The multi-stripe travelling salesman problem

In the classical Travelling Salesman Problem (TSP), the objective function sums the costs for travelling from one city to the next city along the tour. In the q-stripe TSP with q ≥ 1, the objective function sums the costs for travelling from one city to each of the next q cities along the tour. The resulting q-stripe TSP generalizes the TSP and forms a special case of the quadratic assignment problem. We analyze the computational complexity of the q-stripe TSP for various classes of specially structured distance matrices. We derive NP-hardness results as well as polyomially solvable cases. One of our main results generalizes a well-known theorem of Kalmanson from the classical TSP to the q-stripe TSP

The 2021 WHO catalogue of Mycobacterium tuberculosis complex mutations associated with drug resistance: a genotypic analysis.

Background: Molecular diagnostics are considered the most promising route to achievement of rapid, universal drug susceptibility testing for Mycobacterium tuberculosis complex (MTBC). We aimed to generate a WHO-endorsed catalogue of mutations to serve as a global standard for interpreting molecular information for drug resistance prediction. Methods: In this systematic analysis, we used a candidate gene approach to identify mutations associated with resistance or consistent with susceptibility for 13 WHO-endorsed antituberculosis drugs. We collected existing worldwide MTBC whole-genome sequencing data and phenotypic data from academic groups and consortia, reference laboratories, public health organisations, and published literature. We categorised phenotypes as follows: methods and critical concentrations currently endorsed by WHO (category 1); critical concentrations previously endorsed by WHO for those methods (category 2); methods or critical concentrations not currently endorsed by WHO (category 3). For each mutation, we used a contingency table of binary phenotypes and presence or absence of the mutation to compute positive predictive value, and we used Fisher's exact tests to generate odds ratios and Benjamini-Hochberg corrected p values. Mutations were graded as associated with resistance if present in at least five isolates, if the odds ratio was more than 1 with a statistically significant corrected p value, and if the lower bound of the 95% CI on the positive predictive value for phenotypic resistance was greater than 25%. A series of expert rules were applied for final confidence grading of each mutation. Findings: We analysed 41 137 MTBC isolates with phenotypic and whole-genome sequencing data from 45 countries. 38 215 MTBC isolates passed quality control steps and were included in the final analysis. 15 667 associations were computed for 13 211 unique mutations linked to one or more drugs. 1149 (7·3%) of 15 667 mutations were classified as associated with phenotypic resistance and 107 (0·7%) were deemed consistent with susceptibility. For rifampicin, isoniazid, ethambutol, fluoroquinolones, and streptomycin, the mutations' pooled sensitivity was more than 80%. Specificity was over 95% for all drugs except ethionamide (91·4%), moxifloxacin (91·6%) and ethambutol (93·3%). Only two resistance mutations were identified for bedaquiline, delamanid, clofazimine, and linezolid as prevalence of phenotypic resistance was low for these drugs. Interpretation: We present the first WHO-endorsed catalogue of molecular targets for MTBC drug susceptibility testing, which is intended to provide a global standard for resistance interpretation. The existence of this catalogue should encourage the implementation of molecular diagnostics by national tuberculosis programmes. Funding: Unitaid, Wellcome Trust, UK Medical Research Council, and Bill and Melinda Gates Foundation

On the Structure of Diregular Digraphs With Defect 1

The Moore bound for a diregular digraph of degree d and diameter k is M d;k = 1 + d + : : : + d k . It is known that digraphs of order M d;k do not exist for d ? 1 and k ? 1. In this paper we study digraphs of order M d;k \Gamma 1, that is, digraphs with defect 1, denoted by (d; k)-digraphs. If G is a (d; k)-digraph, then for each vertex v of G there exists a vertex w (called the repeat of v) such that there are two walks of lengths k from v to w. In the case of w = v we call v a selfrepeat. To study the existence of (d; k)-digraphs, we may divide the digraphs into two classes according to whether or not they contain a selfrepeat vertex. For d 3 and k 3 we prove that (d; k)-digraphs contain either no selfrepeats or exactly k selfrepeats. Furthermore, we show that every (d; k)-digraph with k selfrepeats must contain a cycle of length k as well as possibly another (d 1 ; k)-digraph as its subdigraph (where d 1 ! d). For diameter 2 we give further conditions for the existence of (d;..

Efficient Steady-State Simulation of Switching Power Converter Circuits

This paper presents a new approach aiming at simulating the steady-state response of DC-DC switching power converters. The proposed method uses the main concept behind the Harmonic Balance (HB) to compute the amplitudes of the harmonic content in the steady-state waveform. The proposed approach extends the basic HB to enable its efficient implementation to the power converter circuits, through developing equivalent frequency-domain-based stamps for ideal switching elements. The new technique is formulated to yield, along with the amplitudes of the harmonics, the switching times in the ideal switching elements, resulting in the convergence of the Newton method being obtained within few iterations. A major advantage in the proposed method is that it enables removing the control circuitry, which reduces the size of the circuit and significantly contributes to the efficiency of the method. Experimental results shows significant speedup over commercial SPICE-based simulators