Spanning tree methods for sampling graph partitions

In the last decade, computational approaches to graph partitioning have made a major impact in the analysis of political redistricting, including in U.S. courts of law. Mathematically, a districting plan can be viewed as a balanced partition of a graph into connected subsets. Examining a large sample of valid alternative districting plans can help us recognize gerrymandering against an appropriate neutral baseline. One algorithm that is widely used to produce random samples of districting plans is a Markov chain called recombination (or ReCom), which repeatedly fuses adjacent districts, forms a spanning tree of their union, and splits that spanning tree with a balanced cut to form new districts. One drawback is that this chain's stationary distribution has no known closed form when there are three or more districts. In this paper, we modify ReCom slightly to give it a property called reversibility, resulting in a new Markov chain, RevReCom. This new chain converges to the simple, natural distribution that ReCom was originally designed to approximate: a plan's stationary probability is proportional to the product of the number of spanning trees of each district. This spanning tree score is a measure of district "compactness" (or shape) that is also aligned with notions of community structure from network science. After deriving the steady state formally, we present diagnostic evidence that the convergence is efficient enough for the method to be practically useful, giving high-quality samples for full-sized problems within several hours. In addition to the primary application of benchmarking of redistricting plans (i.e., describing a normal range for statistics), this chain can also be used to validate other methods that target the spanning tree distribution

Neighbourhood responses to drought in the Western Cape

An extreme drought event occurred in the Western Cape when the mean level of water supply dams declined to 28% of capacity in August 2017 (Odendaal 2019). Our survey of 240 households and 71 businesses identified neighbourhood variations in response to the drought and to local government restrictions in water usage, and in the methods of adaptation that were implemented to mitigate the impact of the disaster. Whereas water consumption declined dramatically in comparison with drought responses in other contexts (Shaw et al. in Am Water Works Assoc 84(10):34–41, 1992, https://doi.org/10. 1002/j.1551-8833.1992.tb05862.x; Miller and Buys in Soc Nat Resour 21(3):244–257, 2008; Buurman et al. in Int J Water Resour Dev 33(1):31–50, 2017, https:// doi.org/10.1080/07900627.2016.1138398; Okaka and Odhiambo in S Afr Geogr J 100(3):378–393, 2018), significant variations in attitude and behaviour emerged between respondents of Western Cape neighbourhoods with different socio-economic profiles. Middle class and older households and waterintensive businesses or organisations were more likely to report substantial decreases in water usage and to be critical of official interventions than were poorer or younger households and small businesses

Challenging Elementary Learners with Programmable Robots during Free Play and Direct Instruction

Computer programming skills are important to many current careers; teaching robot coding to elementary students can start a positive foundation for technological careers, develop problem-solving skills, and growth mindsets. This study, through a repeated measures design involving students in two classrooms at two widelyseparated grade levels (first graders aged 6-7 years and fifth graders aged 10-11 years), determined if allowing students to challenge themselves with coding exercises in the experimental condition resulted in greater learning and more positive attitudes than a more structured set of exercises provided by the teacher in the control condition. Background instruction in coding and using robots occurred before the study began. Students experienced each condition twice for a two-week duration in the eight-week study; a robot performance, scored for technical and creative skills, was presented by students at the end of each two-week period. During the control condition, teachers used direct instruction to teach coding skills; during the experimental condition, students were asked to challenge themselves through free play and inquiry based learning. The results indicated that technical scores for robot performances showed the largest positive effects during the direct instructional portions of the study, while the creative score for robot performances indicated the largest positive effects during the free play rotations. Overall scores for robotic performances indicated a steady growth of skills week after week during the study. The attitudes of the participants remained positive throughout the study

An axiomatization of the ratio/difference representation

If >=r and >=d are two quaternary relations on an arbitrary set A, a ratio/difference representation for >=r and >=d is defined to be a function f that represents >=r as an ordering of numerical ratios and >=d as an ordering of numerical differences. Krantz, Luce, Suppes and Tversky (1971, Foundations of Measurement. New York, Academic Press) proposed an axiomatization of the ratio/difference representation, but their axiomatization contains an error. After describing a counterexample to their axiomatization, Theorem 1 of the present article shows that it actually implies a weaker result: if >=r and >=d are two quaternary retations satisfying the axiomatization proposed by Krantz et al. (1971), and if >=r' and >=d' are the relations that are inverse to >=r and >=d, respectively, then either there exists a ratio/difference representation for >=r and >=d, or there exists a ratio/difference representation for >=r' and >=d', but not both. Theorem 2 identifies a new condition which, when added to the axioms of Krantz et al. (1971), yields the existence of a ratio/difference representation for relations >=r and >=d.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25051/1/0000479.pd

The European Hematology Association Roadmap for European Hematology Research: a consensus document

The European Hematology Association (EHA) Roadmap for European Hematology Research highlights major achievements in diagnosis and treatment of blood disorders and identifies the greatest unmet clinical and scientific needs in those areas to enable better funded, more focused European hematology research. Initiated by the EHA, around 300 experts contributed to the consensus document, which will help European policy makers, research funders, research organizations, researchers, and patient groups make better informed decisions on hematology research. It also aims to raise public awareness of the burden of blood disorders on European society, which purely in economic terms is estimated at €23 billion per year, a level of cost that is not matched in current European hematology research funding. In recent decades, hematology research has improved our fundamental understanding of the biology of blood disorders, and has improved diagnostics and treatments, sometimes in revolutionary ways. This progress highlights the potential of focused basic research programs such as this EHA Roadmap. The EHA Roadmap identifies nine ‘sections’ in hematology: normal hematopoiesis, malignant lymphoid and myeloid diseases, anemias and related diseases, platelet disorders, blood coagulation and hemostatic disorders, transfusion medicine, infections in hematology, and hematopoietic stem cell transplantation. These sections span 60 smaller groups of diseases or disorders. The EHA Roadmap identifies priorities and needs across the field of hematology, including those to develop targeted therapies based on genomic profiling and chemical biology, to eradicate minimal residual malignant disease, and to develop cellular immunotherapies, combination treatments, gene therapies, hematopoietic stem cell treatments, and treatments that are better tolerated by elderly patients

The European Hematology Association Roadmap for European Hematology Research. A Consensus Document

Abstract The European Hematology Association (EHA) Roadmap for European Hematology Research highlights major achievements in diagnosis and treatment of blood disorders and identifies the greatest unmet clinical and scientific needs in those areas to enable better funded, more focused European hematology research. Initiated by the EHA, around 300 experts contributed to the consensus document, which will help European policy makers, research funders, research organizations, researchers, and patient groups make better informed decisions on hematology research. It also aims to raise public awareness of the burden of blood disorders on European society, which purely in economic terms is estimated at Euro 23 billion per year, a level of cost that is not matched in current European hematology research funding. In recent decades, hematology research has improved our fundamental understanding of the biology of blood disorders, and has improved diagnostics and treatments, sometimes in revolutionary ways. This progress highlights the potential of focused basic research programs such as this EHA Roadmap. The EHA Roadmap identifies nine sections in hematology: normal hematopoiesis, malignant lymphoid and myeloid diseases, anemias and related diseases, platelet disorders, blood coagulation and hemostatic disorders, transfusion medicine, infections in hematology, and hematopoietic stem cell transplantation. These sections span 60 smaller groups of diseases or disorders. The EHA Roadmap identifies priorities and needs across the field of hematology, including those to develop targeted therapies based on genomic profiling and chemical biology, to eradicate minimal residual malignant disease, and to develop cellular immunotherapies, combination treatments, gene therapies, hematopoietic stem cell treatments, and treatments that are better tolerated by elderly patients. Received December 15, 2015. Accepted January 27, 2016. Copyright © 2016, Ferrata Storti Foundatio

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead