Spectral solution for the air stripping pollutants removal dynamic model with non linear steady state conditions

This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.

The Port as a “Non Consensual” Organisation: An IC Management Perspective

This paper addresses a gap in the literature concerning the management of Intellectual Capital (IC) in a port, which is a network of independent organizations that act together in the provision of a set of services. As far as the authors are aware, this type of empirical context has been unexplored when regarding knowledge management or IC creation/destruction. Indeed, most research in IC still focus on individual firms, despite the more recent interest placed on the analysis of macro-level units such as regions or nations. In this study, we conceptualise the port as meta-organisation, which has the generic goal of economic development, both for itself and for the region where it is located. It provides us with a unique environment due to its complexity as an “organisation” composed by several organisations, connected by interdependency relationships and, typically, with no formal hierarchy. Accordingly, actors’ interests are not always aligned and in some situations their individual interests can be misaligned with the collective goals of the port. Moreover, besides having their own interests, port actors also have different sources of influence and different levels of power, which can impact on the port’s Collective Intellectual Capital (CIC). Consequently, the management of the port’s CIC can be crucial in order for its goals to be met. With this paper we intend to discuss how the network coordinator (the port authority) manages those complex relations of interest and power in order to develop collaboration and mitigate conflict, thus creating collective intellectual assets or avoiding intellectual liabilities that may emerge for the whole port. The fact that we are studying complex and dynamic processes, about which there is a lack of understanding, in a complex and atypical organisation, leads us to consider the case study as an appropriate method of research. Evidence presented in this study results from preliminary interviews and also from document analysis. Findings suggest that alignment of interests and actions, at both dyadic and networking levels, is critical to develop a context of collaboration/cooperation within the port community and, accordingly, the port coordinator should make use of different types of power in order to ensure that port’s goals are achieved.

Non-colorectal intestinal tract carcinomas in inflammatory bowel disease: results of the 3rd ECCO Pathogenesis Scientific Workshop (II)

Patients with inflammatory bowel diseases (IBD) have an excess risk of certain gastrointestinal cancers. Much work has focused on colon cancer in IBD patients, but comparatively less is known about other more rare cancers. The European Crohn's and Colitis Organization established a pathogenesis workshop to review what is known about these cancers and formulate proposals for future studies to address the most important knowledge gaps. This article reviews the current state of knowledge about small bowel adenocarcinoma, ileo-anal pouch and rectal cuff cancer, and anal/perianal fistula cancers in IBD patients.

Non-enzymatic assay for glucose by using immobilized whole-cells of E. coli containing glucose binding protein fused to fluorescent proteins

Glucose monitoring in vivo is a crucial issue for gaining new understanding of diabetes. Glucose binding protein (GBP) fused to two fluorescent indicator proteins (FLIP) was used in the present study such as FLIP-glu- 3.2 mM. Recombinant Escherichia coli whole-cells containing genetically encoded nanosensors as well as cell-free extracts were immobilized either on inner epidermis of onion bulb scale or on 96-well microtiter plates in the presence of glutaraldehyde. Glucose monitoring was carried out by Förster Resonance Energy Transfer (FRET) analysis due the cyano and yellow fluorescent proteins (ECFP and EYFP) immobilized in both these supports. The recovery of these immobilized FLIP nanosensors compared with the free whole-cells and cell-free extract was in the range of 50–90%. Moreover, the data revealed that these FLIP nanosensors can be immobilized in such solid supports with retention of their biological activity. Glucose assay was devised by FRET analysis by using these nanosensors in real samples which detected glucose in the linear range of 0–24 mM with a limit of detection of 0.11 mM glucose. On the other hand, storage and operational stability studies revealed that they are very stable and can be re-used several times (i.e. at least 20 times) without any significant loss of FRET signal. To author's knowledge, this is the first report on the use of such immobilization supports for whole-cells and cell-free extract containing FLIP nanosensor for glucose assay. On the other hand, this is a novel and cheap high throughput method for glucose assay.

The key role of coligands in novel ruthenium(II)-cyclopentadienyl bipyridine derivatives: Ranging from non-cytotoxic to highly cytotoxic compounds

A new family of eight ruthenium(II)-cyclopentadienyl bipyridine derivatives, bearing nitrogen, sulfur, phosphorous and carbonyl sigma bonded coligands, has been synthesized. Compounds bearing nitrogen bonded coligands were found to be unstable in aqueous solution, while the others presented appropriate stabilities for the biologic assays and pursued for determination of IC50 values in ovarian (A2780) and breast (MCF7 and MDAMB231) human cancer cell lines. These studies were also carried out for the [5: HSA] and [6: HSA] adducts (HSA = human serum albumin) and a better performance was found for the first case. Spectroscopic, electrochemical studies by cyclic voltammetry and density functional theory calculations allowed us to get some understanding on the electronic flow directions within the molecules and to find a possible clue concerning the structural features of coligands that can activate bipyridyl ligands toward an increased cytotoxic effect. X-ray structure analysis of compound [Ru(eta(5)-C5H5)(bipy)(PPh3)][PF6] (7; bipy = bipyridine) showed crystallization on C2/c space group with two enantiomers of the [Ru(eta(5)-C5H5)(bipy)(PPh3)](+) cation complex in the racemic crystal packing. (C) 2015 Elsevier Inc All rights reserved.

Non-venomous snake bite and snake bite without envenoming in a brazilian teaching hospital: analysis of 91 cases

A retrospective survey of 473 cases of snake bite admitted to a Brazilian teaching hospital from 1984 to 1990 revealed 91 cases of bite without envenoming and/or caused by non-venomous snakes. In 17 of these cases the snake was identified, and one patient was bitten by a snake-like reptile (Amphisbaena mertensii). In 43 cases diagnosis was made on clinical grounds (fang marks in the absence of signs of envenoming). The other 30 cases were of patients who complained of being bitten but who did not show any sign of envenoming or fang mark. Most cases occurred in men (66;73%), in the 10-19 years age group (26;29%), in the lower limbs (51/74;69%), between 6 A. M. and 2 P.M. (49;61%) and in the month of April (16; 18%). One patient bitten by Philodryas olfersii developed severe local pain, swelling and redness at the site of the bite, with normal clotting time. The patient bitten by Drymarcon corais was misdiagnosed as being bitten by a snake of the genus Bothrops, was given the specific antivenom, and developed anaphylaxis. One patient bitten by Sibynomorphus mikanii presented prolonged clotting time, and was also given antivenom as a case of Bothrops bite. Correct identification of venomous snakes by physicians is necessary to provide correct treatment to victims of snake bite, avoiding unnecessary distress to the patient, and overprescription of antivenom, which may eventually cause severe untoward effects.

Characterization of the non-apparent clinical form in the initial phase of schistosomiasis mansoni

In this paper the history of 115 recruits that had bathed simultaneously in streams contaminated with Schistosoma mansoni, during military maneuvers, is reported. Thirty four of the infected patients presented the initial phase of the infection diagnosed through epidemiologic, clinical and laboratorial parameters. Three out of the 34 patients did not reveal the clinical picture of the infection, thus being considered representatives of the non-apparent form of the disease. Differences between the intensity of blood eosinophilia, the area of immediate cutaneous reaction and the number of Schistosoma eggs eliminated in the stools proved not to be statistically significant (p>0.05) when the non-apparent and acute cases of schistosomiasis were compared. These cases actually may be considered evidences of the non-apparent form hitherto merely taken for granted in the literature.

Generalized synchronization in a system of several non-autonomous oscillators coupled by a medium

An abstract theory on general synchronization of a system of several oscillators coupled by a medium is given. By generalized synchronization we mean the existence of an invariant manifold that allows a reduction in dimension. The case of a concrete system modeling the dynamics of a chemical solution on two containers connected to a third container is studied from the basics to arbitrary perturbations. Conditions under which synchronization occurs are given. Our theoretical results are complemented with a numerical study.

Antibodies against non-structural c100/3 and structural core antigen of hepatitis C virus (HCV) in hemodialysis patients

Two groups of patients undergoing hemodialysis (HD) maintenance were evaluated for their antibody response to non-structural c100/3 protein and structural core protein of hepatitis C virus (HCV). Forty-six patients (Group 1) never presented liver abnormalities during HD treatment, while 52 patients (Group 2) had either current or prior liver enzyme elevations. Prevalence rates of 32.6% and 41.3% were found for anti-c100/3 and anti-HCV core antibodies, respectively, in patients with silent infections (Group 1). The rate of anti-c100/3 in patients of Group 2 was 71.15% and reached 86.5% for anti-HCV core antibodies. The recognition of anti-c100/3 and anti-core antibodies was significantly higher in Group 2 than in Group 1. A line immunoassay composed of structural and non-structural peptides was used as a confirmation assay. HBV infection, measured by the presence of anti-HBc antibodies, was observed in 39.8% of the patients. Six were HBsAg chronic carriers and 13 had naturally acquired anti-HBs antibodies. The duration of HD treatment was correlated with anti-HCV positivity. A high prevalence of 96.7% (Group 2) was found in patients who underwent more than 5 years of treatment. Our results suggest that anti-HCV core ELISA is more accurate for detecting HCV infection than anti-c100/3. Although the risk associated with the duration of HD treatment and blood transfusion was high, additional factors such as a significant non-transfusional spread of HCV seems to play a role as well. The identification of infective patients by more sensitive methods for HCV genome detection should help to control the transmission of HCV in the unit under study.

Non-uniform printed antenna array for wireless communications in sports arenas

Wireless communications had a great development in the last years and nowadays they are present everywhere, public and private, being increasingly used for different applications. Their application in the business of sports events as a means to improve the experience of the fans at the games is becoming essential, such as sharing messages and multimedia material on social networks. In the stadiums, given the high density of people, the wireless networks require very large data capacity. Hence radio coverage employing many small sized sectors is unavoidable. In this paper, an antenna is designed to operate in the Wi-Fi 5GHz frequency band, with a directive radiation pattern suitable to this kind of applications. Furthermore, despite the large bandwidth and low losses, this antenna has been developed using low cost, off-the-shelf materials without sacrificing quality or performance, essential to mass production. © 2015 EurAAP.

The key role of coligands in novel ruthenium(II)-cyclopentadienyl bipyridine derivatives: ranging from non-cytotoxic to highly cytotoxic compounds

A new family of eight ruthenium(II)-cyclopentadienyl bipyridine derivatives, bearing nitrogen, sulfur, phosphorous and carbonyl sigma bonded coligands, has been synthesized. Compounds bearing nitrogen bonded coligands were found to be unstable in aqueous solution, while the others presented appropriate stabilities for the biologic assays and pursued for determination of IC50 values in ovarian (A2780) and breast (MCF7 and MDAMB231) human cancer cell lines. These studies were also carried out for the [5: HSA] and [6: HSA] adducts (HSA=human serum albumin) and a better performance was found for the first case. Spectroscopic, electrochemical studies by cyclic voltammetry and density functional theory calculations allowed us to get some understanding on the electronic flow directions within the molecules and to find a possible clue concerning the structural features of coligands that can activate bipyridyl ligands toward an increased cytotoxic effect. X-ray structure analysis of compound [Ru(η(5)-C5H5)(bipy)(PPh3)][PF6] (7; bipy=bipyridine) showed crystallization on C2/c space group with two enantiomers of the [Ru(η(5)-C5H5)(bipy)(PPh3)](+) cation complex in the racemic crystal packing.

Prevalence of rubella antibodies in a non-immunized urban population, São Paulo, Brazil

The prevalence of rubella antibodies was evaluated through a ramdom Seroepidemiological survey in 1400 blood samples of 2-14 year old children and in 329 samples of umbilical cord serum. Rubella IgG antibodies were detected by ELISA, and the sera were collected in 1987, five years before the mass vaccination campaign with measles-mumps-rubella vaccine carried out in the city of São Paulo in 1992. A significant increase in prevalence of rubella infection was observed after 6 years of age, and 77% of the individuals aged from 15 to 19 years had detectable rubella antibodies. However, the seroprevalence rose to 90.5% (171/189) in cord serum samples from children whose mothers were 20 to 29 years old, and reached 95.6% in newborns of mothers who were 30 to 34 years old, indicating that a large number of women are infected during childbearing years. This study confirms that rubella infection represents an important Public Health problem in São Paulo city. The data on the seroprevalence of rubella antibodies before the mass vaccination campaign reflects the baseline immunological status of this population before any intervention and should be used to design an adequate vaccination strategy and to assess the Seroepidemiological impact of this intervention.

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.