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.

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.

A new feedback on climate change from the hydrological cycle

An intensification of the hydrological cycle is a likely consequence of global warming. But changes in the hydrological cycle could affect sea-surface temperature by modifying diffusive ocean heat transports. We investigate this mechanism by studying a coupled general circulation model sensitivity experiment in which the hydrological cycle is artificially amplified. We find that the amplified hydrological cycle depresses sea-surface temperature by enhancing ocean heat uptake in low latitudes. We estimate that a 10% increase in the hydrological cycle will contribute a basin-scale sea-surface temperature decrease of around 0.1°C away from high latitudes, with larger decreases locally. We conclude that an intensified hydrological cycle is likely to contribute a weak negative feedback to anthropogenic climate change.

Soils and their distribution on Bambouto volcanic mountain, West Cameroon highland, Central Africa

Morphological, physical and chemical studies were carried out on soils of Mount Bambouto, a volcanic mountain of the West Cameroon highland. These studies show that the soils of this region can be divided into seven groups according to Soils Taxonomy USA [Soil taxonomy: a basic system of soil classification for making and interpreting soils surveys: USDA Agriculture Handbook 436: Washington, DC, US Government Pronting Office, 1975, 754]: lithic dystrandept soils, typical dystrandept soils, oxic dystrandept soils, typical haplohumox soils, typical kandiudox soils, tropopsamment soils and umbriaquox soils. A soils map of this region at scale 1:50,000 has been drawn up, using the seven soils groups above as soil cartography units. These soils are organised into of three main categories: soils with andic characteristics in the upper region of the mountain (lithic dystrandept soils, typical dystrandept soils and oxic dystrandept soils); ferrallitic soils in the lower part of the mountain (typical haplohumox soils and typical kandiudox soils) and imperfectly developed soils (tropopsamment soils and umbraquox soils).

Monte Carlo numerical treatment of large linear algebra problems

In this paper we deal with performance analysis of Monte Carlo algorithm for large linear algebra problems. We consider applicability and efficiency of the Markov chain Monte Carlo for large problems, i.e., problems involving matrices with a number of non-zero elements ranging between one million and one billion. We are concentrating on analysis of the almost Optimal Monte Carlo (MAO) algorithm for evaluating bilinear forms of matrix powers since they form the so-called Krylov subspaces. Results are presented comparing the performance of the Robust and Non-robust Monte Carlo algorithms. The algorithms are tested on large dense matrices as well as on large unstructured sparse matrices.

Gene-nutrient interactions with dietary fat modulate the association between genetic variation of the ACSL1 gene and metabolic syndrome

Long-chain acyl CoA synthetase 1 (ACSL1) plays an important role in fatty acid metabolism and triacylglycerol (TAG) synthesis. Disturbance of these pathways may result in dyslipidemia and insulin resistance, hallmarks of the metabolic syndrome (MetS). Dietary fat is a key environmental factor that may interact with genetic determinants of lipid metabolism to affect MetS risk. We investigated the relationship between ACSL1 polymorphisms (rs4862417, rs6552828, rs13120078, rs9997745, and rs12503643) and MetS risk and determined potential interactions with dietary fat in the LIPGENE-SU.VI.MAX study of MetS cases and matched controls (n = 1,754). GG homozygotes for rs9997745 had increased MetS risk {odds ratio (OR) 1.90 [confidence interval (CI) 1.15, 3.13]; P = 0.01}, displayed elevated fasting glucose (P = 0.001) and insulin concentrations (P = 0.002) and increased insulin resistance (P = 0.03) relative to the A allele carriers. MetS risk was modulated by dietary fat, whereby the risk conferred by GG homozygosity was abolished among individuals consuming either a low-fat (<35% energy) or a high-PUFA diet (>5.5% energy). In conclusion, ACSL1 rs9997745 influences MetS risk, most likely via disturbances in fatty acid metabolism, which was modulated by dietary fat consumption, particularly PUFA intake, suggesting novel gene-nutrient interactions.

Genetic analysis of heat tolerance at anthesis in rice

Genetic analysis of heat tolerance will help breeders produce rice (Oryza sativa L.) varieties adapted to future climates. An F6 population of 181 recombinant inbred lines of Bala (tolerant) × Azucena (susceptible) was screened for heat tolerance at anthesis by measuring spikelet fertility at 30°C (control) and 38°C (high temperature) in experiments conducted in the Philippines and the United Kingdom. The parents varied significantly for absolute spikelet fertility under control (79–87%) and at high temperature (2.9–47.1%), and for relative spikelet fertility (high temperature/control) at high temperature (3.7–54.9%). There was no correlation between spikelet fertility in control and high-temperature conditions and no common quantitative trait loci (QTLs) were identified. Two QTLs for spikelet fertility under control conditions were identified on chromosomes 2 and 4. Eight QTLs for spikelet fertility under high-temperature conditions were identified on chromosomes 1, 2, 3, 8, 10, and 11. The most significant heat-responsive QTL, contributed by Bala and explaining up to 18% of the phenotypic variation, was identified on chromosome 1 (38.35 mega base pairs on the rice physical genome map). This QTL was also found to influence plant height, explaining 36.6% of the phenotypic variation. A comparison with other studies of abiotic (drought, cold, salinity) stresses showed QTLs at similar positions on chromosomes 1, 3, 8, and 10, suggesting common underlying stress-responsive regions of the genome.

Optimal control of nonlinear differential algebraic equation systems

A novel iterative procedure is described for solving nonlinear optimal control problems subject to differential algebraic equations. The procedure iterates on an integrated modified linear quadratic model based problem with parameter updating in such a manner that the correct solution of the original non-linear problem is achieved. The resulting algorithm has a particular advantage in that the solution is achieved without the need to solve the differential algebraic equations . Convergence aspects are discussed and a simulation example is described which illustrates the performance of the technique. 1. Introduction When modelling industrial processes often the resulting equations consist of coupled differential and algebraic equations (DAEs). In many situations these equations are nonlinear and cannot readily be directly reduced to ordinary differential equations.

Conformational analysis of oriented non-crystalline polymers using wide angle X-ray scattering

A procedure is presented for obtaining conformational parameters from oriented but non-crystalline polymers. This is achieved by comparison of the experimental wide angle X-ray scattering with that calculated from models but in such a way that foreknowledge of the orientation distribution function is not required. X-ray scattering intensity values for glassy isotactic poly(methylmethacrylate) are analysed by these techniques. The method could be usefully applied to other oriented molecular systems such as liquid crystalline materials.

Closed loop design for a simple nonlinear aircraft model using eigenstructure assignment

Aircraft systems are highly nonlinear and time varying. High-performance aircraft at high angles of incidence experience undesired coupling of the lateral and longitudinal variables, resulting in departure from normal controlled flight. The aim of this work is to construct a robust closed-loop control that optimally extends the stable and decoupled flight envelope. For the study of these systems nonlinear analysis methods are needed. Previously, bifurcation techniques have been used mainly to analyze open-loop nonlinear aircraft models and investigate control effects on dynamic behavior. In this work linear feedback control designs calculated by eigenstructure assignment methods are investigated for a simple aircraft model at a fixed flight condition. Bifurcation analysis in conjunction with linear control design methods is shown to aid control law design for the nonlinear system.

Revenue-neutral tax policies under price uncertainty: reply

In their comment on my 1990 article, Yeh, Suwanakul, and Mai extend my analysis-which focused attention exclusively on firm output-to allow for simultaneous endogeneity of price, aggregate output, and numbers of firms. They show that, with downward- sloping demand, industry output adjusts positively to revenue-neutral changes in the marginal rate of taxation. This result is significant for two reasons. First, we are more often interested in predictions about aggregate phenomena than we are in predictions about individual firms. Indeed, firm-level predictions are frequently irrefutable since firm data are often unavailable. Second, the authors derive their result under a set of conditions that appear to be more general than those invoked in my 1990 article. In particular, they circumvent the need to invoke specific assumptions about the nature of firms' aversions toward risk. I consider this a useful extension and I appreciate the careful scrutiny of my paper.

Evolutionary and revolutionary effects of transcomputation

Mathematics in Defence 2011 Abstract. We review transreal arithmetic and present transcomplex arithmetic. These arithmetics have no exceptions. This leads to incremental improvements in computer hardware and software. For example, the range of real numbers, encoded by floating-point bits, is doubled when all of the Not-a-Number(NaN) states, in IEEE 754 arithmetic, are replaced with real numbers. The task of programming such systems is simplified and made safer by discarding the unordered relational operator,leaving only the operators less-than, equal-to, and greater than. The advantages of using a transarithmetic in a computation, or transcomputation as we prefer to call it, may be had by making small changes to compilers and processor designs. However, radical change is possible by exploiting the reliability of transcomputations to make pipelined dataflow machines with a large number of cores. Our initial designs are for a machine with order one million cores. Such a machine can complete the execution of multiple in-line programs each clock tick

Global transcriptome analysis and identification of differentially expressed genes after infection of Fragaria vesca with powdery mildew (Podosphaera aphanis)

Background: Podosphaera aphanis, the causal agent of strawberry powdery mildew causes significant economic loss worldwide. Methods: We used the diploid strawberry species Fragaria vesca as a model to study plant pathogen interactions. RNA-seq was employed to generate a transcriptome dataset from two accessions, F. vesca ssp. vesca Hawaii 4 (HW) and F. vesca f. semperflorens Yellow Wonder 5AF7 (YW) at 1 d (1 DAI) and 8 d (8 DAI) after infection. Results: Of the total reads identified about 999 million (92%) mapped to the F. vesca genome. These transcripts were derived from a total of 23,470 and 23,464 genes in HW and YW, respectively from the three time points (control, 1 and 8 DAI). Analysis identified 1,567, 1,846 and 1,145 up-regulated genes between control and 1 DAI, control and 8 DAI, and 1 and 8 DAI, respectively in HW. Similarly, 1,336, 1,619 and 968 genes were up-regulated in YW. Also 646, 1,098 and 624 down-regulated genes were identified in HW, while 571, 754 and 627 genes were down-regulated in YW between all three time points, respectively. Conclusion: Investigation of differentially expressed genes (log2 fold changes �5) between control and 1 DAI in both HW and YW identified a large number of genes related to secondary metabolism, signal transduction; transcriptional regulation and disease resistance were highly expressed. These included flavonoid 3´-monooxygenase, peroxidase 15, glucan endo-1,3-β-glucosidase 2, receptor-like kinases, transcription factors, germin-like proteins, F-box proteins, NB-ARC and NBS-LRR proteins. This is the first application of RNA-seq to any pathogen interaction in strawberry