Factorization methods for Noncommutative KP and Toda hierarchy

We show that the solution space of the noncommutative KP hierarchy is the same as that of the commutative KP hierarchy owing to the Birkhoff decomposition of groups over the noncommutative algebra. The noncommutative Toda hierarchy is introduced. We derive the bilinear identities for the Baker--Akhiezer functions and calculate the $N$-soliton solutions of the noncommutative Toda hierarchy.Comment: 7 pages, no figures, AMS-LaTeX, minor corrections, final version to appear in Journal of Physics

A Planarity Test via Construction Sequences

Optimal linear-time algorithms for testing the planarity of a graph are well-known for over 35 years. However, these algorithms are quite involved and recent publications still try to give simpler linear-time tests. We give a simple reduction from planarity testing to the problem of computing a certain construction of a 3-connected graph. The approach is different from previous planarity tests; as key concept, we maintain a planar embedding that is 3-connected at each point in time. The algorithm runs in linear time and computes a planar embedding if the input graph is planar and a Kuratowski-subdivision otherwise

Vertex Operators for Closed Superstrings

We construct an iterative procedure to compute the vertex operators of the closed superstring in the covariant formalism given a solution of IIA/IIB supergravity. The manifest supersymmetry allows us to construct vertex operators for any generic background in presence of Ramond-Ramond (RR) fields. We extend the procedure to all massive states of open and closed superstrings and we identify two new nilpotent charges which are used to impose the gauge fixing on the physical states. We solve iteratively the equations of the vertex for linear x-dependent RR field strengths. This vertex plays a role in studying non-constant C-deformations of superspace. Finally, we construct an action for the free massless sector of closed strings, and we propose a form for the kinetic term for closed string field theory in the pure spinor formalism.Comment: TeX, harvmac, amssym.tex, 41 pp; references adde

Explorations of the Extended ncKP Hierarchy

A recently obtained extension (xncKP) of the Moyal-deformed KP hierarchy (ncKP hierarchy) by a set of evolution equations in the Moyal-deformation parameters is further explored. Formulae are derived to compute these equations efficiently. Reductions of the xncKP hierarchy are treated, in particular to the extended ncKdV and ncBoussinesq hierarchies. Furthermore, a good part of the Sato formalism for the KP hierarchy is carried over to the generalized framework. In particular, the well-known bilinear identity theorem for the KP hierarchy, expressed in terms of the (formal) Baker-Akhiezer function, extends to the xncKP hierarchy. Moreover, it is demonstrated that N-soliton solutions of the ncKP equation are also solutions of the first few deformation equations. This is shown to be related to the existence of certain families of algebraic identities.Comment: 34 pages, correction of typos in (7.2) and (7.5

Notes on Exact Multi-Soliton Solutions of Noncommutative Integrable Hierarchies

We study exact multi-soliton solutions of integrable hierarchies on noncommutative space-times which are represented in terms of quasi-determinants of Wronski matrices by Etingof, Gelfand and Retakh. We analyze the asymptotic behavior of the multi-soliton solutions and found that the asymptotic configurations in soliton scattering process can be all the same as commutative ones, that is, the configuration of N-soliton solution has N isolated localized energy densities and the each solitary wave-packet preserves its shape and velocity in the scattering process. The phase shifts are also the same as commutative ones. Furthermore noncommutative toroidal Gelfand-Dickey hierarchy is introduced and the exact multi-soliton solutions are given.Comment: 18 pages, v3: references added, version to appear in JHE

TL1A/DR3 axis involvement in the inflammatory cytokine network during pulmonary sarcoidosis

BACKGROUND: TNF-like ligand 1A (TL1A), a recently recognized member of the TNF superfamily, and its death domain receptor 3 (DR3), firstly identified for their relevant role in T lymphocyte homeostasis, are now well-known mediators of several immune-inflammatory diseases, ranging from rheumatoid arthritis to inflammatory bowel diseases to psoriasis, whereas no data are available on their involvement in sarcoidosis, a multisystemic granulomatous disease where a deregulated T helper (Th)1/Th17 response takes place. METHODS: In this study, by flow cytometry, real-time PCR, confocal microscopy and immunohistochemistry analyses, TL1A and DR3 were investigated in the pulmonary cells and the peripheral blood of 43 patients affected by sarcoidosis in different phases of the disease (29 patients with active sarcoidosis, 14 with the inactive form) and in 8 control subjects. RESULTS: Our results demonstrated a significant higher expression, both at protein and mRNA levels, of TL1A and DR3 in pulmonary T cells and alveolar macrophages of patients with active sarcoidosis as compared to patients with the inactive form of the disease and to controls. In patients with sarcoidosis TL1A was strongly more expressed in the lung than the blood, i.e., at the site of the involved organ. Additionally, zymography assays showed that TL1A is able to increase the production of matrix metalloproteinase 9 by sarcoid alveolar macrophages characterized, in patients with the active form of the disease, by reduced mRNA levels of the tissue inhibitor of metalloproteinase (TIMP)-1. CONCLUSIONS: These data suggest that TL1A/DR3 interactions are part of the extended and complex immune-inflammatory network that characterizes sarcoidosis during its active phase and may contribute to the pathogenesis and to the progression of the disease

Pixel and Voxel Representations of Graphs

We study contact representations for graphs, which we call pixel representations in 2D and voxel representations in 3D. Our representations are based on the unit square grid whose cells we call pixels in 2D and voxels in 3D. Two pixels are adjacent if they share an edge, two voxels if they share a face. We call a connected set of pixels or voxels a blob. Given a graph, we represent its vertices by disjoint blobs such that two blobs contain adjacent pixels or voxels if and only if the corresponding vertices are adjacent. We are interested in the size of a representation, which is the number of pixels or voxels it consists of. We first show that finding minimum-size representations is NP-complete. Then, we bound representation sizes needed for certain graph classes. In 2D, we show that, for $k$-outerplanar graphs with $n$ vertices, $\Theta(kn)$ pixels are always sufficient and sometimes necessary. In particular, outerplanar graphs can be represented with a linear number of pixels, whereas general planar graphs sometimes need a quadratic number. In 3D, $\Theta(n^2)$ voxels are always sufficient and sometimes necessary for any $n$-vertex graph. We improve this bound to $\Theta(n\cdot \tau)$ for graphs of treewidth $\tau$ and to $O((g+1)^2n\log^2n)$ for graphs of genus $g$. In particular, planar graphs admit representations with $O(n\log^2n)$ voxels

Indexing Information for Data Forensics

We introduce novel techniques for organizing the indexing structures of how data is stored so that alterations from an original version can be detected and the changed values specifically identified. We give forensic constructions for several fundamental data structures, including arrays, linked lists, binary search trees, skip lists, and hash tables. Some of our constructions are based on a new reduced-randomness construction for nonadaptive combinatorial group testing

Effect of 3-nitrooxypropanol on enteric methane emissions of feedlot cattle fed with a tempered barley-based diet with canola oil

A dose-response experiment was designed to examine the effect of 3-nitrooxypropanol (3-NOP) on methane (CH4) emissions, rumen function and performance of feedlot cattle fed a tempered barley-based diet with canola oil. Twenty Angus steers of initial body weight (BW) of 356 ± 14.4 kg were allocated in a randomized complete block design. Initial BW was used as the blocking criterion. Cattle were housed in individual indoor pens for 112 d, including the first 21 d of adaptation followed by a 90-d finishing period when five different 3-NOP inclusion rates were compared: 0 mg/kg dry matter (DM; control), 50 mg/kg DM, 75 mg/kg DM, 100 mg/kg DM, and 125 mg/kg DM. Daily CH4 production was measured on day 7 (last day of starter diet), day 14 (last day of the first intermediate diet), and day 21 (last day of the second intermediate diet) of the adaptation period and on days 28, 49, 70, 91, and 112 of the finisher period using open circuit respiration chambers. Rumen digesta samples were collected from each steer on the day prior to chamber measurement postfeeding, and prefeeding on the day after the chamber measurement, for determination of rumen volatile fatty acids (VFA), ammonium-N, protozoa enumeration, pH, and reduction potential. Dry matter intake (DMI) was recorded daily and BW weekly. Data were analyzed in a mixed model including period, 3-NOP dose and their interaction as fixed effects, and block as a random effect. Our results demonstrated both a linear and quadratic (decreasing rate of change) effect on CH4 production (g/d) and CH4 yield (g/kg DMI) as 3-NOP dose increased (P < 0.01). The achieved mitigation for CH4 yield in our study ranged from approximately 65.5% up to 87.6% relative to control steers fed a finishing feedlot diet. Our results revealed that 3-NOP dose did not alter rumen fermentation parameters such as ammonium-N, VFA concentration nor VFA molar proportions. Although this experimental design was not focused on the effect of 3-NOP dose on feedlot performance, no negative effects of any 3-NOP dose were detected on animal production parameters. Ultimately, the knowledge on the CH4 suppression pattern of 3-NOP may facilitate sustainable pathways for the feedlot industry to lower its carbon footprint.fals

Cellular dissection of psoriasis for transcriptome analyses and the post-GWAS era

Abstract Background Genome-scale studies of psoriasis have been used to identify genes of potential relevance to disease mechanisms. For many identified genes, however, the cell type mediating disease activity is uncertain, which has limited our ability to design gene functional studies based on genomic findings. Methods We identified differentially expressed genes (DEGs) with altered expression in psoriasis lesions (n = 216 patients), as well as candidate genes near susceptibility loci from psoriasis GWAS studies. These gene sets were characterized based upon their expression across 10 cell types present in psoriasis lesions. Susceptibility-associated variation at intergenic (non-coding) loci was evaluated to identify sites of allele-specific transcription factor binding. Results Half of DEGs showed highest expression in skin cells, although the dominant cell type differed between psoriasis-increased DEGs (keratinocytes, 35%) and psoriasis-decreased DEGs (fibroblasts, 33%). In contrast, psoriasis GWAS candidates tended to have highest expression in immune cells (71%), with a significant fraction showing maximal expression in neutrophils (24%, P < 0.001). By identifying candidate cell types for genes near susceptibility loci, we could identify and prioritize SNPs at which susceptibility variants are predicted to influence transcription factor binding. This led to the identification of potentially causal (non-coding) SNPs for which susceptibility variants influence binding of AP-1, NF-κB, IRF1, STAT3 and STAT4. Conclusions These findings underscore the role of innate immunity in psoriasis and highlight neutrophils as a cell type linked with pathogenetic mechanisms. Assignment of candidate cell types to genes emerging from GWAS studies provides a first step towards functional analysis, and we have proposed an approach for generating hypotheses to explain GWAS hits at intergenic loci.http://deepblue.lib.umich.edu/bitstream/2027.42/109537/1/12920_2013_Article_485.pd