Закон больших чисел при нарушениях статистической устойчивости

Понятие сходимости последовательности случайных величин обобщено на случай сходимости последовательности гиперслучайных величин. Показано, что закон больших чисел имеет место не только при наличии сходимости выборочного среднего к фиксированному числу, но и тогда, когда такой сходимости нет. Установлено, что выборочное среднее случайной величины может сходиться к фиксированному числу, стремиться к плюс бесконечности, минус бесконечности или флуктуировать в пределах определенного интервала, а выборочное среднее гиперслучайной величины может сходиться к фиксированной величине, множеству фиксированных величин (множеству чисел), флуктуировать в непересекающихся интервалах, флуктуировать в пределах одного интервала или стремиться к плюс или минус бесконечности.Поняття збіжності послідовності випадкових величин узагальнено на випадок збіжності послідовності гіпервипадкових величин. Показано, що закон великих чисел має місце не тільки у разі, коли є збіжність вибіркового середнього до фіксованого числа, але й коли такої збіжності немає. Встановлено, що вибіркове середнє випадкових величин може збігатись до фіксованого числа, прямувати до плюс чи мінус нескінченності або флуктувати в межах інтервалу, а вибіркове середнє гіпервипадкової величини може збігатись до фіксованого числа, множини фіксованих чисел, флуктувати в межах інтервалів, що не перетинаються, флуктувати в межах одного інтервалу або прямувати до плюс чи мінус нескінченності.The term sequence convergence of random quantities has been generalized to the sequence convergence of hyper-random quantities. It has been shown that the low of large numbers for random sequence is correct not only when the average tends to fixed number but in case of the absence of the convergence. It has been found that the average of random variables can approach to the fixed number, tend to plus or minus infinity or fluctuate within the interval and the average of hyper-random variable can approach to the fixed number, to the set of fix numbers, fluctuate within the of disjoint intervals, fluctuate within the single interval or tend to plus or minus infinity

Therapeutic switching : from antidermatophytic essential oils to new leishmanicidal products

This study examined whether the antidermatophytic activity of essential oils (EOs) can be used as an indicator for the discovery of active natural products against Leishmania amazonensis. The aerial parts of seven plants were hydro-distilled. Using broth microdilution techniques, the obtained EOs were tested against three strains of dermatophytes (Trichophyton mentagrophytes, Microsporum gypseum and Microsporum canis). To compare the EOs antifungal and antiparasitic effects, the EOs activities against axenic amastigotes of L. amazonensis were concurrently evaluated. For the most promising EOs, their antileishmanial activities against parasites infecting peritoneal macrophages of BALB/c mice were measured. The most interesting antifungal candidates were the EOs from Cymbopogon citratus, Otacanthus azureus and Protium heptaphyllum, whereas O. azureus, Piper hispidum and P. heptaphyllum EOs exhibited the lowest 50% inhibitory concentration (IC50) values against axenic amastigotes, thus revealing a certain correspondence between both activities. The P. hispidum EO was identified as the most promising product in the results from the infected macrophages model (IC50 : 4.7 mu g/mL, safety index: 8). The most abundant compounds found in this EO were sesquiterpenes, notably curzerene and furanodiene. Eventually, the evaluation of the antidermatophytic activity of EOs appears to be an efficient method for identifying new potential drugs for the treatment of L. amazonensis

In vitro antifungal activity of Otacanthus azureus (Linden) Ronse essential oil alone and in combination with azoles

International audienceWe determined the chemical composition and investigated the antifungal activity of Otacanthus azureus (Linden) Ronse essential oil alone or combined with azoles antifungals against a range of human yeasts and dermatophytes. The oil was shown to be composed in majority of sesquiterpenes. Using broth microdilution techniques, it was found to exert interesting in vitro antifungal activities, more particularly against human dermatophytes, with minimum inhibitory concentrations as low as 4µg/ml against a clinical isolate of Trichophyton rubrum. The analysis of the combined effect of this oil with azoles highlighted a pronounced synergism between the oil and ketoconazole or itraconazole, against Candida albicans, C. parapsilosis and Trichophyton mentagrophytes, with fractional inhibitory concentration indices in the 0.1–0.5 range. Interestingly, the oil showed no cytotoxicity on VERO cells (ED50>100µg/ml). According to these results, O. azureus essential oil may be considered a promising natural product in the treatment of human mycoses, more particularly those originating from dermatophytic fungi. Also, it is likely to reduce the minimum effective dose of ketoconazole and itraconazole against Candida species, thus minimizing the side effects of these drugs, and the risk to develop resistances

In vitro antidermatophytic activity of Otacanthus azureus (Linden) Ronse essential oil alone and in combination with azoles

AimsWe determined the chemical composition and investigated the antifungal activity of Otacanthus azureus (Linden) Ronse essential oil (EO) against a range of dermatophytes alone or in combination with azole antifungals. Methods and ResultsAerial parts of the plant were steam-distilled and the obtained oil was analysed by gas chromatography/mass spectrometry and H-1-NMR. It was shown to be largely composed of sesquiterpenes, with the main component being -copaen-4--ol. Using broth microdilution techniques, this oil was found to have remarkable in vitro antifungal activities. Minimum inhibitory concentrations as low as 4g ml(-1) were recorded. The analysis of the combined effect of the O. azureus EO with azoles using chequerboard assays revealed a synergism between the EO and ketoconazole, fluconazole or itraconazole against Trichophyton mentagrophytes. Notably, the O. azureus essential oil showed low cytotoxicity to VERO cells. ConclusionsThe O. azureus essential oil alone or in combination with azoles is a promising antifungal agent in the treatment for human dermatomycoses caused by filamentous fungi. Significance and Impact of the StudyThere is much interest in the study of essential oils for the discovery of new antimicrobial drugs. This study has highlighted the antidermatophytic activity of the O. azureus EO

In vitro antidermatophytic activity of Otacanthus azureus (Linden) Ronse essential oil alone and in combination with azoles.

International audienceAIMS: We determined the chemical composition and investigated the antifungal activity of Otacanthus azureus (Linden) Ronse essential oil (EO) against a range of dermatophytes alone or in combination with azole antifungals. METHODS AND RESULTS: Aerial parts of the plant were steam-distilled and the obtained oil was analysed by gas chromatography/mass spectrometry and (1) H-NMR. It was shown to be largely composed of sesquiterpenes, with the main component being β-copaen-4-α-ol. Using broth microdilution techniques, this oil was found to have remarkable in vitro antifungal activities. Minimum inhibitory concentrations as low as 4 μg ml(-1) were recorded. The analysis of the combined effect of the O. azureus EO with azoles using chequerboard assays revealed a synergism between the EO and ketoconazole, fluconazole or itraconazole against Trichophyton mentagrophytes. Notably, the O. azureus essential oil showed low cytotoxicity to VERO cells. CONCLUSIONS: The O. azureus essential oil alone or in combination with azoles is a promising antifungal agent in the treatment for human dermatomycoses caused by filamentous fungi. SIGNIFICANCE AND IMPACT OF THE STUDY: There is much interest in the study of essential oils for the discovery of new antimicrobial drugs. This study has highlighted the antidermatophytic activity of the O. azureus EO

Antiplasmodial benzophenones from the trunk latex of Moronobea coccinea (Clusiaceae)

In an effort to find antimalarial drugs, a systematic in vitro evaluation on a chloroquine-resistant strain of Plasmodium falciparum (FcB1) was undertaken on sixty plant extracts collected in French Guiana. The methanol extract obtained from the latex of Moronobea coccinea exhibited a strong antiplasmodial activity (95% at 10 mu g/ml). The phytochemical investigation of this extract led to the isolation of eleven polycyclic polyprenylated acylphloroglucinols (PPAPs), from which eight showed potent antiplasmodial activity with IC50 ranged from 3.3 mu M to 37.2 mu M

Antiplasmodial benzophenone derivatives from the root barks of Symphonia globulifera (Clusiaceae)

In an effort to find antimalarial drugs, a systematic in vitro evaluation on a chloroquine-resistant strain of Plasmodium falciparum (FcB1) was undertaken on sixty plant extracts collected in French Guiana. The ethyl acetate extract obtained from the root barks of Symphonia globulifera exhibited a strong antiplasmodial activity (97% at 10 mu g/ml). The phytochemical investigation of this extract led to the isolation of nine polycyclic polyprenylated acylphloroglucinol (PPAPs) compounds and two oxidized derivatives. All compounds showed antiplasmodial activity with IC(50)s ranged from 2.1 to 10.1 mu M. A LC/ESI-MSn study performed on polyprenylated benzophenones previously isolated from Moronobea coccinea provided a reliable method for their detection in the extract and structural elucidation

How can plant defences lead to valuable products? Inspiration from plant complexity in phytochemistry

International audienceIf plants are known for centuries as a valuable source of molecules, complexity remains and can open up numerous perspectives. Plants have indeed evolved a wide range of secondary metabolites as defense, competition or attraction compounds [1]. More particularly, the exceptional biodiversity encountered in the tropics, along with the presence of various pathogens and a strong herbivory especially linked to a rich entomofauna, leads to a promising chemodiversity, due to the constant and dynamic interactions between plants and their environment. Taking into account the role and “raison d'être”[2] of natural products, and the fact that all these molecules work together as complex mixtures can therefore lead to a new point of view, by shifting from the “magic bullet” classical approach to a “herbal shotgun” strategy[3]. We will illustrate the fact that, inspired by their ecological functions, and taking into account synergistic interactions, some therapeutic applications can be found for these versatile mixtures of compounds. In particular we examined whether the antidermatophytic activity of essential oils (EOs) obtained from particularly fragrant plant species from French Guiana could be used as an indicator for the discovery of active natural products against Leishmania amazonensis. A significant correlation was observed between antidermatophytic and antileishmanial activity, confirming the “alternative use” strategy in the case of EOs, and allowed us to highlight P. hispidum Sw. (Piperaceae) EO as a promising antileishmanial product [4]. We also illustrated the importance of synergistic effects through the example of the antifungal EO of Otacanthus azureus (Linden) Ronse (Plantaginaceae) [5] and the biomimetic design of optimized synergistic mixtures thanks to a full factorial experiment approach

Characterization of the chemical diversity of Sextonia rubra fruits by MALDI-CASI-FT-ICR imaging and molecular networks

International audienc

Characterization of the chemical diversity of Sextonia rubra fruits by MALDI-CASI-FT-ICR imaging and molecular networks

International audienc