On prolongations of contact manifolds

We apply spectral sequences to derive both an obstruction to the existence of $n$-fold prolongations and a topological classification. Prolongations have been used in the literature in an attempt to prove that every Engel structure on $M\times\mathbb{S}^1$ with characteristic line field tangent to the fibers is determined by the contact structure induced on a cross section and the twisting of the Engel structure along the fibers. Our results show that this statement needs some modification: to classify the diffeomorphism type of the Engel structure we additionally have to fix a class in the first cohomology of $M$.Comment: 8 pages; corrected an error in Corollary 4.1., this version will appear in Proc. of the Amer. Math. So

Open book decompositions of fibre sums in contact topology

In the present paper we describe compatible open books for the fibre connected sum along binding components of open books, as well as for the fibre connected sum along multi-sections of open books. As an application the first description provides simple ways of constructing open books supporting all tight contact structures on $T^3$, recovering a result by van Horn-Morris, as well as an open book supporting the result of a Lutz twist along a binding component of an open book, recovering a result by Ozbagci--Pamuk.Comment: 18 pages, 15 figure

Constructions of open books and applications of convex surfaces in contact topology

In the present thesis we introduce an extension of the contact connected sum, in the sense that we replace the tight $3$-balls by standard neighbourhoods of Legendrian graphs $G \subset (S^3,\xi_{st})$. By the use of convex surface theory we show that there is a Weinstein cobordism from the original contact manifold to the result of the extended contact connected sum. We approach the analogue of this result in higher dimensions, using different methods, and present a generalised symplectic $1$-handle which is used for the construction of exact symplectic cobordisms. Furthermore we describe compatible open books for the fibre connected sum along binding components of open books as well as for the fibre connected sum along multi-sections of open books. Given a Legendrian knot $L$ with standard neighbourhood $N$ in a closed contact $3$-manifold $(M,\xi)$, the homotopy type of the contact structure $\xi|_{M\setminus N}$ on the knot complement depends on the rotation number of $L$. We give an alternative proof of this folklore theorem, as well as for a second folklore theorem that states, up to stabilisation, the classification of Legendrian knots is purely topological. Let $\zeta$ denote the standard contact structure on the $3$-dimensional torus $T^3$. Denoting by $\Xi{(T^3,\zeta)}$ the connected component of $\zeta$ in the space of contact structures on $T^3$, we show that the fundamental group $\pi_1\big( \Xi{(T^3,\zeta)} \big)$ is isomorphic to $\mathbb{Z}$

Management of Prairie Dog Populations in Wind Cave National Park

Since the late 1920\u27s there have been periodic control programs on black-tailed prairie dogs in Wind Cave National Park. The most recent control effort, which began in 1982, resulted in the reduction of total dogtown acreage from 2,000 to 750 acres. Recent studies carried out within the park have provided managers with more soundly based justification for carrying out control programs. The same information also points to the importance of maintaining prairie dog populations at or above certain minimum levels and the need for integrating this control program with several of the other resource management programs being carried out in the area

A Three-Step Synthesis of an Alkyne Containing Farnesyl Derivative

Farnesylation is a key protein modification for cellular signaling that is unregulated in cancer patients. The goal here is to synthesize an alkyne-containing farnesyl mimic that will allow for the targeting of farnesylated proteins. First, farnesol was THP protected using dihydropyran and PPTs. The THP protected farnesol was then oxidized using SeO2 and tert-butyl hydrogen peroxide and purified using column chromatography. The resulting alcohol was then converted to an alkyne containing ether upon treatment with NaH and BrCH2­CH2CCH. To make the reaction greener, t-Bu-OOH, a harmful solvent used in this synthesis, is to be replaced with an alternative solvent such as hydroperoxide 1, 1-dimethylethyl, or Hydroperoxide-d

Editing, validating and translating of SBGN maps

Motivation: The recently proposed Systems Biology Graphical Notation (SBGN) provides a standard for the visual representation of biochemical and cellular processes. It aims to support more efficient and accurate communication of biological knowledge between different research communities in the life sciences. However, to increase the use of SBGN, tools for editing, validating and translating SBGN maps are desirable

VANTED: A system for advanced data analysis and visualization in the context of biological networks

BACKGROUND: Recent advances with high-throughput methods in life-science research have increased the need for automatized data analysis and visual exploration techniques. Sophisticated bioinformatics tools are essential to deduct biologically meaningful interpretations from the large amount of experimental data, and help to understand biological processes. RESULTS: We present VANTED, a tool for the visualization and analysis of networks with related experimental data. Data from large-scale biochemical experiments is uploaded into the software via a Microsoft Excel-based form. Then it can be mapped on a network that is either drawn with the tool itself, downloaded from the KEGG Pathway database, or imported using standard network exchange formats. Transcript, enzyme, and metabolite data can be presented in the context of their underlying networks, e. g. metabolic pathways or classification hierarchies. Visualization and navigation methods support the visual exploration of the data-enriched networks. Statistical methods allow analysis and comparison of multiple data sets such as different developmental stages or genetically different lines. Correlation networks can be automatically generated from the data and substances can be clustered according to similar behavior over time. As examples, metabolite profiling and enzyme activity data sets have been visualized in different metabolic maps, correlation networks have been generated and similar time patterns detected. Some relationships between different metabolites were discovered which are in close accordance with the literature. CONCLUSION: VANTED greatly helps researchers in the analysis and interpretation of biochemical data, and thus is a useful tool for modern biological research. VANTED as a Java Web Start Application including a user guide and example data sets is available free of charge at