Nutrition Society Silver Medal Lecture Nutrigenetics and personalised nutrition: how far have we progressed and are we likely to get there?

Nutrigenetics and personalised nutrition are components of the concept that in the future genotyping will be used as a means of defining dietary recommendations to suit the individual. Over the last two decades there has been an explosion of research in this area, with often conflicting findings reported in the literature. Reviews of the literature in the area of apoE genotype and cardiovascular health, apoA5 genotype and postprandial lipaemia and perilipin and adiposity are used to demonstrate the complexities of genotype-phenotype associations and the aetiology of apparent between-study inconsistencies in the significance and size of effects. Furthermore, genetic research currently often takes a very reductionist approach, examining the interactions between individual genotypes and individual disease biomarkers and how they are modified by isolated dietary components or foods. Each individual possesses potentially hundreds of 'at-risk' gene variants and consumes a highly-complex diet. In order for nutrigenetics to become a useful public health tool, there is a great need to use mathematical and bioinformatic tools to develop strategies to examine the combined impact of multiple gene variants on a range of health outcomes and establish how these associations can be modified using combined dietary strategies.

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.

Mathematical modelling for the digital society

We argue the case for a new branch of mathematics and its applications: Mathematics for the Digital Society. There is a challenge for mathematics, a strong “pull” from new and emerging commercial and public activities; and a need to train and inspire a generation of quantitative scientists who will seek careers within the associated sectors. Although now going through an early phase of boiling up, prior to scholarly distillation, we discuss how data rich activities and applications may benefit from a wide range of continuous and discrete models, methods, analysis and inference. In ten years time such applications will be common place and associated courses may be embedded within the undergraduate curriculum.

Fast and accurate SCFT calculations for periodic block-copolymer morphologies using the spectral method with Anderson mixing

We study the numerical efficiency of solving the self-consistent field theory (SCFT) for periodic block-copolymer morphologies by combining the spectral method with Anderson mixing. Using AB diblock-copolymer melts as an example, we demonstrate that this approach can be orders of magnitude faster than competing methods, permitting precise calculations with relatively little computational cost. Moreover, our results raise significant doubts that the gyroid (G) phase extends to infinite $\chi N$. With the increased precision, we are also able to resolve subtle free-energy differences, allowing us to investigate the layer stacking in the perforated-lamellar (PL) phase and the lattice arrangement of the close-packed spherical (S$_{cp}$) phase. Furthermore, our study sheds light on the existence of the newly discovered Fddd (O$^{70}$) morphology, showing that conformational asymmetry has a significant effect on its stability.

Observed adaptation to climate change: UK evidence of transition to a well-adapting society

This paper investigates whether and to what extent a wide range of actors in the UK are adapting to climate change, and whether this is evidence of a social transition. We document evidence of over 300 examples of early adopters of adaptation practice to climate change in the UK. These examples span a range of activities from small adjustments (or coping) to building adaptive capacity, implementing actions and creating deeper systemic change in public and private organisations in a range of sectors. We find that adaptation in the UK has been dominated by government initiatives and has principally occurred in the form of research into climate change impacts. These actions within government stimulate a further set of actions at other scales in public agencies, regulatory agencies and regional government (or in the devolved administrations), though with little real evidence of climate change adaptation initiatives trickling down to local government level. The water supply and flood defence sectors, requiring significant investment in large scale infrastructure such as reservoirs and coastal defences, have invested more heavily in identifying potential impacts and adaptations. Economic sectors that are not dependent on large scale infrastructure appear to be investing far less effort and resources in preparing for climate change. We conclude that while the government-driven top-down targeted adaptation approach has generated anticipatory action at low cost, it may also have created enough niche activities to allow for diffusion of new adaptation practices in response to real or perceived climate change. These results have significant implications for how climate policy can be developed to support autonomous adaptors in the UK and other countries.

The strategy makers: thoughts on war and society from Machiavelli and Clausewitz

Introductory chapter. Introduction and excerpts from works of Seigneur de Fourquevaux (1548); Francois Loque – Saillans (1589); Matthew Sutcliffe (1593); Don Bernardino de Mendoza (1595); Paul Hay du Chastelet (1668); Marquis Santa Cruz de Marcenado & Zanthier (1724-30/1775); Guibert (1772); Rühle von Lilienstern (1816/1817).

Representing geometrical knowledge

This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic.

Self-consistent field theory for diblock copolymers grafted to a sphere

An efficient numerical self-consistent field theory (SCFT) algorithm is developed for treating structured polymers on spherical surfaces. The method solves the diffusion equations of SCFT with a pseudospectral approach that combines a spherical-harmonics expansion for the angular coordinates with a modified real-space Crank–Nicolson method for the radial direction. The self-consistent field equations are solved with Anderson-mixing iterations using dynamical parameters and an alignment procedure to prevent angular drift of the solution. A demonstration of the algorithm is provided for thin films of diblock copolymer grafted to the surface of a spherical core, in which the sequence of equilibrium morphologies is predicted as a function of diblock composition. The study reveals an array of interesting behaviors as the block copolymer pattern is forced to adapt to the finite surface area of the sphere.