis and Dramatically Enhances Lung Metastasis in Vivo

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