Minimal classes of graphs of unbounded clique-width defined by finitely many forbidden induced subgraphs

We discover new hereditary classes of graphs that are minimal (with respect to set inclusion) of unbounded clique-width. The new examples include split permutation graphs and bichain graphs. Each of these classes is characterised by a finite list of minimal forbidden induced subgraphs. These, therefore, disprove a conjecture due to Daligault, Rao and Thomasse from 2010 claiming that all such minimal classes must be defined by infinitely many forbidden induced subgraphs. In the same paper, Daligault, Rao and Thomasse make another conjecture that every hereditary class of unbounded clique-width must contain a labelled infinite antichain. We show that the two example classes we consider here satisfy this conjecture. Indeed, they each contain a canonical labelled infinite antichain, which leads us to propose a stronger conjecture: that every hereditary class of graphs that is minimal of unbounded clique-width contains a canonical labelled infinite antichain.Comment: 17 pages, 7 figure

Minimal classes of graphs of unbounded clique-width defined by finitely many forbidden induced subgraphs

We discover new hereditary classes of graphs that are minimal (with respect to set inclusion) of unbounded clique-width. The new examples include split permutation graphs and bichain graphs. Each of these classes is characterised by a finite list of minimal forbidden induced subgraphs. These, therefore, disprove a conjecture due to Daligault, Rao and Thomassé from 2010 claiming that all such minimal classes must be defined by infinitely many forbidden induced subgraphs. In the same paper, Daligault, Rao and Thomassé make another conjecture that every hereditary class of unbounded clique-width must contain a labelled infinite antichain. We show that the two example classes we consider here satisfy this conjecture. Indeed, they each contain a canonical labelled infinite antichain, which leads us to propose a stronger conjecture: that every hereditary class of graphs that is minimal of unbounded clique-width contains a canonical labelled infinite antichain

A Counterexample Regarding Labelled Well-Quasi-Ordering

Korpelainen, Lozin, and Razgon conjectured that a hereditary property of graphs which is well-quasi-ordered by the induced subgraph order and defined by only finitely many minimal forbidden induced subgraphs is labelled well-quasi-ordered, a notion stronger than that of n-well-quasi-order introduced by Pouzet in the 1970s. We present a counterexample to this conjecture. In fact, we exhibit a hereditary property of graphs which is well-quasi-ordered by the induced subgraph order and defined by finitely many minimal forbidden induced subgraphs yet is not 2-well-quasi-ordered. This counterexample is based on the widdershins spiral, which has received some study in the area of permutation patterns

Governance tools for board members : adapting strategy maps and balanced scorecards for directorial action

The accountability of members of the board of directors of publicly traded companies has increased over years. Corresponding to these developments, there has been an inadequate advancement of tools and frameworks to help directorial functioning. This paper provides an argument for design of the Balanced Scorecard and Strategy Maps made available to the directors as a means of influencing, monitoring, controlling and assisting managerial action. This paper examines how the Balanced Scorecard and Strategy Maps could be modified and used for this purpose. The paper suggests incorporating Balanced Scorecards in the Internal Process perspective, ‘internal’ implying here not just ‘internal to the firm’, but also ‘internal to the inter-organizational system’. We recommend that other such factors be introduced separately under a new ‘perspective’ depending upon what the board wants to emphasize without creating any unwieldy proliferation of measures. Tracking the Strategy Map over time by the board of directors is a way for the board to take responsibility for the firm’s performance. The paper makes a distinction between action variables and monitoring variables. Monitoring variables are further divided on the basis of two considerations: a) whether results have been met or not and b) whether causative factors have met the expected levels of performance or not. Based on directorial responsibilities and accountability, we take another look at how the variables could be specified more completely and accurately with directorial recommendations for executives

Integration of kinase and calcium signaling at the level of chromatin underlies inducible gene activation in T cells

TCR signaling pathways cooperate to activate the inducible transcription factors NF-κB, NFAT, and AP-1. In this study, using the calcium ionophore ionomycin and/or PMA on Jurkat T cells, we show that the gene expression program associated with activation of TCR signaling is closely related to specific chromatin landscapes. We find that calcium and kinase signaling cooperate to induce chromatin remodeling at ∼2100 chromatin regions, which demonstrate enriched binding motifs for inducible factors and correlate with target gene expression. We found that these regions typically function as inducible enhancers. Many of these elements contain composite NFAT/AP-1 sites, which typically support cooperative binding, thus further reinforcing the need for cooperation between calcium and kinase signaling in the activation of genes in T cells. In contrast, treatment with PMA or ionomycin alone induces chromatin remodeling at far fewer regions (∼600 and ∼350, respectively), which mostly represent a subset of those induced by costimulation. This suggests that the integration of TCR signaling largely occurs at the level of chromatin, which we propose plays a crucial role in regulating T cell activation

Utilisation of the static Evans method to measure magnetic susceptibilities of transition metal acetylacetonate complexes as part of an undergraduate inorganic laboratory class

The Evans method is routinely utilised to collect paramagnetic susceptibility data via the employment of relevant Nuclear Magnetic Resonance (NMR) methods. As the sample is normally spun, the lack of such a function on benchtop NMR instrumentation required a “static” approach to be employed. We have utilised the static Evan’s method approach to measure the magnetic susceptibilities, and subsequently the effective magnetic moment, of a series of synthesised transition metal acetylacetonate complexes in order to appraise the d-electron configuration. The obtained values were compared to those obtained using a Guoy balance and theoretical calculations. The collection of T1 relaxation data further exemplifies the effect of the paramagnetic centre in terms of aiding relaxation, and therefore links to Magnetic Resonance Imaging (MRI) contrast agents, thus providing students with real-world perspective of the experiment conducted

Zeros of the Möbius function of permutations

We show that if a permutation \pi contains two intervals of length 2, where one interval is an ascent and the other a descent, then the Möbius function \mu[1,\pi] of the interval [1,\pi] is zero. As a consequence, we prove that the proportion of permutations of length $\textit{n}$ with principal Möbius function equal to zero is asymptotically bounded below by (1\ -\ \sfrac{1}{e)^2} \geq 0.3995. This is the first result determining the value of \mu\left[1,\pi\right] for an asymptotically positive proportion of permutations \pi. We further establish other general conditions on a permutation \pi that ensure \mu\left[1,\pi\right]\ =\ 0, including the occurrence in \pi of any interval of the form \alpha\oplus\ 1\ \oplus\ \beta

Classification of gluteal muscle contracture in children and outcome of different treatments

<p>Abstract</p> <p>Background</p> <p>Gluteal muscle contracture (GMC) is a clinical syndrome due to multiple etiologies in which hip movements may be severely limited. The aim of this study was to propose a detailed classification of GMC and evaluate the statistical association between outcomes of different management and patient conditions.</p> <p>Methods</p> <p>One hundred fifty-eight patients, who were treated between January 1995 and December 2004, were reviewed at a mean duration of follow-up of 4.8 years. Statistical analyses were performed using X²and Fisher's exact tests.</p> <p>Results</p> <p>Non-operative management (NOM), as a primary treatment, was effective in 19 of 49 patients (38.8%), while operative management was effective in all 129 patients, with an excellence rating of 83.7% (108/129). The outcome of NOM in level I patients was significantly higher than in level II and III patients (<it>P </it>< 0.05). The results of NOM and operative management in the child group were better than the adolescent group (<it>P </it>< 0.05). Complications in level III were more than in level II.</p> <p>Conclusion</p> <p>NOM was more effective in level I patients than in level II and III patients. Operative management was effective in patients at all levels, with no statistical differences between levels or types. We recommend NOM as primary treatment for level I patients and operative management for level II and III patients. Either NOM or operative management should be carried out as early as possible.</p

Infinitely many minimal classes of graphs of unbounded clique-width

© 2017 Elsevier B.V. The celebrated theorem of Robertson and Seymour states that in the family of minor-closed graph classes, there is a unique minimal class of graphs of unbounded tree-width, namely, the class of planar graphs. In the case of tree-width, the restriction to minor-closed classes is justified by the fact that the tree-width of a graph is never smaller than the tree-width of any of its minors. This, however, is not the case with respect to clique-width, as the clique-width of a graph can be (much) smaller than the clique-width of its minor. On the other hand, the clique-width of a graph is never smaller than the clique-width of any of its induced subgraphs, which allows us to be restricted to hereditary classes (that is, classes closed under taking induced subgraphs), when we study clique-width. Up to date, only finitely many minimal hereditary classes of graphs of unbounded clique-width have been discovered in the literature. In the present paper, we prove that the family of such classes is infinite. Moreover, we show that the same is true with respect to linear clique-width

VISUAL PPINOT: A Graphical Notation for Process Performance Indicators

Process performance indicators (PPIs) allow the quantitative evaluation of business processes, providing essential information for decision making. It is common practice today that business processes and PPIs are usually modelled separately using graphical notations for the former and natural language for the latter. This approach makes PPI definitions simple to read and write, but it hinders maintenance consistency between business processes and PPIs. It also requires their manual translation into lower-level implementation languages for their operationalisation, which is a time-consuming, error-prone task because of the ambiguities inherent to natural language definitions. In this article, Visual ppinot, a graphical notation for defining PPIs together with business process models, is presented. Its underlying formal metamodel allows the automated processing of PPIs. Furthermore, it improves current state-of-the-art proposals in terms of expressiveness and in terms of providing an explicit visualisation of the link between PPIs and business processes, which avoids inconsistencies and promotes their co-evolution. The reference implementation, developed as a complete tool suite, has allowed its validation in a multiple-case study, in which five dimensions of Visual ppinot were studied: expressiveness, precision, automation, understandability, and traceability