Edge Roman domination on graphs

An edge Roman dominating function of a graph $G$ is a function $f\colon E(G) \rightarrow \{0,1,2\}$ satisfying the condition that every edge $e$ with $f(e)=0$ is adjacent to some edge $e'$ with $f(e')=2$. The edge Roman domination number of $G$, denoted by $\gamma'_R(G)$, is the minimum weight $w(f) = \sum_{e\in E(G)} f(e)$ of an edge Roman dominating function $f$ of $G$. This paper disproves a conjecture of Akbari, Ehsani, Ghajar, Jalaly Khalilabadi and Sadeghian Sadeghabad stating that if $G$ is a graph of maximum degree $\Delta$ on $n$ vertices, then $\gamma_R'(G) \le \lceil \frac{\Delta}{\Delta+1} n \rceil$. While the counterexamples having the edge Roman domination numbers $\frac{2\Delta-2}{2\Delta-1} n$, we prove that $\frac{2\Delta-2}{2\Delta-1} n + \frac{2}{2\Delta-1}$ is an upper bound for connected graphs. Furthermore, we provide an upper bound for the edge Roman domination number of $k$-degenerate graphs, which generalizes results of Akbari, Ehsani, Ghajar, Jalaly Khalilabadi and Sadeghian Sadeghabad. We also prove a sharp upper bound for subcubic graphs. In addition, we prove that the edge Roman domination numbers of planar graphs on $n$ vertices is at most $\frac{6}{7}n$, which confirms a conjecture of Akbari and Qajar. We also show an upper bound for graphs of girth at least five that is 2-cell embeddable in surfaces of small genus. Finally, we prove an upper bound for graphs that do not contain $K_{2,3}$ as a subdivision, which generalizes a result of Akbari and Qajar on outerplanar graphs

Antidumping Petition: To File or Not To File

Given the “normal value†of a product as common knowledge in an import-competing market, the profitability of a home firm in filing an antidumping (AD) petition against its foreign rival is shown to depend on the marginal cost differential between the home and foreign firms. When the marginal cost differential is “significantly large,†the home firm's ability to put the foreign firm at the risk of an AD violation is limited. But when the marginal cost differential is “significantly small,†the home firm is able to increase its output and lower the price of the product below its normal value, putting the foreign firm in the situation of an illegal dumping. One interesting implication is that, relative to the case without an AD law, the home firm has a stronger incentive to undertake cost-reducing activities (e.g., R&D investment or the adoption of a more efficient technology) under the law.antidumping laws, antidumping duties, dumping margins

An unusual timing for symptomatic chest pain in an adult chest wall myofibroma: a case report

INTRODUCTION: Myofibromas are benign mesenchymal neoplasms that can present as solitary and multicentric lesions. They can occur in several locations and can occur at any age from neonates to elderly patients. However, most of the lesions are found in neonates and babies. It rarely occurs in adults. CASE PRESENTATION: A 29-year-old Taiwanese man presented with persistent dull chest pain in his right lateral chest wall for 2 weeks. A chest X-ray showed a faint patchy opacity over the periphery of his right upper lung zone. Computed tomography and magnetic resonance imaging showed a lobulated mass at the intercostal space between his right fifth and sixth ribs with contrast enhancement and bone invasion. Malignancy could not be excluded. A percutaneous needle aspiration biopsy failed due to technique issues, so he underwent a thoracotomy and the tumor was excised with Marlex mesh repairs for the thoracic defect. Pathology confirmed a myofibroma without malignancy. He recovered uneventfully and no local recurrence was detected at the 1-year follow-up examination. CONCLUSIONS: Chest wall myofibroma presenting with chest pain has never been reported in adults. It is a challenge to differentiate myofibroma from malignancy in chest wall preoperatively, such as seen in our patient. To the best of our knowledge, this has not been previously reported in the scientific literature. Although myofibroma rarely occurs in the chest wall and adults, it must be suspected in any chest wall tumor presenting with chest pain

Transcription factor activity estimation based on particle swarm optimization and fast network component analysis

Proceedings of the IEEE Engineering in Medicine and Biology Society Conference, 2010, p. 1061-1064Transcription factors (TFs) play an important role in regulating the expression of genes. The accurate measurement of transcription factor activities (TFAs) depends on a series of experimental technologies of molecular biology and is intractable in most practical situations. Some signal processing methods for blind source separation have been applied in the prediction of TFAs from gene expression data. Most of such methods make use of statistical properties of the gene expression data only, leading to the inaccurate detection of TFAs. In contrast, network component analysis (NCA) can provide much improved result through utilizing the structural information of the gene regulatory network. However, the structure of the gene regulatory network, required by NCA, is not available in most practical cases so that NCA is not directly applicable. In this paper, we propose to use particle swarm optimization (PSO) to find the most plausible network structure iteratively from the gene expression data, with the assistance of recently developed fast algorithm for network component analysis (FastNCA). This novel approach to TFA inference can thus take advantage of NCA, even when the required network structure is unknown. The effectiveness of our novel approach has been demonstrated by applications to both simulated data and real gene expression microarray data, in the sense that TFAs can be inferred with high accuracy. © 2010 IEEE.published_or_final_versio