Complexity of token swapping and its variants

AbstractIn the Token Swapping problem we are given a graph with a token placed on each vertex. Each token has exactly one destination vertex, and we try to move all the tokens to their destinations, using the minimum number of swaps, i.e., operations of exchanging the tokens on two adjacent vertices. As the main result of this paper, we show that Token Swapping is W[1]-hard parameterized by the length k of a shortest sequence of swaps. In fact, we prove that, for any computable function f, it cannot be solved in time f(k)no(k/logk) where n is the number of vertices of the input graph, unless the ETH fails. This lower bound almost matches the trivial nO(k)-time algorithm. We also consider two generalizations of the Token Swapping, namely Colored Token Swapping (where the tokens have colors and tokens of the same color are indistinguishable), and Subset Token Swapping (where each token has a set of possible destinations). To complement the hardness result, we prove that even the most general variant, Subset Token Swapping, is FPT in nowhere-dense graph classes. Finally, we consider the complexities of all three problems in very restricted classes of graphs: graphs of bounded treewidth and diameter, stars, cliques, and paths, trying to identify the borderlines between polynomial and NP-hard cases

Expression of human beta-defensins 1 and 2 in kidneys with chronic bacterial infection

BACKGROUND: Constitutive expression and localization of antimicrobial human β-defensin-1 (HBD-1) in human kidneys as a potential mechanism of antimicrobial defense has been previously reported. Inducible expression of human β-defensin-2 (HBD-2) has been described in various epithelial organs but not for the urogenital tract. METHODS: We investigated the gene- and protein expression of HBD-1 and HBD-2 by reverse transcriptase-polymerase chain reaction, and immunohistochemistry in 15 normal human kidney samples and 15 renal tissues with chronic bacterial infection. Additionally, cell culture experiments were performed to study HBD gene expression by real-time RT-PCR in response to inflammatory cytokines TNFα and IL-1β as well as lipopolysaccharide from Gram-negative bacteria. RESULTS: Constitutive HBD-1 gene- and protein expression was detected in normal renal tissue and kidneys with chronic infection. As a novel finding, inducible HBD-2 gene- and protein expression was demonstrated in tubulus epithelia with chronic infection but not in normal renal tissue. In pyelonephritic kidneys HBD-1 and HBD-2 expression showed a similar pattern of localizaton in distal tubules, loops of Henle and in collecting ducts of the kidney. Furthermore, real-time RT-PCR of kidney derived cell lines stimulated with inflammatory agents TNF-α, IL-1β and LPS revealed a strong increase in relative HBD-2 transcription level and also a slight increase in relative HBD-1 transcription level. CONCLUSIONS: Upregulated HBD-2 expression in renal tubulus epithelium indicates a role of a wider range of human defensins for antimicrobial host defense in the urogenital tract than previously recognized

Tetracycline Inducible Gene Manipulation in Serotonergic Neurons

The serotonergic (5-HT) neuronal system has important and diverse physiological functions throughout development and adulthood. Its dysregulation during development or later in adulthood has been implicated in many neuropsychiatric disorders. Transgenic animal models designed to study the contribution of serotonergic susceptibility genes to a pathological phenotype should ideally allow to study candidate gene overexpression or gene knockout selectively in serotonergic neurons at any desired time during life. For this purpose, conditional expression systems such as the tet-system are preferable. Here, we generated a transactivator (tTA) mouse line (TPH2-tTA) that allows temporal and spatial control of tetracycline (Ptet) controlled transgene expression as well as gene deletion in 5-HT neurons. The tTA cDNA was inserted into a 196 kb PAC containing a genomic mouse Tph2 fragment (177 kb) by homologous recombination in E. coli. For functional analysis of Ptet-controlled transgene expression, TPH2-tTA mice were crossed to a Ptet-regulated lacZ reporter line (Ptet-nLacZ). In adult double-transgenic TPH2-tTA/Ptet-nLacZ mice, TPH2-tTA founder line L62-20 showed strong serotonergic β-galactosidase expression which could be completely suppressed with doxycycline (Dox). Furthermore, Ptet-regulated gene expression could be reversibly activated or inactivated when Dox was either withdrawn or added to the system. For functional analysis of Ptet-controlled, Cre-mediated gene deletion, TPH2-tTA mice (L62-20) were crossed to double transgenic Ptet-Cre/R26R reporter mice to generate TPH2-tTA/Ptet-Cre/R26R mice. Without Dox, 5-HT specific recombination started at E12.5. With permanent Dox administration, Ptet-controlled Cre-mediated recombination was absent. Dox withdrawal either postnatally or during adulthood induced efficient recombination in serotonergic neurons of all raphe nuclei, respectively. In the enteric nervous system, recombination could not be detected. We generated a transgenic mouse tTA line (TPH2-tTA) which allows both inducible and reversible transgene expression and inducible Cre-mediated gene deletion selectively in 5-HT neurons throughout life. This will allow precise delineation of serotonergic gene functions during development and adulthood

Mendelian randomisation analyses find pulmonary factors mediate the effect of height on coronary artery disease

British Heart Foundation (BHF) grant RG/14/5/30893Netherlands Organisation for Health Research and Development (ZonMw VIDI 016.136.367)NIDDK grant K12DK094721Intramural Research Program of the Division of Cancer Epidemiology and Genetics, NC