10 research outputs found
Low upper bounds in the LR degrees
No full textAbstractWe say that A≤LRB if every B-random real is A-random—in other words, if B has at least as much derandomization power as A. The LR reducibility is a natural weak reducibility in the context of randomness, and generalizes lowness for randomness. We study the existence and properties of upper bounds in the context of the LR degrees. In particular, we show that given two (or even finitely many) low sets, there is a low c.e. set which lies LR above both. This is very different from the situation in the Turing degrees, where Sacks’ splitting theorem shows that two low sets can join to 0′
Martin-Löf randomness and Galton–Watson processes
No full textAbstractThe members of Martin-Löf random closed sets under a distribution studied by Barmpalias et al. are exactly the infinite paths through Martin-Löf random Galton–Watson trees with survival parameter 23. To be such a member, a sufficient condition is to have effective Hausdorff dimension strictly greater than γ=log232, and a necessary condition is to have effective Hausdorff dimension greater than or equal to γ
Strengthening prompt simplicity
No full textAbstractWe introduce a natural strengthening of prompt simplicity which we call strong promptness, and study its relationship with existing lowness classes. This notion provides a ≤wtt version of superlow cuppability. We show that every strongly prompt c.e. set is superlow cuppable. Unfortunately, strong promptness is not a Turing degree notion, and so cannot characterize the sets which are superlow cuppable. However, it is a wtt-degree notion, and we show that it characterizes the degrees which satisfy a wtt-degree notion very close to the definition of superlow cuppability.Further, we study the strongly prompt c.e. sets in the context of other notions related promptness, superlowness, and cupping. In particular, we show that every benign cost function has a strongly prompt set which obeys it, providing an analogue to the known result that every cost function with the limit condition has a prompt set which obeys it. We also study the effect that lowness properties have on the behaviour of a set under the join operator. In particular we construct an array noncomputable c.e. set whose join with every low c.e. set is low.</jats:p
Indexing Archival Films: Alaska Archival Motion Picture Program
No full textSince the turn of the twentieth century, the state of Alaska has attracted professional and amateur filmmakers eager to document the northern wilderness and its inhabitants. Existing films on Alaska include thousands of feet of historically precious, unedited footage as well as studio productions; they are in demand by research specialists, educators, and filmmakers, as well as nonprofessional Alaskan citizens. Responding to that demand, administrators of the Rasmuson Library at the University of Alaska in Fairbanks launched the Alaska Archival Motion Picture Program to preserve film footage on Alaska and the circumpolar regions and to make it available to a variety of user groups
ON THE STRUCTURE OF THE DEGREES OF RELATIVE PROVABILITY
No full textAbstract. We investigate the structure of the degrees of provability, which measure the proof-theoretic strength of statements asserting the totality of given computable functions. The degrees of provability can also be seen as an extension of the investigation of relative consistency statements for first-order arithmetic (which can be viewed as Π01-statements, whereas statements of totality of computable functions are Π02-statements); and the structure of the degrees of provability can be viewed as the Lindenbaum algebra of true Π02-statements in first-order arithmetic. Our work continues and greatly ex-pands the second author’s paper on this topic by answering a number of open questions from that paper, comparing three different notions of a jump opera-tor and studying jump inversion as well as the corresponding high/low hierar-chies, investigating the structure of true Π01-statements as a substructure, and connecting the degrees of provability to escape and domination properties of computable functions. 1
Comparing levels of organizational learning maturity of colleges and universities participating in traditional and non-traditional (Academic Quality Improvement Project) accreditation processes
No full textPlan BBusiness and industry has successfully embraced the philosophy of organizational learning as tool to achieve its goals and strategic priorities. The purpose of this study is to compare the levels of organizational learning maturity of colleges and universities participating in traditional and non-traditional accreditation processes. A survey instrument was developed to quantify managerial practices at colleges and universities relative to the integral components of a learning organization. The surveys obtained the subjective opinions of faculty at twelve colleges and universities. Six of the institutions are accredited traditionally, while the remaining six are accredited using North Central Association’s alternative accreditation process, AQIP (Academic Quality Improvement Project). Learning Organizations in Higher Education The importance of this study is based on the awareness that higher education is facing increasing accountability standards. Colleges and universities must take a proactive approach to remain competitive. The research focus was to determine if institutions pursing the AQIP accreditation process possessed a higher organizational learning maturity score than those utilizing the traditional accreditation process
