Rollercoasters and Caterpillars

A rollercoaster is a sequence of real numbers for which every maximal contiguous subsequence - increasing or decreasing - has length at least three. By translating this sequence to a set of points in the plane, a rollercoaster can be defined as an x-monotone polygonal path for which every maximal sub-path, with positive- or negative-slope edges, has at least three vertices. Given a sequence of distinct real numbers, the rollercoaster problem asks for a maximum-length (not necessarily contiguous) subsequence that is a rollercoaster. It was conjectured that every sequence of n distinct real numbers contains a rollercoaster of length at least ceil[n/2] for n>7, while the best known lower bound is Omega(n/log n). In this paper we prove this conjecture. Our proof is constructive and implies a linear-time algorithm for computing a rollercoaster of this length. Extending the O(n log n)-time algorithm for computing a longest increasing subsequence, we show how to compute a maximum-length rollercoaster within the same time bound. A maximum-length rollercoaster in a permutation of {1,...,n} can be computed in O(n log log n) time. The search for rollercoasters was motivated by orthogeodesic point-set embedding of caterpillars. A caterpillar is a tree such that deleting the leaves gives a path, called the spine. A top-view caterpillar is one of maximum degree 4 such that the two leaves adjacent to each vertex lie on opposite sides of the spine. As an application of our result on rollercoasters, we are able to find a planar drawing of every n-vertex top-view caterpillar on every set of 25/3(n+4) points in the plane, such that each edge is an orthogonal path with one bend. This improves the previous best known upper bound on the number of required points, which is O(n log n). We also show that such a drawing can be obtained in linear time, when the points are given in sorted order

Fast and Longest Rollercoasters

For k >= 3, a k-rollercoaster is a sequence of numbers whose every maximal contiguous subsequence, that is increasing or decreasing, has length at least k; 3-rollercoasters are called simply rollercoasters. Given a sequence of distinct real numbers, we are interested in computing its maximum-length (not necessarily contiguous) subsequence that is a k-rollercoaster. Biedl et al. (2018) have shown that each sequence of n distinct real numbers contains a rollercoaster of length at least ceil[n/2] for n>7, and that a longest rollercoaster contained in such a sequence can be computed in O(n log n)-time (or faster, in O(n log log n) time, when the input sequence is a permutation of {1,...,n}). They have also shown that every sequence of n >=slant (k-1)^2+1 distinct real numbers contains a k-rollercoaster of length at least n/(2(k-1)) - 3k/2, and gave an O(nk log n)-time (respectively, O(n k log log n)-time) algorithm computing a longest k-rollercoaster in a sequence of length n (respectively, a permutation of {1,...,n}). In this paper, we give an O(nk^2)-time algorithm computing the length of a longest k-rollercoaster contained in a sequence of n distinct real numbers; hence, for constant k, our algorithm computes the length of a longest k-rollercoaster in optimal linear time. The algorithm can be easily adapted to output the respective k-rollercoaster. In particular, this improves the results of Biedl et al. (2018), by showing that a longest rollercoaster can be computed in optimal linear time. We also present an algorithm computing the length of a longest k-rollercoaster in O(n log^2 n)-time, that is, subquadratic even for large values of k <= n. Again, the rollercoaster can be easily retrieved. Finally, we show an Omega(n log k) lower bound for the number of comparisons in any comparison-based algorithm computing the length of a longest k-rollercoaster

Picture Collection Subject Index

The Subject Files cover people, places, objects, design, fashion, buildings, nature, and concepts. Research a time period by looking at subjects that are subdivided chronologically, such as Automobiles, Costume, Family Life, Advertising, Furniture, Interiors, Houses, Street Scenes, and U.S. History. The collection covers many decades, from the 19th century to the present day, and contains many images that you won\u27t find on the internet, and they all circulate!https://digitalcommons.risd.edu/picturecollection_indexes/1000/thumbnail.jp

Wandermust

“Wandermust” is a collection of prose poems that uses both poetic descriptive language and narrative to portray the persona’s experiences in her hometown and abroad. The collection makes use of nonce words as a compositional strategy to facilitate a more visceral reading experience and to develop the persona’s character, since existing words in the English lexicon do not always suffice in conveying the persona’s concept of a sensory experience. Just as the nonce words aid the persona in exploring and expressing her surroundings and her identity, they foster an experience in which the reader can explore and experience the nuances of the English language. By reading new words, the reader travels through and tours the English language; they read words yoked together that may never have been compounded before, process word hybridizations for new and existing ideas, view nouns and adjectives from the angles of verbs, and imagine written sound in new ways. The more intricately descriptive aspects of the poetry also function to breathe life into the settings in which the persona finds herself, turning settings into characters with which she interacts. Some of these prose poems read as flash fictions, whereas others read as run-on sentences or fragmented sentences in a stream-of-consciousness poetic style that reflects the persona’s processing of and curiosity about her surroundings. Both the content of the poems and their fluctuating formats mirror the persona’s restlessness as they portray her continual search for belonging, identity, and fulfillment – a journey that, by the end of the manuscript, she is still undertaking

Alternative Worlds: 3 Short Stories

The following thesis consists of my personal writing and objective writing. First, you will read about my writing process and how I plan to connect this project to my career as a teacher. The format of the stories are as follows: The first version is the “final” version. The versions following are drafts from oldest to most recent. After the stories, I have included my Writer’s Journal. I used the journal as a way to reflect on my work as I completed it. Before you begin reading, thank you for indulging my writing. I hope you enjoy reading it as much I as did writing it

Encouraging Students To “Think Like a Scientist” Through Picture Books Designed to Support Research-Based Science Education

The purpose of this thesis was to develop a series of nonfiction picture books, Think Like a Scientist, to help children see themselves as scientists by stepping into the shoes of real-life scientists. Each book in the series focuses on a crosscutting concept (one of the three dimensions of the Next Generation Science Standards) and how three scientists used the concept when making revolutionary discoveries. Novel to the series are strategically spaced questions that encourage readers to interact with the text by engaging in the same thought processes as real scientists. The series is intended support research-based elementary science education by incorporating phenomena and embedding effective questioning techniques. Think Like a Scientist introduces diverse STEM careers and scientists, scaffolds scientific thought and discussions for both children and adults, reveals the process behind interesting discoveries, and enriches a child’s understanding of the world. Seven picture book manuscripts are followed by a critical essay that describes the series’ research basis, the reasoning behind strategic series development decisions, where the series fits within current nonfiction picture book publishing, and a detailed description of the series

Skyscraping Frontiers

As a space of extremes, the skyscraper has been continually constructed as an urban frontier in American cultural productions. Like its counterpart of the American wilderness, this vertical frontier serves as a privileged site for both subversion and excessive control. Beyond common metaphoric readings, this study models the skyscraper not only as a Foucauldian heterotopia, but also as a complex network of human and nonhuman actors while retracing its development from its initial assemblage during the 19th century to its steady evolution into a smart structure from the mid-20th century onward. It takes a close look at US-American literary and filmic fictions and the ways in which they sought to make sense of this extraordinary structure throughout the 20th and early 21st centuries. More traditional poststructuralist spatial theories are connected with concepts and methods of Actor-Network Theory in a compelling account of the skyscraper’s evolution as reflected in fictional media from early 20th-century short stories via a range of action, disaster and horror films to selected city novels of the 1990s and 2000s