Wavelet-Fourier CORSING techniques for multi-dimensional advection-diffusion-reaction equations

We present and analyze a novel wavelet-Fourier technique for the numerical treatment of multidimensional advection-diffusion-reaction equations based on the CORSING (COmpRessed SolvING) paradigm. Combining the Petrov-Galerkin technique with the compressed sensing approach, the proposed method is able to approximate the largest coefficients of the solution with respect to a biorthogonal wavelet basis. Namely, we assemble a compressed discretization based on randomized subsampling of the Fourier test space and we employ sparse recovery techniques to approximate the solution to the PDE. In this paper, we provide the first rigorous recovery error bounds and effective recipes for the implementation of the CORSING technique in the multi-dimensional setting. Our theoretical analysis relies on new estimates for the local a-coherence, which measures interferences between wavelet and Fourier basis functions with respect to the metric induced by the PDE operator. The stability and robustness of the proposed scheme is shown by numerical illustrations in the one-, two-, and three-dimensional case

Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT

In this paper, we develop a shape optimization-based algorithm for the electrical impedance tomography (EIT) problem of determining a piecewise constant conductivity on a polygonal partition from boundary measurements. The key tool is to use a distributed shape derivative of a suitable cost functional with respect to movements of the partition. Numerical simulations showing the robustness and accuracy of the method are presented for simulated test cases in two dimensions

essHi-C: Essential component analysis of Hi-C matrices

Motivation: Hi-C matrices are cornerstones for qualitative and quantitative studies of genome folding, from its territorial organization to compartments and topological domains. The high dynamic range of genomic distances probed in Hi-C assays reflects in an inherent stochastic background of the interactions matrices, which inevitably convolve the features of interest with largely aspecific ones. Results: Here we introduce a discuss essHi-C, a method to isolate the specific, or essential component of Hi-C matrices from the aspecific portion of the spectrum that is compatible with random matrices. Systematic comparisons show that essHi-C improves the clarity of the interaction patterns, enhances the robustness against sequencing depth, allows the unsupervised clustering of experiments in different cell lines and recovers the cell-cycle phasing of single-cells based on Hi-C data. Thus, essHi-C provides means for isolating significant biological and physical features from Hi-C matrices.Comment: 14 pages, 4 figures. This is the Authors' Original Version of the article, which has been accepted for publication in Bioinformatics published by Oxford University Pres

Damnificados de la reconstrucción post-terremoto. Efectos del modelo en el hábitat rural del Maule

Tras el terremoto y tsunami del 27 de febrero de 2010, la política de reconstrucción implementada por el gobierno de Chile favoreció el liderazgo de los agentes privados en el proceso y propuso soluciones estándar para todos los territorios, con un claro sesgo urbano. Los sectores rurales de la Región del Maule tuvieron que enfrentar un escenario complejo, considerando la debilidad de la institucionalidad local y la falta de incentivos económicos para la actuación del sector privado en la ruralidad, caracterizada por una alta dispersión y baja densidad poblacional. El presente artículo reflexiona acerca de los principales efectos que la política de reconstrucción implementada tuvo sobre la realidad de las comunidades y territorios rurales. Al no existir un marco de política pertinente con el hábitat rural, entendido no solamente como un conjunto de características físicas de un determinado espacio geográfico, sino como el resultado de procesos sociales, históricos e identitarios, los resultados dejan entrever que los programas de intervención pos−terremoto no reconocieron las particularidades del territorio. Esto significó el incremento de la precariedad en el habitar, la pérdida de patrimonio e identidad, y la profundización de los fenómenos de desplazamiento de la población hacia la periferia de las ciudades

A dimension-reduction model for brittle fractures on thin shells with mesh adaptivity

In this paper, we derive a new 2D brittle fracture model for thin shells via dimension reduction, where the admissible displacements are only normal to the shell surface. The main steps include to endow the shell with a small thickness, to express the three-dimensional energy in terms of the variational model of brittle fracture in linear elasticity, and to study the Γ-limit of the functional as the thickness tends to zero. The numerical discretization is tackled by first approximating the fracture through a phase field, following an Ambrosio–Tortorelli like approach, and then resorting to an alternating minimization procedure, where the irreversibility of the crack propagation is rigorously imposed via an inequality constraint. The minimization is enriched with an anisotropic mesh adaptation driven by an a posteriori error estimator, which allows us to sharply track the whole crack path by optimizing the shape, the size, and the orientation of the mesh elements. Finally, the overall algorithm is successfully assessed on two Riemannian settings and proves not to bias the crack propagation

A Dimension-Reduction Model for Brittle Fractures on Thin Shells with Mesh Adaptivity

In this paper we derive a new two-dimensional brittle fracture model for thin shells via dimension reduction, where the admissible displacements are only normal to the shell surface. The main steps include to endow the shell with a small thickness, to express the three-dimensional energy in terms of the variational model of brittle fracture in linear elasticity, and to study the $\Gamma$-limit of the functional as the thickness tends to zero. The numerical discretization is tackled by first approximating the fracture through a phase field, following an Ambrosio-Tortorelli like approach, and then resorting to an alternating minimization procedure, where the irreversibility of the crack propagation is rigorously imposed via an inequality constraint. The minimization is enriched with an anisotropic mesh adaptation driven by an a posteriori error estimator, which allows us to sharply track the whole crack path by optimizing the shape, the size, and the orientation of the mesh elements. Finally, the overall algorithm is successfully assessed on two Riemannian settings and proves not to bias the crack propagation

Model adaptation enriched with an anisotropic mesh spacing for nonlinear equations: application to environmental and CFD problems

Goal of this paper is to suitably combine a model with an anisotropic mesh adaptation for the numerical simulation of nonlinear advection-diffusion-reaction systems and incompressible flows in ecological and environmental applications. Using the reduced-basis method terminology, the proposed approach leads to a noticeable computational saving of the online phase with respect to the resolution of the reference model on nonadapted grids. The search of a suitable adapted model/mesh pair is to be meant, instead, in an offline fashion

Inserción laboral de migrantes en los territorios agrarios de Chile: el caso de la región del Maule

El artículo aborda el proceso de inserción laboral de migrantes en los territorios agrarios chilenos, a partir del caso de la Región del Maule (Chile). Junto con realizar una breve revisión bibliográfica sobre el tema a nivel latinoamericano, se indaga en las motivaciones de las/os inmigrantes para elegir un territorio agrario como lugar de destino, y en sus estrategias de inserción laboral en un contexto caracterizado por una matriz identitaria rural y una estructura de producción local vinculada al ámbito silvoagropecuario. A partir de lo cual, se esbozan algunas reflexiones iniciales sobre las trayectorias laborales es ese sector productivo. Para el desarrollo del estudio, se adoptó una estrategia metodológica mixta, con énfasis en los métodos cualitativos; se realizaron y analizaron 57 entrevistas a migrantes residentes en la Región del Maule. Los resultados muestran que, entre los principales elementos que motivan la elección del Maule como lugar de destino, están las características urbano-rurales del territorio y la posibilidad de acceder a una oferta laboral que –si bien precaria— es abundante, especialmente en el ámbito agrícola. Por otro lado, el patrón de hábitat urbano y la inserción laboral en la rama agrícola de las/os extranjeras/os –especialmente haitianas/os— profundiza la lógica productiva de los territorios agrarios

Topological Constraints in Eukaryotic Genomes and How They Can Be Exploited to Improve Spatial Models of Chromosomes

Several orders of magnitude typically separate the contour length of eukaryotic chromosomes and the size of the nucleus where they are confined. The ensuing topological constraints can slow down the relaxation dynamics of genomic filaments to the point that mammalian chromosomes are never in equilibrium over a cell's lifetime. In this opinion article, we revisit these out-of-equilibrium effects and discuss how their inclusion in physical models can enhance the spatial reconstructions of interphase eukaryotic genomes from phenomenological constraints collected during interphase.Comment: 5 pages, 1 figure, opinion article, submitted for publicatio

SPATIAL INTERPOLATION OF HOURLY GAUGE AND RADAR PRECIPITATION DURING MAP SOP

During MAP SOP (fall 1999) a network of additional automatic rain gauges was installed in the mountains of western Slovenia. The meteorological radar in Fossalon (OSMER, FVG) was operational as well. Raingauges are considered to provide measurements with good point accuracy, but offer little information on the spatial variability of precipitation. On the other hand the radar measurements give very good image of spatial distribution of precipitation, but the absolute quantity of precipitation is unreliable due to several systematic errors, especially occultation in mountainous areas. Different geostatistical approaches are tested to improve spatial distribution of precipitation, using raingauge and radar measurements. The spatial distribution of precipitation shows that the location of precipitation maxima is well correlated to the topographic features of the area and that the operational automatic gauge network is not dense enough to detect the spatial variability of precipitation in a scale of individual watersheds. The use of additional MAP data proved to be of great use, for example for such event as the one of heavy rainfall and debris flow in Loška Koritnica Valley in 2000