The Superpolynomial for Knot Homologies

We propose a framework for unifying the sl(N) Khovanov-Rozansky homology (for all N) with the knot Floer homology. We argue that this unification should be accomplished by a triply graded homology theory which categorifies the HOMFLY polynomial. Moreover, this theory should have an additional formal structure of a family of differentials. Roughly speaking, the triply graded theory by itself captures the large N behavior of the sl(N) homology, and differentials capture non-stable behavior for small N, including knot Floer homology. The differentials themselves should come from another variant of sl(N) homology, namely the deformations of it studied by Gornik, building on work of Lee. While we do not give a mathematical definition of the triply graded theory, the rich formal structure we propose is powerful enough to make many non-trivial predictions about the existing knot homologies that can then be checked directly. We include many examples where we can exhibit a likely candidate for the triply graded theory, and these demonstrate the internal consistency of our axioms. We conclude with a detailed study of torus knots, developing a picture which gives new predictions even for the original sl(2) Khovanov homology.Comment: 46 pages, 30 figures. V2: Minor improvements. To appear in Exp. Mat

A unified Casson-Lin invariant for the real forms of SL(2)

We introduce a unified framework for counting representations of knot groups into $SU(2)$ and $SL(2, \mathbb{R})$. For a knot $K$ in the 3-sphere, Lin and others showed that a Casson-style count of $SU(2)$ representations with fixed meridional holonomy recovers the signature function of $K$. For knots whose complement contains no closed essential surface, we show there is an analogous count for $SL(2, \mathbb{R})$ representations. We then prove the $SL(2, \mathbb{R})$ count is determined by the $SU(2)$ count and a single integer $h(K)$, allowing us to show the existence of various $SL(2, \mathbb{R})$ representations using only elementary topological hypotheses. Combined with the translation extension locus of Culler-Dunfield, we use this to prove left-orderability of many 3-manifold groups obtained by cyclic branched covers and Dehn fillings on broad classes of knots. We give further applications to the existence of real parabolic representations, including a generalization of the Riley Conjecture (proved by Gordon) to alternating knots. These invariants exhibit some intriguing patterns that deserve explanation, and we include many open questions. The close connection between $SU(2)$ and $SL(2, \mathbb{R})$ comes from viewing their representations as the real points of the appropriate $SL(2, \mathbb{C})$ character variety. While such real loci are typically highly singular at the reducible characters that are common to both $SU(2)$ and $SL(2, \mathbb{R})$, in the relevant situations, we show how to resolve these real algebraic sets into smooth manifolds. We construct these resolutions using the geometric transition $S^2 \to \mathbb{E}^2 \to \mathbb{H}^2$, studied from the perspective of projective geometry, and they allow us to pass between Casson-Lin counts of $SU(2)$ and $SL(2, \mathbb{R})$ representations unimpeded.Comment: 147 pages, 24 figure

The Clinical Evaluation of Cobalamin Deficiency by Determination of Methylmalonic Acid in Serum or Urine is not Invalidated by the Presence of Heterozygous Methylmalonic-Acidaemia

Peer Reviewe

Physical dependencies in accident sequence analysis

Includes bibliographical references (leaves 25-26)Supported by the Office of Nuclear Regulatory Research, United States Nuclear Regulatory Commission. NRC-04-88-14

Dynamic event trees in accident sequence analysis

Includes bibliographical references (leaves 14-15)Supported by the Office of Nuclear Regulatory Research, United States Nuclear Regulatory Commission NRC-04-88-14

Metagenomic analysis of historical herbarium specimens reveals a postmortem microbial community

Advances in DNA extraction and next-generation sequencing have made a vast number of historical herbarium specimens available for genomic investigation. These specimens contain not only genomic information from the individual plants themselves, but also from associated microorganisms such as bacteria and fungi. These microorganisms may have colonized the living plant (e.g., pathogens or host-associated commensal taxa) or may result from postmortem colonization that may include decomposition processes or contamination during sample handling. Here we characterize the metagenomic profile from shotgun sequencing data from herbarium specimens of two widespread plant species (Ambrosia artemisiifolia and Arabidopsis thaliana) collected up to 180 years ago. We used blast searching in combination with megan and were able to infer the metagenomic community even from the oldest herbarium sample. Through comparison with contemporary plant collections, we identify three microbial species that are nearly exclusive to herbarium specimens, including the fungus Alternaria alternata, which can comprise up to 7% of the total sequencing reads. This species probably colonizes the herbarium specimens during preparation for mounting or during storage. By removing the probable contaminating taxa, we observe a temporal shift in the metagenomic composition of the invasive weed Am. artemisiifolia. Our findings demonstrate that it is generally possible to use herbarium specimens for metagenomic analyses, but that the results should be treated with caution, as some of the identified species may be herbarium contaminants rather than representing the natural metagenomic community of the host plant

Hybridization Capture Using Short PCR Products Enriches Small Genomes by Capturing Flanking Sequences (CapFlank)

Solution hybridization capture methods utilize biotinylated oligonucleotides as baits to enrich homologous sequences from next generation sequencing (NGS) libraries. Coupled with NGS, the method generates kilo to gigabases of high confidence consensus targeted sequence. However, in many experiments, a non-negligible fraction of the resulting sequence reads are not homologous to the bait. We demonstrate that during capture, the bait-hybridized library molecules add additional flanking library sequences iteratively, such that baits limited to targeting relatively short regions (e.g. few hundred nucleotides) can result in enrichment across entire mitochondrial and bacterial genomes. Our findings suggest that some of the off-target sequences derived in capture experiments are non-randomly enriched, and that CapFlank will facilitate targeted enrichment of large contiguous sequences with minimal prior target sequence information. (Résumé d'auteur

Autobiographical memory specificity in response to verbal and pictorial cues in clinical depression

Background Depressed individuals have been consistently shown to exhibit problems in accessing specific memories of events from their past and instead tend to retrieve categorical summaries of events. The majority of studies examining autobiographical memory changes associated with psychopathology have tended to use word cues, but only one study to date has used images (with PTSD patients). Objective to determine if using images to cue autobiographical memories would reduce the memory specificity deficit exhibited by patients with depression in comparison to healthy controls. Methods Twenty-five clinically depressed patients and twenty-five healthy controls were assessed on two versions of the autobiographical memory test; cued with emotional words and images. Results Depressed patients retrieved significantly fewer specific memories, and a greater number of categorical, than did the controls. Controls retrieved a greater proportion of specific memories to images compared to words, whereas depressed patients retrieved a similar proportion of specific memories to both images and words. Limitations no information about the presence and severity of past trauma was collected. Conclusions results suggest that the overgeneral memory style in depression generalises from verbal to pictorial cues. This is important because retrieval to images may provide a more ecologically valid test of everyday memory experiences than word-cued retrieval