2-factors with k cycles in Hamiltonian graphs

A well known generalisation of Dirac's theorem states that if a graph $G$ on $n\ge 4k$ vertices has minimum degree at least $n/2$ then $G$ contains a $2$-factor consisting of exactly $k$ cycles. This is easily seen to be tight in terms of the bound on the minimum degree. However, if one assumes in addition that $G$ is Hamiltonian it has been conjectured that the bound on the minimum degree may be relaxed. This was indeed shown to be true by S\'ark\"ozy. In subsequent papers, the minimum degree bound has been improved, most recently to $(2/5+\varepsilon)n$ by DeBiasio, Ferrara, and Morris. On the other hand no lower bounds close to this are known, and all papers on this topic ask whether the minimum degree needs to be linear. We answer this question, by showing that the required minimum degree for large Hamiltonian graphs to have a $2$-factor consisting of a fixed number of cycles is sublinear in $n.$Comment: 13 pages, 6 picture

Scaling up antiretroviral therapy in Malawi-implications for managing other chronic diseases in resource-limited countries.

The national scale-up of antiretroviral therapy (ART) in Malawi is based on the public health approach, with principles and practices borrowed from the successful DOTS (directly observed treatment, short course) tuberculosis control framework. The key principles include political commitment, free care, and standardized systems for case finding, treatment, recording and reporting, and drug procurement. Scale-up of ART started in June 2004, and by December 2008, 223,437 patients were registered for treatment within a health system that is severely underresourced. The Malawi model for delivering lifelong ART can be adapted and used for managing patients with chronic noncommunicable diseases, the burden of which is already high and continues to grow in low-income and middle-income countries. This article discusses how the principles behind the successful Malawi model of ART delivery can be applied to the management of other chronic diseases in resource-limited settings and how this paradigm can be used for health systems strengthening

A Robustness Study for the Extraction of Watertight Volumetric Models from Boundary Representation Data

Geometrically induced topology plays a major role in applications such as simulations, navigation, spatial or spatio-temporal analysis and many more. This article computes geometrically induced topology useful for such applications and extends previous results by presenting the unpublished used algorithms to find inner disjoint (d+1)-dimensional simplicial complexes from a set of intersecting d-dimensional simplicial complexes which partly shape their B-Reps (Boundary Representations). CityGML has been chosen as the input data format for evaluation purposes. In this case, the input data consist of planar segment complexes whose triangulated polygons serve as the set of input triangle complexes for the computation of the tetrahedral model. The creation of the volumetric model and the computation of its geometrically induced topology is partly parallelized by decomposing the input data into smaller pices. A robustness analysis of the implementations is given by varying the angular precision and the positional precision of the epsilon heuristic inaccuracy model. The results are analysed spatially and topologically, summarised and presented. It turns out that one can extract most, but not all, volumes and that the numerical issues of computational geometry produce failures as well as a variety of outcomes

Identification of Mixtures of Discrete Product Distributions in Near-Optimal Sample and Time Complexity

We consider the problem of identifying, from statistics, a distribution of discrete random variables $X_1,\ldots,X_n$ that is a mixture of $k$ product distributions. The best previous sample complexity for $n \in O(k)$ was $(1/\zeta)^{O(k^2 \log k)}$ (under a mild separation assumption parameterized by $\zeta$). The best known lower bound was $\exp(\Omega(k))$. It is known that $n\geq 2k-1$ is necessary and sufficient for identification. We show, for any $n\geq 2k-1$, how to achieve sample complexity and run-time complexity $(1/\zeta)^{O(k)}$. We also extend the known lower bound of $e^{\Omega(k)}$ to match our upper bound across a broad range of $\zeta$. Our results are obtained by combining (a) a classic method for robust tensor decomposition, (b) a novel way of bounding the condition number of key matrices called Hadamard extensions, by studying their action only on flattened rank-1 tensors

Geospatial Data Management Research: Progress and Future Directions

Without geospatial data management, today´s challenges in big data applications such as earth observation, geographic information system/building information modeling (GIS/BIM) integration, and 3D/4D city planning cannot be solved. Furthermore, geospatial data management plays a connecting role between data acquisition, data modelling, data visualization, and data analysis. It enables the continuous availability of geospatial data and the replicability of geospatial data analysis. In the first part of this article, five milestones of geospatial data management research are presented that were achieved during the last decade. The first one reflects advancements in BIM/GIS integration at data, process, and application levels. The second milestone presents theoretical progress by introducing topology as a key concept of geospatial data management. In the third milestone, 3D/4D geospatial data management is described as a key concept for city modelling, including subsurface models. Progress in modelling and visualization of massive geospatial features on web platforms is the fourth milestone which includes discrete global grid systems as an alternative geospatial reference framework. The intensive use of geosensor data sources is the fifth milestone which opens the way to parallel data storage platforms supporting data analysis on geosensors. In the second part of this article, five future directions of geospatial data management research are presented that have the potential to become key research fields of geospatial data management in the next decade. Geo-data science will have the task to extract knowledge from unstructured and structured geospatial data and to bridge the gap between modern information technology concepts and the geo-related sciences. Topology is presented as a powerful and general concept to analyze GIS and BIM data structures and spatial relations that will be of great importance in emerging applications such as smart cities and digital twins. Data-streaming libraries and “in-situ” geo-computing on objects executed directly on the sensors will revolutionize geo-information science and bridge geo-computing with geospatial data management. Advanced geospatial data visualization on web platforms will enable the representation of dynamically changing geospatial features or moving objects’ trajectories. Finally, geospatial data management will support big geospatial data analysis, and graph databases are expected to experience a revival on top of parallel and distributed data stores supporting big geospatial data analysis

Genome characteristics of primary carcinomas, local recurrences, carcinomatoses, and liver metastases from colorectal cancer patients

BACKGROUND: Colorectal cancer (CRC) is one of the most common causes of cancer-related deaths in the Western world, and despite the fact that metastases are usually the ultimate cause of deaths, the knowledge of the genetics of advanced stages of this disease is limited. In order to identify potential genetic abnormalities underlying the development of local and distant metastases in CRC patients, we have, by comparative genomic hybridization, compared the DNA copy number profiles of 10 primary carcinomas, 14 local recurrences, 7 peritoneal carcinomatoses, and 42 liver metastases from 61 CRC patients. RESULTS: The median number of aberrations among the primary carcinomas, local recurrences, carcinomatoses, and liver metastases was 10, 6, 13, and 14, respectively. Several genetic imbalances, such as gains of 7, 8q, 13q, and 20, and losses of 4q, 8p, 17p, and 18, were common in all groups. In contrast, gains of 5p and 12p were more common in the carcinomatoses than in other stages of the disease. With hierarchical cluster analysis, liver metastases could be divided into two main subgroups according to clusters of chromosome changes. CONCLUSIONS: Each stage of CRC progression is characterized by a particular genetic profile, and both carcinomatoses and liver metastases are more genetically complex than local recurrences and primary carcinomas. This is the first genome profiling of local recurrences and carcinomatoses, and gains of 5p and 12p seem to be particularly important for the spread of the CRC cells within the peritoneal cavity

A National Survey of Teachers on Antiretroviral Therapy in Malawi: Access, Retention in Therapy and Survival

BACKGROUND: HIV/AIDS is having a devastating effect on the education sector in sub-Saharan Africa. A national survey was conducted in all public sector and private sector facilities in Malawi providing antiretroviral therapy (ART) to determine the uptake of ART by teachers and their outcomes while on treatment. METHODOLOGY/PRINCIPAL FINDINGS: A retrospective cohort study was carried out based on patient follow-up records from ART Registers and treatment master cards in all 138 ART clinics in Malawi; observations were censored on September 30(th) 2006. By this date, Malawi's 102 public sector and 36 private sector ART clinics had registered a total of 72,328 patients for treatment. Of these, 2,643 (3.7%) were teachers. Adjusting for double-registration caused by clinic transfers, it is estimated that 2,380 individual teachers had ever accessed ART. There were 15% of teachers starting ART in WHO clinical stage 1 or 2 with a CD4-lymphocyte count of <or=250/mm(3) and 85% starting in stage 3 or 4. By 30(th) September 2006, 1,850 teachers were alive on ART (3.5% of all teachers in Malawi). The probability of being alive on ART at 6-months, 12-months, 18-months and 24-months after treatment initiation was 84%, 79%, 75% and 73% respectively. Retention in treatment was better for women (adjusted HR = 1.8) and in those starting ART in WHO Clinical Stage 1 and 2 (adjusted HR = 1.8). CONCLUSION/SIGNIFICANCE: Rapid scale up of ART has allowed 2,380 HIV-positive teachers to access life-prolonging treatment. There is evidence that this intervention can help to mitigate some of the shortages of teaching personnel in resource-poor countries affected by a generalised HIV epidemic