On Multiplicative Sidon Sets

Fix integers $b>a\geq1$ with $g:=\gcd(a,b)$. A set $S\subseteq\mathbb{N}$ is \emph{$\{a,b\}$-multiplicative} if $ax\neq by$ for all $x,y\in S$. For all $n$, we determine an $\{a,b\}$-multiplicative set with maximum cardinality in $[n]$, and conclude that the maximum density of an $\{a,b\}$-multiplicative set is $\frac{b}{b+g}$. For $A, B \subseteq \mathbb{N}$, a set $S\subseteq\mathbb{N}$ is \emph{$\{A,B\}$-multiplicative} if $ax=by$ implies $a = b$ and $x = y$ for all $a\in A$ and $b\in B$, and $x,y\in S$. For $1 < a < b < c$ and $a, b, c$ coprime, we give an O(1) time algorithm to approximate the maximum density of an $\{\{a\},\{b,c\}\}$-multiplicative set to arbitrary given precision

The impact of antiretroviral therapy on symptom burden among HIV outpatients with low CD4 count in rural Uganda: nested longitudinal cohort study.

BACKGROUND: Individuals with HIV have a high prevalence of physical and psychological symptoms throughout their disease course. Despite the clinical and public health implications of unresolved pain and symptoms, little is known about the effect of anti-retroviral therapy (ART) on these outcomes. This study aimed to assess the impact on symptom burden for the year after ART initiation in individuals with a CD4 count <200 cells/uL in Uganda. METHODS: HIV-infected, ART-naıve adults referred from voluntary testing and counseling services in rural Uganda for enrollment into a randomized controlled trial to test fluconazole as primary prophylaxis against cryptococcal disease were invited to complete the Memorial Symptom Assessment Scale-Short Form (MSAS-SF) prior to commencing ART and at two subsequent follow up visits. This tool measures self-reported 7-day period prevalence and associated burden of physical and psychological symptoms. Changes in the total number of symptoms and distress indices with time on ART and trial arm were investigated through fitting Linear Mixed Models for repeated measures. RESULTS: During the first year of ART initiation the prevalence of most individual symptoms remained constant. The notable exceptions which improved after commencing ART are as follow; prevalence of pain (prevalence changed from 79% to 60%), weight loss (67% to 31%), lack of appetite (46% to 28%), feeling sad (52% to 25%) and difficulty sleeping (35% to 23%). The total number of symptoms and distress indices reduced after treatment commenced. Of concern was that half or more study participants remained with symptoms of pain (60%), itching (57%), skin changes (53%) and numbness in hands and feet (52%) after starting ART. Sixteen symptoms remained with a burden of 25% or more. CONCLUSION: Despite the beneficial effect of ART on reducing symptoms, some patients continue to experience a high symptom burden. It is essential that HIV services in sub-Saharan Africa integrate management of symptoms into their programmes. TRIAL REGISTRATION: CRYPTOPRO [ISRCTN 76481529 ], November 2004

Arte convenzionale – ovvero – perché non possono esistere artisti realmente anticonformisti

The representation of the artist is generally that of a nonconformist, a lonely Bohemian eager to revolutionise the world from his studio. From this perspective, the traditional interpretation of art history is one of linear progress, spurred on by moments of innovation aiming at new states of conventionalism. This article shows how such a perspective has much to do with the philosophy of modern times, even though it doesn’t provide a satisfactory explanation of the meaning and development of art throughout the centuries, bound as they are instead to the necessity of convention with the values of society (or of its élite) rather than on wild individualism

Co-administration of fluconazole increases nevirapine concentrations in HIV-infected Ugandans.

BACKGROUND: Data from retrospective studies have suggested that there may be an interaction between fluconazole and nevirapine, increasing nevirapine concentrations and potentially leading to hepatotoxicity. METHODS: This study was nested within a large double-blind placebo-controlled study designed to determine if primary prophylaxis with fluconazole (200 mg three times per week) could reduce cryptococcal disease [CRYPTOPRO (ISRCTN 76481529)] in HIV-infected adults in rural south-western Uganda. Detailed pharmacokinetic studies were performed on 49 participants (22 on placebo and 27 on fluconazole) who had been on fluconazole or placebo with nevirapine for > or =4 weeks. RESULTS: The geometric mean pre-dose concentrations of nevirapine were 3865 ng/mL [95% confidence interval (95% CI) 3452-4758 ng/mL] and 5141 ng/mL (95% CI 4760-6595 ng/mL) (P = 0.009) in the placebo and fluconazole arms, respectively. The change in the peak nevirapine concentration in plasma (C(max)) was also higher in the fluconazole arm compared with the placebo arm [median 6546 (95% CI 6040-7974) versus 5126 (95% CI 4739-5773) ng/mL, P = 0.012]. Fluconazole increased the nevirapine area under the curve (AUC) from 0 to 8 h by 29% [geometric mean AUC(0-8) 46 135 (95% CI 42 432-57 173) versus 35 871 (95% CI 32 808-41 372) ng.h/mL, P = 0.016]. In the larger cohort from which the participants were drawn, co-administration of fluconazole did not increase the risk of hepatotoxicity. CONCLUSIONS: Fluconazole led to significant increases in nevirapine exposure, but was not associated with evidence of increased hepatotoxicity

Increased risk of HPV-associated genital cancers in men and women as a consequence of pre-invasive disease

To assess the excess risk of HPV‐associated cancer (HPVaC) in two at‐risk groups – women with a previous diagnosis of high grade cervical intraepithelial neoplasia (CIN3) and both men and women treated for non‐cervical pre‐invasive ano‐genital disease. All CIN3 cases diagnosed in 1989‐2015 in Scotland were extracted from the Scottish cancer registry (SMR06). All cases of pre‐invasive penile, anal, vulval, and vaginal disease diagnosed in 1990‐2015 were identified within the NHS pathology databases in the two largest NHS health boards in Scotland. Both were linked to SMR06 to extract subsequent incidence of HPVaC following the diagnosis of CIN3 or pre‐invasive disease. Standardised incidence ratios were calculated for the risk of acquiring HPVaC for the two at‐risk groups compared with the general Scottish population. Among 69714 females in Scotland diagnosed with CIN3 (890360.9 person‐years), 179 developed non‐cervical HPVaC. CIN3 cases were at 3.2‐fold (95% CI: 2.7 to 3.7) increased risk of developing non‐cervical HPVaC, compared to the general female population. Among 1235 patients diagnosed with non‐cervical pre‐invasive disease (9667.4 person‐years), 47 developed HPVaC. Individuals with non‐cervical pre‐invasive disease had a substantially increased risk of developing HPVaC ‐ 15.5‐fold (95% CI: 11.1 to 21.1) increased risk for females and 28‐fold (11.3 to 57.7) increased risk for males. We report a significant additional risk of HPV‐associated cancer in those have been diagnosed with pre‐invasive HPV‐associated lesions including but not confined to the cervix. Uncovering the natural history of pre‐invasive disease has potential for determining screening, prevention and treatment