Biomass functions and expansion factors in young Norway spruce (Picea abies [L.] Karst) trees

Roots, stems, branches and needles of 160 Norway spruce trees younger than 10 years were sampled in seven forest stands in central Slovakia in order to establish their biomassfunctions (BFs) and biomassexpansionfactors (BEFs). We tested three models for each biomass pool based on the stem base diameter, tree height and the two parameters combined. BEF values decreased for all spruce components with increasing height and diameter, which was most evident in very young trees under 1 m in height. In older trees, the values of BEFs did tend to stabilise at the height of 3–4 m. We subsequently used the BEFs to calculate dry biomass of the stands based on average stem base diameter and tree height. Total stand biomass grew with increasing age of the stands from about 1.0 Mg ha−1 at 1.5 years to 44.3 Mg ha−1 at 9.5 years. The proportion of stem and branch biomass was found to increase with age, while that of needles was fairly constant and the proportion of root biomass did decrease as the stands grew older.

Conjecture, proof, and sense in Wittgenstein's philosophy of mathematics

One of the key tenets in Wittgenstein’s philosophy of mathematics is that a mathematical proposition gets its meaning from its proof. This seems to have the paradoxical consequence that a mathematical conjecture has no meaning, or at least not the same meaning that it will have once a proof has been found. Hence, it would appear that a conjecture can never be proven true: for what is proven true must ipso facto be a different proposition from what was only conjectured. Moreover, it would appear impossible that the same mathematical proposition be proven in different ways. — I will consider some of Wittgenstein’s remarks on these issues, and attempt to reconstruct his position in a way that makes it appear less paradoxical.

Transition of pupils from Key Stage 2 to 3 deemed gifted and talented in mathematics: an initial study

In this article Geoff Tennant and Dave Harries report on the early stages of a research project looking to examine the transition from Key Stage (KS) 2 to 3 of children deemed Gifted and Talented (G&T) in mathematics. An examination of relevant literature points towards variation in definition of key terms and underlying rationale for activities. Preliminary fieldwork points towards a lack of meaningful communication between schools, with primary school teachers in particular left to themselves to decide how to work with children deemed G&T. Some pointers for action are given, along with ideas for future research and a request for colleagues interested in working with us to get in touch.

The Mathematics of Control Theory

This text contains papers presented at the Institute of Mathematics and its Applications Conference on Control Theory, held at the University of Strathclyde in Glasgow. The contributions cover a wide range of topics of current interest to theoreticians and practitioners including algebraic systems theory, nonlinear control systems, adaptive control, robustness issues, infinite dimensional systems, applications studies and connections to mathematical aspects of information theory and data-fusion.

The trees and the bees: using enforcement and income projects to protect forests and rural livelihoods through spatial joint production

Forest managers in developing countries enforce extraction restrictions to limit forest degradation. In response, villagers may displace some of their extraction to other forests, which generates “leakage” of degradation. Managers also implement poverty alleviation projects to compensate for lost resource access or to induce conservation. We develop a model of spatial joint production of bees and fuelwood that is based on forest-compatible projects such as beekeeping in Thailand, Tanzania, and Mexico. We demonstrate that managers can better determine the amount and pattern of degradation by choosing the location of both enforcement and the forest-based activity.

Mathematics as a tool in the Life Sciences

Teaching mathematics to students in the biological sciences is often fraught with difficulty. Students often discover mathematics to be a very 'dry' subject in which it is difficult to see the motivation of learning it given its often abstract application. In this paper I advocate the use of mathematical modelling as a method for engaging students in understanding the use of mathematics in helping to solve problems in the Biological Sciences. The concept of mathematics as a laboratory tool is introduced and the importance of presenting students with relevant, real-world examples of applying mathematics in the Biological Sciences is discussed.

Distributed hoeffding trees for pocket data mining

Collaborative mining of distributed data streams in a mobile computing environment is referred to as Pocket Data Mining PDM. Hoeffding trees techniques have been experimentally and analytically validated for data stream classification. In this paper, we have proposed, developed and evaluated the adoption of distributed Hoeffding trees for classifying streaming data in PDM applications. We have identified a realistic scenario in which different users equipped with smart mobile devices run a local Hoeffding tree classifier on a subset of the attributes. Thus, we have investigated the mining of vertically partitioned datasets with possible overlap of attributes, which is the more likely case. Our experimental results have validated the efficiency of our proposed model achieving promising accuracy for real deployment.

Thorn-dwelling ants provide antiherbivore defence for camelthorn trees, Vachellia erioloba, in Namibia

Ants are widely employed by plants as an antiherbivore defence. A single host plant can associate with multiple, symbiotic ant species, although usually only a single ant species at a time. Different plant-ant species may vary in the degree to which they defend their host plant. In Kenya, ant–acacia interactions are well studied, but less is known about systems elsewhere in Africa. A southern African species, Vachellia erioloba, is occupied by thorn-dwelling ants from three different genera. Unusually, multiple colonies of all these ants simultaneously and stably inhabit trees. We investigated if the ants on V. erioloba (i) deter insect herbivores; (ii) differ in their effectiveness depending on the identity of the herbivore; and (iii) protect the tree against an important herbivore, the larvae of the lepidopteran Gonometa postica. We show that experimental exclusion of ants leads to greater levels of herbivory on trees. The ants inhabiting V. erioloba are an effective deterrent against hemipteran and coleopteran, but not lepidopteran herbivores. Defensive services do not vary among ant species, but only Crematogaster ants exhibit aggression towards G. postica. This highlights the potential of the V. erioloba–ant mutualism for studying ant–plant interactions that involve multiple, simultaneously resident thorn-dwelling ant species.

Soil injections of carbohydrates improve fine root growth of established urban trees

Four established mature tree species (Aesculus hippocastanum L., Betula pendula Roth., Primus avium L. and Quercus rohur L.) commonly planted in UK urban landscapes were subjected to soil injections of the carbohydrate sucrose at 25, 50 and 70g per litre of water. Fine root dry weight was recorded at month 5 following soil injections. Soil injections of sucrose significantly increased fine root dry weight compared to controls, however; growth responses were influenced by species and the concentration of sucrose applied. Results indicate soil injections of sucrose ≥ 50g litre of water may be able to improve root growth of established mature trees. Such a response is desirable as root damage following construction is a frequent problem encountered by established trees growing in UK towns and cities.

Land use intensity and trees on farms in Malawi

Rapidly increasing population densities in Malawi have put a huge strain on the existing agricultural land and the surrounding woodland. Smallholder agriculture is the dominant economic activity of Malawi’s rural population and many farmers have been forced to cultivate marginal lands with less fertile soils, making conditions much more difficult to grow crops. Natural woodland is under increasing pressure from the opening of new lands for cultivation and the increased demand for firewood, timber and other woody resources, with rural households historically obtaining most of their complementary inputs and saleable commodities from nearby areas of forest (Arnold, 1997a). Despite this increasing pressure, woodlands are not being cleared indiscriminately; selected indigenous species are left standing in fields and around households. These are joined by exotic species that are planted and maintained. These trees provide products and services that are vital, yielding food, firewood, building materials and medicine, replenishing soil fertility and protecting against soil erosion. Following a Boserupian approach, this study attempts to establish the reality of a trajectory of enhanced on-farm tree planting and management as population pressure mounts and as part of a more general process of agricultural intensification. The study examines the combination of factors (social, economic, political and environmental) that either stimulate or discourage on-farm tree planting on smallholdings in Malawi, highlighting how woodland resource use changes over a gradient of land use intensity. This study gives a detailed insight into the way that tree planting and management in the smallholder farming system in Malawi works and identifies a trend of increased tree planting/management alongside an increase in agricultural intensification. However, there is no single ‘path’ of intensification; the link between agricultural change and tree planting is complex and there are many trajectories of intensification that a farmer may follow, dependent on his/her social or economic circumstances. The study recommends that agroforestry interventions give rigorous consideration to the needs of the local community, and the suitability of trees to address those needs, before embarking on programmes that advocate tree planting and management as a panacea.

Mathematics applied to the climate system: outstanding challenges and recent progress

The societal need for reliable climate predictions and a proper assessment of their uncertainties is pressing. Uncertainties arise not only from initial conditions and forcing scenarios, but also from model formulation. Here, we identify and document three broad classes of problems, each representing what we regard to be an outstanding challenge in the area of mathematics applied to the climate system. First, there is the problem of the development and evaluation of simple physically based models of the global climate. Second, there is the problem of the development and evaluation of the components of complex models such as general circulation models. Third, there is the problem of the development and evaluation of appropriate statistical frameworks. We discuss these problems in turn, emphasizing the recent progress made by the papers presented in this Theme Issue. Many pressing challenges in climate science require closer collaboration between climate scientists, mathematicians and statisticians. We hope the papers contained in this Theme Issue will act as inspiration for such collaborations and for setting future research directions.

Predicting long-term growth in students' mathematics achievement: the unique contributions of motivation and cognitive strategies

This research examined how motivation (perceived control, intrinsic motivation, and extrinsic motivation), cognitive learning strategies (deep and surface strategies), and intelligence jointly predict long-term growth in students' mathematics achievement over 5 years. Using longitudinal data from six annual waves (Grades 5 through 10; Mage = 11.7 years at baseline; N = 3,530), latent growth curve modeling was employed to analyze growth in achievement. Results showed that the initial level of achievement was strongly related to intelligence, with motivation and cognitive strategies explaining additional variance. In contrast, intelligence had no relation with the growth of achievement over years, whereas motivation and learning strategies were predictors of growth. These findings highlight the importance of motivation and learning strategies in facilitating adolescents' development of mathematical competencies.

Diversity in mathematics assessment equals diversity in opinion?

We undertook a study to investigate the views of both students and staff in our department towards assessment in mathematics, as a precursor to considering increasing the diversity of assessment types. In a survey and focus group there was reasonable agreement amongst the students with regards major themes such as mode of assessment. However, this level of agreement was not seen amongst the staff, where discussions regarding diversity in mathematics assessment definitely revealed a difference of opinion. As a consequence, we feel that the greatest barriers to increasing diversity may be with staff, and so more efforts are needed to communicate to staff the advantages and disadvantages, in order to give them greater confidence in trying a range of assessment types.

Relationship between classroom authority and epistemological beliefs as espoused by primary school mathematics teachers from the very high and very low socio-economic regions in Thailand

This article presents findings of a larger single-country comparative study which set out to better understand primary school teachers’ mathematics education-related beliefs in Thailand. By combining the interview and observation data collected in the initial stage of this study with data gathered from the relevant literature, the 8-belief / 22-item ‘Thai Teachers’ Mathematics Education-related Beliefs’ (TTMEB) Scale was developed. The results of the Mann-Whitney U Test showed that Thai teachers in the two examined socio-economic regions espouse statistically different beliefs concerning the source and stability of mathematical knowledge, as well as classroom authority. Further, these three beliefs are found to be significantly and positively correlated.