Com os rápidos avanços no seqüenciamento do genoma, a compreensão da estrutura de proteínas torna-se uma extensão crucial a esses progressos. Apesar dos significativos avanços tecnológicos recentes, a determinação experimental da estrutura terciária de proteínas ainda é muito lenta se comparada com a taxa de acúmulo de dados das seqüências de aminoácidos. Isto torna o enovelamento de proteínas um problema central para o desenvolvimento da biologia pós-genômica. Em nosso trabalho, fazemos uso de um método de otimização, o Generalized Simulated Annealing (GSA), baseado na termoestatística generalizada por Tsallis. Embora o GSA seja um procedimento geral, sua eficiência depende não apenas da escolha apropriada de parâmetros, mas também das características topológicas da hiper--superfície de energia da função custo. Com o mapeamento dos parâmetros necessários à aplicação do GSA, pode-se reduzir significativamente o número de escolhas, além de tornar possível uma análise do efeito dos parâmetros no comportamento do algoritmo. Como passo inicial, usamos estruturas conhecidas, com as quais os resultados obtidos com o GSA possam ser comparados, como é o caso das polialaninas. Além disso, aplicamos, o GSA a três peptídeos de proteínas ribossomais da família P, de considerável importância no estudo da doença de Chagas. Cada um possui 13 aminoácidos, diferindo em apenas uma mutação não conservativa no terceiro aminoácido. Como os peptídeos não possuem estrutura experimentalmente resolvida, analisamos os resultados obtidos com GSA seguidos por simulações de Dinâmica Molecular. A validade destes resultados é estudada, de forma que, no futuro, estruturas desconhecidas possam ser determinadas com certo grau de confiabilidade. / As the genome sequencing advances, the comprehension of protein structures becomes a crucial extension to these progresses. In spite of the numerous recent technological advances, experimental determination of protein terciary structures is still very slow compared to the accumulated data from amino acid sequences. That is what makes the protein folding a central problem to the development of the pots-genomic era. In this work we use an optimization method, the Generalized Simulated Annealing (GSA), which is based on Tsallis' generalized thermostatistics, to investigate the protein folding problem. Although GSA is a generic procedure, its efficiency depends not only on the appropriate choice of parameters, but also on topological characteristics of the energy hypersurface. By mapping all the GSA parameters, it can be possible to reduce the number of possible choices of them. That also allows an analysis of its effects on the algorithm behavior. As a initial step, we apply GSA to known structures, such as polyalanines. In sequence, we also apply GSA to three more peptides of ribosomal P proteins, which are of considerable importance on the comprehension of Chagas' heart disease. Each one contains 13 amino acids and differ only on the third residue by a non-conservative mutation. As these peptides do not have experimentally resolved structure, we analyze results obtained from GSA followed by Molecular Dynamics simulations. Validity of these results is studied such that, in the future, unknown structures can be determined by this technique with a higher degree of confidence.

The Rijndael cryptosystem uses a particular polynomial to create its constants. All calculations within the encryption and decryption layers are based on this polynomial. This arouse the curiosity to see what happens if the polynomial is substituted by other polynomials. This paper’s main area of study is to investigate the consequences of using different polynomials to construct the Rijndael cryptosystem. To do so, as a phase of this study, a Mathematica package has been created to ease the investigations. As the second phase, using the aforementioned package, some kind of diffusion analysis has been done on the newly constructed Rijndael-like cryptosystems. The fundamental challenge was to figure out the reason of having the particular polynomial chosen. By the end of the experiment, we concluded that choosing other polynomials with the same characteristics as an ingredient of the Rijndael algorithm, does not have any perceptible effects on the diffusion level.

Das Campusnetz - neue Strukturen und Funktionen Neues vom WWW-Server Umstellung der HOME-Verzeichnisse vom NFS ins AFS AFS löst NFS ab! Neue Rechnersysteme - zur allgemeinen Nutzung Superskalarrechner - Inbetriebnahme und Nutzungsmöglichkeiten PC-Integration via SAMBA-Server CD-ROM im Netz Die Programmpakete MATHEMATICA und ANSYS Ueberblick ueber /uni/global-Software Ein weihnachtliches Problem?

Drug metabolism plays an important role in drug absorption and drug elimination. Therefore, it is crucial to understand the mechanism and kinetics of drug metabolism by various drug-metabolizing enzymes (DMEs). Cytochrome P450 enzymes (CYPs) are responsible for the metabolism of more than 60% of the top 200 prescribed drugs. X-ray and NMR data of CYP enzyme suggest that relatively large and flexible active sites are capable of multi-substrate binding. Due to the multiple substrate-binding, CYP reactions tend to show non-Michaelis Menten kinetics (atypical kinetics), multiple metabolite formation and sequential metabolism.To investigate the complexity of cytochrome P450 kinetics, saturation curves and intrinsic clearances (CLint) were simulated for single substrate and multi-substrate models using rate equations and numerical analysis. These models were combined with multiple product formation and sequential metabolism and simulations were performed with random error. All simulation and model fitting was performed using Mathematica. A concentration-dependent metabolite ratio plot can be observed from multi-substrate binding kinetics. Use of single substrate models to characterize multi-substrate data can result in inaccurate kinetic parameters and poor clearance predictions. It has been shown that use of different substrate concentrations may lead to highly variable in vitro CLint estimations when sigmoidal kinetics are observed. Comparing results for use of standard velocity equations with ordinary differential equations (ODEs) clearly shows that ODEs are more versatile and provide better parameter estimates. It would be difficult to derive concentration-velocity relationships for complex models, but these relationships can be easily modeled using numerical methods and ODEs. The model drug diazepam (DZP) was chosen as the probe substrate to demonstrate complex CYP kinetics with specific CYP enzyme sources, including rat liver microsome (RLM), human liver microsome (HLM), purified CYP enzyme isoforms and rat hepatocytes. All saturation curves display non-Michaelis-Menten kinetics, form multiple primary metabolites, and are sequentially metabolized to secondary metabolites. In addition, the sequential metabolism and disposition would be characterized in hepatocytes incubation under flow conditions. To provide in vivo evidence of the atypical kinetics and investigate CYP-mediated sequential metabolism, preliminary intravascular (IV) dosing PK studies with male rats was performed for DZP. In general, DZP and its metabolites were quantitated by LC/MS/MS. Numerical methods were used to solve ODEs and parameterize micro and macro rate constants for the models. It has been shown that more complex models that include explicit enzyme-product complexes can well characterize the datasets for diazepam sequential metabolism with CYP3A4. Uncommon DZP metabolite PK profiles are observed in rat PK studies. In summary, methods of in vitro data analysis are compared, new assays are developed, and new modeling approaches for complex drug and metabolite pharmacokinetics are being investigated. / Pharmaceutical Sciences

Thesis (M. Sc. (Applied Mathematics)) -- University of Limpopo, 2022 / Nanofluids are a class of heat transfer fluids created by suspending nanoparticles in base fluids. Due to their enhanced thermal conductivity, nanofluids are fast replacing conventional heat transfer fluids like water, mineral oil, ethylene glycol and others. They contribute to advancement of technology and modernity through pertinent applications in fields such as biomedical, automotive industry, cooling technologies and many others. This study documents a survey of nanofluids and their applications and an investigation of peristaltic nanofluid flow through a two dimensional microchannel with and without slip effects. Peristaltic fluid transport plays an important role in engineering, technology, science and physiology. The Buongiorno model formulation is employed and the governing equations for peristaltic nanofluid flow in a two dimensional microchannel are non-dimensionalised and solved semi-analytically using the Adomian decomposition method. Series solutions for axial velocity, temperature and nanoparticle concentration profiles are coded into symbolic package MATHEMATICA for easy computation of the numerical solutions. The effects of the various parameters embedded in the model are simulated graphically and discussed quantitatively and qualitatively. The results are compared with those in literature that were obtained using other approximate analytical methods and the homotopy analysis method. The study revealed that the Brownian motion, thermophoresis, buoyance and the slip parameters have significant influence on the peristaltic flow axial velocity, temperature and nanoparticle concetration profiles. In the flow without slip, both the Brownian motion and thermophoresis parameters caused a cooling effect around the channel walls and a marginal temperature enhancement in the channel core region and significant flow reversal was noticed in the channel half-space with maximum axial velocity recording in the channel core region. In the slip flow, both Brownian motion and thermophorisis had a retardation effect on the nanoparticle concentration profile.

Made available in DSpace on 2015-03-04T18:51:09Z (GMT). No. of bitstreams: 1 TeseFlavia.pdf: 12428230 bytes, checksum: 6fb8e9ea53da0aa51093c702fb32bc4a (MD5) Previous issue date: 2009-06-06 / Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior / As the genome sequencing advances, the comprehension of protein structures becomes a crucial extension to these progresses. In spite of the numerous recent technological advances, experimental determination of protein terciary structures is still very slow compared to the accumulated data from amino acid sequences. That is what makes the protein folding a central problem to the development of the pots-genomic era. In this work we use an optimization method, the Generalized Simulated Annealing (GSA), which is based on Tsallis' generalized thermostatistics, to investigate the protein folding problem. Although GSA is a generic procedure, its efficiency depends not only on the appropriate choice of parameters, but also on topological characteristics of the energy hypersurface. By mapping all the GSA parameters, it can be possible to reduce the number of possible choices of them. That also allows an analysis of its effects on the algorithm behavior. As a initial step, we apply GSA to known structures, such as polyalanines. In sequence, we also apply GSA to three more peptides of ribosomal P proteins, which are of considerable importance on the comprehension of Chagas' heart disease. Each one contains 13 amino acids and differ only on the third residue by a non-conservative mutation. As these peptides do not have experimentally resolved structure, we analyze results obtained from GSA followed by Molecular Dynamics simulations. Validity of these results is studied such that, in the future, unknown structures can be determined by this technique with a higher degree of confidence. / Com os rápidos avanços no seqüenciamento do genoma, a compreensão da estrutura de proteínas torna-se uma extensão crucial a esses progressos. Apesar dos significativos avanços tecnológicos recentes, a determinação experimental da estrutura terciária de proteínas ainda é muito lenta se comparada com a taxa de acúmulo de dados das seqüências de aminoácidos. Isto torna o enovelamento de proteínas um problema central para o desenvolvimento da biologia pós-genômica. Em nosso trabalho, fazemos uso de um método de otimização, o Generalized Simulated Annealing (GSA), baseado na termoestatística generalizada por Tsallis. Embora o GSA seja um procedimento geral, sua eficiência depende não apenas da escolha apropriada de parâmetros, mas também das características topológicas da hiper--superfície de energia da função custo. Com o mapeamento dos parâmetros necessários à aplicação do GSA, pode-se reduzir significativamente o número de escolhas, além de tornar possível uma análise do efeito dos parâmetros no comportamento do algoritmo. Como passo inicial, usamos estruturas conhecidas, com as quais os resultados obtidos com o GSA possam ser comparados, como é o caso das polialaninas. Além disso, aplicamos, o GSA a três peptídeos de proteínas ribossomais da família P, de considerável importância no estudo da doença de Chagas. Cada um possui 13 aminoácidos, diferindo em apenas uma mutação não conservativa no terceiro aminoácido. Como os peptídeos não possuem estrutura experimentalmente resolvida, analisamos os resultados obtidos com GSA seguidos por simulações de Dinâmica Molecular. A validade destes resultados é estudada, de forma que, no futuro, estruturas desconhecidas possam ser determinadas com certo grau de confiabilidade.

Made available in DSpace on 2016-04-27T16:57:34Z (GMT). No. of bitstreams: 1 Katia Vigo Ingar.pdf: 7484950 bytes, checksum: 70bd251a7d421ffddde7fa79693993a3 (MD5) Previous issue date: 2014-11-05 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work aimed to analyze the process of visualization during the learning of notions of maximum and minimum local values in functions of two real variables by students of engineering. The methodology of the study is the Artigue Didactic Engineering. The theoretical reference was based on the theory of Semiotic Register by Duval, particularly in the perceptive, discursive, operational and sequential apprehension of a graphic register represented in the CAS Mathematica and in the articulation between the graphic and algebraic registers. Our theoretical referential was also based on the Theory of Didactic Situation by Brousseau, for we got started with situations which have as their main frame the position of the professor-researcher who faces a group of students in a milieu formed by a computer laboratory, questionings and feedback. The a posteriori analysis of didactic situations helped us see that the students presented difficulties converting the register from natural language to algebraic but, anyway, they coordinated three registers of semiotics representation: natural language, algebraic and graphic. In the graphic register presented in the CAS Mathematica, through operational apprehension and by means of optical, positional and mereologic modifications, the students identified the visual variables inherent to the graphic register. To the students it was not easy to articulate the visual variables with the meaningful values of the algebraic register presented in the definitions and theorems of maximum and minimum values of functions of two real variables. Validating results was not simple for them either. Therefore, the study of visualization through the theory of Semiotic Register by Duval proved itself to be the way to the apprehension of maximum and minimum local values of functions of two real variables / Esta pesquisa tem por objetivo analisar o processo de visualização durante a aprendizagem das noções de valores máximos e mínimos locais de funções de duas variáveis reais, de alunos de engenharia. A metodologia do estudo é a Engenharia Didática de Artigue. E o referencial teórico está baseado na Teoria dos Registros de Representação Semiótica de Duval, especificamente nas apreensões perceptiva, discursiva, operatória e sequencial de um registro gráfico representado no CAS Mathematica, e na articulação entre o registro gráfico e o algébrico. Nosso referencial teórico fundamentou-se, também, na teoria das Situações Didáticas de Brousseau, uma vez que iniciamos com a proposta de situações, em cujo cenário está o professor-pesquisador diante de um grupo de alunos, em um milieu constituído por um laboratório de computação, além dos questionamentos e devoluções. Por meio da análise a posteriori das situações didáticas, percebe-se que os alunos apresentaram dificuldades em realizar a conversão do registro da língua natural para o algébrico, mas, mesmo assim, coordenaram três registros de representação semiótica: língua natural, algébrico e gráfico. Já no registro gráfico representado no CAS Mathematica, pela apreensão operatória e por meio das modificações ótica, posicional e mereológica, identificaram as variáveis visuais próprias do registro gráfico, porém, tiveram dificuldade em articulá-las com os valores significantes do registro algébrico, apresentado nas definições e teoremas de valores máximos e mínimos de funções de duas variáveis reais, e em validar os resultados. Portanto, o estudo da visualização, mediante a teoria dos Registros de Representação Semiótica de Duval, mostrou ser um meio para a aprendizagem dos valores máximos e mínimos locais de funções de duas variáveis reais

This paper main goal is to introduce the basic language and programming styles of the mathematical software Mathematica (5.2), and applies it to solve problems in algebra, calculus, linear algebra, probability and statistics. We hope readers can enhance the interest of learning mathematics by the aid of software, verify the common theorem using the software, and solving mathematical problems.

Η κατά συμμετρίες ανάλυση είναι μια σύγχρονή και αποτελεσματική μέθοδος ανάλυσης του μαθηματικού πεδίου των Διαφορικών Εξισώσεων. Στα πλεονεκτήματα της, ο αλγοριθμικός τρόπος με τον οποίο μπορούμε να βρούμε τις συμμετριες ενός συστήματος και η κατακευή λύσεων από αυτές. Όμως, όπως και κάθε άλλη μέθοδος έτσι και αυτή έχει τα μειονεκτήματα της, το μέγεθος και η πολυπλοκότητα των ενδιάμεσων υπολογισμών που απαιτούνται για την εύρεση των συμμετρίων ενός συστήματος αυξάνεται εκθετικά σε σχέση με αυτό. Γεγονός που καθιστά τους υπολογισμούς αυτούς με το χέρι χρονοβόρους και επιρρεπής σε σφάλματα και συνεπώς την ανάγκη για την χρήση αξιόπιστων συμβολικών προγραμμάτων επιτακτική. Για τον σκοπό αυτό αναπτύξαμε το συμβολικό πακέτο Sym για το αλγεβρικό σύστημα Mathematica. Το συμβολικό αυτό πακέτο περιέχει στοιχεία τεχνικής νοημοσύνης και εξιδικευμένες συμβολικές μεθόδους. Στοιχεία που το καθιστούν ένα αποτελεσματικό και ευέλικτο μαθηματικό εργαλείο τόσο στον ερευνητικό τομέα όσο και στην εκπαίδευση. Το παρόν διδακτορικό χωρίζεται σε δύο μέρη, στο πρώτο παρουσιάζουμε τις βασικές έννοιες της κατα συμμετρίες ανάλυσης διαφορικών εξισώσεων και τους λόγους για τους οποίους η χρήση συμβολικών προγραμμάτων βρίσκει πρόσφορο έδαφος. Στο δεύτερο μέρος, παρουσιάζουμε το συμβολικό πακέτο Sym και δύο ερευνητικά αποτελέσματα της χρήσης του. Όσο αναφορά το ίδιο το πακέτο, δίνουμε τα βασικά του χαρακτηριστικά , τον τρόπο λειτουργίας του και τα οφέλη του σε σχέση με τα ήδη υπάρχοντα συμβολικά πακέτα για την εύρεση συμμετριών. Η χρηστικότητα του παρουσιάζεται μέσω δύο ερευνητικών αποτελεσμάτων. Στο πρώτο, εξετάζουμε ενα πρόβλημα από την περιοχή της Γενικής Σχετικότητας, την εύρεση βαρυτικών κυμάτων. Οι συμμετρίες των εξισώσεων πεδίου του Einstein για την μετρική του Bondi καθορίζονται μέσω του Sym και υποβιβάζουμε με αυτές την τάξη του μή γραμμικού συστήματος. Με υποθέσεις εργασίας πάνω στο σύστημα αυτό δίνουμε ειδικές λύσεις οι οποίες είχαν προκύψει παλίοτερα με άλλες μεθόδους. Τέλος, παρουσιάζουμε τις μελλοντικές μας κατευθύνσεις προς την καθορισμό νέων λύσεων με την σωστή φυσική συμπεριφορά που επιβάλει το πρόβλημα. Στο δεύτερο, δίνουμε μια προτότυπη διαδικασία κατηγοριοποίησης διαφορικών εξισώσεων χρησιμοποιώντας τις ένοιες της πλήρους ομάδας συμετρίας και της αξιοσημείωτης κατά Lie διαφορικής εξίσωσης. Με βάση αυτή, επιτυγχάνουμε την συνθέση διαφορικών εξισώσεων κατασκευάζοντας έτσι καινούργιες οικογένεις διαφορικών εξισώσεων περιέχοντες τις αρχικές μας εξισώσεις. / The symmetry analysis is a modern and effective method of mathematical field of differential equations. On its advantages, the algorithmic way for determining the symmetries and constructing solutions. Like any other method it also has its disadvantages; the size and the complexity of the intermediate calculations needed for giving the symmetries is increased exponentially with respect to the equation under investigation. This fact renders the calculations unmanageable by hand and error prone. The need for reliable and fast symbolic tools is apparent. For this reason, we developed a symbolic package called Sym based on the Mathematica program. The package employing artificial intelligent elements and specialized symbolic methods is an effective and versatile mathematical tool ideal for research and education alike. The present thesis consists of two parts; on the first we present the basic notions of the mathematical theory and the reasons that symbolic tools can be utilized. On the second part, we present the symbolic package Sym itself along with two new result employing it. As for the package itself, we give the basic characteristics, its functionality and the benefits using it against the existing programs. Its usefulness is presented through two results. On the first, we study a problem from General Relativity, finding solutions describing gravity waves. The symmetries of the Einstein’s field equations for the radiating Bondi metric are determined from Sym. Using them we reduce the non-linear system. Using specific ansatzes we arrive to specific solutions already found using other methods. Finally, we present our future directions for finding new solutions with the correct physical behavior. On the second, we describe a new procedure for classifying differential equations using the notions of complete symmetry groups and Lie remarkability. Using this procedure we achieved by starting with a set of differential equation to construct a new family that includes the initial set. Future directions include finding a way to link the solutions of the newly constructed family with the solutions of the equations that we use for constructing it.

Zwischen 1630 und 1650 vollzog sich ein Wandel in Athanasius Kirchers Vermittlung des musikalischen Wissens: Musik konzipierte er im Zusammenhang der Universalwissenschaft immer mehr als Zeichen des Weltbildes im Kontext einer christlich-neuplatonischen Pansemiose. Die Studie arbeitet dies am Beispiel der "Institutiones mathematicae" (ca. 1630), der "Mathematica curiosa" (ca. 1640) und der "Musurgia universalis" (1650) heraus. Besonderes Augenmerk gilt Kirchers Umgang mit seinen Quellen, insbesondere Nikolaus von Kues, Robert Fludd und der Tradition der Philosophia perennis. / Between 1630 and 1650, a change in Athanasius Kircher's way to communicate the knowledge of music took place: Within the context of universal science, he conceptualised music increasingly as a symbol for his world view and its Christian-Neoplatonic pansemiosis. This study discusses these issues based on Kircher's "Institutiones mathematicae" (c1630), "Mathematica curiosa" (c1640), and "Musurgia universalis" (1650). Special emphasis lies on Kircher's use of his sources, particularly Nicholas of Cusa, Robert Fludd, and the tradition of Perennial philosophy.