Algebraic structure for the crossing of balanced and stair nested designs

Stair nesting allows us to work with fewer observations than the most usual form of nesting, the balanced nesting. In the case of stair nesting the amount of information for the different factors is more evenly distributed. This new design leads to greater economy, because we can work with fewer observations. In this work we present the algebraic structure of the cross of balanced nested and stair nested designs, using binary operations on commutative Jordan algebras. This new cross requires fewer observations than the usual cross balanced nested designs and it is easy to carry out inference.

Modifications of MCM-22 zeolite through sequential post-synthesis treatments. Implications on the acidic and catalytic behaviour

Desilication and a combination of alkaline followed by acid treatment were applied to MCM-22 zeolite using two different base concentrations. The samples were characterised by powder X-ray diffraction, Al-27 and Si-29 MAS-NMR spectroscopy, SEM, TEM and low temperature N-2 adsorption. The acidity of the samples was study through pyridine adsorption followed by FTIR spectroscopy and by the analyses of the hydroxyl region. The catalytic behaviour, anticipated by the effect of post-synthesis treatments on the acidity and space available inside the two internal pore systems was evaluated by using the model reaction of m-xylene transformation. The generation of mesoporosity was achieved upon alkaline treatment with 0.05 M NaOH solution and practically no additional gain was obtained when the more concentrate solution, 0.1 M, was used. Instead, Al extraction takes place along with Si, as shown by Si-29 and Al-27 MAS-NMR data, followed by Al deposition as extraframework species. Samples submitted to alkaline plus acid treatments present distinct behaviour. When the lowest NaOH solution was used no relevant effect was observed on the textural characteristics. Additionally, when the acid treatment was performed on an already fragilized MCM-22 structure, due to previous desilication with 0.1 M NaOH solution, the extraction of Al from both internal pore systems promotes their interconnection, evolving from a 2-D to a 3-D porous structure. This transformation has a marked effect in the catalytic behaviour, allowing an increase of m-xylene conversion as a consequence of an easier and faster molecular traffic in the 3-D structure. On the other hand, the continuous deposition of extraframework Al species inside the pores leads to a shape selective effect that privileges the formation of the more valuable isomer p-xylene.

Algorithm-oriented design of efficient many-core architectures applied to dense matrix multiplication

Recent integrated circuit technologies have opened the possibility to design parallel architectures with hundreds of cores on a single chip. The design space of these parallel architectures is huge with many architectural options. Exploring the design space gets even more difficult if, beyond performance and area, we also consider extra metrics like performance and area efficiency, where the designer tries to design the architecture with the best performance per chip area and the best sustainable performance. In this paper we present an algorithm-oriented approach to design a many-core architecture. Instead of doing the design space exploration of the many core architecture based on the experimental execution results of a particular benchmark of algorithms, our approach is to make a formal analysis of the algorithms considering the main architectural aspects and to determine how each particular architectural aspect is related to the performance of the architecture when running an algorithm or set of algorithms. The architectural aspects considered include the number of cores, the local memory available in each core, the communication bandwidth between the many-core architecture and the external memory and the memory hierarchy. To exemplify the approach we did a theoretical analysis of a dense matrix multiplication algorithm and determined an equation that relates the number of execution cycles with the architectural parameters. Based on this equation a many-core architecture has been designed. The results obtained indicate that a 100 mm(2) integrated circuit design of the proposed architecture, using a 65 nm technology, is able to achieve 464 GFLOPs (double precision floating-point) for a memory bandwidth of 16 GB/s. This corresponds to a performance efficiency of 71 %. Considering a 45 nm technology, a 100 mm(2) chip attains 833 GFLOPs which corresponds to 84 % of peak performance These figures are better than those obtained by previous many-core architectures, except for the area efficiency which is limited by the lower memory bandwidth considered. The results achieved are also better than those of previous state-of-the-art many-cores architectures designed specifically to achieve high performance for matrix multiplication.

Detect and pointing algorithm's performance for a planar smart antenna array: a review

An adaptive antenna array combines the signal of each element, using some constraints to produce the radiation pattern of the antenna, while maximizing the performance of the system. Direction of arrival (DOA) algorithms are applied to determine the directions of impinging signals, whereas beamforming techniques are employed to determine the appropriate weights for the array elements, to create the desired pattern. In this paper, a detailed analysis of both categories of algorithms is made, when a planar antenna array is used. Several simulation results show that it is possible to point an antenna array in a desired direction based on the DOA estimation and on the beamforming algorithms. A comparison of the performance in terms of runtime and accuracy of the used algorithms is made. These characteristics are dependent on the SNR of the incoming signal.

Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations

An improved class of nonlinear bidirectional Boussinesq equations of sixth order using a wave surface elevation formulation is derived. Exact travelling wave solutions for the proposed class of nonlinear evolution equations are deduced. A new exact travelling wave solution is found which is the uniform limit of a geometric series. The ratio of this series is proportional to a classical soliton-type solution of the form of the square of a hyperbolic secant function. This happens for some values of the wave propagation velocity. However, there are other values of this velocity which display this new type of soliton, but the classical soliton structure vanishes in some regions of the domain. Exact solutions of the form of the square of the classical soliton are also deduced. In some cases, we find that the ratio between the amplitude of this wave and the amplitude of the classical soliton is equal to 35/36. It is shown that different families of travelling wave solutions are associated with different values of the parameters introduced in the improved equations.

GPU implementation of a hyperspectral coded aperture algorithm for compressive sensing

This paper presents a new parallel implementation of a previously hyperspectral coded aperture (HYCA) algorithm for compressive sensing on graphics processing units (GPUs). HYCA method combines the ideas of spectral unmixing and compressive sensing exploiting the high spatial correlation that can be observed in the data and the generally low number of endmembers needed in order to explain the data. The proposed implementation exploits the GPU architecture at low level, thus taking full advantage of the computational power of GPUs using shared memory and coalesced accesses to memory. The proposed algorithm is evaluated not only in terms of reconstruction error but also in terms of computational performance using two different GPU architectures by NVIDIA: GeForce GTX 590 and GeForce GTX TITAN. Experimental results using real data reveals signficant speedups up with regards to serial implementation.

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.

Hyperspectral unmixing algorithm via dependent component analysis

This paper introduces a new method to blindly unmix hyperspectral data, termed dependent component analysis (DECA). This method decomposes a hyperspectral images into a collection of reflectance (or radiance) spectra of the materials present in the scene (endmember signatures) and the corresponding abundance fractions at each pixel. DECA assumes that each pixel is a linear mixture of the endmembers signatures weighted by the correspondent abundance fractions. These abudances are modeled as mixtures of Dirichlet densities, thus enforcing the constraints on abundance fractions imposed by the acquisition process, namely non-negativity and constant sum. The mixing matrix is inferred by a generalized expectation-maximization (GEM) type algorithm. This method overcomes the limitations of unmixing methods based on Independent Component Analysis (ICA) and on geometrical based approaches. The effectiveness of the proposed method is illustrated using simulated data based on U.S.G.S. laboratory spectra and real hyperspectral data collected by the AVIRIS sensor over Cuprite, Nevada.

Algebraic structure for interaction on mixed models

Binary operations on commutative Jordan algebras, CJA, can be used to study interactions between sets of factors belonging to a pair of models in which one nests the other. It should be noted that from two CJA we can, through these binary operations, build CJA. So when we nest the treatments from one model in each treatment of another model, we can study the interactions between sets of factors of the first and the second models.