bluuebunny/crossref_metadata_2025 huggingface dataset:
Some properties of repetends
Authors: Armstrong N. J. , Armstrong R. J.
Published: August 2016

We wish to discuss some aspects of repetends, the repeating sequence of digits in the expansion of a fraction (for illuminating introductions to the subject see [1, 2]). For the most part we restrict consideration here to fractions with a prime denominator. But we do consider the general condition for the length of repetends and examine some special cases when the base of the number system is varied. An illustration of the use of other bases than 10 is given. Then we consider the multiplication of repetends and show a connection with group theory, giving an old result by a new twist.
Triangles in squares
Authors: Yuan Liping , Ding Ren
Published: August 2016

In this paper we find the necessary and sufficient conditions on a, b, c, s for a triangle with sides a, b, c to fit into a square of side s.

Questions about precisely when one shape fits into another attract wide attention. In 1993 Post [1] gave necessary and sufficient conditions on the six sides of two triangles for the first to fit into the second. Recently, the necessary and sufficient conditions for squares to fit in triangles [2], equilateral triangles in triangles [3], rectangles in triangles [4] and rectangles in rectangles [5] are given. In [2] Wetzel asked when a given triangle fits into a given square. In this paper we find the necessary and sufficient conditions on a, b, c, s for a triangle with sides a, b, c to fit into a square of side s. For the sake of convenience, let α, β, γ denote the angles opposite sides a, b, c respectively, and we may assume without loss of generality that a ≥ b ≥ c, which implies that α ≥ β ≥ γ.
Trigonometric identities and functional equations
Authors: Kannappan Pl.
Published: August 2016

Dedicated to Professor S. Kurepa on the occasion of his 73rd birthday. We are familiar with many trigonometric formulas (identities)

leading to five more identities

and so on, where #x211D; is the set of reals.
Cyclic quadrilaterals
Authors: Bradley C. J.
Published: August 2016

In this article I review some of the more advanced results concerning cyclic quadrilaterals, including a number that are new to me and possibly, therefore, to readers. Proofs of theorems are not given, but I give a clear indication of the methods I have used to verify them. The Cabri software package has been used to indicate the correctness of each result. In certain cases the coordinate geometry involved is so complex that Derive had to be used in the proofs. One of the results I have been unable to prove, and this is therefore labelled as a conjecture, though the accuracy of Cabri, which allows figures to be dragged around, is such that we may be confident that it is true.
Beyond the Euler summation formula
Authors: Lewis Barry
Published: August 2016

The Eulerian numbers are not strangers to readers of the Gazette but they are not normally associated with the subject of this article, despite the similarity of their names. This article seeks to use Eulerian numbers in generalised telescoping sums, a role that is a powerful extension of an established technique – the Euler summation formula.
Generalising Pascal's Triangle
Authors: Lewis Barry
Published: August 2016

Pascal's triangle, the Binomial expansion and the recurrence relation between its entries are all inextricably linked. In the normal course of events, the Binomial expansion leads to Pascal's Triangle, and thence to the recurrence relation between its entries. In this article we are going to reverse this process to make it possible to explore a particular type of generalisation of such interlinked structures, by generalising the recurrence relation and then exploring the resulting generalised ‘Pascal Triangle’ and ‘Binomial expansion’. Within the spectrum of generalisations considered, we find exactly four of particular significance: those concerned with the Binomial coefficients, the Stirling numbers of both kinds, and a lesser known set of numbers – the Lah numbers. We also examine the combinatorial properties of the entries in these triangles and a prime number divisibility property that they all share. Thereby, we achieve a remarkable synthesis of these different entities.
Henry Briggs: The Trigonometria Britannica
Authors: Bruce Ian
Published: August 2016

In 1632, Henry Gellibrand, then the Professor of Astronomy at Gresham College, London, arranged for the publishing of the Trigonometria Britannica (T. B.) by Adrian Vlacq in Gouda the following year: the work consisted of two Books, and sets of tables of natural sines in steps of one hundredth of a degree to 15 places, as well as tables of tangents & secants to 10 places, together with their logarithms. The explanatory Book I was the last work of Henry Briggs (1559-1631), Savilian Professor of Geometry at Oxford, and was devoted mainly to the construction of his table of sines; while Book II, written by the youthful Gellibrand on the instigation of the dying Briggs, his mentor, contained instructions and examples on the use of logarithms in solving trigonometrical problems.
Mathematical operators and ways of reasoning
Authors: Ginat David
Published: August 2016

Given a mathematical operator, how should one reason about the outcome of its repeated invocation? This question is relevant in both mathematics and computer science, where iterative operator invocations are core, algorithmic elements.

An initial approach, which one may naturally follow, is to try the operator in diverse situations, observe the results, and suggest a general outcome. Such an approach embodies operational reasoning, where inference derives from ‘behaviours’ of invocation sequences. This may indeed reveal some behavioural characteristics, but is it sufficient for rigorous argumentation of the general outcome? Not quite.
Partitions of primes and other sequences
Authors: McLean K. Robin
Published: August 2016

Let p1, p2, p3, … be the sequence of primes. Take any integer n ⩾ 2 and partition the set {p1p2, … , pn} into two non-empty subsets A and B. Let PA be the product of primes in A and PB be the product of primes in B. No partition exists with PA = PB, because of the uniqueness of prime factorisation, but Fernando Castro’s neat result in [1] asserts that for each n there is a partition for which 1
Functional equations and groups
Authors: Perella Malcolm A.
Published: August 2016

Consider the functional equation

Now let and These are elements of a group, G1 say, which is isomorphic to C2, the cyclic group of order 2, as can be seen from the group table:
The aberrancy of plane curves
Authors: Gordon Russell A.
Published: August 2016

The aberrancy of a plane curve is a property of the curve that is invariant under both translation and rotation. It provides a numerical measure for the non-circularity of the curve at each point of the curve. (Recall that curvature gives an invariant numerical measure of nonlinearity.) The concept of aberrancy has been around for two centuries, but it has received very little attention. We hope to stir a little interest in the concept by presenting four different derivations of the formula for aberrancy. This may appear to be redundant, but there are some good reasons for doing so. First of all, the only derivation for aberrancy in the literature is a bit confusing and makes a few unjustified assumptions. Secondly, the derivations we present are all significantly different from each other and involve some interesting ideas in elementary real analysis. Finally, although the basic idea behind each derivation is simple, the details can become extremely messy unless a proper path is chosen. We encourage the reader to find one or two approaches of particular interest and use the concept of aberrancy as an extended problem set in an undergraduate analysis course or even a further mathematics class in an English school.
About tsunamis
Authors: Brearley Maurice N.
Published: August 2016

A tsunami usually starts on deep ocean water as a result of a submarine earthquake. A tsunami wave is very long, even as much as tens of kilometres, but of only very small amplitude, typically less than half a metre (Bascom [1]). In mid-ocean, the passage of a tsunami is imperceptible, but on reaching a shore it can achieve great heights and can deliver massive surges of water. Before the arrival of the first surge, and between subsequent surges, the water at a shore line usually retracts for a long distance, leaving bare large areas of ocean floor that are normally under water. This paper analyses the behaviour of a tsunami, and explains how its mid-ocean character is transformed to produce such massive surges of water at a shore line.
Numerical integration — a different approach
Authors: Smith Harry V.
Published: August 2016

In common with, I suspect, many people the author does not have access to the NAG library and so, when I was asked recently to calculate the value of the integral

correct to 10 decimal places my first reaction was to try several different calculators as well as several mathematical software packages. On doing so it was disappointing to find they either gave widely differing values such as 7.9065200767, 4.1317217452 or 0.9174196842 or an error message indicating that the method had not converged.
The distribution of the geometric mean
Authors: Wilson David A. L. , Martin Barry
Published: August 2016

Although a number of earlier researchers had used the geometric mean as a convenient statistic to summarise observational data, Gallon is usually credited with being the first to consider its sampling distribution. At Gallon’s request, in 1879 McAlister undertook a pioneering mathematical study, which eventually led to the modern large-sample theory. However, some sixty years elapsed before much attention was paid to small samples from particular parent distributions. Since about 1960, new techniques have made it possible to derive exact sampling distributions for a much wider class of parent distributions. Some work has been done on producing approximate general relationships between the moments of the parent distribution and those of the sample geometric mean but they are of very limited value for small samples and even now it is difficult to find any general description of how the distribution from which a sample is drawn will affect the distribution of its geometric mean and how this will vary with sample size.
The tercentenary of π
Authors: Chambers LI. G.
Published: August 2016

The use of the Greek letter π to denote the ratio of the circumference of a circle to its diameter appears to have been popularised by Euler following his adoption of the symbol in 1737 and later in his many popular textbooks. The original use of the symbol for this purpose was in fact by the Welsh mathematician William Jones who used it his book Synopsis Palmariorum Matheseos published in 1706. This book was described in 1824, over a hundred years later as follows ‘This work has long been esteemed as a compendious, but comprehensive summary of Mathematical Science’.
The arithmetic of cuckoldry in family trees
Authors: Voles Roger
Published: August 2016

Family history research has become a very popular hobby during the last few years due to the ready access to records of births and marriages. Many people have rigorously traced their ancestors back to 1700 and earlier, corresponding to some 12 generations. The principal motivation of most amateur genealogists is to learn about the lives of their forebears and they trust these ‘legal’ records without question and do not usually acknowledge that cuckoldry may have occurred and that their true ancestors may not have been the ones recorded.
On generalised Fibonaccian and Lucasian numbers
Authors: Hilton Peter , Pedersen Jean
Published: August 2016

In [1, Chapter 3, Section 2], we collected together results we had previously obtained relating to the question of which positive integers m were Lucasian, that is, factors of some Lucas number Ln. We pointed out that the behaviors of odd and even numbers m were quite different. Thus, for example, 2 and 4 are both Lucasian but 8 is not; for the sequence of residue classes mod 8 of the Lucas numbers, n ⩾ 0, reads

and thus does not contain the residue class 0*. On the other hand, it is a striking fact that, if the odd number s is Lucasian, then so are all of its positive powers.
Counting zeros of generalised polynomials: Descartes’ rule of signs and Laguerre’s extensions
Authors: Jameson G. J. O.
Published: August 2016

One of the bedrock theorems of mathematics is the statement that a real polynomial of degree n has at most n real zeros. Probably the best-known proof is the algebraic one, by factorisation. But there is also a pleasant analytic proof, by deduction from Rolle’s theorem.

A slightly different question is how many positive zeros a polynomial has. Here the basic result is known as ‘Descartes′ rule of signs’. It says that the number of positive zeros is no more than the number of sign changes in the sequence of coefficients. Descartes included it in his treatise La Géométrie which appeared in 1637. It can be proved by a method based on factorisation, but, again, just as easily by deduction from Rolle’s theorem.
A theorem on concurrent Euler lines
Authors: Bradley C. J.
Published: August 2016

In the configuration, illustrated in Figure 1, ABC is a triangle with I1; I2, I3 the excentres opposite A, B, C respectively. The triangles I1BC, I2CA, I3AB are denoted by T1, T2, T3 respectively. Ok, Hk, are the circumcentre, orthocentre respectively of triangle Tk, k = 1, 2, 3. Lk is the Euler line of Tk, k = 1, 2, 3. Define the point Ek (t) on Lk by the equation
Two remarks about Sudoku squares
Authors: Keedwell A. D.
Published: August 2016

Smallest defining sets

A standard Sudoku square is a 9 × 9 latin square in which each of the nine 3 × 3 subsquares into which it can be separated contains each of the integers 1 to 9 exactly once.

A current problem is to complete such a square when only some of the cells have been filled. These cells are often called ‘givens’. (Such problems are currently (2005) published daily in British newspapers.) In more mathematical terms, the given filled cells constitute a defining set or uniquely completable set for the square if they lead to a unique completion of the square. If, after deletion of any one of these givens, the square can no longer be completed uniquely, the givens form a critical set. The investigation of critical sets for ‘ordinary’ latin squares is a topic of current mathematical interest. (See [1] for more details.)
Cevian axes and related curves
Authors: Fox M. D. , Goggins J. R.
Published: August 2016

When exploring some triangle geometry, we stumbled upon a set of Cevian axes: lines having certain properties in common with the Euler line. These axes yielded interesting results that we had not seen before. However, we have since learnt that many of them were discovered in the 19th Century. We were also unaware that John Rigby had covered much of this ground in unpublished work in the 1990s (private communication). We are therefore reluctant to claim any of our results as new, even though we hope that some may be.
The Hindu method for completing the square
Authors: Renfro Dave L.
Published: August 2016

In a September 2005 note in The Mathematics Teacher, Gordon [1] gave a variation on the method of completing the square that fraction-phobic students are likely to find easier, along with the comment: ‘This variation is so obvious it must have been discovered many times over, but I have never seen it in print and thought it would be useful to disseminate it more widely.’ The method Gordon [1] gave is to multiply by 4a, and then add b2, to both sides of ax2 + bx = −c to produce 4a2x2 + 4abx + b2 = b2 −4ac. The left side of this last equation can be factorised as (2ax + b)2, and now we have a pure quadratic whose solution is straightforward.
Groups of rational functions
Authors: McLean K. Robin
Published: August 2016

In an article full of concrete examples, [1], Malcolm Perella asked what finite groups can be realised as groups of rational functions. When I first thought about this question, I imagined that most of the answers would be easy to locate in standard literature. Some of them are. But several have defied all my attempts to unearth them. I expect that they are hiding somewhere (as we said in our family when precious toys went astray), but they are certainly not in the books where I expected to find them! The present article attempts to answer Perella’s question by referring to appropriate sources where my search has succeeded, and supplying my own answers in other cases. Examples of the groups that arise are given in a series of exercises for readers.
Some plane geometry from a cone the focal distance of an ellipse at a glance
Authors: Davis A. E. L.
Published: August 2016

This article came about as a response to the Supplement to the Gazette Number 514 [1] which consists of an extended version of Sir Christopher Zeeman’s Presidential Address to The Mathematical Association at York in 2004. His intention was to stimulate the teaching of 3-dimensionaI geometry in schools, and his publication will certainly satisfy some long-felt needs. It contains a short section on conies, which seemed relevant to a topic I am already investigating: the level of knowledge of conic geometry potentially available to the Greeks before the time of Apollonius. Professor Zeeman has encouraged me to publish the first stage of this research in the Gazette to provide a background to his discussion.
A geometric interpretation of equal sums of cubes
Authors: Bailey Adam
Published: August 2016

Is there a three-dimensional equivalent of the Pythagorean theorem? It all depends, of course, what one means by equivalent. There are in fact several distinct results which can with some justice be regarded as threedimensional equivalents of the theorem.

One interpretation of the Pythagorean theorem is as a statement about any rectangle, expressing the square of its diagonal as the sum of the squares of its height and length. This readily extends to the case of a rectangular box (cuboid), for which the square of its long diagonal always equals the sum of the squares of its height, length and depth.
The Divine Proportion, matrices and Fibonacci numbers
Authors: Griffiths H. Brian
Published: August 2016

A friendly engineer recently sent me a version of Figure 1 below, and asked me to explain the connection between it and the well-known Fibonacci Problem (FP) about calculating a population of rabbits. He knew that Figure 1 was related to the ‘Divine Proportion’ or ‘Golden Ratio’ ϕ ( = ½(√5 - l), which also occurs in the solution to FP, and wondered how such different problems could be related by such a number. (He unfortunately regarded ϕ as 0.618 exactly, thus missing a lot of stuff to arouse curiosity.) I knew of various references that I could recommend, but none covered all the things my engineer mentioned, so I constructed the following mathematical development, leaving the relations with biology and architecture to be explained in the books referenced later, see for example [1]. A matrix approach is used here, and may be new to those readers of the Gazette who may be quite familiar with the other material.
Computing Farey Series
Authors: Routledge Norman
Published: August 2016

The Farey series of order n, Fn, consists of all the fractions between 0 and 1 (inclusive) with denominators less than or equal to n, arranged in order of magnitude and expressed in their lowest terms, so that for example The most obvious way of computing one is to assign a long series of stores and then insert the terms with denominator 1, with denominator 2, … , shifting the terms already there to make room for the new ones in their correct positions. This may require a large amount of storage and is fairly slow because of the large amount of shifting involved: for instance F1025 has 319765 terms, and occupies 400 printed pages (see Neville [1]). Neville also gives a table related to F100, which has 3045 terms. His procedures, a heroic application of pencil-and-paper methods, are described at the end of this paper.
The cone-paraboloid intercept
Authors: Mahony John
Published: August 2016

Readers might at times have wondered at some of the reflector shapes to be seen at airports and satellite communication centres around the world. Typically, such shapes occur when a cone of energy emanates from a focal point to illuminate an offset portion of a paraboloidal reflector (a parabola of revolution). The purpose of this note is to show how such shapes can be determined mathematically using the tools of trigonometry and geometry established at school level. The cross-section of the energy cone is usually circular but in some instances it is elliptic and it is this case that is the focus of the present article.
Joined up mathematics
Authors: Eastaway Rob
Published: August 2016

Shortly before the start of my term as MA President, a colleague asked me what my theme was going to be for the year. “Do Presidents have themes?”, I asked. He didn’t know, but thought it might be a good idea. As it happens, a perfect theme was handed to me on a plate. Planning for the 2008 Annual Conference was already underway when I joined Council, and it had already been decided that it was to be called ‘Joined Up Mathematics’.
The Soddy spheres of a 4-ball tetrahedron: Part 2
Authors: Fox Michael , Oldknow Adrian , Rigby John , Zeeman Christopher
Published: August 2016

This is the second of two articles presenting new results which extend the Soddy circles of a triangle to Soddy spheres of a special class of tetrahedra. In Part 1 [1], after a brief résumé of the Soddy theorems in two dimensions, we stated the corresponding theorems in three dimensions, discovered partly as the result of computer investigations. These threedimensional Soddy theorems are valid only for a special type of tetrahedron - the four-ball tetrahedron - and we went on to prove some basic results about such tetrahedra.
Quaternions: The hypercomplex number system
Authors: Pulver Sandra
Published: August 2016

Are there solutions of the equation x2 + 1 = 0 ? Carl Fredrich Gauss (1777–1855) conjectured that there was a solution and that it was the square root of - 1 . But since the squares of all real numbers, positive or negative, are positive, Gauss introduced a fanciful idea. His solution to this equation was , which he named i. He integrated i with the real numbers to form a set known as , the complex numbers, where each element in that set was of the form a + bi, where a, . Gauss illustrated this on a graph, the horizontal axis became the real axis and represented the real coefficient, while the vertical axis became the imaginary axis and represented the imaginary coefficient.
Nice symmetric and antisymmetric polynomials
Authors: Groves Jonathan
Published: August 2016

We first present a general property of nice polynomials, which leads to an important modification of the concept of equivalence classes of nice polynomials. We then establish several properties of nice symmetric and antisymmetric polynomials with an odd number of distinct roots. We give a complete description of all nice symmetric and antisymmetric polynomials with three distinct roots. We then apply our results to nice symmetric sextics and octics. As an important application, all the properties we have established have dramatically increased the speed of a computer search for examples, allowing us to discover the first examples of nice symmetric and antisymmetric polynomials with five distinct roots and the first two examples of nice polynomials with six distinct roots.
Reflected circles, and congruent perspective triangles
Authors: Silvester John R.
Published: August 2016

For any three pointsX, Y, Z, let ⊙XYZdenote the circle throughX, Y, Z(the circumcircle of ∆XYZ) or, ifX, Y, Zhappen to be collinear, the lineXYZ. (We shall often regard lines as special circles, circles of infinite radius.) This paper is about the following theorem, and extensions of it:

Theorem 1: Given ∆ABCand a pointP, reflect ⊙PBC, ⊙APC, ⊙ABPin the lines BC, AC, AB respectively. Then the three reflected circles have a common point, Q (see Figure 1).

I do not know if this theorem is new, but I have not come across it in the literature. The reader is invited to prove it by angle-chasing, using circle theorems: let two of the reflected circles meet atQand then prove that this point lies on the third reflected circle. This method is rather diagram-dependent, and does not seem to lead to the extensions of Theorem 1 referred to above in any very obvious manner, so we shall adopt a different approach.
A jigsaw problem
Authors: Shephard G. C.
Published: August 2016

Recently, when solving a jigsaw puzzle, I noticed that many of the pieces were symmetric in some sense; they had either reflective or rotational symmetry. This made me wonder if it was possible for all the pieces in a puzzle to be different shapes, and yet have some prescribed symmetry.
The frog problem: more than you might want to know
Authors: Holton Derek
Published: August 2016

The Frog Problem is a well-known exercise in problem solving that involves a lot of reasonably deep mathematics that is perhaps of more interest than learning a new integration technique. I want to try to expose this mathematics here, not that it is within the scope of all school students but so that it is recognised and possibly offered to at least the brightest pupils.
Prime matrices and prime polynomials
Authors: Beardon Alan F.
Published: August 2016

In an earlier paper in the Gazette the authors of define what it means for a matrix in a set M of n × n matrices to be prime, namely if it is not the product of two matrices in M, neither of which is the identity. They then showed that there are exactly two primes in the set M2 of 2 × 2 matrices with non-negative integral entries and unit determinant, namely
Some odd permutations
Authors: Lewis Barry
Published: August 2016

I recently stumbled on an identity (Theorem 2) that related two types of permutations. It looked like one of those serendipitous pieces of mathematics that led to a simple enumerative result; mostly when this happens it leads joyously to an enumerative proof that was ‘blindingly’ obvious. Except in this case, it wasn’t, I don’t think.
Tribinomial coefficients and Catalan numbers
Authors: Koshy Thomas , Salmassi Mohammad
Published: August 2016

The concept of the ordinary binomial coefficient

can be employed to construct an interesting family of positive integers. Such a family was introduced around 1974 by W. Hansell using the triangular numbers , where we call them tribinomial coefficients since they are binomial coefficients for triangular numbers. To this end, first we define corresponding to and For example,
Mother–infant cultural group selection
Authors: Chisholm James S. , Coall David A. , Atkinson Leslie
Published: August 2016

Richerson et al. argue that “cultural group selection plays an essential role in explaining human cooperation.” We believe that cooperation came first, making culture and thus cultural group selection possible. Cooperation and culture began – and begins – in mother–infant interaction.
Does cultural group selection explain the evolution of pet-keeping?
Authors: Herzog Harold
Published: August 2016

Pet-keeping is highly variable across cultures in both frequency and form. Cultural group selection offers a plausible explanation for the development and spread of this uniquely human phenomenon in that pet-keeping involves an inheritance system, socially transmitted norms and preferences, substantial between-group variation, and (albeit indirectly) intergroup competition.
Contributions of family social structure to the development of ultrasociality in humans
Authors: Nephew Benjamin C. , Pittet Florent
Published: August 2016

The evolution of ultrasociality in humans may have involved the evolutionarily significant mechanisms that govern family social structure in many animal species. Adverse effects of ultrasociality in humans may be mediated by maladaptive effects of modern civilization on family groups, as many of the effects on both families and societies are especially severe in dense populations made possible by agriculture.
Differentiation of individual selves facilitates group-level benefits of ultrasociality
Authors: Ainsworth Sarah E. , Baumeister Roy F. , Vohs Kathleen D.
Published: August 2016

Gowdy & Krall's target article complements our recent theorizing on group behavior. In our comment, we elucidate complementary aspects of the two theories and highlight the importance of differentiation of selves for human groups to reap the benefits of ultrasociality. We propose that achieving optimal group outcomes depends on the differentiation of individual selves.
Autonomy in ants and humans
Authors: Carpendale Jeremy I. M. , Frayn Michael
Published: August 2016

Drawing lessons regarding the consequences of ultrasociality in ants and humans depends crucially on recognizing differences as well as similarities in the way that species are social. We focus on Gowdy & Krall's use of the concept of autonomy to explicate essential differences in the ways in which ants and humans are social.
The continuing evolution of ultrasocial economic organization
Authors: Farley Joshua C.
Published: August 2016

Ultrasociality, as expressed in agricultural, monetary, and fossil fuel economies, has spurred exponential growth in population and in resource use that now threaten civilization. These threats take the form of prisoner's dilemmas. Avoiding collapse requires more cooperative economic organization that must be informed by knowledge of human behavior and cultural evolution. The evolution of a cooperative information economy is one possibility.
Ultrasociality and the division of cognitive labor
Authors: Noles Nicholaus Samuel , Danovitch Judith Harmony
Published: August 2016

Gowdy & Krall describe the development of ultrasociality in terms of economics and the division of labor. We propose that the division of cognitive labor allows humans to behave in an ultrasocial manner without the radical evolutionary changes that are experienced by other species, suggesting that species may traverse different paths to achieve ultrasociality.
A registration problem for functional fingerprinting
Authors: Kaplan David M. , Craver Carl F.
Published: August 2016

Functional fingerprints aggregate over heterogeneous tasks, protocols, and controls. The appearance of functional diversity might be explained by task heterogeneity and conceptual imprecision.
Reason for optimism: How a shifting focus on neural population codes is moving cognitive neuroscience beyond phrenology
Authors: Parkinson Carolyn , Wheatley Thalia
Published: August 2016

Multivariate pattern analysis can address many of the challenges for cognitive neuroscience highlighted in After Phrenology (Anderson 2014) by illuminating the information content of brain regions and by providing insight into whether functional overlap reflects the recruitment of common or distinct computational mechanisms. Further, failing to consider submaximal but reliable population responses can lead to an overly modular account of brain function.
Reply to reviewers: Reuse, embodied interactivity, and the emerging paradigm shift in the human neurosciences
Authors: Anderson Michael L.
Published: August 2016

In this reply to reviewers, I argue that, although reforming the taxonomy of psychology will lead to great insights in the cognitive sciences, it will not result in 1:1 structure-function mappings in the brain; we should expect to see a great deal of irreducible functional diversity in the brain at multiple spatial scales. I further clarify both the promise and the limitations of the analytic techniques for capturing functional diversity and interrogating the taxonomy of psychology; describe the ways in which neural reuse can help us understand human development; further explore the ways in which my proposals for integrating psychology, neuroscience, and evolutionary biology differ from the approach exemplified by contemporary evolutionary psychology; and lay out some new and hopefully interesting avenues for future research.
Streptococcus agalactiaefrom pregnant women: antibiotic and heavy-metal resistance mechanisms and molecular typing
Authors: ROJO-BEZARES B. , AZCONA-GUTIÉRREZ J. M. , MARTIN C. , JAREÑO M. S. , TORRES C. , SÁENZ Y.
Published: August 2016

We investigated the antibiotic and heavy-metal resistance mechanisms, virulence genes and clonal relationships of macrolide- and/or lincosamide-resistant (M+/−LR)Streptococcus agalactiae(group BStreptococcus, GBS) isolates from pregnant women in La Rioja in Northern Spain, a region with a significant immigrant population. In total 375 GBS isolates were recovered during 2011. About three-quarters of isolates were from European nationals and the remainder distributed among 23 other nationalities. Seventy-five (20%) were classified as M+/−LRstrains and 28 (37%) of these were resistant to ⩾3 classes of antibiotics. Capsular serotypes III (29·3%), V (21·3%) and II (12%) were the most frequent. A wide variety of antibiotic resistance genes were detected in M+/−LRstrains; notably, 5·3% harboured thelsa(C) gene associated with cross-resistance, andtet(W) was identified in a single strain. We report, for the first time, the detection of cadmium and copper resistance encoded bytcrB+cadA+cadCgenes in 20 M+/−LRstrains, which raises the possibility of co-selection of antibiotic and heavy-metal resistance disseminated through mobile genetic elements. The M+/−LRstrains were highly diverse by DNA macrorestriction profiles (65 patterns) and 16 multilocus sequence types (STs) distributed among six clonal complexes; the most frequent were ST1, ST19, and ST12, and two strains were novel (ST586 and ST601). In conclusion, a wide diversity of genetic lineages of macrolide, lincosamide and heavy-metal- resistant GBS strains was observed in an ethnically diverse maternal population.
How Relevant to the United Kingdom are the ‘Religious’ Cases of the US Supreme Court?
Authors: Cranmer Frank
Published: August 2016

High-profile cases in the Supreme Court of the United States (‘SCOTUS’) on religion tend to attract a certain amount of academic comment in the United Kingdom but US judgments are cited only infrequently by the superior courts in the UK. In return, SCOTUS rarely cites foreign judgments at all. The reason, it is suggested, is that the effect given by the First Amendment to the US Constitution is to render US case law of less relevance to the UK than, for example, judgments from jurisdictions such as Canada and Australia.
“MedTRIS” (Medical Triage and Registration Informatics System): A Web-based Client Server System for the Registration of Patients Being Treated in First Aid Posts at Public Events and Mass Gatherings
Authors: Gogaert Stefan , Vande veegaete Axel , Scholliers Annelies , Vandekerckhove Philippe
Published: August 2016

First aid (FA) services are provisioned on-site as a preventive measure at most public events. In Flanders, Belgium, the Belgian Red Cross-Flanders (BRCF) is the major provider of these FA services with volunteers being deployed at approximately 10,000 public events annually. The BRCF has systematically registered information on the patients being treated in FA posts at major events and mass gatherings during the last 10 years. This information has been collected in a web-based client server system called “MedTRIS” (Medical Triage and Registration Informatics System). MedTRIS contains data on more than 200,000 patients at 335 mass events. This report describes the MedTRIS architecture, the data collected, and how the system operates in the field. This database consolidates different types of information with regards to FA interventions in a standardized way for a variety of public events. MedTRIS allows close monitoring in “real time” of the situation at mass gatherings and immediate intervention, when necessary; allows more accurate prediction of resources needed; allows to validate conceptual and predictive models for medical resources at (mass) public events; and can contribute to the definition of a standardized minimum data set (MDS) for mass-gathering health research and evaluation.

GogaertS, Vande veegaeteA, ScholliersA, VandekerckhoveP. “MedTRIS” (Medical Triage and Registration Informatics System): a web-based client server system for the registration of patients being treated in first aid posts at public events and mass gatherings. Prehosp Disaster Med. 2016;31(5):557–562.
The moral conundrums of the historian: Claudio Pavone's A Civil War and its legacy
Authors: Schwarz Guri
Published: August 2016

The recent English translation of Caludio Pavone's book on the Italian civil war (1943–1945) represents an occasion to reconsider Resistance historiography and memory politics. This paper discusses Pavone's book and looks back on its genesis, while at the same time reflecting on its legacy. The aim is to offer some insight on the evolution of historiographic narratives concerning the Resistance and the civil war in the last decades.
Why all John's Friends are Dutch, Not German: On the Determiner-Like Characteristics of the Inflection on the Universal Quantifier in West Germanic
Authors: Cirillo Robert
Published: August 2016

The word order in a phrase such asall John's friends, in which a universal quantifier is immediately followed by a genitive, is perfectly grammatical in Dutch but unacceptable in German. This article shows that there are three explanations for this difference between the two closely related languages. First, in German, the Saxon Genitive is a true case assigned in Spec, NP. In contrast, in Dutch and English, genitive case cannot be assigned in Spec, NP without a preposition. The Saxon Genitive in these languages is comparable to a possessive adjective that originates as the head of PossP and moves to D. Second, in a definite DP in a Germanic language, either D or Spec, DP must be occupied; if one of these positions is overtly occupied, and if genitive case has already been assigned, the movement of a genitive phrase to D or Spec, DP is unmotivated and causes ungrammaticality. Third, there is evidence that the-einflection on the universal quantifieralle‘all’ in German and Dutch has the characteristics of a determiner.*
Is China for Sale?
Authors: Meyer Marshall W.
Published: August 2016

Yasheng Huang's Selling China: Foreign Direct Investment during the Reform Era is the first book to be reviewed in Management and Organization Review. Other books bearing on Chinese management that the editors judge to be significant and provocative will be reviewed on an ad hoc basis. Selling China, to be sure, is not about the practice of management in China. Rather, it is about the policies that have created two economies and two managerial systems in China, one domestic and one foreign-invested, and the consequences of these policies. The existence of these two economies and managerial systems lurks in the background of virtually all management research in the Chinese context.
Business Leadership in the Chinese Context: Trends, Findings, and Implications
Authors: Zhang Zhi-Xue , Chen (George) Zhen Xiong , Chen Ya-Ru , Ang Soon
Published: August 2016

Business leaders constitute a powerful driving force for the miraculous growth of the Chinese economy in the past few decades. However, scholars have not developed theories accounting for the unique leadership phenomenon in the Chinese context, characterized by high uncertainty, intense market competition, and constant changes in government regulations and policies. This special issue aims at offering insights regarding business leadership in China. In this paper, we first introduce the three streams of Chinese leadership research, varying in the degree of Chinese context being considered in theory development. We then discuss how Chinese leadership has co-evolved with the transformation of firms and the institutional environment in China. The new values of young employees, born after 1980, are driving the need for leaders to adjust their leadership practices once again. After that, we present a summary of the four papers in this special issue, and the insights they provide to our understanding of leadership and its effectiveness in the Chinese context. Finally, we suggest future research directions for Chinese leadership research.
The Unique Value of Yin-Yang Balancing: A Critical Response
Authors: Li Peter Ping
Published: August 2016

I welcome any well-informed debate over the unique value of Yin-Yang as a cognitive frame in the development of Chinese indigenous management research. The commentary by Xin Li to engage in a debate is timely. Xin Li and I share the same premise that ‘we need indigenous Chinese management research to offer new insights and contribute to the development of truly universal theories’ (Li, X., 2014: 8). That is the common ground upon which we can debate over how best to engage in indigenous research with confidence in balance so as to avoid both overconfidence and under-confidence.

Where we depart from the above common ground is our different perspectives about the value of the Yin-Yang frame. Xin Li challenges my positive perspective on the unique value of the Yin-Yang frame on several dimensions. First, he characterizes my perspective as ‘both/and’ in sharp contrast to Aristotle’s ‘either/or’ logic. Second, he characterizes my perspective as arguing that ‘Yin-Yang thinking is superior to other logical systems and philosophies’ (Li, X., 2014: 8). Third, he implies that my perspective on the Yin-Yang frame is essentially a claim that ‘Westerners cannot think in a non-either/or way’ (Li, X., 2014: 8). Fourth, the above challenges are based upon his basic claim that the Yin-Yang frame is just one form of dialectical framing (Li, X., 2014). Based on these claims, Xin Li warns against the ‘danger of overconfidence’ among Chinese management scholars (Li, X., 2014: 8).
Reflections on Choosing the Appropriate Level of Abstraction in Social Science Research
Authors: Murmann Johann Peter
Published: August 2016

Although researchers often do it subconsciously, every explanation involves choosing a level of abstraction at which the argument proceeds. The dominant North American style of research in Organization Theory, Strategy, and International Business encourages researchers to frame their explanations at the highest level of abstraction where country-level contextual factors are suppressed or ignored. Yet to provide powerful explanations for recent developments in China, researchers are drawn to a greater level of context specificity. This tension is evident in the Child and Marinova (2014) paper. One way to reduce the tension is to identify general causal mechanisms that combine in different ways to produce different results depending on context. This research strategy is more effective than seeking invariant, general patterns of development across all times and places.
Crystal structure of the plant receptor-like kinase TDR in complex with the TDIF peptide
Authors: Morita Junko , Kato Kazuki , Nakane Takanori , Kondo Yuki , Fukuda Hiroo , Nishimasu Hiroshi , Ishitani Ryuichiro , Nureki Osamu
Published: August 2016

In plants, leucine-rich repeat receptor-like kinases (LRR-RKs) perceive ligands, including peptides and small molecules, to regulate various physiological processes. TDIF, a member of the CLE peptide family, specifically interacts with the LRR-RK TDR to inhibit meristem differentiation into tracheary elements, and promotes cell proliferation. Here we report the crystal structure of the extracellular domain of TDR in complex with the TDIF peptide. The extracellular domain of TDR adopts a superhelical structure comprising 22 LRRs, and specifically recognizes TDIF by its inner concave surface. Together with our biochemical and sequence analyses, our structure reveals a conserved TDIF-recognition mechanism of TDR among plant species. Furthermore, a structural comparison of TDR with other plant LRR-RKs suggested the activation mechanism of TDR by TDIF. The structure of this CLE peptide receptor provides insights into the recognition mechanism of the CLE family peptides.
The Mouse Intestinal Bacterial Collection (miBC) provides host-specific insight into cultured diversity and functional potential of the gut microbiota
Authors: Lagkouvardos Ilias , Pukall Rüdiger , Abt Birte , Foesel Bärbel U. , Meier-Kolthoff Jan P. , Kumar Neeraj , Bresciani Anne , Martínez Inés , Just Sarah , Ziegler Caroline , Brugiroux Sandrine , Garzetti Debora , Wenning Mareike , Bui Thi P. N. , Wang Jun , Hugenholtz Floor , Plugge Caroline M. , Peterson Daniel A. , Hornef Mathias W. , Baines John F. , Smidt Hauke , Walter Jens , Kristiansen Karsten , Nielsen Henrik B. , Haller Dirk , Overmann Jörg , Stecher Bärbel , Clavel Thomas
Published: August 2016

Intestinal bacteria influence mammalian physiology, but many types of bacteria are still uncharacterized. Moreover, reference strains of mouse gut bacteria are not easily available, although mouse models are extensively used in medical research. These are major limitations for the investigation of intestinal microbiomes and their interactions with diet and host. It is thus important to study in detail the diversity and functions of gut microbiota members, including those colonizing the mouse intestine. To address these issues, we aimed at establishing the Mouse Intestinal Bacterial Collection (miBC), a public repository of bacterial strains and associated genomes from the mouse gut, and studied host-specificity of colonization and sequence-based relevance of the resource. The collection includes several strains representing novel species, genera and even one family. Genomic analyses showed that certain species are specific to the mouse intestine and that a minimal consortium of 18 strains covered 50–75% of the known functional potential of metagenomes. The present work will sustain future research on microbiota–host interactions in health and disease, as it will facilitate targeted colonization and molecular studies. The resource is available at www.dsmz.de/miBC.
Dynamic contrast-enhanced MRI detects acute radiotherapy-induced alterations in mandibular microvasculature: prospective assessment of imaging biomarkers of normal tissue injury
Authors:   Joint Head and Neck Radiotherapy-MRI Development Cooperative, Sandulache Vlad C. , Hobbs Brian P. , Mohamed Abdallah S.R. , Frank Steven J. , Song Juhee , Ding Yao , Ger Rachel , Court Laurence E. , Kalpathy-Cramer Jayashree , Hazle John D. , Wang Jihong , Awan Musaddiq J. , Rosenthal David I. , Garden Adam S. , Gunn G. Brandon , Colen Rivka R. , Elshafeey Nabil , Elbanan Mohamed , Hutcheson Katherine A. , Lewin Jan S. , Chambers Mark S. , Hofstede Theresa M. , Weber Randal S. , Lai Stephen Y. , Fuller Clifton D.
Published: August 2016

Normal tissue toxicity is an important consideration in the continued development of more effective external beam radiotherapy (EBRT) regimens for head and neck tumors. The ability to detect EBRT-induced changes in mandibular bone vascularity represents a crucial step in decreasing potential toxicity. To date, no imaging modality has been shown to detect changes in bone vascularity in real time during treatment. Based on our institutional experience with multi-parametric MRI, we hypothesized that DCE-MRI can provide in-treatment information regarding EBRT-induced changes in mandibular vascularity. Thirty-two patients undergoing EBRT treatment for head and neck cancer were prospectively imaged prior to, mid-course and following treatment. DCE-MRI scans were co-registered to dosimetric maps to correlate EBRT dose and change in mandibular bone vascularity as measured by Ktrans and Ve. DCE-MRI was able to detect dose-dependent changes in both Ktrans and Ve in a subset of patients. One patient who developed ORN during the study period demonstrated decreases in Ktrans and Ve following treatment completion. We demonstrate, in a prospective imaging trial, that DCE-MRI can detect dose-dependent alterations in mandibular bone vascularity during chemoradiotherapy, providing biomarkers that are physiological correlates of acute of acute mandibular vascular injury and recovery temporal kinetics.