A novel approach for computing C-2-continuous offset of NURBS curves

Computing offset curves is an important geometric operation in areas of CAD/CAM, robotics, cam design and many industrial applications. In this paper, an algorithm for computing offsets of NURBS curves using C-2-continuous B-spline curves is presented. The progenitor curve in database is initially approximated by a line-fitting curve, and then the exact offset of this line-fitting curve is introduced as an initial offset. Based on the initial offset and a set of selected knots, an intended C-2-continuous B-spline curve is subsequently constructed. The method uses a new error-measuring scheme, which is based on the convex hull property of Bezier curves and the idea of cumulative errors, to calculate the global error bound of offset approximation. The method obtains offset curves with C-2 continuity and guarantees that the actual error bound is precisely within the prescribed tolerance. In addition, it also allows one to selectively parametrize the offset curve

NURBS output based tool path generation for freeform pockets

A robust method is proposed to generate tool paths for NURBS-based machining of arbitrarily shaped freeform pockets with islands. Although the input and output are all of higher-degree NURBS curves, only one simple category of geometric entities, i.e., line segments, is required for initial offsetting and for detecting and removing self-intersecting loops. Furthermore, using those linear non-self-intersecting offsets as the legs of NURBS control polygons, NURBS-format tool paths can be smoothly reconstructed with G(1)-continuity, no overcutting, no cusps, and global error control. Since all operations involved in computing tool path curves are linear geometric calculations, the method is robust and simple. Examples with integrated rough and finish cutting tool paths of pockets demonstrate the usefulness and effectiveness of this method

Optimizing Tc in the (Mn,Cr,Ga)As and (Mn,Ga)(As,P) Ternary Alloys

We explore two possible ways to enhance the critical temperature $T_c$ in the dilute magnetic semiconductor Mn$_{0.08}$Ga$_{0.92}$As. Within the context of the double-exchange and RKKY pictures, the ternary alloys Mn$_{x}$Cr$_{0.08-x}$Ga$_{0.92}$As and Mn$_{0.08}$Ga$_{0.92}$As$_y$P$_{1-y}$ might be expected to have $T_c$ higher than the pseudobinary Mn$_{0.08}$Ga$_{0.92}$As. To test whether the expectations from model pictures are confirmed, we employ linear response theory within the local-density approximation to search for theoretically higher critical temperatures in these ternary alloys. Our results show that neither co-doping Mn with Cr, nor alloying As with P improves $T_c$. Alloying with Cr is found to be deleterious to the $T_c$. Mn$_{0.08}$Ga$_{0.92}$As$_y$P$_{1-y}$ shows almost linear dependence of $T_c$ on $y$.Comment: 10 pages, 5 figure

Annulus Amplitudes and ZZ Branes in Minimal String Theory

We study the annulus amplitudes of (p,q) minimal string theory. Focusing on the ZZ-FZZT annulus amplitude as a target-space probe of the ZZ brane, we use it to confirm that the ZZ branes are localized in the strong-coupling region. Along the way we learn that the ZZ-FZZT open strings are fermions, even though our theory is bosonic! We also provide a geometrical interpretation of the annulus amplitudes in terms of the Riemann surface M_{p,q} that emerges from the FZZT branes. The ZZ-FZZT annulus amplitude measures the deformation of M_{p,q} due to the presence of background ZZ branes; each kind of ZZ-brane deforms only one A-period of the surface. Finally, we use the annulus amplitudes to argue that the ZZ branes can be regarded as "wrong-branch" tachyons which violate the bound \alpha<Q/2.Comment: 33 pages, new results in appendix, minor change

Derivation of fluid dynamics from kinetic theory with the 14--moment approximation

We review the traditional derivation of the fluid-dynamical equations from kinetic theory according to Israel and Stewart. We show that their procedure to close the fluid-dynamical equations of motion is not unique. Their approach contains two approximations, the first being the so-called 14-moment approximation to truncate the single-particle distribution function. The second consists in the choice of equations of motion for the dissipative currents. Israel and Stewart used the second moment of the Boltzmann equation, but this is not the only possible choice. In fact, there are infinitely many moments of the Boltzmann equation which can serve as equations of motion for the dissipative currents. All resulting equations of motion have the same form, but the transport coefficients are different in each case.Comment: 15 pages, 3 figures, typos fixed and discussions added; EPJA: Topical issue on "Relativistic Hydro- and Thermodynamics

Fractional Sunburn Threshold UVR Doses Generate Equivalent Vitamin D and DNA Damage in Skin Types I-VI but with Epidermal DNA Damage Gradient Correlated to Skin Darkness

Dermatology-oncolog

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types

What is the Oxygen Isotope Composition of Venus? The Scientific Case for Sample Return from Earth’s “Sister” Planet

Venus is Earth’s closest planetary neighbour and both bodies are of similar size and mass. As a consequence, Venus is often described as Earth’s sister planet. But the two worlds have followed very different evolutionary paths, with Earth having benign surface conditions, whereas Venus has a surface temperature of 464 °C and a surface pressure of 92 bar. These inhospitable surface conditions may partially explain why there has been such a dearth of space missions to Venus in recent years.The oxygen isotope composition of Venus is currently unknown. However, this single measurement (Δ17O) would have first order implications for our understanding of how large terrestrial planets are built. Recent isotopic studies indicate that the Solar System is bimodal in composition, divided into a carbonaceous chondrite (CC) group and a non-carbonaceous (NC) group. The CC group probably originated in the outer Solar System and the NC group in the inner Solar System. Venus comprises 41% by mass of the inner Solar System compared to 50% for Earth and only 5% for Mars. Models for building large terrestrial planets, such as Earth and Venus, would be significantly improved by a determination of the Δ17O composition of a returned sample from Venus. This measurement would help constrain the extent of early inner Solar System isotopic homogenisation and help to identify whether the feeding zones of the terrestrial planets were narrow or wide.Determining the Δ17O composition of Venus would also have significant implications for our understanding of how the Moon formed. Recent lunar formation models invoke a high energy impact between the proto-Earth and an inner Solar System-derived impactor body, Theia. The close isotopic similarity between the Earth and Moon is explained by these models as being a consequence of high-temperature, post-impact mixing. However, if Earth and Venus proved to be isotopic clones with respect to Δ17O, this would favour the classic, lower energy, giant impact scenario.We review the surface geology of Venus with the aim of identifying potential terrains that could be targeted by a robotic sample return mission. While the potentially ancient tessera terrains would be of great scientific interest, the need to minimise the influence of venusian weathering favours the sampling of young basaltic plains. In terms of a nominal sample mass, 10 g would be sufficient to undertake a full range of geochemical, isotopic and dating studies. However, it is important that additional material is collected as a legacy sample. As a consequence, a returned sample mass of at least 100 g should be recovered.Two scenarios for robotic sample return missions from Venus are presented, based on previous mission proposals. The most cost effective approach involves a “Grab and Go” strategy, either using a lander and separate orbiter, or possibly just a stand-alone lander. Sample return could also be achieved as part of a more ambitious, extended mission to study the venusian atmosphere. In both scenarios it is critical to obtain a surface atmospheric sample to define the extent of atmosphere-lithosphere oxygen isotopic disequilibrium. Surface sampling would be carried out by multiple techniques (drill, scoop, “vacuum-cleaner” device) to ensure success. Surface operations would take no longer than one hour.Analysis of returned samples would provide a firm basis for assessing similarities and differences between the evolution of Venus, Earth, Mars and smaller bodies such as Vesta. The Solar System provides an important case study in how two almost identical bodies, Earth and Venus, could have had such a divergent evolution. Finally, Venus, with its runaway greenhouse atmosphere, may provide data relevant to the understanding of similar less extreme processes on Earth. Venus is Earth’s planetary twin and deserves to be better studied and understood. In a wider context, analysis of returned samples from Venus would provide data relevant to the study of exoplanetary systems

Association of genetic variation with systolic and diastolic blood pressure among African Americans: the Candidate Gene Association Resource study

The prevalence of hypertension in African Americans (AAs) is higher than in other US groups; yet, few have performed genome-wide association studies (GWASs) in AA. Among people of European descent, GWASs have identified genetic variants at 13 loci that are associated with blood pressure. It is unknown if these variants confer susceptibility in people of African ancestry. Here, we examined genome-wide and candidate gene associations with systolic blood pressure (SBP) and diastolic blood pressure (DBP) using the Candidate Gene Association Resource (CARe) consortium consisting of 8591 AAs. Genotypes included genome-wide single-nucleotide polymorphism (SNP) data utilizing the Affymetrix 6.0 array with imputation to 2.5 million HapMap SNPs and candidate gene SNP data utilizing a 50K cardiovascular gene-centric array (ITMAT-Broad-CARe [IBC] array). For Affymetrix data, the strongest signal for DBP was rs10474346 (P= 3.6 × 10−8) located near GPR98 and ARRDC3. For SBP, the strongest signal was rs2258119 in C21orf91 (P= 4.7 × 10−8). The top IBC association for SBP was rs2012318 (P= 6.4 × 10−6) near SLC25A42 and for DBP was rs2523586 (P= 1.3 × 10−6) near HLA-B. None of the top variants replicated in additional AA (n = 11 882) or European-American (n = 69 899) cohorts. We replicated previously reported European-American blood pressure SNPs in our AA samples (SH2B3, P= 0.009; TBX3-TBX5, P= 0.03; and CSK-ULK3, P= 0.0004). These genetic loci represent the best evidence of genetic influences on SBP and DBP in AAs to date. More broadly, this work supports that notion that blood pressure among AAs is a trait with genetic underpinnings but also with significant complexit