Minimum Degrees of Minimal Ramsey Graphs for Almost-Cliques

For graphs $F$ and $H$, we say $F$ is Ramsey for $H$ if every $2$-coloring of the edges of $F$ contains a monochromatic copy of $H$. The graph $F$ is Ramsey $H$-minimal if $F$ is Ramsey for $H$ and there is no proper subgraph $F'$ of $F$ so that $F'$ is Ramsey for $H$. Burr, Erdos, and Lovasz defined $s(H)$ to be the minimum degree of $F$ over all Ramsey $H$-minimal graphs $F$. Define $H_{t,d}$ to be a graph on $t+1$ vertices consisting of a complete graph on $t$ vertices and one additional vertex of degree $d$. We show that $s(H_{t,d})=d^2$ for all values $1<d\le t$; it was previously known that $s(H_{t,1})=t-1$, so it is surprising that $s(H_{t,2})=4$ is much smaller. We also make some further progress on some sparser graphs. Fox and Lin observed that $s(H)\ge 2\delta(H)-1$ for all graphs $H$, where $\delta(H)$ is the minimum degree of $H$; Szabo, Zumstein, and Zurcher investigated which graphs have this property and conjectured that all bipartite graphs $H$ without isolated vertices satisfy $s(H)=2\delta(H)-1$. Fox, Grinshpun, Liebenau, Person, and Szabo further conjectured that all triangle-free graphs without isolated vertices satisfy this property. We show that $d$-regular $3$-connected triangle-free graphs $H$, with one extra technical constraint, satisfy $s(H) = 2\delta(H)-1$; the extra constraint is that $H$ has a vertex $v$ so that if one removes $v$ and its neighborhood from $H$, the remainder is connected.Comment: 10 pages; 3 figure

Understanding flare in axial spondyloarthritis:novel insights from daily self-reported flare experience

OBJECTIVES: Our objective was to explore daily self-reported experiences of axial SpA (axSpA) flare based on data entered into the Project Nightingale smartphone app (www.projectnightingale.org), between 5 April 2018 and 1 April 2020. METHODS: Paired t-tests were conducted for mean_flare_on and mean_flare_off scores for each recorded variable. The mean estimated difference between flare and non-flare values for each variable was calculated with 95% CIs. Mean, S.d. and range were reported for flare duration and frequency. Participants with ≥10 days of data entry were included for affinity propagation cluster analysis. Baseline characteristics and mean flare on vs mean flare off values were reported for each cluster. Welch’s t-test was used to assess differences between clusters. RESULTS: A total of 143/189 (75.7%) participants recorded at least one flare. Each flare lasted a mean of 4.30 days (S.d. 6.82, range 1–78), with a mean frequency of once every 35.32 days (S.d. 65.73, range 1–677). Significant relationships were identified between flare status and variable scores. Two clusters of participants were identified with distinct flare profiles. Group 1 experienced less severe worsening of symptoms during flare in comparison to group 2 (P < 0.01). However, they experienced significantly longer flare duration (7.2 vs 3.5 days; P < 0.01), perhaps indicating a prolonged, yet less intense flare experience. Groups were similar in terms of flare frequency and clinical characteristics. CONCLUSIONS: Two clusters of participants were identified with distinct flare experiences but similar baseline clinical characteristics. Smartphone technologies capture subtle changes in disease experience not currently considered in clinical practice

Exploring sub-optimal response to tumour necrosis factor inhibitors in axial spondyloarthritis

Objectives: The aim was to define sub-optimal response to TNF inhibitors (TNFi), compare long-term drug survival rates and identify predictors of sub-optimal response in axial spondyloarthritis (axSpA) patients in a UK cohort. Methods: All axSpA patients attending two centres who commenced TNFi between 2002 and 2016 were included. Routinely recorded patient data were reviewed retrospectively. Patients with paired BASDAI at baseline, 3 and/or 6 months were included for analysis. Sub-optimal response was defined as achieving a ≥ 2-point reduction in BASDAI but not BASDAI50, post-treatment BASDAI remaining at ≥4, and in the opinion of the treating physician these patients demonstrated a meaningful clinical response. Results: Four hundred and ninety-nine patients were included: 82 (16.4%) patients were classified as having a sub-optimal response; 64 (78%) males, 78 (95.1%) AS and 55/67 (82.1%) HLA-B27 positive. Results are reported as the mean (s.d.). Time to diagnosis was 10 (8.6) years, age at diagnosis was 37 (11.7) years, and age at initiating index TNFi was 48 (11.1) years. Individual index TNFi were Humira (adalimumab, n = 41, 50%), Enbrel (etanercept, n = 27, 32.9%), Remicade (infliximab, n = 5, 6.1%), Simponi (golimumab, n = 3, 3.7%) and Cimzia (certolizumab pegol, n = 6, 7.3%). The rate of attrition was greater among sub-optimal responders at 2 and 5 years (P < 0.05), but not at 10 years (P = 0.06), compared with responders. Older age at initiation of TNFi was a predictor of sub-optimal response (odds ratio 1.04, 95% CI 1.01, 1.09, P < 0.05). Conclusion: A significant proportion of patients continued TNFi despite demonstrated sub-optimal response. Further research needs to be undertaken in order to understand this group

Covariant holographic reflected entropy in AdS3/CFT2AdS_3/CFT_2

We substantiate a covariant proposal for the holographic reflected entropy in $CFT$s dual to non-static $AdS$ geometries from the bulk extremal entanglement wedge cross section in the literature with explicit computations in the $AdS_3/CFT_2$ scenario. In this context we obtain the reflected entropy for zero and finite temperature time dependent bipartite mixed states in $CFT_{1+1}$s with a conserved charge dual to bulk rotating extremal and non-extremal BTZ black holes through a replica technique. Our results match exactly with the corresponding extremal entanglement wedge cross section for these bulk geometries in the literature. This constitutes a significant consistency check for the proposal and its possible extension to the corresponding higher dimensional $AdS/CFT$ scenario.Comment: 16 pages, 3 figures, v2 match published versio

Islands and dynamics at the interface

We investigate a family of models described by two holographic CFT$_2$s coupled along a shared interface. The bulk dual geometry consists of two AdS$_3$ spacetimes truncated by a shared Karch-Randall end-of-the-world (EOW) brane. A lower dimensional effective model comprising of JT gravity coupled to two flat CFT$_2$ baths is subsequently realized by considering small fluctuations on the EOW brane and implementing a partial Randall-Sundrum reduction where the transverse fluctuations of the EOW brane are identified as the dilaton field. We compute the generalized entanglement entropy for bipartite states through the island prescription in the effective lower dimensional picture and obtain precise agreement in the limit of large brane tension with the corresponding doubly holographic computations in the bulk geometry. Furthermore, we obtain the corresponding Page curves for the Hawking radiation in this JT braneworld.Comment: 40 pages, 15 figure

Diagnostic delay in axial spondylarthritis:A lost battle?

Diagnostic delay in axial spondylarthritis (axSpA) remains an unacceptable worldwide problem; with evidence suggesting significant detrimental impact both clinically on the individual, and economically on society. There is therefore, a need for global action across various healthcare professions that come into contact with patients living, and suffering, with undiagnosed axSpA. Recent estimates of the median diagnostic delay suggest that globally, individuals with axSpA wait between 2 and 6 years for a diagnosis – revealing a clear benchmark for improvement. This timespan presents a window of opportunity for earlier diagnosis and intervention, which will likely improve patient outcomes. This review describes the current diagnostic delay as estimated across countries and over time, before presenting evidence from published strategies that may be implemented to improve this delay across primary and secondary care, including for specialties treating extra-musculoskeletal manifestations of axSpA (ophthalmology, gastroenterology, dermatology). Ongoing campaigns tackling delayed diagnosis in axSpA are also highlighted