On Exploring Temporal Graphs of Small Pathwidth

We show that the Temporal Graph Exploration Problem is NP-complete, even when the underlying graph has pathwidth 2 and at each time step, the current graph is connected

How Does Object Fatness Impact the Complexity of Packing in d Dimensions?

Packing is a classical problem where one is given a set of subsets of Euclidean space called objects, and the goal is to find a maximum size subset of objects that are pairwise non-intersecting. The problem is also known as the Independent Set problem on the intersection graph defined by the objects. Although the problem is NP-complete, there are several subexponential algorithms in the literature. One of the key assumptions of such algorithms has been that the objects are fat, with a few exceptions in two dimensions; for example, the packing problem of a set of polygons in the plane surprisingly admits a subexponential algorithm. In this paper we give tight running time bounds for packing similarly-sized non-fat objects in higher dimensions. We propose an alternative and very weak measure of fatness called the stabbing number, and show that the packing problem in Euclidean space of constant dimension d >=slant 3 for a family of similarly sized objects with stabbing number alpha can be solved in 2^O(n^(1-1/d) alpha) time. We prove that even in the case of axis-parallel boxes of fixed shape, there is no 2^o(n^(1-1/d) alpha) algorithm under ETH. This result smoothly bridges the whole range of having constant-fat objects on one extreme (alpha=1) and a subexponential algorithm of the usual running time, and having very "skinny" objects on the other extreme (alpha=n^(1/d)), where we cannot hope to improve upon the brute force running time of 2^O(n), and thereby characterizes the impact of fatness on the complexity of packing in case of similarly sized objects. We also study the same problem when parameterized by the solution size k, and give a n^O(k^(1-1/d) alpha) algorithm, with an almost matching lower bound: there is no algorithm with running time of the form f(k) n^o(k^(1-1/d) alpha/log k) under ETH. One of our main tools in these reductions is a new wiring theorem that may be of independent interest

Molecular analysis of Mycobacterium tuberculosis DNA from a family of 18th century Hungarians

The naturally mummified remains of a mother and two daughters found in an 18th century Hungarian crypt were analysed, using multiple molecular genetic techniques to examine the epidemiology and evolution of tuberculosis. DNA was amplified from a number of targets on the Mycobacterium tuberculosis genome, including DNA from IS6110, gyrA, katG codon 463, oxyR, dnaA–dnaN, mtp40, plcD and the direct repeat (DR) region. The strains present in the mummified remains were identified as M. tuberculosis and not Mycobacterium bovis, from katG and gyrA genotyping, PCR from the oxyR and mtp40 loci, and spoligotyping. Spoligotyping divided the samples into two strain types, and screening for a deletion in the MT1801–plcD region initially divided the strains into three types. Further investigation showed, however, that an apparent deletion was due to poor DNA preservation. By comparing the effect of PCR target size on the yield of amplicon, a clear difference was shown between 18th century and modern M. tuberculosis DNA. A two-centre system was used to confirm the findings of this study, which clearly demonstrate the value of using molecular genetic techniques to study historical cases of tuberculosis and the care required in drawing conclusions. The genotyping and spoligotyping results are consistent with the most recent theory of the evolution and spread of the modern tuberculosis epidemic

A gravitational procedure to measure the diffusion coefficient of mater in porous materials : a case study on concrete

A new procedure is presented with which the diffusion coefficient of water in partially saturated porous materials can be measured. The first step in the procedure is the creation of a non-equilibrium situation inside a sample by placing it into a centrifuge. In the second step, the mass of the sample is measured by hanging it from two cables, each connected to a balance. The comparison of the time evolutions of the measured masses and the masses as predicted using Fick’s second law gives the diffusion coefficient