Euler Characteristic of Polyhedral Graphs

Euler characteristic is a topological invariant, a number that describes the shape or structure of a topological space, irrespective of the way it is bent. Many operations on topological spaces may be expressed by means of Euler characteristic. Counting polyhedral graph figures is directly related to Euler characteristic. This paper illustrates the Euler characteristic involvement in figure counting of polyhedral graphs designed by operations on maps. This number is also calculated in truncated cubic network and hypercube. Spongy hypercubes are built up by embedding the hypercube in polyhedral graphs, of which figures are calculated combinatorially by a formula that accounts for their spongy character. Euler formula can be useful in chemistry and crystallography to check the consistency of an assumed structure. This work is licensed under a Creative Commons Attribution 4.0 International License

Land surface response to climate change forcing over Southern Africa

The land surface is important to the climate system for the exchanges of moisture, momentum and heat. Momentum, radiation, and sensible and latent heat fluxes between the atmosphere and the surface will likely affect atmospheric dynamics, temperature, precipitation and humidity fields (Sato et ai., 1989). These may subsequently feed back into the land surface processes as part of a cyclical system. Therefore it is evident that our livelihood is largely dependent on interactions and exchanges between the land surface and climate system (Henderson-Sellers et ai., 1993) and it is thus essential that we gain a better understanding of the interactive sensitivity. This is of particular relevance in the context of the portended future global climate change. In the present study the interactions between the land surface and the atmosphere are considered over the southern African region. This region has a climate showing a high degree of spatial and temporal variability, most notably with rainfall. Regional climates are characterised by summer, winter and all-year-round rainfall. There are steep vegetation gradients and a wide range of vegetation types adapted to suit the variable climate. These factors, combined with the societal implications of changes in the climate and land surface systems, make southern Africa a challenging and important study domain for examining the sensitivity between the different elements of the atmosphere and biosphere. This research makes use of a biosphere model driven by climate change data derived from a general circulation model (GCM). Regions susceptible and sensitive to changes on an annual and seasonal basis are identified and examined. The thesis comprises 8 chapters. The first chapter, Chapter 1, provides some background information on climate change, biosphereatmosphere interactions, GCMs and transient simulations, vegetation models and vegetation representation over southern Africa. This chapter also sets out the research objectives. The following chapter, Chapter 2, introduces the atmospheric GCM model data from the Hadley Centre Model (HadCM2) used in the analysis. The chapter additionally provides a detailed description of the biosphere model, the Integrated Biosphere Simulator (IBIS). Chapter 3 examines the Hadley Centre HadCM2 GCM input data used in driving the biosphere model, while Chapter 4 presents the input forcing data and configuration of the IBIS model. In Chapter 5 the results of the IBIS model simulation are examined on the annual scale and in Chapter 6 the results are examined on the seasonal scale. Some of the implications of climate change are considered in Chapter 7. This chapter also places the HadCM2 GCM model data used in driving IBIS into the context of the latest emissions scenarios. In the final chapter, Chapter 8, an overview summary is provided and conclusions are drawn

Methods to study splicing from high-throughput RNA Sequencing data

The development of novel high-throughput sequencing (HTS) methods for RNA (RNA-Seq) has provided a very powerful mean to study splicing under multiple conditions at unprecedented depth. However, the complexity of the information to be analyzed has turned this into a challenging task. In the last few years, a plethora of tools have been developed, allowing researchers to process RNA-Seq data to study the expression of isoforms and splicing events, and their relative changes under different conditions. We provide an overview of the methods available to study splicing from short RNA-Seq data. We group the methods according to the different questions they address: 1) Assignment of the sequencing reads to their likely gene of origin. This is addressed by methods that map reads to the genome and/or to the available gene annotations. 2) Recovering the sequence of splicing events and isoforms. This is addressed by transcript reconstruction and de novo assembly methods. 3) Quantification of events and isoforms. Either after reconstructing transcripts or using an annotation, many methods estimate the expression level or the relative usage of isoforms and/or events. 4) Providing an isoform or event view of differential splicing or expression. These include methods that compare relative event/isoform abundance or isoform expression across two or more conditions. 5) Visualizing splicing regulation. Various tools facilitate the visualization of the RNA-Seq data in the context of alternative splicing. In this review, we do not describe the specific mathematical models behind each method. Our aim is rather to provide an overview that could serve as an entry point for users who need to decide on a suitable tool for a specific analysis. We also attempt to propose a classification of the tools according to the operations they do, to facilitate the comparison and choice of methods.Comment: 31 pages, 1 figure, 9 tables. Small corrections adde

Reservoir assessment using non-invasive geophysical techniques

This paper describes the use of three geophysical techniques to detect potential seepage that could jeopardise the integrity of reservoir embankments, could induce partial or total collapse and pose a risk to the population nearby. A fast scanning geophysical technique using two dipole electromagnetic (EM) profile apparatus GEM2 provided the first step to detect the weakest points on the selected dams in order to proceed to a more detailed analysis and visualisation of the soil erosion (fissuring or piping) using Electrical Resistivity Tomography (ERT). Finally, Self-Potential surveys were carried out to relate to the EM and ERT anomalies that could be pathways for seepage and changes of the water displacement inside the embankment. The three geophysical techniques used were evaluated in two case studies of reservoirs in locations relevant to flooding issues in Czech Republic. A risk approach based on the geophysical results was undertaken for the reservoirs embankments. The three techniques together were compared for the same problematic section and confirmed seepage by showing similar results. Conclusions were also drawn on the efficiency of using these three techniques as a package to give a comprehensive non-invasive assessment to be used as common practice by local authorities and Environment Agencies whereby remedial action could be recommended to protect assets and civilians

Austrian Social Security Database

The Austrian Social Security Database (ASSD) is a matched firm-worker data set, which records the labor market history of almost 11 million individuals from January 1972 to April 2007. Moreover, more than 2.2 million firms can be identified. The individual labor market histories are described in the follow- ing dimensions: very detailed daily labor market states and yearly earnings at the firm-worker level, together with a limited set of demographic characteris- tics. Additionally the ASSD provides some firm related information, such as geographical location and industry affiliation. This paper is a short description of this huge data base and intended for people using this data in their own empirical work.