Machine-learning of atomic-scale properties based on physical principles

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train from linear functionals of the potential energy, such as the total energy and atomic forces. We then give a detailed account of the Smooth Overlap of Atomic Positions (SOAP) representation and kernel, showing how it arises from an abstract representation of smooth atomic densities, and how it is related to several popular density-based representations of atomic structure. We also discuss recent generalisations that allow fine control of correlations between different atomic species, prediction and fitting of tensorial properties, and also how to construct structural kernels---applicable to comparing entire molecules or periodic systems---that go beyond an additive combination of local environments

STED imaging performance estimation by means of Fourier transform analysis

Due to relatively high powers used in STED, biological samples may be affected by the illumination in the process of image acquisition. Similarly, the performance of the system may be limited by the sample itself. Optimization of the STED parameters taking into account the sample itself is therefore a complex task as there is no clear methodology that can determine the image improvement in an objective and quantitative manner. In this work, a method based on Fourier transform formalism is presented to analyze the performance of a STED system. The spatial frequency distribution of pairs of confocal and STED images are compared to obtain an objective parameter, the Azimuth Averaged Spectral Content Spread (AASCS), that is related to the performance of the system in which the sample is also considered. The method has been first tested on samples of beads, and then applied to cell samples labeled with multiple fluorescent dyes. The results show that a single parameter, the AASCS, can be used to determine the optimal settings for STED image acquisition in an objective way, only by using the information provided by the images from the sample themselves. The AASCS also helps minimize the depletion power, for better preservation of the samples.Peer ReviewedPostprint (published version

On Rendering Synthetic Images for Training an Object Detector

We propose a novel approach to synthesizing images that are effective for training object detectors. Starting from a small set of real images, our algorithm estimates the rendering parameters required to synthesize similar images given a coarse 3D model of the target object. These parameters can then be reused to generate an unlimited number of training images of the object of interest in arbitrary 3D poses, which can then be used to increase classification performances. A key insight of our approach is that the synthetically generated images should be similar to real images, not in terms of image quality, but rather in terms of features used during the detector training. We show in the context of drone, plane, and car detection that using such synthetically generated images yields significantly better performances than simply perturbing real images or even synthesizing images in such way that they look very realistic, as is often done when only limited amounts of training data are available

Single Particle Tracking: Analysis Techniques for Live Cell Nanoscopy.

Single molecule experiments are a set of experiments designed specifically to study the properties of individual molecules. It has only been in the last three decades where single molecule experiments have been applied to the life sciences; where they have been successfully implemented in systems biology for probing the behaviors of sub-cellular mechanisms. The advent and growth of super-resolution techniques in single molecule experiments has made the fundamental behaviors of light and the associated nano-probes a necessary concern among life scientists wishing to advance the state of human knowledge in biology. This dissertation disseminates some of the practices learned in experimental live cell microscopy. The topic of single particle tracking is addressed here in a format that is designed for the physicist who embarks upon single molecule studies. Specifically, the focus is on the necessary procedures to generate single particle tracking analysis techniques that can be implemented to answer biological questions. These analysis techniques range from designing and testing a particle tracking algorithm to inferring model parameters once an image has been processed. The intellectual contributions of the author include the techniques in diffusion estimation, localization filtering, and trajectory associations for tracking which will all be discussed in detail in later chapters. The author of this thesis has also contributed to the software development of automated gain calibration, live cell particle simulations, and various single particle tracking packages. Future work includes further evaluation of this laboratory\u27s single particle tracking software, entropy based approaches towards hypothesis validations, and the uncertainty quantification of gain calibration

The Poisson-Boltzmann model for implicit solvation of electrolyte solutions: Quantum chemical implementation and assessment via Sechenov coefficients.

We present the theory and implementation of a Poisson-Boltzmann implicit solvation model for electrolyte solutions. This model can be combined with arbitrary electronic structure methods that provide an accurate charge density of the solute. A hierarchy of approximations for this model includes a linear approximation for weak electrostatic potentials, finite size of the mobile electrolyte ions, and a Stern-layer correction. Recasting the Poisson-Boltzmann equations into Euler-Lagrange equations then significantly simplifies the derivation of the free energy of solvation for these approximate models. The parameters of the model are either fit directly to experimental observables-e.g., the finite ion size-or optimized for agreement with experimental results. Experimental data for this optimization are available in the form of Sechenov coefficients that describe the linear dependence of the salting-out effect of solutes with respect to the electrolyte concentration. In the final part, we rationalize the qualitative disagreement of the finite ion size modification to the Poisson-Boltzmann model with experimental observations by taking into account the electrolyte concentration dependence of the Stern layer. A route toward a revised model that captures the experimental observations while including the finite ion size effects is then outlined. This implementation paves the way for the study of electrochemical and electrocatalytic processes of molecules and cluster models with accurate electronic structure methods

Symmetry-break in Voronoi tessellations

We analyse in a common framework the properties of the Voronoi tessellations resulting from regular 2D and 3D crystals and those of tessellations generated by Poisson distributions of points, thus joining on symmetry breaking processes and the approach to uniform random distributions of seeds. We perturb crystalline structures in 2D and 3D with a spatial Gaussian noise whose adimensional strength is α and analyse the statistical properties of the cells of the resulting Voronoi tessellations using an ensemble approach. In 2D we consider triangular, square and hexagonal regular lattices, resulting into hexagonal, square and triangular tessellations, respectively. In 3D we consider the simple cubic (SC), body-centred cubic (BCC), and face-centred cubic (FCC) crystals, whose corresponding Voronoi cells are the cube, the truncated octahedron, and the rhombic dodecahedron, respectively. In 2D, for all values α>0, hexagons constitute the most common class of cells. Noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α=0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise with α0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α>2, results converge to those of Poisson-Voronoi tessellations. In 2D, while the isoperimetric ratio increases with noise for the perturbed hexagonal tessellation, for the perturbed triangular and square tessellations it is optimised for specific value of noise intensity. The same applies in 3D, where noise degrades the isoperimetric ratio for perturbed FCC and BCC lattices, whereas the opposite holds for perturbed SCC lattices. This allows for formulating a weaker form of the Kelvin conjecture. By analysing jointly the statistical properties of the area and of the volume of the cells, we discover that also the cells shape heavily fluctuates when noise is introduced in the system. In 2D, the geometrical properties of n-sided cells change with α until the Poisson-Voronoi limit is reached for α>2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established, which agrees with exact asymptotic results. Anomalous scaling relations are observed between the perimeter and the area in the 2D and between the areas and the volumes of the cells in 3D: except for the hexagonal (2D) and FCC structure (3D), this applies also for infinitesimal noise. In the Poisson-Voronoi limit, the anomalous exponent is about 0.17 in both the 2D and 3D case. A positive anomaly in the scaling indicates that large cells preferentially feature large isoperimetric quotients. As the number of faces is strongly correlated with the sphericity (cells with more faces are bulkier), in 3D it is shown that the anomalous scaling is heavily reduced when we perform power law fits separately on cells with a specific number of faces