On the metric dimension of corona product graphs

Given a set of vertices $S=\{v_1,v_2,...,v_k\}$ of a connected graph $G$, the metric representation of a vertex $v$ of $G$ with respect to $S$ is the vector $r(v|S)=(d(v,v_1),d(v,v_2),...,d(v,v_k))$, where $d(v,v_i)$, $i\in \{1,...,k\}$ denotes the distance between $v$ and $v_i$. $S$ is a resolving set for $G$ if for every pair of vertices $u,v$ of $G$, $r(u|S)\ne r(v|S)$. The metric dimension of $G$, $dim(G)$, is the minimum cardinality of any resolving set for $G$. Let $G$ and $H$ be two graphs of order $n_1$ and $n_2$, respectively. The corona product $G\odot H$ is defined as the graph obtained from $G$ and $H$ by taking one copy of $G$ and $n_1$ copies of $H$ and joining by an edge each vertex from the $i^{th}$-copy of $H$ with the $i^{th}$-vertex of $G$. For any integer $k\ge 2$, we define the graph $G\odot^k H$ recursively from $G\odot H$ as $G\odot^k H=(G\odot^{k-1} H)\odot H$. We give several results on the metric dimension of $G\odot^k H$. For instance, we show that given two connected graphs $G$ and $H$ of order $n_1\ge 2$ and $n_2\ge 2$, respectively, if the diameter of $H$ is at most two, then $dim(G\odot^k H)=n_1(n_2+1)^{k-1}dim(H)$. Moreover, if $n_2\ge 7$ and the diameter of $H$ is greater than five or $H$ is a cycle graph, then $dim(G\odot^k H)=n_1(n_2+1)^{k-1}dim(K_1\odot H).

Partial volume correction in arterial spin labeling perfusion MRI: a method to disentangle anatomy from physiology or an analysis step too far?

The mismatch in the spatial resolution of Arterial Spin Labeling (ASL) MRI perfusion images and the anatomy of functionally distinct tissues in the brain leads to a partial volume effect (PVE), which in turn confounds the estimation of perfusion into a specific tissue of interest such as gray or white matter. This confound occurs because the image voxels contain a mixture of tissues with disparate perfusion properties, leading to estimated perfusion values that reflect primarily the volume proportions of tissues in the voxel rather than the perfusion of any particular tissue of interest within that volume. It is already recognized that PVE influences studies of brain perfusion, and that its effect might be even more evident in studies where changes in perfusion are co-incident with alterations in brain structure, such as studies involving a comparison between an atrophic patient population vs control subjects, or studies comparing subjects over a wide range of ages. However, the application of PVE correction (PVEc) is currently limited and the employed methodologies remain inconsistent. In this article, we outline the influence of PVE in ASL measurements of perfusion, explain the main principles of PVEc, and provide a critique of the current state of the art for the use of such methods. Furthermore, we examine the current use of PVEc in perfusion studies and whether there is evidence to support its wider adoption. We conclude that there is sound theoretical motivation for the use of PVEc alongside conventional, 'uncorrected', images, and encourage such combined reporting. Methods for PVEc are now available within standard neuroimaging toolboxes, which makes our recommendation straightforward to implement. However, there is still more work to be done to establish the value of PVEc as well as the efficacy and robustness of existing PVEc methods.Neuro Imaging Researc

Tumour subregion analysis of colorectal liver metastases using semi-automated clustering based on DCE-MRI: Comparison with histological subregions and impact on pharmacokinetic parameter analysis.

PURPOSE: To use a novel segmentation methodology based on dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) to define tumour subregions of liver metastases from colorectal cancer (CRC), to compare these with histology, and to use these to compare extracted pharmacokinetic (PK) parameters between tumour subregions. MATERIALS AND METHODS: This ethically-approved prospective study recruited patients with CRC and ≥1 hepatic metastases scheduled for hepatic resection. Patients underwent DCE-MRI pre-metastasectomy. Histological sections of resection specimens were spatially matched to DCE-MRI acquisitions and used to define histological subregions of viable and non-viable tumour. A semi-automated voxel-wise image segmentation algorithm based on the DCE-MRI contrast-uptake curves was used to define imaging subregions of viable and non-viable tumour. Overlap of histologically-defined and imaging subregions was compared using the Dice similarity coefficient (DSC). DCE-MRI PK parameters were compared for the whole tumour and histology-defined and imaging-derived subregions. RESULTS: Fourteen patients were included in the analysis. Direct histological comparison with imaging was possible in nine patients. Mean DSC for viable tumour subregions defined by imaging and histology was 0.738 (range 0.540-0.930). There were significant differences between Ktrans and kep for viable and non-viable subregions (p < 0.001) and between whole lesions and viable subregions (p < 0.001). CONCLUSION: We demonstrate good concordance of viable tumour segmentation based on pre-operative DCE-MRI with a post-operative histological gold-standard. This can be used to extract viable tumour-specific values from quantitative image analysis, and could improve treatment response assessment in clinical practice

The PHENIX Experiment at RHIC

The physics emphases of the PHENIX collaboration and the design and current status of the PHENIX detector are discussed. The plan of the collaboration for making the most effective use of the available luminosity in the first years of RHIC operation is also presented.Comment: 5 pages, 1 figure. Further details of the PHENIX physics program available at http://www.rhic.bnl.gov/phenix

The Earth: Plasma Sources, Losses, and Transport Processes

This paper reviews the state of knowledge concerning the source of magnetospheric plasma at Earth. Source of plasma, its acceleration and transport throughout the system, its consequences on system dynamics, and its loss are all discussed. Both observational and modeling advances since the last time this subject was covered in detail (Hultqvist et al., Magnetospheric Plasma Sources and Losses, 1999) are addressed

State of the climate in 2013

In 2013, the vast majority of the monitored climate variables reported here maintained trends established in recent decades. ENSO was in a neutral state during the entire year, remaining mostly on the cool side of neutral with modest impacts on regional weather patterns around the world. This follows several years dominated by the effects of either La Niña or El Niño events. According to several independent analyses, 2013 was again among the 10 warmest years on record at the global scale, both at the Earths surface and through the troposphere. Some regions in the Southern Hemisphere had record or near-record high temperatures for the year. Australia observed its hottest year on record, while Argentina and New Zealand reported their second and third hottest years, respectively. In Antarctica, Amundsen-Scott South Pole Station reported its highest annual temperature since records began in 1957. At the opposite pole, the Arctic observed its seventh warmest year since records began in the early 20th century. At 20-m depth, record high temperatures were measured at some permafrost stations on the North Slope of Alaska and in the Brooks Range. In the Northern Hemisphere extratropics, anomalous meridional atmospheric circulation occurred throughout much of the year, leading to marked regional extremes of both temperature and precipitation. Cold temperature anomalies during winter across Eurasia were followed by warm spring temperature anomalies, which were linked to a new record low Eurasian snow cover extent in May. Minimum sea ice extent in the Arctic was the sixth lowest since satellite observations began in 1979. Including 2013, all seven lowest extents on record have occurred in the past seven years. Antarctica, on the other hand, had above-average sea ice extent throughout 2013, with 116 days of new daily high extent records, including a new daily maximum sea ice area of 19.57 million km2 reached on 1 October. ENSO-neutral conditions in the eastern central Pacific Ocean and a negative Pacific decadal oscillation pattern in the North Pacific had the largest impacts on the global sea surface temperature in 2013. The North Pacific reached a historic high temperature in 2013 and on balance the globally-averaged sea surface temperature was among the 10 highest on record. Overall, the salt content in nearsurface ocean waters increased while in intermediate waters it decreased. Global mean sea level continued to rise during 2013, on pace with a trend of 3.2 mm yr-1 over the past two decades. A portion of this trend (0.5 mm yr-1) has been attributed to natural variability associated with the Pacific decadal oscillation as well as to ongoing contributions from the melting of glaciers and ice sheets and ocean warming. Global tropical cyclone frequency during 2013 was slightly above average with a total of 94 storms, although the North Atlantic Basin had its quietest hurricane season since 1994. In the Western North Pacific Basin, Super Typhoon Haiyan, the deadliest tropical cyclone of 2013, had 1-minute sustained winds estimated to be 170 kt (87.5 m s-1) on 7 November, the highest wind speed ever assigned to a tropical cyclone. High storm surge was also associated with Haiyan as it made landfall over the central Philippines, an area where sea level is currently at historic highs, increasing by 200 mm since 1970. In the atmosphere, carbon dioxide, methane, and nitrous oxide all continued to increase in 2013. As in previous years, each of these major greenhouse gases once again reached historic high concentrations. In the Arctic, carbon dioxide and methane increased at the same rate as the global increase. These increases are likely due to export from lower latitudes rather than a consequence of increases in Arctic sources, such as thawing permafrost. At Mauna Loa, Hawaii, for the first time since measurements began in 1958, the daily average mixing ratio of carbon dioxide exceeded 400 ppm on 9 May. The state of these variables, along with dozens of others, and the 2013 climate conditions of regions around the world are discussed in further detail in this 24th edition of the State of the Climate series. © 2014, American Meteorological Society. All rights reserved

Geographical and temporal distribution of SARS-CoV-2 clades in the WHO European Region, January to June 2020

We show the distribution of SARS-CoV-2 genetic clades over time and between countries and outline potential genomic surveillance objectives. We applied three available genomic nomenclature systems for SARS-CoV-2 to all sequence data from the WHO European Region available during the COVID-19 pandemic until 10 July 2020. We highlight the importance of real-time sequencing and data dissemination in a pandemic situation. We provide a comparison of the nomenclatures and lay a foundation for future European genomic surveillance of SARS-CoV-2.Peer reviewe