Near-Optimal Induced Universal Graphs for Bounded Degree Graphs

A graph $U$ is an induced universal graph for a family $F$ of graphs if every graph in $F$ is a vertex-induced subgraph of $U$. For the family of all undirected graphs on $n$ vertices Alstrup, Kaplan, Thorup, and Zwick [STOC 2015] give an induced universal graph with $O\!\left(2^{n/2}\right)$ vertices, matching a lower bound by Moon [Proc. Glasgow Math. Assoc. 1965]. Let $k= \lceil D/2 \rceil$. Improving asymptotically on previous results by Butler [Graphs and Combinatorics 2009] and Esperet, Arnaud and Ochem [IPL 2008], we give an induced universal graph with $O\!\left(\frac{k2^k}{k!}n^k \right)$ vertices for the family of graphs with $n$ vertices of maximum degree $D$. For constant $D$, Butler gives a lower bound of $\Omega\!\left(n^{D/2}\right)$. For an odd constant $D\geq 3$, Esperet et al. and Alon and Capalbo [SODA 2008] give a graph with $O\!\left(n^{k-\frac{1}{D}}\right)$ vertices. Using their techniques for any (including constant) even values of $D$ gives asymptotically worse bounds than we present. For large $D$, i.e. when $D = \Omega\left(\log^3 n\right)$, the previous best upper bound was ${n\choose\lceil D/2\rceil} n^{O(1)}$ due to Adjiashvili and Rotbart [ICALP 2014]. We give upper and lower bounds showing that the size is ${\lfloor n/2\rfloor\choose\lfloor D/2 \rfloor}2^{\pm\tilde{O}\left(\sqrt{D}\right)}$. Hence the optimal size is $2^{\tilde{O}(D)}$ and our construction is within a factor of $2^{\tilde{O}\left(\sqrt{D}\right)}$ from this. The previous results were larger by at least a factor of $2^{\Omega(D)}$. As a part of the above, proving a conjecture by Esperet et al., we construct an induced universal graph with $2n-1$ vertices for the family of graphs with max degree $2$. In addition, we give results for acyclic graphs with max degree $2$ and cycle graphs. Our results imply the first labeling schemes that for any $D$ are at most $o(n)$ bits from optimal

Use of the prognostic biomarker suPAR in the emergency department improves risk stratification but has no effect on mortality:a cluster-randomized clinical trial (TRIAGE III)

Abstract Background Risk stratification of patients in the emergency department can be strengthened using prognostic biomarkers, but the impact on patient prognosis is unknown. The aim of the TRIAGE III trial was to investigate whether the introduction of the prognostic and nonspecific biomarker: soluble urokinase plasminogen activator receptor (suPAR) for risk stratification in the emergency department reduces mortality in acutely admitted patients. Methods The TRIAGE III trial was a cluster-randomized interventional trial conducted at emergency departments in the Capitol Region of Denmark. Eligible hospitals were required to have an emergency department with an intake of acute medical and surgical patients and no previous access to suPAR measurement. Three emergency departments were randomized; one withdrew shortly after the trial began. The inclusion period was from January through June of 2016 consisting of twelve cluster-periods of 3-weeks alternating between intervention and control and a subsequent follow-up of ten months. Patients were allocated to the intervention if they arrived in interventional periods, where suPAR measurement was routinely analysed at arrival. In the control periods suPAR measurement was not performed. The main outcome was all-cause mortality 10 months after arrival of the last patient in the inclusion period. Secondary outcomes included 30-day mortality. Results The trial enrolled a consecutive cohort of 16,801 acutely admitted patients; all were included in the analyses. The intervention group consisted of 6 cluster periods with 8900 patients and the control group consisted of 6 cluster periods with 7901 patients. After a median follow-up of 362 days, death occurred in 1241 patients (13.9%) in the intervention group and in 1126 patients (14.3%) in the control group. The weighted Cox model found a hazard ratio of 0.97 (95% confidence interval, 0.89 to 1.07; p = 0.57). Analysis of all subgroups and of 30-day all-cause mortality showed similar results. Conclusions The TRIAGE III trial found no effect of introducing the nonspecific and prognostic biomarker suPAR in emergency departments on short- or long-term all-cause mortality among acutely admitted patients. Further research is required to evaluate how prognostic biomarkers can be implemented in routine clinical practice. Trial registration clinicaltrials.gov, NCT02643459. Registered 31 December 2015

The Effect of Roast Development Time Modulations on the Sensory Profile and Chemical Composition of the Coffee Brew as Measured by NMR and DHS-GC–MS

The specialty coffee industry is growing and, as a result, there is an accelerated interest in modulating roast profiles to present customers with new and diverse sensory experiences. The present study investigates the chemical and sensory effects of subtle variations in the ‘development time’ phase of the coffee roasting process. Four roast profiles were studied through sensory descriptive analysis (DA), gas chromatography–mass spectrometry (GC–MS), and nuclear magnetic resonance (NMR). Multivariate analysis showed clear separation of DA, GC–MS, and NMR data. A prolonged development time facilitated a statistically significant shift in the chemical and sensory profile of the coffee. The findings suggest that a short development time increases the fruity, sweet and acidic characteristics of the coffee, whereas a longer development time shifts the balance towards a more roasty, nutty, and bitter profile. The results provide evidence that supports the effect of subtle roast profile modulations. This lays a strong foundation for the inclusion of development time as a critical control parameter in the certification system of the Specialty Coffee Association, quality control, and product development strategies