Asymptotic structure of banach spaces

The notion of asymptotic structure of an infinite dimensional Banach space was introduced by Maurey, Milman and Tomczak-Jaegermann. The asymptotic structure consists of those finite dimensional spaces which can be found everywhere `at infinity'. These are defined as the spaces for which there is a winning strategy in a certain vector game. The above authors introduced the class of asymptotic $\ell_p$ spaces, which are the spaces having simplest possible asymptotic structure. Key examples of such spaces are Tsirelson's space and James' space. We prove some new properties of general asymptotic $\ell_p$ spaces and also compare the notion of asymptotic $\ell_2$ with other notions of asymptotic Hilbert space behaviour such as weak Hilbert and asymptotically Hilbertian. We study some properties of smooth functions defined on subsets of asymptotic $\ell_\infty$ spaces. Using these results we show that that an asymptotic $\ell_\infty$ space which has a suitably smooth norm is isomorphically polyhedral, and therefore admits an equivalent analytic norm. We give a sufficient condition for a generalized Orlicz space to be a stabilized asymptotic $\ell_\infty$ space, and hence obtain some new examples of asymptotic $\ell_\infty$ spaces. We also show that every generalized Orlicz space which is stabilized asymptotic $\ell_\infty$ is isomorphically polyhedral. In 1991 Gowers and Maurey constructed the first example of a space which did not contain an unconditional basic sequence. In fact their example had a stronger property, namely that it was hereditarily indecomposable. The space they constructed was `$\ell_1$-like' in the sense that for any $n$ successive vectors $x_1 < \ldots < x_n$, $\frac{1}{f(n)} \sum_{i=1}^n \| x_i \| \leq \| \sum_{i=1}^n x_i \| \leq \sum_{i=1}^n \| x_i \|,$ where $f(n) = \log_2 (n+1)$. We present an adaptation of this construction to obtain, for each $p \in (1, \infty)$, an hereditarily indecomposable Banach space, which is `$\ell_p$-like' in the sense described above. We give some sufficient conditions on the set of types, $\mathscr{T}(X)$, for a Banach space $X$ to contain almost isometric copies of $\ell_p$ (for some $p \in [1, \infty)$) or of $c_0$. These conditions involve compactness of certain subsets of $\mathscr{T}(X)$ in the strong topology. The proof of these results relies heavily on spreading model techniques. We give two examples of classes of spaces which satisfy these conditions. The first class of examples were introduced by Kalton, and have a structural property known as Property (M). The second class of examples are certain generalized Tsirelson spaces. We introduce the class of stopping time Banach spaces which generalize a space introduced by Rosenthal and first studied by Bang and Odell. We look at subspaces of these spaces which are generated by sequences of independent random variables and we show that they are isomorphic to (generalized) Orlicz spaces. We deduce also that every Orlicz space, $h_\phi$, embeds isomorphically in the stopping time Banach space of Rosenthal. We show also, by using a suitable independence condition, that stopping time Banach spaces also contain subspaces isomorphic to mixtures of Orlicz spaces

What topics of peer interactions correlate with student performance in physics courses?

Research suggests that interacting with more peers about physics course material is correlated with higher student performance. Some studies, however, have demonstrated that different topics of peer interactions may correlate with their performance in different ways, or possibly not at all. In this study, we probe both the peers with whom students interact about their physics course and the particular aspects of the course material about which they interacted in six different introductory physics courses: four lecture courses and two lab courses. Drawing on methods in social network analysis, we replicate prior work demonstrating that, on average, students who interact with more peers in their physics courses have higher final course grades. Expanding on this result, we find that students discuss a wide range of aspects of course material with their peers: concepts, small-group work, assessments, lecture, and homework. We observe that in the lecture courses, interacting with peers about concepts is most strongly correlated with final course grade, with smaller correlations also arising for small-group work and homework. In the lab courses, on the other hand, small-group work is the only interaction topic that significantly correlates with final course grade. We use these findings to discuss how course structures (e.g., grading schemes and weekly course schedules) may shape student interactions and add nuance to prior work by identifying how specific types of student interactions are associated (or not) with performance.Comment: Submitted to European Journal of Physic

Context affects student thinking about sources of uncertainty in classical and quantum mechanics

Measurement uncertainty is an important topic in the undergraduate laboratory curriculum. Previous research on student thinking about experimental measurement uncertainty has focused primarily on introductory-level students' procedural reasoning about data collection and interpretation. In this paper, we extended this prior work to study upper-level students' thinking about sources of measurement uncertainty across experimental contexts, with a particular focus on classical and quantum mechanics contexts. We developed a survey to probe students' thinking in the generic question ``What comes to mind when you think about measurement uncertainty in [classical/quantum] mechanics?'' as well as in a range of specific experimental scenarios. We found that students primarily focused on limitations of the experimental setup in classical mechanics and principles of the underlying physics theory in quantum mechanics. Our results suggest that students need careful scaffolding to identify principles in appropriate classical experimental contexts and limitations in appropriate quantum experimental contexts. We recommend that future research probe how instruction in both classical and quantum contexts can help students better understand the range of sources of uncertainty present in classical and quantum experiments.Comment: 15 pages, 8 figure

New perspectives on student reasoning about measurement uncertainty: More or better data

Uncertainty is an important and fundamental concept in physics education. Students are often first exposed to uncertainty in introductory labs, expand their knowledge across lab courses, and then are introduced to quantum mechanical uncertainty in upper-division courses. This study is part of a larger project evaluating student thinking about uncertainty across these contexts. In this research, we investigate advanced physics student thinking about uncertainty by asking them conceptual questions about how a hypothetical distribution of measurements would change if `more' or `better' data were collected in four different experimental scenarios. The scenarios include both classical and quantum experiments, as well as experiments that theoretically result in an expected single value or an expected distribution. This investigation is motivated by our goal of finding insights into students' potential point- and set-like thinking about uncertainty and of shining light on the limitations of those binary paradigms.Comment: 15 pages, 5 figures, accepted to Physical Review Physics Education Researc

Towards understanding startup product development as effectual entrepreneurial behaviors

Software startups face with multiple technical and business challenges, which could make the startup journey longer, or even become a failure. Little is known about entrepreneurial decision making as a direct force to startup development outcome. In this study, we attempted to apply a behaviour theory of entrepreneurial firms to understand the root-cause of some software startup s challenges. Six common challenges related to prototyping and product development in twenty software startups were identified. We found the behaviour theory as a useful theoretical lens to explain the technical challenges. Software startups search for local optimal solutions, emphasise on short-run feedback rather than long-run strategies, which results in vague prototype planning, paradox of demonstration and evolving throw-away prototypes. The finding implies that effectual entrepreneurial processes might require a more suitable product development approach than the current state-of-practice.Comment: This is the author's version of the work. Copyright owner's version can be accessed at https://doi.org/10.1007/978-3-319-69191-6_15, 8th ICSOB 2017, Essen, German

Troubled Worlds: A Course Syllabus about Information Work and the Anthropocene

The goal of this syllabus is to interrogate the material, and socioeconomic processes which underpin our everyday information work. In particular, we examine the relationships developing between contemporary information practices and what problematically gets configured as “nature”—that messy world of non-human entanglements that often exists beyond the purview of innovation work, whether digital software development or industrial engineering. Much recent work on the environmental conditions of computing has sought to break down technology-nature dualisms in order to expose the implication of information technology in broader social and material ecologies. Library and information professionals and researchers are well poised to deepen this inquiry by presenting alternative nature-technology epistemologies grounded in longstanding analyses of information resources and their consumption. The “Troubled Worlds” syllabus starts with a discussion of concerns most obviously germane to the work of most library and information science professionals: practices at the intersection of structuring information and computing. Building on this attention, we turn to humanistic approaches to thinking through the era of dominant human activities widely known as the “Anthropocene” by introducing poetic, artistic, and activist lenses. We explore how artistic objects representing an increasingly troubled natural world raise awareness of the challenges facing it, as well as how they may incorporate and reshape information for aesthetic ends. We then look to questions of disability justice and how it works in blended built and natural spaces as well as the many different ways in which bodies respond to the toxic environments produced by information technologies. We next consider the newer design approaches to library and information research, specifically asking how design perspectives on digital information objects get inscribed in the Anthropocene. Lastly, we consider paradigms of repair and making and analyze the different valences through which information researchers and professionals categorize and contextualize what is possible with them. This compilation does not provide a comprehensive review of the literature on the environment within the information fields. Instead, it extends this literature to promote experimental research and practice. The modules construct an interdisciplinary and provisional path through the related literature in a form that we hope may be continually adjusted, rearranged, and augmented. Pre-print first published online 03/15/202

Sleep quality in middle-aged and elderly Chinese: distribution, associated factors and associations with cardio-metabolic risk factors

Background Poor sleep quality has been associated with increased risk of heart disease, diabetes and mortality. However, limited information exists on the distribution and determinants of sleep quality and its associations with cardio-metabolic risk factors in Chinese populations. We aimed to evaluate this in the current study. Methods A cross-sectional survey conducted in 2005 of 1,458 men and 1,831 women aged 50–70 years from urban and rural areas of Beijing and Shanghai. Using a questionnaire, sleep quality was measured in levels of well, common and poor. Comprehensive measures of socio-demographical and health factors and biomarkers of cardio-metabolic disease were recorded. These were evaluated in association with sleep quality using logistic regression models. Results Half of the population reported good sleep quality. After adjusting for potential confounders, women and Beijing residents had almost half the probability to report good sleep quality. Good physical and mental health (good levels of self-rated health (OR 2.48; 95%CI 2.08 to 2.96) and no depression (OR 4.05; 95%CI 3.12 to 5.26)) related to an increased chance of reporting good sleep quality, whereas short sleep duration (<7 hrs OR 0.10; 95%CI 0.07 to 0.14)) decreased it substantially. There were significant associations between levels of sleep quality and concentrations of plasma insulin, total and LDL cholesterol, and index of insulin resistance. Conclusion Levels of good sleep quality in middle-age and elderly Chinese were low. Gender, geographical location, self-rated health, depression and sleep quantity were major factors associated with sleep quality. Prospective studies are required to distil the factors that determine sleep quality and the effects that sleep patterns exert on cardio-metabolic health

Antecedents and consequences of effectuation and causation in the international new venture creation process

The selection of the entry mode in an international market is of key importance for the venture. A process-based perspective on entry mode selection can add to the International Business and International Entrepreneurship literature. Framing the international market entry as an entrepreneurial process, this paper analyzes the antecedents and consequences of causation and effectuation in the entry mode selection. For the analysis, regression-based techniques were used on a sample of 65 gazelles. The results indicate that experienced entrepreneurs tend to apply effectuation rather than causation, while uncertainty does not have a systematic influence. Entrepreneurs using causation-based international new venture creation processes tend to engage in export-type entry modes, while effectuation-based international new venture creation processes do not predetermine the entry mod