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

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

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

Graph Layouts by t‐SNE

We propose a new graph layout method based on a modification of the t-distributed Stochastic Neighbor Embedding (t-SNE) dimensionality reduction technique. Although t-SNE is one of the best techniques for visualizing high-dimensional data as 2D scatterplots, t-SNE has not been used in the context of classical graph layout. We propose a new graph layout method, tsNET, based on representing a graph with a distance matrix, which together with a modified t-SNE cost function results in desirable layouts. We evaluate our method by a formal comparison with state-of-the-art methods, both visually and via established quality metrics on a comprehensive benchmark, containing real-world and synthetic graphs. As evidenced by the quality metrics and visual inspection, tsNET produces excellent layouts

CCRL2 Expression by Specialized Lung Capillary Endothelial Cells Controls NK-cell Homing in Lung Cancer

Patterns of receptors for chemotactic factors regulate the homing of leukocytes to tissues. Here we report that the CCRL2/chemerin/CMKLR1 axis represents a selective pathway for the homing of natural killer (NK) cells to the lung. C-C motif chemokine receptor-like 2 (CCRL2) is a nonsignaling seven-transmembrane domain receptor able to control lung tumor growth. CCRL2 constitutive or conditional endothelial cell targeted ablation, or deletion of its ligand chemerin, were found to promote tumor progression in a Kras/p53Flox lung cancer cell model. This phenotype was dependent on the reduced recruitment of CD27- CD11b+ mature NK cells. Other chemotactic receptors identified in lung-infiltrating NK cells by single-cell RNA sequencing (scRNA-seq), such as Cxcr3, Cx3cr1, and S1pr5, were found to be dispensable in the regulation of NK-cell infiltration of the lung and lung tumor growth. scRNA-seq identified CCRL2 as the hallmark of general alveolar lung capillary endothelial cells. CCRL2 expression was epigenetically regulated in lung endothelium and it was upregulated by the demethylating agent 5-aza-2'-deoxycytidine (5-Aza). In vivo administration of low doses of 5-Aza induced CCRL2 upregulation, increased recruitment of NK cells, and reduced lung tumor growth. These results identify CCRL2 as an NK-cell lung homing molecule that has the potential to be exploited to promote NK cell-mediated lung immune surveillance