Constructing tree decompositions of graphs with bounded gonality

In this paper, we give a constructive proof of the fact that the treewidth of a graph is at most its divisorial gonality. The proof gives a polynomial time algorithm to construct a tree decomposition of width at most k, when an effective divisor of degree k that reaches all vertices is given. We also give a similar result for two related notions: stable divisorial gonality and stable gonality

Reproducibility of lymphovascular space invasion (LVSI) assessment in endometrial cancer

Aims Lymphovascular space invasion (LVSI) in endometrial cancer (EC) is an important prognostic variable impacting on a patient's individual recurrence risk and adjuvant treatment recommendations. Recent work has shown that grading the extent of LVSI further improves its prognostic strength in patients with stage I endometrioid EC. Despite this, there is little information on the reproducibility of LVSI assessment in EC. Therefore, we designed a study to evaluate interobserver agreement in discriminating true LVSI from LVSI mimics (Phase I) and reproducibility of grading extent of LVSI (Phase II). Methods and results Scanned haematoxylin and eosin (H&E) slides of endometrioid EC (EEC) with a predefined possible LVSI focus were hosted on a website and assessed by a panel of six European gynaecological pathologists. In Phase I, 48 H&E slides were included for LVSI assessment and in Phase II, 42 H&E slides for LVSI grading. Each observer was instructed to apply the criteria for LVSI used in daily practice. The degree of agreement was measured using the two-way absolute agreement average-measures intraclass correlation coefficient (ICC). Reproducibility of LVSI assessment (ICC = 0.64, P < 0.001) and LVSI grading (ICC = 0.62, P < 0.001) in EEC was substantial among the observers. Conclusions Given the good reproducibility of LVSI, this study further supports the important role of LVSI in decision algorithms for adjuvant treatment

Oxidation of AlInAs for current blocking in a photonic crystal laser

To make an electrically pumped photonic crystal membrane laser is a challenging task. One of the problems is how to avoid short circuiting between the p- and n-doped parts of the laser diode, when the membrane thickness is limited to 200-300nm. We propose to use the oxide of AlInAs to realize a current blocking function. In this way, based on submicron selective area re-growth, we aim for electrically injected photonic crystal lasers with high output power, small threshold currents and low power consumption. Here results are presented on the oxidation of AlInAs. The results show that it is feasible to use the oxide of AlInAs for current blocking in an InP-based membrane photonic crystal laser