New differential equations for on-shell loop integrals

We present a novel type of differential equations for on-shell loop integrals. The equations are second-order and importantly, they reduce the loop level by one, so that they can be solved iteratively in the loop order. We present several infinite series of integrals satisfying such iterative differential equations. The differential operators we use are best written using momentum twistor space. The use of the latter was advocated in recent papers discussing loop integrals in N=4 super Yang-Mills. One of our motivations is to provide a tool for deriving analytical results for scattering amplitudes in this theory. We show that the integrals needed for planar MHV amplitudes up to two loops can be thought of as deriving from a single master topology. The master integral satisfies our differential equations, and so do most of the reduced integrals. A consequence of the differential equations is that the integrals we discuss are not arbitrarily complicated transcendental functions. For two specific two-loop integrals we give the full analytic solution. The simplicity of the integrals appearing in the scattering amplitudes in planar N=4 super Yang-Mills is strongly suggestive of a relation to the conjectured underlying integrability of the theory. We expect these differential equations to be relevant for all planar MHV and non-MHV amplitudes. We also discuss possible extensions of our method to more general classes of integrals.Comment: 39 pages, 8 figures; v2: typos corrected, definition of harmonic polylogarithms adde

Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory

We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behaviour, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral \Omega^{(2)}, also plays a key role in a new representation of the remainder function R_6^{(2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) \times (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) \times (parity even) part. The second non-polylogarithmic function, the loop integral \tilde{\Omega}^{(2)}, characterizes this sector. Both \Omega^{(2)} and tilde{\Omega}^{(2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.Comment: 51 pages, 4 figures, one auxiliary file with symbols; v2 minor typo correction

Synthesis of new, single-isomer quaternary ammonium derivatives of beta-cyclodextrin for electrophoretic enantiomer separations

The isolation of individual enantiomers of drugs is an important subject of interest in the pharmaceutical and medical fields, because stereochemistry can have a significant effect on the biological activity of the drug. Therefore, it is important to develop enantiomeric separation methods for the determination of the optical purity of drugs, since the undesired enantiomer is regarded as one of the impurities. The available single isomer anionic cyclodextrins (CD) can resolve the enantiomers of only a few weakly acidic analytes. To rectify this problem, the chloride salts of heptakis(6-deoxy-6-morpholinio)-cyclomaltoheptaose (HMBCD), and mono(6- deoxy-6-N,N,N r,N r,N r-pentamethylethylenediammonio)-cyclomaltoheptaose (PEMEDA-BCD), the first members of the permanently charged, single-isomer cationic cyclodextrin family, have been synthesized. The purity of process intermediates and final products was determined by HPLC-ELSD and indirect UV-detection capillary electrophoresis. Structural identity was verified by 1D and 2D NMR and massBoth cationic CD derivatives have been used for the separation of the enantiomers of strong acid, weak acid, weak base, ampholytic, and neutral analytes by capillary electrophoresis. Because the charge state of these cationic chiral resolving agents is independent of the pH of the buffer, separation could be performed in both low and high pH buffers without compromising the charge density of the resolving agent. Contrary to expectation, the multiply charged HMBCD showed poor complexation with the newly synthesized strong electrolyte test analytes. The weak binding between the analytes and HMBCD resulted in separation of enantiomers of only three strong electrolyte analytes. Strong complexation was observed between PEMEDA-BCD and the anionic and nonionic analytes in both low and high pH buffers, though complexation was stronger in the high pH buffer. Due to strong complexation between the anions and PEMEDA-BCD, only low concentrations of the resolving agent were required to effect good enantiomer resolutions. spectrometry

A vantagem em casa no futebol: comparação entre Copa Libertadores da América e UEFA Champions League

The home advantage in soccer: comparision between Libertadores of American Cup and UEFA Champions LeagueThe objective of this study was to compare the home advantage (HA) in Libertadores of American Cup (LAC) and UEFA Champions League (UCL). We analyzed all matches of group phase (n = 1536) from 2004 to 2011 seasons. To quantify the HA, we use the methodology of recovery percentage points, proposed by POLLARD3, considered HA, values greater than 50%. There were a significant difference (p = 0.010) between LAC (67.8 ± 4%) and UCL (60.5 ± 5%). The magnitude of the mean (mean difference = 0.73, 95% CI: 0.020 to 0.127) was large (h2 = 0.35). We concluded that the HA was higher in LAC than in UCL in this seasons and the factors such as altitude, distance traveled fans characteristics and referee behavior it will be able to help to explain this phenomenon in future studies.O objetivo desse estudo foi comparar a vantagem em casa (VC) entre Copa Libertadores da América (CLA) e UEFA Champions League (UCL). Foram analisadas todas as partidas da fase de grupos (n = 1536) das temporadas 2004 a 2011. Para quantificar a VC, foi utilizada a metodologia de aproveitamento percentual de pontos proposta por POLLARD3, sendo considerado VC valores maiores que 50%. Houve diferença significativa (p = 0,010) para a VC na CLA (67,8 ± 4%) em relação a UCL (60,5 ± 5%). A magnitude das diferenças das médias (diferença média = 0,73; IC 95%: 0,020 a 0,127) foi grande (h2 = 0,35). Conclui-se que a VC foi maior na CLA do que na UCL nas temporadas analisadas e que fatores como altitude, distância de viagem, característica das torcidas e comportamento arbitral poderá ajudar a explicar esse fenômeno em futuros estudos

Estimativa da incidência, análise espacial e epidemiológica da tuberculose no Brasil, 2012 a 2014

Tese (doutorado)—Universidade de Brasília, Faculdade de Ciências da Saúde, Programa de Pós-Graduação em Saúde Coletiva, 2018.No Brasil, a subnotificação de casos de tuberculose dificulta a análise da verdadeira situação epidemiológica da doença em seu território. Ademais, as diversidades socioeconômicas e operacionais do país constituem obstáculo para a estimação da taxa de incidência da tuberculose no nível regional, uma vez que resultam em sistemas de vigilância com diferentes proporções de casos notificados. Diante disso, o objetivo dessa tese foi estimar e mapear a taxa de incidência da tuberculose, corrigida pela subnotificação de casos, nas microrregiões do Brasil, no período de 2012 a 2014. Para tanto, foram feitos estudos ecológicos com dados do Sistema de Informação de Agravos de Notificação (Sinan), relatados em três artigos científicos. Nos artigos 1 e 2, as unidades de análise foram as 558 microrregiões brasileiras. No artigo 1, foram mensurados indicadores de três atributos do sistema de vigilância da tuberculose: qualidade do sistema de informação (completitude e consistência), oportunidade e aceitabilidade. No segundo trabalho, foram consideradas exclusivamente as 508 (91,0%) microrregiões com sistema de informação ótimo ou regular, segundo critérios do primeiro artigo. Foi proposto um estimador indireto da proporção de casos notificados (EIPCN), tendo os indicadores de oportunidade e aceitabilidade como base. O ponto de corte do EIPCN, para a especificação das áreas com provável subnotificação de casos, foi o limite da curva ROC mais apropriado para a identificação de microrregiões com sistema de vigilância ruim. O grupo de áreas com vigilância ruim foi selecionado previamente, com uso de método híbrido de análise de agrupamentos nos indicadores de oportunidade e aceitabilidade do sistema de vigilância. No artigo 3, a taxa de incidência da tuberculose foi estimada mediante modelo Bayesiano espacial. Foi incluída censura à direita na distribuição da taxa de incidência das microrregiões com alta taxa de pobreza e com sistema de vigilância com qualidade dos dados, oportunidade e/ou aceitabilidade ruim. Observou-se 50 (9,0%) microrregiões, localizadas principalmente nas regiões Nordeste e Sudeste, com completitude mediana do sistema de informação inferior a 70%. Entre as microrregiões com completitude superior a esse limite, suspeitou-se de subnotificação de casos em 89 (17,5%), com EIPCN (média entre a proporção de casos que realizaram baciloscopia e a proporção de pessoas aderentes ao tratamento) inferior a 83%. Essas áreas concentraram-se especialmente nos estados do Rio Grande do Sul, Minas Gerais e Bahia. A maior discrepância entre a taxa de incidência notificada e predita pelo modelo Bayesiano ocorreu na região Nordeste, na qual a proporção de casos notificados foi estimada em 88,4%. Logo, houve evidências de que a taxa de incidência obtida diretamenta no Sinan subestima a real situação epidemiológica da tuberculose no país, especialmente na região Nordeste. Os resultados deste trabalho poderão ser utilizados para direcionar estratégias custo-efetivas para a melhoria da notificação de casos de tuberculose no Brasil.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).In Brazil, underreporting of tuberculosis cases makes it difficult to analyze the true epidemiological situation of the disease in its territory. In addition, the socioeconomic and operational diversities of the country constitute an obstacle to the estimation of tuberculosis incidence rate at the regional level, since they result in surveillance systems with different proportions of reported cases. Therefore, the purpose of this thesis was to estimate and map the tuberculosis incidence rate, corrected by the underreporting of cases, in micro-regions of Brazil, from 2012 to 2014. In this regard, ecological studies were done with data from the National Notifiable Diseases Information System (Sinan), presented in three scientific articles. In articles 1 and 2, the units of analysis were the 558 Brazilian micro-regions. In article 1, indicators of three tuberculosis surveillance system attributes were measured: quality of information system (completeness and consistency), opportunity and acceptability. In the second study, only 508 (91.0%) micro-regions with an optimal or regular information system were considered, according to the first article criteria. An indirect estimator of the proportion of reported cases (EIPCN, in the Portuguese abbreviation) was proposed, with the opportunity and acceptability indicators as a basis. The EIPCN cutoff point for specifying areas with probable underreporting of cases was the most appropriate ROC curve limit for the identification of micro-regions with poor surveillance system. The group of areas with poor surveillance was previously selected, using hybrid method of cluster analysis in the opportunity and acceptability indicators of the surveillance system. In article 3, the incidence rate of tuberculosis was estimated using a spatial Bayesian model. It was included right censoring in the incidence rate distribution of micro-regions with high poverty rates and surveillance system with poor data quality, opportunity and/or acceptability. It was observed 50 (9.0%) micro-regions, located mainly in the Northeast and Southeast regions, with a median completeness of the information system of less than 70%. Among the micro-regions with completeness above this limit, underreporting of cases was suspected in 89 (17.5%), with EIPCN (mean between the proportion of cases that underwent sputum smear microscopy and the proportion that have joined the treatment) less than 83%. These areas were especially concentrated in the states of Rio Grande do Sul, Minas Gerais and Bahia. The largest discrepancy between the reported and predicted incidence rate was observed in the Northeast region, in which the proportion of reported cases was estimated in 88.4%. Hence, there was evidence that the Sinan’s incidence rate underestimates the actual epidemiological situation of tuberculosis in the country, especially in the Northeast region. The results of this work can be used to guide cost-effective strategies for improving the notification of tuberculosis cases in Brazil

Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops

We calculate form factors of half-BPS operators in N=4 super Yang-Mills theory at tree level and one loop using novel applications of recursion relations and unitarity. In particular, we determine the expression of the one-loop form factors with two scalars and an arbitrary number of positive-helicity gluons. These quantities resemble closely the MHV scattering amplitudes, including holomorphicity of the tree-level form factor, and the expansion in terms of two-mass easy box functions of the one-loop result. Next, we compare our result for these form factors to the calculation of a particular periodic Wilson loop at one loop, finding agreement. This suggests a novel duality relating form factors to periodic Wilson loops.Comment: 26 pages, 10 figures. v2: typos fixed, comments adde

Transcriptional Robustness Complements Nonsense-Mediated Decay in Humans

In eukaryotes, gene expression is a complex, multi-step process involving transcription, splicing, translation, and post-translational modifications. At each individual step, errors can occur that lead to nonfunctional and potentially toxic proteins. Therefore, eukaryotes have evolved a wide array of solutions to minimize the risk of error.This work was supported by NIH grant R01 GM088344 to COW. The funder had no role in the preparation of the article.Cellular and Molecular Biolog