Counting Flimsy Numbers via Formal Language Theory

Let s_2(n) be the sum of the digits of n when expressed in base 2. For integers n and k, Stolarsky defined n to be k-flimsy if s_2(kn) < s_2(n). In this paper, we generalize the definition of k-flimsy numbers to all bases b, and provide a method to construct a pushdown automaton recognizing the k-flimsy base-b numbers. Using the tools of context-free languages and analytic combinatorics, we use this automaton to determine precise asymptotics for the number of k-flimsy N-digit numbers in base b. Lastly, using the results we obtained, we discuss the natural densities of k-flimsy numbers in base b for all values k and b. Our main results can be found in Theorems 2, 3, 8, and 9

Books without Scent, Shape, or Weight

Over the course of several centuries, the printed book has evolved into a medium which can facilitate deep and attentive reading in a highly productive manner. This ability results to a large extent from specific material properties of paper-based books. As few of these properties can be replicated effectively on digital devices, the transition to screen-based texts invariably leads to different forms of reading. While the immateriality of digital books may affect our capacity to concentrate on texts and to remember their contents, the plasticity and the computability of digital words simultaneously engender innovative ways of engaging with books.Wetensch. publicati

ASME Design Challenge Final Report

The American Society of Mechanical Engineers (ASME) 2016 Student Design Competition Challenge is to construct a compact system that can manufacture a projectile from a standard sheet of paper and propel it a maximum distance

Low- and high-resource opinion summarization

Customer reviews play a vital role in the online purchasing decisions we make. The reviews express user opinions that are useful for setting realistic expectations and uncovering important details about products. However, some products receive hundreds or even thousands of reviews, making them time-consuming to read. Moreover, many reviews contain uninformative content, such as irrelevant personal experiences. Automatic summarization offers an alternative – short text summaries capturing the essential information expressed in reviews. Automatically produced summaries can reflect overall or particular opinions and be tailored to user preferences. Besides being presented on major e-commerce platforms, home assistants can also vocalize them. This approach can improve user satisfaction by assisting in making faster and better decisions. Modern summarization approaches are based on neural networks, often requiring thousands of annotated samples for training. However, human-written summaries for products are expensive to produce because annotators need to read many reviews. This has led to annotated data scarcity where only a few datasets are available. Data scarcity is the central theme of our works, and we propose a number of approaches to alleviate the problem. The thesis consists of two parts where we discuss low- and high-resource data settings. In the first part, we propose self-supervised learning methods applied to customer reviews and few-shot methods for learning from small annotated datasets. Customer reviews without summaries are available in large quantities, contain a breadth of in-domain specifics, and provide a powerful training signal. We show that reviews can be used for learning summarizers via a self-supervised objective. Further, we address two main challenges associated with learning from small annotated datasets. First, large models rapidly overfit on small datasets leading to poor generalization. Second, it is not possible to learn a wide range of in-domain specifics (e.g., product aspects and usage) from a handful of gold samples. This leads to subtle semantic mistakes in generated summaries, such as ‘great dead on arrival battery.’ We address the first challenge by explicitly modeling summary properties (e.g., content coverage and sentiment alignment). Furthermore, we leverage small modules – adapters – that are more robust to overfitting. As we show, despite their size, these modules can be used to store in-domain knowledge to reduce semantic mistakes. Lastly, we propose a simple method for learning personalized summarizers based on aspects, such as ‘price,’ ‘battery life,’ and ‘resolution.’ This task is harder to learn, and we present a few-shot method for training a query-based summarizer on small annotated datasets. In the second part, we focus on the high-resource setting and present a large dataset with summaries collected from various online resources. The dataset has more than 33,000 humanwritten summaries, where each is linked up to thousands of reviews. This, however, makes it challenging to apply an ‘expensive’ deep encoder due to memory and computational costs. To address this problem, we propose selecting small subsets of informative reviews. Only these subsets are encoded by the deep encoder and subsequently summarized. We show that the selector and summarizer can be trained end-to-end via amortized inference and policy gradient methods

Affordable Compact Humanoid Robot for Autism Spectrum Disorder

Autism is a disorder that primarily affects the development of social and communication skills. Interacting with simple humanoid robots has been shown to improve the communication skills of autistic children. Currently, no robots capable of meeting these requirements are both low-cost and available for in-home use. This project produced a design and prototype of a humanoid robot that is non-threatening, affordable, portable, durable, and capable of interaction, and the electronic and control software were developed. This robot has the ability to track the child with its 3-DoF eyes and 3-DoF head, open and close its 1-DoF beak and 1-DoF each eyelids, and raise its 1-DoF each wings. These attributes will give it the ability to be used for therapy and assessment of children with autism

Cross Case Study of an Elementary Engineering Task

Designerly play has been identified as a fundamental component of childhood learning (Baynes, 1994; Petroski, 2003). However, as students enter grade one and beyond, the increasing academic focus has resulted in the loss of opportunities for designerly play (Zhao, 2012). At the same time, there are increasing calls to increase the number, skill, and diversity of STEM workers (Brophy, Portsmore, Klein, & Rogers, 2008). The robotics based Elementary Engineering Curriculum (Heffernan, 2013) - used by students in this study - and other similar projects have the potential to increase the STEM pipeline but elementary engineering is not well-understood. Research is needed to understand how to teach engineering to students as their cognitive, motor, and social skills rapidly develop in elementary school (Alimisis, 2012; Crismond & Adams, 2012; Mead, Thomas, & Weinberg, 2012; Penner, Giles, Lehrer, & Schauble, 1997; Roth, 1996; Schunn, 2009; Wagner, 1999). The literature review and theoretical frameworks chapters of this study determined the most relevant theoretical frameworks, engineering design process models, and existing research that is relevant to a cross-sectional case study of six grade 2 and six grade 6 elementary robotics students in the context of established K-6 elementary robotics curriculum (Heffernan, 2013). Students were videotaped doing an open-ended engineering task based on LEGO robotics using talk-aloud (Ericsson & Simon, 1993) and clinical interview (Ginsburg, 1997) techniques. The engineering design processes were analyzed and compared by age and gender. Significant differences were found in final projects and engineering design process. However, the differences were not, for the most part, related to development or gender, but were related to the complexity of the ride they tried to build and the skills and structural knowledge they brought to the task. The key factors identified consisted of three executive function process skills of cognitive flexibility, causal reasoning, and planning ability, three domain specific process skills of application of mathematics and science, engineering design process skills, and design principles of stability, scale, and the structural knowledge they had of LEGO robotics, most pointedly, LEGO connection knowledge. Implications of these findings for teachers are given