Explicit series solution for a glucose-induced electrical activity model of pancreatic beta-cells

In this work, we present the explicit series solution of a specific mathematical model from the literature, the Deng bursting model, that mimics the glucose-induced electrical activity of pancreatic beta-cells (Deng, 1993). To serve to this purpose, we use a technique developed to find analytic approximate solutions for strongly nonlinear problems. This analytical algorithm involves an auxiliary parameter which provides us with an efficient way to ensure the rapid and accurate convergence to the exact solution of the bursting model. By using the homotopy solution, we investigate the dynamical effect of a biologically meaningful bifurcation parameter rho, which increases with the glucose concentration. Our analytical results are found to be in excellent agreement with the numerical ones. This work provides an illustration of how our understanding of biophysically motivated models can be directly enhanced by the application of a newly analytic method.

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.

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.