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.

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.

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.

Intrapopulational chromosome number variation in Zephyranthes sylvatica Baker (Amaryllidaceae: Hippeastreae) from Northeast Brazil

Zephyranthes Herb. is a taxonomically complex and cytologically variable group, with about 65 species of Neotropical distribution. Chromosome number variability in 32 individuals of a Zephyranthes sylvatica population from Northeast Brazil was investigated. Three cytotypes were found: 2n = 12 (one metacentric, four submetacentric and one acrocentric pairs), in 24 individuals; 2n = 12 + 1B, in five and three individuals with 2n = 18, a triploid cytotype. All diploid individuals showed chromosomes with polymorphism in pair one and two, while in triploids this polymorphism was observed in all chromosome triplets, generally with two homomorphic chromosomes and a higher or lower heteromorphic chromosome. All individuals had reticulated interfasic nucleus and a slightly asymmetric chromosome complement, with one metacentric chromosome pair and the others more submetacentric to acrocentric. These data confirm the cytological variability previously registered for the genus. Mechanisms involved in karyotypic evolution in this population are discussed.

Chromosome studies in some Stevia. Cav. (Compositae) species from Southern Brazil

Karyotypes of six species of the genus Stevia from Southern Brazil were studied, utilizing root tip metaphases. All species were diploid with 2n = 22 chromosomes. It was possible to identify each species by chromosome morphology. The basic chromosome number for Brazilian species of Stevia is X = 11. This number is also found in almost all South American species. We suggest that in Stevia there is an evolutionary trend toward chromosomal rearrangement, caused mainly by pericentric inversions. It was found that, in addition to aneuploidy and polyploidy, chromosomal rearrangements are common in the tribe Eupatorieae.

Chromosome damage in underground coal miners: detection by conventional cytogenetic techniques and by submitting lymphocytes of unexposed individuals to plasma from at-risk groups

Chromosome abnormalities and the mitotic index in lymphocyte cultures and micronuclei in buccal mucosa cells were investigated in a sample of underground mineral coal miners from Southern Brazil. A decreased mitotic index, an excess of micronuclei and a higher frequency of chromosome abnormalities (fragments, polyploidy and overall chromosome alterations) were observed in the miners when compared to age-paired normal controls from the same area. An alternative assay for clastogenesis in occupational exposition was tested by submitting lymphocytes from non-exposed individuals to a pool of plasmas from the exposed population. This assay proved to be very convenient, as the lymphocytes obtained from the same individuals can be used as target as well as control cells. Also, it yielded a larger number of metaphases and of successful cultures than with common lymphocyte cultures from miners. A significantly higher frequency of chromatid gaps, fragments and overall alterations were observed when lymphocytes from control subjects were exposed to miner plasma pools. Control plasma pools did not significantly induce any type of chromosome alterations in the cultures of normal subjects, thus indicating that the results are not due to the effect of the addition of plasma pools per se.

TP53 mutations and loss of heterozygosity of chromosome 17 in colorectal tumors

The incidence of TP53 point mutations and loss of heterozygosity (LOH) of chromosome 17 in colorectal tumors was determined in a group of Brazilian patients. We screened DNA samples from tumors and distal normal mucosa of 39 patients with colorectal cancer, for TP53 mutations by PCR-SSCP (single-strand conformation polymorphism) analysis. Chromosome 17 LOH was investigated using six PCR-based polymorphic markers and one VNTR probe. TP53 mutations were demonstrated in 15/39 of the cases. Mutations were distributed among all exons examined (five to eight), the majority of them being G/C to A/T transitions. LOH of chromosome 17p and 17q was detected in 70 and 46% of the tumors, respectively. There was a significant association between TP53 mutations and LOH in chromosome 17p (P = 0.0035) and 17q (P = 0.03). Although no correlation was observed between TP53 genetic alterations and clinical/ pathological characteristics, the association of TP53 mutations with loss of both chromosome 17 arms may indicate that TP53 inactivation provokes an unstable phenotype in tumor cells in colorectal tumors.

Reading the human Y chromosome: the emerging DNA markers and human genetic history

Reading the human Y chromosome: the emerging DNA markers and human genetic history.

Chromosome polymorphism in Ctenomys minutus (Rodentia-Octodontidae)

A sample of 101 specimens of Ctenomys minutus was collected along its geographic range. Eight karyotypes (2n = 42, 45, 46a, 46b, 47, 48, 49 and 50) were found. The chromosome polymorphisms were due to Robertsonian rearrangements and tandem fusions. The distribution of polymorphisms indicated three population blocks: northern (2n = 49 and 50), central (2n = 46a, 47, and 48) and southern (2n = 42, 45, and 46b). These findings suggest that this species is undergoing a speciation process due to geographic isolation.

Recuperation and improvement of chromosome preparations stained with silver nitrate

Both periodic acid and photographic reagents have been used to remove the silver nitrate residues from cytological preparations. We used potassium ferricyanide to remove AgNO3 salts in cases of excessive chromosome impregnation. This method produced partial decolorization, with contrast enhancement. Counterstaining with Giemsa also promoted a better contrast between chromosome arms and NORs, which were preserved and retained a dark color. Application of this procedure to chromosome preparations treated sequentially for CBG banding/AgNO3 staining promoted complete decolorization of C+ regions, leading to "reverse" C-banding, generally with high contrast.

Chromosome sensitivity to bleomycin in G2 lymphocytes from Down syndrome patients

Several studies have demonstrated that lymphocytes from patients with Down syndrome (DS) exhibit an increased frequency of chromosome aberrations when they are exposed to ionizing radiation or to chemicals at the G0 or G1 phases of the cell cycle, but not at G2, when compared to normal subjects. To determine the susceptibility of DS lymphocytes at G2 phase, bleomycin, a radiomimetic agent, was used to induce DNA breaks in blood cultures from 24 Down syndrome patients. All the patients with DS showed free trisomy 21 (47,XX + 21 or 47,XY + 21). Individuals that showed an average number of chromatid breaks per cell higher than 0.8 were considered sensitive to the drug. No control child showed susceptibility to bleomycin, and among the 24 patients with DS, only one was sensitive to the drug. No significant difference was observed between the two groups, regarding chromatid break frequencies in treated G2 lymphocytes. The distribution of bleomycin-induced breaks in each group of chromosomes was similar for DS and controls. No significant difference was found in the response to bleomycin between male and female subjects. Probably, the main factor involved in chromosome sensitivity of lymphocytes from patients with DS is the phase of the cell cycle in which the cell is treated.

Family names and the length of the Y chromosome in Brazilian blacks

The variability of the lengths of the heterochromatic and euchromatic segments of the human Y chromosome was studied by a quantitative method of densitometric measurement in 60 normal and unrelated black individuals (30 with and 30 without devotional surnames), living in Salvador, Bahia, northeastern Brazil. Thirty normal and unrelated Caucasian individuals of European origin, living in Curitiba, Paraná, south Brazil, were included as controls. The heterochromatic segment and total Y chromosome lengths were greater in caucasians than in blacks without devotional surnames, and these were greater than in blacks with devotional surnames. These findings are in agreement with previous reports of a higher percentage of black ancestry in blacks carrying devotional surnames than those carrying non-devotional ones.

Effect of taxol on chromosome aberrations induced by gamma radiation or by doxorubicin in Chinese hamster ovary cells

Combined therapy with radiation and chemotherapy has being increasingly used in cancer treatment. The effect of combinations of taxol (0.08 mug/ml) with doxorubicin (DXR, 0.5 or 1.0 mug/ml) or gamma radiation (20 or 40 cGy) was examined in two different treatment schedules (pretreatment or simultaneous treatment) using Chinese hamster ovary (CHO) cells treated at the G2 phase of the cell cycle. The results showed that taxol did not have a radiosensitizing effect on the chromosomal aberrations induced by gamma radiation nor did it have a potentiating effect on the chromosomal aberrations induced by DXR in CHO cells treated in the G2 phase of the cell cycle

Chromosome studies in southern Brazilian wheat pest aphids Sitobion avenae, Schizaphis graminum, and Methopolophium dirhodum (Homoptera: Aphididae)

We examined the chromosome set of the aphid species Sitobion avenae, Schizaphis graminum and Methopolophium dirhodum by means of conventional staining and C, NOR, AluI and HaeIII banding methods. These species are considered important pests to several plants of economic interest in Brazil. No variation was observed in the number of chromosomes of S. avenae, whereas there was intraspecific variation in the other two species. Interspecific differences in the response to the banding treatments were observed. Whereas these techniques allowed the identification of several S. graminum chromosome pairs, only the AluI treatment was capable of inducing differential staining in the M. dirhodum chromosomes and no clear patterns emerged when the S. avenae preparations were treated