On an extremal problem for poset dimension

Let $f(n)$ be the largest integer such that every poset on $n$ elements has a $2$-dimensional subposet on $f(n)$ elements. What is the asymptotics of $f(n)$? It is easy to see that $f(n)\geqslant n^{1/2}$. We improve the best known upper bound and show $f(n)=\mathcal{O}(n^{2/3})$. For higher dimensions, we show $f_d(n)=\mathcal{O}\left(n^\frac{d}{d+1}\right)$, where $f_d(n)$ is the largest integer such that every poset on $n$ elements has a $d$-dimensional subposet on $f_d(n)$ elements.Comment: removed proof of Theorem 3 duplicating previous work; fixed typos and reference

Resposta de cordeiros ao parasitismo por Haemonchus contortus previamente infectados com Haemonchus placei.

Com o objetivo de verificar a resposta de cordeiros ao parasitismo por Haemonchus contortus após a primo-infecção com H. placei foi realizado o presente estudo em 39 ovinos divididos em quatro grupos: grupo HCC (controle positivo, primo-infectado com H. contortus e desafiado com H. contortus); HCP (primo-infectado com H. contortus e desafiado com H. placei); HPC (primo-infectado com H. placei e desafiados com H. contortus) e CNE (controle negativo). Os animais foram avaliados através da contagem de ovos por grama de fezes (OPG), carga parasitária e contagem total de leucócitos. Os resultados mostraram que a média da carga parasitária e da contagem total de leucócitos não apresentaram diferença (P > 0,05) entre os grupos. A média de OPG do grupo HCP foi menor em relação aos grupos HCC e HPC (P < 0,05). Os resultados obtidos até o momento mostram que a primo-infecção com H. placei não é capaz de reduzir os níveis de OPG de subsequentes infecções por H. contortus

The Game Saturation Number of a Graph

Given a family F and a host graph H, a graph G ⊆ H is F-saturated relative to H if no subgraph of G lies in F but adding any edge from E(H) - E(G) to G creates such a subgraph. In the F-saturation game on H, players Max and Min alternately add edges of H to G, avoiding subgraphs in F, until G becomes F-saturated relative to H. They aim to maximize or minimize the length of the game, respectively; satg(F;H) denotes the length under optimal play (when Max starts). Let O denote the family of odd cycles and the family of n-vertex trees, and write F for when F = {F}. Our results include satg(O; Kn) = [n/2] [n/2], satg(Tn; Kn) = (n-2/2) + 1 for n ≥ 6, satg(K1,3; Kn) = 2[Tn/2] for n ≥ 8, and satg(P4; Kn) ∈ {[4n/f] , [4n/5]} for n ≥ 5. We also determine satg(P4; Km;n); with m ≥ n, it is n when n is even, m when n is odd and m is even, and m + [n/2] when mn is odd. Finally, we prove the lower bound satg(C4; Kn,n) ≥ 1/21n13/12 – O(n35/36). The results are very similar when Min plays first, except for the P4-saturation game on Km,n.

Tau, prions and Aβ: the triad of neurodegeneration

This article highlights the features that connect prion diseases with other cerebral amyloidoses and how these relate to neurodegeneration, with focus on tau phosphorylation. It also discusses similarities between prion disease and Alzheimer’s disease: mechanisms of amyloid formation, neurotoxicity, pathways involved in triggering tau phosphorylation, links to cell cycle pathways and neuronal apoptosis. We review previous evidence of prion diseases triggering hyperphosphorylation of tau, and complement these findings with cases from our collection of genetic, sporadic and transmitted forms of prion diseases. This includes the novel finding that tau phosphorylation consistently occurs in sporadic CJD, in the absence of amyloid plaques

Prion-specific and surrogate CSF biomarkers in Creutzfeldt-Jakob disease:diagnostic accuracy in relation to molecular subtypes and analysis of neuropathological correlates of p-tau and A beta 42 levels

The differential diagnosis of Creutzfeldt-Jakob disease (CJD) from other, sometimes treatable, neurological disorders is challenging, owing to the wide phenotypic heterogeneity of the disease. Real-time quaking-induced prion conversion (RT-QuIC) is a novel ultrasensitive in vitro assay, which, at variance with surrogate neurodegenerative biomarker assays, specifically targets the pathological prion protein (PrPSc). In the studies conducted to date in CJD, cerebrospinal fluid (CSF) RT-QuIC showed good diagnostic sensitivity (82\u201396%) and virtually full specificity. In the present study, we investigated the diagnostic value of both prion RT-QuIC and surrogate protein markers in a large patient population with suspected CJD and then evaluated the influence on CSF findings of the CJD type, and the associated amyloid-\u3b2 (A\u3b2) and tau neuropathology. RT-QuIC showed an overall diagnostic sensitivity of 82.1% and a specificity of 99.4%. However, sensitivity was lower in CJD types linked to abnormal prion protein (PrPSc) type 2 (VV2, MV2K and MM2C) than in typical CJD (MM1). Among surrogate proteins markers (14-3-3, total (t)-tau, and t-tau/phosphorylated (p)-tau ratio) t-tau performed best in terms of both specificity and sensitivity for all sCJD types. Sporadic CJD VV2 and MV2K types demonstrated higher CSF levels of p-tau when compared to other sCJD types and this positively correlated with the amount of tiny tau deposits in brain areas showing spongiform change. CJD patients showed moderately reduced median A\u3b242 CSF levels, with 38% of cases having significantly decreased protein levels in the absence of A\u3b2 brain deposits. Our results: (1) support the use of both RT-QuIC and t-tau assays as first line laboratory investigations for the clinical diagnosis of CJD; (2) demonstrate a secondary tauopathy in CJD subtypes VV2 and MV2K, correlating with increased p-tau levels in the CSF and (3) provide novel insight into the issue of the accuracy of CSF p-tau and A\u3b242 as markers of brain tauopathy and \u3b2-amyloidosis