Numbers and sets

In this paper I discuss the intuition behind Frege's and Russell's definitions of numbers as sets, as well as Benacerraf's criticism of it. I argue that Benacerraf's argument is not as strong as some philosophers tend to think. Moreover, I examine an alternative to the Fregean-Russellian definition of numbers proposed by Maddy, and point out some problems faced by it.

How real are real numbers?

We discuss mathematical and physical arguments against continuity and in favor of discreteness, with particular emphasis on the ideas of Émile Borel (1871-1956).

Solving Leontief Input-Output Model with Trapezoidal Fuzzy Numbers and Gauss-Seidel Algorithm

In this work a fuzzy linear system is used to solve Leontief input-output model with fuzzy entries. For solving this model, we assume that the consumption matrix from di erent sectors of the economy and demand are known. These assumptions heavily depend on the information obtained from the industries. Hence uncertainties are involved in this information. The aim of this work is to model these uncertainties and to address them by fuzzy entries such as fuzzy numbers and LR-type fuzzy numbers (triangular and trapezoidal). Fuzzy linear system has been developed using fuzzy data and it is solved using Gauss-Seidel algorithm. Numerical examples show the e ciency of this algorithm. The famous example from Prof. Leontief, where he solved the production levels for U.S. economy in 1958, is also further analyzed.

A quantitative view on fuzzy numbers

Since its introduction, fuzzy set theory has become a useful tool in the mathematical modelling of problems in Operations Research and many other fields. The number of applications is growing continuously. In this thesis we investigate a special type of fuzzy set, namely fuzzy numbers. Fuzzy numbers (which will be considered in the thesis as possibility distributions) have been widely used in quantitative analysis in recent decades. In this work two measures of interactivity are defined for fuzzy numbers, the possibilistic correlation and correlation ratio. We focus on both the theoretical and practical applications of these new indices. The approach is based on the level-sets of the fuzzy numbers and on the concept of the joint distribution of marginal possibility distributions. The measures possess similar properties to the corresponding probabilistic correlation and correlation ratio. The connections to real life decision making problems are emphasized focusing on the financial applications. We extend the definitions of possibilistic mean value, variance, covariance and correlation to quasi fuzzy numbers and prove necessary and sufficient conditions for the finiteness of possibilistic mean value and variance. The connection between the concepts of probabilistic and possibilistic correlation is investigated using an exponential distribution. The use of fuzzy numbers in practical applications is demonstrated by the Fuzzy Pay-Off method. This model for real option valuation is based on findings from earlier real option valuation models. We illustrate the use of number of different types of fuzzy numbers and mean value concepts with the method and provide a real life application.

Monte Carlo Hypothesis Testing with The Sharpe Ratio

The purpose of this master thesis was to perform simulations that involve use of random number while testing hypotheses especially on two samples populations being compared weather by their means, variances or Sharpe ratios. Specifically, we simulated some well known distributions by Matlab and check out the accuracy of an hypothesis testing. Furthermore, we went deeper and check what could happen once the bootstrapping method as described by Effrons is applied on the simulated data. In addition to that, one well known RobustSharpe hypothesis testing stated in the paper of Ledoit and Wolf was applied to measure the statistical significance performance between two investment founds basing on testing weather there is a statistically significant difference between their Sharpe Ratios or not. We collected many literatures about our topic and perform by Matlab many simulated random numbers as possible to put out our purpose; As results we come out with a good understanding that testing are not always accurate; for instance while testing weather two normal distributed random vectors come from the same normal distribution. The Jacque-Berra test for normality showed that for the normal random vector r1 and r2, only 94,7% and 95,7% respectively are coming from normal distribution in contrast 5,3% and 4,3% failed to shown the truth already known; but when we introduce the bootstrapping methods by Effrons while estimating pvalues where the hypothesis decision is based, the accuracy of the test was 100% successful. From the above results the reports showed that bootstrapping methods while testing or estimating some statistics should always considered because at most cases the outcome are accurate and errors are minimized in the computation. Also the RobustSharpe test which is known to use one of the bootstrapping methods, studentised one, were applied first on different simulated data including distribution of many kind and different shape secondly, on real data, Hedge and Mutual funds. The test performed quite well to agree with the existence of statistical significance difference between their Sharpe ratios as described in the paper of Ledoit andWolf.

Spontaneous poisoning by larvae of Perreyia flavipes (Pergidae) in sheep

From a flock of 175 Texel sheep 25 animals died after consumption of a sawfly larvae subsequently identified as Perreyia flavipes. The disease occurred in June-July 2006 on a farm located in the county of Encruzilhada do Sul, Rio Grande do Sul, Brazil. Although there were 11 cattle in the same paddock, none of them was affected. High numbers of compact masses containing up to 150 larvae were scattered in the paddock where the animals were grazing. Most affected sheep showed severe apathy during 24-36 h before death, but weakness, muscular tremors and depression were also observed. Necropsy was performed on six sheep and the main macroscopic lesions were hemorrhages in the subcutaneous tissues, endocardium, gallbladder wall, and abomasal mucosa. In all animals was found hydrothorax, hydropericardium, ascites, and mild jaundice. Edema in the abomasal folds, mesentery, perirenal tissues, and gallbladder wall were also seen. The livers were yellowish with disseminated pinpoint hemorrhages in the parenchyma and had an enhanced lobular pattern. Perreyia flavipes larval body fragments and heads were found in the forestomach contents of the six sheep. Feces were scant, dry and formed balls coated by mucus and streaks of blood. Similar contents were also present at the end of the cecum. Prominent microscopic lesions included severe and diffuse periacinar or massive necrosis of hepatocytes associated with multifocal random hemorrhages. Diffuse necrosis of lymphoid follicles in lymph nodes and Peyer's patches, lymphoid depletion and necrosis in germinative centers of the spleen, and diffuse vacuolization in the renal tubular epithelia were also seen.

Numbers and Languages

The thesis presents results obtained during the authors PhD-studies. First systems of language equations of a simple form consisting of just two equations are proved to be computationally universal. These are systems over unary alphabet, that are seen as systems of equations over natural numbers. The systems contain only an equation X+A=B and an equation X+X+C=X+X+D, where A, B, C and D are eventually periodic constants. It is proved that for every recursive set S there exists natural numbers p and d, and eventually periodic sets A, B, C and D such that a number n is in S if and only if np+d is in the unique solution of the abovementioned system of two equations, so all recursive sets can be represented in an encoded form. It is also proved that all recursive sets cannot be represented as they are, so the encoding is really needed. Furthermore, it is proved that the family of languages generated by Boolean grammars is closed under injective gsm-mappings and inverse gsm-mappings. The arguments apply also for the families of unambiguous Boolean languages, conjunctive languages and unambiguous languages. Finally, characterizations for morphisims preserving subfamilies of context-free languages are presented. It is shown that the families of deterministic and LL context-free languages are closed under codes if and only if they are of bounded deciphering delay. These families are also closed under non-codes, if they map every letter into a submonoid generated by a single word. The family of unambiguous context-free languages is closed under all codes and under the same non-codes as the families of deterministic and LL context-free languages.

Non-Linear Unsteady Aerodynamic Response Approximation Using Multi-Layer Functionals

Non-linear functional representation of the aerodynamic response provides a convenient mathematical model for motion-induced unsteady transonic aerodynamic loads response, that accounts for both complex non-linearities and time-history effects. A recent development, based on functional approximation theory, has established a novel functional form; namely, the multi-layer functional. For a large class of non-linear dynamic systems, such multi-layer functional representations can be realised via finite impulse response (FIR) neural networks. Identification of an appropriate FIR neural network model is facilitated by means of a supervised training process in which a limited sample of system input-output data sets is presented to the temporal neural network. The present work describes a procedure for the systematic identification of parameterised neural network models of motion-induced unsteady transonic aerodynamic loads response. The training process is based on a conventional genetic algorithm to optimise the network architecture, combined with a simplified random search algorithm to update weight and bias values. Application of the scheme to representative transonic aerodynamic loads response data for a bidimensional airfoil executing finite-amplitude motion in transonic flow is used to demonstrate the feasibility of the approach. The approach is shown to furnish a satisfactory generalisation property to different motion histories over a range of Mach numbers in the transonic regime.

Composite artistry in the Book of Numbers : a study in biblical narrative conventions

The present thesis discusses the coherence or lack of coherence in the book of Numbers, with special regard to its narrative features. The fragmented nature of Numbers is a well-known problem in research on the book, affecting how we approach and interpret it, but to date there has not been any thorough investigation of the narrative features of the work and how they might contribute to the coherence or the lack of coherence in the book. The discussion is pursued in light of narrative theory, and especially in connection to three parameters that are typically understood to be invoked in the interpretation of narratives: 1) a narrative paradigm, or ‘story,’ meaning events related to each other temporally, causally, and thematically, in a plot with a beginning, middle, and end; 2) discourse, being the expression plane of a narrative, or the devices that an author has at hand in constructing a narrative; 3) the situation or languagegame of the narrative, prototypical examples being factual reports, which seeks to depict a state of affairs, and storytelling narratives, driven by a demand for tellability. In view of these parameters the present thesis argues that it is reasonable to form four groups to describe the narrative material of Numbers: genuine narratives (e.g. Num 12), independent narrative sequences (e.g. Num 5:1-4), instrumental scenes and situations (e.g. Num 27:1-5), and narrative fragments (e.g. Num 18:1). These groups are mixed throughout with non-narrative materials. Seen together, however, the narrative features of these groups can be understood to create an attenuated narrative sequence from beginning to end in Numbers, where one thing happens after another. This sequence, termed the ‘larger story’ of Numbers, concerns the wandering of Israel from Sinai to Moab. Furthermore, the larger story has a fragmented plot. The end-point is fixed on the promised land, Israel prepares for the wandering towards it (Num 1-10), rebels against wandering and the promise and is sent back into the wilderness (Num 13-14), returns again after forty years (Num 21ff.), and prepares for conquering the land (Num 22-36). Finally, themes of the promised land, generational succession, and obedience-disobedience, operate in this larger story. Purity is also a significant theme in the book, albeit not connected to plot in the larger story. All in all, sequence, plot, and theme in the larger story of Numbers can be understood to bring some coherence to the book. However, neither aspect entirely subsumes the whole book, and the four groups of narrative materials can also be understood to underscore the incoherence of the work in differentiating its variegated narrative contents. Numbers should therefore be described as an anthology of different materials that are loosely connected through its narrative features in the larger story, with the aim of informing Israelite identity by depicting a certain period in the early history of the people.

Random amplified polymorphic DNA profiles as a tool for the characterization of Brazilian keratitis isolates of the genus Acanthamoeba

The genus Acanthamoeba comprises free-living amebae identified as opportunistic pathogens of humans and other animal species. Morphological, biochemical and molecular approaches have shown wide genetic diversity within the genus. In an attempt to determine the genetic relatedness among isolates of Acanthamoeba we analyzed randomly amplified polymorphic DNA (RAPD) profiles of 11 Brazilian isolates from cases of human keratitis and 8 American type culture collection (ATCC) reference strains. We found that ATCC strains belonging to the same species present polymorphic RAPD profiles whereas strains of different species show very similar profiles. Although most Brazilian isolates could not be assigned with certainty to any of the reference species, they could be clustered according to pattern similarities. The results show that RAPD analysis is a useful tool for the rapid characterization of new isolates and the assessment of genetic relatedness of Acanthamoeba spp. A comparison between RAPD analyses and morphological characteristics of cyst stages is also discussed.

Normal skin of HIV-infected individuals contains increased numbers of dermal CD8 T cells and normal numbers of Langerhans cells

Dysregulation of the skin immune system (SIS) could explain the high prevalence of skin disorders in HIV+ individuals. The present study was carried out to determine whether alterations in the cell population of SIS and epidermal immunoactivation occur in the normal skin of HIV+ individuals. Forty-five biopsies were taken from the normal upper arm skin of 45 HIV+ patients and of 15 healthy controls. HIV+ individuals were divided into three categories according to their CD4 cell blood count (<200, 200-499 and ³500/µl). Hematoxylin-eosin was used to stain tissue sections for morphological analysis and immunohistochemistry was used for the evaluation of the frequency of macrophages, Langerhans cells, and CD lymphocyte subsets. In addition, semiquantitative analysis of LFA-1, ICAM-1 and HLA-DR was determined in epidermal cells. Macrophages, Langerhans cells, and CD lymphocyte subsets did not differ significantly between any of the patient categories and the control group. When all HIV+ individuals were compared as a group to the control group, a significant increase in dermal CD8+ T lymphocytes (P < 0.01) and lower CD4-CD8 ratios (P < 0.01) were observed in the HIV+ individuals. Epidermal ICAM-1 and HLA-DR expression was negative in both HIV+ and normal skin biopsies. No evidence of a depletion of the SIS population or of epidermal immunoactivation in normal skin from HIV+ individuals was demonstrable, suggesting that alterations in the central immune system are not necessarily reflected in the SIS of HIV-infected patients.

Random amplification of polymorphic DNA reveals clonal relationships among enteropathogenic Escherichia coli isolated from non-human primates and humans

Enteropathogenic Escherichia coli (EPEC) strains are important agents of infantile diarrhea all over the world, gaining even greater importance in developing countries. EPEC have also been isolated from various animal species, but most isolates belong to serotypes that differ from those recovered from humans. However, it has been demonstrated that several isolates from non-human primates belong to the serogroups and/or serotypes related to those implicated in human disease. The objective of this study was to evaluate the genetic differences between thirteen strains isolated from non-human primates and the same number of strains isolated from human infections. Human isolates belonged to the same serogroup/serotype as the monkey strains and the evaluation was done by analysis of random amplified polymorphic DNA. Dendrogram analysis showed that there was no clustering between human and monkey strains. Human and non-human isolates of the EPEC serotypes O127:H40 and O128:H2 shared 90 and 87% of their bands, respectively, indicating strong genomic similarity between the strains, leading to the speculation that they may have arisen from the same pathogenic clone. To our knowledge, this study is the first one comparing genomic similarity between human and non-human primate strains and the results provide further evidence that monkey EPEC strains correlate with human EPEC, as suggested in a previous investigation.

Random-start controlled ovarian stimulation for emergency fertility preservation in a patient with myelodysplastic syndrome: a case report

This study reports a case of a gonadotropin-releasing hormone agonist trigger in a young female with myelodysplastic syndrome (MDS) who underwent fertility preservation using random-start controlled ovarian stimulation. This method involves the stimulation of the ovary regardless of a patient's menstrual-cycle phase. A review of the related literature is also provided. A 17-year-old patient was diagnosed with MDS and required initiation of peripheral blood stem cell transplantation within a maximum of 3 weeks and was in the luteal phase of the menstrual cycle when the possibility of attempting preservation of fertility was presented to her. She opted for a random-start controlled ovarian stimulation with gonadotropins. With successful hemorrhagic prophylaxis, 17 oocytes were retrieved including 10 mature and 7 immature oocytes. Of the immature oocytes, 3 were successfully matured in vitro and a vitrification protocol was used to freeze the 13 mature oocytes.

Optimization of random amplified polymorphic DNA protocol for molecular identification of Lophius gastrophysus

Lophius gastrophysus has important commercial value in Brazil particularly for foreign trade. In this study, we described the optimization of Random Amplified Polymorphic DNA (RAPD) protocol for identification of L. gastrophysus. Different conditions (annealing temperatures, MgCl concentrations, DNA quantity) were tested to find reproducible and adequate profiles. Amplifications performed with primers A01, ² A02 and A03 generate the best RAPD profiles when the conditions were annealing temperature of 36ºC, 25 ng of DNA quantity and 2.5 mM MgCl2. Exact identification of the species and origin of marine products is necessary and RAPD could be used as an accurate, rapid tool to expose commercial fraud.

Análise da pureza genética e discriminação de cultivares de vinca (Catharanthus roseus (L.) G.Don) usando "random amplified polymorphic DNA" em DNA extraído de sementes e folhas

A técnica "Random Amplified Polymorphic DNA" (RAPD) surgiu como uma ferramenta útil para testar a pureza genética e a discriminação de cultivares em muitas espécies. É uma técnica simples, rápida, relativamente de baixo custo e permite o uso de DNA extraído de sementes secas, o que é muito importante em um programa de análise de sementes. O uso desta tecnologia no teste da pureza genética pode ser muito interessante para algumas espécies, como a vinca (Catharanthus roseus (L.) G.Don), pois pouco se conhece a respeito da seqüência de seu DNA. É interessante, também, pelo fato de existir grande número de "primers" comercialmente disponíveis, que podem ser prontamente utilizados para gerar dados. Essa técnica pode ser mais facilmente utilizada para gerar padrões de bandas polimórficas suficientes para discriminar genótipos diferentes. Todavia, no presente estudo, os padrões RAPD de bandas obtidas de amostras de DNA extraído de sementes de vinca em "bulk" foram não-consistentes, o mesmo ocorrendo com o uso de DNA extraído de sementes individuais de um mesmo cultivar, o que evidencia que a técnica não é aplicável para testar a pureza genética e a discriminação de cultivares de vinca. Entretanto, os padrões de bandas RAPD gerados a partir de DNA extraído de tecido foliar de plântulas foram mais reproduzíveis e poderiam ser considerados na caracterização de cultivares.