Visualizing Set Relations and Cardinalities Using Venn and Euler Diagrams

In medicine, genetics, criminology and various other areas, Venn and Euler diagrams are used to visualize data set relations and their cardinalities. The data sets are represented by closed curves and the data set relationships are depicted by the overlaps between these curves. Both the sets and their intersections are easily visible as the closed curves are preattentively processed and form common regions that have a strong perceptual grouping effect. Besides set relations such as intersection, containment and disjointness, the cardinality of the sets and their intersections can also be depicted in the same diagram (referred to as area-proportional) through the size of the curves and their overlaps. Size is a preattentive feature and so similarities, differences and trends are easily identified. Thus, such diagrams facilitate data analysis and reasoning about the sets. However, drawing these diagrams manually is difficult, often impossible, and current automatic drawing methods do not always produce appropriate diagrams. This dissertation presents novel automatic drawing methods for different types of Euler diagrams and a user study of how such diagrams can help probabilistic judgement. The main drawing algorithms are: eulerForce, which uses a force-directed approach to lay out Euler diagrams; eulerAPE, which draws area-proportional Venn diagrams with ellipses. The user study evaluated the effectiveness of area- proportional Euler diagrams, glyph representations, Euler diagrams with glyphs and text+visualization formats for Bayesian reasoning, and a method eulerGlyphs was devised to automatically and accurately draw the assessed visualizations for any Bayesian problem. Additionally, analytic algorithms that instantaneously compute the overlapping areas of three general intersecting ellipses are provided, together with an evaluation of the effectiveness of ellipses in drawing accurate area-proportional Venn diagrams for 3-set data and the characteristics of the data that can be depicted accurately with ellipses

Asteroseismology and Interferometry

Asteroseismology provides us with a unique opportunity to improve our understanding of stellar structure and evolution. Recent developments, including the first systematic studies of solar-like pulsators, have boosted the impact of this field of research within Astrophysics and have led to a significant increase in the size of the research community. In the present paper we start by reviewing the basic observational and theoretical properties of classical and solar-like pulsators and present results from some of the most recent and outstanding studies of these stars. We centre our review on those classes of pulsators for which interferometric studies are expected to provide a significant input. We discuss current limitations to asteroseismic studies, including difficulties in mode identification and in the accurate determination of global parameters of pulsating stars, and, after a brief review of those aspects of interferometry that are most relevant in this context, anticipate how interferometric observations may contribute to overcome these limitations. Moreover, we present results of recent pilot studies of pulsating stars involving both asteroseismic and interferometric constraints and look into the future, summarizing ongoing efforts concerning the development of future instruments and satellite missions which are expected to have an impact in this field of research.Comment: Version as published in The Astronomy and Astrophysics Review, Volume 14, Issue 3-4, pp. 217-36

Stellar Evolution with Rotation in PARSEC v2.0: Tracks and Isochrones for Low- and Intermediate-mass Stars

Rotation is always known as an important ingredient in stellar models. Studying the impacts of rotation on stellar structure and evolution is the goal of my thesis. PARSEC models is being widely used in the astronomical com munity over the last decade. Nevertheless, for the first time, the PARSEC rotating stellar tracks and isochrones are provided to the community, with a suitable range of masses and metallicities. Specifically, we consider the mod els from very low mass up to 14M⊙, and the metallicity ranges from 0.004 to 0.017. The PARSEC V2.0 code is used to perform the calculations, and the dedicated sites are created for delivering them to users. The concurrence between rotation and the convective core overshooting phenomenon has been carefully calibrated in previous works. In this project, I inherit this result and adopt the maximum value of core overshooting ef ficiency parameter λov,max = 0.4. A linear growth from zero of stars that do not develop a convective core to this maximum value where stars already have a fully convective core is adopted for stars with masses in the transition region. The shellular rotation is treated as a purely diffusive process under the assumption of Roche model. Seven initial rotation rates are considered from zero to the extremely close critical velocity (namely, ωi = 0 − 0.99). The mass loss process is now applied during the evolution of stars due to the enhancement caused by rotation, with the suitable adopted rates that depend on the mass range. In this project, the low-mass (0.8 ≳ M ≳ 2M⊙) and intermediate-mass (2 ≳ M ≳ 14M⊙) are the main targets of the analysis in this thesis. The effects of geometrical distortion and rotational mixing are clearly seen in the Hertzsprung-Russell diagram of our tracks. We have seen the rotating stars spend their time longer in the Main-Sequence phase with respect to their non-rotating counterparts. Also, the higher core mass they would have at the post-main-sequence phases. Especially in the case of intermediate-mass stars, where the CNO-cycles are the main channel of nuclear burning during the main-sequence, the enhancement (depletion) of surface nitrogen and helium (carbon and oxygen) are the most evidence of rotational mixing. Indeed, the faster stars rotate the more enhancement/de pletion. As a consequence, with our new models, we can reproduce very well the hook feature of the open cluster M67, as well as the “global” fitting. Furthermore, we also see a hint of at least two populations that harbour in the open cluster NGC 6633 to explain the extended main-sequence and the position of the three He-clump stars. Finally, this new collection of stellar tracks and corresponding isochrones are available online at the dedicated websites, and most suitably used for studies of young and intermediate-age open clusters

Effects of stellar rotation on young cluster HR diagrams

vii, 109 leaves : ill. ; 29 cm.Includes abstract.Includes bibliographical references (leaves 104-109).This thesis investigates the effects of stellar rotation on the HR diagram location of members within young clusters. The rotational effects on luminosity and temperature of a star depend on the viewing angle and the rotation rate of the star and must be included in determining the HR diagram locations. The position of members is used as an indicator of the rotational characteristics of the individual stars. The fraction of clusters with a selected member within restricted ranges of rotation rate and viewing angle has been calculated for each selected member. These selected members are: brightest cluster member, bluest cluster member, and reddest cluster member above a luminosity cutoff. The brightest and bluest members were found to be rapidly rotating and viewed pole-on in 74% and 88% of the clusters respectively. The reddest member above a luminosity cutoff was found to be rapidly rotating and viewed equator on in 94% of the clusters

UNOmaha Problem of the Week (2021-2022 Edition)

The University of Omaha math department\u27s Problem of the Week was taken over in Fall 2019 from faculty by the authors. The structure: each semester (Fall and Spring), three problems are given per week for twelve weeks, with each problem worth ten points - mimicking the structure of arguably the most well-regarded university math competition around, the Putnam Competition, with prizes awarded to top-scorers at semester\u27s end. The weekly competition was halted midway through Spring 2020 due to COVID-19, but relaunched again in Fall 2021, with massive changes. Now there are three difficulty tiers to POW problems, roughly corresponding to easy/medium/hard difficulties, with each tier getting twelve problems per semester, and three problems (one of each tier) per week posted online and around campus. The tiers are named after the EPH classification of conic sections (which is connected to many other classifications in math), and in the present compilation they abide by the following color-coding: Cyan, Green, and Magenta. In practice, when creating the problem sets, we begin with a large enough pool of problem drafts and separate out the ones which are most obviously elliptic or hyperbolic, and then the remaining ones fall into parabolic. The tiers don\u27t necessarily reflect workload, though, only prerequisite mathematical background. Ideally, the solutions to elliptic problems, and any parts of solutions to parabolic and hyperbolic problems not covered in standard undergraduate courses, are meant to test participants\u27 creativity. Beware, though, many solutions also include additional commentary which varies wildly in the reader\u27s assumed mathematical maturity

Statistical Physics of Design

Modern life increasingly relies on complex products that perform a variety of functions. The key difficulty of creating such products lies not in the manufacturing process, but in the design process. However, design problems are typically driven by multiple contradictory objectives and different stakeholders, have no obvious stopping criteria, and frequently prevent construction of prototypes or experiments. Such ill-defined, or "wicked" problems cannot be "solved" in the traditional sense with optimization methods. Instead, modern design techniques are focused on generating knowledge about the alternative solutions in the design space. In order to facilitate such knowledge generation, in this dissertation I develop the "Systems Physics" framework that treats the emergent structures within the design space as physical objects that interact via quantifiable forces. Mathematically, Systems Physics is based on maximal entropy statistical mechanics, which allows both drawing conceptual analogies between design problems and collective phenomena and performing numerical calculations to gain quantitative understanding. Systems Physics operates via a Model-Compute-Learn loop, with each step refining our thinking of design problems. I demonstrate the capabilities of Systems Physics in two very distinct case studies: Naval Engineering and self-assembly. For the Naval Engineering case, I focus on an established problem of arranging shipboard systems within the available hull space. I demonstrate the essential trade-off between minimizing the routing cost and maximizing the design flexibility, which can lead to abrupt phase transitions. I show how the design space can break into several locally optimal architecture classes that have very different robustness to external couplings. I illustrate how the topology of the shipboard functional network enters a tight interplay with the spatial constraints on placement. For the self-assembly problem, I show that the topology of self-assembled structures can be reliably encoded in the properties of the building blocks so that the structure and the blocks can be jointly designed. The work presented here provides both conceptual and quantitative advancements. In order to properly port the language and the formalism of statistical mechanics to the design domain, I critically re-examine such foundational ideas as system-bath coupling, coarse graining, particle distinguishability, and direct and emergent interactions. I show that the design space can be packed into a special information structure, a tensor network, which allows seamless transition from graphical visualization to sophisticated numerical calculations. This dissertation provides the first quantitative treatment of the design problem that is not reduced to the narrow goals of mathematical optimization. Using statistical mechanics perspective allows me to move beyond the dichotomy of "forward" and "inverse" design and frame design as a knowledge generation process instead. Such framing opens the way to further studies of the design space structures and the time- and path-dependent phenomena in design. The present work also benefits from, and contributes to the philosophical interpretations of statistical mechanics developed by the soft matter community in the past 20 years. The discussion goes far beyond physics and engages with literature from materials science, naval engineering, optimization problems, design theory, network theory, and economic complexity.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163133/1/aklishin_1.pd