Generalized Schmidt decomposition and classification of three-quantum-bit states

We prove for any pure three-quantum-bit state the existence of local bases which allow one to build a set of five orthogonal product states in terms of which the state can be written in a unique form. This leads to a canonical form which generalizes the two-quantum-bit Schmidt decomposition. It is uniquely characterized by the five entanglement parameters. It leads to a complete classification of the three-quantum-bit states. It shows that the right outcome of an adequate local measurement always erases all entanglement between the other two parties.

Characterization and classification of soils in the Taquari river basin - Pantanal region, state of Mato Grosso do Sul, Brazil

Among the soils in the Mato Grosso do Sul, stand out in the Pantanal biome, the Spodosols. Despite being recorded in considerable extensions, few studies aiming to characterize and classify these soils were performed. The purpose of this study was to characterize and classify soils in three areas of two physiographic types in the Taquari river basin: bay and flooded fields. Two trenches were opened in the bay area (P1 and P2) and two in the flooded field (P3 and P4). The third area (saline) with high sodium levels was sampled for further studies. In the soils in both areas the sand fraction was predominant and the texture from sand to sandy loam, with the main constituent quartz. In the bay area, the soil organic carbon in the surface layer (P1) was (OC) > 80 g kg-1, being diagnosed as Histic epipedon. In the other profiles the surface horizons had low OC levels which, associated with other properties, classified them as Ochric epipedons. In the soils of the bay area (P1 and P2), the pH ranged from 5.0 to 7.5, associated with dominance of Ca2+ and Mg2+, with base saturation above 50 % in some horizons. In the flooded fields (P3 and P4) the soil pH ranged from 4.9 to 5.9, H+ contents were high in the surface horizons (0.8-10.5 cmol c kg-1 ), Ca2+ and Mg² contents ranged from 0.4 to 0.8 cmol c kg-1 and base saturation was < 50 %. In the soils of the bay area (P1 and P2) iron was accumulated (extracted by dithionite - Fed) and OC in the spodic horizon; in the P3 and P4 soils only Fed was accumulated (in the subsurface layers). According to the criteria adopted by the Brazilian System of Soil Classification (SiBCS) at the subgroup level, the soils were classified as: P1: Organic Hydromorphic Ferrohumiluvic Spodosol. P2: Typical Orthic Ferrohumiluvic Spodosol. P3: Typical Hydromorphic Ferroluvic Spodosol. P4: Arenic Orthic Ferroluvic Spodosol.

Automatic Mapping and Classification of Spatial Environmental Data

The paper deals with the development and application of the generic methodology for automatic processing (mapping and classification) of environmental data. General Regression Neural Network (GRNN) is considered in detail and is proposed as an efficient tool to solve the problem of spatial data mapping (regression). The Probabilistic Neural Network (PNN) is considered as an automatic tool for spatial classifications. The automatic tuning of isotropic and anisotropic GRNN/PNN models using cross-validation procedure is presented. Results are compared with the k-Nearest-Neighbours (k-NN) interpolation algorithm using independent validation data set. Real case studies are based on decision-oriented mapping and classification of radioactively contaminated territories.

A colorectal cancer classification system that associates cellular phenotype and responses to therapy.

Colorectal cancer (CRC) is a major cause of cancer mortality. Whereas some patients respond well to therapy, others do not, and thus more precise, individualized treatment strategies are needed. To that end, we analyzed gene expression profiles from 1,290 CRC tumors using consensus-based unsupervised clustering. The resultant clusters were then associated with therapeutic response data to the epidermal growth factor receptor-targeted drug cetuximab in 80 patients. The results of these studies define six clinically relevant CRC subtypes. Each subtype shares similarities to distinct cell types within the normal colon crypt and shows differing degrees of 'stemness' and Wnt signaling. Subtype-specific gene signatures are proposed to identify these subtypes. Three subtypes have markedly better disease-free survival (DFS) after surgical resection, suggesting these patients might be spared from the adverse effects of chemotherapy when they have localized disease. One of these three subtypes, identified by filamin A expression, does not respond to cetuximab but may respond to cMET receptor tyrosine kinase inhibitors in the metastatic setting. Two other subtypes, with poor and intermediate DFS, associate with improved response to the chemotherapy regimen FOLFIRI in adjuvant or metastatic settings. Development of clinically deployable assays for these subtypes and of subtype-specific therapies may contribute to more effective management of this challenging disease.

Comparison between artificial neural networks and maximum likelihood classification in digital soil mapping

Soil surveys are the main source of spatial information on soils and have a range of different applications, mainly in agriculture. The continuity of this activity has however been severely compromised, mainly due to a lack of governmental funding. The purpose of this study was to evaluate the feasibility of two different classifiers (artificial neural networks and a maximum likelihood algorithm) in the prediction of soil classes in the northwest of the state of Rio de Janeiro. Terrain attributes such as elevation, slope, aspect, plan curvature and compound topographic index (CTI) and indices of clay minerals, iron oxide and Normalized Difference Vegetation Index (NDVI), derived from Landsat 7 ETM+ sensor imagery, were used as discriminating variables. The two classifiers were trained and validated for each soil class using 300 and 150 samples respectively, representing the characteristics of these classes in terms of the discriminating variables. According to the statistical tests, the accuracy of the classifier based on artificial neural networks (ANNs) was greater than of the classic Maximum Likelihood Classifier (MLC). Comparing the results with 126 points of reference showed that the resulting ANN map (73.81 %) was superior to the MLC map (57.94 %). The main errors when using the two classifiers were caused by: a) the geological heterogeneity of the area coupled with problems related to the geological map; b) the depth of lithic contact and/or rock exposure, and c) problems with the environmental correlation model used due to the polygenetic nature of the soils. This study confirms that the use of terrain attributes together with remote sensing data by an ANN approach can be a tool to facilitate soil mapping in Brazil, primarily due to the availability of low-cost remote sensing data and the ease by which terrain attributes can be obtained.

Cinema Roads to the Platonic Image of the Cave

The aim of this article is to prove the real possibility of travelling intellectually to the Platonic image of the cave from different films. In this sense, one can speak of explicit references as in The Conformist by B. Bertolucci or in Shadowlands by R. Attenborough -if one bears in mind the Chronicles of Narnia by C. S. Lewis- or The Picture of Dorian Gray ¿if one bears in mind the well-known O. Wilde¿s novel-, but, on other occasions, although the Platonic influence cannot be proved, for instance in The Truman Show, A Room with a View or Brideshead Revisited, one can perfectly think of these films in order to guide the contemporary audiences to that Platonic image, since Plato himself affirms that it deals with an image which can be easily applied and, in first place, to his idealistic philosophy.

Improving Satellite Image Based Forest Inventory by Using A Priori Site Quality Information

Summary

The Cave by José Saramago: Platonic image versus metaphysics

The cave by José Saramago has as a certain reference the image of the cave of book VII of Plato's Republic and, however, Saramago is not an idealistic or metaphysical writer. This article, taking advantage of the applicability with which Plato endowed his image, defends the urge to be open to the messages sent by the earth, by matter, the urge not to become prisoners in the golden caves of the Western society and, finally, the urge to find our freedom in Nature, phýsis, and not far or beyond, metá, it.

The "image" of the cave and the constant temptation to correct Plato: Benjamin Jowettt as an example

Translations of the first chapters of Book VII of Plato's Republic, in which he introduces the well-known image of the cave, eikón, reveals an astonishing and intriguing variety of interpretations of this image: "allegory", "myth", "fable", "parable", "simile" and "comparison", to cite but a few. Taking as an example the work by Benjamin Jowett, the Victorian translator of Plato, remarkable for its textual accuracy and by means of a close analysis of the terms related to the image, this paper insists on the need to neither interpret nor correct the great ideal philosopher, in this case revealing some evident contradictions that arise when this advice is not followed and pointing out the occasional use of terms extraneous to the Platonic lexicon such as "allegory".

Using numerical classification of profiles based on Vis-NIR spectra to distinguish soils from the Piracicaba Region, Brazil

Considering that information from soil reflectance spectra is underutilized in soil classification, this paper aimed to evaluate the relationship of soil physical, chemical properties and their spectra, to identify spectral patterns for soil classes, evaluate the use of numerical classification of profiles combined with spectral data for soil classification. We studied 20 soil profiles from the municipality of Piracicaba, State of São Paulo, Brazil, which were morphologically described and classified up to the 3rd category level of the Brazilian Soil Classification System (SiBCS). Subsequently, soil samples were collected from pedogenetic horizons and subjected to soil particle size and chemical analyses. Their Vis-NIR spectra were measured, followed by principal component analysis. Pearson's linear correlation coefficients were determined among the four principal components and the following soil properties: pH, organic matter, P, K, Ca, Mg, Al, CEC, base saturation, and Al saturation. We also carried out interpretation of the first three principal components and their relationships with soil classes defined by SiBCS. In addition, numerical classification of the profiles based on the OSACA algorithm was performed using spectral data as a basis. We determined the Normalized Mutual Information (NMI) and Uncertainty Coefficient (U). These coefficients represent the similarity between the numerical classification and the soil classes from SiBCS. Pearson's correlation coefficients were significant for the principal components when compared to sand, clay, Al content and soil color. Visual analysis of the principal component scores showed differences in the spectral behavior of the soil classes, mainly among Argissolos and the others soils. The NMI and U similarity coefficients showed values of 0.74 and 0.64, respectively, suggesting good similarity between the numerical and SiBCS classes. For example, numerical classification correctly distinguished Argissolos from Latossolos and Nitossolos. However, this mathematical technique was not able to distinguish Latossolos from Nitossolos Vermelho férricos, but the Cambissolos were well differentiated from other soil classes. The numerical technique proved to be effective and applicable to the soil classification process.

Public-domain software for root image analysis

In the search for high efficiency in root studies, computational systems have been developed to analyze digital images. ImageJ and Safira are public-domain systems that may be used for image analysis of washed roots. However, differences in root properties measured using ImageJ and Safira are supposed. This study compared values of root length and surface area obtained with public-domain systems with values obtained by a reference method. Root samples were collected in a banana plantation in an area of a shallower Typic Carbonatic Haplic Cambisol (CXk), and an area of a deeper Typic Haplic Ta Eutrophic Cambisol (CXve), at six depths in five replications. Root images were digitized and the systems ImageJ and Safira used to determine root length and surface area. The line-intersect method modified by Tennant was used as reference; values of root length and surface area measured with the different systems were analyzed by Pearson's correlation coefficient and compared by the confidence interval and t-test. Both systems ImageJ and Safira had positive correlation coefficients with the reference method for root length and surface area data in CXk and CXve. The correlation coefficient ranged from 0.54 to 0.80, with lowest value observed for ImageJ in the measurement of surface area of roots sampled in CXve. The IC (95 %) revealed that root length measurements with Safira did not differ from that with the reference method in CXk (-77.3 to 244.0 mm). Regarding surface area measurements, Safira did not differ from the reference method for samples collected in CXk (-530.6 to 565.8 mm²) as well as in CXve (-4231 to 612.1 mm²). However, measurements with ImageJ were different from those obtained by the reference method, underestimating length and surface area in samples collected in CXk and CXve. Both ImageJ and Safira allow an identification of increases or decreases in root length and surface area. However, Safira results for root length and surface area are closer to the results obtained with the reference method.