Paul Shafer

Hubs of knowledge: using the functional link structure in Biozon to mine for biologically significant entities

BackgroundExisting 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.ResultsWe describe a system that builds upon the complex infrastructure of the Biozon database and applies methods similar to those of Google to rank documents that match queries. We explore different prominence models and study the spectral properties of the corresponding data graphs. We evaluate the information content of principal and non-principal eigenspaces, and test various scoring functions which combine contributions from multiple eigenspaces. We also test the effect of similarity data and other variations which are unique to the biological knowledge domain on the quality of the results. Query result sets are assessed using a probabilistic approach that measures the significance of coherence between directly connected nodes in the data graph. This model allows us, for the first time, to compare different prominence models quantitatively and effectively and to observe unique trends.ConclusionOur tests show that the ranked query results outperform unsorted results with respect to our significance measure and the top ranked entities are typically linked to many other biological entities. Our study resulted in a working ranking system of biological entities that was integrated into Biozon at http://biozon.org.

Characterizing the Join-Irreducible Medvedev Degrees

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 and Terwijn. Finally, we prove that the filter generated by the degrees of closed sets is not prime. This solves a problem posed by Bianchini and Sorbi.

Novel subdomains of the mouse olfactory bulb defined by molecular heterogeneity in the nascent external plexiform and glomerular layers

BackgroundIn 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 external plexiform and glomerular layers also form synapses with OSNs. We hypothesized that these cells are important for targeting, and express spatially differentially expressed guidance cues that act to guide OSN axons within the bulb.ResultsWe used laser microdissection and microarray analysis to find genes that are differentially expressed along the dorsal-ventral, medial-lateral, and anterior-posterior axes of the bulb. The expression patterns of these genes divide the bulb into previously unrecognized subdomains. Interestingly, some genes are expressed in both the medial and lateral bulb, showing for the first time the existence of symmetric expression along this axis. We use a regeneration paradigm to show that several of these genes are altered in expression in response to deafferentation, consistent with the interpretation that they are expressed in cells that interact with OSNs.ConclusionWe demonstrate that the nascent external plexiform and glomerular layers of the bulb can be divided into multiple domains based on the expression of these genes, several of which are known to function in axon guidance, synaptogenesis, and angiogenesis. These genes represent candidate guidance cues that may act to guide OSN axons within the bulb during targeting.

Randomness and Semimeasures

A semimeasure is a generalization of a probability measure obtained by relaxing the additivity requirement to superadditivity. We introduce and study several randomness notions for left-c.e. semimeasures, a natural class of effectively approximable semimeasures induced by Turing functionals. Among the randomness notions we consider, the generalization of weak 2-randomness to left-c.e. semimeasures is the most compelling, as it best reflects Martin-Lof randomness with respect to a computable measure. Additionally, we analyze a question of Shen, a positive answer to which would also have yielded a reasonable randomness notion for left-c.e. semimeasures. Unfortunately, though, we find a negative answer, except for some special cases.

EST2Prot: Mapping EST sequences to proteins

BackgroundEST libraries are used in various biological studies, from microarray experiments to proteomic and genetic screens. These libraries usually contain many uncharacterized ESTs that are typically ignored since they cannot be mapped to known genes. Consequently, new discoveries are possibly overlooked.ResultsWe describe a system (EST2Prot) that uses multiple elements to map EST sequences to their corresponding protein products. EST2Prot uses UniGene clusters, substring analysis, information about protein coding regions in existing DNA sequences and protein database searches to detect protein products related to a query EST sequence. Gene Ontology terms, Swiss-Prot keywords, and protein similarity data are used to map the ESTs to functional descriptors.ConclusionEST2Prot extends and significantly enriches the popular UniGene mapping by utilizing multiple relations between known biological entities. It produces a mapping between ESTs and proteins in real-time through a simple web-interface. The system is part of the Biozon database and is accessible at http://biozon.org/tools/est/.

On the logical strengths of partial solutions to mathematical problems

We use the framework of reverse mathematics to address the question of, given a mathematical problem, whether or not it is easier to find an infinite partial solution than it is to find a complete solution. Following Flood [‘Reverse mathematics and a Ramsey-type Konigs lemma’, J. Symb. Log. 77 (2012) 1272–1280], we say that a Ramsey-type variant of a problem is the problem with the same instances but whose solutions are the infinite partial solutions to the original problem. We study Ramsey-type variants of problems related to Konigs lemma, such as restrictions of Konigs lemma, Boolean satisfiability problems and graph coloring problems. We find that sometimes the Ramsey-type variant of a problem is strictly easier than the original problem (as Flood showed with weak Konigs lemma) and that sometimes the Ramsey-type variant of a problem is equivalent to the original problem. We show that the Ramsey-type variant of weak Konigs lemma is robust in the sense of Montalban [‘Open questions in reverse mathematics’, Bull. Symb. Log. 17 (2011) 431–454]: it is equivalent to several perturbations. We also clarify the relationship between Ramsey-type weak Konigs lemma and algorithmic randomness by showing that Ramsey-type weak weak Konigs lemma is equivalent to the problem of finding diagonally non-recursive functions and that these problems are strictly easier than Ramsey-type weak Konigs lemma. This answers a question of Flood.

Reverse mathematics, well-quasi-orders, and Noetherian spaces

A quasi-order Q induces two natural quasi-orders on

Honest elementary degrees and degrees of relative provability without the cupping property

{\mathcal{P}(Q)}