Succinct representation of triangulations with a boundary

We consider the problem of designing succinct geometric data structures while maintaining efficient navigation operations. A data structure is said succinct if the asymptotic amount of space it uses matches the entropy of the class of structures represented. For the case of planar triangulations with a boundary we propose a succinct representation of the combinatorial information that improves to 2.175 bits per triangle the asymptotic amount of space required and that supports the navigation between adjacent triangles in constant time (as well as other standard operations). For triangulations with $m$ faces of a surface with genus g, our representation requires asymptotically an extra amount of 36(g-1)lg m bits (which is negligible as long as g << m/lg m)

Random trees between two walls: Exact partition function

We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labeled by integers representing their position in the target space, with the SOS constraint that adjacent vertices have labels differing by +1 or -1. A non-trivial partition function is obtained whenever the target space is bounded by walls. We concentrate on the two cases where the target space is (i) the half-line bounded by a wall at the origin or (ii) a segment bounded by two walls at a finite distance. The general solution has a soliton-like structure involving elliptic functions. We derive the corresponding continuum scaling limit which takes the remarkable form of the Weierstrass p-function with constrained periods. These results are used to analyze the probability for an evolving population spreading in one dimension to attain the boundary of a given domain with the geometry of the target (i) or (ii). They also translate, via suitable bijections, into generating functions for bounded planar graphs.Comment: 25 pages, 7 figures, tex, harvmac, epsf; accepted version; main modifications in Sect. 5-6 and conclusio

Balanced Schnyder woods for planar triangulations: an experimental study with applications to graph drawing and graph separators

In this work we consider balanced Schnyder woods for planar graphs, which are Schnyder woods where the number of incoming edges of each color at each vertex is balanced as much as possible. We provide a simple linear-time heuristic leading to obtain well balanced Schnyder woods in practice. As test applications we consider two important algorithmic problems: the computation of Schnyder drawings and of small cycle separators. While not being able to provide theoretical guarantees, our experimental results (on a wide collection of planar graphs) suggest that the use of balanced Schnyder woods leads to an improvement of the quality of the layout of Schnyder drawings, and provides an efficient tool for computing short and balanced cycle separators.Comment: Appears in the Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019

Worldwide trends in population-based survival for children, adolescents, and young adults diagnosed with leukaemia, by subtype, during 2000–14 (CONCORD-3) : analysis of individual data from 258 cancer registries in 61 countries

Background Leukaemias comprise a heterogenous group of haematological malignancies. In CONCORD-3, we analysed data for children (aged 0–14 years) and adults (aged 15–99 years) diagnosed with a haematological malignancy during 2000–14 in 61 countries. Here, we aimed to examine worldwide trends in survival from leukaemia, by age and morphology, in young patients (aged 0–24 years). Methods We analysed data from 258 population-based cancer registries in 61 countries participating in CONCORD-3 that submitted data on patients diagnosed with leukaemia. We grouped patients by age as children (0–14 years), adolescents (15–19 years), and young adults (20–24 years). We categorised leukaemia subtypes according to the International Classification of Childhood Cancer (ICCC-3), updated with International Classification of Diseases for Oncology, third edition (ICD-O-3) codes. We estimated 5-year net survival by age and morphology, with 95% CIs, using the non-parametric Pohar-Perme estimator. To control for background mortality, we used life tables by country or region, single year of age, single calendar year and sex, and, where possible, by race or ethnicity. All-age survival estimates were standardised to the marginal distribution of young people with leukaemia included in the analysis. Findings 164563 young people were included in this analysis: 121328 (73·7%) children, 22963 (14·0%) adolescents, and 20272 (12·3%) young adults. In 2010–14, the most common subtypes were lymphoid leukaemia (28205 [68·2%] patients) and acute myeloid leukaemia (7863 [19·0%] patients). Age-standardised 5-year net survival in children, adolescents, and young adults for all leukaemias combined during 2010–14 varied widely, ranging from 46% in Mexico to more than 85% in Canada, Cyprus, Belgium, Denmark, Finland, and Australia. Individuals with lymphoid leukaemia had better age-standardised survival (from 43% in Ecuador to ≥80% in parts of Europe, North America, Oceania, and Asia) than those with acute myeloid leukaemia (from 32% in Peru to ≥70% in most high-income countries in Europe, North America, and Oceania). Throughout 2000–14, survival from all leukaemias combined remained consistently higher for children than adolescents and young adults, and minimal improvement was seen for adolescents and young adults in most countries. Interpretation This study offers the first worldwide picture of population-based survival from leukaemia in children, adolescents, and young adults. Adolescents and young adults diagnosed with leukaemia continue to have lower survival than children. Trends in survival from leukaemia for adolescents and young adults are important indicators of the quality of cancer management in this age group.peer-reviewe

Global survival trends for brain tumors, by histology: analysis of individual records for 556,237 adults diagnosed in 59 countries during 2000–2014 (CONCORD-3)

Background: Survival is a key metric of the effectiveness of a health system in managing cancer. We set out to provide a comprehensive examination of worldwide variation and trends in survival from brain tumors in adults, by histology. Methods: We analyzed individual data for adults (15–99 years) diagnosed with a brain tumor (ICD-O-3 topography code C71) during 2000–2014, regardless of tumor behavior. Data underwent a 3-phase quality control as part of CONCORD-3. We estimated net survival for 11 histology groups, using the unbiased nonparametric Pohar Perme estimator. Results: The study included 556,237 adults. In 2010–2014, the global range in age-standardized 5-year net survival for the most common sub-types was broad: in the range 20%–38% for diffuse and anaplastic astrocytoma, from 4% to 17% for glioblastoma, and between 32% and 69% for oligodendroglioma. For patients with glioblastoma, the largest gains in survival occurred between 2000–2004 and 2005–2009. These improvements were more noticeable among adults diagnosed aged 40–70 years than among younger adults. Conclusions: To the best of our knowledge, this study provides the largest account to date of global trends in population-based survival for brain tumors by histology in adults. We have highlighted remarkable gains in 5-year survival from glioblastoma since 2005, providing large-scale empirical evidence on the uptake of chemoradiation at population level. Worldwide, survival improvements have been extensive, but some countries still lag behind. Our findings may help clinicians involved in national and international tumor pathway boards to promote initiatives aimed at more extensive implementation of clinical guidelines

Cancer data quality and harmonization in Europe: the experience of the BENCHISTA Project – international benchmarking of childhood cancer survival by stage

IntroductionVariation in stage at diagnosis of childhood cancers (CC) may explain differences in survival rates observed across geographical regions. The BENCHISTA project aims to understand these differences and to encourage the application of the Toronto Staging Guidelines (TG) by Population-Based Cancer Registries (PBCRs) to the most common solid paediatric cancers.MethodsPBCRs within and outside Europe were invited to participate and identify all cases of Neuroblastoma, Wilms Tumour, Medulloblastoma, Ewing Sarcoma, Rhabdomyosarcoma and Osteosarcoma diagnosed in a consecutive three-year period (2014-2017) and apply TG at diagnosis. Other non-stage prognostic factors, treatment, progression/recurrence, and cause of death information were collected as optional variables. A minimum of three-year follow-up was required. To standardise TG application by PBCRs, on-line workshops led by six tumour-specific clinical experts were held. To understand the role of data availability and quality, a survey focused on data collection/sharing processes and a quality assurance exercise were generated. To support data harmonization and query resolution a dedicated email and a question-and-answers bank were created.Results67 PBCRs from 28 countries participated and provided a maximally de-personalized, patient-level dataset. For 26 PBCRs, data format and ethical approval obtained by the two sponsoring institutions (UCL and INT) was sufficient for data sharing. 41 participating PBCRs required a Data Transfer Agreement (DTA) to comply with data protection regulations. Due to heterogeneity found in legal aspects, 18 months were spent on finalizing the DTA. The data collection survey was answered by 68 respondents from 63 PBCRs; 44% of them confirmed the ability to re-consult a clinician in cases where stage ascertainment was difficult/uncertain. Of the total participating PBCRs, 75% completed the staging quality assurance exercise, with a median correct answer proportion of 92% [range: 70% (rhabdomyosarcoma) to 100% (Wilms tumour)].ConclusionDifferences in interpretation and processes required to harmonize general data protection regulations across countries were encountered causing delays in data transfer. Despite challenges, the BENCHISTA Project has established a large collaboration between PBCRs and clinicians to collect detailed and standardised TG at a population-level enhancing the understanding of the reasons for variation in overall survival rates for CC, stimulate research and improve national/regional child health plans

Succinct representation of triangulations with a boundary. WADS

Abstract. We consider the problem of designing succinct geometric data structures while maintaining efficient navigation operations. A data structure is said succinct if the asymptotic amount of space it uses matches the entropy of the class of structures represented. For the case of planar triangulations with a boundary we propose a succinct representation of the combinatorial information that improves to 2.175 bits per triangle the asymptotic amount of space required and that supports the navigation between adjacent triangles in constant time (as well as other standard operations). For triangulations with m faces of a surface with genus g, our representation requires asymptotically an extra amount of 36(g − 1) lg m bits (which is negligible as long as g ≪ m / lg m).

Augmenting the connectivity of planar and geometric graphs

In this paper we study some connectivity augmentation problems. We want to make planar graphs 2-vertex (or 2-edge) connected by adding edges such that the resulting graphs remain planar. We show that it is NP-hard to find a minimum-cardinality augmentation that makes a planar graph 2-edge connected. This was known for 2-vertex connectivity. We further show that both problems are hard in a geometric setting, even when restricted to trees. For the special case of convex geometric graphs we give efficient algorithms. We also study the following related problem. Given a plane geometric graph G, two vertices s and t of G, and an integer k, how many edges have to be added to G such that G contains k edge- (or vertex-) disjoint s-t paths? For k=2 we give optimal worst-case bounds; for k=3 we characterize all cases that have a solution

Efficient and practical tree preconditioning for solving Laplacian systems

This work will appear as an extended abstract in the Proc. of the 14th International Symposium on Experimental Algorithms (SEA 2015).We consider the problem of designing efficient iterative methods for solving linear systems. In its full generality, this is one of the oldest problems in numerical analysis with a tremendous number of practical applications. In this paper, we focus on a particular type of linear systems, associated with Laplacian matrices of undirected graphs, and study a class of iterative methods for which it is possible to speed up the convergence through the combinatorial preconditioning. In particular, we consider a class of preconditioners, known as tree preconditioners, introduced by Vaidya, that have been shown to lead to asymptotic speed-up in certain cases. Rather than trying to improve the structure of the trees used in preconditioning, we propose a very simple modification to the basic tree preconditioner, which can significantly improve the performance of the iterative linear solvers in practice. We show that our modification leads to better conditioning for some special graph structures, and provide extensive experimental evidence for the drastic decrease in the complexity of the preconditioned conjugate gradient method for several classes of graphs, including 3D meshes and complex networks