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- Paul Shafer, Timothy Isganitis, Golan Yona
- BMC Bioinformatics
- 2005

Existing biological databases support a variety of queries such as keyword or definition search. However, they do not provide any measure of relevance for the instances reported, and result sets are usually sorted arbitrarily. We describe a system that builds upon the complex infrastructure of the Biozon database and applies methods similar to those of… (More)

- Rupert Hölzl, Paul Shafer
- Ann. Pure Appl. Logic
- 2015

A Martin-Löf test U is universal if it captures all non-Martin-Löf random sequences, and it is optimal if for every ML-test V there is a c ∈ ω such that ∀n(Vn+c ⊆ Un). We study the computational differences between universal and optimal ML-tests as well as the effects that these differences have on both the notion of layerwise computability and the… (More)

Remark. The notes which follow reflect the content of a two day tutorial which took place at the Fields Institute on 5/29 and 5/30 in 2009. Most of the content has existed in the literature for some time (primarily in the original edition of [10]) but has proved difficult to read and digest for various reasons. The only new material contained in these… (More)

- Paul Shafer
- Notre Dame Journal of Formal Logic
- 2011

We characterize the join-irreducible Medvedev degrees as the degrees of complements of Turing ideals, thereby solving a problem posed by Sorbi. We use this characterization to prove that there are Medvedev degrees above the second-least degree that do not bound any join-irreducible degrees above this second-least degree. This solves a problem posed by Sorbi… (More)

- Eric O. Williams, Yuanyuan Xiao, +4 authors David M. Lin
- BMC Developmental Biology
- 2007

In the mouse olfactory system, the role of the olfactory bulb in guiding olfactory sensory neuron (OSN) axons to their targets is poorly understood. What cell types within the bulb are necessary for targeting is unknown. What genes are important for this process is also unknown. Although projection neurons are not required, other cell-types within the… (More)

- Paul Shafer
- J. Symb. Log.
- 2011

We prove that the first-order theory of the Medvedev degrees, the first-order theory of the Muchnik degrees, and the third-order theory of true arithmetic are pairwise recursively isomorphic (obtained independently by Lewis, Nies, and Sorbi [7]). We then restrict our attention to the degrees of closed sets and prove that the following theories are pairwise… (More)

- François G. Dorais, Jeffry L. Hirst, Paul Shafer
- J. Logic & Analysis
- 2012

Using the techniques of reverse mathematics, we analyze the logical strength of statements similar to trichotomy and dichotomy for sequences of reals. Capitalizing on the connection between sequential statements and constructivity, we find computable restrictions of the statements for sequences and constructive restrictions of the original principles. 2010… (More)

- M. K. Marcham, Paul S Keatley, +9 authors Elke Arenholz
- 2011

fluorescence yield M. K. Marcham, P. S. Keatley, A. Neudert, R. J. Hicken, S. A. Cavill, L. R. Shelford, G. van der Laan, N. D. Telling, J. R. Childress, J. A. Katine, P. Shafer, and E. Arenholz School of Physics, University of Exeter, Stocker Road, Exeter, Devon EX4 4QL, United Kingdom Forschungszentrum Dresden-Rossendorf e. V., Institute of Ion Beam… (More)

- François G. Dorais, Jeffry L. Hirst, Paul Shafer
- J. Symb. Log.
- 2015

We prove that the statement “there is a k such that for every f there is a k-bounded diagonally non-recursive function relative to f” does not imply weak König’s lemma over RCA0+BΣ 0 2. This answers a question posed by Simpson. A recursion-theoretic consequence is that the classic fact that every k-bounded diagonally non-recursive function computes a… (More)

- Laurent Bienvenu, Rupert Hölzl, Christopher P. Porter, Paul Shafer
- Notre Dame Journal of Formal Logic
- 2017