Spectral and weak polynomial completeness for the porduct of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F , satisfying the following property: for every monic polynomial f(x) = xn + an-1xn-1 + … +a1x + aο over F, with a root in F and aο = (-1)n det(AB), there are nonsingular matrices X, Y ϵ Fnxn such that X A X-1 Y BY-1 has characteristic polynomial f (x). © 2014 © 2014 Taylor & Francis.

New textures for the lepton mass matrices

We study predictive textures for the lepton mass matrices in which the charged-lepton mass matrix has either four or five zero matrix elements while the neutrino Majorana mass matrix has, respectively, either four or three zero matrix elements. We find that all the viable textures of these two kinds share many predictions: the neutrino mass spectrum is inverted, the sum of the light-neutrino masses is close to 0.1 eV, the Dirac phase delta in the lepton mixing matrix is close to either 0 or pi, and the mass term responsible for neutrinoless double-beta decay lies in between 12 and 22 meV. (C) 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license.

Confronting predictive texture zeros in lepton mass matrices with current data

Several popular Ansatze of lepton mass matrices that contain texture zeros are confronted with current neutrino observational data. We perform a systematic chi(2) analysis in a wide class of schemes, considering arbitrary Hermitian charged-lepton mass matrices and symmetric mass matrices for Majorana neutrinos or Hermitian mass matrices for Dirac neutrinos. Our study reveals that several patterns are still consistent with all the observations at the 68.27% confidence level, while some others are disfavored or excluded by the experimental data. The well-known Frampton-Glashow-Marfatia two-zero textures, hybrid textures, and parallel structures (among others) are considered.

Spectral and weak polynomial completeness for the product of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F, satisfying the following property: for every monic polynomial f (x) = x(n) + a(n-1)x(n-1) +... + a(1)x + a(0) over F, with a root in F and a(0) = (-1)(n) det(AB), there are nonsingular matrices X, Y is an element of F-nxn such that XAX(-1)Y BY-1 has characteristic polynomial f (x).

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.

Weakly spectrally complete pair of matrices

Let and be matrices over an algebraically closed field. Let be elements of such that and . We give necessary and sufficient condition for the existence of matrices and similar to and, respectively, such that has eigenvalues.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.

The Shading Sign: Is It Exclusive of Endometriomas?

OBJECTIVES: To investigate if the shading sign is an exclusive MRI feature of endometriomas or endometrioid tumors, and to analyze its different patterns. METHODS: Three hundred and fourty six women with adnexal masses who underwent 1.5/3-T MRI were included in this retrospective, board-approved study. The shading sign was found in 56 patients, but five cases were excluded due to lack of imaging follow-up or histological correlation. The final sample included 51 women. The type of tumor and the pattern of shading were recorded for each case. RESULTS: Thirty endometriomas and five endometrioid carcinomas were found. The remaining 16 cases corresponded to other benign and malignant tumors. The overall sensitivity, specificity, positive predictive value, and negative predictive value were 73%, 93%, 59%, and 96%, respectively. Restricting the analysis to cystic lesions without solid or fat component, sensitivity, specificity, positive predictive value, and negative predictive value were 73%, 96%, 94%, and 80%. Five shading patterns were identified: layering (15.7%), liquid-liquid level (11.8%), homogenous (45.1%), heterogeneous (11.8%), and focal/multifocal shading within a complex mass (19.6%). No significant correlation was found between these patterns and the type of tumor. CONCLUSIONS: The shading sign is not exclusive of endometriomas or endometrioid tumors. Homogenous shading was the most prevalent pattern in endometriomas and half of the cases with focal/multifocal shading within a complex mass were endometrioid carcinomas.

Acute Otitis Media a Reliable Warning Sign for Primary Immunodeficiencies?- A Critical Appraisal

Acute otitis media (AOM) is the most common infection in childhood, resulting from both anatomic and immunologic specificities of this age group. Recurrent AOM has been defined as one of the warning signs for primary immunodeficiencies (PID), In this study we evaluated the strength of recurrent AOM as clinical predictor of PID. Methods: Retrospective study (August 2010 - December 2013) which included all patients referred to PID appointment because of recurrent AOM (= 8 AOM episodes/year). Syndromic patients or those presenting with another warning sign for PID were excluded. Clinical, demographic and laboratory results were analized and statistical analysis was made using SPSS 20. Results: Seventy-five patients were included (median age 37,8 months; 62,7% male gender), corresponding to 15% of all first appointments. Other comorbidities were present in 20% of the patients and 17% had ORL surgery prior to PID referral. In most patients, the immunologic screening consisted on the evaluation of humoral function, but in selected cases other studies were performed (namely complement and lymphocyte immunophenotyping). A PID was identified in 12 children (16,0%) and the majority of these patients had other distinctive feature (personal or familiar antecedent of infection or auto-immunity, 66,7%, p<0,05). Nine children (12,0%) underwent prophylactic cotrimoxazole. The average length of follow-up was 11,2 months. Conclusion: Despite being a very frequent cause of immunologic screening, in this study recurrent AOM was not found to be a good predictor of underlying PID, unless the patients presents other significant personal or family history.

Characterization of sol-gel matrices with entrapped cutinase

Dissertação para obtenção do Grau de Doutor em Engenharia Química e Bioquímica

Kinect-sign

A nova era da informação que se está a assistir tem possibilitado a criação de novas e vastas coleções de intelecto virtual, como por exemplo o Wikipedia, Corsera, entre outros. Estas ferramentas vieram possibilitar a procura por cultura, resoluções de problemas do quotidiano, novos métodos de aprendizagem, por parte da sociedade em geral. Porém, como é habitual, tem-se vindo a verificar uma certa dificuldade inerente por parte de certas minorias sociais, que não possuem as mesmas capacidades de um indivíduo “normal“. Esta dissertação tem como objetivo a criação de uma ferramenta, em formato de jogo sério, para apoiar o ensino de Língua Gestual Portuguesa a um público ouvinte o -“Kinect Sign”. Com este estudo pretende-se explorar as mais recentes ferramentas de desenvolvimento de jogos, mais conhecidas como Authoring Tools e a sua integração com Natural User interfaces, concretamente o sensor Kinect. A solução apresentada neste documento propõe a utilização desta ferramenta a todos os indivíduos iniciantes que necessitem de uma introdução a esta forma de comunicação, para tornar um pouco menos agressiva a entrada no complexo mundo da linguagem gestual. A validação deste trabalho consistiu no desenvolvimento de um jogo protótipo que incentive os jogadores a aprenderem enquanto jogam. Analisaram-se problemas e tecnologias atuais para se chegar a uma estruturação semelhante a um jogo comum disponível em qualquer superfície comercial e websites dedicados ao género. Posterior apresentação a uma população selecionada a fim de analisar a sua opinião e utilidade do modelo desenvolvido, seguindo-se a resposta a um pequeno questionário.

About using serious games to teach (Portuguese) sign language

Sign language is the form of communication used by Deaf people, which, in most cases have been learned since childhood. The problem arises when a non-Deaf tries to contact with a Deaf. For example, when non-Deaf parents try to communicate with their Deaf child. In most cases, this situation tends to happen when the parents did not have time to properly learn sign language. This dissertation proposes the teaching of sign language through the usage of serious games. Currently, similar solutions to this proposal do exist, however, those solutions are scarce and limited. For this reason, the proposed solution is composed of a natural user interface that is intended to create a new concept on this field. The validation of this work, consisted on the implementation of a serious game prototype, which can be used as a source for learning (Portuguese) sign language. On this validation, it was first implemented a module responsible for recognizing sign language. This first stage, allowed the increase of interaction and the construction of an algorithm capable of accurately recognizing sign language. On a second stage of the validation, the proposal was studied so that the pros and cons can be determined and considered on future works.

Analysis of chromium behaviour and speciation during the electrodialytic process

The interest in chromium (Cr) arises from the widespread use of this heavy metal in various industrial processes that cause its release as liquid, solid and gaseous waste into the environment. The impact of Cr on the environment and living organisms primarily depends on its chemical form, since Cr(III) is an essential micronutrient for humans, other animals and plants, and Cr(VI) is highly toxic and a known human carcinogen. This study aimed to evaluate if the electrodialytic process (ED) is an appropriate treatment for Cr removal, through a critical overview of Cr speciation, before and after the ED experiments, to assess possible Cr(III)-Cr(VI) interconversions during the treatment. ED was the treatment technique applied to two types of matrices containing Cr: chromate copper arsenate (CCA) contaminated soil and municipal solid waste incineration (MSWI) fly ash. In order to study Cr remediation, three EDR set-ups were used: a new set-up, the combined cell (2/3C or 3/2C), with three compartments, alternating current between two anodes and different initial experimental conditions, one set-up with three compartments (3C cell) and the other set-up with two compartments (2C cell). The Cr removal rates obtained in this study were between 10-36% for the soil, and 1-13% for the fly ash. The highest Cr removal rates were achieved in the 26 days experiments: 36% for the soil, 13% for the fly ash. Regarding the 13 days experiments, the highest Cr removal rates were attained with the 2/3C set-up: 24% for the soil, 5% for the fly ash. The analysis of Cr(VI) was performed before and after ED experiments to evaluate eventual changes in Cr speciation during the treatment. This analysis was conducted by two methods: USEPA Method 3060A, for the extraction of Cr(VI); and Hach Company Method 8023, for the detection of Cr(VI). Despite the differences in Cr total concentration, both matrices presented a similar speciation, with Cr(III) being the main species found and Cr(VI) less than 3% of Cr total, before and after the treatment. For fly ash, Cr(VI) was initially below the detection limit of the method and remained that way after the treatment. For soil, Cr(VI) decreased after the treatment. Oxidation of Cr(III) to Cr(VI) did not occur during the ED process since there was no increase in Cr(VI) in the matrices after the treatment. Hence, the results of this study indicate that ED is an appropriate technique to remediate matrices containing Cr because it contributes to Cr removal, without causing Cr(III)-Cr(VI) interconversions.