A generative angular model of protein structure evolution

Recently described stochastic models of protein evolution have demonstrated that the inclusion of structural information in addition to amino acid sequences leads to a more reliable estimation of evolutionary parameters. We present a generative, evolutionary model of protein structure and sequence that is valid on a local length scale. The model concerns the local dependencies between sequence and structure evolution in a pair of homologous proteins. The evolutionary trajectory between the two structures in the protein pair is treated as a random walk in dihedral angle space, which is modeled using a novel angular diffusion process on the two-dimensional torus. Coupling sequence and structure evolution in our model allows for modeling both “smooth” conformational changes and “catastrophic” conformational jumps, conditioned on the amino acid changes. The model has interpretable parameters and is comparatively more realistic than previous stochastic models, providing new insights into the relationship between sequence and structure evolution. For example, using the trained model we were able to identify an apparent sequence–structure evolutionary motif present in a large number of homologous protein pairs. The generative nature of our model enables us to evaluate its validity and its ability to simulate aspects of protein evolution conditioned on an amino acid sequence, a related amino acid sequence, a related structure or any combination thereof

Exploring wind direction and SO2 concentration by circular-linear density estimation

The study of environmental problems usually requires the description of variables with different nature and the assessment of relations between them. In this work, an algorithm for flexible estimation of the joint density for a circular-linear variable is proposed. The method is applied for exploring the relation between wind direction and SO2 concentration in a monitoring station close to a power plant located in Galicia (NW-Spain), in order to compare the effectiveness of precautionary measures for pollutants reduction in two different years.Comment: 17 pages, 7 figures, 2 table

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

Talleres : Colegio Público La Lomada

Basado en el método científico, se pretende llegar a una enseñanza activa, globalizada y relacionada con el medio que rodea al niño. Se propone usar la investigación, observación y experimentación como metodología, partiendo de los intereses del niño. Trata de evitar la separación entre escuela y entorno. Educar para el tiempo libre. Potenciar los lenguajes: oral, escrito, manual, etc. Aplicado a 88 alumnos de EGB de ciclo medio. Se evaluó en base a la observación directa y al cuaderno de campo. El alumno, después de esta experiencia, se ha convertido en agente y no en paciente del proceso educativo. Han descubierto capacidades en sí mismos que antes ignoraban. Han profundizado en unos conocimientos, de tal forma, que ahora conocen mucho mejor el medio en que viven.Gobierno de Canarias. Dirección General de Promoción EducativaCanariasES

A goodness‐of‐fit test for the functional linear model with functional response

The Functional Linear Model with Functional Response (FLMFR) is one of the most fundamental models to assess the relation between two functional random variables. In this paper, we propose a novel goodness-of-fit test for the FLMFR against a general, unspecified, alternative. The test statistic is formulated in terms of a Cram\'er-von Mises norm over a doubly-projected empirical process which, using geometrical arguments, yields an easy-to-compute weighted quadratic norm. A resampling procedure calibrates the test through a wild bootstrap on the residuals and the use of convenient computational procedures. As a sideways contribution, and since the statistic requires a reliable estimator of the FLMFR, we discuss and compare several regularized estimators, providing a new one specifically convenient for our test. The finite sample behavior of the test is illustrated via a simulation study. Also, the new proposal is compared with previous significance tests. Two novel real datasets illustrate the application of the new test.Comment: 24 pages, 2 figures, 10 tables. Suplementary material: 2 pages, 1 figur

Directional–linear nonparametric regression for wildfire analysis

Wildfires represent a threat to natural resources, causing a huge economic and environmen- tal damage, so an effective management of wildfires is required in order to avoid devastating effects. Preventive policies recommend fuel management practices at landscape level, but these measurements will only be successful if strategically placed in order to interfere fire spread in the heading direction. Therefore, characterization of wildfires, with special attention to its main orientation, is important for designing appropriate precautionary plans. This work will be focused on the analysis of wildfire orientation (two–dimensional and three– dimensional) and the implications of this variable over other features of interest, such as wildfire size. The methodological approach that will be followed comprises nonparametric inference for regression models with directional covariate and linear response, including regression estimators based on kernel smoothers and testing procedures, such as goodness–of–fit and no–effect tests

Simulation of Conditioned Diffusions on the Flat Torus

Diffusion processes are fundamental in modelling stochastic dynamics in natural sciences. Recently, simulating such processes on complicated geometries has found applications for example in biology, where toroidal data arises naturally when studying the backbone of protein sequences, creating a demand for efficient sampling methods. In this paper, we propose a method for simulating diffusions on the flat torus, conditioned on hitting a terminal point after a fixed time, by considering a diffusion process in R 2 which we project onto the torus. We contribute a convergence result for this diffusion process, translating into convergence of the projected process to the terminal point on the torus. We also show that under a suitable change of measure, the Euclidean diffusion is locally a Brownian motion.Comment: 10 pages, 6 figures, GSI Conferenc