A Graph-Space Optimal Transport Approach Based on Kaniadakis -Gaussian Distribution for Inverse Problems Related to Wave Propagation.

Data-centric inverse problems are a process of inferring physical attributes from indirect measurements. Full-waveform inversion (FWI) is a non-linear inverse problem that attempts to obtain a quantitative physical model by comparing the wave equation solution with observed data, optimizing an objective function. However, the FWI is strenuously dependent on a robust objective function, especially for dealing with cycle-skipping issues and non-Gaussian noises in the dataset.

Generalized statistics: Applications to data inverse problems with outlier-resistance.

The conventional approach to data-driven inversion framework is based on Gaussian statistics that presents serious difficulties, especially in the presence of outliers in the measurements. In this work, we present maximum likelihood estimators associated with generalized Gaussian distributions in the context of Rényi, Tsallis and Kaniadakis statistics. In this regard, we analytically analyze the outlier-resistance of each proposal through the so-called influence function.

Full-waveform inversion based on generalized Rényi entropy using patched Green's function techniques.

The estimation of physical parameters from data analyses is a crucial process for the description and modeling of many complex systems. Based on Rényi α-Gaussian distribution and patched Green's function (PGF) techniques, we propose a robust framework for data inversion using a wave-equation based methodology named full-waveform inversion (FWI). From the assumption that the residual seismic data (the difference between the modeled and observed data) obeys the Rényi α-Gaussian probability distribution, we introduce an outlier-resistant criterion to deal with erratic measures in the FWI context, in which the classical FWI based on l2-norm is a particular case.

A microfluidic approach for synthesis and kinetic profiling of branched gold nanostructures.

Automatized approaches for nanoparticle synthesis and characterization represent a great asset to their applicability in the biomedical field by improving reproducibility and standardization, which help to meet the selection criteria of regulatory authorities. The scaled-up production of nanoparticles with carefully defined characteristics, including intrinsic morphological features, and minimal intra-batch, batch-to-batch, and operator variability, is an urgent requirement to elevate nanotechnology towards more trustable biological and technological applications. In this work, microfluidic approaches were employed to achieve fast mixing and good reproducibility in synthesizing a variety of gold nanostructures.

A Nanoscale Shape-Discovery Framework Supporting Systematic Investigations of Shape-Dependent Biological Effects and Immunomodulation.

Since it is now possible to make, in a controlled fashion, an almost unlimited variety of nanostructure shapes, it is of increasing interest to understand the forms of biological control that nanoscale shape allows. However, rational investigation of such a vast universe of shapes appears to present intractable fundamental and practical challenges. This has limited the useful systematic investigation of their biological interactions and the development of innovative nanoscale shape-dependent therapies.

Improving Seismic Inversion Robustness via Deformed Jackson Gaussian.

The seismic data inversion from observations contaminated by spurious measures (outliers) remains a significant challenge for the industrial and scientific communities. This difficulty is due to slow processing work to mitigate the influence of the outliers. In this work, we introduce a robust formulation to mitigate the influence of spurious measurements in the seismic inversion process.

Adding Prior Information in FWI through Relative Entropy.

Full waveform inversion is an advantageous technique for obtaining high-resolution subsurface information. In the petroleum industry, mainly in reservoir characterisation, it is common to use information from wells as previous information to decrease the ambiguity of the obtained results. For this, we propose adding a relative entropy term to the formalism of the full waveform inversion.

Tsallis Entropy, Likelihood, and the Robust Seismic Inversion.

The nonextensive statistical mechanics proposed by Tsallis have been successfully used to model and analyze many complex phenomena. Here, we study the role of the generalized Tsallis statistics on the inverse problem theory. Most inverse problems are formulated as an optimisation problem that aims to estimate the physical parameters of a system from indirect and partial observations.

An objective function for full-waveform inversion based on frequency-dependent offset-preconditioning.

Full-waveform inversion (FWI) is a powerful technique to obtain high-resolution subsurface models, from seismic data. However, FWI is an ill-posed problem, which means that the solution is not unique, and therefore the expert use of the information is required to mitigate the FWI ill-posedness, especially when wide-aperture seismic acquisitions are considered. In this way, we investigate the multiscale frequency-domain FWI by using a weighting operator according to the distances between each source-receiver pair.

Full-waveform inversion based on Kaniadakis statistics.

Full-waveform inversion (FWI) is a wave-equation-based methodology to estimate the subsurface physical parameters that honor the geologic structures. Classically, FWI is formulated as a local optimization problem, in which the misfit function, to be minimized, is based on the least-squares distance between the observed data and the modeled data (residuals or errors). From a probabilistic maximum-likelihood viewpoint, the minimization of the least-squares distance assumes a Gaussian distribution for the residuals, which obeys Gauss's error law.

Using single nanoparticle tracking obtained by nanophotonic force microscopy to simultaneously characterize nanoparticle size distribution and nanoparticle-surface interactions.

Comprehensive characterization of nanomaterials for medical applications is a challenging and complex task due to the multitude of parameters which need to be taken into consideration in a broad range of conditions. Routine methods such as dynamic light scattering or nanoparticle tracking analysis provide some insight into the physicochemical properties of particle dispersions. For nanomedicine applications the information they supply can be of limited use.

Arsenic accumulation in Brassicaceae seedlings and its effects on growth and plant anatomy.

We wished to evaluate the effects of arsenic on the morphology and anatomy of Brassica oleracea, Raphanus sativus, Brassica juncea, Brassica oleracea var. capitata and Brassica oleracea var. italica.