Fixed parameter tractable algorithms in combinatorial topology

To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an exponential-time enumeration. However, asymptotically most graphs do not result in any 3-manifold triangulation, which leads to significant "wasted time" in topological enumeration algorithms. Here we give a new algorithm to determine whether a given face pairing graph supports any 3-manifold triangulation, and show this to be fixed parameter tractable in the treewidth of the graph. We extend this result to a "meta-theorem" by defining a broad class of properties of triangulations, each with a corresponding fixed parameter tractable existence algorithm. We explicitly implement this algorithm in the most generic setting, and we identify heuristics that in practice are seen to mitigate the large constants that so often occur in parameterised complexity, highlighting the practicality of our techniques.Comment: 16 pages, 9 figure

Complementary vertices and adjacency testing in polytopes

Our main theoretical result is that, if a simple polytope has a pair of complementary vertices (i.e., two vertices with no facets in common), then it has at least two such pairs, which can be chosen to be disjoint. Using this result, we improve adjacency testing for vertices in both simple and non-simple polytopes: given a polytope in the standard form {x \in R^n | Ax = b and x \geq 0} and a list of its V vertices, we describe an O(n) test to identify whether any two given vertices are adjacent. For simple polytopes this test is perfect; for non-simple polytopes it may be indeterminate, and instead acts as a filter to identify non-adjacent pairs. Our test requires an O(n^2 V + n V^2) precomputation, which is acceptable in settings such as all-pairs adjacency testing. These results improve upon the more general O(nV) combinatorial and O(n^3) algebraic adjacency tests from the literature.Comment: 14 pages, 5 figures. v1: published in COCOON 2012. v2: full journal version, which strengthens and extends the results in Section 2 (see p1 of the paper for details

An evolutionarily-unique heterodimeric voltage-gated cation channel found in aphids

We describe the identification in aphids of a unique heterodimeric voltage-gated sodium channel which has an atypical ion selectivity filter and, unusually for insect channels, is highly insensitive to tetrodotoxin. We demonstrate that this channel has most likely arisen by adaptation (gene fission or duplication) of an invertebrate ancestral mono(hetero)meric channel. This is the only identifiable voltage-gated sodium channel homologue in the aphid genome(s), and the channel's novel selectivity filter motif (DENS instead of the usual DEKA found in other eukaryotes) may result in a loss of sodium selectivity, as indicated experimentally in mutagenised Drosophila channels

Combinatorial 3-manifolds with transitive cyclic symmetry

In this article we give combinatorial criteria to decide whether a transitive cyclic combinatorial d-manifold can be generalized to an infinite family of such complexes, together with an explicit construction in the case that such a family exists. In addition, we substantially extend the classification of combinatorial 3-manifolds with transitive cyclic symmetry up to 22 vertices. Finally, a combination of these results is used to describe new infinite families of transitive cyclic combinatorial manifolds and in particular a family of neighborly combinatorial lens spaces of infinitely many distinct topological types.Comment: 24 pages, 5 figures. Journal-ref: Discrete and Computational Geometry, 51(2):394-426, 201

Single Spin Asymmetry ANA_N in Polarized Proton-Proton Elastic Scattering at s=200\sqrt{s}=200 GeV

We report a high precision measurement of the transverse single spin asymmetry $A_N$ at the center of mass energy $\sqrt{s}=200$ GeV in elastic proton-proton scattering by the STAR experiment at RHIC. The $A_N$ was measured in the four-momentum transfer squared $t$ range $0.003 \leqslant |t| \leqslant 0.035$ \GeVcSq, the region of a significant interference between the electromagnetic and hadronic scattering amplitudes. The measured values of $A_N$ and its $t$-dependence are consistent with a vanishing hadronic spin-flip amplitude, thus providing strong constraints on the ratio of the single spin-flip to the non-flip amplitudes. Since the hadronic amplitude is dominated by the Pomeron amplitude at this $\sqrt{s}$, we conclude that this measurement addresses the question about the presence of a hadronic spin flip due to the Pomeron exchange in polarized proton-proton elastic scattering.Comment: 12 pages, 6 figure

The satisfactory growth and development at 2 years of age of the INTERGROWTH-21st Fetal Growth Standards cohort support its appropriateness for constructing international standards.

BACKGROUND: The World Health Organization recommends that human growth should be monitored with the use of international standards. However, in obstetric practice, we continue to monitor fetal growth using numerous local charts or equations that are based on different populations for each body structure. Consistent with World Health Organization recommendations, the INTERGROWTH-21st Project has produced the first set of international standards to date pregnancies; to monitor fetal growth, estimated fetal weight, Doppler measures, and brain structures; to measure uterine growth, maternal nutrition, newborn infant size, and body composition; and to assess the postnatal growth of preterm babies. All these standards are based on the same healthy pregnancy cohort. Recognizing the importance of demonstrating that, postnatally, this cohort still adhered to the World Health Organization prescriptive approach, we followed their growth and development to the key milestone of 2 years of age. OBJECTIVE: The purpose of this study was to determine whether the babies in the INTERGROWTH-21st Project maintained optimal growth and development in childhood. STUDY DESIGN: In the Infant Follow-up Study of the INTERGROWTH-21st Project, we evaluated postnatal growth, nutrition, morbidity, and motor development up to 2 years of age in the children who contributed data to the construction of the international fetal growth, newborn infant size and body composition at birth, and preterm postnatal growth standards. Clinical care, feeding practices, anthropometric measures, and assessment of morbidity were standardized across study sites and documented at 1 and 2 years of age. Weight, length, and head circumference age- and sex-specific z-scores and percentiles and motor development milestones were estimated with the use of the World Health Organization Child Growth Standards and World Health Organization milestone distributions, respectively. For the preterm infants, corrected age was used. Variance components analysis was used to estimate the percentage variability among individuals within a study site compared with that among study sites. RESULTS: There were 3711 eligible singleton live births; 3042 children (82%) were evaluated at 2 years of age. There were no substantive differences between the included group and the lost-to-follow up group. Infant mortality rate was 3 per 1000; neonatal mortality rate was 1.6 per 1000. At the 2-year visit, the children included in the INTERGROWTH-21st Fetal Growth Standards were at the 49th percentile for length, 50th percentile for head circumference, and 58th percentile for weight of the World Health Organization Child Growth Standards. Similar results were seen for the preterm subgroup that was included in the INTERGROWTH-21st Preterm Postnatal Growth Standards. The cohort overlapped between the 3rd and 97th percentiles of the World Health Organization motor development milestones. We estimated that the variance among study sites explains only 5.5% of the total variability in the length of the children between birth and 2 years of age, although the variance among individuals within a study site explains 42.9% (ie, 8 times the amount explained by the variation among sites). An increase of 8.9 cm in adult height over mean parental height is estimated to occur in the cohort from low-middle income countries, provided that children continue to have adequate health, environmental, and nutritional conditions. CONCLUSION: The cohort enrolled in the INTERGROWTH-21st standards remained healthy with adequate growth and motor development up to 2 years of age, which supports its appropriateness for the construction of international fetal and preterm postnatal growth standards

Effect of event selection on jetlike correlation measurement in d+Au collisions at sNN=200 GeV

AbstractDihadron correlations are analyzed in sNN=200 GeV d+Au collisions classified by forward charged particle multiplicity and zero-degree neutral energy in the Au-beam direction. It is found that the jetlike correlated yield increases with the event multiplicity. After taking into account this dependence, the non-jet contribution on the away side is minimal, leaving little room for a back-to-back ridge in these collisions

Environment and Rural Affairs Monitoring & Modelling Programme ERAMMP - Report-32: National Forest in Wales - Evidence Review

This review was commissioned by Welsh Government (WG) from the Environment and Rural Affairs Monitoring and Modelling Programme (ERAMMP) to provide key evidence of potential benefits and disbenefits of woodland creation, woodland expansion and managing undermanaged woodland, to provide an evidence base to inform the development of a National Forest for Wales. During the commissioning process, WG emphasised that the evidence provided must reflect the collective views of the community by reviewing the literature in an objective way highlighting where evidence is contradictory or weak. Within the time available, evidence of causality of impacts, the likely timescales and magnitude of these impacts should be also be presented, for both positive and negative impacts of woodland expansion and management of undermanaged woodlands. This Evidence Pack should also build on the evidence put forward in the ERAMMP Sustainable Farm Scheme (SFS) (https://erammp.wales/en/resources) which included a range of assessments of the value of intervention measures which promoted trees within a landscape setting for a range of environmental, economic and social outcomes. The required rapid production of the review in four months meant an expert approach of key evidence was expected rather than a systematic review. Key topics to cover were selected, in partnership with WG, focussing on issues that could fundamentally change decision-making going forward. The final agreed list was arranged under a series of high-level subject headings, and the individual reviews published as ERAMMP Reports 33 to 38 and include; Biodiversity; Managing Undermanaged Woodland; Future-proofing our Woodland; Climate Change Mitigation; Ecosystem Services, and Economics and Natural Capital Accounting. An Integrated Assessment was also commissioned to provide a synthesis of cross-cutting themes and dependencies between topics. These ERAMMP reports are all provided as Annexes to this report