New geometric representations and domination problems on tolerance and multitolerance graphs

Tolerance graphs model interval relations in such a way that intervals can tolerate a certain amount of overlap without being in conflict. In one of the most natural generalizations of tolerance graphs with direct applications in the comparison of DNA sequences from different organisms, namely multitolerance graphs, two tolerances are allowed for each interval – one from the left and one from the right side. Several efficient algorithms for optimization problems that are NPhard in general graphs have been designed for tolerance and multitolerance graphs. In spite of this progress, the complexity status of some fundamental algorithmic problems on tolerance and multitolerance graphs, such as the dominating set problem, remained unresolved until now, three decades after the introduction of tolerance graphs. In this article we introduce two new geometric representations for tolerance and multitolerance graphs, given by points and line segments in the plane. Apart from being important on their own, these new representations prove to be a powerful tool for deriving both hardness results and polynomial time algorithms. Using them, we surprisingly prove that the dominating set problem can be solved in polynomial time on tolerance graphs and that it is APX-hard on multitolerance graphs, solving thus a longstanding open problem. This problem is the first one that has been discovered with a different complexity status in these two graph classes. Furthermore we present an algorithm that solves the independent dominating set problem on multitolerance graphs in polynomial time, thus demonstrating the potential of this new representation for further exploitation via sweep line algorithms

Come back Marshall, all is forgiven? : Complexity, evolution, mathematics and Marshallian exceptionalism

Marshall was the great synthesiser of neoclassical economics. Yet with his qualified assumption of self-interest, his emphasis on variation in economic evolution and his cautious attitude to the use of mathematics, Marshall differs fundamentally from other leading neoclassical contemporaries. Metaphors inspire more specific analogies and ontological assumptions, and Marshall used the guiding metaphor of Spencerian evolution. But unfortunately, the further development of a Marshallian evolutionary approach was undermined in part by theoretical problems within Spencer's theory. Yet some things can be salvaged from the Marshallian evolutionary vision. They may even be placed in a more viable Darwinian framework.Peer reviewedFinal Accepted Versio

Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections

We present the most complete list of mirror pairs of Calabi-Yau complete intersections in toric ambient varieties and develop the methods to solve the topological string and to calculate higher genus amplitudes on these compact Calabi-Yau spaces. These symplectic invariants are used to remove redundancies in examples. The construction of the B-model propagators leads to compatibility conditions, which constrain multi-parameter mirror maps. For K3 fibered Calabi-Yau spaces without reducible fibers we find closed formulas for all genus contributions in the fiber direction from the geometry of the fibration. If the heterotic dual to this geometry is known, the higher genus invariants can be identified with the degeneracies of BPS states contributing to gravitational threshold corrections and all genus checks on string duality in the perturbative regime are accomplished. We find, however, that the BPS degeneracies do not uniquely fix the non-perturbative completion of the heterotic string. For these geometries we can write the topological partition function in terms of the Donaldson-Thomas invariants and we perform a non-trivial check of S-duality in topological strings. We further investigate transitions via collapsing D5 del Pezzo surfaces and the occurrence of free Z2 quotients that lead to a new class of heterotic duals.Comment: 117 pages, 1 Postscript figur

Interleukin-6 Receptor Antagonists in Critically Ill Patients with Covid-19.

BACKGROUND: The efficacy of interleukin-6 receptor antagonists in critically ill patients with coronavirus disease 2019 (Covid-19) is unclear. METHODS: We evaluated tocilizumab and sarilumab in an ongoing international, multifactorial, adaptive platform trial. Adult patients with Covid-19, within 24 hours after starting organ support in the intensive care unit (ICU), were randomly assigned to receive tocilizumab (8 mg per kilogram of body weight), sarilumab (400 mg), or standard care (control). The primary outcome was respiratory and cardiovascular organ support-free days, on an ordinal scale combining in-hospital death (assigned a value of -1) and days free of organ support to day 21. The trial uses a Bayesian statistical model with predefined criteria for superiority, efficacy, equivalence, or futility. An odds ratio greater than 1 represented improved survival, more organ support-free days, or both. RESULTS: Both tocilizumab and sarilumab met the predefined criteria for efficacy. At that time, 353 patients had been assigned to tocilizumab, 48 to sarilumab, and 402 to control. The median number of organ support-free days was 10 (interquartile range, -1 to 16) in the tocilizumab group, 11 (interquartile range, 0 to 16) in the sarilumab group, and 0 (interquartile range, -1 to 15) in the control group. The median adjusted cumulative odds ratios were 1.64 (95% credible interval, 1.25 to 2.14) for tocilizumab and 1.76 (95% credible interval, 1.17 to 2.91) for sarilumab as compared with control, yielding posterior probabilities of superiority to control of more than 99.9% and of 99.5%, respectively. An analysis of 90-day survival showed improved survival in the pooled interleukin-6 receptor antagonist groups, yielding a hazard ratio for the comparison with the control group of 1.61 (95% credible interval, 1.25 to 2.08) and a posterior probability of superiority of more than 99.9%. All secondary analyses supported efficacy of these interleukin-6 receptor antagonists. CONCLUSIONS: In critically ill patients with Covid-19 receiving organ support in ICUs, treatment with the interleukin-6 receptor antagonists tocilizumab and sarilumab improved outcomes, including survival. (REMAP-CAP ClinicalTrials.gov number, NCT02735707.)

New Geometric Representations and Domination Problems on Tolerance and Multitolerance Graphs

Tolerance graphs model interval relations in such a way that intervals can tolerate a certain amount of overlap without being in conflict. In one of the most natural generalizations of tolerance graphs with direct applications in the comparison of DNA sequences from different organisms, namely multitolerance graphs, two tolerances are allowed for each interval: one on the left side and the other on the right side. Several efficient algorithms for optimization problems that are NP-hard in general graphs have been designed for tolerance and multitolerance graphs. In spite of this progress, the complexity status of some fundamental algorithmic problems on tolerance and multitolerance graphs, such as the dominating set problem, remained unresolved until now---three decades after the introduction of tolerance graphs. In this paper we introduce two new geometric representations for tolerance and multitolerance graphs, given by points and line segments in the plane. Apart from being important on their own, these new representations prove to be a powerful tool for deriving both hardness results and polynomial time algorithms. Using them, we surprisingly prove that the dominating set problem can be solved in polynomial time on tolerance graphs and that it is APX-hard on multitolerance graphs, thus solving a longstanding open problem. This problem is the first one that has been discovered with a different complexity status in these two graph classes

Biocompatibility and tolerability of a purely bicarbonate-buffered peritoneal dialysis solution.

Contains fulltext : 80497.pdf (publisher's version ) (Open Access)BACKGROUND: Novel peritoneal dialysis solutions are characterized by a minimal content of glucose degradation products and a neutral pH. Many studies have shown the biocompatibility of neutral lactate-buffered solutions; however, until now, the effect of purely bicarbonate-buffered solutions has not been intensively studied in vivo. METHODS: This study was an open label, prospective, crossover multicenter trial to investigate the biocompatibility of a purely bicarbonate-buffered solution (bicPDF) by measuring biocompatibility parameters such as cancer antigen 125 (CA125) in peritoneal effluent. 55 patients were enrolled in the study. After a 2-week run-in phase, 53 patients could be randomized into 2 groups, starting with either standard lactate-buffered peritoneal dialysis fluid (SPDF) for 12 weeks (phase 1) and then switching to bicPDF for 12 weeks (phase 2), or vice versa. Overnight peritoneal effluents were collected at baseline and at the end of phases 1 and 2 and were tested for CA125, hyaluronic acid, vascular endothelial growth factor (VEGF), tumor necrosis factor-alpha (TNF-alpha), interleukin 6 (IL-6), interferon gamma (IFNgamma), and transforming growth factor-beta(1) (TGF-beta1). Total ultrafiltration and residual renal function were also assessed. At the end of the study, pain during fluid exchange and dwell was evaluated using special questionnaires. RESULTS: 34 patients completed the study; 27 of them provided data for analysis of the biocompatibility parameters. CA125 levels in overnight effluent were significantly higher with bicPDF (61.9 +/- 33.2 U/L) than with SPDF (18.6 +/- 18.2 U/L, p < 0.001). Hyaluronic acid levels were significantly lower after the use of bicPDF (185.0 +/- 119.6 ng/mL) than after SPDF (257.4 +/- 174.0 ng/mL, p = 0.013). Both TNF-alpha and TGF-beta1 showed higher levels with the use of bicPDF than with SPDF. No differences were observed for IL-6, VEGF, or IFNgamma levels. We observed an improvement in the glomerular filtration rate with the use of bicPDF but no differences were observed for total fluid loss. Pain scores could be analyzed in 23 patients: there was no difference between the solutions. CONCLUSIONS: The use of a purely bicarbonate-buffered low-glucose degradation product solution significantly changes most of the peritoneal effluent markers measured, suggesting an improvement in peritoneal membrane integrity. Additionally, it seems to have a positive effect on residual renal function