Perspex machine VII: The universal perspex machine

The perspex machine arose from the unification of projective geometry with the Turing machine. It uses a total arithmetic, called transreal arithmetic, that contains real arithmetic and allows division by zero. Transreal arithmetic is redefined here. The new arithmetic has both a positive and a negative infinity which lie at the extremes of the number line, and a number nullity that lies off the number line. We prove that nullity, 0/0, is a number. Hence a number may have one of four signs: negative, zero, positive, or nullity. It is, therefore, impossible to encode the sign of a number in one bit, as floating-, point arithmetic attempts to do, resulting in the difficulty of having both positive and negative zeros and NaNs. Transrational arithmetic is consistent with Cantor arithmetic. In an extension to real arithmetic, the product of zero, an infinity, or nullity with its reciprocal is nullity, not unity. This avoids the usual contradictions that follow from allowing division by zero. Transreal arithmetic has a fixed algebraic structure and does not admit options as IEEE, floating-point arithmetic does. Most significantly, nullity has a simple semantics that is related to zero. Zero means "no value" and nullity means "no information." We argue that nullity is as useful to a manufactured computer as zero is to a human computer. The perspex machine is intended to offer one solution to the mind-body problem by showing how the computable aspects of mind and. perhaps, the whole of mind relates to the geometrical aspects of body and, perhaps, the whole of body. We review some of Turing's writings and show that he held the view that his machine has spatial properties. In particular, that it has the property of being a 7D lattice of compact spaces. Thus, we read Turing as believing that his machine relates computation to geometrical bodies. We simplify the perspex machine by substituting an augmented Euclidean geometry for projective geometry. This leads to a general-linear perspex-machine which is very much easier to pro-ram than the original perspex-machine. We then show how to map the whole of perspex space into a unit cube. This allows us to construct a fractal of perspex machines with the cardinality of a real-numbered line or space. This fractal is the universal perspex machine. It can solve, in unit time, the halting problem for itself and for all perspex machines instantiated in real-numbered space, including all Turing machines. We cite an experiment that has been proposed to test the physical reality of the perspex machine's model of time, but we make no claim that the physical universe works this way or that it has the cardinality of the perspex machine. We leave it that the perspex machine provides an upper bound on the computational properties of physical things, including manufactured computers and biological organisms, that have a cardinality no greater than the real-number line.

Assessment of the consistency of near-infrared water vapor line intensities using high-spectral-resolution ground-based Fourier transform measurements of solar radiation

Calculations of the absorption of solar radiation by atmospheric gases, and water vapor in particular, are dependent on the quality of databases of spectral line parameters. There has been increasing scrutiny of databases such as HITRAN in recent years, but this has mostly been performed on a band-by-band basis. We report nine high-spectral-resolution (0.03 cm(-1)) measurements of the solar radiation reaching the surface in southern England over the wave number range 2000 to 12,500 cm(-1) (0.8 to 5 mm) that allow a unique assessment of the consistency of the spectral line databases over this entire spectral region. The data are assessed in terms of the modeled water vapor column that is required to bring calculations and observations into agreement; for an entirely consistent database, this water vapor column should be constant with frequency. For the HITRAN01 database, the spread in water vapor column is about 11%, with distinct shifts between different spectral regions. The HITRAN04 database is in significantly better agreement (about 5% spread) in the completely updated 3000 to 8000 cm(-1) spectral region, but inconsistencies between individual spectral regions remain: for example, in the 8000 to 9500 cm(-1) spectral region, the results indicate an 18% (+/- 1%) underestimate in line intensities with respect to the 3000 to 8000 cm(-1) region. These measurements also indicate the impact of isotopic fractionation of water vapor in the 2500 to 2900 cm(-1) range, where HDO lines dominate over the lines of the most abundant isotope of H2O.

The cell wall and secretory proteome of a tobacco cell line synthesising secondary wall

The utility of plant secondary cell wall biomass for industrial and biofuel purposes depends upon improving cellulose amount, availability and extractability. The possibility of engineering such biomass requires much more knowledge of the genes and proteins involved in the synthesis, modification and assembly of cellulose, lignin and xylans. Proteomic data are essential to aid gene annotation and understanding of polymer biosynthesis. Comparative proteomes were determined for secondary walls of stem xylem and transgenic xylogenic cells of tobacco and detected peroxidase, cellulase, chitinase, pectinesterase and a number of defence/cell death related proteins, but not marker proteins of primary walls such as xyloglucan endotransglycosidase and expansins. Only the corresponding detergent soluble proteome of secretory microsomes from the xylogenic cultured cells, subjected to ion-exchange chromatography, could be determined accurately since, xylem-specific membrane yields were of poor quality from stem tissue. Among the 109 proteins analysed, many of the protein markers of the ER such as BiP, HSP70, calreticulin and calnexin were identified, together with some of the biosynthetic enzymes and associated polypeptides involved in polymer synthesis. However 53% of these endomembrane proteins failed identification despite the use of two different MS methods, leaving considerable possibilities for future identification of novel proteins involved in secondary wall polymer synthesis once full genomic data are available.

Classification-based probabilistic modeling of texture transition for fast line search tracking and delineation

We introduce a classification-based approach to finding occluding texture boundaries. The classifier is composed of a set of weak learners, which operate on image intensity discriminative features that are defined on small patches and are fast to compute. A database that is designed to simulate digitized occluding contours of textured objects in natural images is used to train the weak learners. The trained classifier score is then used to obtain a probabilistic model for the presence of texture transitions, which can readily be used for line search texture boundary detection in the direction normal to an initial boundary estimate. This method is fast and therefore suitable for real-time and interactive applications. It works as a robust estimator, which requires a ribbon-like search region and can handle complex texture structures without requiring a large number of observations. We demonstrate results both in the context of interactive 2D delineation and of fast 3D tracking and compare its performance with other existing methods for line search boundary detection.

Assessment of the consistency of H2O line intensities over the near-infrared using sun-pointing ground-based Fourier transform spectroscopy

We report on the consistency of water vapour line intensities in selected spectral regions between 800–12,000 cm−1 under atmospheric conditions using sun-pointing Fourier transform infrared spectroscopy. Measurements were made across a number of days at both a low and high altitude field site, sampling a relatively moist and relatively dry atmosphere. Our data suggests that across most of the 800–12,000 cm−1 spectral region water vapour line intensities in recent spectral line databases are generally consistent with what was observed. However, we find that HITRAN-2008 water vapour line intensities are systematically lower by up to 20% in the 8000–9200 cm−1 spectral interval relative to other spectral regions. This discrepancy is essentially removed when two new linelists (UCL08, a compilation of linelists and ab-initio calculations, and one based on recent laboratory measurements by Oudot et al. (2010) [10] in the 8000–9200 cm−1 spectral region) are used. This strongly suggests that the H2O line strengths in the HITRAN-2008 database are indeed underestimated in this spectral region and in need of revision. The calculated global-mean clear-sky absorption of solar radiation is increased by about 0.3 W m−2 when using either the UCL08 or Oudot line parameters in the 8000–9200 cm−1 region, instead of HITRAN-2008. We also found that the effect of isotopic fractionation of HDO is evident in the 2500–2900 cm−1 region in the observations.

Germ-line chimaeras can produce both strains of fowl with high efficiency after partial sterilization

The drug busulphan is known to be cytotoxic to migrating primordial germ cells (PGCs). A technique is described in which doses of 0, 25, 50 and 250 micrograms busulphan in 40 microliters sesame oil were injected into the yolk of White Leghorn eggs incubated for 0, 24, 48 and 72 h. The percentage survival values of these embryos showed that the older the embryo at the time of injection, the greater the survival. Increasing the dose of busulphan decreased the survival. The percentage of embryos showing abnormalities increased with higher doses of busulphan. The number of germ cells in histological sections from gonads of 16-day embryos was estimated and in embryos treated with 50 micrograms and 250 micrograms busulphan the number of germ cells was significantly less than in the controls. Eggs were injected with 50 micrograms busulphan at 24-30 h, and at 50-55 h the embryos received an intravascular injection of a germinal crescent cell suspension containing PGCs from Rhode Island Red embryos. Twenty hatchlings from these experiments were raised to sexual maturity. All these birds were fertile and half of the breeding groups producing offspring from the transferred germ cells at a rate of about 35% of the total. The technique would improve the efficiency of producing transgenic gametes.

An obscured tradition: the sonnet and its fourteen-line predecessors

The sonnet in English is usually located as a sixteenth-century innovation, firmly linked to Italian influences, and frequently associated with a distinctively modern consciousness. Yet the speed and comfort with which the form settled into English reflects the fact that the sonnet per se was preceded by a longstanding tradition of 14-line poems in English written in forms derived from French. Indeed, in terms of formal features, the earliest sonnets in English frequently fray into earlier forms, sharing more with the roundel than with later sonnets. This article considers a number of features of style and content that various writers on the sonnet have argued to be characteristic, sometimes definitive, of the sonnet. These features include repetition, formal unity/division of octave and sestet, use of the volta, asymmetry, argument and development, and a preoccupation with contradictions and the self. The article shows that, while it is true that these features are characteristic of many sonnets, they are not peculiarly characteristic of sonnets, and they can all be found in earlier 14-line poems. Furthermore, a number of the earliest sonnets in English do not themselves possess these ‘sonnet-like’ characteristics. The otherness and the modernity of the sonnet have thus been overstated.

A maize bacterial artificial chromosome (BAC) library from the European flint inbred line F2

We report here the construction and characterisation of a BAC library from the maize flint inbred line F2, widely used in European maize breeding programs. The library contains 86,858 clones with an average insert size of approximately 90 kb, giving approximately 3.2-times genome coverage. High-efficiency BAC cloning was achieved through the use of a single size selection for the high-molecular-weight genomic DNA, and co-transformation of the ligation with yeast tRNA to optimise transformation efficiency. Characterisation of the library showed that less than 0.5% of the clones contained no inserts, while 5.52% of clones consisted of chloroplast DNA. The library was gridded onto 29 nylon filters in a double-spotted 8 × 8 array, and screened by hybridisation with a number of single-copy and gene-family probes. A 3-dimensional DNA pooling scheme was used to allow rapid PCR screening of the library based on primer pairs from simple sequence repeat (SSR) and expressed sequence tag (EST) markers. Positive clones were obtained in all hybridisation and PCR screens carried out so far. Six BAC clones, which hybridised to a portion of the cloned Rp1-D rust resistance gene, were further characterised and found to form contigs covering most of this complex resistance locus.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

Changes of the equilibrium line altitude since the Little Ice Age in the Nepalese Himalayas

Changes of the equilibrium-line altitude (ELA) since the end of the Little Ice Age (LIA) in eastern Nepal have been studied using glacier inventory data. The toe-to-headwall altitude ratios (THARs) for individual glaciers were calculated for 1992, and used to estimate the ELA in 1959 and at the end of the LIA. THAR for debris-free glaciers is found to be smaller than for debris-covered glaciers. The ELAs for debris-covered glaciers are higher than those for debris-free glaciers in eastern Nepal. There is considerable variation in the reconstructed change in ELA (ΔELA) between glaciers within specific regions and between regions. This is not related to climate gradients, but results from differences in glacier aspect: southeast- and south-facing glaciers show larger ΔELAs in eastern Nepal than north- or west-facing glaciers. The data suggest that the rate of ELA rise may have accelerated in the last few decades. The limited number of climate records from Nepal, and analyses using a simple ELA–climate model, suggest that the higher rate of the ΔELA between 1959 and 1992 is a result of increased warming that occurred after the 1970s at higher altitudes in Nepal.

The impact of number mismatch and passives on the real-time processing of relative clauses

Language processing plays a crucial role in language development, providing the ability to assign structural representations to input strings (e.g., Fodor, 1998). In this paper we aim at contributing to the study of children's processing routines, examining the operations underlying the auditory processing of relative clauses in children compared to adults. English-speaking children (6–8;11) and adults participated in the study, which employed a self-paced listening task with a final comprehension question. The aim was to determine (i) the role of number agreement in object relative clauses in which the subject and object NPs differ in terms of number properties, and (ii) the role of verb morphology (active vs. passive) in subject relative clauses. Even though children's off-line accuracy was not always comparable to that of adults, analyses of reaction times results support the view that children have the same structural processing reflexes observed in adults.

Gál-type GCD sums beyond the critical line

We prove that ∑k,ℓ=1N(nk,nℓ)2α(nknℓ)α≪N2−2α(logN)b(α) holds for arbitrary integers 1≤n1<⋯