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We introduce the concept of epidemic-fitted wavelets which comprise, in particular, as special cases the number I(t) of infectious individuals at time t in classical SIR models and their derivatives. We present a novel method for modelling epidemic dynamics by a model selection method using wavelet theory and, for its applications, machine learning-based curve fitting techniques. Our universal models are functions that are finite linear combinations of epidemic-fitted wavelets. We apply our method by modelling and forecasting, based on the Johns Hopkins University dataset, the spread of the current Covid-19 (SARS-CoV-2) epidemic in France, Germany, Italy and the Czech Republic, as well as in the US federal states New York and Florida.

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Abstract. We prove that the cover ideals of all unimodular hypergraphs have the nonincreasing depth function property. Furthermore, we show that the index of depth stability of these ideals is bounded by the number of variables.

The chemical investigation of Homotrigona apicalis propolis collected in Binh Dinh province, Vietnam, led to the isolation of nine compounds, including four sesquiterpenes: spathulenol (1), 1αH,5βH-aromandendrane-4β,10α-diol (2), 1β,6α-dihydroxy-4(15)-eudesmene (3), and 1βH,5βH-aromandendrane-4α,10β-diol (4); three triterpenes: acetyl oleanolic acid (5), 3α-hydroxytirucalla-8,24-dien-21-oic acid (6), and ursolic acid (7); and two xanthones: cochinchinone A (8) and α-mangostin (9). Sesquiterpens 1–4 and triterpene 6 were isolated for the first time from stingless bee propolis. Plants in the Cratoxylum and Aglaia genus were suggested as resin sources of the propolis sample. In the antibacterial activity evaluation, the EtOH extract only showed moderate activity on S. aureus, while the isolated compounds 7–9 showed good antibacterial activity, with IC50 values of 0.56 to 17.33 µg/mL. The EtOH extract displayed selective cytotoxicity against the A-549 cancer cell line, with IC50 values of 22.82 ± 0.86 µg/mL, and the xanthones 8 and 9 exhibited good activity against the KB, HepG-2, and A-549 cancer cell lines, with IC50 values ranging from 7.55 ± 0.25 µg/mL to 29.27 ± 2.07 µg/mL. The cytotoxic effects of xanthones 8 and 9 were determined by the inhibition of the EGFR and HER2 pathways using a molecular docking study. Compounds 8 and 9 displayed strong binding affinity with EFGR and HER2, with values of −9.3 to −9.9 kcal/mol. Compounds 5, 8, and 9 showed potential α-glucosidase inhibitory activities, which were further confirmed by computational studies. The binding energies of compounds 5, 8, and 9 were lower than that of arcabose.

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In this note, we investigate the density of the exponential functional of the fractional Brownian motion. Based on the techniques of Malliavin's calculus, we provide a log-normal upper bound for the density.

Background Heroin use continues to drive HIV transmission in Vietnam, but methamphetamine and alcohol use are growing rapidly and, as in other countries, polysubstance use is widespread. The objective of this study was to understand the interplay between heroin, methamphetamine, and alcohol use among people with opioid use disorder (OUD) and HIV in Vietnam. Methods We conducted 44 in-depth, face-to-face qualitative interviews with people with OUD and HIV who participated in the BRAVO trial of buprenorphine versus methadone in five Vietnam HIV clinics. Interviews probed participants’ experiences of heroin, methamphetamine, and alcohol use and their interplay with HIV/OUD treatment. Interviews were professionally transcribed and analyzed using a thematic analysis approach. Results Of 44 participants interviewed 42 were male, on average 38.8 years of age, with 30 reporting a history of methamphetamine use and 33 reporting a history of alcohol use. Several themes emerged: 1) Methamphetamine and alcohol were perceived to have lower addiction potential than heroin 2) Social settings were key facilitators of alcohol and methamphetamine use 3) Some participants, but not all, used methamphetamine to help quit heroin 4) Consuming alcohol blunted the effects of heroin, while paradoxically serving as a catalyst for heroin use 5) Use of methamphetamine was perceived by many participants to be incompatible with treatment for HIV. Conclusions Participant experiences reflected a significant impact of polysubstance use on treatment of HIV and OUD. Patterns of polysubstance use are subject to common preconceptions of alcohol and methamphetamine as having a low addictive potential, and these substances are deeply enmeshed in the social life of many people with OUD in Vietnam. Interventions to address complex social norms and potential harms of polysubstance use are urgently needed as the population of people receiving medication for OUD (MOUD) increases in Vietnam and globally. Trial registration BRAVO - NCT01936857, September 2013.