Trans-floating-point arithmetic removes nine quadrillion redundancies from 64-bit IEEE 754 floating-point arithmetic

IEEE 754 floating-point arithmetic is widely used in modern, general-purpose computers. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. Modifying the IEEE arithmetic so that it uses transreal arithmetic has a number of advantages. It removes one redundant binade from IEEE floating-point objects, doubling the numerical precision of the arithmetic. It removes eight redundant, relational,floating-point operations and removes the redundant total order operation. It replaces the non-reflexive, floating-point, equality operator with a reflexive equality operator and it indicates that some of the exceptions may be removed as redundant { subject to issues of backward compatibility and transient future compatibility as programmers migrate to the transreal paradigm.

Construction of the transcomplex numbers from the complex numbers

A geometrical construction of the transcomplex numbers was given elsewhere. Here we simplify the transcomplex plane and construct the set of transcomplex numbers from the set of complex numbers. Thus transcomplex numbers and their arithmetic arise as consequences of their construction, not by an axiomatic development. This simplifes transcom- plex arithmetic, compared to the previous treatment, but retains totality so that every arithmetical operation can be applied to any transcomplex number(s) such that the result is a transcomplex number. Our proof establishes the consistency of transcomplex and transreal arithmetic and establishes the expected containment relationships amongst transcomplex, complex, transreal and real numbers. We discuss some of the advantages the transarithmetics have over their partial counterparts.

Transdifferential and transintegral calculus

The set of transreal numbers is a superset of the real numbers. It totalises real arithmetic by defining division by zero in terms of three def- inite, non-finite numbers: positive infinity, negative infinity and nullity. Elsewhere, in this proceedings, we extended continuity and limits from the real domain to the transreal domain, here we extended the real derivative to the transreal derivative. This continues to demonstrate that transreal analysis contains real analysis and operates at singularities where real analysis fails. Hence computer programs that rely on computing deriva- tives { such as those used in scientific, engineering and financial applica- tions { are extended to operate at singularities where they currently fail. This promises to make software, that computes derivatives, both more competent and more reliable. We also extended the integration of absolutely convergent functions from the real domain to the transreal domain.

Transreal arithmetic as a consistent basis for paraconsistent logics

Paraconsistent logics are non-classical logics which allow non-trivial and consistent reasoning about inconsistent axioms. They have been pro- posed as a formal basis for handling inconsistent data, as commonly arise in human enterprises, and as methods for fuzzy reasoning, with applica- tions in Artificial Intelligence and the control of complex systems. Formalisations of paraconsistent logics usually require heroic mathe- matical efforts to provide a consistent axiomatisation of an inconsistent system. Here we use transreal arithmetic, which is known to be consis- tent, to arithmetise a paraconsistent logic. This is theoretically simple and should lead to efficient computer implementations. We introduce the metalogical principle of monotonicity which is a very simple way of making logics paraconsistent. Our logic has dialetheaic truth values which are both False and True. It allows contradictory propositions, allows variable contradictions, but blocks literal contradictions. Thus literal reasoning, in this logic, forms an on-the- y, syntactic partition of the propositions into internally consistent sets. We show how the set of all paraconsistent, possible worlds can be represented in a transreal space. During the development of our logic we discuss how other paraconsistent logics could be arithmetised in transreal arithmetic.

Transreal limits expose category errors in IEEE 754 floating-point arithmetic and in mathematics

The IEEE 754 standard for oating-point arithmetic is widely used in computing. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. The IEEE infinities are said to have the behaviour of limits. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. We elucidate the transreal tangent and extend real limits to transreal limits. Arguing from this firm foundation, we maintain that there are three category errors in the IEEE 754 standard. Firstly the claim that IEEE infinities are limits of real arithmetic confuses limiting processes with arithmetic. Secondly a defence of IEEE negative zero confuses the limit of a function with the value of a function. Thirdly the definition of IEEE NaNs confuses undefined with unordered. Furthermore we prove that the tangent function, with the infinities given by geometrical con- struction, has a period of an entire rotation, not half a rotation as is commonly understood. This illustrates a category error, confusing the limit with the value of a function, in an important area of applied mathe- matics { trigonometry. We brie y consider the wider implications of this category error. Another paper proposes transreal arithmetic as a basis for floating- point arithmetic; here we take the profound step of proposing transreal arithmetic as a replacement for real arithmetic to remove the possibility of certain category errors in mathematics. Thus we propose both theo- retical and practical advantages of transmathematics. In particular we argue that implementing transreal analysis in trans- floating-point arith- metic would extend the coverage, accuracy and reliability of almost all computer programs that exploit real analysis { essentially all programs in science and engineering and many in finance, medicine and other socially beneficial applications.

Dilepton mass spectra in p plus p collisions at root s=200 GeV

PHENIX has measured the electron-positron pair mass spectrum from 0 to 8 GeV/c(2) in p + p collisions at root s = 200 GeV. The contributions from light meson decays to e(+)e(-) pairs have been determined based on measurements of hadron production cross sections by PHENIX. Within the systematic uncertainty of similar to 20% they account for all e(+)e(-) pairs in the mass region below similar to 1 GeV/c(2). The e(+)e(-) pair yield remaining after subtracting these contributions is dominated by semileptonic decays of charmed hadrons correlated through flavor conservation. Using the spectral shape predicted by PYTHIA, we estimate the charm production cross section to be 544 +/- 39(stat) +/- 142(syst) +/- 200(model) pb. which is consistent with QCD calculations and measurements of single leptons by PHENIX. (C) 2008 Elsevier BV. All rights reserved.

Sugar cane variety research for the Caribbean

Includes bibliography

3D osteoarthritic changes in TMJ condylar morphology correlates with specific systemic and local biomarkers of disease

Objective: To assess 3D morphological variations and local and systemic biomarker profiles in subjects with a diagnosis of temporomandibular joint osteoarthritis (TMJ OA).Design: Twenty-eight patients with long-term TMJ OA (39.9 +/- 16 years), 12 patients at initial diagnosis of OA (47.4 +/- 16.1 years), and 12 healthy controls (41.8 +/- 12.2 years) were recruited. All patients were female and had cone beam CT scans taken. TMJ arthrocentesis and venipuncture were performed on 12 OA and 12 age-matched healthy controls. Serum and synovial fluid levels of 50 biomarkers of arthritic inflammation were quantified by protein microarrays. Shape Analysis MANCOVA tested statistical correlations between biomarker levels and variations in condylar morphology.Results: Compared with healthy controls, the OA average condyle was significantly smaller in all dimensions except its anterior surface, with areas indicative of bone resorption along the articular surface, particularly in the lateral pole. Synovial fluid levels of ANG, GDF15, TIMP-1, CXCL16, MMP-3 and MMP-7 were significantly correlated with bone apposition of the condylar anterior surface. Serum levels of ENA-78, MMP-3, PAI-1, VE-Cadherin, VEGF, GM-CSF, TGF beta b1, IFN gamma g, TNF alpha a, IL-1 alpha a, and IL-6 were significantly correlated with flattening of the lateral pole. Expression levels of ANG were significantly correlated with the articular morphology in healthy controls.Conclusions: Bone resorption at the articular surface, particularly at the lateral pole was statistically significant at initial diagnosis of TMJ OA. Synovial fluid levels of ANG, GDF15, TIMP-1, CXCL16, MMP-3 and MMP-7 were correlated with bone apposition. Serum levels of ENA-78, MMP-3, PAI-1, VE-Cadherin, VEGF, GM-CSF, TGF beta 1, IFN gamma, TNF alpha, IL-1 alpha, and IL-6 were correlated with bone resorption. Published by Elsevier Ltd on behalf of Osteoarthritis Research Society International.

State of the Arctic October 2006

This State of the Arctic Report presents a review of recent data by an international group of scientists who developed a consensus on the information content and reliability. The report highlights data primarily from 2000 to 2005 with a first look at winter 2006, providing an update to some of the records of physical processes discussed in the Arctic Climate Impact Assessment (ACIA, 2004, 2005). Of particular note: • Atmospheric climate patterns are shifting (Fig. 1). The late winter/spring pattern for 2000–2005 had new hot spots in northeast Canada and the East Siberian Sea relative to 1980–1999. Late winter 2006, however, shows a return to earlier climate patterns, with warm temperatures in the extended region near Svalbard. • Ocean salinity and temperature profiles at the North Pole and in the Beaufort Sea, which changed abruptly in the 1990s, show that conditions since 2000 have relaxed toward the pre-1990 climatology, although 2001–2004 has seen an increase in northward ocean heat transport through Bering Strait (Fig. 2), which is thought to impact sea ice loss. • Sea ice extent continues to decrease. The sea ice extent in September 2005 was the minimum observed in summer during the satellite era (beginning in 1979), marking an unprecedented series of extreme ice extent minima beginning in 2002 (Fig. 3). The sea ice extent in March 2006 was also the minimum observed in winter during the satellite era. • Tundra vegetation greenness increased, primarily due to an increase in the abundance of shrubs. Boreal forest vegetation greenness decreased, possibly due to drought conditions (Fig. 4). • There is increasing interest in the stability of the Greenland ice sheet. The velocity of outlet glaciers increased in 2005 relative to 2000 and 1995, but uncertainty remains with regard to the total mass balance. • Permafrost temperatures continue to increase. However, data on changes in the active layer thickness (the relatively thin layer of ground between the surface and permafrost that undergoes seasonal freezing and thawing) are less conclusive. While some of the sites show a barely noticeable increasing trend in the thickness of the active layer, most of them do not. • Globally, 2005 was the warmest year in the instrumental record (beginning in 1880), with the Arctic providing a large contribution toward this increase. Many of the trends documented in the ACIA are continuing, but some are not. Taken collectively, the observations presented in this report indicate that during 2000–2005 the Arctic system showed signs of continued warming. However, there are a few indications that certain elements may be recovering and returning to recent climatological norms (for example, the central Arctic Ocean and some wind patterns). These mixed tendencies further illustrate the sensitivity and complexity of the Arctic physical system. They underline the importance of maintaining and expanding efforts to observe and better understand this important component of the climate system to provide accurate predictions of its future state.

Arctic Report Card 2007: Tracking Recent Environmental Changes

Collectively, the observations indicate that the overall warming of the Arctic system continued in 2007. There are some elements that are stabilizing or returning to climatological norms. These mixed tendencies illustrate the sensitivity and complexity of the Arctic System. Atmosphere: Hot spot shifts toward Europe Ocean: North Pole Temperatures at depth returning to 1990s values Sea Ice: Summer extent at record minimum Greenland: Recent warm temperatures associated with net ice loss Biology: increasing tundra shrub cover and variable treeline advance; up to 80% declines in some caribou herds while goose populations double Land: Increase in permafrost temperatures The Arctic Report Card 2007 is introduced as a means of presenting clear, reliable and concise information on recent observations of environmental conditions in the Arctic, relative to historical time series records. It provides a method of updating and expanding the content of the State of the Arctic Report, published in fall 2006, to reflect current conditions. Material presented in the Report Card is prepared by an international team of scientists and is peer-reviewed by topical experts nominated by the US Polar Research Board. The audience for the Arctic Report Card is wide, including scientists, students, teachers, decision makers and the general public interested in Arctic environment and science. The web-based format will facilitate future timely updates of the content.

Nuclear-modification factor for open-heavy-flavor production at forward rapidity in Cu plus Cu collisions at root s(NN)=200 GeV

Background: Heavy-flavor production in p + p collisions is a good test of perturbative-quantum-chromodynamics (pQCD) calculations. Modification of heavy-flavor production in heavy-ion collisions relative to binary-collision scaling from p + p results, quantified with the nuclear-modification factor (R-AA), provides information on both cold-and hot-nuclear-matter effects. Midrapidity heavy-flavor R-AA measurements at the Relativistic Heavy Ion Collider have challenged parton-energy-loss models and resulted in upper limits on the viscosity-entropy ratio that are near the quantum lower bound. Such measurements have not been made in the forward-rapidity region. Purpose: Determine transverse-momentum (p(T)) spectra and the corresponding R-AA for muons from heavy-flavor meson decay in p + p and Cu + Cu collisions at root s(NN) = 200 GeV and y = 1.65. Method: Results are obtained using the semileptonic decay of heavy-flavor mesons into negative muons. The PHENIX muon-arm spectrometers measure the p(T) spectra of inclusive muon candidates. Backgrounds, primarily due to light hadrons, are determined with a Monte Carlo calculation using a set of input hadron distributions tuned to match measured-hadron distributions in the same detector and statistically subtracted. Results: The charm-production cross section in p + p collisions at root s = 200 GeV, integrated over p(T) and in the rapidity range 1.4 < y < 1.9, is found to be d(sigma e (e) over bar)/dy = 0.139 +/- 0.029 (stat)(-0.058)(+0.051) (syst) mb. This result is consistent with a perturbative fixed-order-plus-next-to-leading-log calculation within scale uncertainties and is also consistent with expectations based on the corresponding midrapidity charm-production cross section measured by PHENIX. The R-AA for heavy-flavor muons in Cu + Cu collisions is measured in three centrality bins for 1 < p(T) < 4 GeV/c. Suppression relative to binary-collision scaling (R-AA < 1) increases with centrality. Conclusions: Within experimental and theoretical uncertainties, the measured charm yield in p + p collisions is consistent with state-of-the-art pQCD calculations. Suppression in central Cu + Cu collisions suggests the presence of significant cold-nuclear-matter effects and final-state energy loss.

Celecoxib plus hormone therapy versus hormone therapy alone for hormone-sensitive prostate cancer: first results from the STAMPEDE multiarm, multistage, randomised controlled trial

Long-term hormone therapy alone is standard care for metastatic or high-risk, non-metastatic prostate cancer. STAMPEDE--an international, open-label, randomised controlled trial--uses a novel multiarm, multistage design to assess whether the early additional use of one or two drugs (docetaxel, zoledronic acid, celecoxib, zoledronic acid and docetaxel, or zoledronic acid and celecoxib) improves survival in men starting first-line, long-term hormone therapy. Here, we report the preplanned, second intermediate analysis comparing hormone therapy plus celecoxib (arm D) with hormone therapy alone (control arm A).