Kruskal's Tree Theorem for Acyclic Term Graphs

In this paper we study termination of term graph rewriting, where we restrict our attention to acyclic term graphs. Motivated by earlier work by Plump we aim at a definition of the notion of simplification order for acyclic term graphs. For this we adapt the homeomorphic embedding relation to term graphs. In contrast to earlier extensions, our notion is inspired by morphisms. Based on this, we establish a variant of Kruskal's Tree Theorem formulated for acyclic term graphs. In proof, we rely on the new notion of embedding and follow Nash-Williams' minimal bad sequence argument. Finally, we propose a variant of the lexicographic path order for acyclic term graphs.Comment: In Proceedings TERMGRAPH 2016, arXiv:1609.0301

The solution of the Eulerian gyroscope equations by means of Lie series making use of recurrence formulas

Euler gyroscope equations solved by means of Lie series making use of recurrence formula

Solution of ordinary differential equations by means of Lie series

Solution of ordinary differential equations by Lie series - Laplace transformation, Weber parabolic-cylinder functions, Helmholtz equations, and applications in physic

Lie series for celestial mechanics, accelerators, satellite stabilization and optimization

Lie series applications to celestial mechanics, accelerators, satellite orbits, and optimizatio

The effects of Kv1.3 and IKCa1 channel inhibition on cytokine production and calcium influx of T lymphocytes in rheumatoid arthritis and ankylosing spondylitis

Kv1.3 and IKCa1 lymphocyte potassium channels have been implicated as important targets of selective immunomodulation. We compared the alterations in cytokine production upon selective inhibition of Kv1.3 or IKCa1 channels (by MGTX and TRAM, respectively) in healthy donors (HD), RA and AS patients. We also determined calcium influx kinetics and its sensitivity to Kv1.3 and IKCa1 channel inhibition following PHA activation in CD4, Th1, Th2 and CD8 cells as well as monocytes. The application of TRAM resulted in a lower production of TNF-a and IL1-RA in all three study groups. Inhibition by TRAM had contrary effects on the production of IL-1b and IL-5: While their production was increased by PBMCs of RA patients, this effect was not observed in HD and AS PBMCs. While treatment with MGTX resulted in a similar decrease in calcium influx in the CD4 and Th2 subsets across all study groups, TRAM treatment had opposite effects on RA and HD samples: It decreased calcium influx in the Th2 and CD8 subsets in RA, while only Th1 cells were affected in HDs. The effects of IKCa1 channel inhibition are controversial in samples of RA and AS patients, since it shifts the inflammatory balance into the pro-inflammatory direction

Monocyte chemoattractant proteins in the pathogenesis of systemic sclerosis

Activation of the immune system and increased synthesis of extracellular matrix proteins by fibroblasts are hallmarks in the pathogenesis of SSc. The molecular mechanisms underlying the infiltration of inflammatory cells into the skin and the subsequent activation of fibroblasts are still largely unknown. Chemokines are a family of small molecules that are classified according to the position of the NH2-terminal cysteine motif. Recent data indicate that chemokines and in particular two members of the subfamily of monocyte chemoattractant proteins, MCP-1 (CCL-2) and MCP-3 (CCL-7), might be involved in the pathogenesis of SSc. MCP-1 and -3 are overexpressed by SSc fibroblasts and in skin lesions from SSc patients compared to healthy controls. MCP-1 and -3 are chemotactic for inflammatory cells and stimulate their migration into the skin. In addition to their pro-inflammatory effects, MCP-1 and -3 contribute to tissue fibrosis by activating the synthesis of extracellular matrix proteins in SSc fibroblasts. Therapeutic strategies targeting MCP-1 have revealed promising results in several animal models of SSc. Antagonists against the receptor CCR2 are currently tested in clinical trials of a variety of diseases and also represent interesting candidates for target-directed therapy in SS

Increased expression of CD154 and FAS in SLE patients' lymphocytes

An increased level of apoptotic material and B cell activation leading to autoantibody production are hallmarks of systemic lupus erythematoses (SLE). Increased FAS expression, apoptosis, and CD154-mediated signaling, enabling T-B cell interaction are involved in the pathogenesis of SLE. This study addresses the expression profile of CD154 and FAS in the peripheral blood of patients with SLE, rheumatoid arthritis (RA) and normal healthy control donors. Surface markers on peripheral blood T and B cells from patients and healthy control donors were assessed using flow cytometry. The expression of CD154 and FAS were significantly increased in T and B cells of SLE patients as compared to healthy control donors and RA patients. In SLE and RA patients, FAS expression strongly correlated with CD154 expression on T cells, which was not found in healthy control donors. FAS expression was also associated with the occurrence of anti-DNA antibodies. We demonstrate high CD154 and FAS expression as a characteristic feature of SLE. This pattern may reflect simultaneous activation of apoptosis and activation of B-T cell interaction in SL

The projective translation equation and unramified 2-dimensional flows with rational vector fields

Let X=(x,y). Previously we have found all rational solutions of the 2-dimensional projective translation equation, or PrTE, (1-z)f(X)=f(f(Xz)(1-z)/z); here f(X)=(u(x,y),v(x,y)) is a pair of two (real or complex) functions. Solutions of this functional equation are called projective flows. A vector field of a rational flow is a pair of 2-homogenic rational functions. On the other hand, only special pairs of 2-homogenic rational functions give rise to rational flows. In this paper we are interested in all non-singular (satisfying the boundary condition) and unramified (without branching points, i.e. single-valued functions in C^2\{union of curves}) projective flows whose vector field is still rational. We prove that, up to conjugation with 1-homogenic birational plane transformation, these are of 6 types: 1) the identity flow; 2) one flow for each non-negative integer N - these flows are rational of level N; 3) the level 1 exponential flow, which is also conjugate to the level 1 tangent flow; 4) the level 3 flow expressable in terms of Dixonian (equianharmonic) elliptic functions; 5) the level 4 flow expressable in terms of lemniscatic elliptic functions; 6) the level 6 flow expressable in terms of Dixonian elliptic functions again. This reveals another aspect of the PrTE: in the latter four cases this equation is equivalent and provides a uniform framework to addition formulas for exponential, tangent, or special elliptic functions (also addition formulas for polynomials and the logarithm, though the latter appears only in branched flows). Moreover, the PrTE turns out to have a connection with Polya-Eggenberger urn models. Another purpose of this study is expository, and we provide the list of open problems and directions in the theory of PrTE; for example, we define the notion of quasi-rational projective flows which includes curves of arbitrary genus.Comment: 34 pages, 2 figure