A multiplicação e a divisão de números naturais: uma análise de manuais escolares de 1.º ciclo

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Educação Matemática na Educação Pré-escolar e nos 1.º e 2.º ciclos do Ensino Básico

Unmixing hyperspectral data: independent and dependent component analysis

The development of high spatial resolution airborne and spaceborne sensors has improved the capability of ground-based data collection in the fields of agriculture, geography, geology, mineral identification, detection [2, 3], and classification [4–8]. The signal read by the sensor from a given spatial element of resolution and at a given spectral band is a mixing of components originated by the constituent substances, termed endmembers, located at that element of resolution. This chapter addresses hyperspectral unmixing, which is the decomposition of the pixel spectra into a collection of constituent spectra, or spectral signatures, and their corresponding fractional abundances indicating the proportion of each endmember present in the pixel [9, 10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. The linear mixing model holds when the mixing scale is macroscopic [13]. The nonlinear model holds when the mixing scale is microscopic (i.e., intimate mixtures) [14, 15]. The linear model assumes negligible interaction among distinct endmembers [16, 17]. The nonlinear model assumes that incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [18]. Under the linear mixing model and assuming that the number of endmembers and their spectral signatures are known, hyperspectral unmixing is a linear problem, which can be addressed, for example, under the maximum likelihood setup [19], the constrained least-squares approach [20], the spectral signature matching [21], the spectral angle mapper [22], and the subspace projection methods [20, 23, 24]. Orthogonal subspace projection [23] reduces the data dimensionality, suppresses undesired spectral signatures, and detects the presence of a spectral signature of interest. The basic concept is to project each pixel onto a subspace that is orthogonal to the undesired signatures. As shown in Settle [19], the orthogonal subspace projection technique is equivalent to the maximum likelihood estimator. This projection technique was extended by three unconstrained least-squares approaches [24] (signature space orthogonal projection, oblique subspace projection, target signature space orthogonal projection). Other works using maximum a posteriori probability (MAP) framework [25] and projection pursuit [26, 27] have also been applied to hyperspectral data. In most cases the number of endmembers and their signatures are not known. Independent component analysis (ICA) is an unsupervised source separation process that has been applied with success to blind source separation, to feature extraction, and to unsupervised recognition [28, 29]. ICA consists in finding a linear decomposition of observed data yielding statistically independent components. Given that hyperspectral data are, in given circumstances, linear mixtures, ICA comes to mind as a possible tool to unmix this class of data. In fact, the application of ICA to hyperspectral data has been proposed in reference 30, where endmember signatures are treated as sources and the mixing matrix is composed by the abundance fractions, and in references 9, 25, and 31–38, where sources are the abundance fractions of each endmember. In the first approach, we face two problems: (1) The number of samples are limited to the number of channels and (2) the process of pixel selection, playing the role of mixed sources, is not straightforward. In the second approach, ICA is based on the assumption of mutually independent sources, which is not the case of hyperspectral data, since the sum of the abundance fractions is constant, implying dependence among abundances. This dependence compromises ICA applicability to hyperspectral images. In addition, hyperspectral data are immersed in noise, which degrades the ICA performance. IFA [39] was introduced as a method for recovering independent hidden sources from their observed noisy mixtures. IFA implements two steps. First, source densities and noise covariance are estimated from the observed data by maximum likelihood. Second, sources are reconstructed by an optimal nonlinear estimator. Although IFA is a well-suited technique to unmix independent sources under noisy observations, the dependence among abundance fractions in hyperspectral imagery compromises, as in the ICA case, the IFA performance. Considering the linear mixing model, hyperspectral observations are in a simplex whose vertices correspond to the endmembers. Several approaches [40–43] have exploited this geometric feature of hyperspectral mixtures [42]. Minimum volume transform (MVT) algorithm [43] determines the simplex of minimum volume containing the data. The MVT-type approaches are complex from the computational point of view. Usually, these algorithms first find the convex hull defined by the observed data and then fit a minimum volume simplex to it. Aiming at a lower computational complexity, some algorithms such as the vertex component analysis (VCA) [44], the pixel purity index (PPI) [42], and the N-FINDR [45] still find the minimum volume simplex containing the data cloud, but they assume the presence in the data of at least one pure pixel of each endmember. This is a strong requisite that may not hold in some data sets. In any case, these algorithms find the set of most pure pixels in the data. Hyperspectral sensors collects spatial images over many narrow contiguous bands, yielding large amounts of data. For this reason, very often, the processing of hyperspectral data, included unmixing, is preceded by a dimensionality reduction step to reduce computational complexity and to improve the signal-to-noise ratio (SNR). Principal component analysis (PCA) [46], maximum noise fraction (MNF) [47], and singular value decomposition (SVD) [48] are three well-known projection techniques widely used in remote sensing in general and in unmixing in particular. The newly introduced method [49] exploits the structure of hyperspectral mixtures, namely the fact that spectral vectors are nonnegative. The computational complexity associated with these techniques is an obstacle to real-time implementations. To overcome this problem, band selection [50] and non-statistical [51] algorithms have been introduced. This chapter addresses hyperspectral data source dependence and its impact on ICA and IFA performances. The study consider simulated and real data and is based on mutual information minimization. Hyperspectral observations are described by a generative model. This model takes into account the degradation mechanisms normally found in hyperspectral applications—namely, signature variability [52–54], abundance constraints, topography modulation, and system noise. The computation of mutual information is based on fitting mixtures of Gaussians (MOG) to data. The MOG parameters (number of components, means, covariances, and weights) are inferred using the minimum description length (MDL) based algorithm [55]. We study the behavior of the mutual information as a function of the unmixing matrix. The conclusion is that the unmixing matrix minimizing the mutual information might be very far from the true one. Nevertheless, some abundance fractions might be well separated, mainly in the presence of strong signature variability, a large number of endmembers, and high SNR. We end this chapter by sketching a new methodology to blindly unmix hyperspectral data, where abundance fractions are modeled as a mixture of Dirichlet sources. This model enforces positivity and constant sum sources (full additivity) constraints. The mixing matrix is inferred by an expectation-maximization (EM)-type algorithm. This approach is in the vein of references 39 and 56, replacing independent sources represented by MOG with mixture of Dirichlet sources. Compared with the geometric-based approaches, the advantage of this model is that there is no need to have pure pixels in the observations. The chapter is organized as follows. Section 6.2 presents a spectral radiance model and formulates the spectral unmixing as a linear problem accounting for abundance constraints, signature variability, topography modulation, and system noise. Section 6.3 presents a brief resume of ICA and IFA algorithms. Section 6.4 illustrates the performance of IFA and of some well-known ICA algorithms with experimental data. Section 6.5 studies the ICA and IFA limitations in unmixing hyperspectral data. Section 6.6 presents results of ICA based on real data. Section 6.7 describes the new blind unmixing scheme and some illustrative examples. Section 6.8 concludes with some remarks.

Vertex component analysis: a geometric-based approach to unmix hyperspectral data

Hyperspectral remote sensing exploits the electromagnetic scattering patterns of the different materials at specific wavelengths [2, 3]. Hyperspectral sensors have been developed to sample the scattered portion of the electromagnetic spectrum extending from the visible region through the near-infrared and mid-infrared, in hundreds of narrow contiguous bands [4, 5]. The number and variety of potential civilian and military applications of hyperspectral remote sensing is enormous [6, 7]. Very often, the resolution cell corresponding to a single pixel in an image contains several substances (endmembers) [4]. In this situation, the scattered energy is a mixing of the endmember spectra. A challenging task underlying many hyperspectral imagery applications is then decomposing a mixed pixel into a collection of reflectance spectra, called endmember signatures, and the corresponding abundance fractions [8–10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. Linear mixing model holds approximately when the mixing scale is macroscopic [13] and there is negligible interaction among distinct endmembers [3, 14]. If, however, the mixing scale is microscopic (or intimate mixtures) [15, 16] and the incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [17], the linear model is no longer accurate. Linear spectral unmixing has been intensively researched in the last years [9, 10, 12, 18–21]. It considers that a mixed pixel is a linear combination of endmember signatures weighted by the correspondent abundance fractions. Under this model, and assuming that the number of substances and their reflectance spectra are known, hyperspectral unmixing is a linear problem for which many solutions have been proposed (e.g., maximum likelihood estimation [8], spectral signature matching [22], spectral angle mapper [23], subspace projection methods [24,25], and constrained least squares [26]). In most cases, the number of substances and their reflectances are not known and, then, hyperspectral unmixing falls into the class of blind source separation problems [27]. Independent component analysis (ICA) has recently been proposed as a tool to blindly unmix hyperspectral data [28–31]. ICA is based on the assumption of mutually independent sources (abundance fractions), which is not the case of hyperspectral data, since the sum of abundance fractions is constant, implying statistical dependence among them. This dependence compromises ICA applicability to hyperspectral images as shown in Refs. [21, 32]. In fact, ICA finds the endmember signatures by multiplying the spectral vectors with an unmixing matrix, which minimizes the mutual information among sources. If sources are independent, ICA provides the correct unmixing, since the minimum of the mutual information is obtained only when sources are independent. This is no longer true for dependent abundance fractions. Nevertheless, some endmembers may be approximately unmixed. These aspects are addressed in Ref. [33]. Under the linear mixing model, the observations from a scene are in a simplex whose vertices correspond to the endmembers. Several approaches [34–36] have exploited this geometric feature of hyperspectral mixtures [35]. Minimum volume transform (MVT) algorithm [36] determines the simplex of minimum volume containing the data. The method presented in Ref. [37] is also of MVT type but, by introducing the notion of bundles, it takes into account the endmember variability usually present in hyperspectral mixtures. The MVT type approaches are complex from the computational point of view. Usually, these algorithms find in the first place the convex hull defined by the observed data and then fit a minimum volume simplex to it. For example, the gift wrapping algorithm [38] computes the convex hull of n data points in a d-dimensional space with a computational complexity of O(nbd=2cþ1), where bxc is the highest integer lower or equal than x and n is the number of samples. The complexity of the method presented in Ref. [37] is even higher, since the temperature of the simulated annealing algorithm used shall follow a log( ) law [39] to assure convergence (in probability) to the desired solution. Aiming at a lower computational complexity, some algorithms such as the pixel purity index (PPI) [35] and the N-FINDR [40] still find the minimum volume simplex containing the data cloud, but they assume the presence of at least one pure pixel of each endmember in the data. This is a strong requisite that may not hold in some data sets. In any case, these algorithms find the set of most pure pixels in the data. PPI algorithm uses the minimum noise fraction (MNF) [41] as a preprocessing step to reduce dimensionality and to improve the signal-to-noise ratio (SNR). The algorithm then projects every spectral vector onto skewers (large number of random vectors) [35, 42,43]. The points corresponding to extremes, for each skewer direction, are stored. A cumulative account records the number of times each pixel (i.e., a given spectral vector) is found to be an extreme. The pixels with the highest scores are the purest ones. N-FINDR algorithm [40] is based on the fact that in p spectral dimensions, the p-volume defined by a simplex formed by the purest pixels is larger than any other volume defined by any other combination of pixels. This algorithm finds the set of pixels defining the largest volume by inflating a simplex inside the data. ORA SIS [44, 45] is a hyperspectral framework developed by the U.S. Naval Research Laboratory consisting of several algorithms organized in six modules: exemplar selector, adaptative learner, demixer, knowledge base or spectral library, and spatial postrocessor. The first step consists in flat-fielding the spectra. Next, the exemplar selection module is used to select spectral vectors that best represent the smaller convex cone containing the data. The other pixels are rejected when the spectral angle distance (SAD) is less than a given thresh old. The procedure finds the basis for a subspace of a lower dimension using a modified Gram–Schmidt orthogonalizati on. The selected vectors are then projected onto this subspace and a simplex is found by an MV T pro cess. ORA SIS is oriented to real-time target detection from uncrewed air vehicles using hyperspectral data [46]. In this chapter we develop a new algorithm to unmix linear mixtures of endmember spectra. First, the algorithm determines the number of endmembers and the signal subspace using a newly developed concept [47, 48]. Second, the algorithm extracts the most pure pixels present in the data. Unlike other methods, this algorithm is completely automatic and unsupervised. To estimate the number of endmembers and the signal subspace in hyperspectral linear mixtures, the proposed scheme begins by estimating sign al and noise correlation matrices. The latter is based on multiple regression theory. The signal subspace is then identified by selectin g the set of signal eigenvalue s that best represents the data, in the least-square sense [48,49 ], we note, however, that VCA works with projected and with unprojected data. The extraction of the end members exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. As PPI and N-FIND R algorithms, VCA also assumes the presence of pure pixels in the data. The algorithm iteratively projects data on to a direction orthogonal to the subspace spanned by the endmembers already determined. The new end member signature corresponds to the extreme of the projection. The algorithm iterates until all end members are exhausted. VCA performs much better than PPI and better than or comparable to N-FI NDR; yet it has a computational complexity between on e and two orders of magnitude lower than N-FINDR. The chapter is structure d as follows. Section 19.2 describes the fundamentals of the proposed method. Section 19.3 and Section 19.4 evaluate the proposed algorithm using simulated and real data, respectively. Section 19.5 presents some concluding remarks.

Prevalence of intestinal parasitic infection in five farms in Holambra, São Paulo, Brazil

A parasitological survey was carried out on 222 inhabitants of five farms in Holambra, located 30 km north of Campinas, São Paulo, Brazil, on October 1992. Approximately 70% of the inhabitants were found to be infected with at least one species of intestinal parasite. The positive rates of 6 helminths and 7 protozoan species detected are as follows: 5.4% Ascaris lumbricoides; 8.6% Trichuris trichiura; 19.8% Necator americanus; 10.4% Strongyloides stercoralis; 14% Enterobius vermicularis; 0.9% Hymenolepis nana; 3.2% Entamoeba histolytica; 2.7% E. hartmanni; 9.9% E. coli; 14.0% Endolimax nana; 2.3% Iodamoeba butschlii; 10.4% Giardia lamblia; 37.8% Blastocystis hominis. The positive rates of helminth infection were generaly higher in the younger-group under 16 years-old than those in the elder group aged 16 or more, whereas the infection rates of protozoan species were higher in the elder group. The infection rate of Strongyloides was found to be 10.4% by a newly developed sensitive method (an agarplate culture methods).

Every normal logic program has a 2-valued semantics: theory, extensions, applications, implementations

Trabalho apresentado no âmbito do Doutoramento em Informática, como requisito parcial para obtenção do grau de Doutor em Informática

Optimizing potentiometric ionophore and electrode design for environmental on-site control of antibiotic drugs: Application to sulfamethoxazole

Potentiometric sensors are typically unable to carry out on-site monitoring of environmental drug contaminants because of their high limits of detection (LODs). Designing a novel ligand material for the target analyte and managing the composition of the internal reference solution have been the strategies employed here to produce for the first time a potentiometric-based direct reading method for an environmental drug contaminant. This concept has been applied to sulfamethoxazole (SMX), one of the many antibiotics used in aquaculture practices that may occur in environmental waters. The novel ligand has been produced by imprinting SMX on the surface of graphitic carbon nanostructures (CN) < 500 nm. The imprinted carbon nanostructures (ICN) were dispersed in plasticizer and entrapped in a PVC matrix that included (or not) a small amount of a lipophilic additive. The membrane composition was optimized on solid-contact electrodes, allowing near-Nernstian responses down to 5.2 μg/mL and detecting 1.6 μg/mL. The membranes offered good selectivity against most of the ionic compounds in environmental water. The best membrane cocktail was applied on the smaller end of a 1000 μL micropipette tip made of polypropylene. The tip was then filled with inner reference solution containing SMX and chlorate (as interfering compound). The corresponding concentrations were studied for 1 × 10−5 to 1 × 10−10 and 1 × 10−3 to 1 × 10−8 mol/L. The best condition allowed the detection of 5.92 ng/L (or 2.3 × 10−8 mol/L) SMX for a sub-Nernstian slope of −40.3 mV/decade from 5.0 × 10−8 to 2.4 × 10−5 mol/L.

Mixomas Cardíacos, 13 Anos de Experiência no seu Diagnóstico Ecocardiográfico

INTRODUCTION: Transthoracic echocardiography is the method of choice for the diagnosis of cardiac myxomas, but the transesophageal approach provides a better definition of the location and characteristics of the tumor. The authors review their thirteen years' experience on the echocardiographic diagnosis of this pathology. METHODS: From 1994 to 2007, 41 cardiac tumors were diagnosed in our echocardiographic laboratory, of which 27 (65.85%) were cardiac myxomas. The exams and the patients' clinical files were retrospectively reviewed. RESULTS: Of the 27 patients, 22 (81.5%) were female, with a mean age of 62.1 +/- 13.6 years (25-84 years). The predominant clinical features were due to the obstruction caused by the tumor in more than two thirds of the patients, followed by constitutional symptoms in one third and embolic events in 30%. In the lab results, anemia was found in three patients and elevated sedimentation rate and CRP in two. In two patients the myxoma was found by chance. All the cases were of the sporadic type, although we found a prevalence of thyroid disease of 14% (4 patients). All patients underwent urgent surgical resection except one, in whom surgery was refused due to advanced age and comorbidities. The myxomas followed a typical distribution with 24 (88.8%) located in the left atrium, 18 of them attached to the atrial septum (AS) and two to the mitral valve. In one patient, the tumor involved both atria. The other two cases originated in the right atrium at the AS. Embolic phenomena were more frequent in small tumors (p = 0.027) and in those with a villous appearance (p = 0.032). Obstructive manifestations were associated with larger tumors (p = 0.046) and larger left atria (p = 0.048). In our series, there were no deaths during hospitalization or in the follow-up period of 5.2 +/- 3.7 years in 19 patients. There were two recurrences, both patients being successfully reoperated. CONCLUSION: Myxoma is the most common cardiac tumor. Transesophageal echocardiography provides excellent morphologic definition, aiding in diagnosis and follow-up. Most clinical manifestations are obstructive and are associated with larger tumors. Small tumors with a friable appearance have a higher chance of embolization. Surgical resection is usually curative and the long-term prognosis is excellent.

Molecular screening of Plasmodium sp. asymptomatic carriers among transfusion centers from Brazilian Amazon region

The transmission of malaria in Brazil is heterogeneous throughout endemic areas and the presence of asymptomatic Plasmodium sp. carriers (APCs) in the Brazilian Amazon has already been demonstrated. Malaria screening in blood banks is based on the selection of donors in respect to possible risks associated with travel or residence, clinical evidence and/or inaccurate diagnostic methods thereby increasing the probability of transfusion-transmitted infection. We evaluated the frequency of APCs in four blood services in distinct areas of the Brazilian Amazon region. DNA was obtained from 400 human blood samples for testing using the phenol-chloroform method followed by a nested-PCR protocol with species-specific primers. The positivity rate varied from 1 to 3% of blood donors from the four areas with an average of 2.3%. All positive individuals had mixed infections for Plasmodium vivax and Plasmodium falciparum. No significant differences in the results were detected among these areas; the majority of cases originated from the transfusion centres of Porto Velho, Rondônia State and Macapá, Amapá State. Although it is still unclear whether APC individuals may act as reservoirs of the parasite, efficient screening of APCs and malaria patients in Brazilian blood services from endemic areas needs to be improved.

A agressividade entre pares nas EB21 e EB2/3 do agrupamento de escolas Sophia de Mello Breyner

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Estatística e Gestão de Informação

Evaluation of Helicobacter pylory colonization by serologic test (IgG) and dyspepsia in volunteers from the countryside of Monte Negro, in the Brazilian western Amazon region

The present study intended to analyze the seroprevalence of Helicobacter pylori, IgG, and its relation to dyspepsia in a population from the western Amazon region. During the "Projeto Bandeira Científica", a University of São Paulo Medical School program, in Monte Negro's rural areas, state of Rondônia, 266 blood samples were collected from volunteers. The material was tested for IgG antibodies anti-Helicobacter pylori by ELISA method and the participants were also interviewed on dyspepsia, hygiene and social aspects. Participants aged between five and 81 years old (34 years on average), 149 (56%) were female and 117 (44%) male. We found 210 (78.9%) positive, 50 (18.8%) negative and six (2.3%) undetermined samples. Dyspeptic complaints were found in 226 cases (85.2%). There was no statistical association between dyspepsia and positive serology for H. pylori. We concluded that the seroprevalence in all age categories is similar to results found in other studies conducted in developing countries, including those from Brazil. On the other hand, the seroprevalence found in Monte Negro was higher than that reported in developed countries. As expected, there was a progressive increase in the positivity for H. pylori in older age groups.

Simuladores Fisiológicos na avaliação metrológica de esfigmomanómetros

Este documento apresenta uma avaliação sobre o uso dos simuladores fisiológicos como padrão para avaliação metrológica dos esfigmomanómetros automáticos na estimação da pressão sanguínea pelo método não invasivo (PNI). O presente estudo procurou avaliar o enquadramento destes equipamentos com os procedimentos das normas e recomendações usadas para apreciação metrológica dos esfigmomanómetros digitais. No contexto da prática metrológica existente determinou-se a existência de uma oportunidade de melhoria nos processos relacionados. O trabalho procurou obter resposta a diversas questões, relacionando a medição da pressão pelo método não invasivo, com o uso dos simuladores fisiológicos, o contexto em que estes podem ser usados, as formas de simulação, as medições e os resultados, procurando a perspetiva metrológica como enquadramento. As recomendações existentes [1] [2] [3] [4] [5] [6] [7] [8], são muito claras nos procedimentos, validação e nos desvios permitidos para os monitores da tensão arterial (MTA), equipamento que permite a avaliação dos parâmetros fisiológicos do paciente, no entanto, quando se pretende avançar para outro domínio, como o do uso dos simuladores, em particular para a simulação da PNI, não existem recomendações ou normas tão claras, e não existe sobretudo um padrão de referência que imite a natureza dinâmica que caracteriza a pressão sanguínea. O trabalho procurou ainda estabelecer a ligação entre o método clássico de auscultação (o principio de determinação da PS), a técnica digital de medição e os simuladores, para uma melhor compreensão do que é a pressão sanguínea, e como relacionar a problemática da simulação e a de um padrão de referência. Neste trabalho estão ainda presentes abordagens a diversos tópicos, como as validações clínicas, acessórios, ou a metrologia e que influenciam no final os equipamentos e o contexto que se pretende avaliar. Os diversos equipamentos testados procuraram conter amostras diversificadas, quer para os MTA de uso profissional ou doméstico, assim como para os simuladores. A avaliação dos simuladores foi realizada contra um grupo de MTAs. Foi testada a influência na medição, causada pela mudança de acessórios, ou seja, nos resultados, merecendo consideração pela perspetiva metrológica. No resumo dos testes e do estudo sobre este tema, verificou-se que esta tipologia de equipamentos pode contribuir como complemento do processo de calibração típico (estático). Não constitui por si só um método alternativo, mas permitiu estimar possíveis limites de erro e desvio padrão a partir da observação dos resultados práticos, limites esses inferiores aos processos de validação clínica. Atendendo às particularidades, estimou-se como desvio aceitável um erro mais desvio padrão de 5 + 3 mmHg para o processo de simulação. Contudo considera-se ainda importante os testes adicionais em que o simulador permite, ao verificar as medidas de segurança implementadas no equipamento e a condição dos acessórios, que como verificado afetam os resultados. No entanto nem todos os simuladores se mostram adequados a este processo pelo que a qualidade da seleção do equipamento para este fim pode eventualmente reduzir ainda mais os possíveis limites.

Síntese de algicidas da família da bacilamida e rearranjos de dióximas-1,3 cíclicas com vista a dessimetrização funcional

Dissertação para obtenção do Grau de Doutor em Química Orgânica

Intention recognition, commitment and their roles in the evolution of cooperation

Dissertação para obtenção do Grau de Doutor em Informática

Synthesis and characterization of sugar containing hydrophilic and hydrophobic polymers with potential application in medicine

Dissertation toobtaina Master of Science degree in Bioorganics

Sensitivity of polymerase chain reaction for detection of known aliquots of Trypanosoma cruzi in the blood of mice: an in vitro study

To evaluate the sensitivity of polymerase chain reaction (PCR) to reveal known number of trypomastigote in the blood of mice, three separate experiments were done. First: To eight samples of 500mul of normal mice blood, one aliquot of 1, 2, 3, 4, 5, 10, and 50 trypomastigotes respectively, were added. Second and third: 10 aliquots with 1 and 10 with 2 trypomastigotes were added to samples of 500mul of normal mice blood. Positive control: 500mul of blood containing 100,000 trypomastigotes. For kDNA minicircles amplification by PCR the primers:S35 and S36 were used. PCR revealed products of 330 b.p in the positive controls. When only one sample with the aliquots of 1 or 2 trypomastigotes was examined, results were negative; results were positive with aliquots of 3 to 50 trypomastigotes. In the 2nd and 3rd experiments, 9/10 aliquots with one parasite and 9/10 with 2 trypomastigotes were positive revealing a high sensitivity of this reaction. In conclusion, the presence of one single parasite in 500mul of blood, is enough for a positive PCR. This method could be used as a complement to the various parasitological cure tests in treated mice, when low volumes of blood are individually examined.