Anxiety and abstraction in Nineteenth-Century Mathematics

The paper is in three parts. The first part surveys the current literature in the history of 19th Century mathematics in order to show that the question ‘Did the increasing abstraction of mathematics lead to a sense of anxiety?’ is a new and valid question. I argue that the mathematics of the 19th Century is marked by a growing appreciation of error leading to a note, hesitant at first but persistent by 1900, of anxiety. This mounting disquiet about so many aspects of mathematics after 1850 is seldom discussed. Insofar as this part of the paper is critical of present practice it retains the personal tone of the talk, but also it incorporates some of the helpful suggestions made during the discussion after the talk. The second part explores the issue of anxiety in mathematical life through an interesting account of these issues as they were perceived by one mathematician in 1911, Oscar Perron. The third and final part ventures some conclusions about the value of anxiety as a question for historians of mathematics to pursue

Randomized Sign Test for Dependent Observations on Discrete Choice under Risk

This paper proposes nonparametric statistical procedures for analyzing discrete choice models of affective decision making. We make two contributions to the literature on behavioral economics. Namely, we propose a procedure for eliciting the existence of a Nash equilibrium in an intrapersonal, potential game as well as randomized sign tests for dependent observations on game-theoretic models of affective decision making. This methodology is illustrated in the context of a hypothetical experiment — the Casino Game

Multifunctional photo/thermal catalysts for the reduction of carbon dioxide

The photochemical fixation of CO2 to energy rich products for solar energy storage or feedstock chemicals is an attractive, albeit daunting, challenge. The overall feasibility of CO2 conversion is limited by the availability of efficient photo-active materials that meet the energetic requirements for CO2 reduction and are optically matched to the solar spectrum. Surface modification of TiO2 with earth abundant metal oxides presents one approach to develop visible active photocatalysts through band gap narrowing, while providing catalytic sites to lower the activation energy for CO2 reduction. In this work density functional theory was used to model the effect of surface modification of rutile and anatase using MnOx nanoclusters. The results indicate the formation of inter-band gap states following surface modification with MnOx, but surface water can change this. Oxygen vacancies are predicted to form in supported MnOx and the interaction with CO2 was investigated. MnOx-TiO2 was synthesized and characterised using surface analytical methods and photoelectrochemistry. The interaction of CO2 with the materials under irradiation was probed using in-situ FTIR to interrogate the role of oxygen vacancies in CO2 binding and reaction. These results provide insights into the requirements of a multifunctional catalyst for CO2 conversion

Estimating Nosocomial Infection and its Outcomes in Hospital Patients in England with a Diagnosis of COVID-19 Using Machine Learning

BACKGROUND: COVID-19 nosocomial infections (NIs) may have played a significant role in the dynamics of the pandemic in England, but analysis of their impact at the national scale has been lacking. Our aim was to provide a comprehensive account of NIs, identify their characteristics and outcomes in patients with a diagnosis of COVID-19 and use machine learning modelling to refine these estimates. METHODS: From the Hospital Episodes Statistics database all adult hospital patients in England with a diagnosis of COVID-19 and discharged between March 1st 2020 and March 31st 2021 were identified. A cohort of suspected COVID-19 NIs was identified using four empirical methods linked to hospital coding. A random forest classifier was designed to model the relationship between acquiring NIs and the covariates: patient characteristics, comorbidities, frailty, trust capacity strain and severity of COVID-19 infections. FINDINGS: In total, 374,244 adult patients with COVID-19 were discharged during the study period. The four empirical methods identified 29,896 (8.0%) patients with NIs. The random forest classifier estimated a mean NI rate of 10.5%, with a peak close to 18% during the first wave, but much lower rates thereafter and around 7% in early spring 2021. NIs were highly correlated with longer lengths of stay, high trust capacity strain, greater age and a higher degree of patient frailty. NIs were also found to be associated with higher mortality rates and more severe COVID-19 sequelae, including pneumonia, kidney disease and sepsis. INTERPRETATION: Identification of the characteristics of patients who acquire NIs should help trusts to identify those most at risk. The evolution of the NI rate over time may reflect the impact of changes in hospital management practices and vaccination efforts. Variations in NI rates across trusts may partly reflect different data recording and coding practice

Data consistency in the English Hospital Episodes Statistics database

BACKGROUND: To gain maximum insight from large administrative healthcare datasets it is important to understand their data quality. Although a gold standard against which to assess criterion validity rarely exists for such datasets, internal consistency can be evaluated. We aimed to identify inconsistencies in the recording of mandatory International Statistical Classification of Diseases and Related Health Problems, tenth revision (ICD-10) codes within the Hospital Episodes Statistics dataset in England. METHODS: Three exemplar medical conditions where recording is mandatory once diagnosed were chosen: autism, type II diabetes mellitus and Parkinson's disease dementia. We identified the first occurrence of the condition ICD-10 code for a patient during the period April 2013 to March 2021 and in subsequent hospital spells. We designed and trained random forest classifiers to identify variables strongly associated with recording inconsistencies. RESULTS: For autism, diabetes and Parkinson's disease dementia respectively, 43.7%, 8.6% and 31.2% of subsequent spells had inconsistencies. Coding inconsistencies were highly correlated with non-coding of an underlying condition, a change in hospital trust and greater time between the spell with the first coded diagnosis and the subsequent spell. For patients with diabetes or Parkinson's disease dementia, the code recording for spells without an overnight stay were found to have a higher rate of inconsistencies. CONCLUSIONS: Data inconsistencies are relatively common for the three conditions considered. Where these mandatory diagnoses are not recorded in administrative datasets, and where clinical decisions are made based on such data, there is potential for this to impact patient care

N-acetylaspartate supports the energetic demands of developmental myelination via oligodendroglial aspartoacylase

Breakdown of neuro-glial N-acetyl-aspartate (NAA) metabolism results in the failure of developmental myelination, manifest in the congenital pediatric leukodystrophy Canavan disease caused by mutations to the sole NAA catabolizing enzyme aspartoacylase. Canavan disease is a major point of focus for efforts to define NAA function, with available evidence suggesting NAA serves as an acetyl donor for fatty acid synthesis during myelination. Elevated NAA is a diagnostic hallmark of Canavan disease, which contrasts with a broad spectrum of alternative neurodegenerative contexts in which levels of NAA are inversely proportional to pathological progression. Recently generated data in the nur7 mouse model of Canavan disease suggests loss of aspartoacylase function results in compromised energetic integrity prior to oligodendrocyte death, abnormalities in myelin content, spongiform degeneration, and motor deficit. The present study utilized a next-generation “oligotropic” adeno-associated virus vector (AAV-Olig001) to quantitatively assess the impact of aspartoacylase reconstitution on developmental myelination. AAV-Olig001-aspartoacylase promoted normalization of NAA, increased bioavailable acetyl-CoA, and restored energetic balance within a window of postnatal development preceding gross histopathology and deteriorating motor function. Long-term effects included increased oligodendrocyte numbers, a global increase in myelination, reversal of vacuolation, and rescue of motor function. Effects on brain energy observed following AAV-Olig001-aspartoacylase gene therapy are shown to be consistent with a metabolic profile observed in mild cases of Canavan disease, implicating NAA in the maintenance of energetic integrity during myelination via oligodendroglial aspartoacylase