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.

Virtual reality Post Traumatic Stress Disorder (PTSD) exposure therapy results with active duty OIF/OEF service members

Posttraumatic stress disorder (PTSD) is reported to be caused by exposure to traumatic events including (but not limited to) military combat, violent personal assault, being kidnapped or taken hostage and terrorist attacks. Initial data suggest that at least 1 out of 6 Iraq War veterans are exhibiting symptoms of depression, anxiety and PTSD. Virtual reality (VR) delivered exposure therapy for PTSD has been used with reports of positive outcomes. The aim of the current paper, is to present the rationale and brief description of a Virtual Iraq/Afghanistan PTSD VR therapy application and present initial findings from its use with PTSD patients. Thus far, Virtual Iraq/Afghanistan consists of a series of customizable virtual scenarios designed to represent relevant Middle Eastern VR contexts for exposure therapy, including a city and desert road convoy environment. User-centered design feedback, needed to iteratively evolve the system, was gathered from returning Iraq War veterans in the USA and from a system deployed in Iraq and tested by an Army Combat Stress Control Team. Results from an open clinical trial at San Diego Naval Medical Center of the first 20 treatment completers indicate that 16 no longer met PTSD screening criteria at post-treatment, with only one not maintaining treatment gains at 3 month follow-up.

Considering heteroglossia in language and development in Sub-Saharan Africa

Countries throughout the sub-Saharan (SSA) region have a complex linguistic heritage having their origins in opportunistic boundary changes effected by Western colonial powers at the Berlin Conference 1884-85. Postcolonial language-in-education policies valorizing ex-colonial languages have contributed at least in part to underachievement in education and thus the underdevelopment of human resources in SSA countries. This situation is not likely to improve whilst unresolved questions concerning the choice of language(s) that would best support social and economic development remain. Whilst policy attempts to develop local languages have been discussed within the framework of the African Union, and some countries have experimented with models of multilingual education during the past decade, the goalposts have already changed as a result of migration and trade. This paper argues that language policy makers need to be cognizant of changing language ecologies and their relationship with emerging linguistic and economic markets. The concept of language, within such a framework, has to be viewed in relation to the multiplicity of language markets within the shifting landscapes of people, culture, economics and the geo-politics of the 21st Century. Whilst, on the one hand, this refers to the hegemony of dominant powerful languages and the social relations of disempowerment, on the other hand, it also refers to existing and evolving social spaces and local language capabilities and choices. Within this framework the article argues that socially constructed dominant macro language markets need to be viewed also in relation to other, self-defined, community meso- and individual micro- language markets and their possibilities for social, economic and political development. It is through pursuing this argument that this article assesses the validity of Omoniyi’s argument in this volume, for the need to focus on the concept of language capital within multilingual contexts in the SSA region as compared to Bourdieu’s concept of linguistic capital.  

Evolution of network structure in polymer-stabilised liquid crystals

Experiments were performed to investigate the evolution of structure and morphology of the network in polymer-stabilised liquid crystals. In situ optical microscopy revealed that the morphology was significantly altered by extraction of the LC host, while scanning electron microscopy showed that the network morphology was also dependent on the polymerisation conditions and closely related to the depletion of monomer, as monitored by high performance liquid chromatography. Transmission electron microscopy allowed observation of internal structure, resolving microstructure on the order of 0. 1 μm.

A novel study of the polymerisation process involved in the formation of the network component of polymer-stabilised liquid crystals within electro-optic cells using high performance liquid chromatography

Polymer-stabilised liquid crystals are systems in which a small amount of monomer is dissolved within a liquid crystalline host, and then polymerised in situ to produce a network. The progress of the polymerisation, performed within electro-optic cells, was studied by establishing an analytical method novel to these systems. Samples were prepared by photopolymerisation of the monomer under well-defined reaction conditions; subsequent immersion in acetone caused the host and any unreacted monomer to dissolve. High performance liquid chromatography was used to separate and detect the various solutes in the resulting solutions, enabling the amount of unreacted monomer for a given set of conditions to be quantified. Longer irradiations cause a decrease in the proportion of unreacted monomer since more network is formed, while a more uniform LC director alignment (achieved by decreasing the sample thickness) or a higher level of order (achieved by decreasing the polymerisation temperature) promotes faster reactions.

Biaxial optical properties of thermotropic random copolyesters

The optical microstructures of thin sections of two liquid crystalline polymers are examined in the polarizing microscope. The polymers are random copolyesters based on hydroxybenzoic and hydroxynaphthoic acids (B-N), and hydroxybenzoic acid and ethylene terephthalate (B-ET). Sections cut from oriented samples, so as to include the extrusion direction, show microstructures in which there is no apparent preferred orientation of the axes describing the local optical anisotropy. The absence of preferred orientation in the microstructure, despite marked axial alignment of molecular chain segments as demonstrated by X-Ray diffraction, is interpreted in terms of the polymer having biaxial optical properties. The implication of optical biaxiality is that, although the mesophases are nematic, the orientation of the molecules is correlated about three (orthogonal) axes over distances greater than a micron. The structure is classified as a multiaxial nematic.

Low-cost optical tracking for collaborative applications in immersive virtual environments

We present a novel way of interacting with an immersive virtual environment which involves inexpensive motion-capture using the Wii Remote®. A software framework is also presented to visualize and share this information across two remote CAVETM-like environments. The resulting application can be used to assist rehabilitation by sending motion information across remote sites. The application’s software and hardware components are scalable enough to be used on a desktop computer when home-based rehabilitation is preferred.

Language capital and development: the case of African language publishing for children in South Africa

In recognizing 11 official languages, the 1996 South African Constitution provides a context for the management of diversity with important implications for the redistribution of wealth and power. The development and implementation of the language-in-education policies which might be expected to flow from the Constitution, however, have been slow and ineffective. One of the casualties of government procrastination has been African language publishing. In the absence of well-resourced bilingual education, most learners continue to be taught through the medium of English as a second language. Teachers are reluctant to use more innovative pedagogies without the support of adequate African language materials and publishers are cautious about producing such materials. Nonetheless, activity in this sector offers many opportunities for African language speakers. This paper explores the challenges and constraints for African language publishing for children and argues that market forces and language policy need to work in mutually reinforcing ways. Further progress is necessarily dependent on the political will to implement language-in-education policies that promote additive bilingualism and, in the process, guarantee sales for risk-averse publishers.

Nonlinear set-membership estimation: a support vector machine approach

In this paper a support vector machine (SVM) approach for characterizing the feasible parameter set (FPS) in non-linear set-membership estimation problems is presented. It iteratively solves a regression problem from which an approximation of the boundary of the FPS can be determined. To guarantee convergence to the boundary the procedure includes a no-derivative line search and for an appropriate coverage of points on the FPS boundary it is suggested to start with a sequential box pavement procedure. The SVM approach is illustrated on a simple sine and exponential model with two parameters and an agro-forestry simulation model.

Molecular mechanisms of oestrogen action on growth of human breast cancer cells in culture

Growth responses to oestrogen can be reproducibly obtained using a selection of oestrogen-receptor-containing human breast cancer cell lines, and molecular mechanisms have been shown to include modulation to growth factor/receptor/signalling pathways, cell-cycle proteins, apoptosis, differentiation, adhesion, motility and migration. Considerable progress has been made in understanding the molecular basis of oestrogen action on gene expression through the ligand-activated transcription factors human oestrogen receptor α (ERα) and ERβ and the resulting effects on global gene expression patterns, but the full profile of coordination of the alterations, which brings about changes in cell growth through genomic and non-genomic mechanisms remain to be fully elucidated. Oestrogen regulation of cell growth involves a complex cross-talk between oestrogen receptor and growth factor signalling pathways such that inhibition of one pathway may lead to stimulation of another, which may explain the remarkable ability of human breast cancer cells to escape from any mode of imposed growth inhibition be it oestrogen deprivation or administration of antioestrogen. Although studies on cell growth have focused to date on the effects of physiological oestrogens, many hundreds of environmental chemicals with oestrogenic properties have now been measured in the human breast. Whether or not the weight of evidence eventually establishes any causal link of complex mixtures of environmental oestrogenic chemicals with breast cancer, the presence of so many oestrogenic chemicals in the breast must influence resulting oestrogenic responses, and the impact of this additional oestrogenic burden needs to be taken into account in future studies on growth regulation of human breast cancer cells.

Vocabulary size revisited: the link between vocabulary size and academic achievement

Many researchers have tried to assess the number of words adults know. A general conclusion which emerges from such studies is that vocabularies of English monolingual adults are very large with considerable variation. This variation is important given that the vocabulary size of schoolchildren in the early years of school is thought to materially affect subsequent educational attainment. The data is difficult to interpret, however, because of the different methodologies which researchers use. The study in this paper uses the frequency-based vocabulary size test from Goulden et al (1990) and investigates the vocabulary knowledge of undergraduates in three British universities. The results suggest that monolingual speaker vocabulary sizes may be much smaller than is generally thought with far less variation than is usually reported. An average figure of about 10,000 English words families emerges for entrants to university. This figure suggests that many students must struggle with the comprehension of university level texts.

Protein phosphatase 2A mediates resensitization of the neurokinin 1 receptor

Activated G protein-coupled receptors (GPCRs) are phosphorylated and interact with beta-arrestins, which mediate desensitization and endocytosis. Endothelin-converting enzyme-1 (ECE-1) degrades neuropeptides in endosomes and can promote recycling. Although endocytosis, dephosphorylation, and recycling are accepted mechanisms of receptor resensitization, a large proportion of desensitized receptors can remain at the cell surface. We investigated whether reactivation of noninternalized, desensitized (phosphorylated) receptors mediates resensitization of the substance P (SP) neurokinin 1 receptor (NK(1)R). Herein, we report a novel mechanism of resensitization by which protein phosphatase 2A (PP2A) is recruited to dephosphorylate noninternalized NK(1)R. A desensitizing concentration of SP reduced cell-surface SP binding sites by only 25%, and SP-induced Ca(2+) signals were fully resensitized before cell-surface binding sites started to recover, suggesting resensitization of cell-surface-retained NK(1)R. SP induced association of beta-arrestin1 and PP2A with noninternalized NK(1)R. beta-Arrestin1 small interfering RNA knockdown prevented SP-induced association of cell-surface NK(1)R with PP2A, indicating that beta-arrestin1 mediates this interaction. ECE-1 inhibition, by trapping beta-arrestin1 in endosomes, also impeded SP-induced association of cell-surface NK(1)R with PP2A. Resensitization of NK(1)R signaling required both PP2A and ECE-1 activity. Thus, after stimulation with SP, PP2A interacts with noninternalized NK(1)R and mediates resensitization. PP2A interaction with NK(1)R requires beta-arrestin1. ECE-1 promotes this process by releasing beta-arrestin1 from NK(1)R in endosomes. These findings represent a novel mechanism of PP2A- and ECE-1-dependent resensitization of GPCRs.

Cartels and rent sharing at the farmer–trader interface: evidence from Ghana’s tomato sector

Itinerant traders provide an important route for West Africa’s farmers’ to get their perishable produce rapidly to the distant urban markets. But these farmers often accuse the traders of offering “unfairly” low prices while preventing direct access to these markets. Using Ghana’s tomato sector as a case study, we provide the first detailed exploration of the interface between Ghana’s farmers and traders, combining a theoretical model with novel empirical data on daily sales prices and tomato quality. We find that although the prices traders pay farmers are lower than prices in the urban markets, taking into account transport costs, these prices are higher than farmers receive from the local rural market. Our article suggests that policymakers would do better to focus on opening up access to the urban markets rather than on strengthening farmers’ bargaining power with the traders, which restricts market volumes further and harms farmers unable to sell to traders.