The Critical Phase for Random Graphs with a Given Degree Sequence

We consider random graphs with a fixed degree sequence. Molloy and Reed [11, 12] studied how the size of the giant component changes according to degree conditions. They showed that there is a phase transition and investigated the order of components before and after the critical phase. In this paper we study more closely the order of components at the critical phase, using singularity analysis of a generating function for a branching process which models the random graph with a given degree sequence

Early prediction of response to radiotherapy and androgen-deprivation therapy in prostate cancer by repeated functional MRI: a preclinical study

<p>Abstract</p> <p>Background</p> <p>In modern cancer medicine, morphological magnetic resonance imaging (MRI) is routinely used in diagnostics, treatment planning and assessment of therapeutic efficacy. During the past decade, functional imaging techniques like diffusion-weighted (DW) MRI and dynamic contrast-enhanced (DCE) MRI have increasingly been included into imaging protocols, allowing extraction of intratumoral information of underlying vascular, molecular and physiological mechanisms, not available in morphological images. Separately, pre-treatment and early changes in functional parameters obtained from DWMRI and DCEMRI have shown potential in predicting therapy response. We hypothesized that the combination of several functional parameters increased the predictive power.</p> <p>Methods</p> <p>We challenged this hypothesis by using an artificial neural network (ANN) approach, exploiting nonlinear relationships between individual variables, which is particularly suitable in treatment response prediction involving complex cancer data. A clinical scenario was elicited by using 32 mice with human prostate carcinoma xenografts receiving combinations of androgen-deprivation therapy and/or radiotherapy. Pre-radiation and on days 1 and 9 following radiation three repeated DWMRI and DCEMRI acquisitions enabled derivation of the apparent diffusion coefficient (ADC) and the vascular biomarker <it>K</it>^trans, which together with tumor volumes and the established biomarker prostate-specific antigen (PSA), were used as inputs to a back propagation neural network, independently and combined, in order to explore their feasibility of predicting individual treatment response measured as 30 days post-RT tumor volumes.</p> <p>Results</p> <p>ADC, volumes and PSA as inputs to the model revealed a correlation coefficient of 0.54 (p < 0.001) between predicted and measured treatment response, while <it>K</it>^trans, volumes and PSA gave a correlation coefficient of 0.66 (p < 0.001). The combination of all parameters (ADC, <it>K</it>^trans, volumes, PSA) successfully predicted treatment response with a correlation coefficient of 0.85 (p < 0.001).</p> <p>Conclusions</p> <p>We have in a preclinical investigation showed that the combination of early changes in several functional MRI parameters provides additional information about therapy response. If such an approach could be clinically validated, it may become a tool to help identifying non-responding patients early in treatment, allowing these patients to be considered for alternative treatment strategies, and, thus, providing a contribution to the development of individualized cancer therapy.</p

The early evolution of the H-free process

The H-free process, for some fixed graph H, is the random graph process defined by starting with an empty graph on n vertices and then adding edges one at a time, chosen uniformly at random subject to the constraint that no H subgraph is formed. Let G be the random maximal H-free graph obtained at the end of the process. When H is strictly 2-balanced, we show that for some c>0, with high probability as $n \to \infty$, the minimum degree in G is at least $cn^{1-(v_H-2)/(e_H-1)}(\log n)^{1/(e_H-1)}$. This gives new lower bounds for the Tur\'an numbers of certain bipartite graphs, such as the complete bipartite graphs $K_{r,r}$ with $r \ge 5$. When H is a complete graph $K_s$ with $s \ge 5$ we show that for some C>0, with high probability the independence number of G is at most $Cn^{2/(s+1)}(\log n)^{1-1/(e_H-1)}$. This gives new lower bounds for Ramsey numbers R(s,t) for fixed $s \ge 5$ and t large. We also obtain new bounds for the independence number of G for other graphs H, including the case when H is a cycle. Our proofs use the differential equations method for random graph processes to analyse the evolution of the process, and give further information about the structure of the graphs obtained, including asymptotic formulae for a broad class of subgraph extension variables.Comment: 36 page

Volcanism and the Greenland ice cores: A new tephrochronological framework for the last glacial-interglacial transition (LGIT) based on cryptotephra deposits in three ice cores

Chemical profiles from Greenland ice cores show that the frequency of volcanism was higher during the last glacial-interglacial transition (LGIT) and early Holocene, (17–9 ka b2k) than in any other period during the last 110 kyr. This increased frequency has partly been linked to climate-driven melting of the Icelandic ice sheet during the last deglaciation, with regional isostatic changes thought to alter mantle viscosity and lead to more eruptions. Our study is the first to construct a comprehensive tephrochronological framework from Greenland ice cores over the LGIT to aid in the reconstruction of volcanic activity over this period. The framework is based on extensive high-resolution sampling of three Greenland ice cores between 17.4 and 11.6 ka b2k and comprises a total of 64 cryptotephra deposits from the NGRIP, GRIP and NEEM ice cores. We show that many of these tephras are preserved within the core without an associated chemical signature in the ice, which implies that reconstructions of volcanism based solely on glacio-chemical indicators might underestimate the number of events. Single glass shards from each deposit were geochemically characterised to trace the volcanic source and many of these deposits could be correlated between cores. We show that the 64 deposits represent tephra deposits from 42 separate volcanic events, and of these, 39 are from Iceland, two from the north Pacific region (Japan and USA) and one has an unknown source. Six deposits can be correlated to terrestrial and/or marine tephra deposits in the Northern Hemisphere and the remaining 36 are unreported in other archives. We did not locate tephra from the compositionally distinctive Laacher See eruption (∼13 ka b2k) in our records. Combining our new discoveries with the previously published tephra framework, raises the number of individual tephra horizons found in Greenland ice over this interval to 50. This significantly improves the regional tephrochronological framework, our knowledge of the eruptive history of Iceland during the LGIT and provides new tephra constraints over key LGIT climate events. Consequentially, this framework can guide sampling strategies of future tephra studies in the terrestrial and marine realms aiming to link these records to the Greenland ice cores to assess regional climate synchroneity

Impact of sudden Arctic sea-ice loss on stratospheric polar ozone recovery

We investigate the sensitivity of Northern Hemisphere polar ozone recovery to a scenario in which there is rapid loss of Arctic summer sea ice in the first half of the 21st century. The issue is addressed by coupling a chemistry climate model to an ocean general circulation model and performing simulations of ozone recovery with, and without, an external perturbation designed to cause a rapid and complete loss of summertime Arctic sea ice. Under this extreme perturbation, the stratospheric response takes the form of a springtime polar cooling which is dynamical rather than radiative in origin, and is caused by reduced wave forcing from the troposphere. The response lags the onset of the sea-ice perturbation by about one decade and lasts for more than two decades, and is associated with an enhanced weakening of the North Atlantic meridional overturning circulation. The stratospheric dynamical response leads to a 10 DU reduction in polar column ozone, which is statistically robust. While this represents a modest loss, it has the potential to induce a delay of roughly one decade in Arctic ozone recovery estimates made in the 2006 Scientific Assessment of Ozone Depletion

Balancing Detection and Eradication for Control of Epidemics: Sudden Oak Death in Mixed-Species Stands

Culling of infected individuals is a widely used measure for the control of several plant and animal pathogens but culling first requires detection of often cryptically-infected hosts. In this paper, we address the problem of how to allocate resources between detection and culling when the budget for disease management is limited. The results are generic but we motivate the problem for the control of a botanical epidemic in a natural ecosystem: sudden oak death in mixed evergreen forests in coastal California, in which species composition is generally dominated by a spreader species (bay laurel) and a second host species (coast live oak) that is an epidemiological dead-end in that it does not transmit infection but which is frequently a target for preservation. Using a combination of an epidemiological model for two host species with a common pathogen together with optimal control theory we address the problem of how to balance the allocation of resources for detection and epidemic control in order to preserve both host species in the ecosystem. Contrary to simple expectations our results show that an intermediate level of detection is optimal. Low levels of detection, characteristic of low effort expended on searching and detection of diseased trees, and high detection levels, exemplified by the deployment of large amounts of resources to identify diseased trees, fail to bring the epidemic under control. Importantly, we show that a slight change in the balance between the resources allocated to detection and those allocated to control may lead to drastic inefficiencies in control strategies. The results hold when quarantine is introduced to reduce the ingress of infected material into the region of interest

The Norwegian Earth System Model, NorESM1-M – Part 1: Description and basic evaluation of the physical climate

The core version of the Norwegian Climate Center's Earth System Model, named NorESM1-M, is presented. The NorESM family of models are based on the Community Climate System Model version 4 (CCSM4) of the University Corporation for Atmospheric Research, but differs from the latter by, in particular, an isopycnic coordinate ocean model and advanced chemistry–aerosol–cloud–radiation interaction schemes. NorESM1-M has a horizontal resolution of approximately 2° for the atmosphere and land components and 1° for the ocean and ice components. NorESM is also available in a lower resolution version (NorESM1-L) and a version that includes prognostic biogeochemical cycling (NorESM1-ME). The latter two model configurations are not part of this paper. Here, a first-order assessment of the model stability, the mean model state and the internal variability based on the model experiments made available to CMIP5 are presented. Further analysis of the model performance is provided in an accompanying paper (Iversen et al., 2013), presenting the corresponding climate response and scenario projections made with NorESM1-M

A stratigraphic framework for abrupt climatic changes during the Last Glacial period based on three synchronized Greenland ice-core records: refining and extending the INTIMATE event stratigraphy

Due to their outstanding resolution and well-constrained chronologies, Greenland ice-core records provide a master record of past climatic changes throughout the Last Interglacial–Glacial cycle in the North Atlantic region. As part of the INTIMATE (INTegration of Ice-core, MArine and TErrestrial records) project, protocols have been proposed to ensure consistent and robust correlation between different records of past climate. A key element of these protocols has been the formal definition and ordinal numbering of the sequence of Greenland Stadials (GS) and Greenland Interstadials (GI) within the most recent glacial period. The GS and GI periods are the Greenland expressions of the characteristic Dansgaard–Oeschger events that represent cold and warm phases of the North Atlantic region, respectively. We present here a more detailed and extended GS/GI template for the whole of the Last Glacial period. It is based on a synchronization of the NGRIP, GRIP, and GISP2 ice-core records that allows the parallel analysis of all three records on a common time scale. The boundaries of the GS and GI periods are defined based on a combination of stable-oxygen isotope ratios of the ice (δ18O, reflecting mainly local temperature) and calcium ion concentrations (reflecting mainly atmospheric dust loading) measured in the ice. The data not only resolve the well-known sequence of Dansgaard–Oeschger events that were first defined and numbered in the ice-core records more than two decades ago, but also better resolve a number of short-lived climatic oscillations, some defined here for the first time. Using this revised scheme, we propose a consistent approach for discriminating and naming all the significant abrupt climatic events of the Last Glacial period that are represented in the Greenland ice records. The final product constitutes an extended and better resolved Greenland stratotype sequence, against which other proxy records can be compared and correlated. It also provides a more secure basis for investigating the dynamics and fundamental causes of these climatic perturbations