Matrix Representation of the Stationary Measure for the Multispecies TASEP

In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product formulation and the queueing theory picture of Ferrari and Martin. In particular, in the standard representation, the matrices act on the space of queue lengths. For N > 2 the matrices in fact become tensor products of elements of quadratic algebras. This enables us to give a purely algebraic proof of the stationary measure which we present for N=3.

Design of a Modern Liposome and Bee Venom Formulation for the Traditional VIT-Venom Immunotherapy

Traditional venom immunotherapy uses injections of whole bee venom in buffer or adsorbed in Al (OH)(3) in an expensive, time-consuming way. New strategies to improve the safety and efficacy of this treatment with a reduction of injections would, therefore, be of general interest. It would improve patient compliance and provide socio-economic benefits. Liposomes have a long tradition in drug delivery because they increase the therapeutic index and avoid drug degradation and secondary effects. However, bee venom melittin (Mel) and phospholipase (PLA(2)) destroy the phospholipid membranes. Our central idea was to inhibit the PLA(2) and Mel activities through histidine alkylation and or tryptophan oxidation (with pbb, para-bromo-phenacyl bromide, and/or NBSN-bromosuccinimide, respectively) to make their encapsulations possible within stabilized liposomes. We strongly believe that this formulation will be nontoxic but immunogenic. In this paper, we present the whole bee venom conformation characterization during and after chemical modification and after interaction with liposome by ultraviolet, circular dichroism, and fluorescence spectroscopies. The PLA(2) and Mel activities were, measured indirectly by changes in turbidity at 400(nm), rhodamine leak-out, and hemolysis. The native whole bee venom (BV) presented 78.06% of alpha-helical content. The alkylation (A-BV) and succynilation (S-BV) of BV increased 0.44 and 0.20% of its alpha-helical content. The double-modified venom (S-A-BV) had a 0.74% increase of alpha-helical content. The BV chemical modification induced another change on protein conformations observed by Trp that became buried with respect to the native whole BV. It was demonstrated that the liposomal membranes must contain pbb (SPC:Cho:pbb, 26:7:1) as a component to protect them from aggregation and/or fusion. The membranes containing pbb maintained the same turbidity (100%) after incubation with modified venom, in contrast with pbb-free membranes that showed a 15% size decrease. This size decrease was interpreted as membrane degradation and was corroborated by a 50% rhodamine leak-out. Another fact that confirmed our interpretation was the observed 100% inhibition of the hemolytic activity after venom modification with pbb and NBS (S-A-BV). When S-A-BV interacted with liposomes, other protein conformational changes were observed and characterized by the increase of 1.93% on S-A-BV alpha-helical content and the presence of tryptophan residues in a more hydrophobic environment. In other words, the S-A-BV interacted with liposomal membranes, but this interaction was not effective to cause aggregation, leak-out, or fusion. A stable formulation composed by S-A-BV encapsulated within liposomes composed by SPC:Cho:pbb, at a ratio of 26:7:1, was devised. Large unilamellar vesicles of 202.5 nm with a negative surface charge (-24.29 mV) encapsulated 95% of S-A-BV. This formulation can, now, be assayed on VIT.

A new micro/nanoencapsulated porphyrin formulation for PDT treatment

The highly hydrophobic 5,10,15-triphenyl-20-(3-N-methylpyridinium-yl)porphyrin(3MMe)cationic species was synthesized, characterized and encapsulated in marine atelocollagen/xanthane gum microcapsules by the coacervation method. Further reduction in the capsule size, from several microns down to about 300-400 nm, was carried out successfully by ultrasonic processing in the presence of up to 1.6% Tween 20 surfactant, without affecting the distribution of 3MMe in the oily core. The resulting creamlike product exhibited enhanced photodynamic activity but negligible cytotoxicity towards HeLa cells. The polymeric micro/nanocapsule formulation was found to be about 4 times more phototoxic than the respective phosphatidylcholine lipidic emulsion, demonstrating high potentiality for photodynamic therapy applications. (C) 2009 Elsevier B.V. All rights reserved.

On Aspects of Mathematical Reasoning : Affect and Gender

This thesis explores two aspects of mathematical reasoning: affect and gender. I started by looking at the reasoning of upper secondary students when solving tasks. This work revealed that when not guided by an interviewer, algorithmic reasoning, based on memorising algorithms which may or may not be appropriate for the task, was predominant in the students reasoning. Given this lack of mathematical grounding in students reasoning I looked in a second study at what grounds they had for different strategy choices and conclusions. This qualitative study suggested that beliefs about safety, expectation and motivation were important in the central decisions made during task solving.  But are reasoning and beliefs gendered? The third study explored upper secondary school teachers conceptions about gender and students mathematical reasoning. In this study I found that upper secondary school teachers attributed gender symbols including insecurity, use of standard methods and imitative reasoning to girls and symbols such as multiple strategies especially on the calculator, guessing and chance-taking were assigned to boys. In the fourth and final study I found that students, both male and female, shared their teachers view of rather traditional feminities and masculinities. Remarkably however, this result did not repeat itself when students were asked to reflect on their own behaviour: there were some discrepancies between the traits the students ascribed as gender different and the traits they ascribed to themselves. Taken together the thesis suggests that, contrary to conceptions, girls and boys share many of the same core beliefs about mathematics, but much work is still needed if we should create learning environments that provide better opportunities for students to develop beliefs that guide them towards well-grounded mathematical reasoning. 

Teachers' conceptions about students' mathematical reasoning : Gendered or not?

This study looks at how upper secondary school teachers gender stereotype aspects of students' mathematical reasoning. Girls were attributed gender symbols including insecurity, use of standard methods and imitative reasoning. Boys were assigned the symbols such as multiple strategies especially on the calculator, guessing and chance-taking. 

On the EA-style integrated processing of self-contained mathematical texts

A sound and complete first-order goal-oriented sequent-type calculus is developed with ``large-block'' inference rules. In particular, the calculus contains formal analogues of such natural proof-search techniques as handling definitions and applying auxiliary propositions.

Evidence Algorithm and Processing Formalized Mathematical Texts

The goal of a research programme Evidence Algorithm is a development of an open system of automated proving that is able to accumulate mathematical knowledge and to prove theorems in a context of a self-contained mathematical text. By now, the first version of such a system called a System for Automated Deduction, SAD, is implemented in software. The system SAD possesses the following main features: mathematical texts are formalized using a specific formal language that is close to a natural language of mathematical publications; a proof search is based on special sequent-type calculi formalizing natural reasoning style, such as application of definitions and auxiliary propositions. These calculi also admit a separation of equality handling from deduction that gives an opportunity to integrate logical reasoning with symbolic calculation.

Análise dinâmica de solos submetidos à ação simultânea das três componentes da excitação na base rochosa

Durante a análise sísmica de estruturas complexas, o modelo matemático empregado deveria incluir não só as distribuicões irregulares de massas e de rigidezes senão também à natureza tridimensional da ecitação sísmica. Na prática, o elevado número de graus de liberdade involucrado limita este tipo de análise à disponibilidade de grandes computadoras. Este trabalho apresenta um procedimento simplificado, para avaliar a amplificação do movimento sísmico em camadas de solos. Sua aplicação permitiria estabelecer critérios a partir dos quais avalia-se a necessidade de utilizar modelos de interação solo-estrutura mais complexos que os utilizados habitualmente. O procedimento proposto possui as seguientes características : A- Movimento rígido da rocha definido em termos de três componentes ortagonais. Direção de propagação vertical. B- A ecuação constitutiva do solo inclui as características de não linearidade, plasticidade, dependência da história da carga, dissipação de energia e variação de volume. C- O perfil de solos é dicretizado mediante um sistema de massas concentradas. Utiliza-se uma formulação incremental das equações de movimento com integração directa no domínio do tempo. As propriedades pseudo-elásticas do solo são avaliadas em cada intervalo de integração, em função do estado de tensões resultante da acção simultânea das três componentes da excitação. O correcto funcionamento do procedimento proposto é verificado mediante análises unidimensionais (excitação horizontal) incluindo estudos comparativos com as soluções apresentadas por diversos autores. Similarmente apresentam-se análises tridimensionais (acção simultânea das três componentes da excitação considerando registros sísmicos reais. Analisa-se a influência que possui a dimensão da análise (uma análise tridimensional frente a três análises unidimensionais) na resposta de camadas de solos submetidos a diferentes níveis de exçitação; isto é, a limitação do Princípio de Superposisão de Efeitos.

Towards an ontology for mathematical modeling with application to epidemiology

EMAp - Escola de Matemática Aplicada