The emergence of 4-cycles in polynomial maps over the extended integers

Let $f(x) \in \mathbb{Z}[x]$; for each integer $\alpha$ it is interesting to consider the number of iterates $n_{\alpha}$, if possible, needed to satisfy $f^{n_{\alpha}}(\alpha) = \alpha$. The sets $\{\alpha, f(\alpha), \ldots, f^{n_{\alpha} - 1}(\alpha), \alpha\}$ generated by the iterates of $f$ are called cycles. For $\mathbb{Z}[x]$ it is known that cycles of length 1 and 2 occur, and no others. While much is known for extensions to number fields, we concentrate on extending $\mathbb{Z}$ by adjoining reciprocals of primes. Let $\mathbb{Z}[1/p_1, \ldots, 1/p_n]$ denote $\mathbb{Z}$ extended by adding in the reciprocals of the $n$ primes $p_1, \ldots, p_n$ and all their products and powers with each other and the elements of $\mathbb{Z}$. Interestingly, cycles of length 4, called 4-cycles, emerge for polynomials in $\mathbb{Z}\left[1/p_1, \ldots, 1/p_n\right][x]$ under the appropriate conditions. The problem of finding criteria under which 4-cycles emerge is equivalent to determining how often a sum of four terms is zero, where the terms are $\pm 1$ times a product of elements from the list of $n$ primes. We investigate conditions on sets of primes under which 4-cycles emerge. We characterize when 4-cycles emerge if the set has one or two primes, and (assuming a generalization of the ABC conjecture) find conditions on sets of primes guaranteed not to cause 4-cycles to emerge.Comment: 14 pages, 1 figur

Effects of Environmental Factors on the Abundance of Blacklegged Ticks

The nymphal stage of the blacklegged tick, Ixodes scapularis, is the major vector of Lyme disease, the most common vector-borne disease in North America. Tick abundance has generally been estimated using either flag/drag samples or samples from hosts. However, the biases of these sampling methods have not been adequately studied. We compared samples using both methods from sites in Massachusetts and Wisconsin. Tick abundance was compared with variables related to weather (temperature, relative humidity, and tick adverse moisture events), vegetation (canopy cover, tree density, shrub density, ground vegetation, and leaf litter cover), and host abundance (mice, small mammals, medium sized mammals, and all hosts). A model with relative humidity in the leaf litter and canopy cover variables gave the best prediction of tick numbers per flag/drag sample (R2 = 0.829, p = 0.0006). In contrast, the number of small mammals collected per sample in Sherman traps and pitfall traps gave the best prediction of ticks collected per sample from all hosts (R2 = 0.580, p = 0.0057) and the number of ticks per mouse (R2 = 0.580, p = 0.0057). Therefore, the most significant environmental factors that influence I. scapularis abundance vary, based on the particular location of the tick sampled. Ticks found in leaf litter and ticks found on hosts experience very different environments and the factors that influence their abundance are different, so studies of tick population biology should select sampling methods based on the features of the population under study. These results indicate that risk of encounter with host-seeking ticks is greatest in areas with dense canopy cover and moist leaf litter

Apolipoprotein E4 has extensive conformational heterogeneity in lipid-free and lipid-bound forms

The ε4-allele variant of apolipoprotein E (ApoE4) is the strongest genetic risk factor for Alzheimer\u27s disease, although it only differs from its neutral counterpart ApoE3 by a single amino acid substitution. While ApoE4 influences the formation of plaques and neurofibrillary tangles, the structural determinants of pathogenicity remain undetermined due to limited structural information. Previous studies have led to conflicting models of the C-terminal region positioning with respect to the N-terminal domain across isoforms largely because the data are potentially confounded by the presence of heterogeneous oligomers. Here, we apply a combination of single-molecule spectroscopy and molecular dynamics simulations to construct an atomically detailed model of monomeric ApoE4 and probe the effect of lipid association. Importantly, our approach overcomes previous limitations by allowing us to work at picomolar concentrations where only the monomer is present. Our data reveal that ApoE4 is far more disordered and extended than previously thought and retains significant conformational heterogeneity after binding lipids. Comparing the proximity of the N- and C-terminal domains across the three major isoforms (ApoE4, ApoE3, and ApoE2) suggests that all maintain heterogeneous conformations in their monomeric form, with ApoE2 adopting a slightly more compact ensemble. Overall, these data provide a foundation for understanding how ApoE4 differs from nonpathogenic and protective variants of the protein

Evidence of pathogen-induced immunogenetic selection across the large geographic range of a wild seabird

Over evolutionary time,pathogen challenge shapes theimmunephenotype of the host tobetterrespondtoanincipient threat. The extent and direction of this selection pressure depend on the local pathogen composition, which is in turn determined by biotic and abiotic features of the environment. However, little is known about adaptation to local pathogen threats in wild animals. The Gentoo penguin (Pygoscelis papua) is a species complex that lends itself to the study of immune adaptation becauseof its circumpolardistributionover a large latitudinal range, with littleornoadmixturebetweendifferent clades. Inthis study,we examine thediversity ina key family of innateimmunegenes-theToll-like receptors (TLRs)-across the range of the Gentoo penguin. The three TLRs that we investigated present varying levels of diversity, with TLR4 and TLR5 greatly exceeding the diversity of TLR7.We present evidence of positive selection in TLR4 and TLR5,which points to pathogen-driven adaptation to the local pathogen milieu. Finally, we demonstrate that two positively selected cosegregating sites in TLR5 are sufficient to alter the responsiveness of the receptor to its bacterial ligand, flagellin. Taken together, these results suggest that Gentoo penguins have experienced distinct pathogen-driven selection pressures in different environments, which may be important given the role of the Gentoo penguin as a sentinel species in some of the world's most rapidly changing environments.Fil: Levy, Hila. University of Oxford; Reino UnidoFil: Fiddaman, Steven R.. University of Oxford; Reino UnidoFil: Vianna, Juliana A.. Pontificia Universidad Católica de Chile; Chile. Universidad Católica de Chile; ChileFil: Noll, Daly. Pontificia Universidad Católica de Chile; Chile. Universidad de Chile; ChileFil: Clucas, Gemma V.. Cornell University; Estados UnidosFil: Sidhu, Jasmine K.H.. University of Oxford; Reino UnidoFil: Polito, Michael J.. Louisiana State University; Estados UnidosFil: Bost, Charles A.. Centre D'etudes Biologiques de Chizé; FranciaFil: Phillips, Richard A.. British Antarctic Survey; Reino UnidoFil: Crofts, Sarah. Falklands Conservation; Reino UnidoFil: Miller, Gary D.. University of Western Australia; AustraliaFil: Pistorius, Pierre. Nelson Mandela University; SudáfricaFil: Bonnadonna, Francesco. Université de Montpellier; FranciaFil: Le Bohec, Celine. Université de Strasbourg; FranciaFil: Barbosa, Andres. Consejo Superior de Investigaciones Científicas. Museo Nacional de Ciencias Naturales; EspañaFil: Trathan, Phil. British Antarctic Survey; Reino UnidoFil: Raya Rey, Andrea Nélida. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Austral de Investigaciones Científicas; ArgentinaFil: Frantz, Laurent A.F.. University of London; Reino UnidoFil: Hart, Tom. University of Oxford; Reino UnidoFil: Smith, Adrian L.. University of Oxford; Reino Unid

Combating subclonal evolution of resistant cancer phenotypes

Metastatic breast cancer remains challenging to treat, and most patients ultimately progress on therapy. This acquired drug resistance is largely due to drug-refractory sub-populations (subclones) within heterogeneous tumors. Here, we track the genetic and phenotypic subclonal evolution of four breast cancers through years of treatment to better understand how breast cancers become drug-resistant. Recurrently appearing post-chemotherapy mutations are rare. However, bulk and single-cell RNA sequencing reveal acquisition of malignant phenotypes after treatment, including enhanced mesenchymal and growth factor signaling, which may promote drug resistance, and decreased antigen presentation and TNF-α signaling, which may enable immune system avoidance. Some of these phenotypes pre-exist in pre-treatment subclones that become dominant after chemotherapy, indicating selection for resistance phenotypes. Post-chemotherapy cancer cells are effectively treated with drugs targeting acquired phenotypes. These findings highlight cancer's ability to evolve phenotypically and suggest a phenotype-targeted treatment strategy that adapts to cancer as it evolves

Synthesis and asymmetric hydrogenation of (3E)-1-benzyl-3-[(2-oxopyridin-1(2H)-yl)methylidene]piperidine-2,6-dione

The synthesis of (3E)-1-benzyl-3-[(2-oxopyridin-1(2H)-yl)methylidene]piperidine-2,6-dione 4 from N-benzylglutarimide was achieved in three steps. The asymmetric hydrogenation of 4 gave either the product of partial reduction (10) or full reduction (13), depending on the catalyst which was employed, in high ee in each case. Attempts at asymmetric transfer hydrogenation (ATH) of 4 resulted in formation of a racemic product

By Any Other Name: Heterologous Replacement of the Escherichia coli RNase P Protein Subunit Has In Vivo Fitness Consequences

Bacterial RNase P is an essential ribonucleoprotein composed of a catalytic RNA component (encoded by the rnpB gene) and an associated protein moiety (encoded by rnpA). We construct a system that allows for the deletion of the essential endogenous rnpA copy and for its simultaneous replacement by a heterologous version of the gene. Using growth rate as a proxy, we explore the effects on fitness of heterologous replacement by increasingly divergent versions of the RNase P protein. All of the heterologs tested complement the loss of the endogenous rnpA gene, suggesting that all existing bacterial versions of the rnpA sequence retain the elements required for functional interaction with the RNase P RNA. All replacements, however, exact a cost on organismal fitness, and particularly on the rate of growth acceleration, defined as the time required to reach maximal growth rate. Our data suggest that the similarity of the heterolog to the endogenous version — whether defined at the sequence, structure or codon usage level — does not predict the fitness costs of the replacement. The common assumption that sequence similarity predicts functional similarity requires experimental confirmation and may prove to be an oversimplification

Clouds, Aerosols, and Precipitation in the Marine Boundary Layer: An Arm Mobile Facility Deployment

The Clouds, Aerosol, and Precipitation in the Marine Boundary Layer (CAP-MBL) deployment at Graciosa Island in the Azores generated a 21-month (April 2009–December 2010) comprehensive dataset documenting clouds, aerosols, and precipitation using the Atmospheric Radiation Measurement Program (ARM) Mobile Facility (AMF). The scientific aim of the deployment is to gain improved understanding of the interactions of clouds, aerosols, and precipitation in the marine boundary layer. Graciosa Island straddles the boundary between the subtropics and midlatitudes in the northeast Atlantic Ocean and consequently experiences a great diversity of meteorological and cloudiness conditions. Low clouds are the dominant cloud type, with stratocumulus and cumulus occurring regularly. Approximately half of all clouds contained precipitation detectable as radar echoes below the cloud base. Radar and satellite observations show that clouds with tops from 1 to 11 km contribute more or less equally to surface-measured precipitation at Graciosa. A wide range of aerosol conditions was sampled during the deployment consistent with the diversity of sources as indicated by back-trajectory analysis. Preliminary findings suggest important two-way interactions between aerosols and clouds at Graciosa, with aerosols affecting light precipitation and cloud radiative properties while being controlled in part by precipitation scavenging. The data from Graciosa are being compared with short-range forecasts made with a variety of models. A pilot analysis with two climate and two weather forecast models shows that they reproduce the observed time-varying vertical structure of lower-tropospheric cloud fairly well but the cloud-nucleating aerosol concentrations less well. The Graciosa site has been chosen to be a permanent fixed ARM site that became operational in October 2013.Keywords: Atmosphere-ocean interaction, Decadal variability, Spring season, La Nina, Meridional overturning circulation, Hadley circulationKeywords: Atmosphere-ocean interaction, Decadal variability, Spring season, La Nina, Meridional overturning circulation, Hadley circulatio

Landscape of somatic single nucleotide variants and indels in colorectal cancer and impact on survival

Colorectal cancer (CRC) is a biologically heterogeneous disease. To characterize its mutational profile, we conduct targeted sequencing of 205 genes for 2,105 CRC cases with survival data. Our data shows several findings in addition to enhancing the existing knowledge of CRC. We identify PRKCI, SPZ1, MUTYH, MAP2K4, FETUB, and TGFBR2 as additional genes significantly mutated in CRC. We find that among hypermutated tumors, an increased mutation burden is associated with improved CRC-specific survival (HR=0.42, 95% CI: 0.21-0.82). Mutations in TP53 are associated with poorer CRC-specific survival, which is most pronounced in cases carrying TP53 mutations with predicted 0% transcriptional activity (HR=1.53, 95% CI: 1.21-1.94). Furthermore, we observe differences in mutational frequency of several genes and pathways by tumor location, stage, and sex. Overall, this large study provides deep insights into somatic mutations in CRC, and their potential relationships with survival and tumor features. Large scale sequencing study is of paramount importance to unravel the heterogeneity of colorectal cancer. Here, the authors sequenced 205 cancer genes in more than 2000 tumours and identified additional mutated driver genes, determined that mutational burden and specific mutations in TP53 are associated with survival odds

Can computerized clinical decision support systems improve practitioners' diagnostic test ordering behavior? A decision-maker-researcher partnership systematic review

<p>Abstract</p> <p>Background</p> <p>Underuse and overuse of diagnostic tests have important implications for health outcomes and costs. Decision support technology purports to optimize the use of diagnostic tests in clinical practice. The objective of this review was to assess whether computerized clinical decision support systems (CCDSSs) are effective at improving ordering of tests for diagnosis, monitoring of disease, or monitoring of treatment. The outcome of interest was effect on the diagnostic test-ordering behavior of practitioners.</p> <p>Methods</p> <p>We conducted a decision-maker-researcher partnership systematic review. We searched MEDLINE, EMBASE, Ovid's EBM Reviews database, Inspec, and reference lists for eligible articles published up to January 2010. We included randomized controlled trials comparing the use of CCDSSs to usual practice or non-CCDSS controls in clinical care settings. Trials were eligible if at least one component of the CCDSS gave suggestions for ordering or performing a diagnostic procedure. We considered studies 'positive' if they showed a statistically significant improvement in at least 50% of test ordering outcomes.</p> <p>Results</p> <p>Thirty-five studies were identified, with significantly higher methodological quality in those published after the year 2000 (<it>p </it>= 0.002). Thirty-three trials reported evaluable data on diagnostic test ordering, and 55% (18/33) of CCDSSs improved testing behavior overall, including 83% (5/6) for diagnosis, 63% (5/8) for treatment monitoring, 35% (6/17) for disease monitoring, and 100% (3/3) for other purposes. Four of the systems explicitly attempted to reduce test ordering rates and all succeeded. Factors of particular interest to decision makers include costs, user satisfaction, and impact on workflow but were rarely investigated or reported.</p> <p>Conclusions</p> <p>Some CCDSSs can modify practitioner test-ordering behavior. To better inform development and implementation efforts, studies should describe in more detail potentially important factors such as system design, user interface, local context, implementation strategy, and evaluate impact on user satisfaction and workflow, costs, and unintended consequences.</p