Flip Distance Between Triangulations of a Simple Polygon is NP-Complete

Let T be a triangulation of a simple polygon. A flip in T is the operation of removing one diagonal of T and adding a different one such that the resulting graph is again a triangulation. The flip distance between two triangulations is the smallest number of flips required to transform one triangulation into the other. For the special case of convex polygons, the problem of determining the shortest flip distance between two triangulations is equivalent to determining the rotation distance between two binary trees, a central problem which is still open after over 25 years of intensive study. We show that computing the flip distance between two triangulations of a simple polygon is NP-complete. This complements a recent result that shows APX-hardness of determining the flip distance between two triangulations of a planar point set.Comment: Accepted versio

On the linear fractional self-attracting diffusion

In this paper, we introduce the linear fractional self-attracting diffusion driven by a fractional Brownian motion with Hurst index 1/2<H<1, which is analogous to the linear self-attracting diffusion. For 1-dimensional process we study its convergence and the corresponding weighted local time. For 2-dimensional process, as a related problem, we show that the renormalized self-intersection local time exists in L^2 if $\frac12<H<\frac3{4}$.Comment: 14 Pages. To appear in Journal of Theoretical Probabilit

Under-five mortality: spatial-temporal clusters in Ifakara HDSS in South-eastern Tanzania.

BACKGROUND\ud \ud Childhood mortality remains an important subject, particularly in sub-Saharan Africa where levels are still unacceptably high. To achieve the set Millennium Development Goals 4, calls for comprehensive application of the proven cost-effective interventions. Understanding spatial clustering of childhood mortality can provide a guide in targeting the interventions in a more strategic approach to the population where mortality is highest and the interventions are most likely to make an impact.\ud \ud METHODS\ud \ud Annual child mortality rates were calculated for each village, using person-years observed as the denominator. Kulldorff's spatial scan statistic was used for the identification and testing of childhood mortality clusters. All under-five deaths that occurred within a 10-year period from 1997 to 2006 were included in the analysis. Villages were used as units of clusters; all 25 health and demographic surveillance sites (HDSS) villages in the Ifakara health and demographic surveillance area were included.\ud \ud RESULTS\ud \ud Of the 10 years of analysis, statistically significant spatial clustering was identified in only 2 years (1998 and 2001). In 1998, the statistically significant cluster (p < 0.01) was composed of nine villages. A total of 106 childhood deaths were observed against an expected 77.3. The other statistically significant cluster (p < 0.05) identified in 2001 was composed of only one village. In this cluster, 36 childhood deaths were observed compared to 20.3 expected. Purely temporal analysis indicated that the year 2003 was a significant cluster (p < 0.05). Total deaths were 393 and expected were 335.8. Spatial-temporal analysis showed that nine villages were identified as statistically significant clusters (p < 0.05) for the period covering January 1997-December 1998. Total observed deaths in this cluster were 205 while 150.7 were expected.\ud \ud CONCLUSION\ud \ud There is evidence of spatial clustering in childhood mortality within the Ifakara HDSS. Further investigations are needed to explore the source of clustering and identify strategies of reaching the cluster population with the existing effective interventions. However, that should happen alongside delivery of interventions to the broader population

Enhanced insulin sensitivity associated with provision of mono and polyunsaturated fatty acids in skeletal muscle cells involves counter modulation of PP2A

International audienceAims/Hypothesis: Reduced skeletal muscle insulin sensitivity is a feature associated with sustained exposure to excess saturated fatty acids (SFA), whereas mono and polyunsaturated fatty acids (MUFA and PUFA) not only improve insulin sensitivity but blunt SFA-induced insulin resistance. The mechanisms by which MUFAs and PUFAs institute these favourable changes remain unclear, but may involve stimulating insulin signalling by counter-modulation/repression of protein phosphatase 2A (PP2A). This study investigated the effects of oleic acid (OA; a MUFA), linoleic acid (LOA; a PUFA) and palmitate (PA; a SFA) in cultured myotubes and determined whether changes in insulin signalling can be attributed to PP2A regulation. Principal Findings: We treated cultured skeletal myotubes with unsaturated and saturated fatty acids and evaluated insulin signalling, phosphorylation and methylation status of the catalytic subunit of PP2A. Unlike PA, sustained incubation of rat or human myotubes with OA or LOA significantly enhanced Akt-and ERK1/2-directed insulin signalling. This was not due to heightened upstream IRS1 or PI3K signalling nor to changes in expression of proteins involved in proximal insulin signalling, but was associated with reduced dephosphorylation/inactivation of Akt and ERK1/2. Consistent with this, PA reduced PP2Ac demethylation and tyrosine 307 phosphorylation-events associated with PP2A activation. In contrast, OA and LOA strongly opposed these PA-induced changes in PP2Ac thus exerting a repressive effect on PP2A.Conclusions/Interpretation: Beneficial gains in insulin sensitivity and the ability of unsaturated fatty acids to oppose palmitate-induced insulin resistance in muscle cells may partly be accounted for by counter-modulation of PP2A

Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials

Recent progress in understanding the topological properties of condensed matter has led to the discovery of time-reversal invariant topological insulators. Because of limitations imposed by nature, topologically non-trivial electronic order seems to be uncommon except in small-band-gap semiconductors with strong spin-orbit interactions. In this Article we show that artificial electromagnetic structures, known as metamaterials, provide an attractive platform for designing photonic analogues of topological insulators. We demonstrate that a judicious choice of the metamaterial parameters can create photonic phases that support a pair of helical edge states, and that these edge states enable one-way photonic transport that is robust against disorder.Comment: 13 pages, 3 figure

First Steps towards Underdominant Genetic Transformation of Insect Populations

The idea of introducing genetic modifications into wild populations of insects to stop them from spreading diseases is more than 40 years old. Synthetic disease refractory genes have been successfully generated for mosquito vectors of dengue fever and human malaria. Equally important is the development of population transformation systems to drive and maintain disease refractory genes at high frequency in populations. We demonstrate an underdominant population transformation system in Drosophila melanogaster that has the property of being both spatially self-limiting and reversible to the original genetic state. Both population transformation and its reversal can be largely achieved within as few as 5 generations. The described genetic construct {Ud} is composed of two genes; (1) a UAS-RpL14.dsRNA targeting RNAi to a haploinsufficient gene RpL14 and (2) an RNAi insensitive RpL14 rescue. In this proof-of-principle system the UAS-RpL14.dsRNA knock-down gene is placed under the control of an Actin5c-GAL4 driver located on a different chromosome to the {Ud} insert. This configuration would not be effective in wild populations without incorporating the Actin5c-GAL4 driver as part of the {Ud} construct (or replacing the UAS promoter with an appropriate direct promoter). It is however anticipated that the approach that underlies this underdominant system could potentially be applied to a number of species. Figure

Pediatric Cushing disease: disparities in disease severity and outcomes in the Hispanic and African-American populations.

BackgroundLittle is known about the contribution of racial and socioeconomic disparities to severity and outcomes in children with Cushing disease (CD).MethodsA total of 129 children with CD, 45 Hispanic/Latino or African-American (HI/AA) and 84 non-Hispanic White (non-HW), were included in this study. A 10-point index for rating severity (CD severity) incorporated the degree of hypercortisolemia, glucose tolerance, hypertension, anthropomorphic measurements, disease duration, and tumor characteristics. Race, ethnicity, age, gender, local obesity prevalence, estimated median income, and access to care were assessed in regression analyses of CD severity.ResultsThe mean CD severity in the HI/AA group was worse than that in the non-HW group (4.9±2.0 vs. 4.1±1.9, P=0.023); driving factors included higher cortisol levels and larger tumor size. Multiple regression models confirmed that race (P=0.027) and older age (P=0.014) were the most important predictors of worse CD severity. When followed up a median of 2.3 years after surgery, the relative risk for persistent CD combined with recurrence was 2.8 times higher in the HI/AA group compared with that in the non-HW group (95% confidence interval: 1.2-6.5).ConclusionOur data show that the driving forces for the discrepancy in severity of CD are older age and race/ethnicity. Importantly, the risk for persistent and recurrent CD was higher in minority children

Knot Theory: from Fox 3-colorings of links to Yang-Baxter homology and Khovanov homology

This paper is an extended account of my "Introductory Plenary talk at Knots in Hellas 2016" conference We start from the short introduction to Knot Theory from the historical perspective, starting from Heraclas text (the first century AD), mentioning R.Llull (1232-1315), A.Kircher (1602-1680), Leibniz idea of Geometria Situs (1679), and J.B.Listing (student of Gauss) work of 1847. We spend some space on Ralph H. Fox (1913-1973) elementary introduction to diagram colorings (1956). In the second section we describe how Fox work was generalized to distributive colorings (racks and quandles) and eventually in the work of Jones and Turaev to link invariants via Yang-Baxter operators, here the importance of statistical mechanics to topology will be mentioned. Finally we describe recent developments which started with Mikhail Khovanov work on categorification of the Jones polynomial. By analogy to Khovanov homology we build homology of distributive structures (including homology of Fox colorings) and generalize it to homology of Yang-Baxter operators. We speculate, with supporting evidence, on co-cycle invariants of knots coming from Yang-Baxter homology. Here the work of Fenn-Rourke-Sanderson (geometric realization of pre-cubic sets of link diagrams) and Carter-Kamada-Saito (co-cycle invariants of links) will be discussed and expanded. Dedicated to Lou Kauffman for his 70th birthday.Comment: 35 pages, 31 figures, for Knots in Hellas II Proceedings, Springer, part of the series Proceedings in Mathematics & Statistics (PROMS

Questioning Classic Patient Classification Techniques in Gait Rehabilitation: Insights from Wearable Haptic Technology

Classifying stroke survivors based on their walking abilities is an important part of the gait rehabilitation process. It can act as powerful indicator of function and prognosis in both the early days after a stroke and long after a survivor receives rehabilitation. This classification often relies solely on walking speed; a quick and easy measure, with only a stopwatch needed. However, walking speed may not be the most accurate way of judging individual’s walking ability. Advances in technology mean we are now in a position where ubiquitous and wearable technologies can be used to elicit much richer measures to characterise gait. In this paper we present a case study from one of our studies, where within a homogenous group of stroke survivors (based on walking speed classification) important differences in individual results and the way they responded to rhythmic haptic cueing were identified during the piloting of a novel gait rehabilitation technique

Alpha-particle-induced complex chromosome exchanges transmitted through extra-thymic lymphopoiesis in vitro show evidence of emerging genomic instability

Human exposure to high-linear energy transfer α-particles includes environmental (e.g. radon gas and its decay progeny), medical (e.g. radiopharmaceuticals) and occupational (nuclear industry) sources. The associated health risks of α-particle exposure for lung cancer are well documented however the risk estimates for leukaemia remain uncertain. To further our understanding of α-particle effects in target cells for leukaemogenesis and also to seek general markers of individual exposure to α-particles, this study assessed the transmission of chromosomal damage initially-induced in human haemopoietic stem and progenitor cells after exposure to high-LET α-particles. Cells surviving exposure were differentiated into mature T-cells by extra-thymic T-cell differentiation in vitro. Multiplex fluorescence in situ hybridisation (M-FISH) analysis of naïve T-cell populations showed the occurrence of stable (clonal) complex chromosome aberrations consistent with those that are characteristically induced in spherical cells by the traversal of a single α-particle track. Additionally, complex chromosome exchanges were observed in the progeny of irradiated mature T-cell populations. In addition to this, newly arising de novo chromosome aberrations were detected in cells which possessed clonal markers of α-particle exposure and also in cells which did not show any evidence of previous exposure, suggesting ongoing genomic instability in these populations. Our findings support the usefulness and reliability of employing complex chromosome exchanges as indicators of past or ongoing exposure to high-LET radiation and demonstrate the potential applicability to evaluate health risks associated with α-particle exposure.This work was supported by the Department of Health, UK. Contract RRX95 (RMA NSDTG)