Asymptotically optimal covering designs

A (v,k,t) covering design, or covering, is a family of k-subsets, called blocks, chosen from a v-set, such that each t-subset is contained in at least one of the blocks. The number of blocks is the covering's size}, and the minimum size of such a covering is denoted by C(v,k,t). It is easy to see that a covering must contain at least (v choose t)/(k choose t) blocks, and in 1985 R\"odl [European J. Combin. 5 (1985), 69-78] proved a long-standing conjecture of Erd\H{o}s and Hanani [Publ. Math. Debrecen 10 (1963), 10-13] that for fixed k and t, coverings of size (v choose t)/(k choose t) (1+o(1)) exist (as v \to \infty). An earlier paper by the first three authors [J. Combin. Des. 3 (1995), 269-284] gave new methods for constructing good coverings, and gave tables of upper bounds on C(v,k,t) for small v, k, and t. The present paper shows that two of those constructions are asymptotically optimal: For fixed k and t, the size of the coverings constructed matches R\"odl's bound. The paper also makes the o(1) error bound explicit, and gives some evidence for a much stronger bound

The challenge of mysticism : a primer from a Christian perspective

In this article, I discuss the relevance of the study of mysticism for Christian analytic theologians and philosophers of religion. I begin with a brief consideration of some reasons Christian academics might be reluctant to enter this field, and indicate that, somewhat surprisingly, the study of mysticism is something but seldom addressed in Christian analytic circles. With this background in place, I proceed to the primary two sections of the article. Section I deals with demarcating mysticism: for the purposes of this article alone, an experience will count as mystical if and only if it is strongly unitive, transcends everyday consciousness, and (allegedly) conveys epistemic certainty as to the veracity of the insights acquired. These three criteria are discussed in some depth. Section II turns to the challenge mysticism in this sense might present to the Christian philosopher or theologian. I argue that the phenomenon of mysticism might be seen plausibly to imply one of two conclusions, both of which appear to be unpalatable for the Christian. First, it might suggest certain metaphysical views which prima facie call key tenets of orthodox Christianity into question. Secondly, mystical experience might be understood as the ‘inner meaning’ of Christianity which renders the better part of orthodox Christian belief equally problematic (as evidenced in three Christian mystics I discuss). I then conclude with a reflection on how the discussion might proceed, suggesting once more that Christian analytic theologians and philosophers of religion have scarcely begun to ask the relevant questions, let alone answer them in any persuasive manner.Publisher PDFPeer reviewe

Beauty in ruins

In this project, I explore the idea of finding beauty in dilapidated places. This project consists of 14 photos of ruins taken and edited by me, as well as 14 ekphrastic poems that further explore the beauty in ruins. I arranged the poems and photos in a way that places the reader in an imaginary ruins setting. My goal is for all of the poems to be read as a single work that mimics the experience of exploring an abandoned site. I aim to take the reader on an adventure through ruins and temporalities, highlighting the beauty that is found in the dilapidation along the way.Thesis (B.?)Honors Colleg

Human Perambulation as a Self Calibrating Biometric

This paper introduces a novel method of single camera gait reconstruction which is independent of the walking direction and of the camera parameters. Recognizing people by gait has unique advantages with respect to other biometric techniques: the identification of the walking subject is completely unobtrusive and the identification can be achieved at distance. Recently much research has been conducted into the recognition of frontoparallel gait. The proposed method relies on the very nature of walking to achieve the independence from walking direction. Three major assumptions have been done: human gait is cyclic; the distances between the bone joints are invariant during the execution of the movement; and the articulated leg motion is approximately planar, since almost all of the perceived motion is contained within a single limb swing plane. The method has been tested on several subjects walking freely along six different directions in a small enclosed area. The results show that recognition can be achieved without calibration and without dependence on view direction. The obtained results are particularly encouraging for future system development and for its application in real surveillance scenarios