Algorithms to automatically quantify the geometric similarity of anatomical surfaces

We describe new approaches for distances between pairs of 2-dimensional surfaces (embedded in 3-dimensional space) that use local structures and global information contained in inter-structure geometric relationships. We present algorithms to automatically determine these distances as well as geometric correspondences. This is motivated by the aspiration of students of natural science to understand the continuity of form that unites the diversity of life. At present, scientists using physical traits to study evolutionary relationships among living and extinct animals analyze data extracted from carefully defined anatomical correspondence points (landmarks). Identifying and recording these landmarks is time consuming and can be done accurately only by trained morphologists. This renders these studies inaccessible to non-morphologists, and causes phenomics to lag behind genomics in elucidating evolutionary patterns. Unlike other algorithms presented for morphological correspondences our approach does not require any preliminary marking of special features or landmarks by the user. It also differs from other seminal work in computational geometry in that our algorithms are polynomial in nature and thus faster, making pairwise comparisons feasible for significantly larger numbers of digitized surfaces. We illustrate our approach using three datasets representing teeth and different bones of primates and humans, and show that it leads to highly accurate results.Comment: Changes with respect to v1, v2: an Erratum was added, correcting the references for one of the three datasets. Note that the datasets and code for this paper can be obtained from the Data Conservancy (see Download column on v1, v2

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

Microstructure design using graphs

Thin films with tailored microstructures are an emerging class of materials with applications such as battery electrodes, organic electronics, and biosensors. Such thin film devices typically exhibit a multi-phase microstructure that is confined, and show large anisotropy. Current approaches to microstructure design focus on optimizing bulk properties, by tuning features that are statistically averaged over a representative volume. Here, we report a tool for morphogenesis posed as a graph-based optimization problem that evolves microstructures recognizing confinement and anisotropy constraints. We illustrate the approach by designing optimized morphologies for photovoltaic applications, and evolve an initial morphology into an optimized morphology exhibiting substantially improved short circuit current (68% improvement over a conventional bulk-heterojunction morphology). We show optimized morphologies across a range of thicknesses exhibiting self-similar behavior. Results suggest that thicker films (250 nm) can be used to harvest more incident energy. Our graph based morphogenesis is broadly applicable to microstructure-sensitive design of batteries, biosensors and related applications

Computational Approaches to Simulation and Analysis of Large Conformational Transitions in Proteins

abstract: In a typical living cell, millions to billions of proteins—nanomachines that fluctuate and cycle among many conformational states—convert available free energy into mechanochemical work. A fundamental goal of biophysics is to ascertain how 3D protein structures encode specific functions, such as catalyzing chemical reactions or transporting nutrients into a cell. Protein dynamics span femtosecond timescales (i.e., covalent bond oscillations) to large conformational transition timescales in, and beyond, the millisecond regime (e.g., glucose transport across a phospholipid bilayer). Actual transition events are fast but rare, occurring orders of magnitude faster than typical metastable equilibrium waiting times. Equilibrium molecular dynamics (EqMD) can capture atomistic detail and solute-solvent interactions, but even microseconds of sampling attainable nowadays still falls orders of magnitude short of transition timescales, especially for large systems, rendering observations of such "rare events" difficult or effectively impossible. Advanced path-sampling methods exploit reduced physical models or biasing to produce plausible transitions while balancing accuracy and efficiency, but quantifying their accuracy relative to other numerical and experimental data has been challenging. Indeed, new horizons in elucidating protein function necessitate that present methodologies be revised to more seamlessly and quantitatively integrate a spectrum of methods, both numerical and experimental. In this dissertation, experimental and computational methods are put into perspective using the enzyme adenylate kinase (AdK) as an illustrative example. We introduce Path Similarity Analysis (PSA)—an integrative computational framework developed to quantify transition path similarity. PSA not only reliably distinguished AdK transitions by the originating method, but also traced pathway differences between two methods back to charge-charge interactions (neglected by the stereochemical model, but not the all-atom force field) in several conserved salt bridges. Cryo-electron microscopy maps of the transporter Bor1p are directly incorporated into EqMD simulations using MD flexible fitting to produce viable structural models and infer a plausible transport mechanism. Conforming to the theme of integration, a short compendium of an exploratory project—developing a hybrid atomistic-continuum method—is presented, including initial results and a novel fluctuating hydrodynamics model and corresponding numerical code.Dissertation/ThesisDoctoral Dissertation Physics 201

Courbure discrète : théorie et applications

International audienceThe present volume contains the proceedings of the 2013 Meeting on discrete curvature, held at CIRM, Luminy, France. The aim of this meeting was to bring together researchers from various backgrounds, ranging from mathematics to computer science, with a focus on both theory and applications. With 27 invited talks and 8 posters, the conference attracted 70 researchers from all over the world. The challenge of finding a common ground on the topic of discrete curvature was met with success, and these proceedings are a testimony of this wor

Motion patterns of subviral particles: Digital tracking, image data processing and analysis

At the Institute of Virology, Philipps-University, Marburg, Germany, currently research on the understanding of the transport mechanisms of Ebola- and Marburgvirus nucleocapsids is carried out. This research demands a profound knowledge about the various motion characteristics of the nucleocapids. The analysis of large amounts of samples by conventional manual evaluation is a laborious task and does not always lead to reproducible and comparable results. In a cooperation between the Institute of Virology, Marburg, and the Institute for Biomedical Engineering, University of Applied Sciences, Giessen, Germany, algorithms are developed and programmed that enable an automatic tracking of subviral particles in fluorescence microscopic image sequences. The algorithms form an interface between the biologic and the algorithmic domain. Furthermore, methods to automatically parameterize and classify subviral particle motions are created. Geometric and mathematical approaches, like curvature-, fractal dimension- and mean squared displacement-determination are applied. Statistical methods are used to compare the measured subviral particle motion parameters between different biological samples. In this thesis, the biological, mathematical and algorithmic basics are described and the state of the art methods of other research groups are presented and compared. The algorithms to track, parameterize, classify and statistically analyze subviral particle tracks are presented in the Methods section. All methods are evaluated with simulated data and/or compared to data validated by a virologist. The methods are applied to a set of real fluorescence microscopic image sequences of Marburgvirus infected live-cells. The Results chapter shows that subviral particle motion can be successfully analyzed using the presented tracking and analysis methods. Furthermore, differences between the subviral particle motions in the analyzed groups could be detected. However, further optimization with manually evaluated data can improve the results. The methods developed in this project enhance the knowledge about nucleocapsid transport and may be valuable for the development of effective antiviral agents to cure Ebola- and Marburgvirus diseases. The thesis concludes with a chapter Discussion and Conclusions

Video object segmentation and tracking.

Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, 2005One of the more complex video processing problems currently vexing researchers is that of object segmentation. This involves identifying semantically meaningful objects in a scene and separating them from the background. While the human visual system is capable of performing this task with minimal effort, development and research in machine vision is yet to yield techniques that perform the task as effectively and efficiently. The problem is not only difficult due to the complexity of the mechanisms involved but also because it is an ill-posed problem. No unique segmentation of a scene exists as what is of interest as a segmented object depends very much on the application and the scene content. In most situations a priori knowledge of the nature of the problem is required, often depending on the specific application in which the segmentation tool is to be used. This research presents an automatic method of segmenting objects from a video sequence. The intent is to extract and maintain both the shape and contour information as the object changes dynamically over time in the sequence. A priori information is incorporated by requesting the user to tune a set of input parameters prior to execution of the algorithm. Motion is used as a semantic for video object extraction subject to the assumption that there is only one moving object in the scene and the only motion in the video sequence is that of the object of interest. It is further assumed that there is constant illumination and no occlusion of the object. A change detection mask is used to detect the moving object followed by morphological operators to refine the result. The change detection mask yields a model of the moving components; this is then compared to a contour map of the frame to extract a more accurate contour of the moving object and this is then used to extract the object of interest itself. Since the video object is moving as the sequence progresses, it is necessary to update the object over time. To accomplish this, an object tracker has been implemented based on the Hausdorff objectmatching algorithm. The dissertation begins with an overview of segmentation techniques and a discussion of the approach used in this research. This is followed by a detailed description of the algorithm covering initial segmentation, object tracking across frames and video object extraction. Finally, the semantic object extraction results for a variety of video sequences are presented and evaluated

Computing Local Fractal Dimension Using Geographical Weighting Scheme

The fractal dimension (D) of a surface can be viewed as a summary or average statistic for characterizing the geometric complexity of that surface. The D values are useful for measuring the geometric complexity of various land cover types. Existing fractal methods only calculate a single D value for representing the whole surface. However, the geometric complexity of a surface varies across patches and a single D value is insufficient to capture these detailed variations. Previous studies have calculated local D values using a moving window technique. The main purpose of this study is to compute local D values using an alternative way by incorporating the geographical weighting scheme within the original global fractal methods. Three original fractal methods are selected in this study: the Triangular Prism method, the Differential Box Counting method and the Fourier Power Spectral Density method. A Gaussian density kernel function is used for the local adaption purpose and various bandwidths are tested. The first part of this dissertation research explores and compares both of the global and local D values of these three methods using test images. The D value is computed for every single pixel across the image to show the surface complexity variation. In the second part of the dissertation, the main goal is to study two major U.S. cities located in two regions. New York City and Houston are compared using D values for both of spatial and temporal comparison. The results show that the geographical weighting scheme is suitable for calculating local D values but very sensitive to small bandwidths. New York City and Houston show similar global D results for both year of 2000 and 2016 indicating there were not much land cover changes during the study period