Quantum spin models play an important role in theoretical condensed matter physics and quantum information theory. One numerical technique that is frequently used in studies of quantum spin systems is exact diagonalization. In this approach, numerical methods are used to find the lowest eigenvalues and associated eigenvectors of the Hamilton matrix of the quantum system. The computational problem is thus to determine the lowest eigenpairs of an extremely large, sparse matrix. Although many sophisticated iterative techniques for the determination of a small number of lowest eigenpairs can be found in the literature, most exact diagonalization studies of quantum spin systems have employed the Lanczos algorithm. In contrast to this, other methods have been applied very successfully to the similar problem of electronic structure calculations. The well known VASP code for example uses a Block Davidson method as well as the residual-minimization - direct inversion of the iterative subspace algorithm (RMM-DIIS). The Davidson algorithm is closely related to the Lanczos method but usually needs less iterations. The RMM-DIIS method was originally proposed by Pulay and later modified by Wood and Zunger. The RMM-DIIS method is particularly interesting if more than one eigenpair is sought since it does not require orthogonalization of the trial vectors at each step. In this work I study the efficiency of the Lanczos, Block Davidson and RMM-DIIS method when applied to basic quantum spin models like the spin-1/2 Heisenberg chain, ladder and dimerized ladder. I have implemented all three methods and are currently applying the methods to the different models. In our presentation I will compare the three algorithms based on the number of iterations to achieve convergence, the required computational time. An Intel's Many-Integrated Core architecture with Intel Xeon Phi coprocessor 5110P integrates 60 cores with 4 hardware threads per core was used for RMM-DIIS method, the achieved parallel speedups were compared with those obtained on a conventional multi-core system.

A qualidade microbiológica de medicamentos é fundamental para garantir sua eficácia e segurança. Os métodos convencionais para identificação microbiana em produtos não estéreis são amplamente utilizados, entretanto são demorados e trabalhosos. O objetivo deste trabalho é desenvolver método microbiológico rápido (MMR) para a identificação de contaminantes em produtos farmacêuticos utilizando a espectrofotometria de infravermelho com transformada de Fourier com reflectância total atenuada (FTIR-ATR). Análise de componentes principais (PCA) e análise de discriminantes (LDA) foram utilizadas para obter um modelo de predição com a capacidade de diferenciar o crescimento de oriundo de contaminação por Bacillus subtilis (ATCC 6633), Candida albicans (ATCC 10231), Enterococcus faecium (ATCC 8459), Escherichia coli (ATCC 8739), Micrococcus luteus (ATCC 10240), Pseudomonas aeruginosa (ATCC 9027), Salmonella Typhimurium (ATCC 14028), Staphylococcus aureus (ATCC 6538) e Staphylococcus epidermidis (ATCC 12228). Os espectros de FTIR-ATR forneceram informações quanto à composição de proteínas, DNA/RNA, lipídeos e carboidratos provenientes do crescimento microbiano. As identificações microbianas fornecidas pelo modelo PCA/LDA baseado no método FTIR-ATR foram compatíveis com aquelas obtidas pelos métodos microbiológicos convencionais. O método de identificação microbiana rápida por FTIR-ATR foi validado quanto à sensibilidade (93,5%), especificidade (83,3%) e limite de detecção (17-23 UFC/mL de amostra). Portanto, o MMR proposto neste trabalho pode ser usado para fornecer uma identificação rápida de contaminantes microbianos em produtos farmacêuticos. / Microbiological quality of pharmaceuticals is fundamental in ensuring efficacy and safety of medicines. Conventional methods for microbial identification in non-sterile drugs are widely used, however are time-consuming and laborious. The aim of this paper was to develop a rapid microbiological method (RMM) for identification of contaminants in pharmaceutical products using Fourier transform infrared with attenuated total reflectance spectrometry (FTIR-ATR). Principal components analysis (PCA) and linear discriminant analysis (LDA) were used to obtain a predictive model with capable to distinguish Bacillus subtilis (ATCC 6633), Candida albicans (ATCC 10231), Enterococcus faecium (ATCC 8459), Escherichia coli (ATCC 8739), Micrococcus luteus (ATCC 10240), Pseudomonas aeruginosa (ATCC 9027), Salmonella Typhimurium (ATCC 14028), Staphylococcus aureus (ATCC 6538), and Staphylococcus epidermidis (ATCC 12228) microbial growth. FTIR-ATR spectra provide information of protein, DNA/RNA, lipids, and carbohydrates constitution of microbial growth. Microbial identification provided by PCA/LDA based on FTIR-ATR method were compatible to those obtained using conventional microbiological methods. FTIR-ATR method for rapid identification of microbial contaminants in pharmaceutical products was validated by assessing the sensitivity (93.5%), specificity (83.3%), and limit of detection (17-23 CFU/mL of sample). Therefore, the RMM proposed in this work may be used to provide a rapid identification of microbial contaminants in pharmaceutical products.

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