| 1. |
- Bohler, Cecilia, et al.
(författare)
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Forest-like abstract Voronoi diagrams in linear time
- 2018
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Ingår i: Computational Geometry: Theory and Applications. - : Elsevier BV. - 0925-7721. ; 68, s. 134-145
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Tidskriftsartikel (refereegranskat)abstract
- Abstract Voronoi diagrams are a general framework covering many types of concrete diagrams for different types of sites or distance measures. Generalizing a famous result by Aggarwal et al. we prove the following. Suppose it is known that inside a closed domain D the Voronoi diagram V(S) is a tree, and for each subset S'⊂S, a forest with one face per site. If the order of Voronoi regions of V(S) along the boundary of D is given, then V(S) inside D can be constructed in linear time.
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| 2. |
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| 3. |
- Klein, Rolf, et al.
(författare)
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A Fire Fighter's Problem.
- 2015
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Ingår i: Leibniz International Proceedings in Informatics (LIPIcs). - 1868-8969. ; 34, s. 768-780
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Konferensbidrag (refereegranskat)abstract
- Suppose that a circular fire spreads in the plane at unit speed. A fire fighter can build a barrier at speed v > 1. How large must v be to ensure that the fire can be contained, and how should the fire fighter proceed? We provide two results. First, we analyze the natural strategy where the fighter keeps building a barrier along the frontier of the expanding fire. We prove that this approach contains the fire if v > v_c = 2.6144... holds. Second, we show that any "spiralling" strategy must have speed v > 1.618, the golden ratio, in order to succeed.
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| 4. |
- Klein, Rolf, et al.
(författare)
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Approximation Algorithms for the Geometric Firefighter and Budget Fence Problems
- 2018
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Ingår i: Algorithms. - : MDPI AG. - 1999-4893. ; 11:4
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Tidskriftsartikel (refereegranskat)abstract
- Let R denote a connected region inside a simple polygon, P. By building barriers (typically straight-line segments) in P∖R, we want to separate from R part(s) of P of maximum area. All edges of the boundary of P are assumed to be already constructed or natural barriers. In this paper we introduce two versions of this problem. In the budget fence version the region R is static, and there is an upper bound on the total length of barriers we may build. In the basic geometric firefighter version we assume that R represents a fire that is spreading over P at constant speed (varying speed can also be handled). Building a barrier takes time proportional to its length, and each barrier must be completed before the fire arrives. In this paper we are assuming that barriers are chosen from a given set B that satisfies certain conditions. Even for simple cases (e.g., P is a convex polygon and B the set of all diagonals), both problems are shown to be NP-hard. Our main result is an efficient ≈11.65 approximation algorithm for the firefighter problem, where the set B of allowed barriers is any set of straight-line segments with all endpoints on the boundary of P and pairwise disjoint interiors. Since this algorithm solves a much more general problem—a hybrid of scheduling and maximum coverage—it may find wider applications. We also provide a polynomial-time approximation scheme for the budget fence problem, for the case where barriers chosen from a set of straight-line cuts of the polygon must not cross.
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| 5. |
- Klein, Rolf, et al.
(författare)
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On a Fire Fighter’s Problem
- 2019
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Ingår i: International Journal of Foundations of Computer Science. - 0129-0541. ; 30:02, s. 231-246
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Tidskriftsartikel (refereegranskat)abstract
- Suppose that a circular fire spreads in the plane at unit speed. A single fire fighter can build a barrier at speed v>1. How large must v be to ensure that the fire can be contained, and how should the fire fighter proceed? We contribute two results. First, we analyze the natural curve FFv that develops when the fighter keeps building, at speed v, a barrier along the boundary of the expanding fire. We prove that the behavior of this spiralling curve is governed by a complex function (ewZ−sZ)−1, where w and s are real functions of v. For v>vc=2.6144… all zeroes are complex conjugate pairs. If ϕ denotes the complex argument of the conjugate pair nearest to the origin then, by residue calculus, the fire fighter needs Θ(1/ϕ) rounds before the fire is contained. As v decreases towards vc these two zeroes merge into a real one, so that argument ϕ goes to 0. Thus, curve FFv does not contain the fire if the fighter moves at speed v=vc. (That speed v>vc is sufficient for containing the fire has been proposed before by Bressan et al. [6], who constructed a sequence of logarithmic spiral segments that stay strictly away from the fire.) Second, we show that for any curve that visits the four coordinate half-axes in cyclic order, and in increasing distances from the origin the fire can not be contained if the speed v is less than 1.618…, the golden ratio.
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| 6. |
- Olivier, Cecille, et al.
(författare)
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New strategies for the conduct of clinical trials in paediatric Pulmonary Arterial Hypertension (PAH): Outcome of a multi-stakeholder meeting with patients, academia, industry and regulators held at EMA on Monday 12th June 2017
- 2019
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Ingår i: Journal of the American Heart Association. - 2047-9980. ; 8:10, s. 1-10
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Forskningsöversikt (refereegranskat)abstract
- Aims: Drug development for paediatric pulmonary arterial hypertension (PAH) ispressingly needed. Experts from the US Food and Drug Administration, EuropeanMedicines Agency, Health Canada, key opinion leaders, academia, patients, and industry representatives held a workshop on 12th June 2017 dedicated to addressing challenges and unmet needs. This report summarises the approaches proposed during the meeting to address key issues in extrapolation, trial design, and study endpoints in pediatric drug development.Methods and Results: A pre-workshop stakeholder survey was conducted and showed that most respondents believe the pathophysiology of heritable PAH and some forms of idiopathic PAH is thought to be sufficiently similar in adult and paediatric patients, although the clinical manifestations may differ. In this situation, placebo-controlled trials might not be required to confirm clinical benefit in paediatrics. The study endpoints used to support drug approvals in adults were reviewed to determine if these existing study endpoints can be applied in paediatric PAH efficacy trials. It showed that non-invasive study endpoints, such as the time to clinical worsening, WHO functionalclass, and 6-Minute-Walk-Test could be applicable in paediatric PAH trials, although each presents some limitations in paediatrics.Conclusion: Extrapolation of efficacy from informative adult studies may be appropriate in some forms of PAH. Initial dose-finding studies and exposure-response modelling are warranted in paediatric PAH, followed by an efficacy and safety study to explore the response to treatment and exposure-response relationship. A novel, non-invasive, developmentally-appropriate, and reliable study endpoint needs to be developed.
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| 7. |
- Zweegman, Sonja, et al.
(författare)
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Melphalan, prednisone, and lenalidomide versus melphalan, prednisone, and thalidomide in untreated multiple myeloma.
- 2016
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Ingår i: Blood. - : American Society of Hematology. - 1528-0020 .- 0006-4971. ; 127:9, s. 1109-1116
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Tidskriftsartikel (refereegranskat)abstract
- The combination of melphalan, prednisone and thalidomide (MPT) is considered standard therapy for newly diagnosed patients with multiple myeloma (NDMM) who are ineligible for stem-cell transplantation. Long term treatment with thalidomide is hampered by neurotoxicity. Melphalan, prednisone and lenalidomide, followed by lenalidomide maintenance therapy showed promising results, without severe neuropathy emerging. We randomly assigned 668 NDMM patients, ineligible for stem-cell transplantation, between nine 4-weekly cycles of MPT followed by thalidomide maintenance until disease progression or unacceptable toxicity (MPT-T) and the same MP regimen with thalidomide being replaced by lenalidomide (MPR-R). This multicenter, open-label, randomised phase 3 trial was undertaken by HOVON and the NMSG. The primary endpoint was progression-free survival (PFS). The accrual for the study was completed in October 19, 2012. 318 patients were randomly assigned to receive MPT-T and 319 MPR-R. After a median follow up of 36 months PFS with MPT-T was 20 months (95% CI 18-23 months) versus 23 months (95% CI 19-27 months) with MPR-R (HR 0.87 [0.72-1.04], p=0.12). Response rates were similar, with ≥VGPR 47% and 45% respectively. Hematological toxicity was more pronounced with MPR-R, especially grade 3 and 4 neutropenia: 64 versus 27%. Neuropathy ≥ grade 3 was significantly higher in the MPT-T arm; 16% versus 2% in MPR-R, resulting in a significant shorter duration of maintenance therapy (5 versus 17 months in MPR-R), irrespective of age. MPR-R has no advantage over MPT-T concerning efficacy. The toxicity profile differed with clinically significant neuropathy during thalidomide maintenance versus myelosuppression with MPR.
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