A quantitative analysis of secondary RNA structure using domination based parameters on trees

BACKGROUND: It has become increasingly apparent that a comprehensive database of RNA motifs is essential in order to achieve new goals in genomic and proteomic research. Secondary RNA structures have frequently been represented by various modeling methods as graph-theoretic trees. Using graph theory as a modeling tool allows the vast resources of graphical invariants to be utilized to numerically identify secondary RNA motifs. The domination number of a graph is a graphical invariant that is sensitive to even a slight change in the structure of a tree. The invariants selected in this study are variations of the domination number of a graph. These graphical invariants are partitioned into two classes, and we define two parameters based on each of these classes. These parameters are calculated for all small order trees and a statistical analysis of the resulting data is conducted to determine if the values of these parameters can be utilized to identify which trees of orders seven and eight are RNA-like in structure. RESULTS: The statistical analysis shows that the domination based parameters correctly distinguish between the trees that represent native structures and those that are not likely candidates to represent RNA. Some of the trees previously identified as candidate structures are found to be "very" RNA like, while others are not, thereby refining the space of structures likely to be found as representing secondary RNA structure. CONCLUSION: Search algorithms are available that mine nucleotide sequence databases. However, the number of motifs identified can be quite large, making a further search for similar motif computationally difficult. Much of the work in the bioinformatics arena is toward the development of better algorithms to address the computational problem. This work, on the other hand, uses mathematical descriptors to more clearly characterize the RNA motifs and thereby reduce the corresponding search space. These preliminary findings demonstrate that graph-theoretic quantifiers utilized in fields such as computer network design hold significant promise as an added tool for genomics and proteomics

KURTOSIS

This work reviews the literature on kurtosis from Pearson'e definition in the early 1900's to our days. The evolution of the concept of kurtosis is described and the different ways of quantifying it are compared; graphs that help to understand the ideas are included. Kurtosis is also discussed in the context of bimodality and tests for normality. Simulation results and comments based on our work on the topic are included

Extensive Reorganization of Behavior Accompanies Ontogeny of Aggression in Male Flesh Flies

Aggression, costly in both time and energy, is often expressed by male animals in defense of valuable resources such as food or potential mates. Here we present a new insect model system for the study of aggression, the male flesh fly Sarcophaga crassipalpis, and ask whether there is an ontogeny of aggression that coincides with reproductive maturity. After establishing that reproductive maturity occurs by day 3 of age (post-eclosion), we examined the behavior of socially isolated males from different age cohorts (days 1, 2, 3, 4, and 6) upon introduction, in a test arena, with another male of the same age. The results show a pronounced development of aggression with age. The change from relative indifference to heightened aggression involves a profound increase in the frequency of high-intensity aggressive behaviors between days 1 and 3. Also noteworthy is an abrupt increase in the number of statistically significant transitions involving these full-contact agonistic behaviors on day 2. This elevated activity is trimmed back somewhat by day 3 and appears to maintain a stable plateau thereafter. No convincing evidence was found for escalation of aggression nor the establishment of a dominance relationship over the duration of the encounters. Despite the fact that aggressive interactions are brief, lasting only a few seconds, a major reorganization in the relative proportions of four major non-aggressive behaviors (accounting for at least 96% of the total observation time for each age cohort) accompanies the switch from low to high aggression. A series of control experiments, with single flies in the test arenas, indicates that these changes occur in the absence of the performance of aggressive behaviors. This parallel ontogeny of aggressive and non-aggressive behaviors has implications for understanding how the entire behavioral repertoire may be organized and reorganized to accommodate the needs of the organism

An Aggregate Stochastic Model Incorporating Individual Dynamics for Predation Movements of Anelosimus Studiosus

In this paper, we discuss methods for developing a stochastic model which incorporates behavior differences in the predation movements of Anelosimus studiosus (a subsocial spider). Stochastic models for animal movement and, in particular, spider predation movement have been developed previously; however, this paper focuses on the development and implementation of the necessary mathematical and statistical methods required to expand such a model in order to capture a variety of distinct behaviors. A least squares optimization algorithm is used for parameter estimation to fit a single stochastic model to an individual spider during predation resulting in unique parameter values for each spider. Similarities and variations between parameter values across the spiders are analyzed and used to estimate probability distributions for the variable parameter values. An aggregate stochastic model is then created which incorporates the individual dynamics. The comparison between the optimal individual models to the aggregate model indicate the methodology and algorithm developed in this paper are appropriate for simulating a range of individualistic behaviors

ANÁLISIS DE COMPONENTES PRINCIPALES EN LA DETECCIÓN DE DATOS DISCORDANTES

A pesar de ser el análisis de componentes principales, es una de las técnicasmultivariantes más antiguas del análisis multivariado, su uso hoy en día sigue en boga y esmuy importante. Se presenta su utilización en la detección de datos discordante s y unaaplicación a un conjunto de datos socioeconómicos del Perú

INFLUENCIA DE LOS DATOS DISCORDANTES SOBRE LA MATRIZ DE CORRELACIÓN Y CORRELACIÓN PARCIAL EN UN CONJUNTO DE DATOS MULTIVARlADO

Una parte importante de la utilidad del análisis de influencia es determinar la debilidad de algunos estimadores tradicionales frente a la presencia de datos discordantes tales como los Bj (coeficientesde regresión) y los ri (residuales) en un análisis de regresión; la X (media muestral) en un análisis inferencíal, etc. los cuales han sido desarrollados ampliamente. Pero como muy poco se ha difundido sobre la correlación parcial, tratamos de presentar los efectos que se producen en dichos estimadores ante la presencia de datos discordantes o influyentes con una aplicación a un conjunto de datos socio-económicos del Perú

A Duck's Story - Introducing the Idea of Testing (Statistical) Hypotheses

Created by Edith Seier of East Tennessee State University, this lesson by means of a simple story and a worksheet with questions guides the students from research question to arriving at a conclusion. The whole process is simply reasoning, no formulas. This lesson uses the reasoning already done by the student to introduce the standard vocabulary of testing statistical hypotheses (null & alternative hypotheses, p-value, type I and type II error, significance level). Students need to be familiar with binomial distribution tables. After the duck's story is finished, the class is asked to come up with their own research question, collect the data, do the hypotheses testing and answer their own research question. The teaching material is intended to be flexible depending of the time available. Instructors can choose to do just the interactive lecture type, interactive lecture and activity, or even add the optional material

Confidence Interval for a Coefficient of Dispersion in Nonnormal Distributions

A new confidence interval for the coefficient of dispersion (mean absolute deviation from the median divided by median) is proposed and is shown to perform better than the BCa bootstrap confidence interval

Two Families of Kurtosis Measures

Two families of kurtosis measures are defined as K1(b) = E[ab-|z|] and K2(b) = E[a(1 - |z|b)] where z denotes the standardized variable and a is a normalizing constant chosen such that the kurtosis is equal to 3 for normal distributions. K2(b) is an extension of Stavig\u27s robust kurtosis. As with Pearson\u27s measure of kurtosis β2 = E[z4], both measures are expected values of continuous functions of z that are even, convex or linear and strictly monotonic in ℜ- and in ℜ+. In contrast to β2, our proposed kurtosis measures give more importance to the central part of the distribution instead of the tails. Tests of normality based on these new measures are more sensitive with respect to the peak of the distribution. K1(b) and K2(b) satisfy Van Zwet\u27s ordering and correlate highly with other kurtosis measures such as L-kurtosis and quantile kurtosis