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Auto-regulation, a process wherein a protein negatively regulates its own production, is a common motif in gene expression networks. Negative feedback in gene expression plays a critical role in buffering intracellular fluctuations in protein concentrations around optimal value. Due to the nonlinearities present in these feedbacks, moment dynamics are typically not closed, in the sense that the time derivative of the lower-order statistical moments of the protein copy number depends on high-order moments. Moment equations are closed by expressing higher-order moments as nonlinear functions of lower-order moments, a technique commonly referred to as moment closure. Here, we compare the performance of different moment closure techniques. Our results show that the commonly used closure method, which assumes a priori that the protein population counts are normally distributed, performs poorly. In contrast, conditional derivative-matching, a novel closure scheme proposed here provides a good approximation to the exact moments across different parameter regimes. In summary our study provides a new moment closure method for studying stochastic dynamics of genetic negative feedback circuits, and can be extended to probe noise in more complex gene networks.

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Hyperspectral imaging (HSI) is used in a wide range of applications such as remote sensing, space imagery, mineral detection, and exploration. Unfortunately, it is difficult to acquire hyperspectral images with high spatial and spectral resolution due to instrument limitations. The super-resolution techniques are used to reconstruct low-resolution hyperspectral images. However, traditional superresolution (SR) approaches do not allow direct use of both spatial and spectral information, which is a decisive for an optimal reconstruction. This paper proposes a single image SR algorithm for HSI. The algorithm uses the fact that the spatial and spectral information can be integrated to make an accurate estimate of the high-resolution HSI. To achieve this, two types of spatio-spectral downsampling, and a three-dimensional interpolation are proposed in order to increase coherence between the spatial and spectral information. The resulting reconstructions using the proposed method are up to 2 dB better than traditional SR approaches. Keywords:Hyperspectral imaging, spatio-spectral dimension, three-dimensional interpolation, hyperspectral downsampling. RESUMENLas imágenes hiperespectrales (HSI) son de vital importancia en una amplia gama de aplicaciones, tales como la teledetección, imágenes espaciales, la detección y la exploración de minerales. Desafortunadamente, es difícil adquirir HSI de alta resolución espacio-espectral debido a las limitaciones de los equipos de sensado. Para obtener versiones de HSI de alta calidad se usan técnicas tradicionales de superresolución. Éstas técnicas no permiten el uso directo de la información espacial y espectral que son un factor decisivo para una óptima reconstrucción. En este trabajo se propone la implementación de un novedoso algoritmo de superresolución de una sola imagen hiperespectral. El algoritmo integra la información espacial y espectral en las HSI para realizar una estimación precisa de alta resolución. Esta integración se obtiene mediante el uso de dos tipos de muestreo espacio-espectral y un interpolador tridimensional, que permite aumentar la coherencia de la información inherente en la imagen. Las imágenes resultantes son superiores hasta 2 dB comparas con reconstrucciones obtenidas por enfoques tradicionales.Palabras clave: Imágenes hiperespectrales, dimensión especial-espectral, interpolación tridimensional, sub-muestreo hiperespectral.

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