On facial unique-maximum (edge-)coloring

A facial unique-maximum coloring of a plane graph is a vertex coloring where on each face $\alpha$ the maximal color appears exactly once on the vertices of $\alpha$. If the coloring is required to be proper, then the upper bound for the minimal number of colors required for such a coloring is set to $5$. Fabrici and G\"oring [Fabrici and Goring 2016] even conjectured that $4$ colors always suffice. Confirming the conjecture would hence give a considerable strengthening of the Four Color Theorem. In this paper, we prove that the conjecture holds for subcubic plane graphs, outerplane graphs and plane quadrangulations. Additionally, we consider the facial edge-coloring analogue of the aforementioned coloring and prove that every $2$-connected plane graph admits such a coloring with at most $4$ colors.Comment: 5 figure

Classification and Profiles of Students Based on Their Motivations Concerning Higher Education

Cluster analysis was used to create segments of high school graduates based on their motivations/opinions regarding their future education. Data for this study were collected using a questionnaire distributed to high school graduates following State Matura exam. The students were asked to evaluate the importance of 13 different reasons/causes for choosing the faculty selected as their first choice. The analysis yielded five meaningful clusters of students that differ not only in motivations, but also in achievement on State Matura exams and in their preference regarding the scientific field of their future study

PILOT - A Simple Process Improvement Tool for Small and Midsize Manufacturing Companies

PILOT (Process Improvement by L.O.G.I.C.A. Operational Team) is a complete process improvement pilot study application, providing data collection, entry, analysis and decision making. It is designed primarily as a simple, easy-to-use diagnostic tool for production process description, problem identification and improvement in small and midsize manufacturing companies, characterised by relatively small amounts of data emerging daily. The analysis of the information collected facilitates tracing down the sources of the identified production related problems and finding means for eliminating or minimising them. The statistical methodology utilised includes simple, but useful tabular and graphical techniques, such as Ishikawa \u27s Seven Tools, but also some sophisticated exploratory data analysis methods, e.g. correspondence and cluster analysis. Furthermore, the results of PILOT constitute a good basis for developing more advanced studies, utilising statistical and/or simulation methodologies, and for setting up SPC charting information systems or designed experiments. An effective PILOT application in a midsize company manufacturing department is described for illustrative purposes

Prisdiskriminering : teori og og praktisk anvendelse

Oppgaven formål er å undersøke Lord of the Rings Online og Free-2-Play hybridmodellen. Caset undersøkes i lys av teori omkring prisdiskriminering, hvor det følgende blir undersøkt: - Nødvendige forhold som muliggjør prisdiskriminering - De prisdiskrimineringsstrategier som er blitt benyttet Det ble konstatert at de nødvendige forholdene, som heterogenitet, markedsmakt, redusering av mulighetene for videresalg og overvåkning av kundenes kjøp, var til stede og prisdiskrimineringsstrategier som kvantumsrabatter, kvalitetsforskjeller, mixed- og pure bundling er blitt benyttet. Det ble også konstatert et tilfelle av Coase conjecture-problemet som er blitt omgått ved hjelp av kvalitetsforskjeller. Undertegnede stiller seg kritisk til et par punkter i modellen. Pure bundling er blitt benyttet og det mangler et insentiv for større kjøp av Turbine Points

On facial unique-maximum (edge-)coloring

A facial unique-maximum coloring of a plane graph is a vertex coloring where on each face α the maximal color appears exactly once on the vertices of α. If the coloring is required to be proper, then the upper bound for the minimal number of colors required for such a coloring is set to 5. Fabrici and Göring [5] even con- jectured that 4 colors always suffice. Confi the conjecture would hence give a considerable strengthening of the Four Color Theorem. In this paper, we prove that the conjecture holds for subcubic plane graphs, outerplane graphs and plane quadrangulations. Additionally, we consider the facial edge-coloring analogue of the aforementioned coloring and prove that every 2-connected plane graph admits such a coloring with at most 4 colors.This is a manuscript of an article pulblished as Andova, Vesna, Bernard Lidický, Borut Lužar, and Riste Škrekovski. "On facial unique-maximum (edge-) coloring." Discrete Applied Mathematics 237 (2018): 26-32. doi: 10.1016/j.dam.2017.11.024. Posted with permission.</p

An Improved Protocol for Comprehensive Etiological Characterization of Skin Warts and Determining Causative Human Papillomavirus Types in 128 Histologically Confirmed Common Warts

Human papillomaviruses (HPVs) are etiologically associated with various benign and malignant neoplasms of cutaneous and mucosal epithelia. We describe an improved diagnostic protocol for comprehensive characterization of causative HPV types in common warts, in which broad-spectrum PCRs followed by Sanger sequencing, two previously described and seven newly developed type-specific quantitative real-time PCRs (qPCRs) coupled with the human beta-globin qPCR were used for: (i) diagnosis of HPV infection in warts; (ii) estimation of cellular viral loads of all HPV types detected; and (iii) determination of their etiological role in 128 histologically confirmed fresh-frozen common wart tissue samples. A total of 12 different causative HPV types were determined in 122/126 (96.8%) HPV-positive warts, with HPV27 being most prevalent (27.0%), followed by HPV57 (26.2%), HPV4 (15.1%), HPV2 (13.5%), and HPV65 (7.9%). The cellular viral loads of HPV4 and HPV65 were estimated for the first time in common warts and were significantly higher than the viral loads of HPV2, HPV27, and HPV57. In addition, we showed for the first time that HPV65 is etiologically associated with the development of common warts in significantly older patients than HPV27 and HPV57, whereas HPV4-induced warts were significantly smaller than warts caused by HPV2, HPV27, HPV57, and HPV65

Differences in reporting Pearl Indices in the United States and Europe: Focus on a 91-day extended-regimen combined oral contraceptive with low-dose ethinyl estradiol supplementation.

Regulatory agencies in the United States (US) and Europe differ in requirements for defining pregnancies after the last dose of oral contraceptive, sometimes resulting in discrepant Pearl Indices (PIs) for the same product despite identical clinical data. This brief report highlights one such example, a 91-day extended-regimen combined oral contraceptive (COC).The US- and European-based PI methodologies were compared for a 91-day extended-regimen COC consisting of 84 days of active levonorgestrel/EE 150 μg/30 μg tablets, followed by seven days of EE 10 μg tablets in place of placebo.At the times of approval of the 91-day extended-regimen COC in the US and Europe, the requirements for defining 'on-treatment' pregnancies differed (14-day vs. 2-day rule, respectively). This difference resulted in a higher PI in the US- vs. European-based calculation (1.34 and 0.76, respectively). The differences in the PI should not be interpreted as the extended-regimen COC being less effective in preventing pregnancy in the US compared with Europe

Priporočila za obravnavo bolnikov z melanomom kože

Incidenca melanoma v svetu in Sloveniji še vedno narašča, se je pa preživetje v zadnjih 20 letih izboljšalo, predvsem zaradi zgodnejšega odkrivanja melanoma in enotnih pristopov v primarnem zdravljenju. Posodobljena Priporočila v letu 2024 prinašajo precej novosti, predvsem v diagnostičnih postopkih odkrivanja in zamejitve zgodnjih stadijev melanoma, kot tudi natančnih priporočil sledenja po primarnem zdravljenju, na področju kirurškega zdravljenja in pa predvsem sistemskega zdravljenja, tako metastatske bolezni, predvsem pa v adjuvan- tnem sistemskem zdravljenju v visoko rizičnem stadiju II, in neo- adjuvantnem sistemskem zdravljenju operabilnega melanoma. V tokratna Priporočila smo vključili tudi poglavji prehranskega in paliativnega tima