Iterative actions of normal operators

Let $A$ be a normal operator in a Hilbert space $\mathcal{H}$, and let $\mathcal{G} \subset \mathcal{H}$ be a countable set of vectors. We investigate the relations between $A$, $\mathcal{G}$ , and $L$ that makes the system of iterations $\{A^ng: g\in \mathcal{G},\;0\leq n< L(g)\}$ complete, Bessel, a basis, or a frame for $\mathcal{H}$. The problem is motivated by the dynamical sampling problem and is connected to several topics in functional analysis, including, frame theory and spectral theory. It also has relations to topics in applied harmonic analysis including, wavelet theory and time-frequency analysis.Comment: 14 pages, 0 figure

Classifying Cantor Sets by their Fractal Dimensions

In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovitch and Taylor. We classify these Cantor sets in terms of their h-Hausdorff and h-Packing measures, for the family of dimension functions h, and characterize this classification in terms of the underlying sequences.Comment: 10 pages, revised version. To appear in Proceedings of the AMS

Reliability based design optimization of a multi‐axial load cell using genetic algorithm

A construção de uma célula de carga multiaxial requer ferramentas robustas a fim de analisar o comportamento da mesma quando submetida a carregamentos estáticos e dinâmicos. Neste trabalho, é dada uma ênfase ao problema da otimização de um modelo de célula de carga multiaxial (6 componentes de força) do tipo Lywood, utilizando‐se do conceito de otimização baseada em confiabilidade. É tratado o problema da análise de confiabilidade estrutural, incluindo o efeito da variabilidade geométrica de suas propriedades físicas. A célula de carga foi analisada pelo método de elementos finitos e a restrição da confiabilidade é aplicada para o limite de falha do material. Por meio de mudanças em sua geometria objetivou‐se a maximização da primeira frequência natural e, ao mesmo tempo, a redução de massa e consequente aumento da deformação medida sem que a restrição de confiabilidade das tensões seja violada. São mostradas comparações entre o procedimento determinístico de otimização e o proposto, onde constatou‐se que a otimização determinística apresentou pontos com elevada probabilidade de falha, sendo justificada a aplicação da otimização baseada em confiabilidade para este tipo de problema. Também foram aplicados diferentes valores do fator de segurança ao modelo de otimização, onde foi possível analisar, a posteriori , a confiabilidade do resultado da otimização.The manufacturing process of a multi‐axial load cell requires robust tools to analyze the structural behavior when it is subjected to static and dynamic loads. In this work, it is given focus to the problem of optimizing a multi‐axial load cell model (6 load components) of Lywood type considering concepts of reliability‐based design optimization. The reliability structural analysis problem is handled including the variability effect of geometric and physical properties. The load cell is analyzed by finite element method and the reliability constraint is applied to the strength limit. The objective is the maximization of the first natural frequency and simultaneously reducing the mass and corresponding strains without violating reliability limit set as a limit. Comparisons between the deterministic optimization procedure and the proposed method are presented and it is found that the deterministic optimization points may have a high probability of failure so justifying in this type of problem the reliability‐based optimization. Different values of the safety factor were also tested with the optimization model, and it was possible to analyze, a posteriori, the reliability of the optimization results.La construcción de una célula de carga multiaxial requiere herramientas robustas para analizar el comportamiento de los mismos cuando se somete a cargas estáticas y dinámicas. En este trabajo se da un énfasis al problema de la optimización de un modelo de célula de carga multiaxial (6 componentes de fuerza) de tipo Lywood utilizando el concepto de optimización basado en la confiabilidad. Se abordó el problema de análisis de fiabilidad estructural incluyendo el efecto de la variabilidad geométrica de sus propiedades físicas. La célula de carga se analizó por el método de elementos finitos y la restricción de fiabilidad se aplica al límite de falla del material. A través de cambios en la geometría destinadas a aumentar al máximo la primera frecuencia natural, mientras que se viola la reducción de la masa y el consiguiente aumento de la deformación medido sin la fiabilidad de la restricción de tensiones sea violada. Las comparaciones se muestran entre el procedimiento de optimización determinista y propusieron, donde se encontró que los puntos de optimización deterministas con alta probabilidad de fallo. Fueron también aplicados diferentes valores del factor de seguridad para el modelo de optimización, donde fue posible analizar, retrospectivamente, la confiabilidad del resultado de la optimización.Peer Reviewe

Chance in the Modern Synthesis

The modern synthesis in evolutionary biology is taken to be that period in which a consensus developed among biologists about the major causes of evolution, a consensus that informed research in evolutionary biology for at least a half century. As such, it is a particularly fruitful period to consider when reflecting on the meaning and role of chance in evolutionary explanation. Biologists of this period make reference to “chance” and loose cognates of “chance,” such as: “random,” “contingent,” “accidental,” “haphazard,” or “stochastic.” Of course, what an author might mean by “chance” in any specific context varies. In the following, we first off er a historiographical note on the synthesis. Second, we introduce five ways in which synthesis authors spoke about chance

Abundance Measurements of Titan's Stratospheric HCN, HC3_3N, C3_3H4_4, and CH3_3CN from ALMA Observations

Previous investigations have employed more than 100 close observations of Titan by the Cassini orbiter to elucidate connections between the production and distribution of Titan's vast, organic-rich chemical inventory and its atmospheric dynamics. However, as Titan transitions into northern summer, the lack of incoming data from the Cassini orbiter presents a potential barrier to the continued study of seasonal changes in Titan's atmosphere. In our previous work (Thelen et al., 2018), we demonstrated that the Atacama Large Millimeter/submillimeter Array (ALMA) is well suited for measurements of Titan's atmosphere in the stratosphere and lower mesosphere (~100-500 km) through the use of spatially resolved (beam sizes <1'') flux calibration observations of Titan. Here, we derive vertical abundance profiles of four of Titan's trace atmospheric species from the same 3 independent spatial regions across Titan's disk during the same epoch (2012 to 2015): HCN, HC$_3$N, C$_3$H$_4$, and CH$_3$CN. We find that Titan's minor constituents exhibit large latitudinal variations, with enhanced abundances at high latitudes compared to equatorial measurements; this includes CH$_3$CN, which eluded previous detection by Cassini in the stratosphere, and thus spatially resolved abundance measurements were unattainable. Even over the short 3-year period, vertical profiles and integrated emission maps of these molecules allow us to observe temporal changes in Titan's atmospheric circulation during northern spring. Our derived abundance profiles are comparable to contemporary measurements from Cassini infrared observations, and we find additional evidence for subsidence of enriched air onto Titan's south pole during this time period. Continued observations of Titan with ALMA beyond the summer solstice will enable further study of how Titan's atmospheric composition and dynamics respond to seasonal changes.Comment: 15 pages, 16 figures, 2 tables. Accepted for publication in Icarus, September 201

In vivo Dual Substrate Bioluminescent Imaging

Our understanding of how and when breast cancer cells transit from established primary tumors to metastatic sites has increased at an exceptional rate since the advent of in vivo bioluminescent imaging technologies 1-3. Indeed, the ability to locate and quantify tumor growth longitudinally in a single cohort of animals to completion of the study as opposed to sacrificing individual groups of animals at specific assay times has revolutionized how researchers investigate breast cancer metastasis. Unfortunately, current methodologies preclude the real-time assessment of critical changes that transpire in cell signaling systems as breast cancer cells (i) evolve within primary tumors, (ii) disseminate throughout the body, and (iii) reinitiate proliferative programs at sites of a metastatic lesion. However, recent advancements in bioluminescent imaging now make it possible to simultaneously quantify specific spatiotemporal changes in gene expression as a function of tumor development and metastatic progression via the use of dual substrate luminescence reactions. To do so, researchers take advantage for two light-producing luciferase enzymes isolated from the firefly (Photinus pyralis) and sea pansy (Renilla reniformis), both of which react to mutually exclusive substrates that previously facilitated their wide-spread use in in vitro cell-based reporter gene assays 4. Here we demonstrate the in vivo utility of these two enzymes such that one luminescence reaction specifically marks the size and location of a developing tumor, while the second luminescent reaction serves as a means to visualize the activation status of specific signaling systems during distinct stages of tumor and metastasis development. Thus, the objectives of this study are two-fold. First, we will describe the steps necessary to construct dual bioluminescent reporter cell lines, as well as those needed to facilitate their use in visualizing the spatiotemporal regulation of gene expression during specific steps of the metastatic cascade. Using the 4T1 model of breast cancer metastasis, we show that the in vivo activity of a synthetic Smad Binding Element (SBE) promoter was decreased dramatically in pulmonary metastasis as compared to that measured in the primary tumor 4-6. Recently, breast cancer metastasis was shown to be regulated by changes within the primary tumor microenvironment and reactive stroma, including those occurring in fibroblasts and infiltrating immune cells 7-9. Thus, our second objective will be to demonstrate the utility of dual bioluminescent techniques in monitoring the growth and localization of two unique cell populations harbored within a single animal during breast cancer growth and metastasis

Chance in the Modern Synthesis

The modern synthesis in evolutionary biology is taken to be that period in which a consensus developed among biologists about the major causes of evolution, a consensus that informed research in evolutionary biology for at least a half century. As such, it is a particularly fruitful period to consider when reflecting on the meaning and role of chance in evolutionary explanation. Biologists of this period make reference to “chance” and loose cognates of “chance,” such as: “random,” “contingent,” “accidental,” “haphazard,” or “stochastic.” Of course, what an author might mean by “chance” in any specific context varies. In the following, we first off er a historiographical note on the synthesis. Second, we introduce five ways in which synthesis authors spoke about chance