Efficient and Stable Acoustic Tomography Using Sparse Reconstruction Methods

We study an acoustic tomography problem and propose a new inversion technique based on sparsity. Acoustic tomography observes the parameters of the medium that influence the speed of sound propagation. In the human body, the parameters that mostly influence the sound speed are temperature and density, in the ocean - temperature and current, in the atmosphere - temperature and wind. In this study, we focus on estimating temperature in the atmosphere using the information on the average sound speed along the propagation path. The latter is practically obtained from travel time measurements. We propose a reconstruction algorithm that exploits the concept of sparsity. Namely, the temperature is assumed to be a linear combination of some functions (e.g. bases or set of different bases) where many of the coefficients are known to be zero. The goal is to find the non-zero coefficients. To this end, we apply an algorithm based on linear programming that under some constrains finds the solution with minimum l0 norm. This is actually equivalent to the fact that many of the unknown coefficients are zeros. Finally, we perform numerical simulations to assess the effectiveness of our approach. The simulation results confirm the applicability of the method and demonstrate high reconstruction quality and robustness to noise

Classical potential energy calculations for ApA, CpC, GpG, and UpU. The influence of the bases on RNA subunit conformations

Classical potential energy calculations have been made for the ribodinucleoside monophosphates ApA, CpC, GpG, and UpU. Van der Waal's, electrostatic, and torsional contributions to the energy were calculated, and the energy was minimized with the seven backbone conformational angles as simultaneously variable parameters. At the global minimum, ApA and CpC have conformations like double helical RNA: the angles ω′ and ω are g−g−, the sugar pucker is C3′-endo, and the bases are anti. GpG and UpU, on the other hand, have the ω′,ω angle pair g−t at the global minimum, and for GpG the bases are syn. Energy contour maps for ω′ and ω show two broad, low energy regions for ApA, CpC, and UpU: one is g−g−, and the second encompasses g−t and g+g+ within a single low energy contour. The two regions are connected by a path at 10–13 kcal./mole. For GpG, with bases syn, however, only a small low-energy region at g−t is found. The helical ‘A’ RNA conformation is 8.5 kcal/mole higher for this molecule. Thus, the base composition is shown to influence the conformations adopted by dinucleoside phosphates. Comparison of calculations with experimental data, where available, show good agreement

Minimum cycle and homology bases of surface embedded graphs

We study the problems of finding a minimum cycle basis (a minimum weight set of cycles that form a basis for the cycle space) and a minimum homology basis (a minimum weight set of cycles that generates the $1$-dimensional ($\mathbb{Z}_2$)-homology classes) of an undirected graph embedded on a surface. The problems are closely related, because the minimum cycle basis of a graph contains its minimum homology basis, and the minimum homology basis of the $1$-skeleton of any graph is exactly its minimum cycle basis. For the minimum cycle basis problem, we give a deterministic $O(n^\omega+2^{2g}n^2+m)$-time algorithm for graphs embedded on an orientable surface of genus $g$. The best known existing algorithms for surface embedded graphs are those for general graphs: an $O(m^\omega)$ time Monte Carlo algorithm and a deterministic $O(nm^2/\log n + n^2 m)$ time algorithm. For the minimum homology basis problem, we give a deterministic $O((g+b)^3 n \log n + m)$-time algorithm for graphs embedded on an orientable or non-orientable surface of genus $g$ with $b$ boundary components, assuming shortest paths are unique, improving on existing algorithms for many values of $g$ and $n$. The assumption of unique shortest paths can be avoided with high probability using randomization or deterministically by increasing the running time of the homology basis algorithm by a factor of $O(\log n)$.Comment: A preliminary version of this work was presented at the 32nd Annual International Symposium on Computational Geometr

Convex Cycle Bases

Convex cycles play a role e.g. in the context of product graphs. We introduce convex cycle bases and describe a polynomial-time algorithm that recognizes whether a given graph has a convex cycle basis and provides an explicit construction in the positive case. Relations between convex cycles bases and other types of cycles bases are discussed. In particular we show that if G has a unique minimal cycle bases, this basis is convex. Furthermore, we characterize a class of graphs with convex cycles bases that includes partial cubes and hence median graphs. (authors' abstract)Series: Research Report Series / Department of Statistics and Mathematic

The Forcing Weak Edge Detour Number of a Graph

The forcing weak edge detour numbers of certain classes of graphs are determined

Minimum Cycle Base of Graphs Identified by Two Planar Graphs

In this paper, we study the minimum cycle base of the planar graphs obtained from two 2-connected planar graphs by identifying an edge (or a cycle) of one graph with the corresponding edge (or cycle) of another, related with map geometries, i.e., Smarandache 2-dimensional manifolds