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In much of Europe, the advent of low-input cereal farming regimes between c.ad 800 and 1200 enabled landowners—lords—to amass wealth by greatly expanding the amount of land under cultivation and exploiting the labour of others. Scientific analysis of plant remains and animal bones from archaeological contexts is generating the first direct evidence for the development of such low-input regimes. This article outlines the methods used by the FeedSax project to resolve key questions regarding the ‘cerealization’ of the medieval countryside and presents preliminary results using the town of Stafford as a worked example. These indicate an increase in the scale of cultivation in the Mid-Saxon period, while the Late Saxon period saw a shift to a low-input cultivation regime and probably an expansion onto heavier soils. Crop rotation appears to have been practised from at least the mid-tenth century.
Little is known about who would benefit from Internet-based personalised nutrition (PN) interventions. This study aimed to evaluate the characteristics of participants who achieved greatest improvements (i.e. benefit) in diet, adiposity and biomarkers following an Internet-based PN intervention. Adults (n 1607) from seven European countries were recruited into a 6-month, randomised controlled trial (Food4Me) and randomised to receive conventional dietary advice (control) or PN advice. Information on dietary intake, adiposity, physical activity (PA), blood biomarkers and participant characteristics was collected at baseline and month 6. Benefit from the intervention was defined as ≥5 % change in the primary outcome (Healthy Eating Index) and secondary outcomes (waist circumference and BMI, PA, sedentary time and plasma concentrations of cholesterol, carotenoids and omega-3 index) at month 6. For our primary outcome, benefit from the intervention was greater in older participants, women and participants with lower HEI scores at baseline. Benefit was greater for individuals reporting greater self-efficacy for ‘sticking to healthful foods’ and who ‘felt weird if [they] didn’t eat healthily’. Participants benefited more if they reported wanting to improve their health and well-being. The characteristics of individuals benefiting did not differ by other demographic, health-related, anthropometric or genotypic characteristics. Findings were similar for secondary outcomes. These findings have implications for the design of more effective future PN intervention studies and for tailored nutritional advice in public health and clinical settings.
The early Middle Ages saw a major expansion of cereal cultivation across large parts of Europe thanks to the spread of open-field farming. A major project to trace this expansion in England by deploying a range of scientific methods is generating direct evidence for this so-called ‘Medieval Agricultural Revolution’.
The question of whether international humanitarian law (IHL) has an impact on how armed conflicts are conducted is a controversial one. Sceptics claim that the law is virtually irrelevant in determining State behaviour in armed conflict. Proponents point to its importance in mitigating the suffering caused by war. This paper looks at recent scholarship from historians, political scientists, economists and lawyers that challenges traditional narratives held dear by the law's sceptics and proponents alike. It then discusses implications of these approaches for a current understanding of the role of IHL in today's armed conflicts. The new perspectives allow for a broader understanding of IHL's central issues and permit us to ask more pertinent questions when looking at the law with the aim of putting it to use for the protection of civilians.
The study discusses the mineralogical, geochemical and thermometric properties of rock-forming blue quartz from eight worldwide occurrences. Compared to non-blue quartz, blue quartz contains significant amounts of submicron-sized (1 μm—100 nm) and nanometre-sized (<100 nm) inclusions. Mica, ilmenite and rutile constitute the most abundant submicron-sized inclusions, and are formed probably by syngenetic precipitation in the boundary layer between quartz and melt (entrapment model). Nanometre-sized rutile possibly originated by epigenetic exsolution of Ti from the quartz structure (exsolution model). Rayleigh scattering of light by nano-particulate inclusions best explains the origin of the blue colour. Blue quartz is generally Ti-rich (∼100—300 ppm) and formed at high temperatures (∼700°C—900°C). The large number, and high spatial density, of tiny xenocrystic inclusions of Ti-bearing minerals make calculations of crystallization temperatures using the Ti-in-quartz thermometer unreliable. The geological significance of blue quartz remains obscure.
It is generally known that infinite symmetric groups have few nontrivial normal subgroups (typically only the subgroups of bounded support) and none of small index. (We will explain later exactly what we mean by small). However the standard analysis relies heavily on the axiom of choice. By dint of a lot of combinatorics we have been able to dispense—largely—with the axiom of choice. Largely, but not entirely: our result is that if X is an infinite set with ∣X∣ = ∣X × X∣ then Symm(X) has no nontrivial normal subgroups of small index. Some condition like this is needed because of the work of Sam Tarzi who showed  that, for any finite group G, there is a model of ZF without AC in which there is a set X with Symm(X)/FSymm(X) isomorphic to G.
The proof proceeds in two stages. We consider a particularly useful class of permutations, which we call the class of flexible permutations. A permutation of X is flexible if it fixes at least ∣X∣-many points. First we show that every normal subgroup of Symm(X) (of small index) must contain every flexible permutation. This will be theorem 4. Then we show (theorem 7) that the flexible permutations generate Symm(X).
The two expressions ‘The cumulative hierarchy’ and ‘The iterative conception of sets’ are usually taken to be synonymous. However, the second is more general than the first, in that there are recursive procedures that generate some ill-founded sets in addition to well-founded sets. The interesting question is whether or not the arguments in favour of the more restrictive version – the cumulative hierarchy – were all along arguments for the more general version.
A version of the Erdős-Rado theorem on partitions of the unordered n-tuples from uncountable sets is proved, without using the axiom of choice. The case with exponent 1 is just the Sierpinski-Hartogs' result that .
Driven by our interest in sustainability, the vernacular architecture of Wales and a preference for ‘rational’ over wilfully expressive form, the determination to ‘build simply’ has become an abiding aspiration in the work of the Design Research Unit (dru) at the Welsh School of Architecture, Cardiff University. Established in 1998, dru aims both to apply the School's wider research to architectural commissions and to develop design as a medium of research in its own right. In this paper, various themes that recur in the Unit's recent work are discussed in the context of two current schemes that exemplify this research-based approach to design.
The mechanical response of living tissue is important to understanding the injury-risk associated with impact events. Often, ballistic gelatin or synthetic materials are developed to serve as tissue surrogates in mechanical testing. Unfortunately, current materials are not optimal and present several experimental challenges. Bulk measurement techniques, such as compression and shear testing geometries, do not fully represent the stress states and rate of loading experienced in an actual impact event. Indentation testing induces deviatoric stress states as well as strain rates not typically available to bulk measurement equipment. In this work, a ballistic gelatin and two styrene-isoprene triblock copolymer gels are tested and compared using both macroscale and microscale measurements. A methodology is presented to conduct instrumented indentation experiments on materials with a modulus far below 1 MPa. The synthetic triblock copolymer gels were much easier to test than the ballistic gelatin. Compared to ballistic gelatin, both copolymer gels were found to have a greater degree of thermal stability. All of the materials exhibit strain-rate dependence, although the magnitude of dependence was a function of the loading rate and testing method.
It is shown that, according to NF, many of the assertions of ordinal arithmetic involving the T-function which is peculiar to NF turn out to be equivalent to the truth-in-certain-permutation-models of assertions which have perfectly sensible ZF-style meanings, such as: the existence of wellfounded sets of great size or rank, or the nonexistence of small counterexamples to the wellfoundedness of ∈. Everything here holds also for NFU if the permutations are taken to fix all urelemente.
This essay owes its appearance here to the good offices of Reinhard Kahle who, at short notice, allowed me the opportunity to turn into something publishable a rat's nest of clandestine fragments hitherto available only to the author's friends and students. I had always assumed that they were in any case so heretical that nobody would publish them even if I tidied them up and I am grateful to Kahle for giving me the chance to be burnt rather than merely ignored. The one major regret I now have about the delay caused by my timidity is that in the dozen-or-so years that have passed since the first draughts of this essay were circulated David Lewis has died. Readers familiar with the literature will immediately recognise Lewis as the most important single creator of the Augean stables I am reporting on, and as the writer most likely to wish to maintain them intact as a World Heritage Site. It is true that I thought his ideas terrible, but he defended them with personal integrity and without malice: I enjoyed his company, and am sorry that he is not around to reply.
The three essays out of which it grew were entitled “The modal ather”, “Indexicality” and “The closest possible world”. In the first essay I argue that if possible worlds are to be used at all to explain necessary truth, then at least some truths (those concerning relations between worlds) are necessary in virtue of something other than truth in all those worlds. In the second I argue that the idea that actuality as indexical is in need of a lot of explanation. In the third I argue that there is no logical notion of closest possible world. The essays get progressively more technical, but I preface themwith an introductory essay whose general drift can be caught even by those with no formal background, and insert between the first and second essays a brief sketch of the topological ideas on which ideas of indexicality and proximity (of the two final essays) presumably ultimately rely.
When there are so many textbooks on logic already available, an author of a new one must expect to be challenged for explanations as to why he has added to their number. I have four main excuses. I am not happy with the treatments of well-foundedness nor of the axiomatisation of set theory in any of the standard texts known to me. My third excuse is that, because my first degree was not in mathematics but in philosophy and music, I have always been more preoccupied with philosophical concerns than have most of my colleagues. Both the intension-extension distinction and the use-mention distinction are not only philosophically important but pedagogically important too: this is no coincidence. Many topics in mathematics become much more accessible to students if approached in a philosophically sensitive way. My fourth excuse is that nobody has yet written an introductory book on logic that fully exploits the expository possibilities of the idea of an inductively defined set or recursive datatype. I think my determination to write such a book is one of the sequelæ of reading Conway's beautiful book (2001) based on lectures he gave in Cambridge many years ago when I was a Ph.D. student.
This book is based on my lecture notes and supervision (tutorial) notes for the course entitled “Logic, Computation and Set Theory”, which is lectured in part II (third year) of the Cambridge Mathematics Tripos.