A Lie Algebra Method for Rational Parametrization of Severi-Brauer Surfaces

It is well-known that a Severi-Brauer surface has a rational point if and only if it is isomorphic to the projective plane. Given a Severi-Brauer surface, we study the problem to decide whether such an isomorphism to the projective plane, or such a rational point, does exist; and to construct such an isomorphism or such a point in the affirmative case. We give an algorithm using Lie algebra techniques. The algorithm has been implemented in Magma.Comment: 16 pages some minor revision

Topical and Systemic Cannabidiol Improves Trinitrobenzene Sulfonic Acid Colitis in Mice

Background/Aims: Compounds of Cannabis sativa are known to exert anti-inflammatory properties, some of them without inducing psychotropic side effects. Cannabidiol (CBD) is such a side effect-free phytocannabinoid that improves chemically induced colitis in rodents when given intraperitoneally. Here, we tested the possibility whether rectal and oral application of CBD would also ameliorate colonic inflammation, as these routes of application may represent a more appropriate way for delivering drugs in human colitis. Methods: Colitis was induced in CD1 mice by trinitrobenzene sulfonic acid. Individual groups were either treated with CBD intraperitoneally (10 mg/kg), orally (20 mg/kg) or intrarectally (20 mg/kg). Colitis was evaluated by macroscopic scoring, histopathology and the myeloperoxidase (MPO) assay. Results: Intraperitoneal treatment of mice with CBD led to improvement of colonic inflammation. Intrarectal treatment with CBD also led to a significant improvement of disease parameters and to a decrease in MPO activity while oral treatment, using the same dose as per rectum, had no ameliorating effect on colitis. Conclusion: The data of this study indicate that in addition to intraperitoneal application, intrarectal delivery of cannabinoids may represent a useful therapeutic administration route for the treatment of colonic inflammation. Copyright (C) 2012 S. Karger AG, Base

Recognizing hyperelliptic graphs in polynomial time

Recently, a new set of multigraph parameters was defined, called "gonalities". Gonality bears some similarity to treewidth, and is a relevant graph parameter for problems in number theory and multigraph algorithms. Multigraphs of gonality 1 are trees. We consider so-called "hyperelliptic graphs" (multigraphs of gonality 2) and provide a safe and complete sets of reduction rules for such multigraphs, showing that for three of the flavors of gonality, we can recognize hyperelliptic graphs in O(n log n+m) time, where n is the number of vertices and m the number of edges of the multigraph.Comment: 33 pages, 8 figure

DP1 receptor signaling prevents the onset of intrinsic apoptosis in eosinophils and functions as a transcriptional modulator

Prostaglandin (PG) D2 is the ligand for the G‐protein coupled receptors DP1 (D‐type prostanoid receptor 1) and DP2 (also known as chemoattractant receptor homologous molecule, expressed on Th2 cells; CRTH2). Both, DP1 and DP2 are expressed on the cellular surface of eosinophils; although it has become quite clear that PGD2 induces eosinophil migration mainly via DP2 receptors, the role of DP1 in eosinophil responses has remained elusive. In this study, we addressed how DP1 receptor signaling complements the pro‐inflammatory effects of DP2. We found that PGD2 prolongs the survival of eosinophils via a DP1 receptor‐mediated mechanism that inhibits the onset of the intrinsic apoptotic cascade. The DP1 agonist BW245c prevented the activation of effector caspases in eosinophils and protected mitochondrial membranes from depolarization which—as a consequence—sustained viability of eosinophils. DP1 activation in eosinophils enhanced the expression of the anti‐apoptotic gene BCL‐XL, but also induced pro‐inflammatory genes, such as VLA‐4 and CCR3. In HEK293 cells that overexpress recombinant DP1 and/or DP2 receptors, activation of DP1, but not DP2, delayed cell death and stimulated proliferation, along with induction of serum response element (SRE), a regulator of anti‐apoptotic, early‐response genes. We conclude that DP1 receptors promote the survival via SRE induction and induction of pro‐inflammatory genes. Therefore, targeting DP1 receptors, along with DP2, may contribute to anti‐inflammatory therapy in eosinophilic diseases

On Symbolic Solutions of Algebraic Partial Differential Equations

The final version of this paper appears in Grasegger G., Lastra A., Sendra J.R. and\ud Winkler F. (2014). On symbolic solutions of algebraic partial differential equations, Proc.\ud CASC 2014 SpringerVerlag LNCS 8660 pp. 111-120. DOI 10.1007/978-3-319-10515-4_9\ud and it is available at at Springer via http://DOI 10.1007/978-3-319-10515-4_9In this paper we present a general procedure for solving rst-order autonomous\ud algebraic partial di erential equations in two independent variables.\ud The method uses proper rational parametrizations of algebraic surfaces\ud and generalizes a similar procedure for rst-order autonomous ordinary\ud di erential equations. We will demonstrate in examples that, depending on\ud certain steps in the procedure, rational, radical or even non-algebraic solutions\ud can be found. Solutions computed by the procedure will depend on\ud two arbitrary independent constants

Urine metabolome profiling of immune-mediated inflammatory diseases

Background: Immune-mediated inflammatory diseases (IMIDs) are a group of complex and prevalent diseases where disease diagnostic and activity monitoring is highly challenging. The determination of the metabolite profiles of biological samples is becoming a powerful approach to identify new biomarkers of clinical utility. In order to identify new metabolite biomarkers of diagnosis and disease activity, we have performed the first large-scale profiling of the urine metabolome of the six most prevalent IMIDs: rheumatoid arthritis, psoriatic arthritis, psoriasis, systemic lupus erythematosus, Crohn?s disease, and ulcerative colitis. Methods: Using nuclear magnetic resonance, we analyzed the urine metabolome in a discovery cohort of 1210 patients and 100 controls. Within each IMID, two patient subgroups were recruited representing extreme disease activity (very high vs. very low). Metabolite association analysis with disease diagnosis and disease activity was performed using multivariate linear regression in order to control for the effects of clinical, epidemiological, or technical variability. After multiple test correction, the most significant metabolite biomarkers were validated in an independent cohort of 1200 patients and 200 controls. Results: In the discovery cohort, we identified 28 significant associations between urine metabolite levels and disease diagnosis and three significant metabolite associations with disease activity (PFDR < 0.05). Using the validation cohort, we validated 26 of the diagnostic associations and all three metabolite associations with disease activity (PFDR < 0.05). Combining all diagnostic biomarkers using multivariate classifiers we obtained a good disease prediction accuracy in all IMIDs and particularly high in inflammatory bowel diseases. Several of the associated metabolites were found to be commonly altered in multiple IMIDs, some of which can be considered as hub biomarkers. The analysis of the metabolic reactions connecting the IMID-associated metabolites showed an overrepresentation of citric acid cycle, phenylalanine, and glycine-serine metabolism pathways. Conclusions: This study shows that urine is a source of biomarkers of clinical utility in IMIDs. We have found that IMIDs show similar metabolic changes, particularly between clinically similar diseases and we have found, for the first time, the presence of hub metabolites. These findings represent an important step in the development of more efficient and less invasive diagnostic and disease monitoring methods in IMIDs

Spinal afferent neurons projecting to the rat lung and pleura express acid sensitive channels

BACKGROUND: The acid sensitive ion channels TRPV1 (transient receptor potential vanilloid receptor-1) and ASIC3 (acid sensing ion channel-3) respond to tissue acidification in the range that occurs during painful conditions such as inflammation and ischemia. Here, we investigated to which extent they are expressed by rat dorsal root ganglion neurons projecting to lung and pleura, respectively. METHODS: The tracer DiI was either injected into the left lung or applied to the costal pleura. Retrogradely labelled dorsal root ganglion neurons were subjected to triple-labelling immunohistochemistry using antisera against TRPV1, ASIC3 and neurofilament 68 (marker for myelinated neurons), and their soma diameter was measured. RESULTS: Whereas 22% of pulmonary spinal afferents contained neither channel-immunoreactivity, at least one is expressed by 97% of pleural afferents. TRPV1(+)/ASIC3(- )neurons with probably slow conduction velocity (small soma, neurofilament 68-negative) were significantly more frequent among pleural (35%) than pulmonary afferents (20%). TRPV1(+)/ASIC3(+ )neurons amounted to 14 and 10% respectively. TRPV1(-)/ASIC3(+ )neurons made up between 44% (lung) and 48% (pleura) of neurons, and half of them presumably conducted in the A-fibre range (larger soma, neurofilament 68-positive). CONCLUSION: Rat pleural and pulmonary spinal afferents express at least two different acid-sensitive channels that make them suitable to monitor tissue acidification. Patterns of co-expression and structural markers define neuronal subgroups that can be inferred to subserve different functions and may initiate specific reflex responses. The higher prevalence of TRPV1(+)/ASIC3(- )neurons among pleural afferents probably reflects the high sensitivity of the parietal pleura to painful stimuli