An introduction to differential geometry in econometrics

In this introductory chapter we seek to cover sufficient differential geometry in order to understand its application to Econometrics. It is not intended to be a comprehensive review of either differential geometric theory, nor of all the applications which geometry has found in statistics. Rather it is aimed as a rapid tutorial covering the material needed in the rest of this volume and the general literature. The full abstract power of a modern geometric treatment is not always necessary and such a development can often hide in its abstract constructions as much as it illuminates. In Section 2 we show how econometric models can take the form of geometrical objects known as manifolds, in particular concentrating on classes of models which are full or curved exponential families. This development of the underlying mathematical structure leads into Section 3 where the tangent space is introduced. It is very helpful, to be able view the tangent space in a number of different, but mathematically equivalent ways and we exploit this throughout the chapter. Section 4 introduces the idea of a metric and more general tensors illustrated with statistically based examples. Section 5 considers the most important tool that a differential geometric approach offers, the affine connection. We look at applications of this idea to asymptotic analysis, the relationship between geometry and information theory and the problem of the choice of parameterisation. The last two sections look at direct applications of this geometric framework. In particular at the problem of inference in curved families and at the issue of information loss and recovery. Note that while this chapter aims to give a reasonably precise mathematical development of the required theory an alternative and perhaps more intuitive approach can be found in the chapter by Critchley, Marriott and Salmon later in this volume. For a more exhaustive and detailed review of current geometrical statistical theory see Kass and Vos (1997) or from a more purely mathematical background, see Murray and Rice (1993)

Molecular structure retention relationships in comprehensive two-dimensional gas chromatography

Comprehensive two-dimensional gas chromatography (GC x GC) offers new opportunities to develop relationships between molecular structure and retentions in the two dimensional (2D) separation space defined by the GC x GC retention in each dimension. Whereas single dimension GC provides only one retention property for a solute, and hence the specific relationship between retention and chemical property is not readily apparent or derivable, the 2D presentation of compounds in GC x GC provides a subtle and exquisite correlation of chemical property and retention unlike any other GC experiment. The 'orthogonality' of the two separation dimensions is intimately related to the manner in which different separation mechanisms, available through use of two dissimilar phases, are accessible to the different chemical compounds or classes in a sample mixture, and indeed the specific chemical classes present in the sample. The GC x GC experiment now permits various processes such as chemical decompositions, molecular interconversions, various non-linear chromatography effects, and processes such as slow reversible interactions that may arise with stationary phases or in the injector or column couplings, to be identified and further investigated. Here, we briefly review implementation of the GC x GC method, consider the molecular selectivity of GC x GC, and highlight a selection of molecular processes that can be probed by using GC x GC

Computational information geometry in statistics: foundations

This paper lays the foundations for a new framework for numerically and computationally applying information geometric methods to statistical modelling

Problems with oral formulations prescribed to children: a focus group study of healthcare professionals

Background There is evidence to suggest that adherence with prescribed medication is lower amongst adolescents and children than in adults. Medication adherence rates between 11 and 93 % in paediatric patients have been reported. More research needs to be carried out in order to understand why medicines adherence is low and how adherence can be improved in children with long-term conditions. Personal communication with paediatricians in secondary care has highlighted that problems are most likely to be encountered by parents, carers, nurses and children themselves when administering medicines for prevalent long-term childhood conditions. Objective To explore problems with oral medicines prescribed to paediatric patients from the perspectives of medical practitioners, pharmacists and nurses. Setting Two NHS trusts in the West Midlands, UK. Methods Four focus groups (FG) were conducted. Five nurses, eight medical practitioners and six pharmacists participated in focus groups. The themes explored were problems experienced when prescribing, dispensing and administering oral medicines for children. Main outcome measure Themes evolving from Healthcare professionals reports on problems with administering medicines to paediatric patients. Results Two main themes: sensory and non-sensory emerged from the data. Included within these were taste, texture, colour, smell, size, swallowing, quantity, volume and manipulation with food. Taste was the most commonly reported barrier to medicines administration. Texture was reported to be a significant problem for the learning disability population. Medicines manipulation techniques were revealed across the groups, yet there was limited knowledge regarding the evidence base for such activity. Problems surrounding the supply of Specials medicines were discussed in-depth by the pharmacists. Conclusion Organoleptic and physical properties of medicines are key barriers to medicines administration. A robust scientific evidence-based approach is warranted to inform standardised protocols guiding healthcare professionals to support safe and effective medicines manipulation across all settings. Pharmacists’ knowledge of Specials medicines needs to be recognised as a valuable resource for doctors. Findings of this study should help to optimise paediatric prescribing and direct future formulation work

An elementary account of Amari's expected geometry

Differential geometry has found fruitful application in statistical inference. In particular, Amari’s (1990) expected geometry is used in higher order asymptotic analysis, and in the study of sufficiency and ancillarity. However, we can see three drawbacks to the use of a differential geometric approach in econometrics and statistics more generally. Firstly, the mathematics is unfamiliar and the terms involved can be difficult for the econometrician to fully appreciate. Secondly, their statistical meaning can be less than completely clear, and finally the fact that, at its core, geometry is a visual subject can be obscured by the mathematical formalism required for a rigorous analysis, thereby hindering intuition. All three drawbacks apply particularly to the differential geometric concept of a non metric affine connection. The primary objective of this paper is to attempt to mitigate these drawbacks in the case of Amari’s expected geometric structure on a full exponential family. We aim to do this by providing an elementary account of this structure which is clearly based statistically, accessible geometrically and visually presented

The identification of markers of macrophage differentiation in PMA-stimulated THP-1 Cells and monocyte-derived macrophages

Differentiated macrophages are the resident tissue phagocytes and sentinel cells of the innate immune response. The phenotype of mature tissue macrophages represents the composite of environmental and differentiation-dependent imprinting. Phorbol-12-myristate-13-acetate (PMA) and 1,25-dihydroxyvitamin D3 (VD3) are stimuli commonly used to induce macrophage differentiation in monocytic cell lines but the extent of differentiation in comparison to primary tissue macrophages is unclear. We have compared the phenotype of the promonocytic THP-1 cell line after various protocols of differentiation utilising VD3 and PMA in comparison to primary human monocytes or monocyte-derived macrophages (MDM). Both stimuli induced changes in cell morphology indicative of differentiation but neither showed differentiation comparable to MDM. In contrast, PMA treatment followed by 5 days resting in culture without PMA (PMAr) increased cytoplasmic to nuclear ratio, increased mitochondrial and lysosomal numbers and altered differentiation-dependent cell surface markers in a pattern similar to MDM. Moreover, PMAr cells showed relative resistance to apoptotic stimuli and maintained levels of the differentiation-dependent anti-apoptotic protein Mcl-1 similar to MDM. PMAr cells retained a high phagocytic capacity for latex beads, and expressed a cytokine profile that resembled MDM in response to TLR ligands, in particular with marked TLR2 responses. Moreover, both MDM and PMAr retained marked plasticity to stimulus-directed polarization. These findings suggest a modified PMA differentiation protocol can enhance macrophage differentiation of THP-1 cells and identify increased numbers of mitochondria and lysosomes, resistance to apoptosis and the potency of TLR2 responses as important discriminators of the level of macrophage differentiation for transformed cells

Interpretation of comprehensive two-dimensional gas chromatography data using advanced chemometrics

The power of comprehensive two-dimensional gas chromatography (GC × GC) for the study of complex mixtures has been indisputably proved in the past several decades. This review encompasses the whole of GC × GC-related data processing and summarizes relevant applications. We include theoretical introduction to some specific methods and studies to aid readers' understanding of chemometrics strategies for advanced data interpretation

Effect of rate of pyrolysis on the textural properties of naturally-templated porous carbons from alginic acid

AbstractThe effect of pyrolysis rate on the properties of alginic acid-derived carbonaceous materials, termed Starbon®, was investigated. Thermal Gravimetry-IR was used to prepare porous carbons up to 800°C at several rates and highlighted increased CO2 production at higher pyrolysis rates. N2 porosimetry of the resultant carbons shows how pyrolysis rate affects both the mesopore structure and thus surface area and surface energy. Surface capacity of these carbons was analysed by methylene blue dye adsorption. In general, as the rate of pyrolysis increased, the mesopore content and adsorbent capacity decreased. It is considered here that the rapid production of volatiles at these higher rates causes structural collapse of the non-templated pore network. The work here demonstrates that pyrolysis rate is a key variable which needs to be controlled to maximise the textural properties of Starbon® required for adsorption applications

Using an Augmented Reality App for Flight Training

As the global demand for aviation pilots continues to drastically increase, flight schools are experiencing a large influx of ab-initio flight students. Such flight training programs are seeking innovative, cutting-edge technologies to support these students and expedite their flight training. The ARAir app, a custom app developed by our team, was designed for ab-initio pilots training at the Embry-Riddle Prescott campus. The initial implementation in Spring 2021 included phonetic alphabet practice and strategic radiotelephony that allows students to practice in a self-paced environment with immediate corrective feedback at various levels of complexity. Students can compete against themselves to improve phonetic alphabet knowledge, create initial radio transmissions, read back ATC instructions, and manipulate an aircraft to the correct intended location at the KPRC airport. Based on the survey and interview feedback collected after the initial implementation, additional support for checklist memorization using the Augmented Reality (AR) feature was added to the ARAir app. This presentation will report students’ learning experience with the improved ARAir in the second implementation in Spring 2022

Rapid portable GC-MS analysis for on-site screening of phytochemical leaf oils in an Australian Native Botanic Garden.

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