On the uniform generation of modular diagrams

In this paper we present an algorithm that generates $k$-noncrossing, $\sigma$-modular diagrams with uniform probability. A diagram is a labeled graph of degree $\le 1$ over $n$ vertices drawn in a horizontal line with arcs $(i,j)$ in the upper half-plane. A $k$-crossing in a diagram is a set of $k$ distinct arcs $(i_1, j_1), (i_2, j_2),\ldots,(i_k, j_k)$ with the property $i_1 < i_2 < \ldots < i_k < j_1 < j_2 < \ldots< j_k$. A diagram without any $k$-crossings is called a $k$-noncrossing diagram and a stack of length $\sigma$ is a maximal sequence $((i,j),(i+1,j-1),\dots,(i+(\sigma-1),j-(\sigma-1)))$. A diagram is $\sigma$-modular if any arc is contained in a stack of length at least $\sigma$. Our algorithm generates after $O(n^k)$ preprocessing time, $k$-noncrossing, $\sigma$-modular diagrams in $O(n)$ time and space complexity.Comment: 21 pages, 7 figure

Shapes of topological RNA structures

A topological RNA structure is derived from a diagram and its shape is obtained by collapsing the stacks of the structure into single arcs and by removing any arcs of length one. Shapes contain key topological, information and for fixed topological genus there exist only finitely many such shapes. We shall express topological RNA structures as unicellular maps, i.e. graphs together with a cyclic ordering of their half-edges. In this paper we prove a bijection of shapes of topological RNA structures. We furthermore derive a linear time algorithm generating shapes of fixed topological genus. We derive explicit expressions for the coefficients of the generating polynomial of these shapes and the generating function of RNA structures of genus $g$. Furthermore we outline how shapes can be used in order to extract essential information of RNA structure databases.Comment: 27 pages, 11 figures, 2 tables. arXiv admin note: text overlap with arXiv:1304.739

The Airplane as a Factor in Modern Transportation

This paper was planned with the object of covering the history and development of air transportation from its incep- tion to the present time. The mythology concerning aviation has been taken up at the beginning and this has been followed by a discussion of the earliest experiments in flying. The activities of the Wright Brothers began about 1900 and in 1909 they sold the Wright Flyer to the United States Govern- ment. The development of pre-war and wartime airplanes is next taken up. The World War was significant in airplane history. During this period airplanes were improved tremendously, because of necessity. Following this period, development of aviation ceased for a short time, due to an over abundance of airplanes left over from the wartime production. After this, the manufacture and improvement of airplanes began in earnest. The most recent records of various types of airplanes under different conditions are given, to show the improvements made

Falkland Islands Malvinas Exploitation Report 2015

A series of three reports were published by the Demining Programme Office in the Falkland Islands (Malvinas). This report explains that the need for exploitation was recognised early during the planning for mine clearance operations in the Falkland Islands (Malvinas). Little was known about the state of the mines some 30 years after the conflict, and it was considered important to understand the effects of ageing, along with the implications for issues such as appearance/recognition, functionality and detectability. Exploitation was previously carried out during clearance Phases 1 and 3. This report outlines the work conducted during Phase 4a, where a total of 78 mines and fuses were examined or tested, with 38 mines being fully disassembled. The aim of this report is to outline the findings from the exploitation work, with particular emphasis on: The general condition of the mines Their ability to function, either as designed, or by other mechanisms Significant changes in their characteristics that might affect detectability or sensitivity

On the combinatorics of sparsification

Background: We study the sparsification of dynamic programming folding algorithms of RNA structures. Sparsification applies to the mfe-folding of RNA structures and can lead to a significant reduction of time complexity. Results: We analyze the sparsification of a particular decomposition rule, $\Lambda^*$, that splits an interval for RNA secondary and pseudoknot structures of fixed topological genus. Essential for quantifying the sparsification is the size of its so called candidate set. We present a combinatorial framework which allows by means of probabilities of irreducible substructures to obtain the expected size of the set of $\Lambda^*$-candidates. We compute these expectations for arc-based energy models via energy-filtered generating functions (GF) for RNA secondary structures as well as RNA pseudoknot structures. For RNA secondary structures we also consider a simplified loop-energy model. This combinatorial analysis is then compared to the expected number of $\Lambda^*$-candidates obtained from folding mfe-structures. In case of the mfe-folding of RNA secondary structures with a simplified loop energy model our results imply that sparsification provides a reduction of time complexity by a constant factor of 91% (theory) versus a 96% reduction (experiment). For the "full" loop-energy model there is a reduction of 98% (experiment).Comment: 27 pages, 12 figure

Demining Programme Office in the Falkland Islands - Technical Support 2015

The need for exploitation was recognised early during the planning for mine clearance operations in the Falkland Islands. Little was known about the state of the mines some 30 years after the conflict, and it was considered important to understand the effects of ageing, along with the implications for issues such as appearance/recognition, functionality and detectability. Exploitation was previously carried out during clearance Phases 1 and 3. This report outlines the work conducted during Phase 4a, where samples of the following mines were examined: P4B, SB-33 and SB-81. Presented to the FCO (Foreign and Commonwealth Office) in March 2015

Demining Programme Office in the Falkland Islands - Exploitation 2017

In January 2017, exploitation work was carried out by Fenix Insight Ltd on mines and other ordnance recovered by the Land Release Contractor (LRC). Examination of grenades used in booby traps revealed that one, considered to be complex and dangerous, had been rendered safe by the ageing process. The other, though more familiar, was still fully functional and highly lethal. The findings highlight the continued danger from unexploded ordnance, and the need for threat assessment to be based on technical evidence rather than intuition