Intersecting families of permutations

AbstractLet Sn be the symmetric group on the set X={1,2,…,n}. A subset S of Sn is intersecting if for any two permutations g and h in S, g(x)=h(x) for some x∈X (that is g and h agree on x). Deza and Frankl (J. Combin. Theory Ser. A 22 (1977) 352) proved that if S⊆Sn is intersecting then |S|≤(n−1)!. This bound is met by taking S to be a coset of a stabiliser of a point. We show that these are the only largest intersecting sets of permutations

Evacuation Hazards in Crowded Subway Stations

Underground subway system is the key transportation means in dense urban areas such as Hong Kong. Subway stations are crowded with passengers on the platforms and they are observed to squeeze into the train carriages during rush hours. Putting in platform screen doors made the situation even worse. As reported in the local news, subway management claims that after following the change in maximum capacity from six passengers per meter square to four passengers per meter square, the capacity is only 70% full at rush hours. However, the capacity can be over 90% of full loading under the new calculation. Subway stations become more crowded with an average weekday patronage of nearly 5.3 million passengers.  Subway stations are mostly located in the basement or ground levels connecting the shopping mall, commercial or residential building in downtown areas. The occupancy density of passengers can be much higher than expected during festivals with fireworks show and during large-scale movements such as Occupy Central. Therefore, evacuation time in emergency situation will be prolonged. To have a better understanding of the safety issue in subway stations, evacuation time in emergency situations will be studied in this paper.  Two subway stations, Station A and Station B are selected in this paper to study the evacuation hazard of crowded stations when a fire occurs. Station A is an interchange station between two railway lines, being one of the most crowded stations with high occupancy density. Station B is the first station in the local rail network to feature a special design - “Lift-only Entrancesâ€. This is a deep underground station which lies under 70 m of ground level, the passengers have to be evacuated by lift. The occupancy density in Station B is relatively much lower than Station A under normal conditions at the moment, though the station can be very crowded if there are train delays due to signal failure or other reasons.  In this paper, the evacuation effectiveness of Station A and Station B are estimated in terms of evacuation time in different scenarios by using Hydraulic Model Calculation. Moreover, the special evacuation feature of “Lift-only Entrances†in Station B and the fire safety management strategies for emergency evacuation will be discussed.  Three scenarios will be studied in each station:  Scenario A: Assume that the passengers are evenly distributed in different exits in emergency situation. All the possible factors such as passenger behaviors and conditions are eliminated.  Scenario B: Passengers have a higher tendency to evacuate at the larger exit, this is one of the passenger behaviors in emergency situation. Therefore, the passenger distribution which depends on the exit width will be studied.  Scenario C: Assume that some of the exit routes are blocked.  The most important factor for the above study is the passenger behaviors. As in scenario B, passenger behaviors would affect the evacuation time. Therefore, fire safety management is identified to be a key part in keeping efficient evacuation. For example, a good fire action plan on crowd control is needed

Neurothekeoma palpebrae in association with multiple superficial angiomyxomas : Tegumental Angiomyxoma-Neurothekeoma syndrome (TAN syndrome)

We report a case of 10-year-old Indian girl with history of multiple superficial angiomyxoma, presented with three months history of painless right upper lid swelling. There were no visual dysfunctions. Previously, the patient had multiple superficial angiomyxoma (left pinna, left upper cheek, left upper limb, chest, right axilla, hard palate) and epidermal cyst (chin). The histopathological specimens were negative to S-100 protein antibody. Systemic review and family history was unremarkable. Excision biopsy and upper lid reconstruction were performed. Intraoperatively the tumor was multilobulated, firm, well encapsulated and did not invade the underlying tarsal plate. Histopathological features of the upperlid tumor were consistent with nerves sheath myxoma (neurothekeoma). To the best of the authors’ knowledge, this is the first reported case of neurothekeoma in association with multiple superficial angiomyxoma

The effect of water deficit and excess copper on proline metabolism in Nicotiana benthamiana

Fluctuation in proline content is a widespread phenomenon among plants in response to heavy metal stress. To distinguish between the participation of water deficit and copper on changes in proline metabolism, potted plants and floating leaf discs of tobacco were subjected to CuSO4 treatments. The application of copper increased the proline content in the leaves concomitantly with decreased leaf relative water content and increased abscisic acid (ABA) content in the potted plant. Excess copper increased the expression of two proline synthesis genes, pyrroline-5-carboxylate synthetase (P5CS) and ornithine aminotransferase (OAT) and suppressed proline catabolism gene, proline dehydrogenase (PDH). However, in the experiment with tobacco leaf discs floating on CuSO4 solutions, the excess copper decreased proline content and suppressed the expression of the P5CS, OAT and PDH genes. Therefore, proline accumulation in the potted tobacco plants treated with excess Cu treatment might not be the consequence of the increased copper content in tobacco leaves but rather by the accompanied decrease in water content and/or increased ABA content

Melanocytoma of the optic nerve head: a diagnostic dilemma

The clinical features, autofluorescence, Bscan ultrasonography, optical coherence tomography and fluorescein angiography of the lesion were described. Multiple investigation modalities are needed to confirm the benign nature of the lesion. Careful evaluation and follow-up is crucial to avoid misdiagnosis and erroneous management

Pulsar-wind nebulae and magnetar outflows: observations at radio, X-ray, and gamma-ray wavelengths

We review observations of several classes of neutron-star-powered outflows: pulsar-wind nebulae (PWNe) inside shell supernova remnants (SNRs), PWNe interacting directly with interstellar medium (ISM), and magnetar-powered outflows. We describe radio, X-ray, and gamma-ray observations of PWNe, focusing first on integrated spectral-energy distributions (SEDs) and global spectral properties. High-resolution X-ray imaging of PWNe shows a bewildering array of morphologies, with jets, trails, and other structures. Several of the 23 so far identified magnetars show evidence for continuous or sporadic emission of material, sometimes associated with giant flares, and a few possible "magnetar-wind nebulae" have been recently identified.Comment: 61 pages, 44 figures (reduced in quality for size reasons). Published in Space Science Reviews, "Jets and Winds in Pulsar Wind Nebulae, Gamma-ray Bursts and Blazars: Physics of Extreme Energy Release

Prognostic Value of N-terminal B-type Natriuretic Peptide in Patients with Acute Myocardial Infarction: A Multicenter Study

Background: Several models have been developed to help the clinician in risk stratification for Acute Coronary Syndrome (ACS),such as the TIMI and GRACE risk scores. However, there is conflicting evidence for the prognostic value of NT-ProBNP in acute myocardial infarction (AMI). Objective: (1) To explore the association of NT-proBNP with 30-day clinical outcome in AMI patients. (2) To compare the prognostic value of NT-proBNP with TIMI and GRACE risk scores in AMI patients. Methods: We conducted a multicenter, prospective observational study recruiting patients presented with AMI between 29-October-2015 and 14-January-2017, involving 1 cardiology referral centre and 4 non-cardiology hospitals. NT-proBNP level (Alere Triage®, US)was measured within 24 hours fromthe diagnosis of AMI. Patientswere followed-up for 1 month. Results: A total of 186 patients were recruited, 143 from tertiary cardiology centre and 43 from non-cardiology hospitals. Mean age was 54.7±10.0 years, 87.6% male and 64% were STEMI. The NT-proBNP level ranged from 60 to 16700pg/ml, with a median of 714pg/ml. Using the 75th centile as the cutoff, Kaplan-Meier survival analysis for the 30-day cardiac related mortality was significantly higher for patient with NT-proBNP level of ≥1600pg/ml (6.4% vs. 0.7%, p=0.02). Cox-regression analysis showed that NT-proBNP level of ≥1600pg/ml was an independent predictor of 30-day cardiac related mortality, regardless of TIMI risk score, GRACE score, LV ejection fraction and study hospitals (HR 9.274, p=0.054, 95%CI 0.965, 89.161). Readmission for heart failure at 30-day was also higher for patient with NT-proBNP level of ≥1600pg/ml (HR 9.308, p=0.053, 95%CI 0.969, 89.492). NT-proBNP level was not associated with all-cause mortality, risk of readmission for ACS, arrhythmia and stroke (pN0.05). By adding 50 score to GRACE risk score for NT-proBNP level of ≥1600pg/ml, combination of GraceNT-proBNP scores of more than 200 appeared to be a better independent predictor for 30-day cardiac related mortality (HR:28.28, p=0.004, 95%CI 2.94, 272.1). ROC analysis showed that this new score had 75% sensitivity and 91.2% specificity in predicting 30-day cardiac related mortality (AUC 0.791, p=0.046). Conclusions: NT-proBNP is a useful point-of-care risk stratification biomarker in AMI. It can be combined to the current risk score model for better risk stratification in AMI patients

Maximum multiplicity of matching polynomial roots and minimum path cover in general graphs

Electronic Journal of Combinatorics181