Double Diffusion Encoding Prevents Degeneracy in Parameter Estimation of Biophysical Models in Diffusion MRI

Purpose: Biophysical tissue models are increasingly used in the interpretation of diffusion MRI (dMRI) data, with the potential to provide specific biomarkers of brain microstructural changes. However, the general Standard Model has recently shown that model parameter estimation from dMRI data is ill-posed unless very strong magnetic gradients are used. We analyse this issue for the Neurite Orientation Dispersion and Density Imaging with Diffusivity Assessment (NODDIDA) model and demonstrate that its extension from Single Diffusion Encoding (SDE) to Double Diffusion Encoding (DDE) solves the ill-posedness and increases the accuracy of the parameter estimation. Methods: We analyse theoretically the cumulant expansion up to fourth order in b of SDE and DDE signals. Additionally, we perform in silico experiments to compare SDE and DDE capabilities under similar noise conditions. Results: We prove analytically that DDE provides invariant information non-accessible from SDE, which makes the NODDIDA parameter estimation injective. The in silico experiments show that DDE reduces the bias and mean square error of the estimation along the whole feasible region of 5D model parameter space. Conclusions: DDE adds additional information for estimating the model parameters, unexplored by SDE, which is enough to solve the degeneracy in the NODDIDA model parameter estimation.Comment: 22 pages, 7 figure

Numerical aspects of large-time optimal control of Burgers equation

In this paper, we discuss the efficiency of various numerical methods for the inverse design of the Burgers equation, both in the viscous and in the inviscid case, in long time-horizons. Roughly, the problem consists in, given a final desired target, to identify the initial datum that leads to it along the Burgers dynamics. This constitutes an ill-posed backward problem. We highlight the importance of employing a proper discretization scheme in the numerical approximation of the equation under consideration to obtain an accurate approximation of the optimal control problem. Convergence in the classical sense of numerical analysis does not suffice since numerical schemes can alter the dynamics of the underlying continuous system in long time intervals. As we shall see, this may end up affecting the efficiency on the numerical approximation of the inverse design, that could be polluted by spurious high frequency numerical oscillations. To illustrate this, two well-known numerical schemes are employed: the modified Lax−Friedrichs scheme (MLF) and the Engquist−Osher (EO) one. It is by now well-known that the MLF scheme, as time tends to infinity, leads to asymptotic profiles with an excess of viscosity, while EO captures the correct asymptotic dynamics. We solve the inverse design problem by means of a gradient descent method and show that EO performs robustly, reaching efficiently a good approximation of the minimizer, while MLF shows a very strong sensitivity to the selection of cell and time-step sizes, due to excess of numerical viscosity. The achieved numerical results are confirmed by numerical experiments run with the open source nonlinear optimization package (IPOPT)

The influence of using wet cellulose poultice on nanolime consolidation treatments applied on a limestone

Acknowledgments J.S. Pozo-Antonio was supported by the Ministry of Science and Innovation, Government of Spain through grant number RYC2020- 028902-I. J. Otero’s current research is funded by the European Commission on the Marie Skłodowska-Curie Actions (MSCA-IF) from the European Union’s Horizon 2020 on research and innovation, grant agreement N. 893762 (NANOMORT). Funding for open access charge was provided by Universidade de Vigo/CISUG.Consolidation treatment with nanolime is a common conservation intervention which needs more research to enhance penetration and mechanical properties while also minimizing the undesired white veil on the surface which significantly alters the surface appearance. In this light, the application of a cellulose poultice soaked in distilled water over the treated surface with nanolime tries to prevent the formation of white hazes and to favour nanolime carbonation and penetration in the pore structure. However, the real influence of this practice on the consolidation effectiveness has never been studied yet and is not yet well understood. In order to provide more insights about its most suitable application method, in this study, we investigated the effectiveness of a wet cellulose poultice for two different nanolime consolidation treatments on a weathered limestone. Nanolime has been synthetized by anion exchange processes and dispersed in two mediums: i) water and ii) 50% v/v of water and alcohol. The influence of the poultice on the penetration and aesthetic properties has been studied by drilling resistance measurement, ultrasounds test, stereomicroscopy, measurements of roughness and static contact angle, spectrophotometry and scanning electron microscopy (superficial and cross sectioned samples). Additionally, consolidation effectiveness has been evaluated through the changes in apparent density, open porosity, porosity network in the outer 5 mm of the surface by mercury intrusion porosimetry and surface cohesion by the peeling test. Results show that, contrary to what is usually assumed, samples where a wet cellulose poultice was applied after the consolidant reached the lowest penetration levels and retained lower dry matter in comparison to their counterparts without poultice. A consolidation treatment with nanolime is more complex that it is generally considered, and the application of poultices is not always enhancing consolidation level; the most suitable application procedure must be chosen with regards to the nanolime and substrate specific characteristics.Ministry of Science and Innovation, Government of Spain through grant number RYC2020- 028902-I.European Commission on the Marie Skłodowska-Curie Actions (MSCA-IF) from the European Union’s Horizon 2020 on research and innovation, grant agreement N. 893762 (NANOMORT)Funding for open access charge was provided by Universidade de Vigo/CISU

Lima, una ciudad policéntrica. Un análisis a partir de la localización del empleo

El objetivo de este artículo es el estudio de la conformación de varios centros en Lima Metropolitana (Perú), a la luz del modelo policéntrico. Nos hemos aproximado empíricamente a este proceso a través de la localización espacial de la fuerza laboral, como indicador de la concentración económica en el espacio, debido esto a la escasez de información empírica. Hemos usado datos de empleo georeferenciados a nivel de zonas censales del Censo Económico de 2008 y una combinación de metodologías que nos permitió estimar funciones de densidad.Se identificó diez centros y se les clasificó según su nivel de aglomeración y consolidación de actividades económicas. Los resultados confirman la hipótesis del carácter policéntrico de Lima