On the Computational Complexity of Vertex Integrity and Component Order Connectivity

The Weighted Vertex Integrity (wVI) problem takes as input an $n$-vertex graph $G$, a weight function $w:V(G)\to\mathbb{N}$, and an integer $p$. The task is to decide if there exists a set $X\subseteq V(G)$ such that the weight of $X$ plus the weight of a heaviest component of $G-X$ is at most $p$. Among other results, we prove that: (1) wVI is NP-complete on co-comparability graphs, even if each vertex has weight $1$; (2) wVI can be solved in $O(p^{p+1}n)$ time; (3) wVI admits a kernel with at most $p^3$ vertices. Result (1) refutes a conjecture by Ray and Deogun and answers an open question by Ray et al. It also complements a result by Kratsch et al., stating that the unweighted version of the problem can be solved in polynomial time on co-comparability graphs of bounded dimension, provided that an intersection model of the input graph is given as part of the input. An instance of the Weighted Component Order Connectivity (wCOC) problem consists of an $n$-vertex graph $G$, a weight function $w:V(G)\to \mathbb{N}$, and two integers $k$ and $l$, and the task is to decide if there exists a set $X\subseteq V(G)$ such that the weight of $X$ is at most $k$ and the weight of a heaviest component of $G-X$ is at most $l$. In some sense, the wCOC problem can be seen as a refined version of the wVI problem. We prove, among other results, that: (4) wCOC can be solved in $O(\min\{k,l\}\cdot n^3)$ time on interval graphs, while the unweighted version can be solved in $O(n^2)$ time on this graph class; (5) wCOC is W[1]-hard on split graphs when parameterized by $k$ or by $l$; (6) wCOC can be solved in $2^{O(k\log l)} n$ time; (7) wCOC admits a kernel with at most $kl(k+l)+k$ vertices. We also show that result (6) is essentially tight by proving that wCOC cannot be solved in $2^{o(k \log l)}n^{O(1)}$ time, unless the ETH fails.Comment: A preliminary version of this paper already appeared in the conference proceedings of ISAAC 201

Ultrasonic Measurement of Formability in Thin Ferritic Steel Sheet

The formability of rolled sheet metal is strongly influenced by the texture of the polycrystalline metal. For steel sheet, it is desirable to have high drawability to make automobile body parts, etc. In addition, material homogeneity is desired; that is, material cut from different parts of a rolled sheet should have the same plastic deformation when subjected to deep drawing

One-dimensional quantum magnetism in the S= 1/2 Mo(V) system KMoOP2O7

We present a comprehensive experimental and ab initio study of the S=1/2Mo5+ system, KMoOP2O7, and show that it realizes the S=12 Heisenberg chain antiferromagnet model. Powder neutron diffraction reveals that KMoOP2O7 forms a magnetic network comprised of pairs of Mo5+ chains within its monoclinic P21/n structure. Antiferromagnetic interactions within the Mo5+ chains are identified through magnetometry measurements and confirmed by analysis of the magnetic specific heat. The latter reveals a broad feature centered on TN=0.54 K, which we ascribe to the onset of long-range antiferromagnetic order. No magnetic Bragg scattering is observed in powder neutron-diffraction data collected at 0.05 K, however, which is consistent with a strongly suppressed ordered moment with an upper limit μord<0.15μB. The one-dimensional character of the magnetic correlations in KMoOP2O7 is verified through analysis of inelastic neutron-scattering data, resulting in a model with J2≈34 K and J1≈-2 K for the intrachain and interchain exchange interactions, respectively. The origin of these experimental findings are addressed through density-functional theory calculations

Phase-Diverse Coherent Diffractive Imaging: High Sensitivity with Low Dose

This Letter demonstrates that coherent diffractive imaging (CDI), in combination with phase-diversity methods, provides reliable and artefact free high-resolution images. Here, using x rays, experimental results show a threefold improvement in the available image contrast. Furthermore, in conditions requiring low imaging dose, it is demonstrated that phase-diverse CDI provides a factor of 2 improvement in comparison to previous CDI techniques

Lensing in the Hercules Supercluster

We report Keck LRIS observations of an arc-like background galaxy near the center of Abell 2152 (z=0.043), one of the three clusters comprising the Hercules supercluster. The background object has a redshift z=0.1423 and is situated 25 arcsec north of the primary component of the A2152 brightest cluster galaxy (BCG). The object is about 15 arcsec in total length and has a reddening-corrected R-band magnitude of $m_R = 18.55\pm0.03$. Its spectrum shows numerous strong emission lines, as well as absorption features. The strength of the H-alpha emission would imply a star formation rate \SFR \approx 3h^{-2} \msun yr$^{-1}$ in the absence of any lensing. However, the curved shaped of this object and its tangential orientation along the major axis of the BCG suggest lensing. We model the A2152 core mass distribution including the two BCG components and the cluster potential. We present velocity and velocity dispersion profile measurements for the two BCG components and use these to help constrain the potential. The lens modeling indicates a likely magnification factor of $\sim1.9$ for the lensed galaxy, making A2152 the nearest cluster in which such significant lensing of a background source has been observed. Finally, we see evidence for a concentration of early-type galaxies at $z=0.13$ near the centroid of the X-ray emission previously attributed to A2152. We suggest that emission from this background concentration is the cause of the offset of the X-ray center from the A2152 BCG. The background concentration and the dispersed mass of the Hercules supercluster could add further to the lensing strength of the A2152 cluster.Comment: Accepted for publication in AJ (January 2001). 9 pages; uses emulateapj.sty. The all-important "Figure 1" is included here in GIF format; for a version which includes Figure 1 as a high-resolution Postscript image, see: http://adcam.pha.jhu.edu/~jpb/a2152.ps.g

Tailored elastic surface to body wave Umklapp conversion

Elastic waves guided along surfaces dominate applications in geophysics, ultrasonic inspection, mechanical vibration, and surface acoustic wave devices; precise manipulation of surface Rayleigh waves and their coupling with polarised body waves presents a challenge that offers to unlock the flexibility in wave transport required for efficient energy harvesting and vibration mitigation devices. We design elastic metasurfaces, consisting of a graded array of rod resonators attached to an elastic substrate that, together with critical insight from Umklapp scattering in phonon-electron systems, allow us to leverage the transfer of crystal momentum; we mode-convert Rayleigh surface waves into bulk waves that form tunable beams. Experiments, theory and simulation verify that these tailored Umklapp mechanisms play a key role in coupling surface Rayleigh waves to reversed bulk shear and compressional waves independently, thereby creating passive self-phased arrays allowing for tunable redirection and wave focusing within the bulk medium

Study protocol: A phase III randomised, double-blind, parallel arm, stratified, block randomised, placebo-controlled trial investigating the clinical effect and cost-effectiveness of sertraline for the palliative relief of breathlessness in people with chronic breathlessness

© Published by the BMJ Publishing Group Limited. Introduction: Breathlessness remains a highly prevalent and distressing symptom for many patients with progressive life-limiting illnesses. Evidence-based interventions for chronic breathlessness are limited, and there is an ongoing need for high-quality research into developing management strategies for optimal palliation of this complex symptom. Previous studies have suggested that selective serotonin reuptake inhibitors such as sertraline may have a role in reducing breathlessness. This paper presents the protocol for a large, adequately powered randomised study evaluating the use of sertraline for chronic breathlessness in people with progressive life-limiting illnesses. Methods and analysis: A total of 240 participants with modified Medical Research Council Dyspnoea Scale breathlessness of level 2 or higher will be randomised to receive either sertraline or placebo for 28 days in this multisite, double-blind study. The dose will be titrated up every 3 days to a maximum of 100 mg daily. The primary outcome will be to compare the efficacy of sertraline with placebo in relieving the intensity of worst breathlessness as assessed by a 0-100 mm Visual Analogue Scale. A number of other outcome measures and descriptors of breathlessness as well as caregiver assessments will also be recorded to ensure adequate analysis of participant breathlessness and to allow an economic analysis to be performed. Participants will also be given the option of continuing blinded treatment until either study data collection is complete or net benefit ceases. Appropriate statistical analysis of primary and secondary outcomes will be used to describe the wealth of data obtained. Ethics and dissemination: Ethics approval was obtained at all participating sites. Results of the study will be submitted for publication in peer-reviewed journals and the key findings presented at national and international conferences. Trial registration number ACTRN12610000464066