Hinged Dissections Exist

We prove that any finite collection of polygons of equal area has a common hinged dissection. That is, for any such collection of polygons there exists a chain of polygons hinged at vertices that can be folded in the plane continuously without self-intersection to form any polygon in the collection. This result settles the open problem about the existence of hinged dissections between pairs of polygons that goes back implicitly to 1864 and has been studied extensively in the past ten years. Our result generalizes and indeed builds upon the result from 1814 that polygons have common dissections (without hinges). We also extend our common dissection result to edge-hinged dissections of solid 3D polyhedra that have a common (unhinged) dissection, as determined by Dehn's 1900 solution to Hilbert's Third Problem. Our proofs are constructive, giving explicit algorithms in all cases. For a constant number of planar polygons, both the number of pieces and running time required by our construction are pseudopolynomial. This bound is the best possible, even for unhinged dissections. Hinged dissections have possible applications to reconfigurable robotics, programmable matter, and nanomanufacturing.Comment: 22 pages, 14 figure

Dynamic ham-sandwich cuts in the plane

We design efficient data structures for dynamically maintaining a ham-sandwich cut of two point sets in the plane subject to insertions and deletions of points in either set. A ham-sandwich cut is a line that simultaneously bisects the cardinality of both point sets. For general point sets, our first data structure supports each operation in O(n1/3+ε) amortized time and O(n4/3+ε) space. Our second data structure performs faster when each point set decomposes into a small number k of subsets in convex position: it supports insertions and deletions in O(logn) time and ham-sandwich queries in O(klog4n) time. In addition, if each point set has convex peeling depth k , then we can maintain the decomposition automatically using O(klogn) time per insertion and deletion. Alternatively, we can view each convex point set as a convex polygon, and we show how to find a ham-sandwich cut that bisects the total areas or total perimeters of these polygons in O(klog4n) time plus the O((kb)polylog(kb)) time required to approximate the root of a polynomial of degree O(k) up to b bits of precision. We also show how to maintain a partition of the plane by two lines into four regions each containing a quarter of the total point count, area, or perimeter in polylogarithmic time.Engineering and Applied Science

Contact tracing is an imperfect tool for controlling COVID-19 transmission and relies on population adherence.

Emerging evidence suggests that contact tracing has had limited success in the UK in reducing the R number across the COVID-19 pandemic. We investigate potential pitfalls and areas for improvement by extending an existing branching process contact tracing model, adding diagnostic testing and refining parameter estimates. Our results demonstrate that reporting and adherence are the most important predictors of programme impact but tracing coverage and speed plus diagnostic sensitivity also play an important role. We conclude that well-implemented contact tracing could bring small but potentially important benefits to controlling and preventing outbreaks, providing up to a 15% reduction in R. We reaffirm that contact tracing is not currently appropriate as the sole control measure

The Cold Peace: Russo-Western Relations as a Mimetic Cold War

In 1989–1991 the geo-ideological contestation between two blocs was swept away, together with the ideology of civil war and its concomitant Cold War played out on the larger stage. Paradoxically, while the domestic sources of Cold War confrontation have been transcended, its external manifestations remain in the form of a ‘legacy’ geopolitical contest between the dominant hegemonic power (the United States) and a number of potential rising great powers, of which Russia is one. The post-revolutionary era is thus one of a ‘cold peace’. A cold peace is a mimetic cold war. In other words, while a cold war accepts the logic of conflict in the international system and between certain protagonists in particular, a cold peace reproduces the behavioural patterns of a cold war but suppresses acceptance of the logic of behaviour. A cold peace is accompanied by a singular stress on notions of victimhood for some and undigested and bitter victory for others. The perceived victim status of one set of actors provides the seedbed for renewed conflict, while the ‘victory’ of the others cannot be consolidated in some sort of relatively unchallenged post-conflict order. The ‘universalism’ of the victors is now challenged by Russia's neo-revisionist policy, including not so much the defence of Westphalian notions of sovereignty but the espousal of an international system with room for multiple systems (the Schmittean pluriverse)

Clonal architecture of secondary acute myeloid leukemia

BACKGROUND: The myelodysplastic syndromes are a group of hematologic disorders that often evolve into secondary acute myeloid leukemia (AML). The genetic changes that underlie progression from the myelodysplastic syndromes to secondary AML are not well understood. METHODS: We performed whole-genome sequencing of seven paired samples of skin and bone marrow in seven subjects with secondary AML to identify somatic mutations specific to secondary AML. We then genotyped a bone marrow sample obtained during the antecedent myelodysplastic-syndrome stage from each subject to determine the presence or absence of the specific somatic mutations. We identified recurrent mutations in coding genes and defined the clonal architecture of each pair of samples from the myelodysplastic-syndrome stage and the secondary-AML stage, using the allele burden of hundreds of mutations. RESULTS: Approximately 85% of bone marrow cells were clonal in the myelodysplastic-syndrome and secondary-AML samples, regardless of the myeloblast count. The secondary-AML samples contained mutations in 11 recurrently mutated genes, including 4 genes that have not been previously implicated in the myelodysplastic syndromes or AML. In every case, progression to acute leukemia was defined by the persistence of an antecedent founding clone containing 182 to 660 somatic mutations and the outgrowth or emergence of at least one subclone, harboring dozens to hundreds of new mutations. All founding clones and subclones contained at least one mutation in a coding gene. CONCLUSIONS: Nearly all the bone marrow cells in patients with myelodysplastic syndromes and secondary AML are clonally derived. Genetic evolution of secondary AML is a dynamic process shaped by multiple cycles of mutation acquisition and clonal selection. Recurrent gene mutations are found in both founding clones and daughter subclones. (Funded by the National Institutes of Health and others.

An imperfect tool: contact tracing could provide valuable reductions in COVID-19 transmission if good adherence can be achieved and maintained.

Emerging evidence suggests that contact tracing has had limited success in the UK in reducing the R number across the COVID-19 pandemic. We investigate potential pitfalls and areas for improvement by extending an existing branching process contact tracing model, adding diagnostic testing and refining parameter estimates. Our results demonstrate that reporting and adherence are the most important predictors of programme impact but tracing coverage and speed plus diagnostic sensitivity also play an important role. We conclude that well-implemented contact tracing could bring small but potentially important benefits to controlling and preventing outbreaks, providing up to a 15% reduction in R, and reaffirm that contact tracing is not currently appropriate as the sole control measure.</jats:p

Multiple and Multidimensional life transitions in the context of life-limiting health conditions:Longitudinal study focussing on perspectives of Young Adults, Families and Professionals

Background: There is a dearth of literature that investigates life transitions of young adults (YAs) with life-limiting conditions, families and professionals. The scant literature that is available has methodological limitations, including not listening to the voice of YAs, collecting data retrospectively, at one time point, from one group’s perspective and single case studies. The aim of this study was to address the gaps found in our literature review and provide a clearer understanding of the multiple and multi-dimensional life transitions experienced by YAs and significant others, over a period of time. Methods: This qualitative study used a longitudinal design and data were collected using semi-structured interviews over a 6-month period at 3 time points. Participants included 12 YAs with life-limiting conditions and their nominated significant others (10 family members and 11 professionals). Data were analysed using a thematic analysis approach. Results: Life transitions of YA and significant others are complex; they experience multiple and multi-dimensional transitions across several domains. The findings challenge the notion that all life transitions are triggered by health transitions of YAs, and has highlighted environmental factors (attitudinal and systemic) that can be changed to facilitate smoother transitions in various aspects of their lives. Conclusions: This study makes a unique and significant contribution to literature. It provides evidence and rich narratives for policy makers and service providers to change policies and practices that are in line with the needs of YAs with life-limiting conditions as they transition to adulthood. Families and professionals have specific training needs that have not yet been met fully