The Structure of Chromatic Polynomials of Planar Triangulation Graphs and Implications for Chromatic Zeros and Asymptotic Limiting Quantities

We present an analysis of the structure and properties of chromatic polynomials $P(G_{pt,\vec m},q)$ of one-parameter and multi-parameter families of planar triangulation graphs $G_{pt,\vec m}$, where ${\vec m} = (m_1,...,m_p)$ is a vector of integer parameters. We use these to study the ratio of $|P(G_{pt,\vec m},\tau+1)|$ to the Tutte upper bound $(\tau-1)^{n-5}$, where $\tau=(1+\sqrt{5} \ )/2$ and $n$ is the number of vertices in $G_{pt,\vec m}$. In particular, we calculate limiting values of this ratio as $n \to \infty$ for various families of planar triangulations. We also use our calculations to study zeros of these chromatic polynomials. We study a large class of families $G_{pt,\vec m}$ with $p=1$ and $p=2$ and show that these have a structure of the form $P(G_{pt,m},q) = c_{_{G_{pt}},1}\lambda_1^m + c_{_{G_{pt}},2}\lambda_2^m + c_{_{G_{pt}},3}\lambda_3^m$ for $p=1$, where $\lambda_1=q-2$, $\lambda_2=q-3$, and $\lambda_3=-1$, and $P(G_{pt,\vec m},q) = \sum_{i_1=1}^3 \sum_{i_2=1}^3 c_{_{G_{pt}},i_1 i_2} \lambda_{i_1}^{m_1}\lambda_{i_2}^{m_2}$ for $p=2$. We derive properties of the coefficients $c_{_{G_{pt}},\vec i}$ and show that $P(G_{pt,\vec m},q)$ has a real chromatic zero that approaches $(1/2)(3+\sqrt{5} \ )$ as one or more of the $m_i \to \infty$. The generalization to $p \ge 3$ is given. Further, we present a one-parameter family of planar triangulations with real zeros that approach 3 from below as $m \to \infty$. Implications for the ground-state entropy of the Potts antiferromagnet are discussed.Comment: 57 pages, latex, 15 figure

New Records of the Cryptogenic Soft Coral Genus Stragulum (Tubiporidae) from the Eastern Caribbean and the Persian Gulf

The monotypic soft coral genus Stragulum van Ofwegen and Haddad, 2011 (Octocorallia: Malacalcyonacea: Tubiporidae) was originally described from Brazil, southwest Atlantic Ocean. Here, we report the first records of the genus from the eastern Caribbean and the Persian Gulf in the northwest Indian Ocean. We compare the morphological features of specimens, together with molecular data from three commonly used barcoding markers (COI, mtMutS, 28S rDNA) and 308 ultraconserved elements (UCE) and exon loci sequenced using a target-enrichment approach. The molecular and morphological data together suggest that specimens from all three localities are the same species, i.e., Stragulum bicolor van Ofwegen and Haddad, 2011. It is still not possible to establish the native range of the species or determine whether it may be an introduced species due to the limited number of specimens included in this study. However, the lack of historical records, its fouling abilities on artificial substrates, and a growing number of observations support the invasive nature of the species in Brazilian and Caribbean waters and therefore suggest that it may have been introduced into the Atlantic from elsewhere. Interestingly, the species has not shown any invasive behaviour in the Persian Gulf, where it has been found only on natural, rocky substrates. The aim of the present report is to create awareness of this taxon with the hope that this will lead to new records from other localities and help to establish its native range

A synthesis of European seahorse taxonomy, population structure, and habitat use as a basis for assessment, monitoring and conservation

Accurate taxonomy, population demography, and habitat descriptors inform species threat assessments and the design of effective conservation measures. Here we combine published studies with new genetic, morphological and habitat data that were collected from seahorse populations located along the European and North African coastlines to help inform management decisions for European seahorses. This study confirms the presence of only two native seahorse species (Hippocampus guttulatus and H. hippocampus) across Europe, with sporadic occurrence of non-native seahorse species in European waters. For the two native species, our findings demonstrate that highly variable morphological characteristics, such as size and presence or number of cirri, are unreliable for distinguishing species. Both species exhibit sex dimorphism with females being significantly larger. Across its range, H. guttulatus were larger and found at higher densities in cooler waters, and individuals in the Black Sea were significantly smaller than in other populations. H. hippocampus were significantly larger in Senegal. Hippocampus guttulatus tends to have higher density populations than H. hippocampus when they occur sympatrically. Although these species are often associated with seagrass beds, data show both species inhabit a wide variety of shallow habitats and use a mixture of holdfasts. We suggest an international mosaic of protected areas focused on multiple habitat types as the first step to successful assessment, monitoring and conservation management of these Data Deficient speciespublishersversionPeer reviewe

Low connectivity between shallow, mesophotic and rariphotic zone benthos

© 2019 Massachussetts Medical Society. All rights reserved. Worldwide coral reefs face catastrophic damage due to a series of anthropogenic stressors. Investigating how coral reefs ecosystems are connected, in particular across depth, will help us understand if deeper reefs harbour distinct communities. Here, we explore changes in benthic community structure across 15-300 m depths using technical divers and submersibles around Bermuda. We report high levels of floral and faunal differentiation across depth, with distinct assemblages occupying each depth surveyed, except 200-300 m, corresponding to the lower rariphotic zone. Community turnover was highest at the boundary depths of mesophotic coral ecosystems (30-150 m) driven largely by taxonomic turnover and to a lesser degree by ordered species loss (nestedness). Our work highlights the biologically unique nature of benthic communities in the mesophotic and rariphotic zones, and their limited connectivity to shallow reefs, thus emphasizing the need to manage and protect deeper reefs as distinct entities

Latent Structures based-Multivariate Statistical Process Control: a paradigm shift

The basic fundamentals of statistical process control (SPC) were proposed by Walter Shewhart for data-starved production environments typical in the 1920s and 1930s. In the 21st century, the traditional scarcity of data has given way to a data-rich environment typical of highly automated and computerized modern processes. These data often exhibit high correlation, rank deficiency, low signal-to-noise ratio, multistage and multiway structures, and missing values. Conventional univariate and multivariate SPC techniques are not suitable in these environments. This article discusses the paradigm shift to which those working in the quality improvement field should pay keen attention. We advocate the use of latent structure based multivariate statistical process control methods as efficient quality improvement tools in these massive data contexts. This is a strategic issue for industrial success in the tremendously competitive global market.This research work was partially supported by the Spanish Ministry of Economy and Competitiveness under the project DPI2011-28112-C04-02.Ferrer, A. (2014). Latent Structures based-Multivariate Statistical Process Control: a paradigm shift. Quality Engineering. 26(1):72-91. https://doi.org/10.1080/08982112.2013.846093S7291261Aparisi, F., Jabaioyes, J., & Carrion, A. (1999). Statistical properties of the lsi multivariate control chart. Communications in Statistics - Theory and Methods, 28(11), 2671-2686. doi:10.1080/03610929908832445Arteaga, F., & Ferrer, A. (2002). Dealing with missing data in MSPC: several methods, different interpretations, some examples. Journal of Chemometrics, 16(8-10), 408-418. doi:10.1002/cem.750Bersimis, S., Psarakis, S., & Panaretos, J. (2007). Multivariate statistical process control charts: an overview. 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Cross-validation in PCA models with the element-wise k-fold (ekf) algorithm: theoretical aspects. Journal of Chemometrics, 26(7), 361-373. doi:10.1002/cem.2440Duchesne, C., Liu, J. J., & MacGregor, J. F. (2012). Multivariate image analysis in the process industries: A review. Chemometrics and Intelligent Laboratory Systems, 117, 116-128. doi:10.1016/j.chemolab.2012.04.003Efron, B., & Gong, G. (1983). A Leisurely Look at the Bootstrap, the Jackknife, and Cross-Validation. The American Statistician, 37(1), 36-48. doi:10.1080/00031305.1983.10483087Ferrer, A. (2007). Multivariate Statistical Process Control Based on Principal Component Analysis (MSPC-PCA): Some Reflections and a Case Study in an Autobody Assembly Process. Quality Engineering, 19(4), 311-325. doi:10.1080/08982110701621304Fuchs, C. (1998). Multivariate Quality Control. doi:10.1201/9781482273731Geladi, P., & Kowalski, B. R. (1986). Partial least-squares regression: a tutorial. 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IEEE Control Systems, 22(5), 10-25. doi:10.1109/mcs.2002.1035214Kourti, T. (2005). Application of latent variable methods to process control and multivariate statistical process control in industry. International Journal of Adaptive Control and Signal Processing, 19(4), 213-246. doi:10.1002/acs.859Kourti, T. (2006). Process Analytical Technology Beyond Real-Time Analyzers: The Role of Multivariate Analysis. Critical Reviews in Analytical Chemistry, 36(3-4), 257-278. doi:10.1080/10408340600969957Kourti, T., & MacGregor, J. F. (1996). Multivariate SPC Methods for Process and Product Monitoring. Journal of Quality Technology, 28(4), 409-428. doi:10.1080/00224065.1996.11979699Liu, R. Y. (1995). Control Charts for Multivariate Processes. Journal of the American Statistical Association, 90(432), 1380-1387. doi:10.1080/01621459.1995.10476643Liu, R. Y., Singh, K., & Teng*, J. H. (2004). DDMA-charts: Nonparametric multivariate moving average control charts based on data depth. 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(2007). Integration of colour and textural information in multivariate image analysis: defect detection and classification issues. Journal of Chemometrics, 21(1-2), 10-23. doi:10.1002/cem.1026Bisgaard, S., Doganaksoy, N., Fisher, N., Gunter, B., Hahn, G., Keller-McNulty, S., … Wu, C. F. J. (2008). The Future of Industrial Statistics: A Panel Discussion. Technometrics, 50(2), 103-127. doi:10.1198/004017008000000136Stoumbos, Z. G., Reynolds, M. R., Ryan, T. P., & Woodall, W. H. (2000). The State of Statistical Process Control as We Proceed into the 21st Century. Journal of the American Statistical Association, 95(451), 992-998. doi:10.1080/01621459.2000.10474292Tracy, N. D., Young, J. C., & Mason, R. L. (1992). Multivariate Control Charts for Individual Observations. Journal of Quality Technology, 24(2), 88-95. doi:10.1080/00224065.1992.12015232Wierda, S. J. (1994). Multivariate statistical process control—recent results and directions for future research. 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Climatic regions as an indicator of forest coarse and fine woody debris carbon stocks in the United States

<p>Abstract</p> <p>Background</p> <p>Coarse and fine woody debris are substantial forest ecosystem carbon stocks; however, there is a lack of understanding how these detrital carbon stocks vary across forested landscapes. Because forest woody detritus production and decay rates may partially depend on climatic conditions, the accumulation of coarse and fine woody debris carbon stocks in forests may be correlated with climate. This study used a nationwide inventory of coarse and fine woody debris in the United States to examine how these carbon stocks vary by climatic regions and variables.</p> <p>Results</p> <p>Mean coarse and fine woody debris forest carbon stocks vary by Köppen's climatic regions across the United States. The highest carbon stocks were found in regions with cool summers while the lowest carbon stocks were found in arid desert/steppes or temperate humid regions. Coarse and fine woody debris carbon stocks were found to be positively correlated with available moisture and negatively correlated with maximum temperature.</p> <p>Conclusion</p> <p>It was concluded with only medium confidence that coarse and fine woody debris carbon stocks may be at risk of becoming net emitter of carbon under a global climate warming scenario as increases in coarse or fine woody debris production (sinks) may be more than offset by increases in forest woody detritus decay rates (emission). Given the preliminary results of this study and the rather tenuous status of coarse and fine woody debris carbon stocks as either a source or sink of CO₂, further research is suggested in the areas of forest detritus decay and production.</p

Healthier prisons: The role of a prison visitors' centre

Since the inception of the prison as a ‘setting’ for health promotion, there has been a focus on how the health of those men and women who spend ‘time inside’ can at least be maintained and if possible, enhanced, during their prison sentence. This paper presents findings from a mainly qualitative evaluation of a prison visitors' centre in the UK. It reports experiences of prisoners' families, prisoners, prison staff, the local community and the ways in which the visitors' centre has contributed positively to their health and well-being. In addition, key stakeholders were interviewed to ascertain the role this visitors' centre has in policy frameworks related to re-offending. The findings from this evaluation underscore how the visitors' centre improved the quality of visits, and contributed towards the maintenance of family ties through the help and support it provides for families and prisoners. The paper concludes by suggesting that visitors' centres are an essential part of a modern prison service helping to address the government's health inequalities agenda

North America's net terrestrial CO2 exchange with the atmosphere 1990–2009

Scientific understanding of the global carbon cycle is required for developing national and international policy to mitigate fossil fuel CO2 emissions by managing terrestrial carbon uptake. Toward that understanding and as a contribution to the REgional Carbon Cycle Assessment and Processes (RECCAP) project, this paper provides a synthesis of net land–atmosphere CO2 exchange for North America (Canada, United States, and Mexico) over the period 1990–2009. Only CO2 is considered, not methane or other greenhouse gases. This synthesis is based on results from three different methods: atmospheric inversion, inventory-based methods and terrestrial biosphere modeling. All methods indicate that the North American land surface was a sink for atmospheric CO2, with a net transfer from atmosphere to land. Estimates ranged from −890 to −280 Tg C yr−1, where the mean of atmospheric inversion estimates forms the lower bound of that range (a larger land sink) and the inventory-based estimate using the production approach the upper (a smaller land sink). This relatively large range is due in part to differences in how the approaches represent trade, fire and other disturbances and which ecosystems they include. Integrating across estimates, "best" estimates (i.e., measures of central tendency) are −472 ± 281 Tg C yr−1 based on the mean and standard deviation of the distribution and −360 Tg C yr−1 (with an interquartile range of −496 to −337) based on the median. Considering both the fossil fuel emissions source and the land sink, our analysis shows that North America was, however, a net contributor to the growth of CO2 in the atmosphere in the late 20th and early 21st century. With North America's mean annual fossil fuel CO2 emissions for the period 1990–2009 equal to 1720 Tg C yr−1 and assuming the estimate of −472 Tg C yr−1 as an approximation of the true terrestrial CO2 sink, the continent's source : sink ratio for this time period was 1720:472, or nearly 4:1

Accounting for density reduction and structural loss in standing dead trees: Implications for forest biomass and carbon stock estimates in the United States

<p>Abstract</p> <p>Background</p> <p>Standing dead trees are one component of forest ecosystem dead wood carbon (C) pools, whose national stock is estimated by the U.S. as required by the United Nations Framework Convention on Climate Change. Historically, standing dead tree C has been estimated as a function of live tree growing stock volume in the U.S.'s National Greenhouse Gas Inventory. Initiated in 1998, the USDA Forest Service's Forest Inventory and Analysis program (responsible for compiling the Nation's forest C estimates) began consistent nationwide sampling of standing dead trees, which may now supplant previous purely model-based approaches to standing dead biomass and C stock estimation. A substantial hurdle to estimating standing dead tree biomass and C attributes is that traditional estimation procedures are based on merchantability paradigms that may not reflect density reductions or structural loss due to decomposition common in standing dead trees. The goal of this study was to incorporate standing dead tree adjustments into the current estimation procedures and assess how biomass and C stocks change at multiple spatial scales.</p> <p>Results</p> <p>Accounting for decay and structural loss in standing dead trees significantly decreased tree- and plot-level C stock estimates (and subsequent C stocks) by decay class and tree component. At a regional scale, incorporating adjustment factors decreased standing dead quaking aspen biomass estimates by almost 50 percent in the Lake States and Douglas-fir estimates by more than 36 percent in the Pacific Northwest.</p> <p>Conclusions</p> <p>Substantial overestimates of standing dead tree biomass and C stocks occur when one does not account for density reductions or structural loss. Forest inventory estimation procedures that are descended from merchantability standards may need to be revised toward a more holistic approach to determining standing dead tree biomass and C attributes (i.e., attributes of tree biomass outside of sawlog portions). Incorporating density reductions and structural loss adjustments reduces uncertainty associated with standing dead tree biomass and C while improving consistency with field methods and documentation.</p