13 research outputs found

    The Unbearable Hardness of Unknotting

    Get PDF
    We prove that deciding if a diagram of the unknot can be untangled using at most k Reidemeister moves (where k is part of the input) is NP-hard. We also prove that several natural questions regarding links in the 3-sphere are NP-hard, including detecting whether a link contains a trivial sublink with n components, computing the unlinking number of a link, and computing a variety of link invariants related to four-dimensional topology (such as the 4-ball Euler characteristic, the slicing number, and the 4-dimensional clasp number)

    Learning to Unknot

    Get PDF
    We introduce natural language processing into the study of knot theory, as made natural by the braid word representation of knots. We study the UNKNOT problem of determining whether or not a given knot is the unknot. After describing an algorithm to randomly generate N-crossing braids and their knot closures and discussing the induced prior on the distribution of knots, we apply binary classification to the UNKNOT decision problem. We find that the Reformer and shared-QK Transformer network architectures outperform fully-connected networks, though all perform well. Perhaps surprisingly, we find that accuracy increases with the length of the braid word, and that the networks learn a direct correlation between the confidence of their predictions and the degree of the Jones polynomial. Finally, we utilize reinforcement learning (RL) to find sequences of Markov moves and braid relations that simplify knots and can identify unknots by explicitly giving the sequence of unknotting actions. Trust region policy optimization (TRPO) performs consistently well for a wide range of crossing numbers and thoroughly outperformed other RL algorithms and random walkers. Studying these actions, we find that braid relations are more useful in simplifying to the unknot than one of the Markov moves

    Annual Report 2018-2019

    Get PDF
    LETTER FROM THE DEAN I am pleased to share with you the 2018-19 College of Computing and Digital Media (CDM) annual report, highlighting the important work done by our faculty, students, and staff. We’ve said this before, and we’ll say it again: it was a big year. In 2018-19, programs across all three of our schools (Computing, Cinematic Arts, and Design) were ranked nationally. Our faculty were published in dozens of scholarly journals, screened their films over 100 times, and had their work exhibited globally. Student and alumni accomplishments included an Emmy nomination, a first place win in a Department of Energy competition, and features in trade publications--to name just a few. We worked to create new programs (including undergraduate and graduate comedy filmmaking programs in collaboration with The Second City) and continued our work in others (our NSF- funded Medical Informatics Experiences program celebrated its fifteenth year). Our makerspace, the Idea Realization Lab, clocked its 10,000th visit as we made plans to open a new IRL in Lincoln Park. And, we will continue to create the innovative programs and facilities that make us CDM. You can look forward to new programs like industrial design, and new labs that focus on everything from Internet of Things to design industry collaborations. I am proud of our CDM community, and I hope you feel that same sense of pride as you read through this report. David MillerDeanhttps://via.library.depaul.edu/cdmannual/1002/thumbnail.jp

    Imagination Bound: A Theoretical Imperative

    Get PDF
    Kant’s theory of productive imagination falls at the center of the critical project. This is evident in the 1781 Critique of Pure Reason, where Kant claims that the productive imagination is a “fundamental faculty of the human soul” and indispensable for the construction of experience. And yet, in the second edition of 1787 Kant seemingly demotes this imagination as a mere “effect of the understanding on sensibility” and all but withdraws its place from the Transcendental Deduction. In his 1929 Kant and the Problem of Metaphysics, Martin Heidegger provided an explanation for the revisions between 1781 and 1787. Heidegger suggested that the Critique was supposed to be a foundation for Kant’s metaphysics of morals, which holds that practical reason is freely bound by a categorical imperative. Yet after 1781 Kant recognized that the Critique implicates the productive imagination as the “unknown root” of the faculties of understanding and sensibility. If the 1781 Critique reveals this imagination to be the source of theoretical rules and practical imperatives, then, according to Heidegger, Kant could not but “shrink back” from this shocking discovery. A faculty so intimately tied to sensibility, and hence contingency and particularity, is a poor progenitor of freedom and universal rules. I think there is some truth to Heidegger’s explanation. But I also think there is something more important to draw from the revisions between 1781 and 1787. In this dissertation, I assume that something about the productive imagination did frighten Kant. But, pace Heidegger, I do not think that Kant shrank back from his initial position. Rather, I argue that the revisions clarify a theory that was implicit in 1781 but made explicit by 1787. If the imagination is a power for representation, which is at times a dream and at times a veridical experience, then the difference lies in the rule according to which the construction of the representation is bound. Furthermore, I argue that Kant’s revisions reveal a duty to bind the reproductive imagination according to a common concept, what Kant sometimes refers to as common sense. This is what I call the theoretical imperative

    Exodus: a Mormon history tour

    Get PDF
    Exodus: A Mormon History Tour is a creative nonfiction journey narrative that traces the author\u27s path in and out of the Church of Jesus Christ of Latter-day Saints, commonly referred to as the Mormon church. This memoir piece includes elements of the Bible\u27s Exodus story and essential Mormon history and theology, with a focus on Joseph Smith, the church\u27s founder. Through a fragmented though chronological form, the memoir offers a variously spiritual, logical, emotional, and psychological exploration of issues surrounding faith and spirituality, spiritual knowledge, inculcation of belief, memory, record keeping, self-representation, and so on. The piece is interspersed with and undergirded by depictions of landscapes of northern Utah

    An apparent ugliness: fashion and dressing poor

    Get PDF
    Whereas fashion’s drive keeps us in a constant embrace with changing styles, this thesis has at its centre the question: “What happens when modern fashion is no longer driven by beauty and glamour?” Arguably, the rise of what we call fashion and its liberation of beauty from classical canons occurred simultaneously during the nineteenth century. Umberto Eco writes, “beauty could now express itself by making opposites converge, so that ugliness was no longer the negation of beauty, but its other face”. Moreover, we hear repeatedly that we coexist with contrasting models of beauty “because the opposition beautiful/ugly no longer has any aesthetic value: ugly and beautiful would be two possible options to be experienced neutrally”. That is, both beauty and ugliness are made up of interdependent and complex references. Thus the thesis is a tour through what will be called “apparent ugliness” and the spectrum of ugliness in fashion as a way to discuss our relationship with style and our social bodies. In parallel, the thesis tracks the changing way we think about our clothes and their state of appearance. Structurally, each chapter explores the concept of apparent ugliness as the positive reformation of holes, stains, tears and the clothing of the poor in fashion. An apparent ugliness is the historical supplement, I argue, behind the current trend for poor looks. This redrawing of the traditional aesthetic drivers of fashion make dressing poor a complex field of study. At its heart, ugliness reconfigures those features deliberately kept at fashion’s margins as acceptable, even high street style. The thesis is a hermeneutic study: it wants to interpret ugliness in fashion. In exposing the mechanics of fashion, in revealing the seams as it were of those traditional drivers of fashion – beauty and glamour – we see the destruction of the illusion of fashion and an unknotting of many of the certainties around how and why we dress the way we do. Thus dressing poor represents a willful instability in its relationship to beauty and offers an alternative way to think through the history of fashion

    Adultery in the Novel

    Get PDF
    Originally published in 1979. Adultery is a dominant feature in chivalric literature; it becomes a major concern in Shakespeare's last plays; and it forms the central plot of novels from Anna Karenina to Couples. Tony Tanner proposes that transgressions of the marriage contract take on a special significance in the "bourgeois novels" of the eighteenth and nineteenth centuries. His interpretation begins with the general topic of adultery in literature and then zeroes in on three works—Rousseau's La Nouvelle Héloïse, Goethe's Die Wahlverwandtschaften, and Flaubert's Madame Bovary. His interpretation encompasses the role of women, the structure of the family, social mores, and the history of sexuality

    Many Seasons of Love

    Get PDF
    Published in August 2001.This publication may contain explicit sexual literary descriptions and/or artistic depictions.E-zineRevised August 2009Released for open distribution at request of the publisher on 2020-12-08; by Jeannette Ho 2020-12-17
    corecore