Multiple Reflection Symmetry Detection via Linear-Directional Kernel Density Estimation

Symmetry is an important composition feature by investigating similar sides inside an image plane. It has a crucial effect to recognize man-made or nature objects within the universe. Recent symmetry detection approaches used a smoothing kernel over different voting maps in the polar coordinate system to detect symmetry peaks, which split the regions of symmetry axis candidates in inefficient way. We propose a reliable voting representation based on weighted linear-directional kernel density estimation, to detect multiple symmetries over challenging real-world and synthetic images. Experimental evaluation on two public datasets demonstrates the superior performance of the proposed algorithm to detect global symmetry axes respect to the major image shapes

Langevin diffusions on the torus: estimation and applications

We introduce stochastic models for continuous-time evolution of angles and develop their estimation. We focus on studying Langevin diffusions with stationary distributions equal to well-known distributions from directional statistics, since such diffusions can be regarded as toroidal analogues of the Ornstein–Uhlenbeck process. Their likelihood function is a product of transition densities with no analytical expression, but that can be calculated by solving the Fokker–Planck equation numerically through adequate schemes. We propose three approximate likelihoods that are computationally tractable: (i) a likelihood based on the stationary distribution; (ii) toroidal adaptations of the Euler and Shoji–Ozaki pseudo-likelihoods; (iii) a likelihood based on a specific approximation to the transition density of the wrapped normal process. A simulation study compares, in dimensions one and two, the approximate transition densities to the exact ones, and investigates the empirical performance of the approximate likelihoods. Finally, two diffusions are used to model the evolution of the backbone angles of the protein G (PDB identifier 1GB1) during a molecular dynamics simulation. The software package sdetorus implements the estimation methods and applications presented in the paper

Directional Statistics in Protein Bioinformatics

This chapter shows how toroidal diffusions are convenient methodological tools for modelling protein evolution in a probabilistic framework. The chapter addresses the construction of ergodic diffusions with stationary distributions equal to well-known directional distributions, which can be regarded as toroidal analogues of the Ornstein-Uhlenbeck process. The important challenges that arise in the estimation of the diffusion parameters require the consideration of tractable approximate likelihoods and, among the several approaches introduced, the one yielding a specific approximation to the transition density of the wrapped normal process is shown to give the best empirical performance on average. This provides the methodological building block for Evolutionary Torus Dynamic Bayesian Network (ETDBN), a hidden Markov model for protein evolution that emits a wrapped normal process and two continuous-time Markov chains per hidden state. The chapter describes the main features of ETDBN, which allows for both "smooth" conformational changes and "catastrophic" conformational jumps, and several empirical benchmarks. The insights into the relationship between sequence and structure evolution that ETDBN provides are illustrated in a case study.Comment: 26 pages, 13 figure

Histopathologic features of the vagus nerve after electrical stimulation in swine

This paper describes the histological features of the vagus nerve after its stimulation with an electrostimulation system that is being developed for morbid obesity treatment. An electrostimulation system was implanted laparoscopically around the ventral vagal trunk of five Large White female pigs (49.63±1.94kg.). Vagal nerve stimulation was performed by continuous constant voltage current pulses. Thoracic samples of both ventral and dorsal vagal trunks were obtained thoracoscopically one month after implantation. Animals were sacrificed one month after thoracoscopic vaguectomy. Tissue samples were then harvested from the vagal nerve at the implantation site, 1cm cranial to it, thoracic portion of ventral and dorsal vagal trunks, sub-diaphragmatic dorsal vagal trunk, left and right vagus nerves. Specimens were analysed with light microscope. The severity of the lesions was graded from 0 to 4 (0: no lesion, 1: mild, 2: moderate, 3: severe and 4: extremely severe), taking into account fibrosis, vascularization, necrosis, fiber degeneration and inflammation. Electrode implantation resulted in thickened epineurium and endoneural connective tissue. The greatest lesion score was evidenced at the leads implantation site in the ventral vagal trunk, followed by, in order of decreasing lesion severity, left vagus nerve, thoracic portion of ventral vagal trunk, subdiaphragmatic dorsal vagal trunk, thoracic portion of dorsal vagal trunk and right vagus nerve. The stimulation device used in this study caused connective tissue growth, greatest in the samples located closer to the implantation site. However, there was no sign of altered vascularization in any studied specimen