Optimal polygonal L1 linearization and fast interpolation of nonlinear systems

The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using polygonal (continuous piecewise linear) models under the L1 norm. A thorough error analysis is developed to guide an optimal design of two kinds of polygonal approximations in the asymptotic case of a large budget of evaluation subintervals N. The method allows the user to obtain the level of linearization (N) for a target approximation error and vice versa. It is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), allowing real-time performance of computationally demanding applications. The quality and efficiency of the technique has been measured in detail on two nonlinear functions that are widely used in many areas of scientific computing and are expensive to evaluate.

Robust Image Registration with Global Intensity Transformation

This paper presents a registration method for images with global illumination variations. The method is based on a joint iterative optimization (geometric and photometric) of the L1 norm of the intensity error. Two strategies are compared to directly find the appropriate intensity transformation within each iteration: histogram specification and the solution obtained by analyzing the necessary optimality conditions. Such strategies reduce the search space of the joint optimization to that of the geometric transformation between the images.

Learning an L1-regularized Gaussian Bayesian Network in the Equivalence Class Space

Learning the structure of a graphical model from data is a common task in a wide range of practical applications. In this paper, we focus on Gaussian Bayesian networks, i.e., on continuous data and directed acyclic graphs with a joint probability density of all variables given by a Gaussian. We propose to work in an equivalence class search space, specifically using the k-greedy equivalence search algorithm. This, combined with regularization techniques to guide the structure search, can learn sparse networks close to the one that generated the data. We provide results on some synthetic networks and on modeling the gene network of the two biological pathways regulating the biosynthesis of isoprenoids for the Arabidopsis thaliana plant

Qualitative behaviour of L1 and L2 standard deviation in insulations measurements according to standard UNE EN ISO 140-4

Knowledge of the uncertainty of measurement of testing results is important when results have to be compared with limits and specifications. In the measurement of sound insulation following standards UNE EN ISO 140-4 the uncertainty of the final magnitude is mainly associated to the average sound pressure levels L1 and L2 measured. A parameter that allows us to quantify the spatial variation of the sound pressure level is the standard deviation of the pressure levels measured at different points of the room. In this work, for a wide number of measurements following standards UNE EN ISO 140-4 we analyzed qualitatively the behaviour of the standard deviation for L1 and L2. The study of sound fields in enclosed spaces is very difficult. There are a wide variety of rooms with different sound fields depending on factors as volume, geometry and materials. In general, we observe that the L1 and L2 standard deviations contain peaks and dips independent on characteristics of the rooms at single frequencies that could correspond to critical frequencies of walls, floors and windows or even to temporal alterations of the sound field. Also, in most measurements according to UNE EN ISO 140-4 a large similitude between L1 and L2 standard deviation is found. We believe that such result points to a coupled system between source and receiving rooms, mainly at low frequencies the shape of the L1 and L2 standard deviations is comparable to the velocity level standard deviation on a wall

Arabidopsis DELLA and two HD-ZIP transcription factors regulate GA signalling in the epidermis through the L1 cis-element

Gibberellins (GAs) are plant hormones that affect plant growth and regulate gene expression differentially across tissues. To study the molecular mechanisms underlying GA signaling in Arabidopsis thaliana, we focused on a GDSL lipase gene (LIP1) induced by GA and repressed by DELLA proteins. LIP1 contains an L1 box promoter sequence, conserved in the promoters of epidermis-specific genes, that is bound by ATML1, an HD-ZIP transcription factor required for epidermis specification. In this study, we demonstrate that LIP1 is specifically expressed in the epidermis and that its L1 box sequence mediates GA-induced transcription. We show that this sequence is overrepresented in the upstream regulatory regions of GA-induced and DELLA-repressed transcriptomes and that blocking GA signaling in the epidermis represses the expression of L1 box–containing genes and negatively affects seed germination. We show that DELLA proteins interact directly with ATML1 and its paralogue PDF2 and that silencing of both HD-ZIP transcription factors inhibits epidermal gene expression and delays germination. Our results indicate that, upon seed imbibition, increased GA levels reduce DELLA protein abundance and release ATML1/PDF2 to activate L1 box gene expression, thus enhancing germination potential.