Cluster mutation-periodic quivers and associated Laurent sequences

We consider quivers/skew-symmetric matrices under the action of mutation (in the cluster algebra sense). We classify those which are isomorphic to their own mutation via a cycle permuting all the vertices, and give families of quivers which have higher periodicity. The periodicity means that sequences given by recurrence relations arise in a natural way from the associated cluster algebras. We present a number of interesting new families of non-linear recurrences, necessarily with the Laurent property, of both the real line and the plane, containing integrable maps as special cases. In particular, we show that some of these recurrences can be linearised and, with certain initial conditions, give integer sequences which contain all solutions of some particular Pell equations. We extend our construction to include recurrences with parameters, giving an explanation of some observations made by Gale. Finally, we point out a connection between quivers which arise in our classification and those arising in the context of quiver gauge theories.Comment: The final publication is available at www.springerlink.com. 42 pages, 35 figure

Twenty-six years of HIV science: an overview of anti-HIV drugs metabolism

From the identification of HIV as the agent causing AIDS, to the development of effective antiretroviral drugs, the scientific achievements in HIV research over the past twenty-six years have been formidable. Currently, there are twenty-five anti-HIV compounds which have been formally approved for clinical use in the treatment of AIDS. These compounds fall into six categories: nucleoside reverse transcriptase inhibitors (NRTIs), nucleotide reverse transcriptase inhibitors (NtRTIs), non-nucleoside reverse transcriptase inhibitors (NNRTIs), protease inhibitors (PIs), cell entry inhibitors or fusion inhibitors (FIs), co-receptor inhibitors (CRIs), and integrase inhibitors (INIs). Metabolism by the host organism is one of the most important determinants of the pharmacokinetic profile of a drug. Formation of active or toxic metabolites will also have an impact on the pharmacological and toxicological outcomes. Therefore, it is widely recognized that metabolism studies of a new chemical entity need to be addressed early in the drug discovery process. This paper describes an overview of the metabolism of currently available anti-HIV drugs.Da identificação do HIV como o agente causador da AIDS, ao desenvolvimento de fármacos antirretrovirais eficazes, os avanços científicos na pesquisa sobre o HIV nos últimos vinte e seis anos foram marcantes. Atualmente, existem vinte e cinco fármacos anti-HIV formalmente aprovados pelo FDA para utilização clínica no tratamento da AIDS. Estes compostos são divididos em seis classes: inibidores nucleosídeos de transcriptase reversa (INTR), inibidores nucleotídeos de transcriptase reversa (INtTR), inibidores não-nucleosídeos de transcriptase reversa (INNTR), inibidores de protease (IP), inibidores da entrada celular ou inibidores de fusão (IF), inibidores de co-receptores (ICR) e inibidores de integrase (INI). O metabolismo consiste em um dos maiores determinantes do perfil farmacocinético de um fármaco. A formação de metabólitos ativos ou tóxicos terá impacto nas respostas farmacológicas ou toxicológicas do fármaco. Portanto, é amplamente reconhecido que estudos do metabolismo de uma nova entidade química devem ser realizados durante as fases iniciais do processo de desenvolvimento de fármacos. Este artigo descreve uma abordagem do metabolismo dos fármacos anti-HIV atualmente disponíveis na terapêutica

Arithmetic for closed balls

Inspired by circular complex interval arithmetic, an arithmetic for closed balls in Rn is pursued. In this sense, the properties of certain operations on closed balls in Rn, some of which related either to the Hadamard product of vectors or to the 2-fold vector cross product when n є {3, 7}, are studied. In particular, known results for operations on closed balls in C, which can be identified with R2, are extended to closed balls in Rn

Correlation between ethylene emission and skin colour changes during papaya (Carica papaya L.) fruit ripening

The skin colour changes and ethylene emission rates were monitored during papaya (C. papaya L.) fruit ripening. Two groups of papaya (‘Formosa’ and ‘Solo’) were applied in this study. The total colour difference was used as measured parameter and the corresponding half time of its saturation was used as correlation parameter. A high correlation factor between the saturation half time and corresponding climacteric peak time was found. It was concluded that high ethylene emission rate in ‘Solo’ fruit promotes a quick change of the total colour difference